Physics

"At present, physicists are enamoured of symmetry and search only for continuous pictures of fundamental physics. Maybe, one day, they will be motivated to look at possible structures of a fundamentally discrete world."

"Theoretical physicists live in a classical world, looking out into a quantum-mechanical world. The latter we describe only subjectively, in terms of procedures and results in our classical domain."

"Physics is to be regarded not so much as the study of something a priori given, but rather as the development of methods of ordering and surveying human experience. In this respect our task must be to account for such experience in a manner independent of individual subjective judgement and therefore objective in the sense that it can be unambiguously communicated in ordinary human language."

"Physicists use the wave theory on Mondays, Wednesdays and Fridays and the particle theory on Tuesdays, Thursdays and Saturdays"

"Physics is really nothing more than a search for ultimate simplicity, but so far all we have is a kind of elegant messiness."

"Physics is not just a set of true facts and s and things like that. In many ways it's kind of an attitude. It's a way of thinking about different things."

"Its utility is to allow us to foresee and to foretell physical phenomena...[I]t suggests definite experiments which might never have been thought of, and permits us to anticipate new relationships and new laws and to discover new facts...[B]y establishing a rational connection between seemingly unconnected phenomena, it enables us to detect the harmony and unity of nature which lie concealed under an outward appearance of chaos."

"Star after star from Heaven’s high arch shall rush, Suns sink on suns, and systems systems crush, Headlong, extinct, to one dark centre fall, And Death and Night and Chaos mingle all! —Till o’er the wreck, emerging from the storm, Immortal lifts her changeful form, Mounts from her funeral pyre on wings of flame, And soars and shines, another and the same."

"The human imagination, including the creative scientific imagination, can ultimately function only by evoking potential or imagined sense impressions... I confess I never met an experimental physicist who does not think of the hydrogen atom by evoking a visual image of what he would see if the particular atomic model with which he is working existed literally on a scale accessible to the sense impressions - even while realizing that in fact the so-called internal structure of the hydrogen atom is in principle inaccessible to direct sensory perception. This situation has far-reaching consequences for the method of experimental investigation."

"Mathematical physics represents the purest image that the view of nature may generate in the human mind; this image presents all the character of the product of art; it begets some unity, it is true and has the quality of sublimity; this image is to physical nature what music is to the thousand noises of which the air is full..."

"And so in its actual procedure physics studies not these inscrutable qualities, but pointer-readings which we can observe, The readings, it is true, reflect the fluctuations of the world-qualities; but our exact knowledge is of the readings, not of the qualities. The former have as much resemblance to the latter as a telephone number has to a subscriber."

"The supreme task of the physicist is the discovery of the most general elementary laws from which the world-picture can be deduced logically. But there is no logical way to the discovery of these elemental laws. There is only the way of intuition, which is helped by a feeling for the order lying behind the appearance, and this Einfühlung [literally, empathy or 'feeling one's way in'] is developed by experience."

"How strange is the lot of us mortals! Each of us is here for a brief sojourn; for what purpose he knows not, though he sometimes thinks he senses it. But without deeper reflection one knows from daily life that one exists for other people — first of all for those upon whose smiles and well-being our own happiness is wholly dependent, and then for the many, unknown to us, to whose destinies we are bound by the ties of sympathy. A hundred times every day I remind myself that my inner and outer life are based on the labors of other men, living and dead, and that I must exert myself in order to give in the same measure as I have received and am still receiving..."

"No current physics experiment or theory explains the nature—or even the existence—of emotions, money, fine art, football games, or people. What can physics say about such things?"

"Physics is the model of what a successful science should be. It provides the basis for the other physical sciences and biology because everything in our world, including ourselves, is made of the same fundamental particles, whose interactions are governed by the same fundamental forces."

"Physics represents the ultimate reductionist subject: Physicists reduce matter first to molecules, then to atoms, then to nuclei and electrons, and so on, the goal being always to reduce complexity to simplicity. The extraordinary success of that approach is based on the concept of an isolated system. Experiments carried out on systems isolated from external interference are designed to identify the essential causal elements underlying physical reality. The problem is that no real physical or biological system is truly isolated, physically or historically."

"The "paradox" is only a conflict between reality and your feeling of what reality "ought to be.""

"Eppur si muove."

"Even if there is only one possible unified theory, it is just a set of rules and equations. What is it that breathes fire into the equations and makes a universe for them to describe? The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe. Why does the universe go to all the bother of existing?"

"It’s the strangeness of the universe that has always been my favorite part of physics."

"Who hath measured the waters in the hollow of his hand, and meted out heaven with the span, and comprehended the dust of the earth in a measure, and weighed the mountains in scales, and the hills in a balance?"

"The concepts which now prove to be fundamental to our understanding of nature—a space which is finite; a space which is empty, so that one point [of our 'material' world] differs from another solely in the properties of space itself; four-dimensional, seven- and more dimensional spaces; a space which for ever expands; a sequence of events which follows the laws of probability instead of the law of causation—or alternatively, a sequence of events which can only be fully and consistently described by going outside of space and time—all these concepts seem to my mind to be structures of pure thought, incapable of realisation in any sense which would properly be described as material."

"Today there is a wide measure of agreement, which on the physical side of science approaches almost to unanimity, that the stream of knowledge is heading towards a non-mechanical reality; the universe begins to look more like a great thought than like a great machine. Mind no longer appears as an accidental intruder into the realm of matter; we are beginning to suspect that we ought rather to hail it as a creator and governor of the realm of matter."

"And the substance out of which this bubble is blown, the soap-film, is empty space welded onto empty time."

"Physics and philosophy are at most a few thousand years old, but probably have lives of thousands of millions of years stretching away in front of them. They are only just beginning to get under way."

"Who is this that darkeneth counsel by words without knowledge? Gird up now thy loins like a man; for I will demand of thee, and answer thou me. Where wast thou when I laid the foundations of the earth? declare, if thou hast understanding. Who hath laid the measures thereof, if thou knowest? or who hath stretched the line upon it? Whereupon are the foundations thereof fastened? or who laid the corner stone thereof?"

"It is impossible, and it has always been impossible, to grasp the meaning of what we nowadays call physics independently of its mathematical form."

"If I were forced to sum up in one sentence what the Copenhagen interpretation says to me, it would be 'Shut up and calculate!'"

"For every symmetry there comes a constraint...If physics is to look the same when the origin of time is shifted...[o]nly those processes that conserve energy are allowed. ...If physical law is to be immune to the arbitrary displacement of our spatial axes, then nature requires the conservation of . ...If the laws are to be unaffected by the arbitrary rotation of a coordinate system, then must be conserved...If the laws are to be the same for all inertial observers, then the space-time interval must be invariant...[A]nother constraint...so beautiful as to make one jaw drop in wonder...symmetry creates force...[T]he symmetry of identical particles forces matter...to be enrolled as either or ...Bosons, typified by the photon, carry the fundamental forces that cause fermions to attract and repel. Fermions, led by electrons and quarks, become constituents of ordinary matter...Gravity. Electromagnetism. The strong force. The weak force. Each is called into being by the requirements of a particular local symmetry."

"All science is either physics or stamp collecting."

"The physicist ... engages in complex and difficult calculations, involving the manipulating of ideal, mathematical quantities that, at first glance, are wholly lacking in the music of the living world and the beauty of the resplendent cosmos. It would seem as if there exists no relationship between these quantities and reality. Yet these ideal numbers that cannot be grasped by one's senses, these numbers that only are meaningful from within the system itself, only meaningful as part of abstract mathematical functions, symbolize the image of existence. ... As a result of scientific man's creativity there arises an ordered, illumined, determined world, imprinted with the stamp of creative intellect, of pure reason and clear cognition. From the midst of the order and lawfulness we hear a new song, the song of the creature to the Creator, the song of the cosmos to its Maker."

"Science deals with but a partial aspect of reality, and... there is no faintest reason for supposing that everything science ignores is less real than what it accepts. ...Why is it that science forms a closed system? Why is is that the elements of reality it ignores never come in to disturb it? The reason is that all the terms of physics are defined in terms of one another. The abstractions with which physics begins are all it ever has to do with..."

"As soon as we venture on the paths of the physicist, we learn to weigh and measure, to deal with time and space and mass and their related concepts, and to find more and more our knowledge expressed and our needs satisfied through the concept of number, as in the dreams of Plato and Pythagoras."

"The medieval theologians would not be surprised at a prerequisite of a degree in physics for a degree in theology. In their time, the highest degree in philosophy—which included the most advanced knowledge of physics of the day—was a prerequisite before a student was permitted to begin study for a degree in theology...Kenny has shown the Aquinas' Five Ways—his five proofs of God's existence—are absolutely dependent on Aristotelian physics...Aquinas...was one of the leading scholars of Aristotelian physics...and...was primarily responsible for...[its] general acceptance throughout Europe. We could call Aquinas a great physicist as well as a great theologian, for, although Aristotelian physics was wrong, it was an essential precursor of modern physics."

"The power and beauty of physical laws is that they apply everywhere, whether or not you choose to believe in them. In other words, after the laws of physics, everything else is opinion."

"It has seemed to me for some years that among physicists there is almost a cult, although certainly not an organized one, which I please to call a cult of obscurity. The creed of the cult is that a member disgraces the profession if he ever writes, lectures or teaches intelligibly to anyone but his immediate colleagues in the profession."

"Our judge is not God or governments, but Nature."

"I had spent six years slugging my way through many dozens of physics textbooks that were carefully written with the best of pedagogical plans, but there was something missing. Physics is the most interesting subject in the world because it is about how the world works, and yet the textbooks had been thoroughly wrung of any connection with the real world. The fun was missing."

"The physical doctrine of the atom has got into a state which is strongly suggestive of the epicycles of astronomy before Copernicus."

"... it's one thing in physics to write down the equations, but then you have to solve them — and that is sometimes easier said than done."

"If two systems are both in thermal equilibrium with a third system, then they are in thermal equilibrium with each other."

"In a closed system (i.e. there is no transfer of matter into or out of the system), the first law states that the change in internal energy of the system (ΔU) is equal to the difference between the heat supplied to the system (Q) and the work (W) done by the system on its surroundings. (Note, an alternate sign convention, not used in this article, is to define W as the work done on the system by its surroundings): \Delta U_{\rm system} = Q - W."

"When two initially isolated systems are combined into a new system, then the total internal energy of the new system, U, will be equal to the sum of the internal energies of the two initial systems, U1 and U2: U_{\rm system} = U_1 + U_2."

"When two initially isolated systems in separate but nearby regions of space, each in thermodynamic equilibrium with itself but not necessarily with each other, are then allowed to interact, they will eventually reach a mutual thermodynamic equilibrium. The sum of the entropies of the initially isolated systems is less than or equal to the total entropy of the final combination. Equality occurs just when the two original systems have all their respective intensive variables (temperature, pressure) equal; then the final system also has the same values."

"According to the second law, in a reversible heat transfer, an element of heat transferred, \delta Q, is the product of the temperature (T), both of the system and of the sources or destination of the heat, with the increment (dS) of the system's conjugate variable, its entropy (S):"

"A system's entropy approaches a constant value as its temperature approaches absolute zero."

"Every mathematician knows it is impossible to understand an elementary course in thermodynamics."

"In order to consider in the most general way the principle of the production of motion by heat, it must be considered independently of any mechanism or any particular agent. It is necessary to establish principles applicable not only to steam engines but to all imaginable heat-engines, whatever the working substance and whatever the method by which it is operated."

"Machines which do not receive their motion from heat... can be studied even to their smallest details by the mechanical theory. ...A similar theory is evidently needed for heat-engines. We shall have it only when the laws of Physics shall be extended enough, generalized enough, to make known beforehand all of the effects of heat acting in a determined manner on any body."

"The production of heat alone is not sufficient to give birth to the impelling powerː it is necessary that there should also be cold; without it the heat would be useless. And in fact, if we should find about us only bodies as hot as our furnaces... What should we do with it if once produced? We should not presume that we might discharge it into the atmosphere... the atmosphere would not receive it. It does receive it under the actual condition of things only because.. it is at a lower temperature, otherwise it... would be already saturated."

"Heat can evidently be a cause of motion only by virtue of the changes of volume or of form which it produces in bodies. These changes are not caused by uniform temperature but rather by alternations of heat and cold."

"The driving power of heat is independent of the agents used to realize it; its value is uniquely fixed by the temperatures of the bodies between which the transfer of caloric is made."

"A theory is the more impressive the greater the simplicity of its premises, the more different kinds of things it relates, and the more extended its area of applicability. Therefore the deep impression that classical thermodynamics made upon me. It is the only physical theory of universal content which I am convinced will never be overthrown, within the framework of applicability of its basic concepts."

"The effects of heat are subject to constant laws which cannot be discovered without the aid of mathematical analysis. The object of the theory is to demonstrate these laws; it reduces all physical researches on the propagation of heat, to problems of the integral calculus, whose elements are given by experiment. No subject has more extensive relations with the progress of industry and the natural sciences; for the action of heat is always present, it influences the processes of the arts, and occurs in all the phenomena of the universe."

"Newton and his theories were a step ahead of the technologies that would define his age. Thermodynamics, the grand theoretical vision of the nineteenth century, operated in the other direction with practice leading theory. The sweeping concepts of energy, heat, work and entropy, which thermodynamics (and its later form, statistical mechanics) would embrace, began first on the shop floor. Originally the domain of engineers, thermodynamics emerged from their engagement with machines. Only later did this study of heat and its transformation rise to the heights of abstract physics and, finally, to a new cosmological vision."

"[I]n the nineteenth century, even the could be reduced to mechanics by the assumption that heat really consists of a complicated statistical motion of the smallest parts of matter. By combining the concepts of the mathematical theory of probability with the concepts of Newtonian mechanics Clausius, Gibbs and Boltzmann were able to show that the fundamental laws in the theory of heat could be interpreted as statistical laws following from Newton's mechanics when applied to very complicated mechanical systems."

"The second closed system of concepts was formed in the... nineteenth century... with the theory of heat. Though the theory... could finally be connected with mechanics through... statistical mechanics, it... [was not] a part of mechanics. ...[T]he phenomenological theory of heat uses... concepts that have no counterpart in other branches of physics, like: , specific heat, entropy, free energy, etc. If... one goes... to a statistical interpretation... considering heat as energy, distributed statistically among... many degrees of freedom due to... atomic structure of matter, then heat is no more connected with mechanics than with electrodynamics or other parts of physics. The central concept... is... probability, closely connected with the concept of entropy... [T]he statistical theory of heat requires the concept of energy. But any coherent set of axioms and concepts in physics will necessarily contain the concepts of energy, and and the law that these ...must under certain conditions be conserved. This follows if the coherent set is intended to describe... features of nature... correct at all times and everywhere... [i.e.,] features that do not depend on space and time... [i.e.,] that are invariant under arbitrary translations in space and time, s in space and the Galileo or . Therefore, the theory of heat can be combined with any of the other closed systems of concepts."

"Even the laws of thermodynamics... can be recast in terms of information — Shannon entropy, the laws of bits of information. But this view generates its own paradox at the origin of life. ...Place information at the heart of life, and there is a problem with the emergence of function ...the origin of biological information. There are problems... in understanding why we age and die... diseases... and how experiences can give rise to conscious mind. ...A far better question ...what processes animate cells and set them apart from inanimate matter?"

"The driving force of is thermodynamics. ...[I]n this context ...the chemical need to react (to dissipate energy) in the same way that water needs to flow downhill."

"If the Krebs cycle is ordained by thermodynamics, then it should take place spontaneously in some suitably propitious envirnonment, even in the absence of s."

"The whole science of heat is founded Thermometry and Calorimetry, and when these operations are understood we may proceed to the third step, which is the investigation of those relations between the thermal and the mechanical properties of substances which form the subject of Thermodynamics. The whole of this part of the subject depends on the consideration of the Intrinsic Energy of a system of bodies, as depending on the temperature and physical state, as well as the form, motion, and relative position of these bodies. Of this energy, however, only a part is available for the purpose of producing mechanical work, and though the energy itself is indestructible, the available part is liable to diminution by the action of certain natural processes, such as conduction and radiation of heat, friction, and viscosity. These processes, by which energy is rendered unavailable as a source of work, are classed together under the name of the Dissipation of Energy."

"Heat may be generated and destroyed by certain processes, and this shows that heat is not a substance."

"Isn’t thermodynamics considered a fine intellectual structure, bequeathed by past decades, whose every subtlety only experts in the art of handling Hamiltonians would be able to appreciate?"

"Thermodynamics is a funny subject. The first time you go through it, you don't understand it at all. The second time you go through it, you think you understand it, except for one or two small points. The third time you go through it, you know you don't understand it, but by that time you are so used to it, it doesn't bother you any more."

"If the water flow down by a gradual natural channel, its potential energy is gradually converted into heat by fluid friction, according to an admirable discovery made by Mr Joule of Manchester above twelve years ago, which has led to the greatest reform that physical science has experienced since the days of Newton. From that discovery, it may be concluded with certainty that heat is not matter, but some kind of motion among the particles of matter; a conclusion established, it is true, by Sir Humphrey Davy and Count Rumford at the end of last century, but ignored by even the highest scientific men during a period of more than forty years."

"Thermodynamics is more like a mode of reasoning than a body of physical law. ...we can think of thermodynamics as a certain pattern of arrows that occurs again and again in very different physical contexts, but, wherever this pattern of explanation occurs, the arrows can be traced back by the methods of statistical mechanics to deeper laws and ultimately to the principles of elementary particle physics. ...the fact that a scientific theory finds applications to a wide variety of different phenomena does not imply anything about the autonomy of this theory from deeper physical laws."

"The Second Law recognizes that there is a fundamental dissymmetry in Nature... All around us are aspects of the dissymmetry: hot objects become cool, but cool objects do not spontaneously become hot; a bouncing ball comes to rest, but a stationary ball does not spontaneously begin to bounce. Here is the feature of Nature that both Kelvin and Clausius disentangled from the conservation of energy: although the total quantity of energy must be conserved in any process (which is their revised version of what Carnot had taken to be the conservation of the quantity of caloric), the distribution of that energy changes in an irreversible manner. The Second Law is concerned with the natural direction of change of the distribution of energy, something that is quite independent of its total quantity."

"The choice (or accident) of s creates a sense of time directionality in a physical environment. The 'arrow' of entropy increase is a reflection of the improbability of those initial conditions which are entropy-decreasing in a closed physical system. ... Everywhere... in the Universe, we discern that closed physical systems evolve in the same sense from ordered states towards a state of complete disorder called . This cannot be a consequence of known laws of change, since... these laws are time symmetric—they permit... time-reverse... The initial conditions play a decisive role in endowing the world with its sense of temporal direction. ...some prescription for initial conditions is crucial if we are to understand... A Theory of Everything needs to be complemented by some such independent prescription which appeals to simplicity, economy, or some other equally metaphysical notion to underpin its credibility. The only radically different alternative... a belief that the type of mathematical description of Nature... —that of causal equations with starting conditions—is just an artefact of our own preferred categories of thought and merely an approximation... At a deeper level, a sharp divide between those aspects of reality that we habitually call 'laws' and... 'initial conditions' may simply not exist."

"The second law of thermodynamics is, without a doubt, one of the most perfect laws in physics. Any reproducible violation of it, however small, would bring the discoverer great riches as well as a trip to Stockholm. The world’s energy problems would be solved at one stroke. It is not possible to find any other law (except, perhaps, for super selection rules such as charge conservation) for which a proposed violation would bring more skepticism than this one. Not even Maxwell’s laws of electricity or Newton’s law of gravitation are so sacrosanct, for each has measurable corrections coming from quantum effects or general relativity. The law has caught the attention of poets and philosophers and has been called the greatest scientific achievement of the nineteenth century. Engels disliked it, for it supported opposition to Dialectical Materialism, while Pope Pius XII regarded it as proving the existence of a higher being."

"If one applies this to the universe in total, one reaches a remarkable conclusion. ...Namely, if, in the universe, heat always shows the endeavour to change its distribution in such a way that existing temperature differences are thereby smoothened, then the universe must continually get closer and closer to the state, where the forces cannot produce any new motions, and no further differences exist."

"The more the universe approaches this limiting condition in which the entropy is maximum, the more do the occasions of further change diminish; and supposing this condition to be at last completely attained, no further change could evermore take place, and the universe would be in a state of unchanging death."

"In the year 1900 Max Planck wrote... E = hv, where E is the energy of a light wave, v is its , and h is... . It said that energy and frequency are the same thing measured in different units. Planck's constant gives you a rate of exchange for for converting frequency into energy... But in the year 1900 this made no physical sense. Even Plank himself did not understand it. ...Now Hawking has written down an equation which looks rather like Planck's equation... S = kA, where S is the entropy of a black hole, A is the area of its surface, and k is... Hawking's constant. Entropy means roughly the same thing as the of an object. ...Hawking's equation says that entropy is really the same thing as area. The exchange rate... is given by Hawking's constant... But what does it really mean to say that entropy and area are the same thing? We are as far away from understanding that now as Planck was of understanding quantum mechanics in 1900. ...[T]his equation will emerge as a central feature of the still unborn theory which will tie together gravitation and quantum mechanics and thermodynamics."

"The law that entropy always increases holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations — then so much the worse for Maxwell's equations. If it is found to be contradicted by observation — well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation."

"The paradox that immediately bothers everyone who learns about the second law is this: If systems tend to become more disordered, why, then, do we see so much order around us? ...It seems to conflict with our "creation myth": In the beginning, there was a big bang. ...no one is saying that the second law of thermodynamics is wrong, just that there is a contrapuntal process organizing things at a higher level."

"Nothing in life is certain except death, taxes and the second law of thermodynamics. All three are processes in which useful or accessible forms of some quantity, such as energy or money, are transformed into useless, inaccessible forms of the same quantity. That is not to say that these three processes don't have fringe benefits: taxes pay for roads and schools; the second law of thermodynamics drives cars, computers and metabolism; and death, at the very least, opens up tenured faculty positions."

"Life is nature's solution to the problem of preserving information despite the second law of thermodynamics."

"The reactions that break down large molecules into small ones do not require an input of energy, but the reactions that build up large molecules require an input of energy. This is consistent with the laws of thermodynamics, which say that large, orderly molecules tend to break down into small, disorderly molecules."

"No one has yet succeeded in deriving the second law from any other law of nature. It stands on its own feet. It is the only law in our everyday world that gives a direction to time, which tells us that the universe is moving toward equilibrium and which gives us a criteria for that state, namely, the point of maximum entropy, of maximum probability. The second law involves no new forces. On the contrary, it says nothing about forces whatsoever."

"A good many times I have been present at gatherings of people who, by the standards of the traditional culture, are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists. Once or twice I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics. The response was cold: it was also negative. Yet I was asking something which is the scientific equivalent of: Have you read a work of Shakespeare's?"

"My own introduction to entropy was as an undergraduate mechanical engineering student. Neither I nor any of the other students knew anything about the molecular theory of heat, and I bet that the professor didn't either. The course... was so confusing that I...couldn't make any sense of it. Worst of all was the concept of entropy. We were told that if you heat something a small amount, the change in thermal energy, divided by the temperature, is the change of its entropy. Everyone copied it down but no one understood what it meant. It was as incomprehensible to me as "The change in the number of sausages divided by the onionization is called floogelweiss.""

"Organic evolution has its physical analogue in the universal law that the world tends, in all its parts and particles, to pass from certain less probable to certain more probable configurations or states. This is the second law of thermodynamics. It has been called the law of evolution of the world; and we call it, after Clausius, the Principle of Entropy, which is a literal translation of Evolution in Greek."

"It is impossible by means of inanimate material agency, to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects. [Footnote: ] If this axiom be denied for all temperatures, it would have to be admitted that a self-acting machine might be set to work and produce mechanical effect by cooling the sea or earth, with no limit but the total loss of heat from the earth and sea, or in reality, from the whole material world."

"1. There is at present in the material world a universal tendency to the dissipation of mechanical energy. 2. Any restoration of mechanical energy, without more than an equivalent of dissipation, is impossible in inanimate material processes, and is probably never effected by means of organized matter, either endowed with vegetable life or subjected to the will of an animated creature. 3. Within a finite period of time past, the earth must have been, and within a finite period of time to come the earth must again be, unfit for the habitation of man as at present constituted, unless operations have been, or are to be performed, which are impossible under the laws to which the known operations going on at present in the material world are subject."

"In classical physics, most of the fundamental laws of nature were concerned either with the stability of certain configurations of bodies, e.g. the solar system, or else with the conservation of certain properties of matter, e.g. mass, energy, angular momentum or spin. The outstanding exception was the famous Second Law of Thermodynamics, discovered by Clausius in 1850. This law, as usually stated, refers to an abstract concept called entropy, which for any enclosed or thermally isolated system tends to increase continually with lapse of time. In practice, the most familiar example of this law occurs when two bodies are in contact: in general, heat tends to flow from the hotter body to the cooler. Thus, while the First Law of Thermodynamics, viz. the conservation of energy, is concerned only with time as mere duration, the Second Law involves the idea of trend. Milne developed his cosmology by taking this idea of trend to be fundamental, regarding the expansion of the universe as its supreme manifestation."

"It’s the Second Law of Thermodynamics: Sooner or later everything turns to shit."

"In this house, we obey the laws of thermodynamics!"

"Zeroth: You must play the game. First: You can't win. Second: You can't break even. Third: You can't quit the game."

"Ludwig Boltzmann"

"Nicolas Léonard Sadi Carnot"

"Rudolf Clausius"

"Entropy (thermodynamics)"

"Josiah Willard Gibbs"

"James Clerk Maxwell"

"Steam engine"

"William Thomson"

"Aku: Samurai fool! Your efforts are in vain again! This gateway to the past is once more beyond your-Ey? You can fly?!"

"Of course the vary a good deal. John’s, for instance, had a lagoon with flamingoes flying over it at which John was shooting, while Michael, who was very small, had a flamingo with lagoons flying over it."

"Vainly the fowler's eye Might mark thy distant flight to do thee wrong, As, darkly painted on the crimson sky, Thy figure floats along."

"Thou little bird, thou dweller by the sea, Why takest thou its melancholy voice, And with that boding cry Along the waves dost thou fly?"

"Flying is years and years of utter boredom punctuated by moments of sheer terror"

"Ours is the commencement of a flying age, and I am happy to have popped into existence at a period so interesting."

"Lest I make the people fly off from that city like a wild dove from its tree, lest I make them fly around like a bird over its well-founded nest."

"All flight is based upon producing air pressure, all flight energy consists in overcoming air pressure."

"Restat iter cœlo: cœlo tentabimus ire; Da veniam cœpto, Jupiter alte, meo."

"One way remains—by air: by air a way we'll try; Pardon the bold adventure, Jove most high!"

"I just want to fly: put your arms around me baby, I just want to fly."

"Once you have tasted flight, you will forever walk the earth with your eyes turned skyward, for there you have been, and there you will always long to return."

"Across the narrow beach we flit, One little sand-piper and I; And fast I gather, bit by bit, The scattered drift-wood, bleached and dry, The wild waves reach their hands for it, The wild wind raves, the tide runs high, As up and down the beach we flit, One little sand-piper and I."

"For some years I have been afflicted with the belief that flight is possible to man."

"A flight ticket is a paper or electronic document that contains passenger information as well as flight information, including origin and destination, flight time, arrival time, and flight number."

"The person who merely watches the flight of a bird gathers the impression that the bird has nothing to think of but the flapping of its wings. As a matter of fact this is a very small part of its mental labor. To even mention all the things the bird must constantly keep in mind in order to fly securely through the air would take a considerable part of the evening. If I take this piece of paper, and after placing it parallel with the ground, quickly let it fall, it will not settle steadily down as a staid, sensible piece of paper ought to do, but it insists on contravening every recognized rule of decorum, turning over and darting hither and thither in the most erratic manner, much after the style of an untrained horse. Yet this is the style of steed that men must learn to manage before flying can become an everyday sport. The bird has learned this art of equilibrium, and learned it so thoroughly that its skill is not apparent to our sight. We only learn to appreciate it when we try to imitate it."

"But the speed was power, and the speed was joy, and the speed was pure beauty."

"In Einstein’s corrected formula m has the value m=\frac {{m}_}{\sqrt} where the “rest mass” m0 represents the mass of a body that is not moving and c is the speed of light, which is about 3×105 km⋅sec−1 or about 186,000 mi⋅sec−1."

"LT Pete "Maverick" Mitchell: I feel a need… a need for speed."

"Be wise with speed; A fool at forty is a fool indeed."

"Ares (The God of War) hates those who hesitate."

"It would be relevant … to point out the sinister part played by speed, by belief in speed as a value, by, in a word, a kind of impatience that has had a profound effect in changing even the very rhythms of the life of the spirit for the worse."

"Ease and speed in doing a thing do not give the work lasting solidity or exactness of beauty."

"Speed has never killed anyone. Suddenly becoming stationary, that's what gets you."

"Speed is the essence of war. Take advantage of the enemy's unpreparedness; travel by unexpected routes and strike him where he has taken no precautions."

"And fire a mine in China, here With sympathetic gunpowder."

"Striking the electric chain wherewith we are darkly bound."

"Controlling fires is an enormously difficult challenge. Our research has shown that by applying large electric fields we can suppress flames very rapidly. We're very excited about the results of this relatively unexplored area of research."

"We will make electricity so cheap that only the rich will burn candles."

"In 1881, Edison built electricity generating stations at Pearl Street in Manhattan and Holborn in London. Within a year, he was selling electricity as a commodity. A year later, the first electric motors were driving manufacturing machinery. Yet by 1900, less than 5% of mechanical drive power in American factories was coming from electric motors. The age of steam lingered."

"Is it a fact—or have I dreamt it—that by means of electricity, the world of matter has become a great nerve, vibrating thousands of miles in a breathless point of time? Rather, the round globe is a vast head, a brain, instinct with intelligence: or shall we say it is itself a thought, nothing but thought, and no longer the substance which we dreamed it."

"Without electricity, there can be no art."

"Speed the soft intercourse from soul to soul, And waft a sigh from Indus to the Pole."

"I'll put a girdle round about the earth In forty minutes."

"Too like the lightning, which doth cease to be Ere one can say "It lightens.""

"At the beginning of the Great Depression, the vast majority of rural communities across the United States had little or no access to electricity. The cost of connecting to private electric lines was so prohibitive that many rural communities turned to organizing amongst themselves to find creative solutions to electrification. In 1935, the federal government established the Rural Electrification Administration (REA) to support the formation of rural electric cooperatives. Over the following decades, this initiative thoroughly transformed rural life, extending electricity to rural businesses, farms, schools, and households and establishing a large network of utilities cooperatives that continue to provide services to rural areas today."

"One can prophesy with a Daniel's confidence that skilled electricians will settle the battles of the near future. But this is the least. In its effect upon war and peace, electricity offers still much greater and more wonderful possibilities. To stop war by the perfection of engines of destruction alone, might consume centuries and centuries. Other means must be employed to hasten the end."

"Electric current, after passing into the earth travels to the diametrically opposite region of the same and rebounding from there, returns to its point of departure with virtually undiminished force. The outgoing and returning currents clash and form nodes and loops similar to those observable on a vibrating cord. To traverse the entire distance of about twenty-five thousand miles, equal to the circumference of the globe, the current requires a certain time interval, which I have approximately ascertained. In yielding this knowledge, nature has revealed one of its most precious secrets, of inestimable consequence to man. So astounding are the facts in this connection, that it would seem as though the Creator, himself, had electrically designed this planet just for the purpose of enabling us to achieve wonders which, before my discovery, could not have been conceived by the wildest imagination."

"Go hug your girlfriend! Or if you don't have any, go find one! You won't find the meaning of life with electricity!"

"Stretches, for leagues and leagues, the Wire, A hidden path for a Child of Fire— Over its silent spaces sent, Swifter than Ariel ever went, From continent to continent."

"While Franklin's quiet memory climbs to heaven, Calming the lightning which he thence hath riven."

"And stoic Franklin's energetic shade Robed in the lightnings which his hand allay'd."

"To put a girdle round about the world."

"A vast engine of wonderful delicacy and intricacy, a machine that is like the tools of the Titans put in your hands. This machinery, in its external fabric so massive and so exquisitely adjusted, and in its internal fabric making new categories of thought, new ways of thinking about life."

"Notwithstanding my experiments with electricity the thunderbolt continues to fall under our noses and beards; and as for the tyrant, there are a million of us still engaged at snatching away his sceptre."

"But matchless Franklin! What a few Can hope to rival such as you. Who seized from kings their sceptred pride And turned the lightning's darts aside."

"A million hearts here wait our call, All naked to our distant speech— I wish that I could ring them all And have some welcome news for each."

"An ideal's love-fraught, imperious call That bids the spheres become articulate."

"This is a marvel of the universe: To fling a thought across a stretch of sky— Some weighty message, or a yearning cry, It matters not; the elements rehearse Man's urgent utterance, and his words traverse The spacious heav'ns like homing birds that fly Unswervingly, until, upreached on high, A quickened hand plucks off the message terse."

"Eripuit cælo fulmen, mox sceptra tyrannis."

"Russia is the largest energy power. The country with a unique energy system, one of the leaders in generating electricity and supplying it to the global market. This is the result of your hard work and professionalism. Each of you (energy complex's worker and veteran) does everything to ensure that the country's energy system stays reliable."

"Col. Olcott, was taken to task for asserting in one of his lectures that Electricity is matter. Such, nevertheless, is the teaching of the Occult Doctrine. "Force," "Energy," may be better names for it, so long as European Science knows so little about its true nature; yet matter it is, as much as Ether is matter, since it is as atomic, though indeed several removes from Ether. p. 136"

"It seems ridiculous to argue that because a thing is imponderable to Science, therefore it cannot be called matter. Electricity is "immaterial," in the sense that its molecules are not subject to perception and experiment; yet it may be — and Occultism says it is — atomic; therefore it is matter. But even supposing it were unscientific to speak of it in such terms, once Electricity is called in Science a source of Energy, Energy simply, and a Force — where is that Force or that Energy which can be thought of without thinking of matter? p. 137"

"Electricity is not only Substance, but that it is an emanation from an Entity, which is neither God nor Devil, but one of the numberless Entities that rule and guide our world, according to the eternal Iaw of Karma. p. 137"

"The Aurora Borealis and Australis (Aurora)... take place at the very centres of terrestrial electric and magnetic forces. The two Poles are said to be the store-houses, the receptacles and liberators, at the same time, of cosmic and terrestrial Vitality (Electricity), from the surplus of which the Earth, had it not been for these two natural safety-valves, would have been rent to pieces long ago. p. 226"

"If, as Sir William Grove says, the electricity we handle is but the result of ordinary matter affected by something invisible, the intimate generating power" of every Force, the "one omnipresent influence," then it only becomes natural that one should believe as the Ancients did; namely, that every Element is dual in its nature. p.508"

"Sir William Grove... in a lecture at the London Institution, in 1842, was the first to show that "heat, light, may be considered as affections of matter itself, and not of a distinct ethereal, 'imponderable,' fluid [a state of matter now] permeating it." Yet, perhaps, for some Physicists... Force and Forces were tacitly "Spirit [and hence Spirits] in Nature." What several rather mystical Scientists taught was that light, heat, magnetism, electricity and gravity, etc., were not the final Causes of the visible phenomena, including planetary motion, but were themselves the secondary effects of other Causes, for which Science in our day cares very little, but in which Occultism believes; for the Occultists have exhibited proofs of the validity of their claims in every age. And in what age were there no Occultists and no Adepts? p. 525"

"The science of electricity, which was not yet in existence when he [Boehme] wrote, is there anticipated [in his writings]; and not only does Boehme describe all the now known phenomena of that force, but he even gives us the origin, generation, and birth of electricity, itself. p. 535"

"We have an important scientific corroboration for one of our fundamental dogmas — namely, that (a) the Sun is the store-house of Vital Force, which is the Noumenon of Electricity; and {b) that it is from its mysterious, never-to-be-fathomed depths, that issue those lifecurrents which thrill through Space, as through the organisms of every living thing on Earth. p. 579"

"The Nasmyth willow leaves, mistaken by Sir John Herschell for "solar inhabitants," are the reservoirs of solar vital energy; "the vital electricity that feeds the whole system; the sun in abscondito ;being thus the storehouse of our little Cosmos, self-generating its vital fluid, and ever receiving as much as it gives out," and the visible Sun only a window cut into the real solar palace and presence, which, however, shews without distortion the interior work. p. 592"

"We are told that Mr. Keely defines electricity "as a certain form of atomic vibration." In this he is quite right; but this is Electricity on the terrestrial plane, and through terrestrial correlations. p. 613"

"Light is the first begotten, and the first emanation of the Supreme, and Light is Life, says the Evangelist [and the Kabalist]. Both are electricity — the life principle, the Anima Mundi — pervading the Universe, the electric vivifier of all things. p. 633"

"(Ptolemy) left in his Optics, the earliest surviving table of angles of refraction from air to water. ...This table, quoted and requoted until modern times, has been admired... A closer glance at it, however, suggests that there was less experimentation involved in it than originally was thought, for the values of the angles of refraction form an arithmetic progression of second order... As in other portions of Greek Science, confidence in mathematics was here greater than that in the evidence of the senses, although the value corresponding to 60° agrees remarkably well with experience."

"As men of inward light are wont To turn their optics in upon't."

"Music is the arithmetic of sounds as optics is the geometry of light."

"Regardless of the prophetic value of Dirac’s description [on interference] his was probably the first discussion... including a coherent beam of light. In other words, Dirac wrote the first chapter in laser optics."

"Why has not man a microscopic eye? For this plain reason, Man is not a Fly. Say, what the use, were finer optics giv'n, T' inspect a mite, not comprehend the heav'n?"

"Contemporary with Vitellio and Peccam was... Roger Bacon, a man of almost universal genius, and who wrote on almost every branch of science. He frequently quotes Alhazen on the subject of optics, and seems to have carefully studied his writings, as well as those of other Arabians, which were the fountains of natural knowledge in those days, and which had been introduced into Europe by means of the Moors in Spain. Notwithstanding the pains this great man took with the subject of opticks, it does not appear that, with respect to theory, he made any considerable advance upon what Alhazen had done before him."

"For any man with half an eye, What stands before him may espy; But optics sharp it needs I ween, To see what is not to be seen."

"Intuition is the wisdom formed by feeling and instinct - a gift of knowing without reasoning... Belief is ignited by hope and supported by facts and evidence - it builds alignment and creates confidence. Belief is what sets energy in motion and creates the success that breeds more success."

"There are as many types of motion or change as there are meanings of the word 'is'."

"The fulfilment of what exists potentially, in so far as it exists potentially, is motion."

"In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead."

"That which is in locomotion must arrive at the half-way stage before it arrives at the goal."

"Questions do not change the truth. But they give it motion."

"If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless."

"Newton... not only found a precise mathematical use for concepts like force, mass, inertia; he gave new meanings to the old terms space, time, and motion, which had hitherto been unimportant but were now becoming the fundamental categories of men's thinking."

"The motions of the heavenly bodies could be charted according to Ptolemy just as correctly as according to Copernicus."

"Nicholas of Cusa... dared to teach that there is nothing at all without motion in the universe — the latter is infinite in all directions, possessing no centre — and that the earth travels its course in common with the other stars. That this widening of the intellectual horizon of the age, with the suggestion of new centres of interest, was a decisive factor in Copernicus' personal development, the brief biographical sketch which he gives of himself in the De Revolutionibus strongly suggests."

"It is in the admission of ignorance and the admission of uncertainty that there is a hope for the continuous motion of human beings in some direction that doesn't get confined, permanently blocked, as it has so many times before in various periods in the history of man."

"Sunrise offered a very beautiful spectacle; the water was quite unruffled, but the motion communicated by the tides was so great that, although there was not a breath of air stirring, the sea heaved slowly with a grand and majestic motion."

"You control your future, your destiny. What you think about comes about. By recording your dreams and goals on paper, you set in motion the process of becoming the person you most want to be. Put your future in good hands - your own."

"Something in the way she moves attracts me like no other lover…"

"Movement through space is fundamental to life: movement of the entire organism, such as walking; movement of a part of the organism, such as an arm; movement of materials within the organism, such as food in the stomach; movement of offspring into the external world, as in birth. Each is a mechanism indispensable to virtually all members of the animal kingdom. In the end, it is muscle that accomplishes movement. As a consequence, muscle is the most abundant tissue in most animals and accounts for much of the energy-consuming cellular work in an active animal."

"Yet it is in this loneliness that the deepest activities begin. It is here that you discover act without motion, labor that is profound repose, vision in obscurity, and, beyond all desire, a fulfillment whose limits extend to infinity."

"Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it."

"I can calculate the motion of heavenly bodies, but not the madness of people."

"The alternation of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed."

"Whatever is always in motion is immortal."

"The connection to place, to the land, the wind, the sun, stars, the moon... it sounds romantic, but it's true - the visceral experience of motion, of moving through time on some amazing machine - a few cars touch on it, but not too many compared to motorcycles. I always felt that any motorcycle journey was special."

"Look at what you want to change, gather a few people who believe in it like you do, and start moving forward. It's important to remember that you don't always need a destination. Sometimes, you just have to make forward motion. And you absolutely can."

"Revenge... is like a rolling stone, which, when a man hath forced up a hill, will return upon him with a greater violence, and break those bones whose sinews gave it motion."

"Painting is concerned with all the 10 attributes of sight; which are: Darkness, Light, Solidity and Colour, Form and Position, Distance and Propinquity, Motion and Rest."

"One purpose of physics is to study the motion of objects—how fast they move, for example, and how far they move in a given amount of time. NASCAR engineers are fanatical about this aspect of physics as they determine the performance of their cars before and during a race. Geologists use this physics to measure tectonic-plate motion as they attempt to predict earthquakes. Medical researchers need this physics to map the blood flow through a patient when diagnosing a partially closed artery, and motorists use it to determine how they might slow sufficiently when their radar detector sounds a warning."

"Sex is an emotion in motion."

"The fate of this man or that man was less than a drop, although it was a sparkling one, in the great blue motion of the sunlit sea."

"There is a very interesting analogy between the evolution of the atom and of man in the two methods of unfoldment that are followed. We have seen that the atom has its own atomic life, and that every atom of substance in the solar system is likewise a little system in itself, having a positive centre, or central sun, with the electrons, or the negative aspect, revolving in their orbits around it. Such is the internal life of the atom, its self-centred aspect."

"The atom is now being studied along a newer line... Much of the earlier teaching of physical science has been revolutionised by the discovery of radium, and the more scientists find out, the more it becomes apparent (as they themselves realise), that we are standing on the threshold of very great discoveries, and are on the eve of profound revelations. In the human being, as he evolves and develops, these two stages can equally be seen. There is the early or atomic stage, in which a man's whole centre of interest lies within himself, within his own sphere, where self-centredness is the law of his being, a necessary protective stage of evolution. He is purely selfish, and concerned primarily with his own affairs. This is succeeded by a later stage, in which a man's consciousness begins to expand, his interests begin to lie outside his own particular sphere, and the period arrives in which he is feeling for the group to which he belongs. This stage might be viewed as corresponding to that of radio-activity. He is now not only a self-centred life, but he is also beginning to have a definite effect upon his surroundings. He is turning his attention from his own personal selfish life, and is seeking his greater centre. From being simply an atom he is, in his turn, becoming an electron, and coming under the influence of the great central Life which holds him within the sphere of Its influence."

"Life is a partial, continuous, progressive, multiform and conditionally interactive self-realization of the potentialities of atomic electron states."

"The Atoms of Democritus And Newton's Particles of light Are sands upon the Red sea shore Where Israel's tents do shine so bright."

"We have grasped the mystery of the atom and rejected the Sermon on the Mount."

"We must be clear that when it comes to atoms, language can be used only as in poetry. The poet, too, is not nearly so concerned with describing facts as with creating images and establishing mental connections."

"We can still use the objectifying language of classical physics to make statements about observable facts. For instance, we can say that a photographic plate has been blackened, or that cloud droplets have formed. But we can say nothing about the atoms themselves. And what predictions we base on such findings depend on the way we pose our experimental question, and here the observer has freedom of choice. Naturally, it still makes no difference whether the observer is a man, an animal, or a piece of apparatus, but it is no longer possible to make predictions without reference to the observer or the means of observation."

"In all chemical investigations, it has justly been considered an important object to ascertain the relative weights of the simples which constitute a compound. But unfortunately the enquiry has terminated here; whereas from the relative weights in the mass, the relative weights of the ultimate particles or atoms of the bodies might have been inferred, from which their number and weight in various other compounds would appear, in order to assist and to guide future investigations, and to correct their results. Now it is one great object of this work, to shew the importance and advantage of ascertaining the relative weights of the ultimate particles, both of simple and compound bodies, the number of simple elementary particles which constitute one compound particle, and the number of less compound particles which enter into the formation of one more compound particle. If there are two bodies, A and B, which are disposed to combine, the following is the order in which the combinations may take place, beginning with the most simple: namely, 1 atom of A + 1 atom of B = 1 atom of C, binary 1 atom of A + 2 atoms of B = 1 atom of D, ternary 2 atoms of A + 1 atom of B = 1 atom of E, ternary 1 atom of A + 3 atoms of B = 1 atom of F, quaternary 3 atoms of A and 1 atom of B = 1 atom of G, quaternary"

"δοκεῖ δὲ αὐτῶι τάδε· ἀρχὰς εἶναι τῶν ὅλων ἀτόμους καὶ κενόν, τὰ δ'ἀλλα πάντα νενομίσθαι [δοξάζεσθαι]."

"If the motion to be discussed here can actually be observed, together with the laws it is expected to obey, then classical thermodynamics can no longer be viewed as applying to regions that can be distinguished even with a microscope, and an exact determination of actual atomic sizes becomes possible. On the other hand, if the prediction of this motion were to be proved wrong, this fact would provide a far-reaching argument against the molecular-kinetic conception of heat."

"The unleashed power of the atom has changed everything save our modes of thinking and we thus drift toward unparalleled catastrophe."

"… Several of Thomson’s colleagues thought he was joking when he argued that the electron was smaller than the atom and was a constituent of every atom; to many scientists, the idea that there could exist matter smaller than the atom was inconceivable. Yet he was proved right."

"If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis (or the atomic fact, or whatever you wish to call it) that all things are made of atoms—little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence, you will see, there is an enormous amount of information about the world, if just a little imagination and thinking are applied."

"Another way to remember their size is this: if an apple is magnified to the size of the earth, then the atoms in the apple are approximately the size of the original apple."

"[A]ll these successive triumphs of research, Dalton’s, Kirchhoff’s, Mendeléeff’s, greatly as they have added to our store of knowledge, have gone but little way to solve the problem which the elementary atoms have for centuries presented to mankind. What the atom of each element is, whether it is a movement, or a thing, or a vortex, or a point having inertia, whether there is any limit to its divisibility, and, if so, how that limit is imposed, whether the long list of elements is final, or whether any of them have any common origin, all these questions remain surrounded by a darkness as profound as ever. The dream which lured the alchemists to their tedious labours, and which may be said to have called chemistry into being, has assuredly not been realised, but it has not yet been refuted. The boundary of our knowledge in this direction remains where it was many centuries ago."

"But what if we could see them?" "We shall never be able to see atoms themselves, only their effects." "That's a poor excuse of an answer. For the same remark a pplies to things in general. In the case of a cat, too, all you can see is the reflection of light rays, i.e., the effects of the cat, and not the cat itself. And when you stroke its fur, the situation is much the same!"

"Hynes here too: account of the funeral probably. Thumping. Thump. This morning the remains of the late Mr Patrick Dignam. Machines. Smash a man to atoms if they got him caught. Rule the world today. His machineries are pegging away too. Like these, got out of hand: fermenting. Working away, tearing away. And that old grey rat tearing to get in."

"And in the corner by the window gable was a shelf with some books, and some from a circulating library. She looked. There were books about Bolshevist Russia, books of travel, a volume about the atom and the electron, another about the composition of the earth’s core, and the causes of earthquakes: then a few novels: then three books on India. So! He was a reader after all."

"A man concerned about the state of his soul will not usually be much helped by thinking about the spheres or the structure of the atom."

"I don't believe that atoms exist!"

"In the very beginnings of science, the parsons, who managed things then, Being handy with hammer and chisel, made gods in the likeness of men; Till commerce arose, and at length some men of exceptional power Supplanted both demons and gods by the atoms, which last to this hour. Yet they did not abolish the gods, but they sent them well out of the way, With the rarest of nectar to drink, and blue fields of nothing to sway. From nothing comes nothing, they told us—naught happens by chance, but by fate; There is nothing but atoms and void, all else is mere whims out of date! Then why should a man curry favour with beings who cannot exist, To compass some petty promotion in nebulous kingdoms of mist? But not by the rays of the sun, nor the glittering shafts of the day, Must the fear of the gods be dispelled, but by words, and their wonderful play. So treading a path all untrod, the poet-philosopher sings Of the seeds of the mighty world—the first-beginnings of things; How freely he scatters his atoms before the beginning of years; How he clothes them with force as a garment, those small incompressible spheres! Nor yet does he leave them hard-hearted—he dowers them with love and with hate, Like spherical small British Asses in infinitesimal state; Till just as that living Plato, whom foreigners nickname Plateau, Drops oil in his whisky-and-water (for foreigners sweeten it so); Each drop keeps apart from the other, enclosed in a flexible skin, Till touched by the gentle emotion evolved by the prick of a pin: Thus in atoms a simple collision excites a sensational thrill, Evolved through all sorts of emotion, as sense, understanding, and will (For by laying their heads all together, the atoms, as councillors do, May combine to express an opinion to every one of them new). There is nobody here, I should say, has felt true indignation at all, Till an indignation meeting is held in the Ulster Hall; Then gathers the wave of emotion, then noble feelings arise, Till you all pass a resolution which takes every man by surprise. Thus the pure elementary atom, the unit of mass and of thought, By force of mere juxtaposition to life and sensation is brought; So, down through untold generations, transmission of structureless germs Enables our race to inherit the thoughts of beasts, fishes, and worms. We honour our fathers and mothers, grandfathers and grandmothers too; But how shall we honour the vista of ancestors now in our view? First, then, let us honour the atom, so lively, so wise, and so small; The atomists next let us praise, Epicurus, Lucretius, and all. Let us damn with faint praise Bishop Butler, in whom many atoms combined To form that remarkable structure it pleased him to call—his mind. Last, praise we the noble body to which, for the time, we belong, Ere yet the swift whirl of the atoms has hurried us, ruthless along, The British Association—like Leviathan worshipped by Hobbes, The incarnation of wisdom, built up of our witless nobs, Which will carry on endless discussions when I, and probably you, Have melted in infinite azure—in English, till all is blue."

"As for the atoms, they have been in far worse rows before they became naturalised in my brain, but they forget the days before, etc. At any rate the atoms are a very tough lot, and can stand a great deal of knocking about, and it is strange to find a number of them combining to form a man of feeling."

"In your letter you apply the word imponderable to a molecule. Don't do that again. It may also be worth knowing that the aether cannot be molecular. If it were, it would be a gas, and a pint of it would have the same properties as regards heat, etc., as a pint of air, except that it would not be so heavy. Under what form (right or light) can an atom be imagined? Bezonian! speak or die! Now I must go to post with two dogs in the rain.—Your afft. friend"

"We have now got what seems to be definite proof that an X ray which spreads out in a spherical form from a source as a wave through the aether can when it meets an atom collect up all its energy from all round and concentrate it on the atom. It is as if when a circular wave on water met an obstacle, the wave were all suddenly to travel round the circle and disappear all round and concentrate its energy on attacking the obstacle. Mechanically of course this is absurd, but mechanics have in this direction been for some time a broken reed."

"As far as materialistic atomism goes: this is one of the most well-refuted things in existence. In Europe these days, nobody in the scholarly community is likely to be so unscholarly as to attach any real significance to it, except as a handy household tool (that is, as an abbreviated figure of speech)."

"Over the last century, physicists have used light quanta, electrons, alpha particles, X-rays, gamma-rays, protons, neutrons and exotic sub-nuclear particles for this purpose [scattering experiments]. Much important information about the target atoms or nuclei or their assemblage has been obtained in this way. In witness of this importance one can point to the unusual concentration of scattering enthusiasts among earlier Nobel Laureate physicists. One could say that physicists just love to perform or interpret scattering experiments."

"Atoms are round balls of wood invented by Dr. Dalton."

"… A particle, on the other hand, has discrete properties which it carries with it. And so the remarkable thing was the discovery, in investigations of various atomic phenomena, of an apparent paradox."

"Nothing exists, save atoms and their combinations. There is no atom, which wouldn't periodically take part in life."

"[The] structural theory is of extreme simplicity. It assumes that the molecule is held together by links between one atom and the next: that every kind of atom can form a definite small number of such links: that these can be single, double or triple: that the groups may take up any position possible by rotation round the line of a single but not round that of a double link: finally that with all the elements of the first short period [of the periodic table], and with many others as well, the angles between the valencies are approximately those formed by joining the centre of a regular tetrahedron to its angular points. No assumption whatever is made as to the mechanism of the linkage. Through the whole development of organic chemistry this theory has always proved capable of providing a different structure for every different compound that can be isolated. Among the hundreds of thousands of known substances, there are never more isomeric forms than the theory permits."

"For every atom belonging to me as good belongs to you."

"The history of science shows that sharp definitions lead to trouble. Dogmatism in science is usually mistaken, because the conviction of certainty expresses a psychological compulsion, never any truly compelling reasons or facts. When a view attains wide popularity and seems obviously beyond question, its decline has usually begun or will begin very soon. In 1892 W. W. Rouse Ball of Trinity College, Cambridge, who was well informed on competent opinion—J. J. Thomson was also at Trinity—wrote: "The popular view is that every atom of any particular kind is a minute indivisible article possessing definite qualities, everlasting in its properties, and infinitely hard." Rouse Ball wisely added descriptions of two rival atomic doctrines: Boscovich's point centres, and another based on twists in an elastic solid aether. Four years later the hard everlasting atom began its rapid exit from physics."

"The matter which we suppose to be the main constituent of the universe is built out of small self-contained building-blocks, the chemical atoms. It cannot be repeated too often that the word "atom" is nowadays detached from any of the old philosophical speculations: we know precisely that the atoms with which we are dealing are in no sense the simplest conceivable components of the universe. On the contrary, a number of phenomena, especially in the area of spectroscopy, lead to the conclusion that atoms are very complicated structures. So far as modern science is concerned, we have to abandon completely the idea that by going into the realm of the small we shall reach the ultimate foundation of the universe. I believe we can abandon this idea without any regret. The universe is infinite in all directions, not only above us in the large but also below us in the small. If we start from our human scale of existence and explore the content of the universe further and further, we finally arrive, both in the large and in the small, at misty distances where first our senses and then even our concepts fail us."

"There must be what Mr. Gladstone many years ago called "a blessed act of oblivion". We must all turn our backs upon the horrors of the past. We must look to the future. We cannot afford to drag forward across the years that are to come the hatreds and revenges which have sprung from the injuries of the past."

"The point at issue between the two theories [A and B theory] is whether 'time' really is, in some deep ontological sense, differentiated into past, present and future. ...Reichenbach and Whitrow propose that there is indeed such a type of event and this is the 'becoming', or 'coming into being' of factual states-of-affairs in the physical world. Reichenbach ...claimed that 'becoming' is in fact made manifest through the Uncertainty Principle of Heisenberg: "The concept of becoming, he wrote, acquires a meaning in physics: The present, which separates the future from the past, is the moment when that which was undetermined becomes determined, and 'becoming' means the same as 'becoming determined' ". Whitrow expressed ..."The past is the determined, the present is the moment of 'becoming' when events become determined, and the future is as-yet undetermined. Although neither Reichenbach nor Whitrow developed their thesis at any length, the general purport of what they meant is clear: there is a basic chance element in nature, at least at the micro-level, and the moment of 'becoming', which they identify with 'the present', is marked by a transition from what is merely possible to what is factual. However... this important attempt to provide a physical basis for the A-theory is by no means immune from criticism."

"The question Whether one generation of men has a right to bind another, seems never to have been started either on this or our side of the water…. I set out on this ground, which I suppose to be self evident, "that the earth belongs in usufruct to the living:" that the dead have neither powers nor rights over it."

"Like my three brothers before me, I pick up a fallen standard. Sustained by their memory of our priceless years together I shall try to carry forward that special commitment to justice, to excellence, to courage that distinguished their lives."

"The dogmas of the quiet past, are inadequate to the stormy present. The occasion is piled high with difficulty, and we must rise with the occasion. As our case is new, so we must think anew and act anew. We must disenthrall ourselves, and then we shall save our country."

"Our duty is to preserve what the past has had to say for itself, and to say for ourselves what shall be true for the future."

"Whereof what's past is prologue, what to come In yours and my discharge."

"An overflowing pot must be emptied before anything new can be added. If you cling to the sorrows of the past, how can you make space for the happiness and joy of the present?"

"More and more Emerson recedes grandly into history, as the future he predicted becomes a past."

"There is nothing new under the sun."

"Man must have been conscious of memories and purposes long before he made any explicit distinction between past, present, and future."

"Nuclear magnetic resonance spectroscopy depends on the absorption of energy when the nucleus of an atom is excited from its lowest energy spin state to the next higher one. The nuclei of several elements can be studied by NMR. The two elements that are the most common in organic molecules (carbon and hydrogen) have isotopes (1H and 13C) capable of giving NMR spectra that are rich in structural information. A proton nuclear magnetic resonance (1H NMR) spectrum tells us about the environments of the various hydrogens in a molecule; a carbon-13 nuclear magnetic resonance (13C NMR) spectrum does the same for the carbon atoms. Separately and together 1H and 13C NMR take us a long way toward determining a substance’s molecular structure. We’ll develop most of the general principles of NMR by discussing 1H NMR, then extend them to 13C NMR. The 13C NMR discussion is shorter, not because it is less important than 1H NMR, but because many of the same principles apply to both techniques."

"In subsequent chapters, discussions regarding a number of nuclear magnetic resonance (NMR) techniques that could not be implemented when nuclear magnetic resonance was first discovered are presented. Their advent required, for example, strong magnetic fields and/or cryoprobes to accommodate limited sample availability. Pulsed field gradients (PFGs) have improved solvent suppression, have enabled efficient selective excitation, and have made accessible a different time range to diffusion coefficient measurement. Such developments have, of course, been made in parallel with increasing access to powerful computers and sophisticated software, permitting speedy processing and analysis of the various types and sizes of acquired data sets. Instrumental and software developments in the past 30 to 40 years have meant that NMR spectroscopy is now used in a wide range of scenarios. Synthetic chemists use NMR to elucidate structures of small molecules. It is employed in pharmaceutical industries for structure elucidation and drug development and screening (Chapter 3, Section 7.1). Biochemistry and biotechnology sectors utilise NMR to probe solution structures and functions of biological polymers (Chapter 7), and it is increasingly used in biomedicine (in particular, biomarker discovery; Chapter 6) for the analysis of complex matrices. Materials science (both soft and hard matters) is another application area in which solution and solid-state NMR has proved extremely valuable. While not an exhaustive list of applications, this is an illustration of the breadth of science that has benefitted from this analytical technique."

"The electron paramagnetic resonance discovered by Evgenii Konstantinovich is undoubtedly a first-class thing. It is a pity that nuclear magnetic resonance 'floated away'. Clearly, if Evgenii Konstantinovich had worked in better conditions, he would have done much more."

"In the absence of an external magnetic field, the spins of magnetic nuclei are oriented randomly. When a sample containing these nuclei is placed between the poles of a strong magnet, however, the nuclei adopt specific orientations, much as a compass needle orients in the earth’s magnetic field. A spinning 1H or 13C nucleus can orient so that its own tiny magnetic field is aligned either with (parallel to) or against (antiparallel to) the external field. The two orientations don’t have the same energy, however, and aren’t equally likely. The parallel orientation is slightly lower in energy by an amount that depends on the strength of the external field, making this spin state very slightly favored over the antiparallel orientation. ... If the oriented nuclei are irradiated with electromagnetic radiation of the proper frequency, energy absorption occurs and the lower-energy state “spinflips” to the higher-energy state. When this spin-flip occurs, the magnetic nuclei are said to be in resonance with the applied radiation—hence the name nuclear magnetic resonance."

"For magnetic fields that can be routinely produced in the laboratory, the transitions between energy levels for nuclear magnetic dipoles occur in the radio-frequency range, and the transitions between energy levels for unpaired electron spins occur in the microwave range. Nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR) yield such valuable structural information that they have become indispensable in chemistry."

"The nuclei of certain elements, including 1H nuclei (protons) and 13C(carbon-13) nuclei, behave as though they were magnets spinning about an axis. When a compound containing protons or carbon-13 nuclei is placed in a very strong magnetic field and simultaneously irradiated with electromagnetic energy of the appropriate frequency, nuclei of the compound absorb energy through a process called magnetic resonance. The absorption of energy is quantized. ... We can use NMR spectra to provide valuable information about the structure of any molecule we might be studying. In the following sections we shall explain how four features of a molecule’s proton NMR spectrum can help us arrive at its structure."

"Back at Caltech, my research was going strong, and we had four different laboratories busy with experiments and people. In one of these laboratories, we were continuing with our work on coherence; in others, advancing techniques for shorter time resolution and for developing an optical analog for nuclear magnetic resonance (NMR). In NMR, the spin of nuclei with their transitions at radio frequencies is used for a variety of applications, ranging from the studies of molecular structure to magnetic resonance imaging (MRI), which is now commonly used in hospitals throughout the world."

"MOLECULE, n. The ultimate, indivisible unit of matter. It is distinguished from the corpuscle, also the ultimate, indivisible unit of matter, by a closer resemblance to the atom, also the ultimate, indivisible unit of matter. Three great scientific theories of the structure of the universe are the molecular, the corpuscular and the atomic. A fourth affirms, with Haeckel, the condensation of precipitation of matter from ether -- whose existence is proved by the condensation of precipitation. The present trend of scientific thought is toward the theory of ions. The ion differs from the molecule, the corpuscle and the atom in that it is an ion. A fifth theory is held by idiots, but it is doubtful if they know any more about the matter than the others."

"Deep in the sea all molecules repeat the patterns of one another till complex new ones are formed. They make others like themselves and a new dance starts.Growing in size and complexity living things masses of atoms DNA, protein dancing a pattern ever more intricate."

"Such a shared-electron bond, first proposed in 1916 by G. N. Lewis, is called a covalent bond. The neutral collection of atoms held together by covalent bonds is called a molecule."

"A diatomic molecule is a molecule with one atom too many."

"Net molecular polarity is measured by a quantity called the dipole moment and can be thought of in the following way: assume that there is a center of mass of all positive charges (nuclei) in a molecule and a center of mass of all negative charges (electrons). If these two centers don’t coincide, then the molecule has a net polarity. The dipole moment, μ (Greek mu), is defined as the magnitude of the charge Q at either end of the molecular dipole times the distance r between the charges, μ = Q × r. Dipole moments are expressed in debyes(D), where 1 D = 3.336 ×10-30 coulomb meter (C · m) in SI units. For example, the unit charge on an electron is 1.60 ×10-19 C. Thus, if one positive charge and one negative charge are separated by 100 pm (a bit less than the length of a typical covalent bond), the dipole moment is 1.60 ×10-29 C · m, or 4.80 D.… In contrast with water, methanol, and ammonia, molecules such as carbon dioxide, methane, ethane, and benzene have zero dipole moments. Because of the symmetrical structures of these molecules, the individual bond polarities and lone-pair contributions exactly cancel."

"In my own field, x-ray crystallography, we used to work out the structure of minerals by various dodges which we never bothered to write down, we just used them. Then Linus Pauling came along to the laboratory, saw what we were doing and wrote out what we now call Pauling's Rules. We had all been using Pauling's Rules for about three or four years before Pauling told us what the rules were."

"...all the work of the crystallographers serves only to demonstrate that there is only variety everywhere they suppose uniformity...that innature there is nothing absolute, nothing perfectly regular."

"I miss the old days, when nearly every problem in X-ray crystallography was a puzzle that could be solved only by much thinking."

"Since modern crystallography dawned with X-ray diffraction experiments on crystals by Max von Laue in 1912 and William and Lawrence Bragg (a father and son team) in 1913, and was recognized by Nobel prizes in physics for von Laue in 1914 and the Braggs in 1915, the discipline has informed almost every branch of the natural sciences."

"Aeroplanes fly safely because crystallography tests computer models of materials under stress. Drugs are more potent because crystallographers can see and modify how molecules interact with target sites in cells. An X-ray diffraction instrument on NASA’s Curiosity rover is now even studying the mineralogy of Mars."

"Crystallography is increasingly focusing its resources on large multidisciplinary facilities, such as powerful X-ray and neutron sources."

"Crystallographers have a raft of methods at their disposal. Von Laue scattered X-ray photons from atoms. Now experimenters can also bombard crystal lattices with electrons and neutrons, and exploit properties such as the polarization of photons and neutrons and their interactions with magnetic fields."

"It takes a very special breed of scientist to do this work...it is an area of science in which women dominate."

"Thanks to the methods that [Crystallographers] have devised for investigating crystal structures, an entirely new world has been opened and has already in part been explored with marvelous exactitude. The significance of these methods, and of the results attained by their means, cannot as yet be gauged in its entirety, however imposing its dimensions already appear to be."

"Crystallography remains a cutting-edge field, and one that, if harnessed properly, could contribute as much in the next 100 years as it did in the previous 100. The development of the x-ray free-electron laser, for example, is a monumental technical achievement, and one that seems more suited to the world of 2114 than 1914, or even 2014."

"Crystallographers should take a lesson from particle physicists and create a body run by scientists for the governance of large international x-ray and neutron facilities. It should be guided by input from regular meetings of researchers from across the scientific community. This will ensure that the next generation of infrastructure will have the strongest possible scientific case, articulated clearly."

"Researchers hope to be able to get diffraction patterns from individual molecules, allowing them to watch biomolecules moving and interacting in a completely natural setting, surrounded by water, instead of trapped in the artificial environment of a crystal. That’s my future vision for crystallography. Get away from being a coroner imaging dead molecules, and instead get molecular movies."

"A cold coming they had of it, at this time of the year; just the worst time of the year to take a journey, and specially a long journey, in."

"Do you wish to honor the Body of the Savior? Do not despise it when it is naked. Do not honor it in church with silk vestments while outside it is naked and numb with cold. He who said, “This is my body,” and made it so by his word, is the same that said, “You saw me hungry and you gave me no food. As you did it not to the least of these, you did it not to me.” Honor him then by sharing your property with the poor. For what God needs is not golden chalices but golden souls."

"If I was not assured by the best authority on earth that the world is to be destroyed by fire, I should conclude that the day of destruction is at hand, but brought on by means of an agent very opposite to that of heat."

"People ask the way to Cold Mountain. Cold Mountain? There is no road that goes through. Even in summer the ice doesn't melt; Though the sun comes out, the fog is blinding. How can you hope to get there by aping me? Your heart and mine are not alike. If your heart were the same as mine, Then you could journey to the very center!"

"Here I stand In the light of day! Let the storm rage on! The cold never bothered me anyway!"

"Despite the growing interest in the field of ultracold chemistry, experimental progress has been hampered by a lack of appropriate methods to trap and cool molecules. Laser cooling, while very successful, is limited to a small number of atoms in the Periodic Table because few atoms and no molecules have closed cycling transitions. The main methods to produce cold molecules of chemical interest can be divided into two groups. Buffer gas cooling relies on collisions with cold helium in a dilution refrigerator to cool paramagnetic molecules and trap them in a magnetic trap. Super-sonic expansion is used by other methods to precool the molecules. The resulting cold molecular beams have been slowed and trapped in some experiments by interactions with pulsed electric fields Stark decelerator, by interactions with pulsed optical fields, by spinning the nozzle, and by billiardlike collisions. Finally, laser-cooled alkali-metal atoms are used to produce cold molecules via photoassociation. None of these methods have, to date, achieved the phase space densities required to observe reaction dynamics at ultracold temperatures. We recently demonstrated a general method to stop and eventually trap paramagnetic atoms. Our method is based on the interaction of a paramagnetic particle with pulsed magnetic fields. It operates in analogy with the Stark decelerator by reducing the kinetic energy of a para-magnetic atom passing through a series of pulsed electro-magnetic coils. The amount of kinetic energy removed by each stage is equal to the Zeeman energy shift that the atom experiences at the time the fields are switched off."

"Future work will extend the coilgun method to trap molecules of chemical interest. Once they are in a magnetic trap, they can be cooled to near the single photon recoil limit using the method of single photon cooling, as demonstrated recently with trapped atoms. The application of this method to cooling of molecules is particularly promising."

"Living in a cold house, apartment, or other building can cause hypothermia. In fact, hypothermia can happen to someone in a nursing home or group facility if the rooms are not kept warm enough. If someone you know is in a group facility, pay attention to the inside temperature and to whether that person is dressed warmly enough. People who are sick may have special problems keeping warm. Do not let it get too cold inside and dress warmly. Even if you keep your temperature between 60°F and 65°F, your home or apartment may not be warm enough to keep you safe. This is a special problem if you live alone because there is no one else to feel the chilliness of the house or notice if you are having symptoms of hypothermia. Here are some tips for keeping warm while you're inside: * Set your heat to at least 68–70°F. To save on heating bills, close off rooms you are not using. Close the vents and shut the doors in these rooms, and keep the basement door closed. Place a rolled towel in front of all doors to keep out drafts. * Make sure your house isn't losing heat through windows. Keep your blinds and curtains closed. If you have gaps around the windows, try using weather stripping or caulk to keep the cold air out. * Dress warmly on cold days even if you are staying in the house. Throw a blanket over your legs. Wear socks and slippers. *When you go to sleep, wear long underwear under your pajamas, and use extra covers. Wear a cap or hat. * Make sure you eat enough food to keep up your weight. If you don't eat well, you might have less fat under your skin. Body fat helps you to stay warm. *Drink alcohol moderately, if at all. Alcoholic drinks can make you lose body heat. *Ask family or friends to check on you during cold weather. If a power outage leaves you without heat, try to stay with a relative or friend. You may be tempted to warm your room with a space heater. But, some space heaters are fire hazards, and others can cause carbon monoxide poisoning. The Consumer Product Safety Commission has information on the use of space heaters."

"There is an apocryphal story, that when the German philosopher Goethe lay dying, he was supposed to have opened his eyes, and said, “Light. Please, God. Let me have light. I must have light.” And, a hundred years later, the Spanish philosopher Unomono, upon hearing what had been supposedly Goethe’s final statement, is suppose to have responded: “No. Impossible. Goethe would not have asked for light. Not light. He would have asked for warmth. He would have said, ‘Please, God, let me have warmth. I must have warmth. Men do not die of the darkness. They die of the cold. It is the frost that kills. And this warmth I talk of, this is the warmth of love.”’"

"It's too cold outside for angels to fly."

"I love thee, I love but thee, With a love that shall not die Till the sun grows cold, And the stars are old, And the leaves of the Judgment Book unfold!"

"In order that a pendulum may continue to make the same number of oscillations in a given time, it must be shortened as it is carried towards the equator; and the variation of its length in different latitudes affords an accurate measurement of the force of gravity. But the force of gravity has known relation to the figure of the earth, which, therefore, may be determined, by observing the length of the seconds pendulum at different points on its surface."

"All the colours look brighter now. Everything they say seems to sound new. Slipping into tomorrow too quick, Yesterday always too good to forget. Stop the swing of the pendulum! Let us through!"

"Man! Thou pendulum betwixt a smile and tear."

"For the better part of my last semester at Garden City High, I constructed a physical pendulum and used it to make a “precision” measurement of gravity. The years of experience building things taught me skills that were directly applicable to the construction of the pendulum. Twenty-five years later, I was to develop a refined version of this measurement using laser-cooled atoms in an atomic fountain interferometer."

"If it is possible to have a linear unit that depends on no other quantity, it would seem natural to prefer it. Moreover, a mensural unit taken from the earth itself offers another advantage, that of being perfectly analogous to all the real measurements that in ordinary usage are also made upon the earth, such as the distance between two places or the area of some tract, for example. It is far more natural in practice to refer geographical distances to a quadrant of a great circle than to the length of a pendulum."

"Idiot. Above her head was the only stable point in the cosmos, the only refuge from the damnation of the panta rei, and she guessed it was the Pendulum's business. A moment later the couple went off -- he, trained on some textbook that had blunted his capacity for wonder, she, inert and insensitive to the thrill of the infinite, both oblivious of the awesomeness of their encounter -- their first and last encounter -- with the One, the Ein-Sof, the Ineffable. How could you fail to kneel down before this altar of certitude?”"

"Politics is a pendulum whose swings between anarchy and tyranny are fueled by perpetually rejuvenated illusions."

"Ideas came with explosive immediacy, like an instant birth. Human thought is like a monstrous pendulum; it keeps swinging from one extreme to the other."

"When young Galileo, then a student at Pisa, noticed one day during divine service a chandelier swinging backwards and forwards, and convinced himself, by counting his pulse, that the duration of the oscillations was independent of the arc through which it moved, who could know that this discovery would eventually put it in our power, by means of the pendulum, to attain an accuracy in the measurement of time till then deemed impossible, and would enable the storm-tossed seaman in the most distant oceans to determine in what degree of longitude he was sailing?"

"I simply state that I'm a product of a versatile mind in a restless generation — with every reason to throw my mind and pen in with the radicals. Even if, deep in my heart, I thought we were all blind atoms in a world as limited as a stroke of a pendulum, I and my sort would struggle against tradition; try, at least, to displace old cants with new ones. I've thought I was right about life at various times, but faith is difficult. One thing I know. If living isn't seeking for the grail it may be a damned amusing game."

"I shall explain a System of the World differing in many particulars from any yet known, answering in all things to the common Rules of Mechanical Motions: This depends upon three Suppositions. First, That all Cœlestial Bodies whatsoever, have an attraction or gravitating power towards their own Centers, whereby they attract not only their own parts, and keep them from flying from them, as we may observe the Earth to do, but that they do also attract all the other Cœlestial bodies that are within the sphere of their activity; and consequently that not only the Sun and Moon have an influence upon the body and motion the Earth, and the Earth upon them, but that Mercury also Venus, Mars, Saturn and Jupiter by their attractive powers, have a considerable influence upon its motion in the same manner the corresponding attractive power of the Earth hath a considerable influence upon every one of their motions also. The second supposition is this, That all bodies whatsoever that are put into a direct and simple motion, will continue to move forward in a straight line, till they are by some other effectual powers deflected and bent into a Motion, describing a Circle, Ellipse, or some other more compounded Curve Line. The third supposition is, That these attractive powers are so much the more powerful in operating, by how much the nearer the body wrought upon is to their own Centers. Now what these several degrees are I have not yet experimentally verified; but it is a notion, which if fully prosecuted as it ought to be, will mightily assist the Astronomer to reduce all the Cœlestial Motions to a certain rule, which I doubt will never be done true without it. He that understands the nature of the Circular Pendulum and Circular Motion, will easily understand the whole ground of this Principle, and will know where to find direction in Nature for the true stating thereof. This I only hint at present to such as have ability and opportunity of prosecuting this Inquiry, and are not wanting of Industry for observing and calculating, wishing heartily such may be found, having myself many other things in hand which I would first complete and therefore cannot so well attend it. But this I durst promise the Undertaker, that he will find all the Great Motions of the World to be influenced by this Principle, and that the true understanding thereof will be the true perfection of Astronomy."

"To all appearance, the phenomena exhibited by the pendulum are not to be accounted for by impact: in fact, it is usually assumed that corresponding phenomena would take place if the earth and the pendulum were situated in an absolute vacuum, and at any conceivable distance from one another. If this be so, it follows that there must be two totally different kinds of causes of motion: the one impact—a vera causa [true cause], of which, to all appearance, we have constant experience; the other, attractive or repulsive 'force'—a metaphysical entity which is physically inconceivable."

"So the pendulum swings, now violently, now slowly; and every institution not only carries within it the seeds of its own dissolution, but prepares the way for its most hated rival."

"The pendulum of the mind alternates between sense and nonsense, not between right and wrong."

"The history of human thought recalls the swinging of a pendulum which takes centuries to swing. After a long period of slumber comes a moment of awakening. Then thought frees herself from the chains with which those interested — rulers, lawyers, clerics — have carefully enwound her. She shatters the chains. She subjects to severe criticism all that has been taught her, and lays bare the emptiness of the religious political, legal, and social prejudices amid which she has vegetated. She starts research in new paths, enriches our knowledge with new discoveries, creates new sciences."

"The length of the pendulum and that of the meridian are the two principal means offered by Nature for fixing the unity of linear measurements. Both being independent of moral revolutions, they can undergo no detectable alteration short of enormous changes in the physical constitution of the earth. The first method is easily applicable, but has the disadvantage of making the measurement of distance depend on two elements that are heterogeneous to it, gravity and time, the division of [the latter of] which, moreover, is arbitrary. It was decided, therefore, to adopt the second method, which appears to have been employed in early antiquity, so natural is it for man to relate the units of distance by which travels to the dimensions of the globe that he inhabits. In moving about this globe, he may thus know by the simple denomination of the distance the proportion it bears to the entire circumference of the earth. This has the further advantage of making nautical and celestial measurements correspond. The navigator often needs to determine, one from the other, the distance he has traversed and [the length of] the celestial arc lying between the zenith at this point of departure and that at his destination.It is important, therefore, that one of these magnitudes should be the expression of the other, with no difference except in the units. But to that end, the fundamental linear unit must be an aliquot part of the terrestrial meridian, which corresponds to one of the divisions of the curcumferance.Thus the choice of the meter came down to that of unity of angles."

"The person who observes a clock, sees in it not only the pendulum swinging to and fro, and the dial-plate, and the hands moving, for a child can see all this; but he sees also the parts of the clock, and in what connection the suspended weight stands to the wheel-work, and the pendulum to the moving hands."

"Time is a valuable thing Watch it fly by as the pendulum swings Watch it count down to the end of the day The clock ticks life away"

"Pendulums have been carried about the world and the times of swing of the same pendulum have been exactly measured in widely different latitudes. The results of these measurements show quite conclusively that the weight of the bob of a given pendulum increases as we travel polewards from the equator, and we may thus described the change. If we had a perfect pendulum clock compensated for temperature change and barometer change (for if the density of the air changes, so does the effect on the buoyancy of the pendulum change), then on removal from the equator to this country it would gain about 130 seconds a day, and on removal from the equator to the pole it would gain about 216 seconds a day."

"In many ways, America is on the receiving end of a pendulum that has been swung with great force, and for a long time, outward into the world. The impact is a wake-up call on every level."

"Imagine you want to know the sex of your unborn child. There are several approaches. You could, for example, do what the late film star ... Cary Grant did before he was an actor: In a carnival or fair or consulting room, you suspend a watch or a plumb bob above the abdomen of the expectant mother; if it swings left-right it's a boy, and if it swings forward-back it's a girl. The method works one time in two. Of course he was out of there before the baby was born, so he never heard from customers who complained he got it wrong.... But if you really want to know, then you go to amniocentesis, or to sonograms; and there your chance of being right is 99 out of 100. ... If you really want to know, you go to science."

"Life swings like a pendulum backward and forward between pain and boredom."

"For FRICTION is inevitable because the Universe is FULL of God's works. For the PERPETUAL MOTION is in all works of Almighty GOD. For it is not so in the engines of man, which are made of dead materials, neither indeed can be. For the Moment of bodies, as it is used, is a false term—bless God ye Speakers on the Fifth of November. For Time and Weight are by their several estimates. For I bless GOD in the discovery of the LONGITUDE direct by the means of GLADWICK. For the motion of the PENDULUM is the longest in that it parries resistance. For the WEDDING GARMENTS of all men are prepared in the SUN against the day of acceptation. For the wedding Garments of all women are prepared in the MOON against the day of their purification. For CHASTITY is the key of knowledge as in Esdras, Sir Isaac Newton & now, God be praised, in me. For Newton nevertheless is more of error than of the truth, but I am of the WORD of GOD."

"Our advanced and fashionable thinkers are, naturally, out on a wide swing of the pendulum, away from the previous swing of the pendulum.... They seem to have an un-argue-out-able position, as is the manner of sophists, but this is no guarantee that they are right."

"Now if this electron is displaced from its equilibrium position, a force that is directly proportional to the displacement restores it like a pendulum to its position of rest."

"My loyalties will not be bound by national borders, or confined in time by one nation's history, or limited in the spiritual dimension by one language and culture. I pledge my allegiance to the damned human race, and my everlasting love to the green hills of Earth, and my intimations of glory to the singing stars, to the very end of space and time."

"Why should the thirst for knowledge be aroused, only to be disappointed and punished? My volition shrinks from the painful task of recalling my humiliation; yet, like a second Prometheus, I will endure this and worse, if by any means I may arouse in the interiors of Plane and Solid Humanity a spirit of rebellion against the Conceit which would limit our Dimensions to Two or Three or any number short of Infinity."

"According to the big bang model, space, time, and matter simultaneously expanded into physical existence.... Hence, the mathematical of the space=time combines space and time together under a single coordinate system which is specified by length, width, and height while 'time' is considered as the fourth dimension of the co-ordinate."

"Eternity isn't some later time. Eternity isn't a long time. Eternity has nothing to do with time. Eternity is that dimension of here and now which thinking and time cuts out. This is it. And if you don't get it here, you won't get it anywhere. And the experience of eternity right here and now is the function of life. There's a wonderful formula that the Buddhists have for the Bodhisattva, the one whose being (sattva) is illumination (bodhi), who realizes his identity with eternity and at the same time his participation in time. And the attitude is not to withdraw from the world when you realize how horrible it is, but to realize that this horror is simply the foreground of a wonder and to come back and participate in it."

"We have created characters and animated them in the dimension of depth, revealing through them to our perturbed world that the things we have in common far outnumber and outweigh those that divide us."

"It's bigger on the inside!"

"In a sensible theory there are no [dimensionless] numbers whose values are determinable only empirically. I can, of course, not prove that ... dimensionless constants in the laws of nature, which from a purely logical point of view can just as well have other values, should not exist. To me in my 'Gottvertrauen' [faith in God] this seems evident, but there might be few who have the same opinion ..."

"Space has always been the spiritual dimension of architecture. It is not the physical statement of the structure so much as what it contains that moves us."

"Imaginary time is a new dimension, at right angles to ordinary, real time."

"Bailey reached up and shook his arm. "Snap out of it. What the hell are you talking about, four dimensions? Time is the fourth dimension; you can't drive nails into that.""

"Human rights, of course, must include the right to religious freedom, understood as the expression of a dimension that is at once individual and communitarian — a vision that brings out the unity of the person while clearly distinguishing between the dimension of the citizen and that of the believer."

"The supremacy of expediency is being refuted by time and truth. Time is an essential dimension of existence defiant of man's power, and truth reigns in supreme majesty, unrivaled, inimitable, and can never be defeated."

"Faith is sensitiveness to what transcends nature, knowledge and will, awareness of the ultimate, alertness to the holy dimension of all reality. Faith is a force in man, lying deeper than the stratum of reason and its nature cannot be defined in abstract, static terms. To have faith is not to infer the beyond from the wretched here, but to perceive the wonder that is here and to be stirred by the desire to integrate the self into the holy order of living. It is not a deduction but an intuition, not a form of knowledge, of being convinced without proof, but the attitude of mind toward ideas whose scope is wider than its own capacity to grasp. Such alertness grows from the sense for the meaningful, for the marvel of matter, for the core of thoughts. It is begotten in passionate love for the significance of all reality, in devotion to the ultimate meaning which is only God."

"We actually have a candidate for the mind of God. The mind of God we believe is cosmic music, the music of strings resonating through 11 dimensional hyperspace. That is the mind of God."

"How sickness enlarges the dimension of a man's self to himself!"

"Design in art, is a recognition of the relation between various things, various elements in the creative flux. You can't invent a design. You recognize it, in the fourth dimension. That is, with your blood and your bones, as well as with your eyes."

"Science by itself has no moral dimension. But it does seek to establish truth. And upon this truth morality can be built."

"Lois Lane: I can’t describe what Mxyzptlk then became. He had height, width, depth, and a couple of other things, too."

"She was no scholar in geometry or aught else, but she felt intuitively that the bend and slant of the way she went were somehow outside any other angles or bends she had ever known. They led into the unknown and the dark, but it seemed to her obscurely that they led into deeper darkness and mystery than the merely physical, as if, though she could not put it clearly even into thoughts, the peculiar and exact lines of the tunnel had been carefully angled to lead through poly-dimensional space as well as through the underground — perhaps through time, too."

"Time is relative, it can stretch and squeeze, but it can't run backwards. The only thing that can move across dimensions like time is gravity. … Look, Cooper, they're creatures of at least five dimensions, to them the past might be a canyon they can climb into and the future a mountain they can climb up... but to us it's not, okay?"

"Are you trying to tell me that this gadget's got a fourth dimensional extension?" Paradine demanded. "Not visually, anyway," Holloway denied. "All I say is that our minds, conditioned to Euclid, can see nothing in this but an illogical tangle of wires. But a child especially a baby might see more. Not at first. It'd be a puzzle, of course. Only a child wouldn't be handicapped by too many preconceived ideas."

"We are not in the Eighth dimension, we are over New Jersey. Hope is not lost."

"There is a fifth dimension beyond that which is known to man. It is a dimension as vast as space and as timeless as infinity. It is the middle ground between light and shadow, between science and superstition, and it lies between the pit of man's fears and the summit of his knowledge. This is the dimension of imagination. It is an area which we call the Twilight Zone."

"You are about to enter another dimension, a dimension not only of sight and sound but of mind. A journey into a wondrous land of imagination. Next stop, the Twilight Zone!"

"You're traveling through another dimension, a dimension not only of sight and sound but of mind. A journey into a wondrous land of imagination. Next stop, the Twilight zone!"

"You're traveling through another dimension, a dimension not only of sight and sound but of mind. A journey into a wondrous land whose boundaries are that of imagination. That's the signpost up ahead — your next stop, the Twilight Zone!"

"You are traveling through another dimension, a dimension not only of sight and sound but of mind. A journey into a wondrous land whose boundaries are that of imagination. Your next stop, the Twilight Zone!"

"You unlock this door with the key of imagination. Beyond it is another dimension—a dimension of sound, a dimension of sight, a dimension of mind. You're moving into a land of both shadow and substance, of things and ideas. You've just crossed over into the Twilight Zone."

"In a mathematical sense, space is manifoldness, or combination of numbers. Physical space is known as the 3-dimension system. There is the 4-dimension system, there is the 10-dimension system."

"He sat back down again in his armchair. “Of course, that name really isn’t accurate. I suppose a pentaract should really be a four-dimensional pentagon, and this is meant to be a picture of a five-dimensional cube.”"

"When you listen to a thought, you are aware not only of the thought but also of yourself as the witness of the thought. A new dimension of consciousness has come in."

"Make it your practice to withdraw attention from past and future whenever they are not needed. Step out of the time dimension as much as possible in everyday life."

"Well, I do not mind telling you I have been at work upon this geometry of Four Dimensions for some time. Some of my results are curious. For instance, here is a portrait of a man at eight years old, another at fifteen, another at seventeen, another at twenty-three, and so on. All these are evidently sections, as it were, Three-Dimensional representations of his Four-Dimensioned being, which is a fixed and unalterable thing."

"If I am recalling an incident very vividly I go back to the instant of its occurrence; I become absent minded, as you say. I jump back for a moment. Of course we have no means of staying back for any length of time any more than a savage or an animal has of staying six feet above the ground. But a civilized man is better off than the savage in this respect. He can go up against gravitation in a balloon, and why should we not hope that ultimately he may be able to stop or accelerate his drift along the Time Dimension; or even to turn about and travel the other way?"

"There is no difference between Time and any of the three dimensions of Space except that our consciousness moves along it."

"Perhaps the first to approach the fourth dimension from the side of physics, was the Frenchman, Nicole Oresme, of the fourteenth century. In a manuscript treatise, he sought a graphic representation of the Aristotelian forms, such as heat, velocity, sweetness, by laying down a line as a basis designated longitudo, and taking one of the forms to be represented by lines (straight or circular) perpendicular to this either as a latitudo or an altitudo. The form was thus represented graphically by a surface. Oresme extended this process by taking a surface as the basis which, together with the latitudo, formed a solid. Proceeding still further, he took a solid as a basis and upon each point of this solid he entered the increment. He saw that this process demanded a fourth dimension which he rejected; he overcame the difficulty by dividing the solid into numberless planes and treating each plane in the same manner as the plane above, thereby obtaining an infinite number of solids which reached over each other. He uses the phrase "fourth dimension" (4am dimensionem)."

"I search for the realness, the real feeling of a subject, all the texture around it... I always want to see the third dimension of something... I want to come alive with the object."

"Physics deals with a great many quantities that have both size and direction, and it needs a special mathematical language —the language of vectors —to describe those quantities. This language is also used in engineering, the other sciences, and even in common speech."

"When the equinox entered Pisces, the Savior of the World "appeared as the Fisher of Men.""

"The number of the dead long exceedeth all that shall live. The night of time far surpasseth the day, and who knows when was the Æquinox? Every hour adds unto that current arithmetick, which scarce stands one moment."

"At the equinox when the earth was veiled in a late rain, wreathed with wet poppies, waiting spring The ocean swelled for a far storm and beat its boundary, the ground-swell shook the beds of granite. I gazing at the boundaries of granite and spray, the established sea-marks, felt behind me Mountain and plain, the immense breadth of the continent, before me the mass and double stretch of water."

"I've always assumed that every time a child is born, the Divine reenters the world. Okay? That's the meaning of the Christmas story. And every time that child's purity is corrupted by society, that's the meaning of the Crucifixion story. Your man Jesus stands for that child, that pure spirit, and as its surrogate, he's being born and put to death again and again, over and over, every time we inhale and exhale, not just at the vernal equinox and on the twenty-fifth of December."

"I do not know if you appreciate the fact that long papers have a way of frightening readers, who feel that they have not time to dip into them."

"Bohr proposed in the first place that the energies of atoms are quantized, in the sense that the atom exists in only a discrete set of states, with energies (in increasing order) E1, E2, . . . . The frequency of a photon emitted in a transition m → n or absorbed in a transition n → m is given by Einstein’s formula E = hν and energy conservation by \nu=(E_m-E_n)/h. … Bohr’s formulas could be used not only for single-electron atoms, like hydrogen or singly ionized helium, but also roughly for the innermost orbits in heavier atoms, where the charge of the nucleus is not screened by electrons, and we can take Ze as the actual charge of the nucleus."

"There are at present fundamental problems in theoretical physics awaiting solution, e.g., the relativistic formulation of quantum mechanics and the nature of atomic nuclei (to be followed by more difficult ones such as the problem of life), the solution of which problems will presumably require a more drastic revision of our fundamental concepts than any that have gone before. Quite likely these changes will be so great that it will be beyond the power of human intelligence to get the necessary new ideas by direct attempts to formulate the experimental data in mathematical terms."

"At this point an enigma presents itself which in all ages has agitated inquiring minds. How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? Is human reason, then, without experience, merely by taking thought, able to fathom the properties of real things? In my opinion the answer to this question is, briefly, this: as far as the propositions of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."

"Mathematicians are only dealing with the structure of reasoning, and they do not really care what they are talking about. They do not even need to know what they are talking about, or, as they themselves say, whether what they say is true. I will explain that. You state the axioms, such-and-such is so, and such-and-such is so. What then? The logic can be carried out without knowing what the such-and-such words mean. If the statements about the axioms are carefully formulated and complete enough, it is not necessary for the man who is doing the reasoning to have any knowledge of the meaning of the words in order to deduce new conclusions in the same language. … But the physicist has meaning to all his phrases. That is a very important thing that a lot of people who come to physics by way of mathematics do not appreciate. Physics is not mathematics, and mathematics is not physics. One helps the other. But in physics you have to have an understanding of the connection of words with the real world."

"In general, the rate of evaporation (m) of a substance in a high vacuum is related to the pressure (p) of the saturated vapor by the equation m=\sqrt{\frac{M}{2\pi RT}}p. Red phosphorus and some other substances probably form exceptions to this rule."

"One of the most natural questions when one looks at the mass of uncorrelated data on elementary particle interactions is whether a systematic pattern is emerging from this complexity. The penetration of controlled laboratory experiments into the multi-Bev energy region can only make such a question more acute."

"It's a remarkable fact that matter at the subatomic level consists of tiny chunks, with vast empty spaces in between. Even more remarkable, these tiny chunks come in a small number of different types (electrons, protons, neutrons, pi mesons, neutrinos, and so on), which are then replicated in astronomical quantities to make all the "stuff" around us. And these replicas are absolutely perfect copies—not just "pretty similar," like two Fords coming off the same assembly line, but utterly indistinguishable."

"Even with our best understanding in traditional physics, there are dozens of different things that we can call elementary particles. The idea of string theory is to get all the different elementary particles — muons, neutrinos, electrons, up quarks, gluons, and so on — as different states of vibration of one basic string."

"[T]he Aristotelian doctrine of inertia was a doctrine of rest—it was motion, not rest, that always required to be explained."

"[T]he peculiar character of that Aristotelian universe... things... in motion had to be accompanied by a mover all of the time. A universe... [that] had the door half-way open for spirits...unseen hands had to be in constant operation... sublime Intelligences had to roll the planetary spheres... Alternatively, bodies had to be endowed with souls and aspirations... [M]atter itself seemed to possess mystical qualities."

"When mons. Descartes's philosophical Romance, by the Elegance of its Style and the plausible Accounts of natural Phænomena, had overthrown the Aristotelian Physics, the World received but little Advantage by the Change: For instead of a few Pedants, who, most of them, being conscious of their Ignorance, concealed it with hard Words and pompous Terms; a new Set of Philosophers started up, whose lazy Disposition easily fell in with a Philosophy, that required no Mathematicks to understand it, and who taking a few Principles for granted, without examining their Reality or Consistence with each other, fancied they could solve all Appearances mechanically by Matter and Motion; and, in their smattering Way, pretended to demonstrate such things, as perhaps Cartesius himself never believed; his Philosophy (if he bad been in earnest) being unable to stand the test of the Geometry which he was Master of."

"With the discovery of the law of inertia and the subsequent downfall of the Aristotelian theory of motion on which Kepler had based his work, his physical theories soon became outmoded and were then rendered obsolete by Newton's work. Yet Kepler's laws of planetary motion remained, so that Edmond Halley could write in his review of Newton's Principia that the first eleven propositions were found to agree with the phenomena of celestial motions, as discovered by the great sagacity and diligence of Kepler."

"Gaukroger believes that contemporary physicists concern themselves with a kind of mathematical knowledge that“ is clearly not the same as that derived by abstraction from individual cases.” Indeed, he goes goes so far as to claim that true scientific knowledge, “cannot be attained, at least in [Aristotelian] physics and cosmology."

"Let it be conceived that the [or a] particle acquires a tendency to move, and that nevertheless it does not move. It is then in a condition totally different from that in which it was at first. A cause competent to produce motion is operating upon it, but for some reason or other, is unable to give rise to motion. If the obstacle is removed, the energy which was there, but could not manifest itself, at once gives rise to motion. While the restraint lasts, the energy of the particle is merely potential; and the case supposed illustrates what is meant by potential energy. In this contrast of the potential with the actual, modern physics is turning to account the most familiar of Aristotelian distinctions—that between δύναμιζ [potential] and ένέργεια [action, effect, entelechy, power or energy]."

"[An] example of the hubris of contemporary science is the rigorous banishment of the word "purpose" from its vocabulary. This is probably an aftermath of the reaction against the animism of Aristotelian physics, where stones accelerated their fall because of their impatience to get home, and against a teleological world-view in which the purpose of the stars was to serve as chronometers for man's profit. From Galileo onward, "final causes" were relegated into the realm of superstition, mechanical causality reigned supreme. ...The mechanistic universe gradually disintegrated, but the mechanistic notion of causality survived until Heisenberg's indeterminacy principle proved its untenability."

"I could easily believe that Aristotle had stumbled, but not that, on entering physics, he had totally collapsed. Might not the fault be mine rather than Aristotle's, I asked myself. Perhaps his words had not always meant to him and his contemporaries quite what they meant to me and mine. Feeling that way, I continued to puzzle over the text, and my suspicions ultimately proved well-founded. I was sitting at my desk with the text of Aristotle's Physics open in front of me and with a four-colored pencil in my hand. Looking up, I gazed abstractedly out the window of my room -- the visual image is one I still retain. Suddenly the fragments in my head sorted themselves out in a new way, and fell into place together. My jaw dropped, for all at once Aristotle seemed a very good physicist indeed, but of a sort I'd never dreamed possible. Now I could understand why he had said what he'd said, and what his authority had been. Statements that had previously seemed egregious mistakes, now seemed at worst near misses within a powerful and generally successful tradition. That sort of experience -- the pieces suddenly sorting themselves out and coming together in a new way -- is the first general characteristic of revolutionary change that I shall be singling out after further consideration of examples. Though scientific revolutions leave much piecemeal mopping up to do, the central change cannot be experienced piecemenal, one step at a time. Instead, it involves some relatively sudden and unstructured transformation in which some part of the flux of experience sorts itself out differently and displays patterns that were not visible before."

"For Aristotelian physics the membership of an object in a given class was of critical importance, because for Aristotle the class defined the essence or essential nature of the object, and thus determined its behavior in both positive and negative respects."

"The attitude of Aristotelian physics toward lawfulness takes a new direction. So long as lawfulness remained limited to such processes as occurred repeatedly in the same way, it is evident, not only that the young physics still lacked the courage to extend the principle to all physical phenomena, but also that the concept of lawfulness still had a fundamentally historic, a temporally particular, significance. Stress was laid not upon the “general validity” which modem physics understands by lawfulness, but upon the events in the historically given world which displayed the required stability. The highest degree of lawfulness, beyond mere frequency, was characterized by the idea of the always eternal."

"Galileo's comprehension of the concept of acceleration, which he defined as a change of velocity either in magnitude or direction... was an abstract idea that no one seems to have thought much about before. And in using it to test the still accepted Aristotelian precept that a moving object requires a force to maintain it, Galileo easily demonstrated that it is not motion but rather acceleration which cannot occur without an external force. Deliberately rejecting common sense as a prejudiced witness, he let nature herself speak in the form of a "hard, smooth and very round ball" rolling down a "very straight" ideal groove lined with polished parchment, and then rolling up another groove, clocking each roll "hundreds or times"... he showed that, while downward motion (helped by gravity force) makes speed increase and upward motion (hindered by gravity force) makes speed decrease, there is always a "boundary case" in between... where speed remains constant (without any appreciable force)—and that, by reducing friction, this boundary case can be made to approach a horizontal level where gravity has no effect. Similarly testing... he also drafted a law of falling bodies: "that the distances traversed, during equal intervals of time... stand to one another in the same ratio as the odd numbers beginning with unity." And his beautiful analysis of a cannonball's trajectory into horizontal and vertical components... was one day to be of enormous help to Isaac Newton in solving the riddle of gravity."

"The victory of orthodox Christian doctrine over classical thought was to some extent a , for the theology that triumphed over Greek philosophy has continued to be shaped ever since by the language and the thought of classical metaphysics. For example, the Fourth Lateran Council in 1215 decreed that "in the sacrament of the altar... the bread is transubstantiated into the body [of Christ]." ...Most of the theological expositions of the term "" have interpreted "substance" [according] to the meaning given this term ...in the fifth book of Aristotle's Metaphysics; transubstantiation, then, would appear to be tied to the acceptance of Aristotelian metaphysics or even of Aristotelian physics. ...Transubstantiation is an individual instance of what has been called the problem of "the hellenization of Christianity.""

"The medieval theologians would not be surprised at a prerequisite of a degree in physics for a degree in theology. In their time, the highest degree in philosophy—which included the most advanced knowledge of physics of the day—was a prerequisite before a student was permitted to begin study for a degree in theology ...Kenny has shown the Aquinas' Five Ways—his five proofs of God's existence—are absolutely dependent on Aristotelian physics... Aquinas... was one of the leading scholars of Aristotelian physics... and... was primarily responsible for... [its] general acceptance throughout Europe. We could call Aquinas a great physicist as well as a great theologian, for, although Aristotelian physics was wrong, it was an essential precursor of modern physics."

"It is said, that Alexander the Great wrote to his former tutor to this effect; "You have not done well in publishing these lectures; for how shall we, your pupils, excel other men, if you make that public to all, which we learnt from you." To this Aristotle is said to have replied; "My Lectures are published and not published; they will be intelligible to those who heard them, and to none beside." This may very easily be a story invented and circulated among those who found the work beyond their comprehension; and it cannot be denied, that to make out the meaning and reasoning of every part, would be a task very laborious and difficult, if not impossible."

"Feynman comments that the renormalization theory is simply way to sweep difficulties under the rug. All the players, Tomonaga, Schwinger and Feynman feel that the theory that they have developed is intellectually not satisfactory. What they have provided is only a conservative solution but what is needed is a radical innovation and a revolutionary departure similar to what has been made in the nineteen thirties by Bohr, Heisenberg, Schrödinger and Dirac."

"Hence most physicists are very satisfied with the situation. They say: "Quantum electrodynamics is a good theory, and we do not have to worry about it any more." I must say that I am very dissatisfied with the situation, because this so-called "good theory" does involve neglecting infinities which appear in its equations, neglecting them in an arbitrary way. This is just not sensible mathematics. Sensible mathematics involves neglecting a quantity when it turns out to be small—not neglecting it just because it is infinitely great and you do not want it!"

"A new technique has been developed for carrying out the renormalization of mass and charge in quantum electrodynamics, which is completely general in that it results not merely in divergence-free solutions for particular problems but in divergence-free equations of motion which are applicable to any problem. Instead of using a power-series expansion in the whole radiation interaction, the new method uses expansions in powers of the high-frequency part of the interaction. The convergence of the perturbation theory is thereby much improved. The method promises to be especially useful in applications to meson theory."

"So it appears that the only things that depend on the small distances between coupling points are the values for n and j-theoretical numbers that are not directly obseroable any- way; everything else, which can be observed, seems not to be affected. The shell game that we play to find n and j is technically called "renormalization." But no matter how clever the word, it is what I would call a dippy process! Having to resort to such hocus-pocus has prevented us from proving that the theory of quantum electrodynamics is mathematically self-consistent. It's surprising that the theory still hasn't been proved self-consistent one way or the other by now; I suspect that renormalization is not mathematically legitimate. What is certain is that we do not have a good mathematical way to describe the theory of quantum electrodynamics: such a bunch of words to describe the connection between n and j and m and e is not good mathematics."

"During the Symposium on the Past Decade in Particle Theory at the University of Texas at Austin in April 1970, I had occasion to bring Dirac and Feynman together for a discussion at dinner. Dirac told Feynman that the relativistic quantum electrodynamics in its present form was an ugly theory, and before tackling the more difficult problems of elementary particle physics 'one must try to solve the problems of quantum electrodynamics. Electrodynamics is something we know most about, and we must find a consistent theory of it rather than get rid of the infinities in an arbitrary manner.' Feynman agreed with Dirac."

"After such successes, it is not surprising that quantum electrodynamics in its simple renormalizable version has become generally accepted as the correct theory of photons and electrons. Nevertheless, despite the experimental success of the theory, and even though the infinities in this theory all cancel when one handles them correctly, the fact that the infinities occur at all continues to produce grumbling about quantum electrodynamics and similar theories. Dirac in particular always referred to renormalization as sweeping the infinities under the rug. I disagreed with Dirac and argued the point with him at conferences at Coral Gables and Lake Constance. Taking account of the difference between the bare charge and mass of the electron and their measured values is not merely a trick that is invented to get rid of infinities; it is something we would have to do even if everything was finite. There is nothing arbitrary or ad hoc about the procedure; it is simply a matter of correctly identifying what we are actually measuring in laboratory measurements of the electron’s mass and charge. I did not see what was so terrible about an infinity in the bare mass and charge as long as the final answers for physical quantities turn out to be finite and unambiguous and in agreement with experiment. It seemed to me that a theory that is as spectacularly successful as quantum electrodynamics has to be more or less correct, although we may not be formulating it in just the right way. But Dirac was unmoved by these arguments. I do not agree with his attitude toward quantum electrodynamics, but I do not think that he was just being stubborn; the demand for a completely finite theory is similar to a host of other aesthetic judgments that theoretical physicists always need to make."

"The quantum field theory of electrons and photons in the late 1940s had scored a tremendous success. Theorists – Feynman, Schwinger, Tomonaga, Dyson – had figured out after decades of effort how to do calculations preserving not only Lorentz invariance but also the appearance of Lorentz invariance at every stage of the calculation. This allowed them to sort out the infinities in the theory that had been noticed in the early 1930s by Oppenheimer and Waller, and that had been the bête noire of theoretical physics throughout the 1930s. They were able to show in the late 1940s that these infinities could all be absorbed into a redefinition, called a renormalization, of the electron mass and charge and the scales of the various fields. And they were able to do calculations of unprecedented precision, which turned out to be verified by experiment: calculations of the Lamb shift and the anomalous magnetic moment of the electron."

"Little things affect big things, but they rarely affect very big things. Instead, little things affect slightly bigger things. And these, in turn, affect slightly bigger things too. But as you go up the chain, you lose the information about what came long before... In the 1970s a mathematical formalism was developed that makes these ideas concrete. This formalism is called the renormalisation group and provides a framework to describe physics at different scales. The renormalisation group gets little coverage in popular science articles, yet is arguably the single most important advance in theoretical physics in the past 50 years. While zoologists may have little need to talk to particle physicists, the right way to understand both the Higgs boson and the flocking of starlings is through the language of the renormalisation group."

"[W]hen we have ideas and pictures that are extremely useful, they acquire elements of reality in and of themselves. But, philosophically, it is instructive to look at the degree to which such objects are purely instrumental—merely useful tools—and the extent to which physicists seriously suppose they embody an essence of reality... it is possible to view the renormalization group as merely an instrument or a computational device. On the other hand, at one extreme, one might say: ‘‘Well, the partition function itself is really just a combinatorial device.’’ But most practitioners tend to think of it (and especially its logarithm, the free energy) as rather more basic!"

"To assert that there exists an order parameter in essence says: ‘‘I may not understand the microscopic phenomena at all’’ (as was historically, the case for superfluid helium), ‘‘but I recognize that there is a microscopic level and I believe it should have certain general, overall properties especially as regards locality and symmetry: those then serve to govern the most characteristic behavior on scales greater than atomic.’’ ... Know the nature of the order parameter—suppose, for example, it is a complex number and like a wave function—then one knows much about the macroscopic nature of a physical system! ... Landau's introduction of the order parameter exposed a novel and unexpected foliation or level in our understanding of the physical world. Traditionally, one characterizes statistical mechanics as directly linking the microscopic world of nuclei and atoms (on length scales of 10-13 to 10-8 cm) to the macroscopic world of say, millimeters to meters. But the order parameter, as a dynamic, fluctuating object in many cases intervenes on an intermediate or mesoscopic level characterized by scales of tens or hundreds of angstroms up to microns (say, 10-6.5 to 10-3.5 cm)."

"There was a period when cosmology got started. There were some important works in the 30s—the Einstein-Infeld-Hoffman ideas equations]. ...Unified Field theories were the bane of GR in those days. Einstein... was convinced that physics should be primarily geometry... about 10 years later, maybe 15, Steven Weinberg was convinced that geometry was irrelevant... the important stuff is just field theory. ...Weinberg, later... collaborated in proving that physics really is geometry. Except not the geometry of space-time... it's the geometry of the graph paper on which the properties of space-time are conceptually plotted... the idea of a curved connection. If you want to plot... any physical quantity... like a , s, s, etc. you need to plot it on curved graph paper. But Einstein... didn't have that broad an idea of geometry..."

"Regarding the study of the universe on scales of less than... 108 lt-yr... [T]he "top-down"... or "pancake" theory of Zel'dovich et al... [predicts that] pancakes of gas comparable to a were formed first... then galaxies... formed by fragmentation... [into] high-density regions... along lines, filaments and points... The problem of the missing mass, or ... and... of the agreement with the observed level of isotropy of the blackbody radiation... are explained in this top-down model by massive neutrinos... which formed early condensations in the homogeneous plasma... [were] originally moving with relativistic speeds... [and] are usually called Hot Dark Matter. [Another] theory is the "bottom-up" scenario discussed by Lemaître and supported by... Peebles et al... [in which] galaxies were first formed by gravitational interaction... [and] only afterwards... a hierarchy of clusters formed. Some versions of [this] theory explain the missing mass problem... by... exotic particles such as "s," "s," "s," and "s," predicted by some unified field theories. This exotic form of dark matter, moving... much slower than the massive neutrinos, is... called Cold Dark Matter. Mixed models, hot plus cold dark matter, have also been proposed..."

"You could not imagine the sum-over-histories picture being true for a part of nature and untrue for another part. You could not imagine it being true for electrons and untrue for gravity. It was a unifying principle that would either explain everything or explain nothing. And this made me profoundly skeptical. I knew how many great scientists had chased this will-o’-the-wisp of a unified theory. The ground of science was littered with the corpses of dead unified theories. Even Einstein had spent twenty years searching for a unified theory and had found nothing that satisfied him. I admired Dick tremendously, but I did not believe he could beat Einstein at his own game."

"Until the end of the thirties, the only accepted fundamental interactions were the electromagnetic and the gravitational, plus, tentatively, something like the “mesonic” or “nuclear” interaction. The physical fields considered in the framework of “unified field theory” including, after the advent of quantum (wave-) mechanics, the satisfying either Schrödinger’s or Dirac’s equation, were all assumed to be classical fields. The quantum mechanical wave function was taken to represent the field of the electron, i.e., a matter field. In spite of this, the construction of quantum field theory had begun already around 1927. ...Nowadays, it seems mandatory to approach unification in the framework of quantum field theory."

"[B]y quantum field theory the dichotomy between matter and fields in the sense of a dualism is minimised as every field carries its particle-like quanta. Today’s unified field theories appear in the form of gauge theories; matter is represented by operator valued spin-half quantum fields (s) while the “forces” mediated by “exchange particles” are embodied in gauge fields, i.e., quantum fields of integer spin (s). The space-time geometry used is rigidly fixed, and usually taken to be or, within string and membrane theory, some higher-dimensional also loosely called “space-time”, although its signature might not be Lorentzian and its dimension might be 10, 11, 26, or some other number larger than four. A satisfactory inclusion of gravitation into the scheme of quantum field theory still remains to be achieved."

"Seventy-five years ago this month, The New York Times reported that Albert Einstein had completed his unified field theory — a theory that promised to stitch all of nature's forces into a single, tightly woven mathematical tapestry. But as had happened before and would happen again, closer scrutiny revealed flaws that sent Einstein back to the drawing board. Nevertheless, Einstein's belief that he'd one day complete the unified theory rarely faltered. Even on his deathbed he scribbled equations in the desperate but fading hope that the theory would finally materialize. It didn't."

"No other theory known to science [other than superstring theory] uses such powerful mathematics at such a fundamental level. ...because any unified field theory first must absorb the Riemannian geometry of Einstein's theory and the Lie groups coming from quantum field theory... The new mathematics, which is responsible for the merger of these two theories, is topology, and it is responsible for accomplishing the seemingly impossible task of abolishing the infinities of a quantum theory of gravity."

"If the possibilities anticipated here prove to be viable, quantum mechanics would cease to be an independent discipline. It would melt into a deepened ‘theory of matter’ which would have to be built up from regular solutions of non-linear differential equations, – in an ultimate relationship it would dissolve in the ‘world equations’ of the Universe. Then, the dualism ‘matter-field’ would have been overcome as well as the dualism ‘corpuscle-wave’."

"When Einstein, Weyl, and others began their work on unified field theory, it was natural to assume that this task consisted exclusively of the union of gravitation with electromagnetism. To be sure, the separateness of these two fields posed no conflicts or paradoxes. There were no puzzles such as the nor curious coincidences like the . Nevertheless, it seemed physically well-motivated and appealing to ask, Do nature's only two fields of force, both long-range in character, have a common origin?"

"Einstein’s dissent from quantum mechanics and immersion in the search for a unified field theory were not failures but anticipations. After all, even if many string theorists would disagree with Einstein about the incompleteness of quantum mechanics, much of what goes on in string theory these days looks a lot like what Einstein was doing in his Princeton years, which was trying to find new mathematics that might extend general relativity to a unification of all the forces and particles in nature."

"[A unified field theory is] a theory joining the gravitational and the electromagnetic field into one single hyperfield whose equations represent the conditions imposed on the geometrical structure of the universe."

"A new theory by the author has been added, which draws the physical inferences consequent on the extension of the foundations of geometry beyond Reimann... and represents an attempt to derive from world-geometry not only gravitational but also electromagnetic phenomena. Even if this theory is still only in its infant stage, I feel convinced that it contains no less truth than Einstein's Theory of Gravitation—whether this amount of truth is unlimited or, what is more probable, is bounded by the Quantum Theory."

"With Mie's view of matter there is contrasted another, according to which matter is a limiting singularity of the field, but charges and masses are force-fluxes in the field. This entails a new and more cautious attitude towards the whole problem of matter."

"Although the Special Theory of Relativity does not account for electromagnetic phenomena, it explains many of their properties. General Relativity, however, tells us nothing about . In Einstein's space-time continuum gravitational forces are absorbed in the geometry, but the electromagnetic forces are quite unaffected. Various attempts have been made to generate the geometry of space-time so as to produce a unified field theory incorporating both gravitational and electromagnetic forces."

"The resemblance between the Coulomb force and Newton's gravitational force is very impressive. ...[T]he similarity between a planetary system and the electromagnetic structure of an atom... is due to the resemblance between their laws of interaction. ...After the creation of GTR, there followed attempts to reformulate electromagnetic theory in a similar way, attempts to construct a geometric theory of the , and attempts to create a unified field theory which would combine gravitation and electromagnetism. All... failed. The gravitational field acts universally; it imparts equal accelerations to all objects. This... permits one to describe gravity by a change in the properties of... spacetime... The electromagnetic field does not have such a universality; various bodies... have different ratios of charge to mass and experience different accelerations. ...Roughly speaking, the electromagnetic field has energy; and this energy has weight... [T]he equations of GTR for a spacetime which contains an electromagnetic field necessarily force the field to satisfy Maxwell's equations. ...The idea of defining all fields by varying the spacetime curvatures that they create is... ' Its most articulate exponent is... John Archibald Wheeler."

"Elegant derivations from first principles — which often proved tractable only when applied to idealized situations — were of little value to the many colleagues who needed to fine-tune electronics components for maximum efficiency... Schwinger rearranged his equations in terms of measurable inputs and outputs, just as his engineering colleagues at the Rad Lab had done with real-world electronics. By recasting the calculation, Schwinger managed to calculate the effects of quantum fluctuations on the electron's energy levels and obtain an answer that matched Lamb's measurement to an extraordinary precision. As it turned out, Japanese physicist Sin-Itiro Tomonaga had accomplished the same goal a few years earlier. Tomonaga's work on radar during the war had proven similarly essential to his theoretical approach. This war-forged pragmatism produced enormously impressive research and influenced a generation of leading scientists... Anything that smacked of 'interpretation', or worse, 'philosophy', began to carry a taint for many scientists who had come through the wartime projects. Conceptual scrutiny of foundations struck many as a luxury. The wartime style was reinforced in the United States by exponentially rising university enrolments after the war. The new classroom realities left little space for informal discussion of philosophy or foundations. The Rad Lab rallying cry of “Get the numbers out” shaded into “Shut up and calculate!”"

"You can’t blame most physicists for following this ‘shut up and calculate’ ethos because it has led to tremendous develop­ments in nuclear physics, atomic physics, solid­ state physics and particle physics."

"Thinking about foundations pays off in the long run. David Mermin once summarized a popular attitude towards quantum theory as “Shut up and calculate!”. We suggest an alternative slogan: “Shut up and contemplate!”"

"In contemplating the papers Einstein wrote in 1905, I often find myself wondering which of them is the most beautiful. It is a little like asking which of Beethoven’s symphonies is the most beautiful."

"1905 is often described as Einstein’s annus mirabilis: a wonderful year in which he came up with three remarkable ideas. These were the Brownian motion in fluids, the photoelectric effect and the special theory of relativity. Each of these was of a basic nature and also had a wide impact on physics."

"Are we to foresee a mechanising synergy under brute force, or a synergy of sympathy? Are we to foresee man seeking to fulfil himself collectively upon himself, or personally on a greater than himself? Refusal or acceptance of Omega? A conflict may supervene. In that case the noosphere, in the course of and by virtue of the process which draws it together, will, when it has reached its point of unification, split into two zones each attracted to an opposite pole of adoration. Thought has never completely united upon itself here below. Universal love would only vivify and detach finally a fraction of the noosphere so as to consummate it—the part which decided to "cross the threshold", to get outside itself into the other. ... The death of the materially exhausted planet; the split of the noosphere, divided on the form to be given to its unity; and simultaneously (endowing the event with all its significance and with all its value) the liberation of that percentage of the universe which, across time, space and evil, will have succeeded in laboriously synthesising itself to the very end. Not an indefinite progress, which is an hypothesis contradicted by the convergent nature of noogenesis, but an ecstasy transcending the dimensions and the framework of the visible universe."

"Depending on the initial condition of the system (initial alphabet and number of elements) the co-evolution of nested local and global hierarchies continues until the system reaches a maximum value of complexity. At least for nuclear systems a quantitative variable called "complexity" can be defined, which increases in an irreversible manner during stellar evolution (Winiwarter, 1983). This variable C is composed of an informational measure I describing the variety of the computed formulas and an energetic measure R describing the relative binding energy or "synergy" permitting the coherence of the system. Once the maximum complexity of the system is reached, it breaks down. A catastrophic "implosion" destroys local and global hierarchical structures. In some cases—depending on the initial conditions—this "implosion" is accompanied by an "explosion" emitting computed local formulas into space. These emitted local formulas can be captured and re-entered into the initial conditions of a future gnostic cycle."

"SYN'ERGY, Synergi'a, Synenergi'a, (F.) Synergie; from συν, 'with,' and εργον, 'work.' A correlation or concourse of action between different organs in health; and, according to some, in disease."

"In the mystērion of the church, the participation of men in God is effected through their "cooperation" or "synergy"; to make this participation possible once more is the goal of the incarnation."

"Als Physiker, der sein ganzes Leben der nüchternen Wissenschaft, der Erforschung der Materie widmete, bin ich sicher von dem Verdacht frei, für einen Schwarmgeist gehalten zu werden. Und so sage ich nach meinen Erforschungen des Atoms dieses: Es gibt keine Materie an sich. Alle Materie entsteht und besteht nur durch eine Kraft, welche die Atomteilchen in Schwingung bringt und sie zum winzigsten Sonnensystem des Alls zusammenhält. Da es im ganzen Weltall aber weder eine intelligente Kraft noch eine ewige Kraft gibt—es ist der Menschheit nicht gelungen, das heißersehnte Perpetuum mobile zu erfinden—so müssen wir hinter dieser Kraft einen bewußten intelligenten Geist annehmen. Dieser Geist ist der Urgrund aller Materie. Translation: As a man who has devoted his whole life to the most clearheaded science, to the study of matter, I can tell you as a result of my research about the atoms this much: There is no matter as such! All matter originates and exists only by virtue of a force which brings the particles of an atom to vibration and holds this most minute solar system of the atom together. . . . We must assume behind this force the existence of a conscious and intelligent Spirit. This Spirit is the matrix of all matter."

"In short, synergy is the consequence of the energy expended in creating order. It is locked up in the viable system created, be it an organism or a social system. It is at the level of the system. It is not discernible at the level of the system. It is not discernible at the level of the system's components. Whenever the system is dismembered to examine its components, this binding energy dissipates. An ordered library offers systemic possibilities, such as rapid search, selection, and aggregation, that cannot be explained by looking at the books themselves. These possibilities only exist because of the investment made in defining and creating interrelations between the books, their physical arrangement and the catalogues."

"Germain's theory of art converged with social psychology in his enthusiastic review of Henri Mazel's Synergie sociale of 1896. Germain found affinities in Mazel's theories of collective energies and cultural regeneration and attached his own notion of the individual's development through moral beauty to Mazel's "culture of will, of moral energy; through love". In La synergie sociale Mazel argued that Darwinian theory failed to account for "social synergy", or "social love", a collective evolutionary drive. The highest civilizations were the work not only of the elite but of the masses too; those masses must be led, however, for the crowd, a feminine and unconscious force, could not distinguish between good and evil. Socialists and anarchists who preached mediocrity led the attack on exceptional individuals—saints, heroes, or artists."

"Synergy That there is a universal principle, operating in every department of nature and at every stage in evolution, which is conservative, creative, and constructive, has been evident to me for many years, but it required long meditation and extensive observation to discover its true nature. After having fairly grasped it I was still troubled to reduce it to its simplest form, and characterize it by an appropriate name. I have at last fixed upon the word synergy as the term best adapted to express its twofold character of energy and mutuality, or the systematic and organic working together of the antithetical forces of nature. The third and equally essential and invariable quality of creation or construction is still lacking in the name chosen, unless we assume, as I think we may do, that work implies some product, to distinguish it from simple activity."

"Synergy is a synthesis of work, or synthetic work, and this is what is everywhere taking place. It may be said to begin with the primary atomic collision in which mass, motion, time, and space are involved, and to find its simplest expression in the formula for force (\tfrac{ms}{t^2}), which implies a plurality of elements, and signifies an interaction of these elements. … It further seems probable that vortex motion is based on this principle, or is the same principle, and it is through this that some expect the problem of the nature of gravitation to find its solution."

"The true nature of the universal principle of synergy pervading all nature and creating all the different kinds of structure that we observe to exist, must now be made clearer. Primarily and essentially it is a process of equilibration, i.e., the several forces are first brought into a state of partial equilibrium. It begins in collision, conflict, antagonism, and opposition, and then we have the milder phases of antithesis, competition, and interaction, passing next into a modus vivendi, or compromise, and ending in collaboration and cooperation. … The entire drift is toward economy, conservatism, and the prevention of waste."

"I have characterized the social struggle as centrifugal and social solidarity as centripetal. Either alone is productive of evil consequences. Struggle is essentially destructive of the social order, while communism removes individual initiative. The one leads to disorder, the other to degeneracy. What is not seen—the truth that has no expounders—is that the wholesome, constructive movement consists in the properly ordered combination and interaction of both these principles. This is social synergy, which is a form of cosmic synergy, the universal constructive principle of nature."

"The mediating role of the brain can perhaps be best envisaged in terms of synergetic concepts: In thinking or making plans certain parts of the brain undergo coherent, collective activity states of possibly a great number of neurons, where concepts or ideas function as, or are represented by, order parameters of these collective activities. This would mean that in H. Haken's terminology of synergetics neurons or certain states of them (as parts of World 1) become enslaved by elements of World 2 (psychic events) and World 3 (mental entities)."

"As we have seen, Hermann Haken assumed neurons were sub-systems in the brain whereas "thoughts" (Gedanken) represent the order parameters. According to the concepts of synergetics both parts have to react on different timescales in order for the sub-systems to be "enslaved". That holds true for the brain: while the neurons fire on a timescale of milliseconds the perception of new content (Gedanken) varies by tenths of a second."

"I have to ask you, sir, are you familiar with the word “synergy”?...I have been a visitor at 320 universities and colleges around the world and always have asked those university audiences “How many of you are familiar with the word ‘synergy’?” I can say authoritatively that less than 10 percent of university audiences and less than 1 percent of non-university audiences are familiar with the word and meaning of synergy. Synergy is not a popular word."

"The word synergy is a companion to the word “energy.” Energy and synergy. The prefix “syn” of synthesis meaning “with, to integrate” and the “en” of energy means “separating out ” Man is very familiar with energy, he has learned to separate out, or isolate certain behaviors of total nature and thus has become familiar with many of the separate natural behaviors such as optics. But the only partially isolatable behavior is always modifyingly employed by the whole. If humans had to purchase their many separate organs, stomachs, livers, endocrine glands, tongues, eyeballs, and bowels and thereafter to assemble those parts into logical interfunctioning, they would never do so. All those parts had to be preassembled and unitarily skinned in and coordinately operated by multiquadrillions of atoms in the brain which after 16 years of practical spontaneous coordination becomes so aesthetically acceptable one to the other that as it sings, dances, and smiles one is inclined to procreate with the other."

"Synergy is to energy as integration is to differentiation"

"The word “synergy” means “Behavior of whole systems unpredicted by behavior of any of the systems parts.” Nature is comprehensively synergetic. Since synergy is the only word having that meaning and we have proven experimentally that it is not used by the public, we may conclude that society does not understand nature"

"I find all of our world society is operating exclusively in parts. We know this because the word synergy is unknown popularly and it is the only word that means “behavior of wholes unpredicted by behavior of their parts.” This proves that society does not even think that it has a need for such a word. This discloses that society does not think that there are behaviors of wholes unpredicted by the parts. It thinks statistics and probability are all that we need but if “probability” and “statistics” were of any power at all we could not have a stock market or gambling for we would know exactly how things are coming out and no one would bet against the probability."

"Because nature is entirely synergetic and because your problems of representing a society ignorant of such fundamentals are greatly increased you need to pay great attention to learning how to comprehend synergy and thereafter how to educate all of humanity in the shortest time how to comprehend and usefully cope with omni-synergetic universe"

"I will give you one very simple example of synergy. All our metallic alloys are synergetic. We will examine chrome-nickel steel. The outstanding characteristic of metallic strength is its ability to cohere in one piece. We test the metals tensile strength per square inch of cross section of the tested sample. The very high number of pounds-per-square-inch tensile strength of chrome-nickel steel has changed our whole economy because it retained its structural integrity at so high a temperature as to make possible the jet engine which has halved the time it takes to fly around the world."

"If we have two spherical bodies of equal mass at a given distance from each other and insert a third spherical body of the same mass half way between the two we do not double the mass attraction between any two of the three. We increase the attraction by 2 to the second power which is 4. Halving the distance fourfolds the inter-mass attraction. When we bring a galaxy of iron atoms together with the chromium atoms and a galaxy of nickel atoms they all fit neatly between one another and bring about the multifolding of their intercoherency. But there is nothing in one body by itself that says that it will have mass attraction. This can only be discovered by experimenting with two and more bodies. And even then there is no explanation of why there must be mass attraction and why it should increase as the second power of the relative increase of proximity. That is synergy."

"Our school systems are all nonsynergetic. We take the whole child and fractionate the scope of his or her comprehending coordination by putting the children in elementary schools—to become preoccupied with elements or isolated facts only. Thereafter we force them to choose some specialization, forcing them to forget the whole. ... We may well ask how it happened that the entire scheme of advanced education is devoted exclusively to ever narrower specialization. We find that the historical beginnings of schools and tutoring were established, and economically supported by illiterate and vastly ambitious warlords who required a wide variety of brain slaves with which to logistically and ballistically overwhelm those who opposed their expansion of physical conquest. They also simultaneously DIVIDED and CONQUERED any and all "bright ones" who might otherwise rise within their realms to threaten their supremacy. The warlord vitiated their threat by making them all specialists and reserving to himself exclusively the right to think about and act comprehensively. The warlord made all those about him differentiators and reserved the function of integration to himself."

"Science's self-assumed responsibility has been self-limited to disclosure to society only of the separate, supposedly physical (because separately weighable) atomic component isolations data. Synergetic integrity would require the scientists to announce that in reality what had been identified heretofore as physical is entirely metaphysical — because synergetically weightless. Metaphysical has been science's designation for all weightless phenomena such as thought. But science has made no experimental finding of any phenomena that can be described as a solid, or as continuous, or as a straight surface plane, or as a straight line, or as infinite anything. We are now synergetically forced to conclude that all phenomena are metaphysical; wherefore, as many have long suspected—like it or not—"life is but a dream"."

"There is nothing that a single massive sphere will or can ever do by itself that says it will both exert and yield attractively with a neighboring massive sphere and that it yields progressively: every time the distance between the two is halved, the attraction will be fourfolded. This unpredicted, only mutual behavior is synergy."

"There are progressive degrees of synergy, called synergy-of-synergies, which are complexes of behavior aggregates holistically unpredicted by the separate behaviors of any of their subcomplex components. Any subcomplex aggregate is only a component aggregation of an even greater event aggregation whose comprehensive behaviors are never predicted by the component aggregates alone. There is a synergetic progression in Universe—a hierarchy of total complex behaviors entirely unpredicted by their successive subcomplexes' behaviors. It is manifest that Universe is the maximum synergy-of-synergies, being utterly unpredicted by any of its parts."

"Bell's most famous paper in this area — published with Roman Jackiw in Il Nuovo Cimento in 1969 and cited more than any other of his papers — was the discovery, clarified to some extent by Stephen Adler, of the Bell-Jackiw—Adler anomaly. At the time, theory predicted that the neutral pion could not decay into two photons, but this had been observed in experiments. Bell, Jackiw and Adler were able to explain the observed decays theoretically by adding an "anomalous" term resulting from the divergences of quantum field theory. A condition that the "anomaly" produced agreement with experiment was that the sum of the charges of the elementary fermions had to be zero. This provided support for the idea that quarks come in three colours, now part of the widely accepted Standard Model."

"One of the problems has to do with the speed of light and the difficulties involved in trying to exceed it. You can't. Nothing travels faster than the speed of light with the possible exception of bad news, which obeys its own special laws."

"You will begin to touch heaven, Jonathan, in the moment that you touch perfect speed. And that isn't flying a thousand miles an hour, or a million, or flying at the speed of light. Because any number is a limit, and perfection doesn't have limits. Perfect speed, my son, is being there."

"Fermat had recourse to the principle of the economy of nature. Heron and Olympiodorus had pointed out in antiquity that, in reflection, light followed the shortest possible path, thus accounting for the equality of angles. During the medieval period Alhazen and Grosseteste had suggested that in refraction some such principle was also operating, but they could not discover the law. Fermat, however, not only knew (through Descartes) the law of refraction, but he also invented a procedure—equivalent to the differential calculus—for maximizing and minimizing a function of a single variable. … Fermat applied his method … and discovered, to his delight, that the result led to precisely the law which Descartes had enunciated. But although the law is the same, it will be noted that the hypothesis contradicts that of Descartes. Fermat assumed that the speed of light in water to be less than that in air; Descartes' explanation implied the opposite."

"The speed of light sucks."

"One of the funniest examples of these kinds of statistics comes from Evolution: Possible or Impossible by James F. Coppedge [who] cites an article by Ulric Jelinek … which claims that the odds are 1 in 10^243 against "two thousand atoms" (the size of one particular protein molecule) ending up in precisely that particular order "by accident." Where did Jelenik get that figure? From Pierre Lecompte du Nouy... who in turn got it from Charles-Eugene Guye, a physicist who died in 1942. Guye had merely calculated the odds of these atoms lining up by accident if "a volume" of atoms the size of the Earth were "shaken at the speed of light." In other words, ignoring all the laws of chemistry, which create preferences for the formation and behavior of molecules, and ignoring that there are millions if not billions of different possible proteins--and of course the result has no bearing on the origin of life, which may have begun from an even simpler protein. This calculation is thus useless for all these reasons, and is typical in that it comes to Coppedge third-hand (and thus to us fourth-hand), and is hugely outdated (it was calculated before 1942, even before the discovery of DNA), and thus fails to account for over half a century of scientific progress."

"Hubble's law predicts that galaxies beyond ...the Hubble distance, recede faster than the speed of light ...this distance is about 14 billion light years. ...galaxies with a redshift of about 1.5—...150 percent longer than the laboratory reference value—are receding at the speed of light. Equivalently, we are receding from those galaxies..."

"The radiation of the cosmic microwave background... has a red shift of about 1,000. ...the hot plasma of the early universe ...was receding from our location at about 50 times the speed of light."

"A light beam that is farther than the Hubble distance of 14 billion light-years ...cannot keep up with the stretching space."

"When you are next out of doors on a summer night, turn your head towards the zenith. Almost vertically above you will be shining the brightest star of the northern skies—Vega of the Lyre, twenty-six years away at the speed of light, near enough to the point of no return for us short-lived creatures. Past this blue-white beacon, fifty times as brilliant as our sun, we may send our minds and bodies, but never our hearts. For no man will ever turn homewards beyond Vega, to greet again those he knew and loved on Earth."

"Another topic deserving discussion is Einstein’s modification of Newton’s law of gravitation. In spite of all the excitement it created, Newton’s law of gravitation is not correct! It was modified by Einstein to take into account the theory of relativity. According to Newton, the gravitational effect is instantaneous, that is, if we were to move a mass, we would at once feel a new force because of the new position of that mass; by such means we could send signals at infinite speed. Einstein advanced arguments which suggest that we cannot send signals faster than the speed of light, so the law of gravitation must be wrong. By correcting it to take the delays into account, we have a new law, called Einstein’s law of gravitation. One feature of this new law which is quite easy to understand is this: In the Einstein relativity theory, anything which has energy has mass—mass in the sense that it is attracted gravitationally. Even light, which has an energy, has a “mass.” When a light beam, which has energy in it, comes past the sun there is an attraction on it by the sun. Thus the light does not go straight, but is deflected. During the eclipse of the sun, for example, the stars which are around the sun should appear displaced from where they would be if the sun were not there, and this has been observed."

"For over 200 years the equations of motion enunciated by Newton were believed to describe nature correctly, and the first time that an error in these laws was discovered, the way to correct it was also discovered. Both the error and its correction were discovered by Einstein in 1905.Newton’s Second Law, which we have expressed by the equation F=\frac {d\left({mv}\right)}{dt} was stated with the tacit assumption that m is a constant, but we now know that this is not true, and that the mass of a body increases with velocity. In Einstein’s corrected formula m has the value m=\frac {{m}_}{\sqrt} where the “rest mass” m0 represents the mass of a body that is not moving and c is the speed of light, which is about 3×105 km⋅sec−1 or about 186,000 mi⋅sec−1."

"The strangest explanation was put forth by an Irish physicist, George Francis Fitzgerald. Perhaps, he said, the ether wind puts pressure on a moving object, causing it to shrink a bit in the direction of motion. To determine the length of a moving object, its length at rest must be multiplied by the following simple formula, in which \scriptstyle v^2 is the velocity of the object multiplied by itself, \scriptstyle c^2 is the velocity of light multiplied by itself: \scriptstyle \sqrt{1-\frac{v^2}{c^2}}. ...The speed of light in an unobtainable limit; when this is reached the formula becomes \scriptstyle \sqrt{1-\frac{c^2}{c^2}} which reduces to 0. ...In other words, if an object could obtain the speed of light, it would have no length at all in the direction of its motion!"

"In the special theory of relativity, the speed of light becomes... a new absolute. ...Regardless of the motion of its source, light always moves through space with the same constant speed."

"Two ships are passing each other with uniform speed close to that of light. As they pass, a beam of light on the other ship is sent from the ceiling to the floor. There it strikes a mirror and is reflected back to the ceiling again. You will see the path of this light as a V [shape]. If you had sufficiently accurate instruments (of course no such instrument exists), you could clock the time it takes this light beam to traverse the V-shaped path. By dividing the length of the path by the time, you obtain the speed of light. ...an astronaut inside the other ship is doing the same thing [measuring his light beam's speed]. From his point of view... the light simply goes down and up along the same line, obviously a shorter distance than along the V that you observed. ...he also obtains the speed of light. ...But his light path is shorter. ...There is only one possible explanation: his clock is slower. Of course, the situation is perfectly symmetrical. If you send a beam down and up inside your ship, he will see its path as V-shaped. He will deduce that your clock is slower."

"If the ships could attain a relative speed equal to that of light, observers on each ship would think the other ship had shrunk to zero in length, acquired an infinite mass, and that time on the other ship had slowed to a full stop! If inertial mass did not vary in this way, then the steady application of force, such as the force supplied by rocket motors, could keep increasing a ship's velocity until it passed the speed of light. ...When the ship has contracted to one-tenth its rest length, its relativistic mass has become ten times as great. ...ten times as much force is required to produce the same increase in speed."

"The speed of light can never be reached. If it were reached, the outside observer would find that the ship had shrunk to zero length, had acquired an infinite mass, and was exerting an infinite force with its rocket motors. Astronauts inside the ship would observe no changes in themselves, but they would find the cosmos hurtling backward with the speed of light, cosmic time at a standstill, every star flattened to a disk and infinitely massive."

"Nothing in nature or the cosmos is ever completely still — as I write this, several wild Mallards have returned to the Museum courtyard and are creating a frantic spectacle of water and wings as they dive and attack in their annual spring ritual. Further from home, a supermassive black hole at the center of a galaxy 56 million light years from Earth has recently been observed to be spinning at close to the speed of light."

"The false report that measuring one of the photons immediately affects the other leads to all sorts of unfortunate conclusions. ...the alleged effect ...would violate the requirement of relativity theory that no signal... can travel faster than the speed of light. If it were to do so, it would appear to observers in some states of motion that the signal were traveling backward in time."

"[A]fter a close study of the experimental work of Michael Faraday,... James Clerk Maxwell succeeded in uniting electricity and magnetism in the framework of the '. ...Beyond uniting... all... electric and magnetic phenomena in one mathematical framework, Maxwell's theory showed—quite unexpectedly, that electromagnetic disturbances travel at a fixed and never-changing speed that turns out to equal that of light. From this, Maxwell realized that visible light itself is nothing but a particular kind of electromagnetic wave... Maxwell's theory also showed that all electromagnetic waves—visible light among them—are the epitome of the peripatetic traveler. They never stop. They never slow down. Light always travels at light speed."

"The alternative physics is a physics of light. Light is composed of photons, which have no antiparticle. This means that there is no dualism in the world of light. The conventions of relativity say that time slows down as one approaches the speed of light, but if one tries to imagine the point of view of a thing made of light, one must realize that what is never mentioned is that if one moves at the speed of light there is no time whatsoever. There is an experience of time zero. … The only experience of time that one can have is of a subjective time that is created by one's own mental processes, but in relationship to the Newtonian universe there is no time whatsoever. One exists in eternity, one has become eternal. The universe is aging at a staggering rate all around one in this situation, but that is perceived as a fact of this universe—the way we perceive Newtonian physics as a fact of this universe. One has transited into the eternal mode. One is then apart from the moving image; one exists in the completion of eternity."

"But here is my mark, and there is where I'm supposed to look, and believe me, the power and the pleasure and the emotion of this moment is as constant as the speed of light. It will never be diminished, nor will my appreciation."

"Einstein had drawn attention to nonlocality in 1935 in an effort to show that quantum mechanics must be flawed. ...Einstein proposed a thought experiment—now called the EPR experiment—involving two particles that spring from a common source and fly in opposite directions. According to the standard model of quantum mechanics, neither particle has a definite position or momentum before it is measured; but by measuring the momentum of one particle, the physicist instantaneously forces the other particle to assume a fixed position... Deriding this effect as "spooky action at a distance," Einstein argued that it violated both common sense and his own theory of special relativity, which prohibits the propagation of effects faster than the speed of light; quantum mechanics must therefore be an incomplete theory. In 1980, however, a group of French physicists carried out a version of the EPR experiment and showed that it did indeed give rise to spooky action. (The reason that the experiment does not violate special relativity is that one cannot exploit nonlocality to transmit information.)"

"What Einstein actually said was that nothing can accelerate to the speed of light because its mass would become infinite. Einstein said nothing about entities already traveling at the speed of light or faster."

"In 5 billion years, the expansion of the universe will have progressed to the point where all other galaxies will have receded beyond detection. Indeed, they will be receding faster than the speed of light, so detection will be impossible. Future civilizations will discover science and all its laws, and never know about other galaxies or the cosmic background radiation. They will inevitably come to the wrong conclusion about the universe......We live in a special time, the only time, where we can observationally verify that we live in a special time."

"The great attraction of cultural anthropology in the past was precisely that it seemed to offer such a richness of independent natural experiments; but unfortunately it is now clear that there has been a great deal of historical continuity and exchange among those "independent" experiments, most of which have felt the strong effect of contact with societies organized as modern states. More important, there has never been a human society with unlimited resources, of three sexes, or the power to read other people's minds, or to be transported great distances at the speed of light. How then are we to know the effect on human social organization and history of the need to scrabble for a living, or of the existence of males and females, or of the power to make our tongues drop manna and so to make the worse appear the better reason? A solution to the epistemological impotence of social theory has been to create a literature of imagination and logic in which the consequences of radical alterations in the conditions of human existence are deduced. It is the literature of science fiction. … [S]cience fiction is the laboratory in which extraordinary social conditions, never possible in actuality, are used to illumine the social and historical norm. … Science fiction stories are the Gedanken experiments of social science."

"The laws of economics are subject to the laws of physics. The physical processes that govern this planet and the continued life upon it place as stringent an upper limit on economic growth as the speed of light does on our knowledge of the universe."

"Everybody tends to merge his identity with other people at the speed of light. It's called being mass man."

"Attention spans get very weak at the speed of light, and that goes along with a very week identity."

"It is hard to understand how this infinitely dense singularity can evaporate into nothing. For matter inside the black hole to leak out into the universe requires that it travel faster than the speed of light."

"A much faster speed of light in the infant universe solved the horizon problem and therefore explained the overall smoothness of the temperatures of the CMB radiation, because light now traveled extremely quickly between all parts of the expanding but not inflating universe."

"Inflation itself proceeds at a speed faster than the measured speed of light."

"Minkowski's idea and the solution of the twin paradox can best be explained by means of an analogy between space and spacetime... Time as a fourth dimension rests vertically on the other three—just as in space the vertical juts out of the two-dimensional plane as a third dimension. Distances through spacetime comprise four dimensions, just as space has three. The more you go in one direction, the less is left for the others. When a rigid body is at rest and does not move in any of the three dimensions, all of its motion takes place on the time axis. It simply grows older. ...The faster he moves away from his frame of reference... and covers more distance in the three dimensions of space, the less of his motion through spacetime as a whole is left over for the dimension of time. ...Whatever goes into space is deducted from time. ...In comparison with the distances light travels, all distances in the dimensions of space, even those involving airplane travel, are so very small that we essentially move only along the time axis, and we age continually. Only if we are able to move away from our frame of reference very quickly, like the traveling twin... would the elapsed time shrink to near zero, as it approached the speed of light. Light itself... covers its entire distance through spacetime only in the three dimensions of space... Nothing remains for the additional dimension... the dimension of time... Because light particles do not move in time, but with time, it can be said that they do not age. For them "now" means the same thing as "forever." They always "live" in the moment. Since for all practical purposes we do not move in the dimensions of space, but are at rest in space, we move only along the time axis. This is precisely the reason we feel the passage of time. Time virtually attaches to us."

"Einstein's famous theory of relativity states that while phenomena appear different to someone close to a black hole, traveling close to the speed of light, or in a falling elevator here on earth, scientists in profoundly different environments will nevertheless always discover the same underlying laws of nature."

"Communication becomes the defining characteristic of homo sapiens; we are the species that speaks. We utter the words that create our world, and have learned to take our words and translate them into the ethereal play of zeros and ones, lay them out, at the speed of light, first on a wire, then a radio wave, and lately, on a beam of light, so that the voice, once constrained by mouth and ear, now straddles the entire planet in thirty millionths of a second, messages pinging back and forth, not unlike the meeting points of a synaptic gap, using photons as neurotransmitters, and each network router the equivalent of a synapic junction, deciding whether to activate or extinguish each message that crosses the continents, connected now in a seamless, endless web of knowledge, more than two billion pages, more than any one of us could ever read or know, the collected and collective intelligence of a species that seems to have made information the central mystery of culture, the project of civilization, and the goal of being."

"The principle of the limiting character of the velocity of light. This statement... is not an arbitrary assumption but a physical law based on experience. In making this statement, physics does not commit the fallacy of regarding absence of knowledge as evidence for knowledge to the contrary. It is not absence of knowledge of faster signals, but positive experience which has taught us that the velocity of light cannot be exceeded. For all physical processes the velocity of light has the property of an infinite velocity. In order to accelerate a body to the velocity of light, an infinite amount of energy would be required, and it is therefore physically impossible for any object to obtain this speed. This result was confirmed by measurements performed on electrons. The kinetic energy of a mass point grows more rapidly than the square of its velocity, and would become infinite for the speed of light."

"Once we overcome our fear of being tiny, we find ourselves on the threshold of a vast and awesome Universe that utterly dwarfs—in time, in space, and in potential—the tidy anthropocentric proscenium of our ancestors. We gaze across billions of light-years of space to view the Universe shortly after the Big Bang, and plumb the fine structure of matter. We peer down into the core of our planet, and the blazing interior of our star. We read the genetic language in which is written the diverse skills and propensities of every being on Earth. We uncover hidden chapters in the record of our origins, and with some anguish better understand our nature and prospects. We invent and refine agriculture, without which almost all of us would starve to death. We create medicines and vaccines that save the lives of billions. We communicate at the speed of light, and whip around the Earth in an hour and a half. We have sent dozens of ships to more than seventy worlds, and four spacecraft to the stars. We are right to rejoice in our accomplishments, to be proud that our species has been able to see so far, and to judge our merit in part by the very science that has so deflated our pretensions."

"The idea that as I walk in this direction my watch goes slightly slower and I am contracted in the direction of motion and my mass has increased slightly does not correspond to everyday experience. ...the reason that it does not correspond to common sense is that we are not in the habit of traveling close to the speed of light. We may one day be in that habit, and then the Lorentz transformations will be natural, intuitive."

"Some of the effects predicted by the theory [of loop quantum gravity] appear to be in conflict with one of the principles of Einstein's special theory of relativity... that the speed of light is a universal constant. ...Photons of higher energy travel slightly slower than low-energy photons. ...the principle of [general] relativity is preserved but Einstein's special theory of relativity requires modification. ...A photon can have an energy-dependent speed without violating the principle of [general] relativity!"

"'New Science' must demolish the Constants, supposedly Absolute, ... for example: Speed of Light must be increased a Billionfold, in order to achieve Extraterrestrial Communication."

"One thing leads to another, and soon you are searching for answers to basic questions.Another time during lectures on Classical Logic, we were introduced to an “experimentum crucis”. It was illustrated by the deciding experiment of Fizeau on the speed of light in water as compared to its speed in air. Since wave theory predicts that speed in water is less, and corpuscular theory (with point particles) predicts it would be faster, this is supposed to have selected the wave theory is correct. But then how would one accommodate the photoelectric effect? Then it turns out that if the “corpuscle” of light had a finite size, corpuscular theory also predicts lower speed of light in water. But then one can ask how come photoelectric emission being prompt even in feeble light, how could the energy of a photon spread over π(λ/2)2 act as a whole and liberate a single photoelectron! This leads us to question the square of the amplitude being interpreted as the probability of the particle being formed in the immediate vicinity. How do probabilities enter quantum mechanics? Thus the questions (and the quest) go on."

"The more I learn about light the more I realize, man, we don't know anything about light... It's just bizarre... a particle has its own proper time which slows down as you speed up. But at the speed of light... there's no time. That's bizarre … that we can, right now, as you know, see — interact with the light that has come from the birth of the universe. So … from our point of view, that light traveled for 14 billion years but from the point of view of the light it's the moment of creation."

"Nature may reach the same result in many ways. Like a wave in the physical world, in the infinite ocean of the medium which pervades all, so in the world of organisms, in life, an impulse started proceeds onward, at times, may be, with the speed of light, at times, again, so slowly that for ages and ages it seems to stay, passing through processes of a complexity inconceivable to men, but in all its forms, in all its stages, its energy ever and ever integrally present. A single ray of light from a distant star falling upon the eye of a tyrant in bygone times may have altered the course of his life, may have changed the destiny of nations, may have transformed the surface of the globe, so intricate, so inconceivably complex are the processes in Nature. In no way can we get such an overwhelming idea of the grandeur of Nature than when we consider, that in accordance with the law of the conservation of energy, throughout the Infinite, the forces are in a perfect balance, and hence the energy of a single thought may determine the motion of a universe."

"Changing electric fields produce magnetic fields, and changing magnetic fields produce electric fields. Thus the fields can animate one another in turn, giving birth to self-reproducing disturbances that travel at the speed of light. Ever since Maxwell, we understand that these disturbances are what light is."

"E = mc2 really applies only to isolated bodies at rest. In general, when you have moving bodies, or interacting bodies, energy and mass aren't proportional. E = mc2 simply doesn't apply. ...For moving bodies, the correct mass-energy equation is E=\frac {mc^2} {\sqrt{1-\frac{v^2} {c^2}}} where v is the velocity. For a body at rest (v=0), this becomes E = mc2. ...we must consider the special case of particles with zero mass... examples include photons, color gluons, and gravitons. If we attempt to put m = 0 and v = c in our general mass-energy equation, both the numerator and denominator on the right-hand-side vanish, and we get the nonsensical relation E = 0/0. The correct result is that the energy of a photon can take any value. ...The energy E of a photon is proportional to the frequency f of the light it represents. ...they are related by the Planck-Einstein-Schrödinger equation E = hf, where h is Plank's constant."

"Bolder even than Riemann, Clifford confessed his belief (1870) that matter is only a manifestation of curvature in a space-time manifold. This embryonic divination has been acclaimed as an anticipation of Einstein’s (1915–16) relativistic theory of the gravitational field. The actual theory, however, bears but slight resemblance to Clifford’s rather detailed creed. As a rule, those mathematical prophets who never descend to particulars make the top scores. Almost anyone can hit the side of a barn at forty yards with a charge of buckshot."

"Unfortunately, scientists adore the Minkowski theory because, secretly they detest the 3+1 formula as not entirely objective, since man is the one to add the time; and yet Einstein has shown that there is no universal, or god-given cosmic time, thus making man supreme in the determination of physical reality. So the Minkowski proposal that enables them to pretend (it is only a pretence because it is not true, even Eddington told us so), is preferred. 'S=ct...', as Russell has averred, makes things easy for the mathematicians, but it is not true of the physical world (the same Russell said it is an artefact); therefore the concept of curved space-time and time travel based on it are all bogus science."

"General relativity (GR) is a geometric theory of gravitation: a gravitational field is simply curved spacetime. The gravitational time dilation implied by the equivalence principle... can be interpreted as showing the warpage of spacetime in the time direction."

"In GR, the mass/energy source determines the metric function through the field equation. ...In this approach, gravity is the structure of spacetime and is not regarded as a force (that brings about acceleration). Thus a test-body will move in a force-free way in such a curved spacetime; it is natural to expect it to follow in this spacetime the shortest and straightest possible trajectory, the geodesic curve..."

"We may conceive our space to have everywhere a nearly uniform curvature, but that slight variations of the curvature may occur from point to point, and themselves vary with the time. These variations of the curvature with the time may produce effects which we not unnaturally attribute to physical causes independent of the geometry of our space. We might even go so far as to assign to this variation of the curvature of space 'what really happens in that phenomenon which we term the motion of matter.'"

"Every artist's strictly illimitable country is himself. An artist who plays that country false has committed suicide;and even a good lawyer cannot kill the dead. But a human being who's true to himself — whoever himself may be — is immortal;and all the atomic bombs of all the antiartists in spacetime will never civilize immortality."

"Mathematicians call the infinite curvature limit of spacetime a singularity. In this picture, then, the big bang emerges from a singularity. The best way to think about singularities is as boundaries or edges of spacetime. In this respect they are not, technically, part of spacetime itself... So the first moment of the universe — in this highly simplified picture — is not a moment or a place at all, but a boundary to moments and places. ...it signals a "no further" warning."

"The discovery of Minkowski... is to be found... in the fact of his recognition that the four-dimensional space-time continuum of the theory of relativity, in its most essential formal properties, shows a pronounced relationship to the three-dimensional continuum of Euclidean geometrical space. In order to give due prominence to this relationship, however, we must replace the usual time co-ordinate t by an imaginary magnitude, \sqrt -1\cdot ct, proportional to it. Under these conditions, the natural laws satisfying the demands of the (special) theory of relativity assume mathematical forms, in which the time co-ordinate plays exactly the same role as the three space-coordinates. Formally, these four co-ordinates correspond exactly to the three space co-ordinates in Euclidean geometry. ...These inadequate remarks can give the reader only a vague notion of the important idea contributed by Minkowski. Without it the general theory of relativity... would perhaps have got no farther than its long clothes."

"Every physical description resolves itself into a number of statements, each of which refers to the space-time coincidence of two events A and B. In terms of Gaussian co-ordinates, every such statement is expressed by the agreement of their four co-ordinates x1, x2, x3, x4. Thus in reality, the description of the time-space continuum by means of Gauss co-ordinates completely replaces the description with the aid of a body of reference, without suffering from the defects of the latter mode of description; it is not tied down to the Euclidean character of the continuum which has to be represented."

"The use of rigid reference-bodies, in the sense of the method followed in the special theory of relativity, is in general not possible in space-time description. The Gauss co-ordinate system has to take the place of the body of reference. The following statement corresponds to the fundamental idea of the general principle of relativity: "All Gaussian co-ordinate systems are essentially equivalent for the formulation of the general laws of nature.""

"To say that the four-dimensional continuum "exists now" implies that all cross sections "exist now" or, in other words, that the cross section t = t0 is identical with the cross-section t = t1. Otherwise, it could not exist "now." If we allow for this confusing way of thinking, the assertion that the "four-dimensional space-time continuum" has always existed and we are merely traveling through it asserts no more than the statement that the three-dimensional space continuum changes in time. ...if we call the ...space-time continuum a "reality," we are encouraged to adopt Lagrange's assertion that mechanics is a four-dimensional geometry, and to say that the four-dimensional continuum "exists now," and that therefore all future events exist now, and the "future" consists in our moving through the... continuum. But exactly as before Minkowski's formulation... we must also admit that the use of the word "now" in the formulation is rather misleading. By "now" we mean the cross section of the four-dimensional space-time continuum that is defined by t = t0. Therefore it is self-contradictory that any future instant of time t > t0 can exist "now." Use has often been made of this four-dimensional space-time continuum to "prove" that the future is "predetermined." ... The four-dimensional formulation is a useful instrument for the presentation of physical events, but it cannot be interpreted in our everyday language by simply speaking about the... space-time continuum as we have been accustomed to speak about our ordinary three-dimensional space."

"Think, for a moment, of a cheetah, a sleek, beautiful animal, one of the fastest on earth, which roams freely on the savannas of Africa. In its natural habitat, it is a magnificent animal, almost a work of art, unsurpassed in speedor grace by any other animal. Now, think of a cheetah that has been captured and thrown into a miserable cage in a zoo. It has lost its original grace and beauty, and is put on display for our amusement. We see only the broken spirit of the cheetah in the cage, not its original power and elegance. The cheetah can be compared to the laws of physics, which are beautiful in their natural setting. The natural habitat of the laws of physics is higher-dimensional space-time. However, we can only measure the laws of physics when they have been broken and placed on display in a cage, which is our three-dimensional laboratory. We can only see the cheetah when its grace and beauty have been stripped away."

"Einstein proclaimed that all objects in the universe are always traveling through spacetime at one fixed speed—that of light. ...this one fixed speed can be shared between the different ...space and time dimensions ...If an object is sitting still ...all of the object's motion is used to travel through one dimension ...time ...all objects that are at rest ...age—at exactly the same rate or speed. If an object does move through space... some of the previous motion through time must be diverted. ...its clock will tick more slowly if it moves through space. ...The speed of an object through space is thus merely a reflection of how much of its motion through time is diverted. ...the maximum speed through space occurs if all of an object's motion through time is diverted to motion through space. But having used up all of its motion through time, this is the fastest speed through space ...something traveling at light speed through space will have no speed left for motion through time. Thus light does not get old; a photon that emerged from the big bang is the same age today as it was then. There is no passage of time at light speed."

"In a paper he sent to Einstein in 1919, Kaluza made an astounding suggestion. He proposed that the spatial fabric of the universe might possess more than the three dimensions... it provided an elegant and compelling framework for weaving together Einstein's general relativity and Maxwell's electromagnetic theory into a single, unified conceptual framework. ...implicit in Kaluza's work and subsequently made explicit and refined by... Oskar Klein in 1926... the spatial fabric of our universe may have both extended and curled-up dimensions. ... Einstein had formulated general relativity in the familiar setting of a universe with three spatial dimensions and one time dimension. The mathematical formalism... however, could be extended fairly directly to write down analogous equations for a universe with additional space dimensions. Under the "modest" assumption of one additional space dimension, Kaluza... derived the new equations. ...Kaluza found extra equations... those Maxwell had written down in the 1880s for deriving the electromagnetic force! ...Kaluza had united Einstein's theory of gravity with Maxwell's theory of light."

"Much as Kaluza found that a universe with five spacetime dimensions provided a framework for unifying electromagnetism and gravity, and much as string theorists found that a universe with ten spacetime dimensions provided a framework for unifying quantum mechanics and general relativity, Witten found that a universe with eleven spacetime dimensions provided a framework for unifying all string theories."

"The subject of this book is the structure of space-time on length-scales from 10-13 cm, the radius of an elementary particle, up to 1028 cm, the radius of the universe. ...we base our treatment on Einstein's General Theory of Relativity. This theory leads to two remarkable predictions about the universe: first, that the final fate of massive stars is to collapse behind an event horizon to form a 'black hole' which will contain a singularity; and secondly, that there is a singularity in our past which constitutes, in some sense, a beginning to the universe."

"This picture would explain why we haven't been over run by tourists from the future."

"The conclusion of this lecture is that rapid space-travel, or travel back in time, can't be ruled out, according to our present understanding. They would cause great logical problems, so let's hope there's a Chronology Protection Law, to prevent people going back, and killing our parents. But science fiction fans need not lose heart. There's hope in string theory."

"Then the theory of relativity came and explained the cause of the failure. Electric action requires time to travel from one point of space to another, the simplest instance of this being the finite speed of travel of light... Thus electromagnetic action may be said to travel through space and time jointly. But by filling space and space alone [excluding time] with an ether, the pictorial representations had all supposed a clear-cut distinction between space and time."

"Space-Time. In 1908... Minkowski stated the whole content of the theory in a new and very elegant form. Hitherto the laws of nature had been thought of as describing phenomena which occurred in three-dimensional space, while time flowed on uniformly and imperturbably in another and quite distinct dimension of its own. Minkowski now supposed that this fourth dimension of time was not detached from and independent of the three dimensions of space. He introduced a new four-dimensional space to which ordinary space contributed three dimensions, and time one; we may call it 'space-time'. ...The succession of positions which a particle occupied in ordinary space at a succession of instants of time would be represented by a line in space-time; this he called the 'world-line' of the particle. ...Newton's absolute space and absolute time fell out of science, and they carried much with them in their fall. First to go was the concept of simultaneity. ...It now became necessary to find a way of treating gravitation which should not involve simultaneity. Einstein found this through the medium of his 'Principle of Equivalence'."

"Any region of space-time that has no gravitating mass in its vicinity is uncurved, so that the geodesics here are straight lines, which means that particles move in straight courses at uniform speeds (Newton's first law). But the world-lines of planets, comets and terrestrial projectiles are geodesics in a region of space-time which is curved by the proximity of the sun or earth... No force of gravitation is... needed to impress curvature on world-lines; the curvature is inherent in the space..."

"The mark of Platonic philosophy is a radical dualism. The Platonic world is not one of unity; and the abyss which in many ways results from this bifurcation appears in innumerable forms. It is not one, but two worlds, which Plato sees when with the eyes of his soul he envisages a transcendent, spaceless, and timeless realm of the Idea, the thing-in-itself, the true, absolute reality of tranquil being, and when to this transcendent realm he opposes the spacetime sphere of his sensuous perception—a sphere of becoming in motion, which he considers to be only a domain of illusory semblance, a realm which in reality is not-being."

"The uomo universale of the Renaissance, who was artist and craftsman, philosopher and inventor, humanist and scientist, astronomer and monk, all in one, split up into his component parts. Art lost its mythical, science its mystical inspiration; man became again deaf to the harmony of the spheres. The Philosophy of Nature became ethically neutral, and "blind" became the favourite adjective for the working of natural law. The space-spirit hierarchy was replaced by the space-time continuum. ...man's destiny was no longer determined from "above" by a super-human wisdom and will, but from "below" by the sub-human agencies of glands, genes, atoms, or waves of probability. ...they could determine his fate, but could provide him with no moral guidance, no values and meaning. A puppet of the Gods is a tragic figure, a puppet suspended on his chromosomes is merely grotesque."

"[By moving] I'm making sounds on the drums of spacetime"… "Space itself wobbles and rumbles like a drum... Black holes can bang on spacetime like mallets on a drum."

"Time exists not by itself; but simply from the things which happen, the sense apprehends what has been done in time past, as well as what is present, and what is to follow after."

"Descartes... fell back on his original confusion of matter with space—space being, according to him, the only form of substance, and all existing things but affections of space. This error... forms one of the ultimate foundations of the system of Spinoza."

"Minkowski's idea and the solution of the twin paradox can best be explained by means of an analogy between space and spacetime... Time as a fourth dimension rests vertically on the other three—just as in space the vertical juts out of the two-dimensional plane as a third dimension. Distances through spacetime comprise four dimensions, just as space has three. The more you go in one direction, the less is left for the others. When a rigid body is at rest and does not move in any of the three dimensions, all of its motion takes place on the time axis. It simply grows older. ...The faster he moves away from his frame of reference... and covers more distance in the three dimensions of space, the less of his motion through spacetime as a whole is left over for the dimension of time. ...Whatever goes into space is deducted from time. ...In comparison with the distances light travels, all distances in the dimensions of space, even those involving airplane travel, are so very small that we essentially move only along the time axis, and we age continually. Only if we are able to move away from our frame of reference very quickly, like the traveling twin... would the elapsed time shrink to near zero, as it approached the speed of light. Light itself... covers its entire distance through spacetime only in the three dimensions of space... Nothing remains for the additional dimension... the dimension of time... Because light particles do not move in time, but with time, it can be said that they do not age. For them "now" means the same thing as "forever." They always "live" in the moment. Since for all practical purposes we do not move in the dimensions of space, but are at rest in space, we move only along the time axis. This is precisely the reason we feel the passage of time. Time virtually attaches to us."

"Hitherto I have laid down the definitions of such words as are less known, and explained the sense in which I would have them to be understood in the following discourse. I do not define time, space, place and motion, as being well known at all. Only I must observe, that the vulgar conceive those quantities under no other notions but from the relation they bear to sensible objects. And thence arise certain prejudices, for the removing of which, it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common. I. Absolute, true and mathematical time, of itself, and from its own nature, flows equably without regard to anything external, and by another name is called duration: relative, apparent and common time is some sensible and external (whether accurate or unequable) measure of duration by means of motion, which is commonly used instead of true time; such as an hour, a day, a month or a year. II. Absolute space, in its own nature, without regard to any thing external, remains always similar and immovable. Relative space is some moveable dimension or measure of the absolute spaces; which our senses determine by its position to bodies; and which is vulgarly taken for immovable space; such is the dimension of a subterraneous, an æreal, or celestial space, determined by its position in respect of the earth. Absolute and relative space, are the same in figure and magnitude; but they do not remain always numerically the same. For if the earth, for instance, moves, a space of our air, which relatively and in respect of the earth remains always the same, will at one time be one part of the absolute space into which the air passes, at another time it will be another part of the same, and so, absolutely understood, it will be perpetually mutable. III. Place is a part of space which a body takes up, and is according to the space, either absolute or relative. I say, a part of space; not the situation, nor the external surface of the body. For the places of equal solids, are always equal; but their superficies, by reason of their dissimilar figures, are often unequal. Positions properly have no quantity, nor are they so much the places themselves, as the properties of places. The motion of the whole is the same thing with the sum of the motions of the parts; that is, the translation of the whole, out of its place, is the same thing with the sum of the translations of the parts out of their places; and therefore the place of the whole, is the same thing with the sum of the places of the parts; and for that reason, it is internal, and in the whole body. IV. Absolute motion, is the translation of a body from one absolute place into another; and relative motion, the translation from one relative place into another. Thus in a ship under sail, the relative place of a body is that part of the ship which the body possesses; or that part of its cavity which the body fills, and which therefore moves together with the ship: and relative rest, is the continuance of the body in the same part of the ship, or of its cavity. But real, absolute rest, is the continuance of the body in the same part of that immovable space, in which the ship itself, its cavity, and all that it contains, is moved. Wherefore, if the earth is really at rest, the body which relatively rests in the ship, will really and absolutely move with the same velocity which the ship has on the earth. But if the earth also moves, the true and absolute motion of the body will arise, partly from the true motion of the earth, in immovable space; partly from the relative motion of the ship on the earth: and if the body moves also relatively in the ship; its true motion will arise, partly from the true motion of the earth, in immovable space, and partly from the relative motions as well of the ship on the earth, as of the body in the ship; and from these relative motions will arise the relative motion of the body on the earth."

"Guth... wanted to hear... Alex Vilenkin... describe a new theory of the origin of the universe, of how it could have emerged from nothing. Vilenkin's version of the infant universe... was a kind of metaphysical mole. ...a bubble of universe, space-time, had "tunneled" into a Wheeleresque superspace of possible space-times and then tunneled again into "real" space and time. ...But from where had the universe tunneled into this realm..? In Vilenkin's words, "from nothing." ...Vilenkin's tiny bubble... inflated and went through the standard expansion and evolution of the big bang. ...he, Guth, and Sidney Coleman sat and had a conversation that Lewis Carroll might have enjoyed, about nothing. ..."Nothing," answered Vilenkin... "is no time, no space." ..."There is an epoch without time," [Coleman] said finally as the shadows lengthened. "It is an enternity. So we make a quantum leap from eternity into time." Then, as good physicists did, they repaired to a Chinese restaurant."

"The idea of having an ambient space-time of some specific dimension seems to play less of a role in string theory than in conventional physics, and certainly less than the kind of role that I would myself feel comfortable with. It is particularly difficult to assess the functional freedom that is involved in a physical theory unless one has a clear idea of its actual space-time dimensionality."

"Ever since Hermann Minkowski's now infamous comments in 1908 concerning the proper way to view space-time, the debate has raged as to whether or not the universe should be viewed as a four-dimensional, unified whole wherein the past, present, and future are regarded as equally real or whether the views espoused by the possibilists, historicists, and presentests regarding the unreality of the future (and, for presentests, the past) are more accurate. Now, a century after Minkowski's proposed block universe first sparked debate, we present a new, more conclusive argument in favor of eternalism."

"The structure of space-time, taken as a whole, is the subject matter of the science called cosmology. Since you are asking about all space and all time in cosmology, you are interested in the entire universe, everywhere and everywhen, viewed as a static geometrical object."

"A person's lifeworm is a tangle of atomic worldlines. A braid. The dotty little atoms trace out smooth lines in spacetime: you are the pattern that these lines make up. There is no one single atom that is exclusively yours. I breathe an atom out, you breathe it in. Your garbage helps my tomatoes grow. And so the little spacetime threads weave us all together. The human race is a single vast tapestry, linked by our shared food and air. There are larger links as well: sperm, egg and umblilicus. Each family tree is an organic whole. Your spacetime body tapers back to the threads of mother's egg and father's sperm. And children, if you have them, are forever rooted in your flesh."

"When, in youth, I learned what was called "philosophy" … no one ever mentioned to me the question of "meaning." Later, I became acquainted with Lady Welby's work on the subject, but failed to take it seriously. I imagined that logic could be pursued by taking it for granted that symbols were always, so to speak, transparent, and in no way distorted the objects they were supposed to "mean." Purely logical problems have gradually led me further and further from this point of view. Beginning with the question whether the class of all those classes which are not members of themselves is, or is not, a member of itself; continuing with the problem whether the man who says "I am lying" is lying or speaking the truth; passing through the riddle "is the present King of France bald or not bald, or is the law of excluded middle false?" I have now come to believe that the order of words in time or space is an ineradicable part of much of their significance – in fact, that the reason they can express space-time occurrences is that they are space-time occurrences, so that a logic independent of the accidental nature of spacetime becomes an idle dream. These conclusions are unpleasant to my vanity, but pleasant to my love of philosophical activity: until vitality fails, there is no reason to be wedded to one's past theories."

"It ought to arouse our suspicions that people who spend enormous efforts on interpreting [Martin Heidegger's] work disagree on the fundamental question whether he was an idealist. For the purposes of this discussion, his lack of a resolute commitment to the basic facts is enough. Suppose you took the notion of Dasein seriously, in the sense that you thought it referred to a real phenomenon in the real world. Your first question would be: How does the brain cause Dasein and how does Dasein exist in the brain? Or if you thought the brain was not the right explanatory level you would have to say exactly how and where Dasein is located in the space time trajectory of the organism and you would have to locate the right causes, both the micro causes that are causing Dasein and its causal effects on the organic processes of the organism. There is no escaping the fact that we all live in one space-time continuum, and if Dasein exists it has to be located and causally situated in that continuum. Furthermore, if you took Dasein seriously you would then have to ask how does Dasein fit into the biological evolutionary scheme? Do other primates have it? Other mammals? What is its evolutionary function? I can’t find an answer to these questions in Heidegger or even a sense that he is aware of them or takes them seriously. But taking these questions seriously is the price of taking Dasein seriously, unless of course you are denying the primordiality of the basic facts."

"In Newton's system of mechanics... there is an absolute space and an absolute time. In Einstein's theory time and space are interwoven, and the way in which they are interwoven depends on the observer. Instead of three plus one we have four dimensions."

"It may be helpful to a good understanding of the conception of the physical universe implied by the general theory of relativity, to consider the different definitions of a straight line. ...In the old mechanics, there are four of these, viz.: (1) ray of light, (2) the track of a material particle not subject to any forces, (3) a stretched cord, (4) an axis of rotation. The fourth definition is the one favored by the great mathematician Henri Poincaré. ...Are they still identical in the theory of relativity? The definitions 1 and 2 define the straight line as a projection on the three-dimensional space x, y, z of a geodesic in the four-dimensional space-time continuum. This projection will be a geodesic in three-dimensional space only under very special conditions. In the general case the two projections will differ from each other, and neither of them will be a geodesic. Also the projection may be a geodesic in one system of coordinates but not in another. The stretched cord is by definition a geodesic in the three-dimensional space. As a rule, this will not be a geodesic in the four-dimensional continuum. The rotation axis is also by definition a line in three-dimensional space. The definition, however, presupposes the possibility of the rotation of a rigid body, which would be possible only in a homogeneous, isotropic, and statical field, i.e., in a world without any material bodies... in it, which by their gravitational field would upset the isotropy. The definition is thus meaningless in the general theory of relativity."

"Spacetime... turns out to be discrete, described by a structure called spin foam."

"In string theory one studies strings moving in a fixed classical spacetime. ...what we call a background-dependent approach. ...One of the fundamental discoveries of Einstein is that there is no fixed background. The very geometry of space and time is a dynamical system that evolves in time. The experimental observations that energy leaks from binary pulsars in the form of gravitational waves—at the rate predicted by general relativity to the... accuracy of eleven decimal places—tell us that there is no more a fixed background of spacetime geometry than there are fixed crystal spheres holding the planets up."

"The hypothesis underlying all approaches to the landscape is that there is a cosmological setting in which different regions or epochs of the universe can have different effective laws. This implies the existence of spacetime regions not directly observable... These regions must either be in the past of our big bang, or far enough away from us to be causally unrelated."

"The positive energy theorem was for half a century or more an open challenge to relativists. Many attempts were made to prove flat spacetime was stable, but none completely succeeded completely until a majestic tour de force of geometric reasoning of Shoen and Yau. This was followed two years later by a proof of Witten, which was as elegant as it was short. It is this proof of Witten’s that we take as a template here for the quantum theory."

"Minkowski, building on Einstein's work, had now discovered that the Universe is made of a four-dimensional "spacetime" fabric that is absolute, not relative."

"Einstein was guided by a principle he had inferred from the known properties of gravitation, the principle of the equivalence of gravitational forces to inertial effects such as centrifugal force. The development of the Standard Model was guided by a principle called gauge symmetry, a generalization of the well-known property of electricity that it is only differences of voltages that matter, not voltages themselves. But we have not discovered any fundamental principle that governs M-theory. The various approximations to this theory look like string or field theories in spacetimes of different dimensionalities, but it seems probable that the fundamental theory is not to be formulated in spacetime at all. Quantum field theory is powerfully constrained by principles concerning the nature of four-dimensional spacetime that are incorporated in the special theory of relativity. How can we get the ideas we need to formulate a truly fundamental theory, when this theory is meant to describe a realm where all intuitions derived from life in spacetime become inapplicable?"

"Minkowski calls a spatial point existing at a temporal point a world point. These coordinates are now called 'space-time coordinates'. The collection of all imaginable value systems or the set of space-time coordinates Minkowski called the world. This is now called the manifold. The manifold is four-dimensional and each of its space-time points represents an event."

"There are really four dimensions, three which we call the three planes of Space, and a fourth, Time. There is, however, a tendency to draw an unreal distinction between the former three dimensions and the latter, because it happens that our consciousness moves intermittently in one direction along the latter from the beginning to the end of our lives. ...Really this is what is meant by the Fourth Dimension, though some people who talk about the Fourth Dimension do not know they mean it. It is only another way of looking at Time. There is no difference between Time and any of the three dimensions of Space except that our consciousness moves along it. ...space, as our mathematicians have it, is spoken of as having three dimensions, which one may call Length, Breadth, and Thickness, and is always definable by reference to these planes, each at right angle to the others. But some philosophical people have been asking why three dimensions particularly—why not another direction at right angles to the other three?—and have even tried to construct a Four Dimensional geometry. Professor Simon Newcomb was expounding this to the New York Mathematical Society only a month or so ago. You know how on a flat surface, which has only two dimensions, we can represent a figure of a Three-Dimensional solid, and similarly they think that by models of three dimensions they could represent one of four—if they could master the perspective of the thing. See?"

"And now, in our time, there has been unloosed a cataclysm which has swept away space, time, and matter hitherto regarded as the firmest pillars of natural science, but only to make place for a view of things of wider scope, and entailing a deeper vision."

"The scene of action of reality is not a three-dimensional Euclidean space but rather a four-dimensional world, in which space and time are linked together indissolubly. However deep the chasm may be that separates the intuitive nature of space from that of time in our experience, nothing of this qualitative difference enters into the objective world which physics endeavors to crystallize out of direct experience. It is a four-dimensional continuum, which is neither "time" nor "space". Only the consciousness that passes on in one portion of this world experiences the detached piece which comes to meet it and passes behind it as history, that is, as a process that is going forward in time and takes place in space. ... It is remarkable that the three-dimensional geometry of the statical world that was put into a complete axiomatic system by Euclid has such a translucent character, whereas we have been able to assume command over the four-dimensional geometry only after a prolonged struggle and by referring to an extensive set of physical phenomena and empirical data. Only now the theory of relativity has succeeded in enabling our knowledge of physical nature to get a full grasp of the fact of motion, of change in the world."

"Spacetime tells matter how to move; matter tells spacetime how to curve."

"In 1908 the famous mathematician Minkowski made a remarkable discovery concerning the Lorentz formulae. He showed that, although each observer had his own private space and private time, a public concept which is the same for all observers can be formed by combining space and time in a particular way. If we regard an inverval of time as a kind of 'distance' in the time dimension, we can convert it into a true distance by multiplying it by the velocity of light, c; in other words, with any time interval we can associate a definite spatial interval, namely the distance which light can travel in empty space in that period. If, according to a particular observer, the difference in time between any two events is T, this associated spatial interval is cT. Then, if R is the space-distance between these two events, Minkowski showed that the difference of the squares of cT and R has the same value for all observers in uniform relative motion. The square root of this quantity is called the space-time interval between the two events. Hence, although time and three-dimensional space depend on the observer, this new concept of space-time is the same for all observers."

"Space-time is curved in the neighborhood of material masses, but it is not clear whether the presence of matter causes the curvature of space-time or whether this curvature is itself responsible for the existence of matter."

"With regard to the Newtonian concept of absolute rotation, Eddington admitted that Einstein's plenum does in fact provide a world-wide inertial frame, with respect to which it can be measured. Nevertheless, Eddington believed that Einstein attributed to important a role to matter, for in his universe it appears that not only the metrical properties, as in General Relativity, but the very existence of space depends on the existence of matter. Eddington preferred to regard matter as a manifestation of the 'structure' of space-time."

"Shortly after Einstein published his original memoir... de Sitter constructed an alternative static world-model... unlike Einstein's, space-time has an intrinsic structure of its own, independent of the presence of matter. ...there is, strictly speaking, no matter or radiation. ...whereas a test particle in Einstein's universe will remain at rest if it has no initial motion, a similar particle introduced in de Sitter's world will immediately acquire an ever-increasing velocity of recession from the observer. Moreover, in de Sitter's model, space-time is 'hyperbolic'. There is no absolute time, and each observer will perceive a horizon at which time will appear to him to stand still. ...This phenomenon. of course, is only apparent, like a rainbow. At any point on the (relative) horizon the time-flux experienced by an observer there will be the same as the original observer. Thus in de Sitter's world there will be an apparent slowing-down of distant atomic vibrations, if these keep standard time. Consequently the radiation from a distant nebula will appear to be shifted toward the red... This effect, of course, will be supplemented by the Doppler effect, due to the relative recession of the nebula regarded as a test particle."

"According to the special theory there is a finite limit to the speed of causal chains, whereas classical causality allowed arbitrarily fast signals. Foundational studies... soon revealed that this departure from classical causality in the special theory is intimately related to its most dramatic consequences: the relativity of simultaneity, time dilation, and length contraction. By now it had become clear that these kinematical effects are best seen as consequences of Minkowski space-time, which in turn incorporates a nonclassical theory of causal structure. However, it has not widely been recognized that the converse of this proposition is also true: the causal structure of Minkowski space-time contains within itself the entire geometry (topoligical and metrical structure) of Minkowski space-time. ...The problem of the independence of topological and metrical structures of space-time was clearly recognized by early writers on relativity such as Russell (1954) and, of course, Eddington..."

"Replacing particles by strings is a naive-sounding step, from which many other things follow. In fact, replacing Feynman graphs by Riemann surfaces has numerous consequences: 1. It eliminates the infinities from the theory. ...2. It greatly reduces the number of possible theories. ...3. It gives the first hint that string theory will change our notions of spacetime. Just as in QCD, so also in gravity, many of the interesting questions cannot be answered in perturbation theory. In string theory, to understand the nature of the Big Bang, or the quantum fate of a black hole, or the nature of the vacuum state that determines the properties of the elementary particles, requires information beyond perturbation theory... Perturbation theory is not everything. It is just the way the [string] theory was discovered."

"We can describe general relativity using either of two mathematically equivalent ideas: curved space-time or metric field. Mathematicians, mystics and specialists in general relativity tend to like the geometric view because of its elegance. Physicists trained in the more empirical tradition of high-energy physics and quantum field theory tend to prefer the field view, because it corresponds better to how we (or our computers) do concrete calculations. ...the field view makes Einstein's theory of gravity look more like the other successful theories of fundamental physics, and so makes it easier to work toward a a fully integrated, unified description of all the laws. ...I'm a field man."

"The traditional “cosmological” Multiverse considers that there might be physical realms inaccessible to us due to their separation in space-time. The quantum Multiverse arises from entities that occupy the same space-time, but are distant in Hilbert space – or in the jargon, decoherent."

"In an infinite universe, every point in space-time is the center."

"The principle of the invariant velocity of light states that in whatever Galilean system we might have operated, the measured velocity of light in vacuo would always be the same. ...The mathematical translation of this principle of physics yields us the following equation, which must remain invariably zero in value for all Galilean frames:dx^2 + dy^2 + dz^2 -c^2dt^2 = 0 (using differentials)[ Note: the above is derived from the velocity of light c being equal to the change in length divided by the change in time, i.e., \frac{\vartriangle l}{\vartriangle t} = c, or expressed as differentials, \frac{dl}{dt} = c, which implies \frac{dl^2}{dt^2} = c^2 and {dl^2} - c^2dt^2 = 0. But, by the Pythagorean theorem, {dl^2} = {dx^2} + {dy^2} + {dz^2} ]. From a purely mathematical standpoint problems of this type form a branch of mathematics known as the theory of invariants. ...the transformations to which it was necessary to subject these variables (in order to satisfy the condition of invariance...), were given by a wide group of transformations known as conformal transformations. Conformal transformations are those which vary the shape of the lines while leaving the values of their angles of intersections unaltered. They are of wide use in maps, e.g., in Mercator's projection or in the stereographic projection. But when, in addition, the relative velocity is taken into consideration it is seen that conformal transformations are far too general. ...when the required restrictions are imposed we find that the rules of transformation according to which the space and time co-ordinates of one Galilean observer are connected with those of another depend in a very simple way on the relative velocity v existing between the two systems. These rules of transformation are given by the Lorentz-Einstein transformations."

"The discovery of the invariantdx^2 + dy^2 + dz^2 -c^2dt^2whose value we shall designate ds^2 marks the date of immense importance in the history of natural philosophy. ...It mattered not whether we were situated in this frame or in that one; in every case ...it still maintained the same value when referred to any other frame. ...we were in the presence of something which, contrary to a distance in space or a duration in time, transcended our variable points of view ...a common absolute world underlying the relativity of physical space and time. Minkowski immediately recognised in the mathematical form of this invariant the expression of the square of the distance in a four-demensional continuum. This distance was termed the Einsteinian interval, or, more simply, the interval. ...The continuum was neither space nor time, but it pertained to both ...it may appear strange that measurements with clocks can be co-ordinated with measurements with rods or scales. This difficulty, however, need not arrest us; for although dt is a time which can only be measured with a clock, yet cdt, being the product of a velocity by a time, is a spatial length since it represents the distance covered by light in the time dt."

"Minkowski demonstrated the significance of the expression for ds^2 by taking the new variable T = ict, where i stands for \sqrt{-1}. With this change, ds^2 can be written:ds^2 = dx^2 + dy^2 + dz^2 + dT^2,which is the expression of the square of a distance in a four-dimensional Euclidean space when a Cartesian co-ordinate system is taken. Since this expression is to remain unmodified in value and form in all Galilean frames, we must conclude that in a space-time representation a passage from one Galilean frame to another is given by a rotation of our four-dimensional Cartesian space-time mesh-system. Now rotation constitutes... a variation in the co-ordinates of the points of the continuum. In other words, they correspond to mathematical transformations. The transformations which accompany a rotation of a Cartesian co-ordinate system are of a particularly simple nature; they are called "orthogonal transformations." It follows that if we write out the orthogonal transformations for Minkowski's four-dimensional Euclidean space-time, we should obtain ipso facto the celebrated Lorentz-Einstein transformations which represent the passage from one Galilean system to another. ...we obtain the following result: Two Galilean systems moving with a relative velocity v are represented by two space-time Cartesian co-ordinate systems differing in orientation by the imaginary angle \theta, where \theta is connected with v by the formula tan\theta = \frac{iv}{c}."

"With the rejection of such classical absolutes as length and duration, our ability to conceive of an objective impersonal world, independent of the presence of an observer, seems to be imperiled. The great merit of Minkowski was to show that an absolute world could nevertheless be imagined, although it was a far different world from that of classical physics. In Minkowski's world the absolute which supersedes the absolute length and duration of classical physics is the Einsteinian interval. ... Thus suppose that, as measured in our Galilean frame of reference, two flashes occur at points A and B, situated at a distance l apart, and suppose the flashes are separated in time by an interval t. If we change our frame of reference, both l and t will change in value, becoming l and t respectively, exhibiting by their changes the relativity of length and duration. In Minkowski's words, "Henceforth space and time themselves are mere shadows." On the other hand, the mathematical construct l^2 - c^2t^2 will remain invariant, and so we shall have l^2 - c^2t^2 = l'^2 - c^2t'^2. It is this invariant expression, which involves both length and duration, or both space and time, which constitutes the Einsteinian interval; and the objective world which it cannotes is the world of four-dimensional space-time. The Einsteinian interval... remains the same for all observers, just as distance alone or duration alone were mistakenly believed to remain the same for all observers in classical physics. ...the Einsteinian interval still remains an invariant as measured for all frames of reference, whether accelerated or not. In the case of accelerated frames, however, we must restrict our attention to Einsteinan intervals of infinitesimal magnitude, and then add up the intervals when finite magnitudes are involved."

"In the study of electricity and magnetism we may consider phenomena in which conditions do not vary as time passes by; the electric charges and the magnets remain at rest, and the currents flowing in fixed wires do not vary in intensity. Conditions are then termed stationary [static]; it is as though time played no part. The laws which govern this type of phenomena were discovered empirically over a century ago, and were expressed mathematically in terms of spatial vectors. The problem of ascertaining how electric and magnetic phenomena would behave when conditions ceased to be stationary was one that could not be predicted; further experimental research was necessary before the general laws could be obtained. Even so, the difficulties were considerable, and it needed Maxwell's genius to establish the laws from the incomplete array of experimental evidence then at hand. All this work extended over nearly a century; it was slow and laborious. Yet, had men realised that our world was one of four-dimensional Minkowskian space-time, and not one of separate space and time, things would have been different. By extending the well-known stationary laws to four-dimensional space-time, through the mere addition of time components to the various trios of space ones, we should have written out inadvertently the laws governing varying fields, or, in other words, we should have constructed Maxwell's celebrated equations. Electromagnetic induction, discovered experimentally by Faraday, the additional electrical term introduced tentatively by Maxwell, radio waves, everything in the electromagnetics of the field, could have been foreseen at one stroke of the pen. A century of painstaking effort could have been saved. We are assuming that a four-dimensional vector calculus would have been in existence; but this is purely a mathematical question."

"In classical science, it was strange to find that action... should yet present the artificial aspect of an energy in space multiplied by a duration. As soon, however, as we realise that the fundamental continuum of the universe is one of space-time and not one of separate space and time, the reason for the importance of the seemingly artificial combination of space with time in the expression for the action receives a very simple explanation. Henceforth, action is no longer energy in a volume of space multiplied by a duration; it is simply energy in a volume of the world, that is to say, in a volume of four-dimensional space-time. Designating a volume of space-time by d\omega, we haved\omega = dxdydzdt,so that our principle of action, \partial A = 0, becomes\partial \int\,L\,d\omega = 0.Now there is a perfect symmetry between the rôles of space and time."

"When we realize the important rôle played by space-time in our attempts to avoid a belief in absolute rotation, we can well understand that the doctrine of the relativity of all motion would have been absurd in Newton's day. ...any speaker prior to, say, the year 1900 could never have anticipated the discovery of space-time, for its sole justification arose from the negative experiments in optics and electrodynamics attempted at about that time. As for Newton, not only did he know nothing of the non-mechanical negative experiments, but in addition, the equations of electrodynamics had not been discovered... even if he had conceived of space-time through some divine inspiration, he could never have utilised it for the purpose of establishing the relativity of all motion. His ignorance of non-Euclidean geometry would have rendered the task impossible. In fact, space-time, in the seventeenth century, would have been a hindrance, and the sole result of its premature introduction into science would have been to muddle everything up and render the discovery of Newton's law of gravitation well-nigh impossible."

"In the Vortex that lies beyond time and space tumbled a police box that was not a police box."

"Doc Brown: I foresee two possibilities. One: coming face-to-face with herself thirty years older would put her into shock and she'd simply pass out. Or two: the encounter could create a time paradox, the result of which could cause a chain reaction that would unravel the very fabric of the spacetime continuum and destroy the entire universe! Granted, that's a worst-case scenario. The destruction might in fact be very localised, limited to merely our own galaxy. Marty McFly: Well, that's a relief."

""Imagination is creativity playing outside the realms of intelligence or knowledge. Imagination entangles within the quantum brain of the world and self." *"

"We seek ourselves in quests so deep,"

"In later years, Pauli seems to have decided that Bohr himself was not a complete supporter of the Copenhagen interpretation. ...He felt that the real Copenhagen interpretation did insist that the mind was something that you could not avoid referring to in formulating quantum mechanics. Pauli thought, as far as I can judge, that the division between system and apparatus was ultimately between mind and matter."

"Matter, in our view, is an aggregate of ‘images’. And by ‘image’ we mean a certain existence which is more than that which the idealist calls a representation, but less than that which the realist calls a thing,—an existence placed half-way between the ‘thing’ and the ‘representation’. This conception of matter is simply that of common sense."

"Of course, we must avoid postulating a new element for each new phenomenon. But an equally serious mistake is to admit into the theory only those elements which can now be observed. For the purpose of a theory is not only to correlate the results of observations that we already know how to make, but also to suggest the need for new kinds of observations and to predict their results. In fact, the better a theory is able to suggest the need for new kinds of observations and to predict their results correctly, the more confidence we have that this theory is likely to be good representation of the actual properties of matter and not simply an empirical system especially chosen in such a way as to correlate a group of already known facts."

"Deep down the consciousness of mankind is one. This is a virtual certainty because even in the vacuum matter is one; and if we don't see this, it's because we are blinding ourselves to it."

"His philosophical solution of the spiritual problem lay in his affirmation of the identity of the mind and matter and in his assurance that the entire universe can be regarded as readily from the point of view of its consciousness... as it can be viewed as inert matter."

"It is mere rubbish thinking, at present, of origin of life; one might as well think of origin of matter. —"

"I recently listened to a talk by a famous biologist. He spoke about... scientific materialism and religious transcendentalism. He said, "...they are incompatible and mutually exclusive." This seems to be a widely accepted view... I do not share it. I do not know what the word "materialism" means. ...I judge matter to be an imprecise and ...old-fashioned concept ...[M]atter is the way particles behave when a large number of them are lumped together. When we examine matter in the finest detail in experiments of particle physics, we see it behaving as an active agent... Its actions are... unpredictable. It makes what appear to be arbitrary choices between alternative possibilities. Between matter... and mind... there seems to be only a difference of degree... We stand... midway between the unpredictability of matter and the unpredictability of God. This view... may not be true, but it is... logically consistent and compatible with... experiments of modern physics. Therefore... scientific materialism and religious transcendentalism are neither incompatible nor mutually exclusive. We have learned that matter... does not limit God's freedom to make it do what he pleases."

"Matter in quantum mechanics is not an inert substance but an active agent, constantly making choices between alternative possibilities according to probabilistic laws. ...It appears that mind, as manifested by the capacity to make choices, is to some extent inherent in every electron. ...Our brains appear to be devices for the amplification of the mental component of the quantum choices made by molecules inside our heads. ...There is evidence from peculiar features of the laws of nature that the universe as a whole is hospitable to the growth of mind. ...an extension of the Anthropic Principle up to a universal scale."

"Natural science served as - if we overlook the hasty identification of mind and matter which had its origin in natural science - as a shining and fruitful example to psychology."

"Popular thought, supported by desires common to all human beings, readily accepts the view that mind is essentially different from matter, that its laws are in every respect different from the laws of material nature, and that the brain, being a part of the material nature, is simply the special tool used by the mind in its intercourse with nature."

"Leibniz reversed the traditional conception of mind and matter by applying attributes of matter (in terms of sensory experience) to mind. Mind is what it experiences. Every mind or soul becomes an independent attribute of the universe, divinely ordered or arranged. Leibniz’s focus truly was mind."

"Materialism in its literal sense is long since dead. But its place has been taken by other philosophies which represent a virtually equivalent outlook. The tendency today is not to reduce everything to manifestations of matter—since matter now has only a minor place in the physical world—but to reduce it to manifestations of the operation of natural law... laws of the type prevailing in geometry, mechanics, and physics which are found to have this common characteristic—that they are ultimately reducible to mathematical equations. ...[T]hey are laws which, unlike human law, are never broken. It is the belief in the universal dominance of scientific law which is nowadays generally meant by materialism."

"To the naked eye it was a dense, solid object, but its lattice of tiny nuclei immersed in an insubstantial fog of electrons was one part matter to two hundred trillion parts empty space."

"He said that the beginning of the universe was mind and matter, mind being the creator and matter that which came into being."

"Epicurus held an opinion almost the opposite of all others. He supposed that the beginnings of the universals were atoms and a void; that the void was as it were the place of the things that will be; but that the atoms were matter, from which all things are."

"The fundamental principle of the atheism of Spinoza is the doctrine of the simplicity of the universe, and the unity of that substance, in which he supposes both thought and matter to inhere. There is only one substance, says he, in the world; and that substance is perfectly simple and indivisible, and exists every where, without any local presence. Whatever we discover externally by sensation; whatever we feel internally by reflection; all these are nothing but modifications of that one, simple, and necessarily existent being, and are not possest of any separate or distinct existence. Every passion of the soul; every configuration of matter, however different and various, inhere in the same substance, and preserve in themselves their characters of distinction, without communicating them to that subject, in which they inhere."

"The upward progress of terrestrial life towards individuality has found apparently insurmountable obstacles, gross material difficulties before it, but once more through consciousness it finds wings, and, laughing at matter, flies over lightly where it could not climb."

"The entire cosmos is made out of one and the same world-stuff, operated by the same energy as we ourselves. "Mind" and "matter" appears as two aspects of our unitary mind-bodies. There is no separate supernatural realm: all phenomena are part of one natural process of evolution. There is no basic cleavage between science and religion; they are both organs of evolving humanity."

"Matter gave birth to a passion that has no equal, which proceeded from something contrary to nature. Then there arises a disturbance in its whole body."

"Will matter then be destroyed or not? The Savior said, All nature, all formations, all creatures exist in and with one another, and they will be resolved again into their own roots. For the nature of matter is resolved into the roots of its own nature alone."

"By... confounding the properties of matter with those of space he arrives at the logical conclusion, that if the matter within a vessel could be entirely removed the space within the vessel would no longer exist. In fact he assumes that all space must be always full of matter."

"Descartes... fell back on his original confusion of matter with space—space being, according to him, the only form of substance, and all existing things but affections of space. This error... forms one of the ultimate foundations of the system of Spinoza."

"Whilst Copernicus has persuaded us to believe, contrary to all the senses, that the earth does not stand fast Boscovich has taught us to abjure the belief in the last thing that stood fast of the earth—the belief in "substance," in "matter," in the earth-residuum, and particle-atom: it is the greatest triumph over the senses that has hitherto been gained on earth. One must, however, go still further, and also declare war... against the "atomistic requirements" which still lead a dangerous after-life in places where no one suspects them, like the more celebrated "metaphysical requirements": one must also above all give the finishing stroke to that other and more portentous atomism which Christianity has taught best and longest, the soul-atomism. Let it be pemitted to designate by this expression the belief which regards the soul as something indestructible, eternal, indivisible, as a monad, as an atomon : this belief ought to be expelled from science!"

"What now is the answer to the question as to the bridge between the perception of the senses and the concepts, which is now reduced to the question as to the bridge between the outer perceptions and those inner image-like representations. It seems to me one has to postulate a cosmic order of nature — outside of our arbitrariness— to which the outer material objects are subjected as are the inner images... The organizing and regulating has to be posited beyond the differentiation of physical and psychical... I am all for it to call this "organizing and regulating" "archetypes." It would then be inadmissible to define these as psychic contents. Rather, the above-mentioned inner pictures (dominants of the collective unconscious, see Jung) are the psychic manifestations of the archetypes, but which would have to produce and condition all nature laws belonging to the world of matter. The nature laws of matter would then be the physical manifestation of the archetypes."

"The modern scientific concept of Matter first emerged between the 17th and 18th centuries, and therefore has no continuity or homogeneity with Democritus, Epicurus and Lucretius."

"Matter is substance that may be perceived through the medium of the senses. It has form, colour, weight, taste, smell; is hard or soft, moveable, or immoveable. Those who are acquainted with the principles of Natural Philosophy, will perceive that some of these properties are inherent in matter, and that others depend on circumstances. The human body is a material substance; that is, it has the properties of matter—so has a stone or a rock."

"What is mind? no matter; what is matter? never mind."

"We must therefore not be discouraged by the difficulty of interpreting life by the ordinary laws of physics. For that is just what is to be expected from the knowledge we have gained of the structure of living matter. We must also be prepared to find a new type of physical law prevailing in it. Or are we to term it a non-physical, not to say a super-physical, law?"

"Matter and energy seem granular in structure, and so does "life", but not so mind."

"My opinion concerning God differs widely from that which is ordinarily defended by modern Christians. For I hold that God is of all things the cause immanent, as the phrase is, not transient. I say that all things are in God and move in God, thus agreeing with Paul, and, perhaps, with all the ancient philosophers, though the phraseology may be different ; I will even venture to affirm that I agree with all the ancient Hebrews, in so far as one may judge from their traditions, though these are in many ways corrupted. The supposition of some, that I endeavour to prove in the Tractatus Theologico-Politicus the unity of God and Nature (meaning by the latter a certain mass or corporeal matter), is wholly erroneous."

"To those who ask why God did not so create all men, that they should be governed only by reason, I give no answer but this: because matter was not lacking to him for the creation of every degree of perfection from highest to lowest; or, more strictly, because the laws of his nature are so vast, as to suffice for the production of everything conceivable by an infinite intelligence."

"The matter which we suppose to be the main constituent of the universe is built out of small self-contained building-blocks, the chemical atoms. It cannot be repeated too often that the word "atom" is nowadays detached from any of the old philosophical speculations: we know precisely that the atoms with which we are dealing are in no sense the simplest conceivable components of the universe. On the contrary, a number of phenomena, especially in the area of spectroscopy, lead to the conclusion that atoms are very complicated structures. So far as modern science is concerned, we have to abandon completely the idea that by going into the realm of the small we shall reach the ultimate foundations of the universe. I believe we can abandon this idea without any regret. The universe is infinite in all directions, not only above us in the large but also below us in the small. If we start from our human scale of existence and explore the content of the universe further and further, we finally arrive, both in the large and in the small, at misty distances where first our senses and then even our concepts fail us."

"What matter itself is we know not, but its properties and powers are essentially opposite, "toto genere," to those of mind. From the Infinite Mind matter in its nature must stand yet more perfectly distinct. It has even been argued that, since the effect cannot possess qualities which are not in the cause, and since the effect, in this instance, is material, the cause must be material also; or if the Infinite One be purely spiritual, then matter can be no creation but must have existed eternally. ...But it is not necessary that the effect should be of the same nature with the cause."

"In 1763 a Croatian Jesuit named Roger Joseph Boscovich (1711 - 1787) identified the ultimate implication of this mechanical atomic theory. One of the crucial aspects of Isaac Newton's laws of motion is their predictive capability. If we know how an object is moving at any instant - how fast, and in which direction - and if, furthermore, we know the forces acting on it, we can calculate its future trajectory exactly. This predictability made it possible for astronomers to use Newton's laws of motion and gravity to calculate, for example, when future solar eclipses would happen. Boscovich realized that if all the world is just atoms in motion and collision, then an all-seeing mind "could, from a continuous arc described in an interval of time, no matter how small, by all points of matter, derive the law [that is, a universal map] of forces itself … Now, if the law of forces were known, and the position, velocity and direction of all the points at any given instant, it would be possible for a mind of this type to foresee all the necessary subsequent motions and states, and to predict all the phenomena that necessarily followed from them.""

"We have come a long way from the classical ideal of objective descriptions. In quantum mechanics the departure from this ideal has been even more radical. We can still use the objectifying language of classical physics to make statements about observable facts. For instance, we can say that a photographic plate has been blackened, or that cloud droplets have formed. But we can say nothing about the atoms themselves."

"Who sees the future? Let us have free scope for all directions of research; away with dogmatism, either atomistic or anti-atomistic!"

"It seems not absurd to conceive that at the first Production of mixt Bodies, the Universal Matter whereof they among other Parts of the Universe consisted, was actually divided into little Particles of several sizes and shapes variously mov'd."

"Neither is it impossible that of these minute Particles divers of the smallest and neighbouring ones were here and there associated into minute Masses or Clusters, and did by their Coalitions constitute great store of such little primary Concretions or Masses as were not easily dissipable into such Particles as compos'd them."

"I shall not peremptorily deny, that from most of such mixt Bodies as partake either of Animal or Vegetable Nature, there may by the Help of the Fire, be actually obtain'd a determinate number (whether Three, Four or Five, or fewer or more) of Substances, worthy of differing Denominations."

"It may likewise be granted, that those distinct Substances, which Concretes generally either afford or are made up of, may without very much Inconvenience be call'd the Elements or Principles of them."

"And, to prevent mistakes, I must advertize You, that I now mean by Elements, as those Chymists that speak plainest do by their Principles, certain Primitive and Simple, or perfectly unmingled bodies; which not being made of any other bodies, or of one another, are the Ingredients of which all those call'd perfectly mixt Bodies are immediately compounded, and into which they are ultimately resolved: now whether there be any one such body to be constantly met with in all, and each, of those that are said to be Elemented bodies, is the thing I now question."

"Fraunhofer's publication of 1814 did not receive prompt recognition, nor did his papers of 1821 and 1823. Physicists were fighting over the emission and wave theories of light. The attention of chemists was concentrated upon Dalton's atomic theory and the Berthollet-Proust controversy over the law of definite proportions. The full explanation of the new fact brought forth by Fraunhofer was not given for nearly forty years. He himself had failed to find the key to the hieroglyphics of the solar lines, the "Fraunhofer lines," nor had he clearly defined the role which the spectral lines were destined to play in chemical analysis."

"To try to make a model of an atom by studying its spectrum is like trying to make a model of a grand piano by listening to the noise it makes when thrown downstairs."

"In 1738 Daniel Bernoulli correctly derived Boyle's law by assuming gases consisted of collections of particles that continuously collided with the container walls."

"Dalton did not propose atoms as an abstraction or mathematical device; Dalton's atoms were physical. ...Despite its foundation in dubious hypothesis and its erroneous initial results, Dalton's theory was just the breakthrough that was needed. For the first time it allowed chemists to interpret mass relationships rationally."

"I have raised a question which may be regarded as heretical. At the time when our modern conception of chemistry first dawned... the average chemist... accepted the elements as ultimate facts... absolutely simple, incapable of transmutation or decomposition, each a kind of barrier behind which we could not penetrate. ...[H]e said they were self-existent from all eternity ...But in our times... we cannot help asking what are the elements, whence do they come, what is their signification? ...These elements perplex us in our researches, baffle us in our speculations, and haunt us in our very dreams. They stretch like an unknown sea before us—mocking, mystifying and murmuring strange revelations and possibilities. If I venture to say that... elements are not simple and primordial... but have evolved from simpler matters—or... one sole kind of matter—I... give formal utterance to an idea... for some time "in the air" of science. Chemists, physicists, philosophers of the highest merit declare explicitly their belief that the seventy... elements of our text-books are not the which we must never hope to pass."

"Sweet exists by convention, bitter by convention, colour by convention; atoms and Void (alone) exist in reality."

"By convention (νόμω) sweet is sweet, by convention bitter is bitter, by convention hot is hot, by convention cold is cold, by convention color is color. But in reality there are atoms and the void. That is, the objects of sense are supposed to be real and it is customary to regard them as such, but in truth they are not. Only the atoms and the void are real"

"There cannot exist any atoms or parts of matter that are of their own nature indivisible. For however small we suppose these parts to be, yet because they are necessarily extended, we are always able in thought to divide any one of them into two or more smaller parts, and may accordingly admit their divisibility. ...and although we should even suppose that God had reduced any particle of matter to a smallness so extreme that it did not admit of being further divided, it would nevertheless be improperly styled indivisible, for though God had rendered the particle so small that it was not in the power of any creature to divide it, he could not however deprive himself of the ability to do so... Wherefore, absolutely speaking, the smallest extended particle is always divisible..."

"If the idea of physical reality had ceased to be purely atomic, it still remained for the time being purely mechanistic; people still tried to explain all events as the motion of inert masses; indeed no other way of looking at things seemed conceivable. Then came the great change, which will be associated for all time with the names of Faraday, Clerk Maxwell, and Hertz."

"If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generation of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis... that all things are made of atoms — little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence, you will see, there is an enormous amount of information about the world, if just a little imagination and thinking are applied."

"The atomic theory was not generally accepted in the time of Democritus, largely because of its deterministic character, for it allows no chance, choice, or free will."

"The problem was that although ideas like statistical mechanics and the kinetic theory worked at the practical level to provide a mathematical description of what was going on, nobody had seen atoms—more to the point, given the technology of the time it was physically impossible to see atoms. This left the door open to for philosophers such as Ernst Mach to argue that the atomic hypothesis was no more than a hypothesis, what is known as a heuristic device, meaning just because things in the macroscopic world behave as if they were made of atoms that doesn't prove that they are... Mach regarded atoms as no more than a convenient fiction, which provided a basis for physicists to make calculations; anything that could not be detected by the human senses, he argued, was not the proper subject of scientific debate. Einstein disagreed, and argued the case for atoms with his friends. He became obsessed with the idea, and determined that if no one else could prove that atoms were real, he would do it himself."

"In the Brownian motion paper, Einstein... calculations involved the relationship between osmotic pressure, viscosity, and the way individual particles suspended in the liquid diffuse... He realized that the kick produced by a single molecule hitting a particle as large as a pollen grain could not produce a measurable shift... But the large particle is constantly being bombarded... if you take a very small time interval, then just by chance at that instant the particle will be receiving more kicks on one side. The combined effect will shift the particle by a minute amount... Einstein discovered that it gradually moved farther from its starting point... as a random walk. He showed the distance ... depends on the square root of the time... This is called "root mean square" displacement and the equation Einstein worked out for displacement involves the temperature of the liquid, its viscosity, the radius of the particle and Avogadro's number. ...He also realized that if the predicted displacement could be measured... the same equation... could be used to give a value of Avogadro's number. ...It was extremely difficult to make the observations... but in 1908... Jean-Baptiste Perrin finally succeeded. ...Perrin's results exactly matched the predictions from Einstein's theory. ...The whole package finally established the reality of atoms and molecules, and the validity of the kinetic theory..."

"Light and matter are both single entities, and the apparent duality arises in the limitations of our language. It is not surprising that our language should be incapable of describing the processes occurring within the atoms, for, as has been remarked, it was invented to describe the experiences of daily life, and these consist only of processes involving exceedingly large numbers of atoms. Furthermore, it is very difficult to modify our language so that it will be able to describe these atomic processes, for words can only describe things of which we can form mental pictures, and this ability, too, is a result of daily experience. Fortunately, mathematics is not subject to this limitation, and it has been possible to invent a mathematical scheme — the quantum theory — which seems entirely adequate for the treatment of atomic processes; for visualisation, however, we must content ourselves with two incomplete analogies — the wave picture and the corpuscular picture."

"The thought of the great epistemological difficulties with which the visual atom concept of earlier physics had to contend gives us the hope that the abstracter atomic physics developing at present will one day fit more harmoniously into the great edifice of Science."

"There is a fundamental error in separating the parts from the whole, the mistake of atomizing what should not be atomized. Unity and complementarity constitute reality."

"It was the quantitative relationship between electrochemical change and current which interested Faraday... It was not until after Faraday's death that the significance of his laws of electrolysis for atomic theory was realized. In 1881 von Helmholtz pointed out that if elementary substances are composed of atoms, it follows from Faraday's laws of electrolysis that electricity also is composed of elementary portions which behave like atoms of electricity. Investigations on the conduction of electricity by gases led to the identification of the electron as the fundamental unit of electricity at the end of the century. Faraday's positive and negative ions are therefore atoms (or groups of atoms or radicals) with a deficiency or an excess of an integral number of electrons, where the integral number is the valency of the atom. The ions move in opposite directions through the solution to the electrodes where their charges are neutralised, causing them to be discharged to neutral atoms or radicals. These are the primary electrode reactions, of which the deposition of silver on a platinum cathode in the silver coulometer is a typical example."

"I adopt Mr. Darwin's hypothesis, therefore, subject to the production of proof that physiological species may be produced by selective breeding; just as a physical philosopher may accept the undulatory theory of light, subject to the proof of the existence of the hypothetical ether; or as the chemist adopts the atomic theory, subject to the proof of the existence of atoms; and for exactly the same reasons, namely, that it has an immense amount of primâ facie probability: that it is the only means at present within reach of reducing the chaos of observed facts to order; and lastly, that it is the most powerful instrument of investigation which has been presented to naturalists since the invention of the natural system of classification and the commencement of the systematic study of embryology."

"With respect to the ultimate constitution of... masses, the same two antagonistic opinions which had existed since the time of Democritus and of Aristotle were still face to face. According to the one, matter was discontinuous and consisted of minute indivisible particles or atoms, separated by a universal vacuum; according to the other, it was continuous, and the finest distinguishable, or imaginable, particles were scattered through the attenuated general substance of the plenum. A rough analogy to the latter case would be afforded by granules of ice diffused through water; to the former, such granules diffused through absolutely empty space."

"In the latter part of the eighteenth century, the chemists had arrived at several very important generalisations... However plainly ponderable matter seemed to be originated and destroyed in their operations, they proved that, as mass or body, it remained indestructible and ingenerable... a certain number of the chemically separable kinds of matter were unalterable by any known means (except in so far as they might be made to change their state from solid to fluid, or vice versâ)... and that the properties of these several kinds of matter were always the same, whatever their origin. All other bodies were found to consist of two or more of these, which thus took the place of the four 'elements' of the ancient philosophers. Further, it was proved that, in forming chemical compounds, bodies always unite in a definite proportion by weight, or in simple multiples of that proportion, and that, if any one body were taken as a standard, every other could have a number assigned to it as its proportional combining weight. It was on this foundation of fact that Dalton based his re-establishment of the old atomic hypothesis on a new empirical foundation."

"The gradual reception of the undulatory theory of light necessitated the assumption of the existence of an 'ether' filling all space. But whether this ether was to be regarded as a strictly material and continuous substance was an undecided point, and hence the revived atomism escaped strangling in its birth. For it is clear, that if the ether is admitted to be a continuous material substance, Democritic atomism is at an end and Cartesian continuity takes its place."

"The real value of the new atomic hypothesis... did not lie in the two points which Democritus and his followers would have considered essential—namely, the indivisibility of the 'atoms' and the presence of an interatomic vacuum—but in the assumption that, to the extent to which our means of analysis take us, material bodies consist of definite minute masses, each of which, so far as physical and chemical processes of division go, may be regarded as a unit—having a practically permanent individuality. ...that smallest material particle which under any given circumstances acts as a whole."

"At times the success of a concept in one area of science may have a retarding effect upon progress in other areas. ..."the Law of Definite Proportions," was established... only after a long battle between Berthollet and Proust. The success of the Proust position was so decisive that the matter received little critical study during the decades which followed. Possibly this was for the best as far as the progress of chemistry was concerned. Had chemists concerned themselves with the composition of solutions, glasses, and alloys the establishment of atomic theory might have been even slower than it was."

"Anyone who had studied the vicissitudes of atomic theory during the period between 1810 and 1860 recognizes the tremendous problems which faced chemists of that day in connection with atomic weights, equivalent weights, reliable formulas, and matters of that sort. The Law of Definite Proportions was a useful concept in helping bring order out of chaos. ...Had chemists had to face the fact of variable composition in some of their common compounds it is doubtful if atomic theory might have been established as soon as it was. It is in solid state chemistry that the Law of Definite Proportions has been found wanting. Not only in the case of metallic compounds are peculiar atomic ratios of the component elements to be found, but even in such solids as metallic oxides and sulfides. Ferrous oxide (FeO) presents a particularly fine example... Although the compound is frequently mentioned in freshman chemistry courses to illustrate the Law of Definite Proportions... on accurate analysis... the ratio is somewhat between the range of 0.84 to 0.95 atoms of iron per atom of oxygen. ...The existence of a considerable number of such compounds has led to the proposal that compounds be classified as Berthollides and Daltonides; the term Berthollide referring to such compounds as cuprous sulfide with a somewhat variable domposition, and Daltonide referring to those with precisely fixed atomic ratios."

"It is sometimes desirable to have experimental data which is not completely precise. Had Berthollet been successful in convincing the chemical world that compounds do not have fixed proportions, the development of the atomic theory would have been greatly hindered. The fact that the Proust position became the accepted one in view of the work of Dalton, meant that the trials and errors toward a successful formulation of chemical compounds would ultimately succeed on the basis of an atomic philosophy. Once the atomic philosophy was clearly developed, the existence of the Berthollides could still be incorporated into chemical philosophy on the basis of studies of solid state physics. This illustrates clearly... the fact that science progresses from one state of approximation to another, and that progress may well be hindered when so much precise information is available that broad and useful concepts are overlooked."

"Now his principal doctrines were these. That atoms and the vacuum were the beginning of the universe; and that everything else existed only in opinion."

"His opinions are these. The first principles of the universe are atoms and empty space; everything else is merely thought to exist. The worlds are unlimited; they come into being and perish. Nothing can come into being from that which is not nor pass away into that which is not. Further, the atoms are unlimited in size and number, and they are borne along in the whole universe in a vortex, and therby generate all composite things – fire, water, air, earth; for even these are conglomerations of given atoms. And it is because of their solidity that these atoms are impassive and unalterable. The sun and the moon have been composed of such smooth and spherical masses [i.e. atoms], and so also the soul, which is identical with reason. We see by virtue of the impact of images upon our eyes."

"All those who maintain a vacuum are more influenced by imagination than by reason. When I was a young man, I also gave in to the notion of a vacuum and atoms; but reason brought me into the right way. ...The least corpuscle is actually subdivided in infinitum, and contains a world of other creatures, which would be wanting in the universe, if that corpuscle was an atom, that is, a body of one entire piece without subdivision. In like manner, to admit a vacuum in nature, is ascribing to God a very imperfect work... space is only an order of things as time also is, and not at all an absolute being. ...Now, let us fancy a space wholly empty. God could have placed some matter in it, without derogating in any respect from all other things: therefore he hath actually placed some matter in that space: therefore, there is no space wholly empty: therefore all is full. The same argument proves that there is no corpuscle, but what is subdivided. ...there must be no vacuum at all; for the perfection of matter is to that of a vacuum, as something to nothing. And the case is the same with atoms: What reason can any one assign for confining nature in the progression of subdivision? These are fictions merely arbitrary, and unworthy of true philosophy. The reasons alleged for a vacuum, are mere sophisms."

"Loschmidt reasoned that in a liquid, the atoms or molecules would be more or less squeezed up against each other, so the volume of a liquid would be straightforwardly the volume of an individual molecule multiplied by the number of them. ...The diameter he came up with was a little less than one millionth of a millimeter—by modern standards a pretty fair answer. ...To critics... Loschschmidt's analysis still didn't prove anything. ...in the absence of tangible evidence that atoms existed, it was mere mathematics, empty theorizing. Loschmidt had shown that if atoms existed, they must have a certain size—but that first "if" had not been overcome."

"Traditionally, [physics] had concerned itself with searching out quantitative relationships between measurable phenomena... To go beyond this, to explain observable facts in terms of unobservable but alledgedly "real" entities such as atoms, was to go beyond what many physicists regarded as the limits of their discipline. What was happening in the second half of the 19th century, was the birth of the subject we now call theoretical physics... a puzzling innovation. ...As well as having a hand in kinetic theory, ...In 1864, ...Maxwell's theory introduced a new idea, the electromagnetic field. Over atoms and electromagnetic fields, the same question arose: real or imaginary?"

"The last thirty years have seen the beginning and development of a new period in physics and chemistry, namely the atomic period. In contrast to the period preceding it where nature's processes were described in terms of continua, recent developments have emphasized the discrete structure of the submicroscopic universe. Thus, today one hears of the atoms of matter, the atoms of electricity, and even the atoms of energy, the quanta. ...[T]he atomic theory of matter is the oldest and perhaps the most complete. ...[B]ecause of its relative simplicity the problem of the atomic theory of gases, in the form of the kinetic theory of gases, has attained the highest degree of perfection in this field. Its admirable methods of analysis are therefore indispensable..."

"Heraclitus. ...change and incessant movement is the basis, and the only basis, of all things and that what is illusory is the idea of a central, or indeed of any other, unity: the Universe is a stream of incessant and infinitely minute changes. The Atomists. From this springs naturally the atomistic theory of Leucippus and Democritus. This theory is an endeavour to give a sort of solidity and reality to the mutability of Heraclitus, whilst retaining his controversial advantages in the denial of an all-embracing One. The veritable original of things is taken by these Atomists to be, not one, but innumerable, indefinitely minute, homogeneous atoms, the mere mechanical combination of which makes up the variety of nature."

"However well fitted atomic theories may be to reproduce certain groups of facts, the physical inquirer who has laid to heart Newton's rules will only admit those theories as provisional helps. and will strive to attain, in some more natural way, a satisfactory substitute."

"The atomic theory plays a part in physics similar to that of certain auxilliary concepts in mathematics; it is a mathematical model for facilitating the mental reproduction of facts. Although we represent vibrations by the harmonic formula, the phenomena of cooling by exponentials, falls by squares of times, etc., no one will fancy that vibrations in themselves have anything to do with the circular functions, or the motions of falling bodies with squares. It has simply been observed that the relations between the quantities investigated were similar to certain relations obtaining between familiar mathematical functions, and these more familiar ideas are employed as an easy means of supplementing experience. Natural phenomena whose relations are not similar to those functions with which we are familiar, are at present very difficult to reconstruct. But the progress of mathematics may facilitate the matter."

"Avogadro... suggested in 1811 that the same volumes of different gases contain the same number of particles under the same conditions of temperature and pressure. ...Avogadro's hypothesis raised the difficulty that when one volume of hydrogen combined with one volume of chlorine, two volumes of hydrogen chloride were produced, implying that the atoms of hydrogen and chlorine were split into halves during the process of combination. Avogadro overcame this difficulty by supposing that the fundamental particles of hydrogen, chlorine, and other gases, were molecules containing two atoms of the element, and that chemical combination between two gases resulted in the splitting up of the elementary molecules and the formation of compound molecules in which there was one atom of each element... Avogadro's hypothesis... was not accepted until the 1860's, as it demanded that the atoms of the same element should combine together to form molecules. Dalton and others rejected such a conception, for they held that like atoms must repel one another and could not combine. Moreover, Dalton... thought that the various species of atoms differed not only in their atomic weights, but also in their sizes, and the number per unit volume in the gaseous state."

"In studying the constitution of bodies we are forced from the very beginning to deal with particles which we cannot observe. For whatever may be our ultimate conclusions as to molecules and atoms, we have experimental proof that bodies may be divided into parts so small that we cannot perceive them. Hence, if we are careful to remember that the word particle means a small part of a body, and that it does not involve any hypothesis as to the ultimate divisibility of matter, we may consider a body as made up of particles, and we may also assert that in bodies or parts of bodies of measurable dimensions, the number of particles is very great indeed."

"The ancient Greek philosopher, Democritus, propounded an hypothesis of the constitution of matter, and gave the name of atoms to the ultimate unalterable parts of which he imagined all bodies to be constructed. In the 17th century, Gassendi revived this hypothesis, and attempted to develope it, while Newton used it with marked success in his reasonings on physical phenomena; but the first who formed a body of doctrine which would embrace all known facts in the constitution of matter, was Roger Joseph Boscovich, of Italy, who published at Vienna, in 1759, a most important and ingenious work, styled Theoria Philosophiæ Naturalis ad unicam legem virium, in Natura existentium redacta. This is one of the most profound contributions ever made to science; filled with curious and important information, and is well worthy of the attentive perusal of the modern student. In more recent days, the theory of Boscovich has received further confirmation and extension in the researches of Dalton, Joule, Thomson, Faraday, Tyndall, and others."

"The atomic theory may be regarded in two distinct ways, ...The older and vague atomic theory professed to be a theory of the constitution of bodies and to afford the basis for a physical explanation of physical phenomena; in order to do this, forces of attraction and repulsion between the particles of matter had to be assumed, and elaborate calculations as to the integral or resultant effect of these elementary forces had to be instituted, or at least formulated. ...ingenious as those theories were, they led to no results in the direction of the calculation of the molar and molecular properties of bodies, or if they did, they yielded none which could not be gained by the opposite view which regarded matter as continuous. The atomic theory, however, did good service from another point of view, when through Richter, Dalton, Proust, and Berzelius the fact that bodies combine only in definite proportions of weight, or their simple multiples, became firmly established. The authors of this discovery were driven to the atomic view of matter as the most convenient method of expressing the formulæ of chemical compounds."

"There is here a whole new branch of spectroscopy, which is sure to tell one much about the nature of an atom."

"In... A New System of Chemical Philosophy published in 1808, John Dalton laid the foundations of the atomic theory: he assumed chemical action to be an action between very minute particles of elements and compounds, and all the minute particles of the same element, or compound, to be exactly the same size and weight. ...his hypothesis assumed the accuracy and universal applicability of those generalisations which are now called the laws of chemical combination."

"Now, if the molecules possess anything which is ever so distantly related to sensation, and we cannot doubt it, since each one feels the presence, the certain condition, the peculiar forces of the other, and, accordingly, has the inclination to move, and under circumstances really begins to move—becomes alive as it were; moreover, since such molecules are the elements which cause pleasure and pain; if, therefore, the molecules feel something that is related to sensation, then this must be pleasure, if they can respond to attraction and repulsion, i.e. follow their inclination or disinclination; it must be displeasure if they are forced to execute some opposite movement, and it must be neither pleasure nor displeasure if they remain at rest."

"If a fluid be composed of particles mutually flying [fleeing from] each other, and the density be as the compression, the centrifugal forces [repulsion] of the particles will be reciprocally proportional to the distances of their centres. And, vice versa, particles flying each other with forces that are reciprocally proportional to the distances of their centres, compose an elastic [liquid or gas], whose density is as the compression."

"Dalton, the mathematical tutor, following up the lead of Newton, combined the whole of the results of quantitative measurement which had accumulated up to his time, in a comprehensive theory, based on the concept of the chemical atom."

"The results of a scrutiny of the materials of chemical science from a mathematical standpoint are pronounced in two directions. In the first we observe crude, qualitative notions, such as fire-stuff, or phlogiston, destroyed; and at the same time we perceive definite measurable quantities such as fixed air, or oxygen, taking their place. In the second direction we notice the establishment of generalizations, laws, or theories, in which a mass of quantitative data is reduced to order and made intelligible. Such are the law of conservation of matter, the laws of chemical combination, and the atomic theory."

"The Atomic Theory and the Periodic Law have been given prominence, since their neglect unfailingly leads to obscurity and triviality."

"The old mechanical and atomic hypotheses have, during recent years, become so plausible that they have ceased to seem like hypotheses; atoms are no longer just a convenient fiction. It seems almost as if we could see them, now that we know how to count them. ...The kinetic theory of gases has thus received unexpected corroboration. ...The remarkable counting of the number of atoms by Perrin completed the triumph of the atomic theory. ...In the processes used with the Brownian phenomenon, or in those used for the law of radiation, we do not deal directly with the number of atoms, but with their degrees of freedom of movement. In that process where we consider the blue of the sky, the mechanical properties of the atoms come into play; the atoms are looked upon as producing an optical discontinuity. ...The atom of the chemist is now a reality. But that does not mean that we have reached the ultimate limit of the divisibility of matter. When Democritus invented the atom he considered it as the absolutely indivisible element within which there would be nothing further to distinguish. That is what the word meant in Greek. ... the atom of the chemist would not have satisfied him since that is not indivisible; it is not a true element; it is not free from mystery, from secrets. The chemist's atom is a universe. Democritus would have considered, even after so much trouble in finding it, that we were still only at the beginning of our search—these philosophers are never satisfied. ...This atom disintegrates into yet smaller atoms. What we call radioactivity is the perpetual breaking up of atoms. ...Each atom is like a sort of solar system where the small negative electrons play the role of planets revolving around the great... sun. ...the atom of a radioactive body is a universe within itself and a world subject to chance."

"The study of the radio-active substances and of the discharge of electricity through gases has supplied very strong experimental evidence in support of the fundamental ideas of the existing atomic theory. It has also indicated that the atom itself is not the smallest unit of matter but is a complicated structure made up of a number of smaller bodies."

"What we are nowadays hearing of the language of spectra is a true 'music of the spheres' in order and harmony that becomes ever more perfect in spite of the manifold variety. The theory of spectral lines will bear the name of Bohr for all time. But yet another name will be permanently associated with it, that of Planck. All integral laws of spectral lines and of atomic theory spring originally from the quantum theory. It is the mysterious organon on which Nature plays her music of the spectra, and according to the rhythm of which she regulates the structure of the atoms and nuclei."

"The atomistic theory of matter appears in well established and elaborated form in various systems of Hindu philosophy... The oldest of these systems... appears to be that of the Vaiseshika, attributed to Kanada... Whether or no the... theory antedated Democritus... is... uncertain. Professor Garbe's opinion is that beyond a doubt the Indian theory is a long time after the theory of Leucippus and Democritus. L. Mabilleau, on the other hand, considers the Vaiseshika system as several centuries earlier than Democritus. ...This theory recognizes nine distinct entities constituting the universe. These are earth, water, fire, air (or wind), ether (akasa), time, space, soul, and "manas." ...Time, space, and soul are not material, though existent. The "manas" is the medium through which impressions of sense are conveyed to the soul. The first four, therefore, correspond to the four elements of Empedocles; the fifth, ether, can be compared with little similarity to the ether of Aristotle. The first four elements are composed of atoms which are eternal, never created nor destroyed. Each of these four elements exists as atoms and also as aggregates of atoms. As atoms, they are imperishable. The elements which we see or feel are aggregates of atoms and as such are subject to change, but the atoms, which are invisible, do not change. ...Akasa, or ether, is assumed not to consist of atoms, but is infinite in extent, continuous and eternal. It cannot be apprehended by the senses, but is the carrier of sound. It is also described... as all-pervasive, occupying the same space that is occupied by the various forms of matter, and therefore devoid of the property of impenetrability, characterizing the atoms of other elements."

"Boyle entertains the hypothesis of a universal matter, the concept of atoms of different shapes and sizes, and the possibility of existence of substances that might properly be called elements... The atomic theory as originally conceived by Democritus and Epicurus, developed by Lucretius, and resurrected by Gassendi from about 1647 on, was doubtless the source from which Boyle derived his ideas, ...as he cites both Epicurus and Gassendi. Boyle, however... avoids any dogmatic assertion of these hypotheses. It is plain, however, that these atoms or "corpuscles" as he calls them are a constant element of his thought."

"The final step... came in the late 1850s. Up to that time [evidence supporting] the atomic theory had been entirely... chemical... Within... physics, however, the theory had made little progress beyond the brilliant guesswork of Newton's Optics. As a result of Clausius' and Maxwell's new theory of heat and gases, physics at last caught up with chemistry. ...This theory was not entirely new. In outline its mathematical foundations had been worked out [as early as the 1730s] by Daniel Bernoulli... [who] demonstrated that random agitation of the atoms of air would explain Boyle's Law just as well as Newton's theory of repulsive forces; but although ... extended this explanation into a dynamical theory of heat it remained a minority view... overshadowed by Boerhaave's and Lavoisier's [heat as a] material theory. Around 1800... a few... were positively sceptical about caloric... Benjamin Thompson... observed that friction would generate unlimited quantities of heat... though... the material theory retained the allegiance of leading scientists for another half-century."

"Between Bernoulli and Maxwell... Euler, d'Alembert, Lagrange and Hamilton expounded Newton's dynamics] in more and more general forms, until at last all [mechanical] processes... were seen as conforming to... the Principle of the Conservation of Energy, and the Principle of Least Action. This mathematical drive... continued, overflowing beyond... mechanics... [and into] processes involving nonmechanical factors: heat, electricity, vitality, and chemical change... The most comprehensive exposition was given in 1847 by Hermann von Helmholtz... In 1848, J. P. Joule [demonstrated that]... whether he produced heat by the passage of an electric current, or by mechanical effort, the conversion took place at fixed, measurable rates. ...[I]t was natural to look again for an explanation ...Perhaps the production of heat by friction merely transferred mechanical energy from a visible level to an invisible one... the increased motion of the molecules... Clausius and Maxwell turned this view... into a fully-developed branch of mathematics (...from 1857 to 1866.) ...[H]eat theory had been united into the general theory of 'matter in motion'... the random agitation of vast numbers of invisibly-small particles."

"From Dalton in 1803 to Maxwell in 1866 the atomic picture of matter had progressively taken on shape and detail: by Maxwell's time it... lay at the heart of the classical system. ...all matter was composed of ponderable atoms and, with the 'death' of caloric, the division between corporeals and incorporeals became absolutely sharp. The known incorporeal agencies—radiant heat, light, magnetisim and electricity—had to be dealt with in terms of other concepts."

"The question whether our elementary atoms are in their nature indivisible, or whether they are built up of smaller particles, is one upon which I, as a chemist, have no hold whatever, and I may say that in chemistry the question is not raised by any evidence whatever."

"The physical doctrine of the atom has got into a state which is strongly suggestive of the epicycles of astronomy before Copernicus."

"The absence of effects due to the earth's motion relative to the ether can be explained on the electromagnetic theory if it is supposed that this theory covers all phenomena. This appears to be a strong argument in favor of the purely electrical nature of matter. It will be convenient now to mention the chief electrical theories of atomic structure which have been proposed. According to Sir J. J. Thomson, atoms consist of solid spheres of positive electricity inside which negative electrons move about freely. ...The electrons will distribute themselves uniformly throughout the sphere so as to neutralize it as completely as possible and can vibrate about their positions of equilibrium. According to Sir J. Larmor, atoms consist of a number of positive and negative electrons describing orbits about each other. ...On this view an atom is a sort of small gaseous nebula without any sort of solid foundation. A third theory recently adopted by Rutherford regards the atom as containing a nucleus of positive electricity with negative electrons outside it; probably describing orbits around it. On this view the atom is a sort of minute solar system. The positive nucleus... provides a definite foundation fixing the identity of the atom. The same may be said of the sphere in Sir J. J. Thomson's theory. ... The most important property of atoms is their extraordinary stability... Negative electrons can be knocked out of atoms by the impact of rapidly moving particles such as the cathode rays and α rays, yet the atoms retain their identity and after regaining negative electrons are unaffected. Facts like these appear to be decisive against Sir J. Larmor's theory. ... These [monatomic] gases ...give spectra containing many lines so that it is certain that their atoms contain electrons which can vibrate. It is necessary to suppose that collisions between these atoms do not set their electrons in vibration, which seems to require the electrons to be protected in some way. This seems to be strongly in favor of Sir J. J. Thomson's theory and against the other two theories, for if the electrons were describing orbits outside it is hard to see how they could escape violent disturbance during a collision. ... Sir J. Larmor's theory and Rutherford's planetary theory are difficult to reconcile with the idea that atoms become firmly fixed together in compounds and rigid solids. On such theories we should expect to have nothing but gases and liquids and only very simple compounds. ... The scattering of α rays led Rutherford to adopt the idea of a positive nucleus, since some α rays are turned through a larger angle than can be explained by the electric forces due to a charge equal to that on one electron. It may be, however, that other forces besides ordinary electric force act on α rays when moving through matter. The α rays are helium atoms which have a radius about 10-8 cm., so that they probably only get through by displacing the atoms of the matter. If we suppose the positive sphere of one atom can not penetrate into that of another then the scattering of a rays by matter can probably be explained on Sir J. J. Thomson's theory."

"Have not the small Particles of Bodies certain Powers, Virtues, or Forces, by which they act at a distance, not only upon the Rays of Light for reflecting, refracting, and inflecting them, but also upon one another for producing a great Part of the Phænomena of Nature? For it's well known that Bodies act one upon another by the Attractions of Gravity, Magnetism, and Electricity; and these Instances shew the Tenor and Course of Nature, and make it not improbable but that there may be more attractive Powers than these. For Nature is very consonant and conformable to her self. How these Attractions may be perform'd, I do not here consider. What I call Attraction may be perform'd by impulse, or by some other means unknown to me. I use that Word here to signify only in general any Force by which Bodies tend towards one another, whatsoever be the Cause. For we must learn from the Phenomena of Nature what Bodies attract one another, and what are the Laws and Properties of the Attraction, before we enquire the Cause by which the Attraction is perform'd. The Attractions of Gravity, Magnetism, and Electricity, reach to very sensible distances, and so have been observed by vulgar Eyes, and there may be others which reach to so small distances as hitherto escape Observation; and perhaps electrical Attraction may reach to such small distances, even without being excited by Friction."

"And when Water and Oil of Vitriol poured successively into the same Vessel grow very hot in the mixing, does not this Heat argue a great Motion in the Parts of the Liquors? And does not this Motion argue, that the Parts of the two Liquors in mixing coalesce with Violence, and by consequence rush towards one another with an accelerated Motion?"

"And when Aqua fortis, or Spirit of Vitriol poured upon Filings of Iron, dissolves the Filings with a great Heat and Ebullition, is not this Heat and Ebullition effected by a violent Motion of the Parts, and does not that Motion argue that the acid Parts of the Liquor rush towards the Parts of the Metal with violence, and run forcibly into its Pores till they get between its outmost Particles, and the main Mass of the Metal, and surrounding those Particles loosen them from the main Mass, and set them at liberty to float off into the Water? And when the acid particles, which alone would distil with an easy Heat, will not separate from the Particles of the Metal without a very violent Heat, does not this confirm the Attraction between them?"

"And is it not from the mutual Attraction of the Ingredients that they stick together for compounding these Minerals... And the same Question may be put concerning all, or almost all the gross Bodies in Nature. For all the Parts of Animals and Vegetables are composed of Substances volatile and fix'd, fluid and solid, as appears by their Analysis; and so are Salts and Minerals, so far as Chymists have been hitherto able to examine their Composition."

"The Parts of all homogeneal hard Bodies which fully touch one another, stick together very strongly. And for explaining how this may be, some have invented hooked Atoms, which is begging the Question; and others tell us that Bodies are glued together by rest, that is, by an occult Quality, or rather by nothing; and others, that they stick together by conspiring Motions, that is, by relative rest amongst themselves. I had rather infer from their Cohesion, that their Particles attract one another by some Force, which in immediate Contact is exceeding strong, at small distances performs the chymical Operations above-mention'd, and reaches not far from the Particles with any sensible Effect."

"If two plane polish'd Plates of Glass... be laid together, so that their sides be parallel and at a very small distance from one another, and then their lower edges be dipped into Water, the Water will rise up between them. And the less the distance of the Glasses is, the greater will be the height to which the Water will rise. ...And in like manner, Water ascends between two Marbles polish'd plane, when their polished sides are parallel, and at a very little distance from one another. And if slender Pipes of Glass be dipped at one end into stagnating Water, the Water will rife up within the Pipe, and the height to which it rises will be reciprocally proportional to the Diameter of the Cavity of the Pipe, and will equal the height to which it rises between two Planes of Glass, if the Semidiameter of the Cavity of the Pipe be equal to the distance between the Planes, or thereabouts. And these Experiments succeed after the same manner in vacuo as in the open Air, (as hath been tried before the Royal Society,) and therefore are not influenced by the Weight or Pressure of the Atmosphere. ...There are therefore Agents in Nature able to make the Particles of Bodies stick together by very strong Attractions. And it is the Business of experimental Philosophy to find them out."

"And thus Nature will be very conformable to her self and very simple, performing all the great Motions of the heavenly Bodies by the Attraction of Gravity which intercedes those Bodies, and almost all the small ones of their Particles by some other attractive and repelling Powers which intercede the Particles. The Vis inertiæ is a passive Principle by which Bodies persist in their Motion or Rest, receive Motion in proportion to the Force impressing it, and resist as much as they are resisted. By this principle alone there never could have been any Motion in the World. Some other Principle was necessary for putting Bodies into Motion; and now they are in Motion, some other Principle is necessary for conserving the Motion."

"[C]onsider the scalar ... the change in the electrons' interference pattern is a nonlocal effect of the electric field in the capacitor. This nonlocal effect is action at a distance! The electric field, acting at a distance on the electrons, yields a measurable effect (the change in the electrons' interference pattern). So quantum nonlocality does permit action at a distance. There is a constraint similar to the one we guessed. It is called (relativistic) causality. The principle of causality states that there is no way to send a message faster than light. We do not expect nonrelativistic quantum mechanics to obey this principle, because in nonrelativistic quantum mechanics there is no maximum speed. However... Nonlocal quantum correlations obey causality, because they are useless for sending messages. The Aharonov-Bohm effect, too, obeys causality: ...the change in the electrons' interference pattern - lies within the future light cone of the field. In each example we find that quantum nonlocality obeys causality."

"For several centuries, there has been a strong feeling that nonlocal theories are not acceptable in physics. ...Newton felt very uneasy about action-at-a-distance and... Einstein regarded it as 'spooky'. But... one can see nothing basically irrational about such an idea. Rather it seems to be most reasonable to keep an open mind on the subject and therefore allow oneself to explore this possibility. If the price of avoiding nonlocality is to make an intuitive explanation impossible, one has to ask whether the cost is not too great."

"In the long debate about action at a distance versus contact action we also find a concern with the effective individuation of particles and subsystems and with distant action. Belief in contact action goes back to Aristotle and Eudoxes, based on the self-evident regulative principle that a thing cannot act where it is not. For them, causal explanations were essential for true science. For Descartes too, there could be no vacuum and what may appear to be empty is actually filled with an aether. After the Principia, there were basically two camps on the "gravity dilemma." The one, among whose members were the Cartesians, Leibniz, and Huygens, maintained that an ether was required to allow any intelligible explanation of gravitational phenomena. The other, notably represented by Newton's ally... , took gravity to be evidence for God's action. ...God is everywhere and, hence, "instantaneous" action... is no mystery. The basic motivating factor in demanding contact action was that of intelligibility. Maxwell put the matter quite succinctly when he argued for "a force of the old school—a case of vis a tergo—a shove from behind."

"Frans van Luteren (1991), in his extensive... study of conceptions of gravity in the eighteenth and nineteenth centuries, demonstrates that a quest for intelligibility was uppermost for several physicists who attempted [to challenge the absolute non-locality doctrine with] ether-type explanations for action-at-a-distance."

"Classical electrodynamics is generally understood to be the paradigm of a local and causal physical theory. ...[A] theory with real fields realistically appears to be a local theory. ...But what, exactly, is it for a theory to be local or nonlocal? ...Informally, locality principles are often introduced in causal terms. Newtonian graviational theory... is said to be nonlocal because it allows action-at-a-distance, while the theory of special relativity is often said to imply the locality condition that there can be no superliminal causal propogation. According to a widespread view, however, the notion of causation should have no place in fundamental physics... Thus, Bertrand Russell famously argued that in the advanced sciences the notion of functional dependency has replaced that of causation... "a relic of a bygone age..." ...Russell was wrong. ...I will appeal to Dirac's classical theory of the electron ....the most promising candidate for a fully consistent theory of classical charged particles, is causally nonlocal. ...[T]he theory allows for forces to act where they are not and for superliminal causal propogation."

"To soothe the theologians, who in his time were pressing so hardly upon Galileo, Descartes was content to say that the operation by which God maintains the world is similar to that by which he created it; so that, if it had pleased him, instead of creating it instantaneously, to allow these laws of evolution to operate, the result would have been what we now see. He began by assuming space to be occupied by perfectly homogeneous and continuous matter. He then supposed this solid substance to be divided into parcels of various shape and size, each of them animated by motion in various directions. These would observe the laws of motion as Descartes defines them:—1. Each would maintain its own condition of rest or motion or magnitude, until altered by contact with another. 2. In such contact the gain or loss of motion to one body would be exactly compensated by the loss or gain to another—the total quantity of motion in the world remaining invariable. 3. Owing to constant contacts, motion would be usually in curved lines, the moving body tending always to follow the tangent to the curve. The result after a period of time would be the differentiation of primitive matter into three kinds. The moving portions of matter, by constant attrition, would be for the most part converted into spheroidal molecules of various sizes. Some larger masses of irregular shape would amalgamate into solid masses; the finer particles rubbed off from the molecules would insert themselves between them, vibrating with far more rapid motion than they. This vibrating ethereal substance would collect towards the centre of a vortex, and form a sun or star: round it would revolve aërial matter, and plunged amidst this, at various distances, the solid masses of the planets. How by degrees yet further differentiation took place... so that the various metals and crystals arose, and finally plant life, and animal life... is described in the Principia and in the Treatise on Man."

"[L]ocality... reflects our ability to construct the "big picture" like a jigsaw puzzle, starting with a description of the most basic interactions among elementary particles."

"In fact every theory in the history of physics before quantum theory was EPR-local. So the discovery that the world is not EPR-local (i.e. that any physical theory that makes accurate predictions cannot be EPR-local) would mark a radical break in the history of physics."

"I must ask you to go over very old ground, and to turn your attention to a question which has been raised again and again ever since man began to think. The question is that of the transmission of force. We see two bodies at a distance from each other exert a mutual influence on each other's motion. Does this mutual action depend on the existence of some third thing, some medium of communication, occupying the space between the bodies, or do the bodies act on each other immediately, without the intervention of anything else? The mode in which Faraday was accustomed to look at phenomena of this kind differs from that adapted by many modern inquirers, and my special aim will be to enable you to place yourselves at Faraday's point of view, and to point out the scientific value of that conception of lines of force which, in his hands, became the key to the science of electricity. ... Why... should we not admit that the familiar mode of communicating motion by pushing and pulling... is the type and exemplification of all action between bodies, even in case in which we can observe nothing between..."

"The generation that grew up with Newtonian gravity found the theory entirely natural. For millennia, natural philosophers recoiled from nonlocality; in the eighteenth century, they embraced it. ...And no sooner did scholars get used to Newtonian nonlocality when along came another U-turn and a new generation went back to thinking that the world had to be—just had to be—local, thereby setting up our present predicament. ...Naturalistic explanations tend to be local. In our experience, when you want something to move... you need to go over and push on it... Thales suggested that earthquakes occur [not by the arbitrary will of gods, but] because the land is floating on a subterranean ocean... occasionally rocking back and forth. The cause is in direct contact with the effect. ...The concept of space was the atomists' [e.g., Democritus and Lucretius] creation. ...matter needs a venue to exist and move. ...If atoms were the athletes and space the playing field, locality was the rulebook. ...The atomists held that atoms interact only by direct contact."

"Descartes' objective was comprehensibility—to make the workings of nature completely transparent. Locality was essential to this goal. Objects interacted strictly locally: they moved in straight lines until they collided; only then did they change course. Like Democritus and Aristotle, Descartes offered no real evidence for this principle."

"It is inconceivable that inanimate brute matter should, without the mediation of something else, which is not material, operate upon and affect other matter without mutual contact, as it must be, if gravitation, in the sense of Epicurus, be essential and inherent in it. And this is one reason why I desired you would not ascribe innate gravity to me. That gravity should be innate, inherent, and essential to matter, so that one body can act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man, who has in philosophical matters a competent faculty of thinking, can ever fall into it. Gravity must be caused by an agent acting constantly according to certain laws; but whether this agent is material or immaterial, I have left to the consideration of my readers."

"The principle of locality states that no instantaneous transmission of physical influences between spatially separated physical systems ("action at a distance") is allowed, or... that physical systems can only be physically influenced by their immediate environment. ...[The] broader principle states that any possible definitive determinations concerning any given system—its physical state; the application of technology (such as a measurement, which, rather than a prediction, definitely determines a physical state of a quantum system); the falsifiability of claims concerning quantum systems, and so forth—is local."

"[T]he view that the ultimate theory... should be more in accord with the fundamental principles of quantum theory need not imply that such a theory will be any form of quantum theory currently known, such as quantum mechanics or quantum field theory. ...[These] are far from complete or free of deficiencies even within their proper scope. Some new or perhaps now unimaginable theories and very likely new principles may be required to approach the ultimate constitution of nature. Will these theories retain the locality principle? My Bayesian bet would be that this will more likely than not to be the case, but one cannot be certain."

"Quantum mechanics has an axiomatic structure, exposed by von Neumann, Dirac and others. The axioms... tell us that every state of a system corresponds to a vector in a complex , every physical observable corresponds to linear hermitian operator acting on that Hilbert space, etc. ...Special relativity can be deduced... from two axioms: the equivalence of inertial reference frames, and the constancy of the speed of light. Both axioms have clear physical meaning. By contrast, the numerous axioms of quantum mechanics have [none]... the new axioms are hardly more natural than the old. offers hope... a remarkable property of... nonlocality. ...Bell showed, quantum correlations could not arise in any theory in which all variables obey relativistic causality. On the other hand, quantum correlations themselves obey relativistic causality—we cannot exploit quantum correlations to transmit signals at superliminal speeds (ar at any speed). That quantum mechanics combines nonlocality and causality is wondrous... Shimony has aptly called the nonlocality manifest in quantum correlations "passion at a distance"... [and] has raised the question whether nonlocality and causality can peacefully coexist in any other theory besides quantum mechanics."

"The results of experiments on Bell-type arrangements have forced the conceptual issue of quantum non-locality into focus. ...[A]ny physically adequate quantum theory must violate the Principle of Locality. Yet the idea... still sits uncomfortably with most of us. ...The kind of non-locality... has been described as 'benign' since it cannot be used for any kind of signalling... and therefore does not explicitly violate Special Relativity. It is fortunate that parts of the universe do not constantly exhibit non-local behaviors so that we can continue to use established scientific methods to investigate the world. However... non-locality does not necessitate a causality."

"What is the 'means' by which the non-local connection is actualized? ...[S]ome possible responses ...(1) The connection is mediated ...by particles or fields that propogate at superliminal fields. ...(2) The connection propogates backward in time. ...(3) Physical space has more than three spatial dimensions. ...(4) [P]hysical space is not simply connected. ... Option (2) violates the Principle of Causality. ... Based on the results of tests of Bell-type inequalities... non-local connections have at least the features... (a) not decreasing with distance; (b) cannot be shielded against; and (c) are highly selective in what they effect. The[se] features are consistent with Option (4)..."

"Although Einstein's general theory of relativity predicts that there can exist... a singularity in our past, it provides no reason why... a creation out of nothing should occur. ...There are ways of avoiding... a past singularity. If gravity were ever to become a repulsive... force in the distant past then the Universe need not have experienced a singular beginning."

"Einstein's general theory of relativity... was needed not because of conspicuous failures of Newton's theory... but because of inconsistencies between it and the requirements of electromagnetic theory, which Einstein had revised earlier in his special theory of relativity."

"In the early 1960s general relativity experienced a sudden revival in connection with astrophysical discoveries far removed from its original domain, which had essentially been confined to the solar system. The physicist Clifford Will coined the phrase “Renaissance of General Relativity” to describe the process through which general relativity became an internationally visible, highly active field of research in which theoretical explorations went hand in hand with new astrophysical discoveries such as s and the radiation. The systematic exploration of exact solutions, and the understanding of space-time singularities and of the physical reality of gravitational waves, all came only after the low-water-mark period, in the wake of the renaissance of general relativity."

"The theoretical developments involving general relativity in the period prior to the renaissance made use of central principles of Einstein’s theory and of his s and methodology; the physicists who pursued these developments mostly did so, however, not to explore general relativity for its own sake but, rather, from an ulterior motive—the construction of some sort of successor theory. This goal they did not achieve. They did not consider general relativity itself to be a theory fundamental enough to warrant detailed theoretical study, nor did they believe that it held much empirical potential beyond what was already known. There was one central exception to this latter belief, and that is cosmology."

"If I were giving this lecture fifty years from now, the word "gravitation" would be as old-fashioned as the word "phlogiston" is to us. Relativity has certainly demoted gravitation as a real explanation, just as Priestley's and Lavoisier's analyses and decoding of chemical reactions destroyed the word "phlogiston.""

"Differential geometry originally sneaked into theoretical physics through Einstein's theory of general relativity."

"Up to the early 1950s, general relativity was a little-frequented subject, amongst physicists—a theory that had to be praised, but that could be safely ignored. ...Its supporting evidence was sparse, questionable, and unstable: essentially it reduced to the changing experimental verdicts on the three notorious tests."

"There was difficulty reconciling the Newtonian theory of gravitation with its instantaneous propagation of forces with the requirements of special relativity; and Einstein working on this difficulty was led to a generalization of his relativity—which was probably the greatest scientific discovery that was ever made."

"General relativity was considered by Einstein as his most important discovery... a new theory of gravitation bringing in a very powerful kind of symmetry. This symmetry is of importance in physics only where gravitational fields occur, while the symmetry previously... of special relativity, is of importance in all physics. So that this further symmetry... although it is such a wonderful mathematical theory, does not have the big effect on physics."

"I might say that my recent work has been very much concerned with Einstein’s general relativity, and I believe that the times and the distances which are to be used in Einstein’s general relativity are not the same as the times and distances which would be provided by atomic clocks. There are good theoretical reasons for believing that that is so and for believing that gravitational forces are getting weaker, compared to electric forces, as the world gets older."

"Oh leave the Wise our measures to collate One thing at least is certain, light has weight One thing is certain, and the rest debate— Light rays, when near the Sun, do not go straight."

"The theoretical view of the actual universe, if it is in correspondence to our reasoning, is the following. The curvature of space is variable in time and place, according to the distribution of matter, but we may roughly approximate it by means of a spherical space. ...this view is logically consistent, and from the standpoint of the general theory of relativity [is most obvious] lies nearest at hand; whether, from the standpoint of present astronomical knowledge, it is tenable, will not be discussed here. In order to arrive at this consistent view, we admittedly had to introduce an extension of the field equations of gravitation, which is not justified by our actual knowledge of gravitation. It is to be emphasized, however, that a positive curvature of space is given by our results, even if the supplementary term [] is not introduced. The term is necessary only for the purpose of making possible a quasi-static distribution of matter, as required by the fact of the small velocity of the stars."

"To begin with the difference between my conception and Newton's law of gravitation: Please imagine the earth removed, and in its place suspended a box as big as a room or a whole house and inside a man naturally floating in the centre, there being no for force whatever pulling him. Imagine, further, this box being, by a rope or other contrivance, suddenly jerked to one side, which is scientifically termed 'difform motion,' as opposed to 'uniform motion.' The person would then naturally reach bottom on the opposite side. The result would consequently be the same as if he obeyed Newton's law of gravitation, while, in fact, there is no gravitation exerted whatever, which proves that difform motion will in every case produce the same effects as gravitation. I have applied this new idea to every kind of difform motion and have thus developed mathematical formulas which I am convinced give more precise results than those based on Newton's theory. Newton's formulas, however, are such close approximations that it was difficult to find by observation any obvious disagreement with experience."

"The other constraint in our choice of concepts... lies in Einstein's call for frugality and simplicity. ...the aim of any good theoretical system is "the greatest possible sparsity of the logically independent elements (basic concepts and axioms)." Any redundancy or elaboration must be avoided, for "it is the grand object of all theory to make these irreducible elements as simple and as few in number as possible." For example, it was, in his view, "an unsatisfactory feature of classical mechanics that in its fundamental laws the same mass appears in two different roles, namely as an inertial mass in the laws of motion, and as a gravitational mass in the law of gravitation." The equivalence of these two interpretations of mass signaled to him a truth which needed to be stated as a basic axiom (in General Relativity Theory), rather than saddling the theory with a proliferation which did not seem to be inherent in phenomena."

"A scientific theory is usually felt to be better than its predecessors not only in the sense that it is a better instrument for discovering and solving puzzles but also because it is somehow a better representation of what nature is really like. One often hears that successive theories grow ever closer to, or approximate more and more closely to, the truth. Apparently generalizations like that refer not to the puzzle-solutions and the concrete predictions derived from a theory but rather to its ontology, to the match, that is, between the entities with which the theory populates nature and what is “really there.” Perhaps there is some other way of salvaging the notion of ‘truth’ for application to whole theories, but this one will not do. There is, I think, no theory-independent way to reconstruct phrases like ‘really there’; the notion of a match between the ontology of a theory and its “real” counterpart in nature now seems to me illusive in principle. Besides, as a historian, I am impressed with the implausability of the view. I do not doubt, for example, that Newton’s mechanics improves on Aristotle’s and that Einstein’s improves on Newton’s as instruments for puzzle-solving. But I can see in their succession no coherent direction of ontological development. On the contrary, in some important respects, though by no means in all, Einstein’s general theory of relativity is closer to Aristotle’s than either of them is to Newton’s."

"The theory of gravitational fields, constructed on the basis of the theory of relativity, is called the general theory of relativity. It was established by Einstein (and finally formulated by him in 1915), and represents probably the most beautiful of all existing physical theories. It is remarkable that it was developed by Einstein in a purely deductive manner and only later was substantiated by astronomical observations."

"The number of those actively engaged in research in general relativity ... remain[ed] small in the 1930s, 1940s, and early 1950s. ... once said to me, 'You only had to know what your six best friends were doing and you would know what was happening in general relativity.' ...However, in the 1930s a new element... briefly attracted attention, then stayed... quiescent for a quarter of a century. ...J. Robert Oppenheimer and... decided to study the relative influence of nuclear and gravitational influences in s. ...Their work attracted... Richard Chase Tolman. ...there appeared in 1939, a pair of papers, one by Tolman on the static solution of Einstein's field equations for fluid spheres... and one... by Oppenheimer and ... In this paper, the foundations are laid for a general relativistic theory of . ...Half a year later, the paper... by Oppenheimer and came out... Thus began the physics of s..."

"It thus characterizes not only the gravitational field but also the behaviour of measuring rods and clocks, i.e. the metric of the four-dimensional world which contains the geometry of ordinary three-dimensional space as a special case. This fusion of two previously quite disconnected subjects—metric and gravitation—must be considered as the most beautiful achievement of the general theory of relativity."

"The great triumph of the theory of relativity lies in its absorbing the universal force of gravitation into one geometric structure... Einstein's achievements would be substantially as great even though it were not for... observational tests."

"Einstein asked himself a question... how can the sun and the Earth "attract" each other without touching..? ...[H]e imagined that the sun and the Earth each modified the space and time that surrounded them, just as a body in water displaces the water... This modification of the structure of time influences in turn the movement of the bodies, causing them to "fall" toward one another. ...The Earth is a large mass and slows down time in its vicinity. ...If things fall, it is due to this slowing of time. ...Where time passes uniformly, in interplanetary space, things do not fall. ...[H]ere on ...our planet, the movement of things inclines naturally toward where time passes more slowly, as when we run ...into the sea and the resistance of the water on our legs makes us fall headfirst... [T]ime passes more slowly for your feet than it does for your head."

"In the past, the thesis that this conversation is eternal sometimes provoked a few chuckles, but then I realised that it was worth remembering that Einstein's relativity, although with a logic very different from mine, says that future and past events are no less real than present ones. So much so that when Popper spoke with Einstein, he called him Parmenides. Interviewer: The English physicist Julian Barbour asserts that time does not exist and that events are like postcards hanging on a clothesline, all present at the same time... Severino: Yes, he slightly varied the image that Popper used with Einstein of frames wrapped in a reel. But neither of them can explain the camera or the movement of the gaze that passes from one postcard to another. To do so requires a logic [...] that science cannot provide. In general, science believes that the mind is a special thing among things. This is where the theory of experience, which scientists tend to neglect, comes into play. Experience is the transcendental mind; it does not enter or exit a field of vision but is the place where everything enters and exits. To understand what the unwinding of the frames or the gaze that flows over the postcards is, we need to introduce the concept of transcendental consciousness, which was glimpsed in some way by idealism, that is, the place within which the eternal occurs. The so-called becoming of the world cannot be the beginning of being and the cessation of being, but is the appearing and disappearing of the eternal in that transcendental consciousness."

"Despite the weakness of the early experimental evidence for general relativity, Einstein’s theory became the standard textbook theory of gravitation in the 1920s and retained that position from then on, even while the various eclipse expeditions of the 1920s and 1930s were reporting at best equivocal evidence for the theory. … Perhaps all of us were just gullible and lucky, but I do not think that is the real explanation. I believe that the general acceptance of general relativity was due in large part to the attractions of the theory itself—in short, to its beauty."

"... I don’t see any reason why anyone today would take Einstein’s general theory of relativity seriously as the foundation of a quantum theory of gravitation, if by Einstein’s theory is meant the theory with a Lagrangian density given by just the term {\sqrt{g} R / 16 \pi G}. It seems to me there’s no reason in the world to suppose that the Lagrangian does not contain all the higher terms with more factors of the curvature and/or more derivatives, all of which are suppressed by inverse powers of the Planck mass, and of course don’t show up at any energy far below the Planck mass, much less in astronomy or particle physics. Why would anyone suppose that these higher terms are absent?"

"September 1959 to September 1960—a year with great portents for Einstein's general theory of relativity. ...a paper by Robert V. Pound and Glen A. Rebka, Jr. ...entitled "Apparent Weight of Photons"... described the first successful laboratory measurement of the... gravitational red shift of light... A few months later, in June 1960... there appeared a paper by... Roger Penrose... "A Approach to General Relativity." ...[which] outlined a very elegant and streamlined technique for solving certain problems in general relativity. ...Later that summer ... ...[put] the finishing touches on his Ph.D. thesis ..."Mach's Principle and a Varying Gravitational Constant." ...[which] presented the equations for ...an alternative to Einstein's ...a "scaler-tensor" theory of gravity ...[eventually] known as the ."

"Thomas Matthews and prepared to... make some observations of a radio source they denoted 3C48... interested in... [the] visible light... on the night of September 26, 1960 they took a photographic plate of the area... Conventional wisdom... told them that they would find a cluster of galaxies... Instead... subsequent observations... and throughout 1961 showed... its spectrum of colors was highly unusual... its brightness and luminosity varied widely and rapidly... it was only "quasi" stellar. Hence the name quasi stellar radio source or ""... It was a remarkable year for general relativity, because it contained all the signs that a renaissance was about to begin. ...an era in which general relativity would become an active and exciting branch of physics, after almost a half century in the backwaters."

"GTR has an extreme inner beauty and elegance; the construction of the GTR required the introduction of only one constant—the constant of gravitation. ...GTR produces the following: (1) Newton's law of gravitation, itself; (2) a foundation that enables one to apply Newton's law to the interaction of bodies surrounded by infinitely expanding matter; and (3) Friedmann's nonstationary cosmological model, including the prediction of the Hubble redshift for the spectra of distant objects. Only secondarily do we cite the three famous tests...—the precession of Mercury's perihelion, the deflection of a light beam passin near the Sun, and the variation of the frequency of light in a gravitational field."

"Albert Einstein"

"Relativity Simply Explained"

"Special relativity"

"Theory of relativity"

"I very much enjoyed your delightful explanation of the formation of meanders. It just happens that my wife had asked me about the “teacup phenomenon” a few days earlier, but I did not know a rational explanation. She says that she will never stir her tea again without thinking of you."

"The first formulation of (part of) mechanics by means of a variational principle... is due to Maupertuis in 1746 in a paper called "Les lois du mouvement et du repos déduites d'un principe métaphysique" (Laws of motion and rest deduced from a metaphysical principle). Maupertuis had first introduced the principle of least action in optics in 1744. ...Through experimentation, he found that this quantity depends on mass, velocity, and distance. He called the product of the three factors "action" and accordingly expressed a "principle of the least quantity of action"..."

"Of no little importance are Euler's labors in analytical mechanics. ...He worked out the theory of the rotation of a body around a fixed point, established the general equations of motion of a free body, and the general equation of hydrodynamics. He solved an immense number and variety of mechanical problems, which arose in his mind on all occasions. Thus on reading Virgil's lines. "The anchor drops, the rushing keel is staid," he could not help inquiring what would be the ship's motion in such a case. About the same time as Daniel Bernoulli he published the Principle of the Conservation of Areas and defended the principle of "least action," advanced by P. Maupertius. He wrote also on tides and on sound."

"Let the mass of the projectile be M, and let its speed be v while being moved over an infinitesimal distance ds. The body will have a momentum Mv that, when multiplied by the distance ds, will give , the momentum of the body integrated over the distance ds. Now I assert that the curve thus described by the body to be the curve (from among all other curves connecting the same endpoints) that minimizes\int Mv\,dsor, provided that M is constant along the path,M\int v\,ds."

"After having worked in the theory of light and gravitation, he announced, in 1744, a new minimum principle, the Principle of Least Action, from which he claimed he could deduce the behavior of light and masses in motion. The principle asserts that nature always behaves so as to minimize an integral known technically as action, and amounting to the integral of the product of mass, velocity, and distance traversed by a moving object. From this principle he deduced the Newtonian laws of motion. With sometimes suitable and sometimes questionable interpretation of the quantities involved, Maupertuis managed to show that optical phenomena, too, could be deduced from this principle. Hence, to an extent at least, he succeeded in uniting the optics of the eighteenth century and mechanical phenomena. ... Maupertuis advocated his principle for theological reasons. ...He ...proclaimed his principle to be not only a universal law of nature but also the first scientific proof of the existence of God, for it was "so wise a principle as to be worthy only of a Supreme Being."

"The minimum principle that unified the knowledge of light, gravitation, and electricity of Hamilton's time no longer suffices to relate these fundamental branches of physics. Within fifty years of its creation, the belief that Hamilton's principle would outlive all other physical laws of physics was shattered. Minimum principles have since been created for separate branches of physics... but these are not only restricted... but seem to be contrived... The hope of revising the principle so that it will achieve the unification... still drives mathematicians. This is the problem to which... Einstein devoted the last years of his life. Stripped of the theological associations, the belief of a minimum principle still activates physical science. ... A single minimum principle, a universal law governing all processes in nature, is still the direction in which the search for simplicity is headed, with the price of simplicity now raised from a mastery of differential equations to a mastery of the calculus of variations."

"Maupertuis really had no principle, properly speaking, but only a vague formula, which was forced to do duty as the expression of different familiar phenomena not really brought under one conception. ...Maupertuis' performance, though it had been unfavorably criticized by all mathematicians, is, nevertheless, sort of invested with a sort of historical halo. It would seem almost as if something of the pious faith of the church had crept into mechanics. However, the mere endeavor to gain a more extensive view... was not altogether without results. Euler, at least, if not also Gauss, was stimulated by the attempt of Maupertuis."

"Euler's view is, that the purposes of the phenomena of nature afford as good a basis of explanation as their causes. If this position is taken, it will be presumed a priori that all natural phenomena present a maximum or a minimum. ...in the solution of mechanical problems... it is possible... to find the expression which in all cases is made maximum or minimum. Euler is thus not led astray... and proceeds much more scientifically than Maupertuis. He seeks an expression whose variation put = 0 gives the ordinary equations of mechanics. For a single body moving under the action of forces Euler finds the requisite expression in the formula ∫vds, where ds denotes the element of the path and v the corresponding velocity. This expression is smaller for the path actually taken... therefore, by seeking the path that makes ∫vds a minimum, we can also determine the path. ...In the simplest cases Euler's principle is easily verified. ... The consideration of the motion of a projectile... will also show that the quantity ∫vds is smaller for the parabola than for any other neighboring curve; smaller, even, than for the straight line... between the same terminal points. ... Jacobi pointed out that we cannot assert that ∫vds for the actual motion is a minimum, but simply that the variation of this expression, in its passage to an infinitely adjacent neighboring path, is = 0. ...unquestionably various other integral expressions may be devised that give by variation the ordinary equations of motion, without its following that the integral expressions in question must possess... any particular physical significance. The striking fact remains, however, that so simple and expression as ∫vds does possess the property mentioned."

"I must now explain what I mean by the quantity of action. A certain action is necessary for the carrying of a body from one point to another: this action depends on the velocity which the body has and the space which it describes; but it is neither the velocity nor the space taken separately. The quantity of action varies directly as the velocity and the length of path described; it is proportional to the sum of the spaces, each being multiplied by the velocity with which the body describes it. It is this quantity of action which is here the true expense (dépense) of nature, and which she economizes as much as possible in the motion of light."

"After so many great men have worked on this subject, I almost do not dare to say that I have discovered the universal principle upon which all these laws are based, a principle that covers both elastic and inelastic collisions and describes the motion and equilibrium of all material bodies. This is the principle of least action, a principle so wise and so worthy of the supreme Being, and intrinsic to all natural phenomena; one observes it at work not only in every change, but also in every constancy that Nature exhibits. In the collision of bodies, motion is distributed such that the quantity of action is as small as possible, given that the collision occurs. At equilibrium, the bodies are arranged such that, if they were to undergo a small movement, the quantity of action would be smallest. The laws of motion and equilibrium derived from this principle are exactly those observed in Nature. We may admire the applications of this principle in all phenomena: the movement of animals, the growth of plants, the revolutions of the planets, all are consequences of this principle. The spectacle of the universe seems all the more grand and beautiful and worthy of its Author, when one considers that it is all derived from a small number of laws laid down most wisely. Only thus can we gain a fitting idea of the power and wisdom of the supreme Being, not from some small part of creation for which we know neither the construction, usage, nor its relationship to other parts. What satisfaction for the human spirit in contemplating these laws of motion and equilibrium for all bodies in the universe, and in finding within them proof of the existence of Him who governs the universe!"

"When a change occurs in Nature, the quantity of action necessary for that change is as small as possible. The quantity of action is the product of the mass of the bodies times their speed and the distance they travel. When a body is transported from one place to another, the action is proportional to the mass of the body, to its speed and to the distance over which it is transported."

"It [science] has as its highest principle and most coveted aim the solution of the problem to condense all natural phenomena which have been observed and are still to be observed into one simple principle, that allows the computation of past and more especially of future processes from present ones. ...Amid the more or less general laws which mark the achievements of physical science during the course of the last centuries, the principle of least action is perhaps that which, as regards form and content, may claim to come nearest to that ideal final aim of theoretical research."

"Fermat making use of the argument that Nature could not be wasteful, and was bound for this reason to cause the rays of light to travel between two points in the shortest time possible, was able to deduce from this proposition the laws of reflexion and refraction. Though we do not now attach any weight to the premise, we accept the conclusion."

"There are certain general principles or theorems in mechanics, such as Lagrange's equations, Hamilton's principle, the principle of least work, and Gauss' principle of least constraint, which afford general solutions of certain types of problems. Such general principles have therefore the advantage over ordinary methods in that once having found the general solution, any particular problem may be solved by merely routine processes."

"We find... that Mie's Electrodynamics exists in a compressed form in Hamilton's Principle—analogously to the manner in which the development of mechanics attains its zenith in the principle of action. Whereas in mechanics, however, a definite function L of action corresponds to every given mechanical system and has to be deducted from the constitution of the system, we are here concerned with a single system, the world. This is where the real problem of matter takes its beginning: we have to determine the "function of action," the world-function L, belonging to the world. For the present it leaves us in perplexity. If we choose an arbitrary L, we get a "possible" world governed by this function of action, which will be perfectly intelligible to us—more so than the actual world—provided that our mathematical analysis does not fail us. We are, of course, then concerned in discovering the only existing world, the real world for us. Judging from what we know of physical laws, we may expect the L which belongs to it to be distinguished by having simple mathematical properties. Physics, this time as a physics of fields, is again pursuing the object of reducing the totality of natural phenomena to a single physical law: it was believed that this goal was almost within reach once before when Newton's Principia, founded on the physics of mechanical point-masses was celebrating its triumphs. But the treasures of knowledge are not like ripe fruits that may be plucked from a tree."

"Above all, the ominous clouds of those phenomena that we are with varying success seeking to explain by means of the quantum of action, are throwing their shadows over the sphere of physical knowledge, threatening no one knows what new revolution."

"The present investigations are concerned with the history of the Principle of Least Action in the hands of Maupertuis, Euler, and others. The subject is of great importance in the history of mechanics, both because the principle of least action became, in the hands of Lagrange, "the mother," as Jacobi expressed it, "of our analytical mechanics," and because the animistic tendency displayed in the search for a maximum or a minimum principle in physics undoubtedly had a great influence on such moulders of mechanical theory as Euler, Lagrange (in his early work), Hamilton, Gauss, and in our own times, Willard Gibbs. ...much in this chapter of the evolution of mechanics—one may even say, of thought in general—has been misquoted or misunderstood by even eminent authorities."

"Besides Lagrange's early printed works, his correspondence with Euler allows us to form some impression of the stimulating effect which the principle of least action had on Lagrange's mind at the beginning of his career. Lagrange's correspondence with Euler extends from 1754... to 1775... Already in 1754 Lagrange announces that he has made "some observations about the maxima and minima which are in the actions of nature." In a letter of August 12, 1755 Lagrange informs Euler that he had a new and simpler method of solving isoperimetrical problems and gives a full statement of it. This discovery of what was afterwards called "the calculus of variations" certainly gave the principle of least action an additional attractiveness to Lagrange; he speaks in a letter of May 19, 1756, of his meditations "on the application of the principle of least action to the whole of dynamics." Lagrange's interest in the principle of least action seems to have evaporated when he observed that, when developed, the integrand is the variational form of d'Alembert's principle, and that it is simpler and equally effective to start with the equations of motion divorced from the integration. This is Lagrange's point of view in 1788. The earliest date at which this change in point of view is... 1764. In a letter of Sept 15, 1782, to Laplace, Lagrange says that he has almost finished a mechanical treatise uniquely founded on "the principle or formula" given in... his memoir of 1780 on the libration of the moon."

"Maupertuis's first enunciation of the law of the least quantity of action was in a memoir read to the French Academy on April 15th, 1744, entitled "Accord de différentes Loix de la Nature qui avoient jusqu'ici paru incompatibles." The laws in question appear to be those of the reflection and of the refraction of light. When a ray of light in a uniform medium travels from one point to another, either without meeting an obstacle or with meeting a reflecting surface, nature leads it by the shortest path and in the shortest time. But when a ray is refracted by passing from a uniform medium to one of different density, the ray neither describes the shortest space nor does it take the shortest time about it. As Fermat showed, the time would be the shortest if light moved more quickly in rarer media, but Newton proved that, as Descartes had believed, light moves more quickly in denser media. Maupertuis's discovery was that light neither takes always the shortest path nor always that path which it describes in the shortest time, but "that for which the quantity of action is the least.""

"In order to understand the significance of Action, let us consider any mechanical system passing from an initial configuration P to a final configuration Q. Classical science defined the action A of this system as the difference between its total kinetic energy... and its total potential energy... taken at every instant and then summated over the entire period of time during which the system passed from the initial state P to the final state Q. Now the total kinetic and potential energies of the system at any instant are given by\iiint\,T\,dx\,dy\,dz~ ~and~ \iiint\,V\,dx\,dy\,dz,where T and V represent the densities of the kinetic and potential energies of every point throughout the space occupied by the system. Accordingly, the expression of the action will be given byA = \iiiint\,(T-V)\,dx\,dy\,dz\,dt~ ~or~ \iiiint\,L\,dx\,dy\,dz\,dt....we have merely replaced (T - V) by a single letter L... referred to as the function of action (also called Lagrangian function). Roughly speaking, action was thus in the nature of the product of a duration by an energy contained in a volume of space. On no account may this action be confused with the action dealt with in Newton's law of action and reaction, also expressible as the principle of conservation of momentum. Still less may it be confused with the term "action" which appears in philosophical writings. ...the laws of mechanics can be expressed in a highly condensed form when the concept of action is introduced. Various forms may be given to the principle of Action; here we consider only the form... called Hamilton's Principle of Stationary Action. If we restrict our attention to the very simplest case, we may state Hamilton's principle as follows: If we consider all the varied paths along which a conservative system may be guided, so that it will pass in a given time from a definite initial configuration P to a definite configuration Q, we shall find that the course the system actually follows, of its own accord, is always such that along it the action is a minimum (or a maximum). ...the principle of action issues ...from the laws of classical mechanics ...A priori, we have no means of deciding whether the laws governing physical phenomena of a non-mechanical nature—those of electromagnetics, for example—would issue from the same principle of action."

"When Maxwell had proved that his equations of electromagnetics could be thrown into a form compatible with the principle of action, and when he succeeded in amalgamating electricity, magnetism and optics into one science, the universal validity of the principle was accepted. Inasmuch as this principle includes that of the conservation of energy, we can understand why the principle of action was often referred to as the supreme principle of physical science. ...when the principle of action is satisfied by a phenomenon, an indefinite of different mechanical interpretations of the phenomenon are theoretically possible. In the case of electrodynamic phenomena, however, in view of the complicated hypotheses which he was compelled to postulate, Maxwell abandoned all attempts to discover the precise mechanical interpretation which would correspond to reality."

"The principle... imposes the condition that the natural evolution of any system must be such as to render the action a maximum or a minimum. Could we but express this condition in terms of the usual physical magnitudes, we should be enabled to map out in advance the series of intermediary states through which the phenomenon would pass. From this knowledge we should derive the expression of the laws which governed the evolution of the phenomenon. Here... a twofold problem presents itself. First, we must succeed in finding the correct mathematical expression for the action; and, secondly, we must be in a position to solve the purely mathematical problem of determining under what conditions the action will be a maximum or a minimum. Now all problems of maxima and minima are solve by means of the calculus of variations, a form of calculus we owe chiefly to Lagrange. According to the methods of this calculus, we establish under what conditions a magnitude is a maximum or minimum by discovering under what conditions it will be stationary. ... When a stone is thrown into the air, it ascends with decreasing speed, then seems to hesitate for a brief period of time as it hovers near the point of maximum height before it starts to fall back again towards the earth. During this brief period of hesitation at the apex of its trajectory, the stone is said to remain "stationary." We can recognize a stationary state by observing that when it is reached no perceptible changes take place over a short period of time. In this way, we understand the connection which exists between the stationary condition and the presence of a maximum or a minimum. In mathematics small variations are represented by the letter δ; hence the stationary condition of the action, or again, the principle of action, is expressed by\partial A = 0,~ ~i.e.,~\partial \iiiint\,L\,dx\,dy\,dz\,dt = 0....Lamor applied this method to the phenomena of electricity and magnetism and showed how Maxwell's laws of electrodynamics could be deduced from a suitable mathematical expression L defining the electromagnetic function of action."

"When the theory of relativity supplanted classical science, it was recognised that the classical equations of mechanics were only approximate, and it became necessary to reformulate the principle of action so as to render it compatible... This work was carried out by the pure mathematicians—by Klein and Hilbert in particular. It was then found that a principle of action differing but slightly from the classical one could be obtained."

"In classical science, it was strange to find that action... should yet present the artificial aspect of an energy in space multiplied by a duration. As soon, however, as we realise that the fundamental continuum of the universe is one of space-time and not one of separate space and time, the reason for the importance of the seemingly artificial combination of space with time in the expression for the action receives a very simple explanation. Henceforth, action is no longer energy in a volume of space multiplied by a duration; it is simply energy in a volume of the world, that is to say, in a volume of four-dimensional space-time. Designating a volume of space-time by d\omega, we haved\omega = dxdydzdt,so that our principle of action, \partial A = 0, becomes\partial \int\,L\,d\omega = 0.Now there is a perfect symmetry between the rôles of space and time."

"From the expression for the atom of energy or quantum hv, where h is a constant and v is the frequency of the radiation, it is obvious that there exist as many different types of quanta of energy as there exist different frequencies of radiation. There is no unique type of quantum of energy in nature. That which is universal is not the quantum of energy hv, but the constant h. It can be shown that Planck's constant h is not a mere number; it represents some definite abstract mathematical entity, and that entity is action. We must assume, therefore, that there exist atoms of action in nature, just as there exist atoms of matter. ...we must possess a fairly thorough understanding of what is meant by action, as also of the part this important entity plays in science. ...the atomicity of action ...suggests that change is always discontinuous ...a series of jerks or jumps."

"History of science"

"Classical mechanics"

"The globe of the Earth stands supportless in space... Just as the [spherical] bulb of a Kadamba flower is covered all around by blossoms, just so is the globe of the Earth surrounded by all creatures, terrestrial as well as aquatic."

"There are some oddities in the perspective with which we see the world. The fact that we live at the bottom of a deep gravity well, on the surface of a gas covered planet going around a nuclear fireball 90 million miles away and think this to be normal is obviously some indication of how skewed our perspective tends to be, but we have done various things over intellectual history to slowly correct some of our misapprehensions."

"Anaxagoras... speaks absurdly concerning the permanency of the infinite: for he says that the infinite itself supports itself; and this because it is in itself: for nothing else contains it. As if where any thing is it is naturally there. But this is not true: for a thing may be situated in a certain place by force, and not where it is naturally adapted to be. If, therefore, the whole is by no means moved; for that which is established in itself, and is in itself, is necessarily immoveable; yet it should be said why it is not naturally adapted to be moved: for it is not just that he who thus speaks should be dismissed; since there may be any thing else which is not moved; but nothing hinders it from being naturally adapted to be moved: for earth also is not borne along; nor if it were infinite could it be locally moved, in consequence of being restrained by the middle. It would not, however, remain in the middle, because there is not any other place into which it could be moved, but because it is not natural to it so to be moved. Though, indeed, it might be said, that the earth supports itself. If, therefore, this is not the cause of the permanency of the earth if it were infinite, but its gravity is the cause; and that which is heavy abides in the middle, and the earth is in the middle: in like manner also, the infinite will abide in itself, through some other cause, and not because it is infinite, and will itself support itself. At the same time likewise, it is manifest, that it is necessary every part of it should abide: for as the infinite abides supported in itself; so likewise whatever part of it is assumed, will abide in itself: for the places of the whole and the part are of the same species; as of the whole earth and a clod, the place is downward; and of the whole of fire, and a spark, the place is upward. So that if the place of the infinite is in itself, there will be the same place also of a part of the infinite. It will abide therefore, in itself. And, in short, it is evident that it is impossible to say that there is an infinite body, and at the same time that there is a certain place for bodies, if every sensible body either possesses gravity or levity. And if it is heavy, it has a natural tendency to the middle; but if light, it naturally tends upward: for it is necessary that an infinite body should be such. But it is impossible that the whole should be passive in either way, or the half in both ways: for how will you divide? Or how will one part of the infinite be above, and another below? Or how will it have extremes or a middle? Further still; every sensible body is in place; but the species and differences of place are upward and downward, before and behind, to the right hand and to the left: and these things not only thus subsist with relation to us, and by position, but have a definite subsistence in the universe itself. But it is impossible that these things should be in the infinite: and in short it is impossible that there should be an infinite place."

"Moreover, force, gravity, and words of that kind, are often, and not unwisely, used in the concrete; in such a way that they know the movement of the body, the difficulty of resistance, etc. But when they are used by philosophers to signify certain natures, precise and abstract from all these, which are neither subject to the senses, nor can be understood by any power of the mind, nor can they be shaped by the imagination, they in turn give rise to errors and confusion."

"The earth attracts inert bodies in space towards itself. The attracted body appears to fall down on the earth. Since the space is homogeneous, where will the earth fall?"

"GRAVITATION, n. The tendency of all bodies to approach one another with a strength proportion to the quantity of matter they contain -- the quantity of matter they contain being ascertained by the strength of their tendency to approach one another. This is a lovely and edifying illustration of how science, having made A the proof of B, makes B the proof of A."

"Our two greatest problems are gravity and paper work. We can lick gravity, but sometimes the paperwork is overwhelming."

"In order that a pendulum may continue to make the same number of oscillations in a given time, it must be shortened as it is carried towards the equator; and the variation of its length in different latitudes affords an accurate measurement of the force of gravity. But the force of gravity has known relation to the figure of the earth, which, therefore, may be determined, by observing the length of the seconds pendulum at different points on its surface."

"Cotes's Preface [to the 2nd edition of Principia] is of historical importance... It is interpreted as advocating the theory of "action at a distance", and the theory that gravity is an innate property of matter. Phrases in Newton's Principia appear to carry a similar implication. ...In these expressions, the "bodies" or the "corpuscles" are represented as active, as "attracting." They are not passive like a chip of wood carried about by a eddy in a pool, or like a planet passively swept through space by a Cartesian vortex. It was easy, therefore, to jump to an inference that in the Newtonian theory, gravity was an innate, inherent property of matter. ...such an interpretation was made by writers on the European continent, for example by Huygens, Lalande, [Jean Baptiste] Bordas-Demoulin, and others. Thus, after the publication of the Principia in 1687, Huygens... abandoned the explanation of the planetary motion by Descartes' theory of vortices, and published his adherence to Newton's celestial mechanics. But Huygens did not accept the view that gravitation was an innate property of matter, a view which he attributed to Newtonian philosophy. On this point Huygens rejected what interpreted to be the tenet of Newton, and continued his adhesion to the tenet of Descartes. While the reader of the first edition of Principia had some justification in attributing to Newton the view that gravity was an innate property of matter, they were nevertheless mistaken. In the first edition Newton had made no explicit declaration on this point. ...Newton was no more a believer in gravity as an innate property of bodies than was Descartes. But the readers of the first edition of Principia had no means of knowing this."

"Newtonian action at a distance is spoken of as "immediate action." Newton, on the other hand, postulates an agent and gives it time to act. To be sure, in his calculations of gravitational attractions, he assumes, as a necessary approximation (having no experimental data on the speed of propagation of gravitational action), that the action is instantaneous, but not so in his talks on gravity. In a letter to Boyle he considers the cause of gravitation between two approaching bodies. They "make the ether between them begin to rarify"; and again, in his hypothesis on light, he says, "So may the gravitating attraction of the earth be caused by the continual condensation of some other such like ethereal spirit... in such a way... as to cause it [this spirit] from above to descend with great celerity for a supply; in which descent it may bear down with it the bodies it pervades, with force proportional to the superficies of all their parts it acts upon.""

"Laplace made the assumption that the transmission of gravity is not instantaneous, and he found that in order to produce the known effects in the secular acceleration of the moon, gravity must travel seven million times faster than the speed of light. ...Laplace's calculation has been found to be incomplete, and his velocity of gravity illusory."

"For the better part of my last semester at Garden City High, I constructed a physical pendulum and used it to make a “precision” measurement of gravity. The years of experience building things taught me skills that were directly applicable to the construction of the pendulum. Twenty-five years later, I was to develop a refined version of this measurement using laser-cooled atoms in an atomic fountain interferometer."

"The essence of Riemann's discoveries consists in having shown that there exist a vast number of possible types of spaces, all of them perfectly self-consistent. When, therefore, it comes to deciding which one of these possible spaces real space will turn out to be, we cannot prejudge... Experiment and observation alone can yield us a clue. To a first approximation, experiment and observation prove space to be Euclidean, and this accounts for our natural belief... merely by force of habit. But experiment is necessarily innacurate, and we cannot foretell whether our opinions will not have to be modified when our experiments are conducted with greater accuracy. Riemann's views thus place the problem of space on an empirical basis excluding all a priori assertions on the subject. ...the relativity theory is very intimately connected with this empirical philosophy; for... Einstein is compelled to appeal to a varying non-Euclideanism of four-dimensional space-time in order to account with extreme simplicity for gravitation. ...had the extension of the universe been restricted on a priori grounds... to three dimensional Euclidean space, Einstein's theory would have been rejected on first principles. ...as soon as we recognise that the fundamental continuum of the universe and its geometry cannot be posited a priori... a vast number of possibilities are thrown open. Among these the four-dimensional space-time of relativity, with its varying degrees of non-Euclideanism, finds a ready place."

"With the new views advocated by Riemann... the texture, structure or geometry of space is defined by the metrical field, itself produced by the distribution of matter. Any non-homogeneous distribution of matter would then entail a variable structure of geometry for space from place to place. ... Riemann's exceedingly speculative ideas on the subject of the metrical field were practically ignored in his day, save by the English mathematician Clifford, who translated Riemann's works, prefacing them to his own discovery of the non-Euclidean Clifford space. Clifford realised the potential importance of the new ideas and suggested that matter itself might be accounted for in terms of these local variations of the non-Euclidean space, thus inverting in a certain sense Riemann's ideas. But in Clifford's day this belief was mathematically untenable. Furthermore, the physical exploration of space seemed to yield unvarying Euclideanism. ...it was reserved for the theoretical investigator Einstein, by a stupendous effort of rational thought, based on a few flimsy empirical clues, to unravel the mystery and to lead Riemann's ideas to victory. (In all fairness to Einstein... he does not appear to have been influenced directly by Riemann.) Nor were Clifford's hopes disappointed, for the varying non-Euclideanism of the continuum was to reveal the mysterious secret of gravitation, and perhaps also of matter, motion, and electricity. ... Einstein had been led to recognize that space of itself was not fundamental. The fundamental continuum whose non-Euclideanism was fundamental was... one of Space-Time... possessing a four-dimensional metrical field governed by the matter distribution. Einstein accordingly applied Riemann's ideas to space-time instead of to space... He discovered that the moment we substitute space-time for space (and not otherwise), and assume that free bodies and rays of light follow geodesics no longer in space but in space-time, the long-sought-for local variations in geometry become apparent. They are all around us, in our immediate vicinity... We had called their effects gravitational effects... never suspecting that they were the result of those very local variations in the geometry for which our search had been in vain....the theory of relativity is the theory of the space-time metrical field."

"Let us revert to the metrical field, as defining the space-time structure. Although Riemann had attributed the existence of the structure, or metrical field, of space to the binding forces of matter, there is not the slightest indication in Einstein's special theory that any such view is going to be developed later on; in fact, it does not appear that Einstein was influenced in the slightest degree by Riemann's ideas. ...in the special theory, the problem of determining whence the structure, or field, arises, what it is, what causes it, is not even discussed in a tentative manner. Space-time, with its flat structure, is assumed to be given or posited by the Creator. But in the general theory the entire situation changes when Einstein accounts for gravitation, hence for a varying lay of the metrical field, in terms of a varying non-Euclidean structure of space-time around matter. We are then compelled to recognise not only that the metrical field regulates the behaviour of material bodies and clocks, as was also the case in the special theory, but, furthermore, that a reciprocal action takes place and that matter and energy in turn must affect the lay of the metrical field. But we are still a long way from Riemann's view that the field is not alone affected but brought into existence by matter; and it is only when we consider the cosmological part of Einstein's theory that this idea of Riemann's may possibly be vindicated. And here we come to a parting of the ways with de Sitter and Eddington on one side, Einstein and Thirring on the other, and Weyl somewhere in between the two extremes."

"In the year 1900 Max Planck wrote... E = hv, where E is the energy of a light wave, v is its , and h is... . It said that energy and frequency are the same thing measured in different units. Plank's constant gives you a rate of exchange for for converting frequency into energy... But in the year 1900 this made no physical sense. Even Plank himself did not understand it. ...Now Hawking has written down an equation which looks rather like Plank's equation... S = kA, where S is the entropy of a black hole, A is the area of its surface, and k is... Hawking's constant. Entropy means roughly the same thing as the of an object. ...Hawking's equation says that entropy is really the same thing as area. The exchange rate... is given by Hawking's constant... But what does it really mean to say that entropy and area are the same thing? We are as far away from understanding that now as Planck was of understanding quantum mechanics in 1900. ...[T]his equation will emerge as a central feature of the still unborn theory which will tie together gravitation and quantum mechanics and thermodynamics."

"Light-waves in passing a massive body such as the sun are deflected through a small angle. This is additional evidence that the Newtonian picture of gravitation as a tug is inadequate. You cannot deflect waves by tugging at them, and clearly another representation of the agency which deflects them must be found."

"The Newtonian scheme says that the planet tends to move in a straight line, but the sun's gravity pulls it away. Einstein says that the planet tends to take the shortest route and does take it."

"Einstein's law of gravitation controls a geometrical quantity curvature in contrast to Newton's law which controls a mechanical quantity of force."

"Enter superstring theory. The concept that particles are really tiny strings dates from the 1960s, but it took on wings in 1974, when John Schwarz... and Joel Scherk... came to terms with what had been an ugly blemish in their calculations. String theory kept predicting the existence of a particle with zero mass and a spin of two. Schwarz and Scherk realized that this unwelcome particle was nothing other than the graviton, the quantum carrier of gravitational force (Although there is no quantum theory of gravity yet, it is possible to specify some of the characteristics of the quantum particle thought to convey it.) This was liberating: The calculations were saying not only that string theory might be the way to a fully unified account of all particles and forces but that one could not write a string theory without incorporating gravity. Ed Witten... recalled that this news constituted "the greatest intellectual thrill of my life."

"We postulate: It shall be impossible, by any experiment whatsoever performed inside such a box, to detect a difference between an acceleration relative to the nebulae and gravity. That is, an accelerating box in some gravitational field is indistinguishable from a stationary box in some different gravitational field. How much like Einstein this sounds, how reminiscent of his postulate of special relativity! We know the principle of equivalence works for springs, (as we knew special relativity worked for electrodynamics), and we extend it by fiat to all experiments whatsoever. We are used to such procedures by now, but how originally brilliant it was in 1911—what a brilliant, marvelous man Einstein was!"

"One other test of gravity... is the question of whether the pull is exactly proportional to the mass... and changes in velocity are inversely proportional to the mass... That means that two objects of different mass will change their velocity in the same manner in a gravitational field. ...That is Galileo's old experiment from the Leaning Tower of Pisa. ...How accurate is it? It was measured in an experiment by ...Eötvös in 1909 and ...by Dicke, and is known to one part in 10,000,000,000. ...[S]uppose you wanted to know whether the pull is exactly proportional to the inertia. The earth is going around the sun, so the things are thrown out by inertia. But they are attracted by the sun to the extent that they have ... So if they are attracted to the sun in a different proportion from that thrown out by inertia, one will be pulled towards the sun, and the other away from it, and so, hanging them on opposite ends of a rod on another Cavendish quartz fiber, the thing will twist towards the sun. It does not twist at this accuracy, so we know that the sun's attraction to two objects is exactly proportional to its coefficient of inertia; in other words, its mass."

"Poetry had a much more serious beginning than is usually imagin'd, and... the Muses have of late days mightily deviated from their original Gravity."

"Edward Witten is fond of declaring that string theory had already made a dramatic and experimentally confirmed prediction: "String theory had the remarkable property of predicting gravity." What Witten means by this is that both Newton and Einstein developed theories of gravity because their observations of the world clearly showed them that gravity exists, and that, therefore, it required an accurate and consistent explanation. On the contrary, a physicist studying string theory—even if he or she was completely unaware of general relativity—would be inexorably led to it by the string framework."

"Much as Kaluza found that a universe with five spacetime dimensions provided a framework for unifying electromagnetism and gravity, and much as string theorists found that a universe with ten spacetime dimensions provided a framework for unifying quantum mechanics and general relativity, Witten found that a universe with eleven spacetime dimensions provided a framework for unifying all string theories."

"He used to say the left-hand side of his equation is beautiful and the right-hand side is ugly. Much of what he was doing in the latter part of his career was trying to move the right-hand side to the left... and understand matter as a geometrical structure. To build matter itself from geometry—that in a sense is what string theory does. ...especially in a theory like the heterotic string which is inherently a theory of gravity in which the particles of matter as well as the other forces of nature emerge in the same way that gravity emerges from geometry. Einstein would have been pleased with this, at least with the goal, if not the realization. ...He would have liked the fact that there is an underlying geometrical principle — which, unfortunately, we don’t really yet understand."

"It turns out that the energy of a gravitational field—any gravitational field—is negative. During inflation, as the universe gets bigger and bigger and more and more matter is created, the total energy of matter goes upward by an enormous amount. Meanwhile, however, the energy of gravity becomes more and more negative. The negative gravitational energy cancels the energy in matter, so the total energy of the system remains whatever it was when inflation started—presumably something very small. ...This capability for producing matter in the universe is one crucial difference between the inflationary model and the previous model."

"The miracle of physics that I'm talking about here is something that was actually known since the time of Einstein's general relativity; that gravity is not always attractive. Gravity can act repulsively. Einstein introduced this in 1916... in the form of the cosmological constant, and the original motivation of modifying the equations of general relativity to allow this was because Einstein thought that the universe was static, and he realized that ordinary gravity would cause the universe to collapse if it was static. ...The fact that general relativity can support this gravitational repulsion, still being consistent with all the principles that general relativity incorporates, is the important thing which Einstein himself did discover.."

"Inflation takes advantage of this possibility... to let gravity be the repulsive force that drove the universe into the period of expansion that we call the Big Bang. In fact, when one combines general relativity with conventional ideas, now, in particle physics there really is a pretty clear indication, I should say, not quite a prediction... that at very high energy densities one expects to find states of matter which literally turn gravity on its head and cause gravity to become repulsive."

"What it takes to produce a gravitational repulsion is a negative pressure. According to general relativity, it turns out... both pressures and energy densities can produce gravitational fields, unlike Newtonian physics, where it's only mass densities that produce gravitational fields."

"A positive pressure produces an attractive gravitational field... Positive pressures are just sort of normal pressures and attractive gravity is normal gravity, so normal pressures produce normal gravity, but it is possible to have negative pressures, and negative pressures produce repulsive gravity, and that's the secret of what makes inflation possible."

"The gravitational repulsion created by this small patch of repulsive gravity material would be, then, the driving force of the Big Bang and it would cause the region to undergo exponential expansion... there is a certain doubling time, and if you wait the same amount of time it doubles again, and if you wait the same amount of time it doubles again... and it's because these doublings build up so dramatically, it doesn't take very much time to build the whole universe. In about 100 doublings this tiny patch of 10-28 cm can become large enough, not to be the universe, but to be a small marble-sized region which will then ultimately become the observed universe, as it continues to coast outward after inflation ends."

"Einstein is the only figure in the physical sciences with a stature that can be compared with Newton. Newton is reported to have said "If I have seen further than other men, it is because I stood on the shoulders of giants." This remark is even more true of Einstein who stood on the shoulders of Newton. Both Newton and Einstein put forward a theory of mechanics and a theory of gravity but Einstein was able to base General Relativity on the mathematical theory of curved spaces that had been constructed by Riemann while Newton had to develop his own mathematical machinery. It is therefore appropriate to acclaim Newton as the greatest figure in mathematical physics and the Principia is his greatest achievement."

"Bodies like the earth are not made to move on curved orbits by a force called gravity; instead, they follow the nearest thing to a straight path in a curved space, which is called a geodesic. A geodesic is the shortest (or longest) path between two nearby points."

"The universe would have expanded in a smooth way from a single point. As it expanded, it would have borrowed energy from the gravitational field, to create matter. As any economist could have predicted, the result of all that borrowing, was inflation. The universe expanded and borrowed at an ever-increasing rate. Fortunately, the debt of gravitational energy will not have to be repaid until the end of the universe."

"'I should here have described some Clocks and Time-keepers of great use, nay absolute necessity in these and many other Astronomical observations, but that I reserve them for some attempts that are hereafter to follow, about the various wayes I have tryed, not without good success of improving Clocks and Watches and adapting them for various uses, as for accurating Astronomy, completing the Tables of the fixt stars to Seconds, discovery of Longitude, regulating Navigation and Geography, detecting the properties and effects of motions for promoting secret and swift conveyance and correspondence, and many other considerable scrutinies of nature: And shall only for the present hint that I have in some of my foregoing observations discovered some new Motions even in the Earth it self, which perhaps were not dreamt of before, which I shall hereafter more at large describe, when further tryalls have more fully confirmed and compleated these beginnings. At which time also I shall explaine a Systeme of the World, differing in many particulars from any yet known, answering in all things to the common Rules of Mechanicall Motions: This depends upon three Suppositions. First, that all Cœlestial Bodies whatsoever, have an attraction or gravitating power towards their own Centers, whereby they attract not only their own parts, and keep them, from flying from them, as we may observe the Earth to do, but that they do also attract all the other Cœlestial Bodies that are within the sphere of their activity; and consequently that not only the Sun and the Moon have an influence upon the body and motion of the Earth, and the Earth upon them, but that Mercury also, Venus, Mars, Saturne, and Jupiter by their attractive powers, have a considerable influence upon its motion as in the same manner the corresponding attractive power of the Earth hath a considerable influence upon every one of their motions also. The second supposition is this, That all bodys whatsoever that are put into direct and simple motion, will so continue to move forward in a streight line, till they are by some other effectual powers deflected and bent into a Motion describing a Circle, Ellipsis, or some other more compounded Curve Line. The third supposition is, That these attractive powers are so much the more powerful in operating, by how much nearer the body wrought upon is to their own Centers. Now what these several degrees are I have not yet experimentally verified;'—But these degrees and proportions of the power of attraction in the celestiall bodys and motions, were communicated to Mr. Newton by R. Hooke in the yeare 1678, by letters, as will plainely appear both by the coppys of the said letters, and the letters of Mr. Newton in answer to them, which are both in the custody of the said R. H., both which also were read before the Royall Society at their publique meeting, as appears by the Journall book of the said Society.—'but it is a notion which if fully prosecuted as it ought to be, will mightily assist the astronomer to reduce all the Cœlestiall motions to a certaine rule, which I doubt will never be done true without it. He that understands the natures of the Circular Pendulum and Circular Motion, will easily understand the whole ground of this Principle, and will know where to find direction in nature for the true stating thereof. This I only hint at present to such as have ability and opportunity of prosecuting this Inquiry, and are not wanting of Industry for observing and calculating, wishing heartily such may be found, having my self many other things in hand which I would first compleat, and therefore cannot so well attend it. But this I durst promise the Undertaker, that he will find all the great Motions of the World to be influenced by this Principle, and that the true understanding thereof will be the true perfection of Astronomy.'"

"Having enumerated some of the most remarkable Proprieties of Gravity, we come in the next place to consider what may be the Cause thereof. And first, I believe I shall not need to say much against the Opinion of Intelligent Matter, which supposes every part of Matter to act understandingly, for that being supposed, all Philosophy is vain, and there needs no farther Inquiry into Nature. And secondly, I have as little to say to its Cousin-german Opinion, viz. the Regimen of an Hylarchick Spirit. And 3ly, The Epicurean Atoms seem to me to give as little of Explanation almost as either of the former. And 4ly, For the Peripatetick Doctrine of tendency to the Center of the Universe, besides that the Foundation is false, the Earth being proved not to be in the Center, 'tis not yet understood what the tendency is. 5ly, The Cartesian Doctrine and that of Mr. Hobbs are both insufficient, because they do not give any reason why Bodies should descend towards the Center under or near the Poles. 6ly, Nor will the Magnetism of Gilbert or Kepler serve; for, as I shall afterwards shew, that is a Propriety distinct from Gravity, and of quite another nature."

"I could... largely explain, and plainly evince, that the Motions of several Bodies at a distance, are caused by the internal motion of the founding Body; and that this Power of moving is every way propagated by the ambient Medium, which excites in solid Bodies at a distance, a similar Motion. I could farther also prove, that every one of these distinct internal Motions of Bodies, as that of Light, and that of Sound, have distinct and differing Mediums, by which those Motions are communicated from the affecting to the affected Body: And so I conceive also that the Medium of Gravity may be distinct and differing both from that of Light, and from that of Sound. I conceive then, that the Gravity of the Earth may be caused by some internal Motion of the internal or central Parts of the Earth; which internal and central Motion may be caused, generated and maintained by the Motion of the external and all the intermediate parts of its Body: So that the whole Globe of the Earth may contribute to this Motion, as it will happen to a Globe of Glass or solid Mettal, to any part of which no internal Motion can be communicated, without at the same time affecting the whole with the same Motion. And I shall most plainly and evidently prove, when I come to the Explication of Magnetism, that this is undeniably performed and effected by this means."

"If light takes the path with the least time between two points, and light beams bend under the influence of gravity, then the shortest distance between two points is a curved line. Einstein was shocked by this conclusion: If light could be observed traveling in a curved line, it would mean that space itself is curved."

"Einstein independently discovered Riemann's original program, to give a purely geometric explanation to the concept of "force." …To Riemann, the bending and warping of space causes the appearance of a force. Thus forces do not really exist; what is actually happening is that space itself is being bent out of shape. The problem with Riemann's approach... was that he had no idea specifically how gravity or electricity and magnetism caused the warping of space. ...Here Einstein succeeded where Riemann failed."

"Many other powers in nature, have an analogy to gravity, but extend to less distances, and observe laws somewhat different. It has been found very difficult to account for them mechanically. For this purpose, some have imagined certain effluvia to proceed from bodies, or atmospheres environing them; others have invented vortices; but all their attempts have hitherto proved unsatisfactory. That such powers take place in nature, and contribute to produce its chief phænomena, is most evident; but their causes are very obscure, and hardly accessible by us. In all the cases when bodies seem to act upon each other at a distance, and tend towards one another without any apparent cause impelling them, this force has been commonly called attraction and this term is frequently used by Sir Isaac Newton. But he gives repeated cautions that he pretends not, by the use of this term, to define the nature of the power, or the manner in which it acts. Nor does he ever affirm, or insinuate, that a body can act upon another at a distance, but by the intervention of other bodies. It is of the utmost importance in philosophy to establish a few general powers in nature, upon unquestionable evidence, to determine their laws, and trace their consequences, however obscure the causes of those powers may be; and this he has done with great success."

"However commodious the term attraction may be, to avoid an useless and tedious circumlocution, yet because it was used by the school-men to cover their ignorance, the adversaries of Sir Isaac Newton's philosophy have taken an unjust handle from his use of this term, after all his precautions, to depreciate and even ridicule his doctrines; by which they only convince us that they neither understand them, nor have impartially and duly considered them. Mr. Leibnitz made use of this same term, in the same sense with Sir Isaac Newton, before he set up in opposition to him; and it is often to be met with in the writings of the most accurate philosophers, who have used it without always guarding against the abuse of it, as he has done. A term of art has been often employed by crafty men, with too much success, to raise a dislike against their opponents, and mislead the unwary, and to disgust them from enquiring into the truth; but such disingenuity is unworthy of philosophers. No writer hath appeared against Sir Isaac Newton, of late, by whom this argument, tho' altogether groundless, is not insisted on at great length; and sometimes adorned with the embellishments of wit and humour; but if the reader will take the trouble to compare their descriptions with Sir Isaac Newtons own account, he will easily perceive how little it was minded by them; and that the sum of all their art and skill amounts to this only, that they were able to expose a creature of their own imagination. Possibly some unskilful men may have fancied that bodies might attract each other by some charm or unknown virtue, without being impelled or acted upon by other bodies, or by any other powers of whatever kind; and some may have imagined that a mutual tendency may be essential to matter, tho' this is directly contrary to the inertia of body described above; but surely Sir Isaac Newton has given no ground for charging him with either of these opinions: he has plainly signified that he thought that those powers arose from the impulses of a subtile ætherial medium that is diffused over the universe, and penetrates the pores of grosser bodies. It appears from his letters to Mr. Boyle that this was his opinion early; and if he did not publish it sooner, it proceeded from hence only, that he found he was not able from experiment and observation to give a satisfactory account of this medium, and the manner of its operation, in producing the chief phænomena of nature."

"Accordingly, we find in his Optical Queries and in his letters to Boyle, that Newton had very early made the attempt to account for gravitation by means of the pressure of a medium, and that the reason he did not publish those investigations "proceeded from hence only, that he found he was not able, from experiment and observation, to give a satisfactory account for this medium, and the manner of its operation in producing the chief phenomena of Nature." The doctrine of direct action at a distance cannot claim for its author the discoverer [Newton] of universal gravitation. It was first asserted by Roger Cotes, in his preface to the Principia... According to Cotes, it is by experience that we learn that all bodies gravitate. We do not learn in any other way that they are extended, movable, or solid. Gravitation, therefore, has as much right to be considered an essential property of matter as extension, mobility, or impenetrability. And when the Newtonian philosophy gained ground in Europe, it was the opinion of Cotes, rather than than that of Newton that became most prevalent, till at last Boscovich propounded his theory, that matter is a congeries of mathematical points, each endowed with the power of attracting or repelling the others according to fixed laws. In his world, matter is unextended, and contact is impossible. He did not forget, however, to endow his mathematical points with inertia."

"Could it be, nevertheless, that Einstein's theory is wrong? Might it be necessary to modify it—to find a new theory of gravity that can explain both the stronger gravity and the apparent antigravity being observed today—rather than simply throwing in invisible things to make the standard model work?"

"To physicists such as myself, the huge amount of invisible dark matter needed to make Einstein's theory fit the astrophysical data is reason enough for exploring modified gravity theories."

"A large part of the relativity community is in denial—refusing even to contemplate the idea that black holes may not exist in nature, or seriously consider the idea that any kind of new matter such as the new putative dark energy can play a fundamental role in gravity theory."

"Giving up Einstein's theory of gravity is simply unacceptable to many in the community. It may take a new generation of physicists to view the evidence with unclouded eyes."

"It offends reason to believe that a well-established natural law can admit of exceptions. A natural law must hold everywhere and always, or be invalid. I cannot believe, for example, that the universal law of gravitation, which governs the physical world, is ever suspended in any instance or at any point of the universe. Now I consider economic laws comparable to natural laws, and I have just as much faith in the principle of the division of labor as I have in the universal law of gravitation. I believe that while these principles can be disturbed, they admit of no exceptions."

"Were I to assume an hypothesis, it should be this... First, it is to be supposed therein, that there is an æthereal medium much of the same constitution with air, but far rarer, subtler, and more strongly elastic. Of the existence of this medium the motion of a pendulum in a glass exhausted of air almost as quickly as in the open air, is no inconsiderable argument. But it is not to be supposed that this medium is one uniform matter, but compounded, partly of the main phlegmatic body of æther, partly of other various æthereal spirits, much after the manner, that air is compounded of the phlegmatic body of air intermixed with various vapours and exhalations: for the electric and magnetic effluvia, and gravitating principle, seem to argue such variety. Perhaps the whole frame of nature may be nothing but various contextures of some certain æthereal spirits, or vapours, condensed as it were by precipitation, much after the manner, that vapours are condensed into water, or exhalations into grosser substances, though not so easily condensible; and after condensation wrought into various forms; at first by the immediate hand of the Creator; and ever since by the power of nature; which, by virtue of the command, increase and multiply, became a complete imitator of the copies set her by the protoplast. Thus perhaps may all things be originated from æther."

"So may the gravitating attraction of the earth be caused by the continual condensation of some other such like ethereal spirit, not of the main body of phlegmatic ether, but of something very thinly and subtilely diffused through it, perhaps of an unctuous or gummy, tenacious, and springy nature, and bearing much of the same relation to ether, which the vital aereal spirit, requisite for the conservation of flame and vital motions, does to air. For, if such an ethereal spirit may be condensed in fermenting or burning bodies, or otherwise coagulated in the pores of the earth and water, into some kind of humid active matter, for the continual uses of nature, adhering to the sides of those pores, after the manner that vapours condense on the sides of a vessel; the vast body of the earth, which may be every where to the very centre in perpetual working, may continually condense so much of this spirit, as to cause it from above to descend with great celerity for a supply; in which descent it may bear down with it the bodies it pervades, with force proportional to the superficies of all their parts it acts upon; nature making a circulation by the slow ascent of as much matter out of the bowels of the earth in an aereal form, which for a time constitutes the atmosphere; but being continually buoyed up by a new air, exhalations and vapours rising underneath, at length, (some part of the vapours which return in rain excepted,) vanishes again into the ethereal spaces, and there perhaps in time relents, and is attenuated into its first principle: for nature is a perpetual worker, generating fluids out of solids, and solids out of fluids, fixed things out of volatile, and volatile out of fixed, subtile out of gross, and gross out of subtile; some things to ascend, and make the upper terrestrial juices, rivers, and atmosphere; and by consequence others to descend for a requital to the former."

"I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena is to be called a hypothesis, and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy."

"The truth is, my notions about things of this kind are so indigested, that I am not well satisfied myself in them; and what I am not satisfied in, I can scarce esteem to fit to be communicated to others; especially in natural philosophy, where there is no end of fancying. But because I am indebted to you... I could not forbear to take the opportunity of conveying this to you... I shall set down one conjecture more... it is about the cause of gravity. For this end I will suppose aether to consist of parts differing from one another in subtilty by indefinite degrees; that in the pores of bodies there is less of the grosser aether, in proportion to the finer, than in open spaces; and consequently, that in the great body of the earth there is much less of the grosser aether, in proportion to the finer, than in the regions of the air; and that yet the grosser aether in the air affects the upper regions of the earth, and the finer aether in the earth the lower regions of the air, in such a manner, that from the top of the air to the surface of the earth, and again from the surface of the earth to the centre thereof, the aether is insensibly finer and finer. Imagine now any body suspended in the air, or lying on the earth, and the aether being by the hypothesis grosser in the pores, which are in the upper parts of the body, than in those which are in its lower parts, and that grosser aether being less apt to be lodged in those pores than the finer aether below, it will endeavour to get out and give way to the finer aether below, which cannot be, without the bodies descending to make room above for it to go out into."

"Our design, not respecting arts, but philosophy, and our subject, not manual, but natural powers, we consider chiefly those things which relate to gravity, levity, elastic force, the resistance of fluids, and the like forces, whether attractive or impulsive; and therefore we offer this work as mathematical principles of philosophy; for all the difficulty of philosophy seems to consist in this — from the phenomena of motions to investigate the forces of nature, and then from these forces to demonstrate the other phenomena..."

"This most beautiful System of the Sun, Planets and Comets, could only proceed from the counsel and dominion of an intelligent and powerful being. And if the fixed Stars are the centers of other like systems, these being form'd by the like wise counsel, must be all subject to the dominion of One; especially, since the light of the fixed Stars is of the same nature with the light of the Sun, and from every system light passes into all the other systems. And lest the systems of the fixed Stars should, by their gravity, fall on each other mutually, he hath placed those Systems at immense distances one from another."

"In the beginning of the year 1665 I found the method of approximating Series and the Rule for reducing any dignity of any Binomial into such a series. The same year in May I found the method of tangents of Gregory and Slusius, and in November had the direct method of Fluxions, and the next year in January had the Theory of Colours, and in May following I had entrance into the inverse method of Fluxions. And the same year I began to think of gravity extending to the orb of the Moon, and having found out how to estimate the force with which [a] globe revolving within a sphere presses the surface of the sphere, from Kepler's Rule of the periodical times of the Planets being in a sesquialterate proportion of their distances from the centers of their orbs I deduced that the forces which keep the Planets in their Orbs must [be] reciprocally as the squares of their distances from the centers about which they revolve: and thereby compared the force requisite to keep the Moon in her orb with the force of gravity at the surface of the earth, and found them answer pretty nearly. All this was in the two plague years of 1665 and 1666, for in those days I was in the prime of my age for invention, and minded Mathematicks and Philosophy more than at any time since. What Mr Hugens has published since about centrifugal forces I suppose he had before me. At length in the winter between the years 1676 and 1677 I found the Proposition that by a centrifugal force reciprocally as the square of the distance a Planet must revolve in an Ellipsis about the center of the force placed in the lower umbilicus of the Ellipsis and with a radius drawn to that center describe areas proportional to the times. And in the winter between the years 1683 and 1684 this Proposition with the Demonstration was entered in the Register book of the R. Society. And this is the first instance upon record of any Proposition in the higher Geometry found out by the method in dispute. In the year 1689 Mr Leibnitz, endeavouring to rival me, published a Demonstration of the same Proposition upon another supposition, but his Demonstration proved erroneous for want of skill in the method."

"You sometimes speak of Gravity as essential and inherent to Matter. Pray do not ascribe that Notion to me; for the Cause of Gravity is what I do not pretend to know, and therefore would take more Time to consider it."

"It is inconceivable that inanimate brute Matter, should, without the mediation of something else, which is not material, operate on and affect other Matter without mutual Contact, as it must be, if Gravitation in the sense of Epicurus, be essential and inherent in it. And this is one Reason why I desired you would not ascribe innate Gravity to me. That Gravity should be innate, inherent and essential to Matter so that one Body may act upon another at a Distance thro' a Vacuum, without the Mediation of any thing else, by and through which their Action and Force may be conveyed, from one to another, is to me so great an Absurdity, that I believe that no Man who has in philosophical Matters a competent Faculty of thinking, can ever fall into it. Gravity must be caused by an Agent acting constantly according to certain Laws; but whether this Agent be material or immaterial, I have left for the Consideration of my Readers."

"Weyl considered an aspect about general relativity... the nonpreservation of direction in a curved space. ...[He] decided to consider the possibility that length was also not preserved. ...To effect this change mathematically, Weyl had to make a slight modification in the structure of general relativity. He assumed that in addition to the usual metric (set of numbers or variables) that described the gravitational field, there was another one related to length. ...amazingly when the result was analyzed Maxwell's equations mysteriously appeared. It almost seemed as if a bit of magic had occurred and scientists quickly became interested in the miracle. ...but with detailed analysis the theory was shown to be flawed. Einstein was the first to put his finger on the flaw. ...Weyl soon acknowledged the flaw and laid his theory to rest. It may have been a failure (actually it was not an entire failure; a similar idea is used today in modern field theory), but it did accomplish something important: it got people interested in the possibility that the electromagnetic and gravitational field could be unified. Einstein soon began working on an alternative theory, as did others."

"How... can we understand the connexion between Force and Matter? Matter is known to us only through its manifestations of Force: our ultimate test of Matter is the ability to resist: abstract its resistance and there remains nothing but empty extension. Yet, on the other hand, resistance is equally unthinkable apart from Matter—apart from something extended. Not only... are centres of force devoid of extension unimaginable; but, as an inevitable corollary, we cannot imagine either extended or unextended centres of force to attract and repel other such centres at a distance, without the intermediation of some kind of matter. ...the hypothesis of Newton, equally with that of Boscovich, is open to the charge that it supposes one thing to act upon another through a space which is absolutely empty—a supposition which cannot be represented in thought. This charge is indeed met by the introduction of a hypothetical fluid existing between the atoms or centres. But the problem is not thus solved: it is simply shifted, and re-appears when the constitution of this fluid is inquired into."

"But if justice be a natural principle, then it is necessarily an immutable one; and can no more be changed—by any power inferior to that which established it—than can the law of gravitation, the laws of light, the principles of mathematics, or any other natural law or principle whatever; and all attempts or assumptions, on the part of any man or body of men—whether calling themselves governments, or by any other name—to set up their own commands, wills, pleasure, or discretion, in the place of justice, as a rule of conduct for any human being, are as much an absurdity, an usurpation, and a tyranny, as would be their attempts to set up their own commands, wills, pleasure, or discretion in the place of any and all the physical, mental, and moral laws of the universe."

"According to Newton's law of gravity, every object in the universe attracts every other object... with a gravitational force... F = \frac{m M G}{R^2}... almost as famous as E = mc^2... On the left side is the force, F, between two masses... On the right side, the bigger mass is M and the smaller mass is m. ...The last symbol... G, is a numerical constant called Newton's constant. ...Ironically, Newton never knew the value of his own constant. ...G was too small to measure until the end of the eighteenth century. ...Cavendish found that the force between a pair of one-kilogram masses separated by one meter is approximately 6.6 x 10-11 newtons. (The Newton is... about one-fifth of a pound.) ...Newton had one lucky break... the special mathematical properties of the inverse square law. ...[B]y the miracle of mathematics, you can pretend that the entire mass is located at a single point. This... allowed Newton to calculate the ... Escape \; velocity = \sqrt{2MG/R} ... the bigger the mass [M] and the smaller the radius R, the larger the escape velocity."

"I would like to emphasize at the opening of this symposium that the often quoted ratio M/L is in fact the ratio V2r/L of the directly observable quantities V, r, and L. This ratio V2r/L can only be interpreted as an indicator of mass to light ratio if we assume that Newton's law of gravitational attraction is correct on the scale of galaxies. Since Keplerian behavior is essentially never seen in extra-galactic systems, I might be so bold as to suggest that the validity of Newton's law should be seriously questioned. I hope that the observers who have definite evidence that Keplerian behavior has been observed in any system will emphasize that evidence at this meeting."

"Men of splendid talents are generally too quick, too volatile, too adventurous, and too unstable to be much relied on; whereas men of common abilities, in a regular, plodding routine of business, act with more regularity and greater certainty. Men of the best intellectual abilities are apt to strike off suddenly, like the tangent of a circle, and cannot be brought into their orbits by attraction or gravity — they often act with such eccentricity as to be lost in the vortex of their own reveries. Brilliant talents in general are like the ignes fatui; they excite wonder, but often mislead. They are not, however, without their use; like the fire from the flint, once produced, it may be converted, by solid, thinking men, to very salutary and noble purposes."

"Just as an iron ball surrounded by pieces of magnet does not fall though standing (supportless) in the sky, in the same way this (globe of the) Earth though supportless does not fall as it is prevented by (the attraction of) the stars and planets."

"Just as a house lizard runs about on the surface of a pitcher lying in open space, so do the human beings move about comfortably all around the Earth."

"A new theory by the author has been added, which draws the physical inferences consequent on the extension of the foundations of geometry beyond Reimann... and represents an attempt to derive from world-geometry not only gravitational but also electromagnetic phenomena. Even if this theory is still only in its infant stage, I feel convinced that it contains no less truth than Einstein's Theory of Gravitation—whether this amount of truth is unlimited or, what is more probable, is bounded by the Quantum Theory."

"It is quite easy to include a weight for empty space in the equations of gravity. Einstein did so in 1917, introducing what came to be known as the cosmological constant into his equations. His motivation was to construct a static model of the universe. To achieve this, he had to introduce a negative mass density for empty space, which just canceled the average positive density due to matter. With zero total density, gravitational forces can be in static equilibrium. Hubble's subsequent discovery of the expansion of the universe, of course, made Einstein's static model universe obsolete. ...The fact is that to this day we do not understand in a deep way why the vacuum doesn't weigh, or (to say the same thing in another way) why the cosmological constant vanishes, or (to say it in yet another way) why Einstein's greatest blunder was a mistake."

"The dark matter really does look like matter. It does not look like a modification of gravity."

"Frank Wilczek, 26:01 of 40:44"

"String theory is extremely attractive because gravity is forced upon us. All known consistent string theories include gravity, so while gravity is impossible in quantum field theory as we have known it, it is obligatory in string theory."

"Even though it is, properly speaking, a postprediction, in the sense that the experiment was made before the theory, the fact that gravity is a consequence of string theory, to me, is one of the greatest theoretical insights ever."

"If supersymmetry plays the role in physics that we suspect it does, then it is very likely to be discovered by the next generation of particle accelerators, either at Fermilab... or at CERN... Discovery of supersymmetry would be one of the real milestones in physics, made even more exciting by its close links to still more ambitious theoretical ideas. Indeed, supersymmetry is one of the basic requirements of "string theory," which is the framework in which theoretical physicists have had some success in unifying gravity with the rest of the elementary particle forces. Discovery of supersymmetry would would certainly give string theory an enormous boost."

"It was found [in the 1970s], unexpectedly and without anyone really having a concept for it, that the rules of perturbation theory can be changed in a way that makes relativistic quantum gravity inevitable rather than impossible. The change is made by replacing point particles by strings. Then Feynman graphs are replaced by Riemann surfaces, which are smooth - unlike the graphs, which have singularities at interaction vertices. The Riemann surfaces can degenerate to graphs in many different ways. In field theory, the interactions occur at the vertices of a Feynman graph. By contrast, in string theory, the interaction is encoded globally, in the topology of a Riemann surface, any small piece of which is like any other. This is reminiscent of how non-linearities are encoded globally in twistor theory."

"Replacing particles by strings is a naive-sounding step, from which many other things follow. In fact, replacing Feynman graphs by Riemann surfaces has numerous consequences: 1. It eliminates the infinities from the theory. ...2. It greatly reduces the number of possible theories. ...3. It gives the first hint that string theory will change our notions of spacetime. Just as in QCD, so also in gravity, many of the interesting questions cannot be answered in perturbation theory. In string theory, to understand the nature of the Big Bang, or the quantum fate of a black hole, or the nature of the vacuum state that determines the properties of the elementary particles, requires information beyond perturbation theory... Perturbation theory is not everything. It is just the way the [string] theory was discovered."

"It is observed by Bacon, in his essay on the opinions of Parmenides, that the most ancient philosophers, Empedocles, Anaxagoras, Anaximenes, Heraclitus, and Democritus, submitted their minds to things as they found them; but that Plato made the world subject to ideas, and Aristotle made even ideas, as well as all other things, subservient to words; the minds of men beginning to be occupied, in those times, with idle discussions and verbal disputations, and the correct investigation of nature being wholly neglected. Plato entertained, however, some correct notions respecting the distinction of denser from rarer matter by its greater inertia; and it would be extremely unjust to deny a very high degree of merit to Aristotle's experimental researches, in various parts of natural philosophy, and in particular to the vast collection of real information contained in his works on natural history. Aristotle attributed absolute levity to fire, and gravity to the earth, considering air and water as of an intermediate nature. By gravity the ancients appear in general to have understood a tendency towards the centre of the earth, which they considered as identical with that of the universe; and as long as they entertained this opinion, it was almost impossible that they should suspect the operation of a mutual attraction in all matter, as a cause of gravitation. The first traces of this more correct opinion respecting it are found in the works of Plutarch."

"William Gilbert published a famous book on the magnet in 1600 and laid himself open to the gibes of Sir Francis Bacon for being one of those people so taken by their pet subject of research that they could only see the whole universe transposed into terms of it. Having made a spherical magnet called a ', and having found that it revolved when placed in a magnetic field, he decided that the whole earth was a magnet, that gravity was a form of magnetic attraction, and that the principles of the magnet accounted for the workings of the Copernican system as a whole. Kepler and Galileo were both influenced by this view, and with Kepler, it became an integral part of his system, a basis for the doctrine of almost universal gravitation."

"Descartes was liable to be misled by too easy an acceptance of data that had been handed down by scholastic writers. ...two grand Aristotelian principles helped to condition the form of the universe as he reconstructed it—first, the view that a vacuum is impossible, and secondly, the view that objects could only influence one another if they actually touched—there could be no such thing as attraction, no such thing as . ...Descartes insisted that every fraction of space should be fully occupied all the time by continuous matter... infinitely divisible. The particles were... packed so tightly that one of them could not move without communicating the commotion to the rest. The matter formed whirlpools in the skies, and it was because the planets were caught each in its own whirlpool that they were carried around... all similarly caught in a larger whirlpool, which had the sun as its centre... Gravity itself was the result of these whirlpools of invisible matter which had the effect of sucking things down towards their centre. ...In the time of Newton the system of Descartes and the theory of vortices or whirlpools proved to be vulnerable to both mathematical and experimental attack."

"In the middle of the 1660s, Borelli, Newton, Huygens and Hooke were wrestling with various parts of the same planetary problems, some of them treading on one another's heels in the study of the nature of light... in England, experiments with the pendulum clock had started independently, and Christopher Wren, , William Balle and Laurence Rooke appear to have unaugurated the enquiry into laws of motion, Robert Hooke performing most of the experiments. The 1670s must represent one of the greatest decades in the scientific revolution, if not the climax... and in both London and Paris... achievements... were of a remarkable nature. So far as the gravitational theory... our attention ought to be directed not merely to Newton... but to the combined operations of the English group. The Royal Society... following Baconian principles, sought to collect... the data necessary for the establishment of the Copernican hypothesis... ideally... "freely communicating their methods and pooling their gains." Here the names... in the forefront are... Isaac Newton, Robert Hooke, Edmond Halley and Christopher Wren."

"Hooke... followed Bacon in his attempt to demonstrate that the effects of gravity on a body must diminish as the body was sunk into the bowels of the earth. He sought to discover how far the effects were altered at great heights or in the region of the equator; and he threw light on the problem by observations and experiments on the pendulum. From the globular shapes of the heavenly bodies and the stable conformations of the ridges on the moon he deduced that the moon and the planets had gravity; and by 1666 he saw the motion of a comet (for example) as incurvated by the pull of the sun... and suggested that the motion of the planets might be explicable on the kind of principles that account for the motion of a pendulum. In 1674 he was suggesting that by this route one could arrive at a mechanical system of the planets which would be "the true perfection of astronomy." He pointed out that... account must be taken of the force which all heavenly bodies must be presumed to be exerting on one another. ...By 1678 he had formulated the idea of gravitation as a universal principle; and by 1679 he, too, had discovered that the diminution of the force of gravity is proportional to the square of the distance. ...But ...Hooke did not produce the mathematical demonstrations of his system."

"Rigid bodies can be divided into two types: unconstrained rigid bodies, such as the pieces from a breaking up fighter plane in Pearl Harbor, and rigid bodies connected by joints which constrain their degrees of freedom (known as articulated rigid bodies), such as the battle droids in Star Wars: Episode I or Davy Jones’ beard in Pirates of the Caribbean: Dead Man's Chest."

"The study of waves is important to virtually every branch of science and engineering. Indeed, waves are also important to everyday life. Sound waves allow us to hear, and electromagnetic waves allow us to see."

"The mass gap is the reason, if you will, that we do not see classical nonlinear Yang-Mills waves. They are a good approximation only under inaccessible conditions. I have spent most of my career wishing that we had a really good way to quantitatively understand the mass gap in four-dimensional gauge theory. I hope that this problem will be solved one day."

"The mathematical theory of critical phenomena is currently undergoing intense development. Intertwined with the science of phase transitions, it draws on ideas from probability theory and statistical physics."

"[A]s a liquid changes into a gas at the critical temperature T_c, the heat capacity diverges as c \sim \frac{1}{\left|T-T_c\right|^{0.11008 \ldots}}. The exponent is not known precisely. It is thought not to be a rational number, but should instead be viewed as a universal mathematical constant, similar to \pi"

"A little reflection will show that law of the inert and the gravitational mass is equivalent to the assertion that the acceleration imparted to a body by a gravitational field is independent of the nature of the body. For Newton's equation of motion in a gravitational field, written out in full, is (Inert mass) . (Acceleration) = (Intensity of the gravitational field) . (Gravitational mass). It is only when there is numerical equality between the inert and gravitational mass that the acceleration is independent of the nature of the body."

"We postulate: It shall be impossible, by any experiment whatsoever performed inside such a box, to detect a difference between an acceleration relative to the nebulae and gravity. That is, an accelerating box in some gravitational field is indistinguishable from a stationary box in some different gravitational field. How much like Einstein this sounds, how reminiscent of his postulate of special relativity! We know the principle of equivalence works for springs, (as we knew special relativity worked for electrodynamics), and we extend it by fiat to all experiments whatsoever. We are used to such procedures by now, but how originally brilliant it was in 1911—what a brilliant, marvelous man Einstein was!"

"In fact, how could you tell inside a space ship whether you are sitting on the earth or are accelerating in free space? According to Einstein’s equivalence principle there is no way to tell if you only make measurements of what happens to things inside!"

"[T]he gravitational force allows us to declare that all observers—regardless of their state of motion—are on absolutely equal footing. Even those whom we would normally think of as accelerating may claim to be at rest, since they can attribute the force they feel to their being emersed in a gravitational field. In this sense gravity enforces the symmetry: it ensures the equal validity of all possible observational points of view, all possible frames of reference."

"Are any of nature's fundamental parameters truly constant? ... Extensions of Albert Einstein’s theory of general relativity can realize variations in Newton’s constant. In the simplest such extension, one adds a scalar field ... The predictions of the extended theory may be described in terms of two so-called post-Einstein parameters β and γ, whose values are exactly 1 in general relativity. A recent experiment ... has determined that (γ – 1) = (2.1 ± 2.3) × 10–5, a constraint that represents an order-of-magnitude improvement over previous results. Modifications of general relativity typically lead to violations of the equivalence principle. Tests of the principle, in turn, can be used to set model-dependent constraints on the variations of fundamental couplings."

"... what is the motivation for the special gauge invariant Lagrangians that we use in the standard model and general relativity? One possible answer is that quantum theories of mass zero, spin one particles violate Lorentz invariance unless the fields are coupled in a gauge invariant way, while quantum theories of mass zero, spin two particles violate Lorentz invariance unless the fields are coupled in a way that satisfies the equivalence principle."

"I have no trouble publishing in Soviet astrophysical journals, but my work is unacceptable to the American astrophysical journals."

"The peer review system is satisfactory during quiescent times, but not during a revolution in a discipline such as astrophysics, when the establishment seeks to preserve the status quo."

"Students using astrophysical textbooks remain essentially ignorant of even the existence of plasma concepts, despite the fact that some of them have been known for half a century. The conclusion is that astrophysics is too important to be left in the hands of astrophysicists who have gotten their main knowledge from these textbooks. Earthbound and space telescope data must be treated by scientists who are familiar with laboratory and magnetospheric physics and circuit theory, and of course with modern plasma theory."

"The greatest astronomers of the first half of the 20th century were the astrophysicists. For example, Arthur Eddington, Cecilia Payne, Hans Bethe, and Subrahmanyan Chandrasekhar elucidated the physical nature of stars using the new quantum theories of atomic, nuclear and particle physics. In recent decades, about half of the prizes of the American Astronomical Society are awarded for work in astrophysics and half in astronomy."

"It is regrettable that Voigt's original ideas were unnoticed and, hence, did not play a role in the vigorous development of special relativity, somewhat similar to Poincare's work in 1905. Lorentz, Poincare, Einstein and others did not refer to Voigt's paper in their works. It appears that young Pauli was an early physicist to mention Voigt's transformation in his book 'Theory of Relativity', published in 1921, but no further comment was made."

"The great merit of Minkowski was to show that an absolute world could nevertheless be imagined, although it was a far different world from that of classical physics. In Minkowski's world the absolute which supersedes the absolute length and duration of classical physics is the Einsteinian interval. ... Thus suppose that, as measured in our Galilean frame of reference, two flashes occur at points A and B, situated at a distance l apart, and suppose the flashes are separated in time by an interval t. If we change our frame of reference, both l and t will change in value, becoming l and t respectively, exhibiting by their changes the relativity of length and duration. In Minkowski's words, "Henceforth space and time themselves are mere shadows." On the other hand, the mathematical construct l^2 - c^2t^2 will remain invariant, and so we shall have l^2 - c^2t^2 = l'^2 - c^2t'^2. It is this invariant expression, which involves both length and duration, or both space and time, which constitutes the Einsteinian interval; and the objective world which it cannotes is the world of four-dimensional space-time. The Einsteinian interval... remains the same for all observers, just as distance alone or duration alone were mistakenly believed to remain the same for all observers in classical physics. ...the Einsteinian interval still remains an invariant as measured for all frames of reference, whether accelerated or not."

"A four dimensional continuum described by the co ordinates x1, x2, x3, x4, was called "world" by Minkowski, who also termed a point-event a "world point." From a "happening" in three-dimensional space, physics becomes, as it were, an "existence" in the four-dimensional world. This four dimensional "world" bears a close similarity to the three-dimensional "space" of Euclidean analytical geometry. ...We can regard Minkowski's "world" in a formal manner as a four-dimensional Euclidean space (with imaginary time co-ordinate); the Lorentz transformation corresponds to a "rotation" of the co-ordinate system in the four-dimensional world."

"The discovery of Minkowski... is to be found... in the fact of his recognition that the four-dimensional space-time continuum of the theory of relativity, in its most essential formal properties, shows a pronounced relationship to the three-dimensional continuum of Euclidean geometrical space. In order to give due prominence to this relationship, however, we must replace the usual time co-ordinate t by an imaginary magnitude, \sqrt -1\cdot ct, proportional to it. Under these conditions, the natural laws satisfying the demands of the (special) theory of relativity assume mathematical forms, in which the time co-ordinate plays exactly the same role as the three space-coordinates. Formally, these four co-ordinates correspond exactly to the three space co-ordinates in Euclidean geometry. ...These inadequate remarks can give the reader only a vague notion of the important idea contributed by Minkowski. Without it the general theory of relativity... would perhaps have got no farther than its long clothes."

"For over 200 years the equations of motion enunciated by Newton were believed to describe nature correctly, and the first time that an error in these laws was discovered, the way to correct it was also discovered. Both the error and its correction were discovered by Einstein in 1905.Newton’s Second Law, which we have expressed by the equation F=\frac {d\left({mv}\right)}{dt} was stated with the tacit assumption that m is a constant, but we now know that this is not true, and that the mass of a body increases with velocity. In Einstein’s corrected formula m has the value m=\frac {{m}_}{\sqrt} where the “rest mass” m0 represents the mass of a body that is not moving and c is the speed of light, which is about 3×105 km⋅sec−1 or about 186,000 mi⋅sec−1."

"The impressions received by the two observers A0 and A would be alike in all respects. It would be impossible to decide which of them moves or stands still with respect to the ether, and there would be no reason for preferring the times and lengths measured by the one to those determined by the other, nor for saying that either of them is in possession of the "true" times or the "true" lengths. This is a point which Einstein has laid particular stress on, in a theory in which he starts from what he calls the principle of relativity, i.e., the principle that the equations by means of which physical phenomena may be described are not altered in form when we change the axes of coordinates for others having a uniform motion of translation relatively to the original system. I cannot speak here of the many highly interesting applications which Einstein has made of this principle. His results concerning electromagnetic and optical phenomena ...agree in the main with those which we have obtained... the chief difference being that Einstein simply postulates what we have deduced, with some difficulty and not altogether satisfactorily, from the fundamental equations of the electromagnetic field. By doing so, he may certainly take credit for making us see in the negative result of experiments like those of Michelson, Rayleigh and Brace, not a fortuitous compensation of opposing effects, but the manifestation of a general and fundamental principle. Yet, I think, something may also be claimed in favour of the form in which I have presented the theory. I cannot but regard the ether, which can be the seat of an electromagnetic field with its energy and vibrations, as endowed with a certain degree of substantiality, however different it may be from all ordinary matter. ...it seems natural not to assume at starting that it can never make any difference whether a body moves through the ether or not, and to measure distances and lengths of time by means of rods and clocks having a fixed position relatively to the ether. It would be unjust not to add that, besides the fascinating boldness of its starting point, Einstein's theory has another marked advantage over mine. Whereas I have not been able to obtain for the equations referred to moving axes exactly the same form as for those which apply to a stationary system, Einstein has accomplished this by means of a system of new variables slightly different from those which I have introduced."

"Between 1968 and 2005 I’ve learned a lot about explaining special relativity. One pedagogical discovery has been especially valuable. Anybody wishing to understand the subject must be able to visualize how certain events taking place, say, in a railroad station, are described from the point of view of a passenger passing through that station on a uniformly moving train and, conversely, how events taking place on such a train appear to a person standing in the station. Without the ability to translate from one such description to another, one cannot begin to understand relativity. But all introductions to relativity that I know of, including my own 1968 book, take the ability to do this for granted. They immediately require the reader to apply this unused, undeveloped, often nonexistent skill to some highly counterintuitive phenomena. In explaining relativity this process often leads to descriptions from two different perspectives, which appear, at first glance, to contradict each other. Faced with an apparent paradox, people who have never before thought about transforming station descriptions to train descriptions and vice versa quite reasonably assume that they must have done something wrong in the transcription. Rather than seeking an understanding of why the contradiction is only apparent, they lose confidence in the analytical technique that gave rise to it. In this respect the pedagogy of the standard approach to relativity is terrible. One introduces a crucial and unfamiliar conceptual technique— changing descriptions from one “frame of reference” to another—by immediately applying it to some unusual and highly counterintuitive cases. The most important thing I learned in teaching relativity to many generations of Cornell undergraduates, none of them science majors, is that one must begin teaching them the technique of changing frames of reference by applying that technique to some entirely commonplace, highly intuitive examples. There are many such ways to develop these skills, and they enable one to learn much that is not at all obvious, though never paradoxical."

"Another thing I have learned since 1968 is that one should emphasize as early as possible that although objects moving at the speed of light famously behave in some very strange ways, the behavior of objects moving at speeds comparable to the speed of light can be just as peculiar. The peculiarity of motion at the speed of light is just a special case of a more general peculiarity of all motion, which becomes prominent only at extremely high speeds. That more general peculiarity can be expressed by an elementary but precise rule that it is possible and useful to formulate at a very early stage of the subject."

"I. Redefine the foot. II. View nonrelativistic collisions from different frames. III. Immediately introduce relativistic velocity addition law. IV. Immediately introduce relativity of simultaneity. V. Give numerical illustrations. VI. Minkowski diagrams, direct from Einstein’s postulates. VII. Don’t bother with the spacetime Lorentz transformation."

"The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."

"The whole world appears resolved into such world-lines. And I should like to say beforehand that, according to my opinion, it would be possible for the physical laws to find their fullest expression as correlations of these world-lines."

"The word postulate of relativity... appears to me very stale... I should rather like to give this statement the name Postulate of the absolute world (or briefly, world-postulate)."

"In a Newtonian view, space and time are separate and different. Symmetries of the laws of physics are combinations of rigid motions of space and an independent shift in time. But... these transformations do not leave Maxwell's equations invariant. Pondering this, the mathematicians Henri Poincaré and Hermann Minkowski were led to a new view of the symmetries of space and time, on a purely mathematical level. If they had described these symmetries in physical terms, they would have beaten Einstein to relativity, but they avoided physical speculations. They did understand that symmetries in the laws of electromagnetism do not affect space and time independently but mix them up. The mathematical scheme describing these intertwined changes is known as the Lorentz group, after the physicist, Hendrik Lorentz."

"Poincaré came very close to inventing special relativity in the years 1900-1904, showing in particular that Lorentz transformations form a group; hence in the case of the Poincaré group, the name is accurate."

"The strangest explanation [for the Michelson–Morley experiment] was put forth by an Irish physicist, . Perhaps, he said, the ether wind puts pressure on a moving object, causing it to shrink a bit in the direction of motion. To determine the length of a moving object, its length at rest must be multiplied by the following simple formula, in which \scriptstyle v^2 is the velocity of the object multiplied by itself, \scriptstyle c^2 is the velocity of light multiplied by itself: \scriptstyle \sqrt{1-\frac{v^2}{c^2}}."

"The speed of light in an unobtainable limit; when this is reached the formula becomes \scriptstyle \sqrt{1-\frac{c^2}{c^2}} which reduces to 0. ...In other words, if an object could obtain the speed of light, it would have no length at all in the direction of its motion!"

"FitzGerald's theory was put into elegant mathematical form by the Dutch physicist Hendrick Antoon Lorentz, who had independently thought of the same explanation. ...The theory came to be known as the Lorentz-FitzGerald contraction theory."

"Lorentz made an important addition to his original theory. He introduced changes in time. Clocks, he said, would be slowed down by the ether wind, and in just such a way as to make the velocity of light always measure 299,800 meters per second."

"Einstein, following the steps of Ernst Mach... said... There is no ether wind. He did not say that there was no ether; only... [that the ether] is of no value in measuring uniform motion."

"The special theory of relativity carries the classical relativity of Newton forward another step. It says that in addition to being unable to detect the train's motion by a mechanical experiment, it is also impossible to detect its motion by an optical experiment."

"It is not possible to measure uniform motion in any absolute way."

"In the special theory of relativity, the speed of light becomes... a new absolute. ...Regardless of the motion of its source, light always moves through space with the same constant speed."

"There is no absolute time throughout the universe by which absolute simultaneity can be measured. Absolute simultaneity of distant events is a meaningless concept."

"If an astronaut traveled as fast as light his clock would stop completely."

"If two spaceships are in relative motion, an observer on each ship will measure the other ship as contracted slightly in the direction of its motion. ...The theory does not say that each ship is shorter than the other; it says that astronauts on each ship measure the other ship as shorter."

"Two ships are passing each other with uniform speed close to that of light. As they pass, a beam of light on the other ship is sent from the ceiling to the floor. There it strikes a mirror and is reflected back to the ceiling again. You will see the path of this light as a V [shape]. If you had sufficiently accurate instruments (of course no such instrument exists), you could clock the time it takes this light beam to traverse the V-shaped path. By dividing the length of the path by the time, you obtain the speed of light. ...an astronaut inside the other ship is doing the same thing [measuring his light beam's speed]. From his point of view... the light simply goes down and up along the same line, obviously a shorter distance than along the V that you observed. ...he also obtains the speed of light. ...But his light path is shorter. ...There is only one possible explanation: his clock is slower. Of course, the situation is perfectly symmetrical. If you send a beam down and up inside your ship, he will see its path as V-shaped. He will deduce that your clock is slower."

"All three variables—length, time, mass—are covered by the same Lorentz contraction [ \scriptstyle \sqrt{1-\frac{v^2}{c^2}} ]... Length and the rate of clocks vary in the same direct proportion, so the formula is the same for each. Mass... varies in the inverse proportion... \scriptstyle \frac{1} {\sqrt{1-\frac{v^2}{c^2}}}."

"The speed of light can never be reached. If it were reached, the outside observer would find that the ship had shrunk to zero length, had acquired an infinite mass, and was exerting an infinite force with its rocket motors. Astronauts inside the ship would observe no changes in themselves, but they would find the cosmos hurtling backward with the speed of light, cosmic time at a standstill, every star flattened to a disk and infinitely massive."

"All [of Newton's] fundamental laws of mechanics involved statements concerning accelerations, changes in the velocities... rather than the velocities themselves. These accelerations were tied to the distances between the bodies... [F]or collecting data relevant to an experimental confirmation of Newton's laws... one may consider equivalent all observers who, relative to one another, are engaged in straight-line and unaccelerated motion. ...Such an observer will be called an inertial observer; relative to him, the motion of a forcefree body will be unaccelerated. If an inertial observer is considered the hub of a scaffolding... one calls the whole framework an inertial frame of reference, or for short, an inertial frame. ...The equal validity of all inertial frames... and the non-existence of one frame representing absolute rest, is known as the principle of relativity. [It] remained unquestioned for about two hundred years. ...[T]here was no such thing as absolute rest, or absolute motion, for that matter, but only absolute acceleration... governed by the forces resulting from the proximity of other bodies."

"Based on Faraday's earlier work, Maxwell stressed the notion of fields, in contrast to Newton's emphasis on the direct action of bodies on each other across empty space ('). Faraday and Maxwell regarded the effect of an electrically charged body as giving rise to stresses in its immediate surroundings... [and] in ever widening circles, gradually diminishing... These stresses... [i.e.,] the fields are intermediaries between the material particles and assume the burden of Newton's action at a distance. ...[O]ne set of Maxwell's equations is to the effect that, in the presence of a magnetic field which changes in the course of time, an electric field arises which is not caused by the presence of any electric charge. This [is] the law of electromagnetic induction... From his theory, Maxwell... predicted that magnetic fields propogate at... the speed of light. ...The laws of mechanics involve only accelerations, not velocities: the laws of electromagnetism involve a universal velocity [c]..."

"If there is such a thing as a universal speed... Newtonian physics... must be reviewed. As long as the laws of physics were concerned only with accelerations... no conceivable experiment... would lead to the selection of one particular frame of reference as fundamental. But if in empty space light propogates at the universal speed... then a careful determination of the apparent speed of light relative to laboratory apparatus should reveal the [absolute] velocity of that apparatus.... There should exist one frame of reference with respect to which light does travel everywhere at the speed c. Call this... the frame of absolute rest. ...[W]ith respect to any other frame...the apparent speed of light should be less than c in the direction in which the frame is traveling relative to the frame of absolute rest; it should be greater than c in the opposite direction."

"Quel che l'huom vede Amor gli fa invisibile E l'invisibil fa vedere Amore."

"When you ain't got nothing, you got nothing to lose You're invisible now, you got no secrets to conceal."

"If the Standard Model describes the world successfully, how can there be physics beyond it, such as supersymmetry? There are two reasons. First, the Standard Model does not explain aspects of the study of the large-scale universe, cosmology. For example, the Standard Model cannot explain why the universe is made of matter and not antimatter, nor can it explain what constitutes the dark matter of the universe. Supersymmetry suggests explanations for both of these mysteries. Second, the boundaries of physics have been changing. Now scientists ask not only how the world works (which the Standard Model answers) but why it works that way (which the Standard Model cannot answer). Einstein asked "why" earlier in the twentieth century, but only in the past decade or so have the "why" questions become normal scientific research in particle physics rather than philosophical afterthoughts."

"As for the Standard Model, we now know that the roles of asymptotic freedom, monopoles, and instantons are crucial in our present picture of quark confinement, the hadron spectrum, the scaling phenomena, and jet physics. The renormalized theory allows us to reproduce the observed data on the Z and W bosons with unprecedented precision. The Standard Model, as a gauge theory with fermions and at most only one scalar, is indeed tremendously successful."

"It is a characteristic of successful theories that they provide further understanding in many different areas of the field, in elegant and unsuspected ways. As for the Standard Model, we now know the the roles of asymptotic freedom, monopoles and instantons are crucial in our present picture of quark confinement, the hadron spectrum, the scaling phenomena and jet physics. The renormalization theory allows us to reproduce the observed data on the Z and W bosons with unprecedented precision. The Standard Model, as a gauge theory with fermions and at most only one scalar, is indeed tremendously successful."

"A theoretical foundation for the Standard Model has been established through the work of Yang, Mills, 't Hooft, Veltman, Faddeev, Popov, Fradkin, Tyutin, Feynman, Gell-Mann, Bryce DeWitt, Mandelstam, Slavnov, Taylor, Zinn-Justin, B. Lee, Gross, Wilczek, Politzer, Becchi, Rouet, Stora, Nambu, Goldstone, Higgs, Brout, Englert, Bouchiat, Iliopoulos, Meyer, and many, many others."

"In the 1960s and 1970s Newton's anticipation became justified. A theory was developed, the so-called Standard Model, of strong, weak, and electromagnetic forces that describe all the forces that have ever been observed acting within atoms, molecules, or atomic nuclei. It's a theory that's quite successful in comparison with observation. Nevertheless, we have glimpses of a hidden world beneath this level of the Standard Model of things going on at very much smaller scales of distance than the size of an atomic nucleus."

"The Standard Model is so complex it would be hard to put it on a T-shirt — though not impossible; you'd just have to write kind of small."

"Instead of three species of elementary particle which were known in the 1920s, we now have sixty-one. Instead of three states of matter... we now have six or more. Instead of a few succinct equations to summarize the universe of physics, we now have a luxuriant growth of mathematical structures, as diverse as the phenomena that they attempt to describe. So we have to come back to the rain forest, intellectually as well as geographically."

"I recently listened to a talk by a famous biologist. He spoke about... scientific materialism and religious transcendentalism. He said, "...they are incompatible and mutually exclusive." This seems to be a widely accepted view... I do not share it. I do not know what the word "materialism" means. ...I judge matter to be an imprecise and ...old-fashioned concept ...[M]atter is the way particles behave when a large number of them are lumped together. When we examine matter in the finest detail in experiments of particle physics, we see it behaving as an active agent... Its actions are... unpredictable. It makes what appear to be arbitrary choices between alternative possibilities. Between matter... and mind... there seems to be only a difference of degree... We stand... midway between the unpredictability of matter and the unpredictability of God. This view... may not be true, but it is... logically consistent and compatible with... experiments of modern physics. Therefore... scientific materialism and religious transcendentalism are neither incompatible nor mutually exclusive. We have learned that matter... does not limit God's freedom to make it do what he pleases."

"Someone said imagine that CERN (where the World Wide Web was invented for particle physics) had one penny for each use, then particle physics would have all the funding it could use."

"It can rightly be said that symmetry, gauge theories, and spontaneous symmetry breaking have been the three pegs upon which modern particle physics rests."

"During the SSC debate, Anderson and other condensed-matter physicists repeatedly made the point that the knowledge gained in elementary-particle physics would be unlikely to help them to understand emergent phenomena like superconductivity. This is certainly true, but I think beside the point, because that is not why we are studying elementary particles; our aim is to push back the reductive frontier, to get closer to whatever simple and general theory accounts for everything in nature. ... experience shows that the ideas developed in one field can prove very useful in the other. Sometimes these ideas become transformed in translation, so that they even pick up a renewed value to the field in which they were first conceived. The example that concerns me is an idea that elementary-particle physicists learnt from condensed-matter theory – specifically from the BCS theory. It is the idea of spontaneous symmetry breaking."

"The discovery of asymptotic freedom might make it seem obvious that Feynman diagrams would now litter physicists' scratch pads and blackboards even more densely than before. After all, Dyson had domesticated Feynman's diagrams in the first place as aids for making perturbative calculations. Yet asymptotic freedom did not herald a straight forward return to Dyson's original techniques. For one thing, writing down the so-called Feynman rules proved formidable in the new models."

"If Dirac’s idea restores the stability of the spectrum by introducing a stable vacuum where all negative energy states are occupied, the so-called , it also leads directly to the conclusion that a single-particle interpretation of the Dirac equation is not possible."

"Aristotle believed that the world did not come into being at some time in the past; it had always existed and it would always exist, unchanged in essence for ever. He placed a high premium on symmetry and believed that the sphere was the most perfect of all shapes. Hence the universe must be spherical. ...An important feature of the spherical shape... was the fact that when a sphere rotates it does not cut into empty space where there is no matter and it leaves no empty space behind. ...A vacuum was impossible. It could no more exist than an infinite physical quantity. ...Circular motion was the most perfect and natural movement of all."

"These rays, as generated in the , are not homogeneous, but consist of bundles of different wave-lengths, analogous to what would be differences of colour could we see them as light. Some pass easily through flesh, but are partially arrested by bone, while others pass with almost equal facility through bone and flesh."

"Now his principal doctrines were these. That atoms and the vacuum were the beginning of the universe; and that everything else existed only in opinion."

"Question 6. What Picks the Correct Vacuum? This is one of the great mysteries of the theory which appears, at least when treated perturbatively, to possess an enormous number of acceptable (stable) vacuum states. Why, for example, don't we live in ten dimensions? Does the theory possess a unique vacuum, in which case all dimensionless physical parameters would be calculable or is the vacuum truly degenerate, in which case we would have free parameters? ..."

"Where a calculator like the today is equipped with 18,000 s and weighs 30 tons, computers in the future may have only 1,000 vacuum tubes and perhaps weigh only 1½ tons."

"When you look at a vacuum in a quantum theory of fields, it isn't exactly nothing."

"With respect to the ultimate constitution of... masses, the same two antagonistic opinions which had existed since the time of Democritus and of Aristotle were still face to face. According to the one, matter was discontinuous and consisted of minute indivisible particles or atoms, separated by a universal vacuum; according to the other, it was continuous, and the finest distinguishable, or imaginable, particles were scattered through the attenuated general substance of the plenum. A rough analogy to the latter case would be afforded by granules of ice diffused through water; to the former, such granules diffused through absolutely empty space."

"The real value of the new atomic hypothesis... did not lie in the two points which Democritus and his followers would have considered essential—namely, the indivisibility of the 'atoms' and the presence of an interatomic vacuum—but in the assumption that, to the extent to which our means of analysis take us, material bodies consist of definite minute masses, each of which, so far as physical and chemical processes of division go, may be regarded as a unit—having a practically permanent individuality. ...that smallest material particle which under any given circumstances acts as a whole."

"The primitive atomic theory, which has served as the scaffolding for the edifice of modern physics and chemistry, has been quietly dismissed. I cannot discover that any contemporary physicist or chemist believes in the real indivisibility of atoms, or in an interatomic matterless vacuum. Atoms appear to be used as mere names for physico-chemical units which have not yet been subdivided, and 'molecules' for physico-chemical units which are aggregates of the former. And these individualised particles are supposed to move in an endless ocean of a vastly more subtle matter—the ether."

"In general, the rate of evaporation (m) of a substance in a high vacuum is related to the pressure (p) of the saturated vapor by the equation m=\sqrt{\frac{M}{2\pi RT}}p. Red phosphorus and some other substances probably form exceptions to this rule."

"All those who maintain a vacuum are more influenced by imagination than by reason. When I was a young man, I also gave in to the notion of a vacuum and atoms; but reason brought me into the right way. ...The least corpuscle is actually subdivided in infinitum, and contains a world of other creatures, which would be wanting in the universe, if that corpuscle was an atom, that is, a body of one entire piece without subdivision. In like manner, to admit a vacuum in nature, is ascribing to God a very imperfect work... space is only an order of things as time also is, and not at all an absolute being. ...Now, let us fancy a space wholly empty. God could have placed some matter in it, without derogating in any respect from all other things: therefore he hath actually placed some matter in that space: therefore, there is no space wholly empty: therefore all is full. The same argument proves that there is no corpuscle, but what is subdivided. ...there must be no vacuum at all; for the perfection of matter is to that of a vacuum, as something to nothing. And the case is the same with atoms: What reason can any one assign for confining nature in the progression of subdivision? These are fictions merely arbitrary, and unworthy of true philosophy. The reasons alleged for a vacuum, are mere sophisms."

"To those who maintained the existence of a plenum as... principle, nature's abhorrence of a vacuum was a sufficient reason for imagining an all-surrounding aether, even though every other argument should be against it. ...Descartes ...made ...matter a necessary condition of extension... It is only when we remember the extensive and mischievous influence on science... that we can appreciate the horror of aethers which sober-minded men had during the 18th century, and which... descended even to... John Stuart Mill. ...Newton himself... endeavoured to account for gravitation by differences of pressure in an aether... The only aether which has survived is that which was invented by Huygens to explain the propagation of light. The evidence for... the luminiferous aither has accumulated as additional phenomena of light and other radiations have been discovered; and the properties of this medium... have been found to be... those required to explain electromagnetic phenomena. ...the interplanetary and interstellar spaces are not empty..."

"To make way for the regular and lasting Motions of the Planets and Comets, it's necessary to empty the Heavens of all Matter, except perhaps some very thin Vapours, Steams or Effluvia, arising from the Atmospheres of the Earth, Planets and Comets, and from such an exceedingly rare Æthereal Medium … A dense Fluid can be of no use for explaining the Phænomena of Nature, the Motions of the Planets and Comets being better explain'd without it. It serves only to disturb and retard the Motions of those great Bodies, and make the frame of Nature languish: And in the Pores of Bodies, it serves only to stop the vibrating Motions of their Parts, wherein their Heat and Activity consists. And as it is of no use, and hinders the Operations of Nature, and makes her languish, so there is no evidence for its Existence, and therefore it ought to be rejected. And if it be rejected, the Hypotheses that Light consists in Pression or Motion propagated through such a Medium, are rejected with it. And for rejecting such a Medium, we have the authority of those the oldest and most celebrated philosophers of ancient Greece and Phoenicia, who made a vacuum and atoms and the gravity of atoms the first principles of their philosophy, tacitly attributing Gravity to some other Cause than dense Matter. Later Philosophers banish the Consideration of such a Cause out of natural Philosophy, feigning Hypotheses for explaining all things mechanically, and referring other Causes to Metaphysicks: Whereas the main Business of natural Philosophy is to argue from Phenomena without feigning Hypotheses, and to deduce Causes from Effects, till we come to the very first Cause, which certainly is not mechanical."

"If all the properties of the universe, such as charge and momentum, balanced out, as Guth, who was a fan as well as a scholar of theories of nothing, pointed out to me, no laws of physics forbade the spontaneous appearance of the universe—or a quantum piece of one. ...Nothing, some physicist implied, might be the ultimate symmetry, everywhere, everywhen the same... Mostly we knew what nothing was not. It was not anything. But it was the possibility of everything. And perhaps such beauty, nothing, was unstable. And the result was every once in an eternity it twitched. ...The first soul brave enough to suggest the universe was indeed nothing was Ed Tryon... [who] blurted it out during a seminar with Sciama, "Suppose the universe is just a quantum fluctuation." Everybody laughed. ... Tryon eventually published these notions in Nature in 1975 and was mostly ignored. Peebles and Dicke had mentioned his work in their famous 1979 paper about enigmas and conundrums."

"When the Higgs field froze and symmetry broke, Tye and Guth knew, energy had to be released... Under normal circumstance this energy went into beefing up the masses of particles like the weak force bosons that had been massless before. If the universe supercooled, however, all this energy would remain unreleased... according to Einstein, it was the density of matter and energy in the universe that determined the dynamics of space-time. ...The issue of had been a tricky problem for physics ever since Einstein. According to quantum theory, even the ordinary "true" vacuum should be boiling with energy—infinite energy... due to the the so-called s that produced the transient dense dance of s. This energy... could exert a repulsive force on the cosmos just like the infamous cosmological constant... quantum theories had reinvented it in the form of vacuum fluctuations. The orderly measured pace of the expansion of the universe suggested strongly that the cosmological constant was zero, yet quantum theory suggested it was infinite. Not even Hawking claimed to understand the cosmological constant problem... a trapdoor deep at the heart of physics."

"I have endeavoured to attain this end (viz. the production of a vacuum in the cylinder) in another way. As water has the property of elasticity, when converted into steam by heat, and afterwards of being so completely recondensed by cold, that there does not remain the least appearance of this elasticity, I have thought that it would not be difficult to work machines in which, by means of a moderate heat and at a small cost, water might produce that perfect vacuum which has vainly been sought by means of gunpowder."

"It's illegal to make superpositions with different vacua. That's one of the rules of quantum field theory."

"His reluctance to pay for elaborate or expensive equipment, perhaps the result of an impoverished childhood, had established the legendary "sealing wax-and-string" tradition of the Cavendish, where everyday materials were ingeniously used to make and patch up experimental equipment, with sealing wax proving particularly useful for vacuum seals."

"Natura abhorret vacuum. (Nature abhors a vacuum.)"

"The first machine of Papin was very similar to the gunpowder-engine... of Huyghens. In place of gunpowder, a small quantity of water is placed at the bottom of the cylinder, A; a fire is built beneath it, "the bottom being made of very thin metal," and the steam formed soon raises the piston, B, to the top where a latch, E, engaging a notch in latch engaging the piston rod, H, holds it up until it is desired that it shall drop. The fire being removed, the steam condenses, and a vacuum is formed below the piston, and the latch, E, being disengaged, the piston is driven down by the superincumbent atmosphere and raises the weight which has been, meantime, attached to a rope... passing from the piston rod over pulleys... The machine had a cylinder two and a half inches in diameter, and raised 60 pounds once a minute; and Papin calculated that a machine of a little more than two feet diameter of cylinder and of four feet stroke would raise 8,000 pounds four feet per minute—i.e., that it would yield about one horse-power."

"In June, 1699, Captain Savery exhibited a model of his engine before the Royal Society, and the experiments he made with it succeeded to their satisfaction. ...One of the steam vessels being filled with steam, condensation was produced by projecting cold water, from a small cistern E, against the vessel; and into the partial vacuum made by that means, the water, by the pressure of the atmosphere, was forced up the descending main D, from a depth of about twenty feet..."

"[E]xperiments with a simple little machine, designed to mimic certain elementary features of animal behavior... Consisting only of two vacuum tubes, two motors, a photoelectric cell and a touch contact, all enclosed in a tortoise-shaped 'shell, the model was a species of artificial creature which could explore its surroundings and seek out favorable conditions. It was named Machine speculatrix."

"There is one topic I was not sorry to skip: the relativistic wave equation of Dirac. It seems to me that the way this is usually presented in books on quantum mechanics is profoundly misleading. Dirac thought that his equation was a relativistic generalization of the non-relativistic time-dependent that governs the for a in an external electromagnetic field. For some time after, it was considered to be a good thing that Dirac’s approach works only for particles of spin one half, in agreement with the known spin of the electron, and that it entails states, states that when empty can be identified with the electron’s . Today we know that there are particles like the W^\pm W bosons] that are every bit as elementary as the electron, and that have distinct antiparticles, and yet have spin one, not spin one half. The right way to combine relativity and quantum mechanics is through the quantum theory of fields, in which the Dirac wave function appears as the matrix element of a quantum field between a one-particle state and the vacuum, and not as a probability amplitude."

"It is quite easy to include a weight for empty space in the equations of gravity. Einstein did so in 1917, introducing what came to be known as the cosmological constant into his equations. His motivation was to construct a static model of the universe. To achieve this, he had to introduce a negative mass density for empty space, which just canceled the average positive density due to matter. With zero total density, gravitational forces can be in static equilibrium. Hubble's subsequent discovery of the expansion of the universe, of course, made Einstein's static model universe obsolete. ...The fact is that to this day we do not understand in a deep way why the vacuum doesn't weigh, or (to say the same thing in another way) why the cosmological constant vanishes, or (to say it in yet another way) why Einstein's greatest blunder was a mistake."

"The phase transition paradigm: The standard model of fundamental physics incorporates, as one of its foundational principles, the idea that “empty space” or “vacuum” can exist in different phases, typically associated with different amounts of symmetry. Moreover, the laws of the standard model itself suggest that phase transitions will occur, as functions of temperature. Extensions of the standard model to build in higher symmetry (gauge unification or especially supersymmetry) can support effective vacua with radically different properties, separated by great distance or by domain walls. That would be a form of failure of universality, in our sense, whose existence is suggested by the standard model."

"Some assert that there is absolutely no vacuum; others that, while no continuous vacuum is exhibited in nature, it is to be found distributed in minute portions through air, water, fire and all other substances: and this latter opinion, which we will presently demonstrate to be true from sensible phenomena, we adopt."

"Vessels which seem to most men empty are not empty, as they suppose, but full of air. Now the air, as those who have treated of physics are agreed, is composed of particles minute and light, and for the most part invisible. If, then, we pour water into an apparently empty vessel, air will leave the vessel proportioned in quantity to the water which enters it. This may be seen from the following experiment. Let the vessel which seems to be empty be inverted, and, being carefully kept upright, pressed down into water; the water will not enter it even though it be entirely immersed: so that it is manifest that the air, being matter, and having itself filled all the space in the vessel, does not allow the water to enter. Now, if we bore the bottom of the vessel, the water will enter through the mouth, but the air will escape through the hole. Again, if, before perforating the bottom, we raise the vessel vertically, and turn it up, we shall find the inner surface of the vessel entirely free from moisture, exactly as it was before immersion."

"The particles of the air are in contact with each other, yet they do not fit closely in every part, but void spaces are left between them, as in the sand on the sea shore: the grains of sand must be imagined to correspond to the particles of air, and the air between the grains of sand to the void spaces between the particles of air. Hence, when any force is applied to it, the air is compressed, and, contrary to its nature, falls into the vacant spaces from the pressure exerted on its particles: but when the force is withdrawn, the air returns again to its former position from the elasticity of its particles, as is the case with horn shavings and sponge, which, when compressed and set free again, return to the same position and exhibit the same bulk."

"Thus, if a light vessel with a narrow mouth be taken and applied to the lips, and the air be sucked out and discharged, the vessel will be suspended from the lips, the vacuum drawing the flesh towards it that the exhausted space may be filled. It is manifest from this that there was a continuous vacuum in the vessel. The same may be shown by means of the egg-shaped cups used by physicians, which are of glass, and have narrow mouths. When they wish to fill these with liquid, after sucking out the contained air, they place the finger on the vessel's mouth and invert them into the liquid; then, the finger being withdrawn, the water is drawn up into the exhausted space, though the upward motion is against its nature. Very similar is the operation of cupping-glasses, which, when applied to the body, not only do not fall though of considerable weight, but even draw the contiguous matter toward them through the apertures of the body."

"They... who assert that there is absolutely no vacuum may invent many arguments on this subject, and perhaps seem to discourse most plausibly though they offer no tangible proof. If, however, it be shewn by an appeal to sensible phenomena that there is such a thing as a continuous vacuum, but artificially produced; that a vacuum exists also naturally, but scattered in minute portions ; and that by compression bodies fill up these scattered vacua, those who bring forward such plausible arguments in this matter will no longer be able to make good their ground."

"Vacuum stands and remains a mathematical space. A cube placed in a vacuum would not displace anything, as it would displace air or water in a space already containing those fluids."

"In a vacuum which is imagined as infinite there cannot be local differences, both on account of its infinity, and also because of the fact that the vacuum, if it exists, would have no nature but a privation, and therefore it can have no natural differences."

"The space of the real physical world must be considered full, that is a plenum, because a vacuum could have no physical existence."

"When the engineers of Cosmo de Medicis wished to raise water higher than thirty-two feet by means of a sucking-pump, they found it impossible to take it higher than thirty-one feet. Galileo, the Italian sage, was applied to in vain for a solution of the difficulty. It had been the belief of all ages that the water followed the piston, from the horror which nature had of a vacuum, and Galileo improved the dogma by telling the engineers that this horror was not felt, or at least not shown, beyond heights of thirty one feet! At his desire, however, his disciple Toricelli investigated the subject. He found, that when the fluid raised was mercury, the horror of a vacuum did not extend beyond 30 inches, because the mercury would not rise to a greater height; and hence he concluded that a column of water 31 feet high, and one of mercury 30 inches, exerted the same pressure upon the same base, and that the antagonist force which counterbalanced them must in both cases be the same; and having learned from Galileo that the air was a heavy fluid, he concluded, and he published the conclusion in 1645, that the weight of the air was the cause of the rise of water to 31 feet and of mercury to 30 inches. Pascal repeated these experiments in 1646, at before more than 500 persons, among whom were five or six Jesuits of the College, and he obtained precisely the same results as Toricelli. The explanation of them, however, given by the Italian philosopher, and with which he was unacquainted, did not occur to him; and though he made many new experiments on a large scale with tubes of glass 50 feet long, they did not conduct him to any very satisfactory results. He concluded that the vacuum above the water and the mercury contained no portion of either of these fluids, or any other matter appreciable by the senses; that all bodies have a repugnance to separate from a state of continuity, and admit a vacuum between them; that this repugnance is not greater for a large vacuum than a small one; that its measure is a column of water 31 feet high, and that beyond this limit, a great or a small vacuum is formed above the water with the same facility, provided no foreign obstacle prevents it. These experiments and results were published by our author in 1647, under the title of Nouvelles Experiences touchant le Vuide; but no sooner had they appeared, than they experienced, from the Jesuits, and the followers of Aristotle, the most violent opposition."

"To these objections Pascal replied in two letters, addressed to [Stephen] Noel; but though he had no difficulty in overturning the contemptible reasoning of his antagonist, he found it necessary to appeal to new and more direct experiments. The explanation of Toricelli had been communicated to him a short time after the publication of his work; and assuming that the mercury in the Toricellian tube was suspended by the weight or pressure of the air, he drew the conclusion that the mercury would stand at different heights in the tube, if the column of air was more or less high. These differences, however, were too small to be observed under ordinary circumstances; and he therefore conceived the idea of observing the mercury at Clermont, a town in Auvergne... and on the top of the Puy de Dome, a mountain 500 toises above Clermont The state of his own health did not permit him to undertake a journey... but in a letter dated the 15th November 1647, he requested his brother-in-law, M. Perier, to go... M. Perier began the experiment by pouring into a vessel sixteen pounds of quicksilver which he had rectified... He then took two [straight] glass tubes, four feet long, of the same bore, and hermetically sealed at one end, and open at the other; and making the ordinary experiment of a vacuum with both, he found that the mercury stood in each of them at the same level... This experiment was repeated twice with the same result. One of these... was left under the care of M. Chastin... who undertook to observe and mark any changes... and the party... set out, with the other tube, for the summit of the Puy de Dome... Upon arriving there, they found that the mercury stood at the height of 23 inches, and 2 lines—no less than 3 inches and 1½ lines lower... The party was "struck with admiration and astonishment at this result;" and "so great was their surprise, that they resolved to repeat the experiment under various forms." During their descent of the mountain, they repeated the experiment at Lafond de l'Arbre, an intermediate station... and they found the mercury to stand at the height of 25 inches, a result with which the party was greatly pleased, as indicating the relation between the height of the mercury and the height of the station. Upon reaching the Minimes, they found that the mercury had not changed its height..."

"Pascal's Treatise [De la Pesanteur de la Masse de l'Air] on the weight of the whole mass of air forms the basis of the modern science of Pneumatics. In order to prove that the mass of air presses by its weight on all the bodies which it surrounds, and also that it is elastic and compressible, he carried a balloon half filled with air to the top of the Puy de Dome. It gradually inflated itself as it ascended, and when it reached the summit it was quite full, and swollen, as if fresh air had been blown into it; or what is the same thing, it swelled in proportion as the weight of the column of air which pressed upon it was diminished. When again brought down, it became more and more flaccid, and when it reached the bottom, it resumed its original condition. ...[H]e shews that all the phenomena and effects hitherto ascribed to the horror of a vacuum arise from the weight of the mass of air; and after explaining the variable pressure of the atmosphere in different localities, and in its different states, and the rise of water in pumps, he calculates that the whole mass of air round our globe weighs 8,983,889,440,000,000,000 French pounds."

"Newcomen's invention was radically different from that of Savery or any other single person. Papin invented the cylinder and piston as a means for transforming energy into motion. At first he used the explosive force of gunpowder, and later the use of the expansive force of steam, to raise the piston, and then by removing the fire to cause it to fall again. He made no further use of this principle. Savery discovered that the sudden condensation of steam made a vacuum that he utilized to draw up water. His pumps were actually used to drain mines, but were never satisfactory. They had to be placed within the mine to be drained, not over forty feet from the bottom, and then could be used to force up water an additional height of perhaps 100 feet. Beyond this the process must be repeated. ... Newcomen used Papin's cylinder and piston, and Savery's principle of the condensation of steam to produce a vacuum. But unlike Papin he used the expansive force of steam to do his work, and unlike Savery he used a cylinder and piston actuated by alternate expansion and condensation of steam to transform heat into mechanical motion."

"At first [Newcomen] made a double cylinder, using the space between for condensing water. This was not very satisfactory. The vacuum was secured very slowly and imperfectly. ...One day the engine made two or three motions quickly and powerfully. Newcomen immediately examined the cylinder and found a small hole, through which a small jet from the water that was on top of the piston to make it steam tight, was spurting into the cylinder. He... dispensed with the outer water jacket and injected the water for condensation, through a small pipe in the bottom of the cylinder. It... increased the speed of the engine from eight to fifteen strokes a minute, besides getting the advantage of a good vacuum."

"The spooky ether was persistent. It took an Einstein to remove it from the Universe. ...Gradually, over the last twenty years, the vacuum has turned out to be more unusual, more fluid, less empty, and less intangible than even Einstein could have imagined. Its presence is felt on the very smallest and largest dimensions over which the forces of Nature act."

"The physicist's concept of nothing—the vacuum... began as empty space—the void... turned into a stagnant ether through which all the motions of the Universe swam, vanished in Einstein's hands, then re-emerged in the twentieth-century quantum picture of how Nature works."

"The quantum revolution showed us why the old picture of a vacuum as an empty box was untenable. ...Gradually, this exotic new picture of quantum nothingness succumbed to experimental exploration... in the form of s, light bulbs and s. Now the 'empty' space itself started to be probed. ...There was always something left: a that permeated every fibre of the Universe."

"Einstein showed us that the Universe might contain a mysterious form of vacuum energy. ...Last year, two teams of astronomers used Earth's most powerful telescopes... to gather persuasive evidence for the reality of the cosmic . Its effects are dramatic. It is accelerating the expansion of the Universe."

"It appears that the strong interactions and electromagnetic interactions are invariant with respect to C, P, and T separately, while the weak interactions do not conserve P or C. All experimental results are consistent with the assumption the T invariance holds true for all interactions; consequently, from the CPT theorem, weak interactions must be invariant under CP. One could not, then, determine if the photographed scene were a scene of particles viewed normally, or a scene of antiparticles projected in a mirror."

"The weak force... least fits into our typical picture of what a force should do. ...the categories of 'attractive' and 'repulsive' do not really fit the weak force ... because it has the ability to change particles from one type to another. ...The weak force can change one into another provided they are in the same generation. The electron can be changed into an electron and vice versa, but the electron cannot be turned into the ..."

"In his theory of beta reactivity Fermi introduced a new type of interactions among elementary particles, which today we call "weak interactions". Many new manifestations of weak interactions, which could be interpreted using Fermi's 1933 theory, were found in the following decades. The study of weak interactions has led to surprising discoveries, among which the violation of specular symmetry (known as parity symmetry or P symmetry), and the violation of time reversal symmetry (T symmetry) and of the symmetry between matter and antimatter (CP symmetry)."

"The... weak force... couples to both s and s, and is very short-ranged due to the large rest mass of the messenger quanta involved. Its effective strength is usually many orders of magnitude weaker than electromagnetism, and its action can cause particles to change identity, as when a neutron decays. Unlike the electromagnetic and strong forces, the weak force violates parity conservation."

"For the weak force... universality of coupling strength is not readily apparent. ic weak forces are very different in nature from ic weak processes."

"How can s be produced in the center of the sun and how can they be detected in laboratories here on earth if they are subject neither to the strong force nor to the electromagnetic one? Another force, the so-called weak force, is responsible. The electron neutrino does participate in that interaction, along with the electron."

"The weak force gives rise to reactions... These reactions involve a change of flavor... one version involving the exchange of a positively charged quantum and the other the exchange of a negatively charged quantum. The existence of such quanta was first discussed by some of us in the late 1950s, and they were discovered at CERN twenty-five years later, in experiments that procured a Nobel prize for Carlo Rubbia and Simon van der Meer. The quanta are usually called W + and W -, as they were designated in a celebrated paper by T. D. Lee and C. N. Yang..."

"In 1952... I tried to explain the behavior of the new "strange particles," so called because they were copiously produced as though strongly interacting and yet decayed slowly as though weakly interacting. (Here "slowly" means a half-life of something like a ten billionth of a second... a strongly interacting particle means... a ten trillionth of a second, roughly the time it takes for light to cross such a particle.) ...I thought of assigning these strange particles isotopic spin I = 5/2... But the notion failed to work... I was invited to talk at the Institute for Advanced Study... By a slip of the tongue I said "I = 1" instead... Immediately I stopped dead, realizing I = 1 would do the job. ...But what about the alleged rule that ic strongly interacting particle states had to have values of I like 1/2 or 3/2 or 5/2? ...the rule was merely a superstition... unnecessary baggage that had come along with the useful concept of isotopic spin... [which now] could have wider applications than before. ...[T]he strange particle states differ from more familiar ones such as neutron or proton or s by having at least one s or "strange" quark in place of a u or d quark. Only the weak interaction can convert one flavor of quark into another, and that process happens slowly."

"The strong and weak forces are less familiar because their strength rapidly diminishes over all but subatomic distance scales; they are the s. This is why these two forces were discovered only much more recently. The strong force is responsible for keeping quarks "glued" together inside of protons and neutrons and keeping protons and neutrons tightly crammed together inside atomic nuclei. The weak force is best known for the radioactive decay of substances such as uranium and cobalt."

"In 1933 Enrico Fermi suggested that beta radioactivity, and the manner in which the neutron spontaneously decayed, could be described using a formalism similar to that developed by Dirac for the electromagnetic force, but 10-10 times weaker. With its range of only about 1/1,000th the diameter of the nucleus, it could not play a role in binding the nucleus, but it could affect individual s. The fact that the metastable particles exhibited the same characteristic time of 10-10 second indicated that this weak force acted on many types of particles. ...a 'characteristic time' ...being the time for an interaction across a nucleus 3 fm in diameter; an event taking place in a shorter time [than 10-23 seconds for the strong force] has 'no meaning'. ...For electromagnetic interactions, the strength is 10-3 of the strong force, and so the characteristic time is longer (10-20 [seconds]); this is roughly the time for a photon to cross an atom."

"In addition to transforming a neutron into a proton and vice versa, the weak force was evidently responsible for the decay of a muon into an electron. ...[W]hen the strange particles were found to decay without s it was realized that the force was more complex than had been posited in Fermi's theory of beta decay. Nevertheless, the fact that aspects of the force could be explained by an electromagnetic formalism implied that these forces shared an underlying symmetry."

"The mass of the W and Z prevents the weak force from extending beyond their Compton length (about a hundredth the size of a proton)..."

"[T]he work of a number of theoretical physicists in the 1960s culminated in the electroweak theory that is designed to unify electromagnetism and the weak force... This theory is sometimes called the 'GWS Theory', from... Sheldon Glashow, Steven Weinberg and Abdus Salam... The main feature of the theory is that at extremely high temperatures the electromagnetic and weak forces are two components of a single force, the electroweak force. The symmetry between the two forces would only be apparent at temperatures of trillions of degrees... in the Big Bang. At lower temperatures... electromagnetism remains a long range force, but the weak force takes on the characteristics of... a very weak force that acts over extremely short distances. ...But the theory is dependent on the existence of the Higgs particle..."

"[W]hat shall we say, then, to a nuclear event such as... beta decay... in which a neutron turns into a proton and also shoots out an electron together with an antineutrino? ...Coming from within... is the weak interaction. Not in all nuclei, but certainly in many... the weak interaction sometimes subverts the neutrons and protons bound otherwise so strongly. It takes only a change in flavor. The weak force, with the weak interaction charges as the source, transforms a into an and hence a into a . At the same time, an electron and antineutrino spring loose... The strong force plays no part here, since neither the electron nor the antineutrino carries a strong interaction charge. Electrically neutral, the antineutrino escapes the electromagnetic force as well. ...the weak force ...allows a neutron to decay into a proton, electron, and antineutrino. The four particles all carry weak interaction charges, and their common endowment makes them all actors in a single play."

"s were among the most paradoxical members of the zoo of elementary particles that were discovered after the war. Produced during radioactive decay, they supposedly had neither charge nor mass and they traveled, consequently, at the speed of light. Their only interaction with the world (besides gravity) was by something called the "weak" force, which causes some kinds of radioactive decay. It was so weak that, according to calculations, a typical neutrino could pass through a million miles of water unhindered—stars and planets were transparent to them."

"Antoine-Henri Becquerel discovered radioactivity. Becquerel's discovery preceded J. J. Thomson's... electron by one year. Radioactivity comes in three kinds, called alpha, beta, and gamma. ...only one ...(beta) has to do with the weak interactions. Today we know that the beta rays were actually electrons emitted by neutrons in the nucleus. ...Nothing in QED or QCD explains how a neutron can emit an electron and become a proton. ...Becquerel didn't know ...that another particle flew off... the antiparticle of the ghostly neutrino. ...The neutrino ...doesn't emit photons. It doesn't emit s. This means it [does not experience the respective electromagnetic or s] that electrically charged particles or s experience. The W-boson is key to the neutrino's activities. Not only can the electrons and quarks emit W-bosons—so too can the neutrino. ...[O]ne of the two d-quarks in a neutron can emit a W-boson and become a u-quark, thus turning a neutron into a proton. ...the W-boson is exchanged, where in a QED diagram, the photon would be exchanged. ...weak interactions are very closely related to the electric forces due to photons. ...The W-boson... splits into two particles: an electron and a neutrino "moving backward in time,"... an antineutrino. That's what Becquerel would have seen... had he had a powerful enough microscope."

"The weak force does not seem to hold anything together, only to break it apart. ...we do not observe s of the weak force. ...So the weak force seems a force apart... Interwoven with the surprising story of the weak force has been the story of s, arguably the most intriguing of the fundamental particles. ...the neutrinos provide a unique and valuable mirror on the weak force. ...In the 1920s, and for a while disputed the energy spectrum of electrons emitted in β decay. ...Chadwick demonstrated... that the spectrum was continuous, i.e. the electron could take on a whole range of energies. ...contrary to the single line expected from energy conservation if only... the electron and the nucleus, were involved... Neils Bohr advocated abandoning energy conservation... but in 1930 Wolfgang Pauli daringly proposed an unseen... neutrino... Pauli's intuition... inspired Enrico Fermi in his 'tentative theory of β decay'... to become the basis for ideas of a universal weak force."

"The first intimations that β decay is but one manifestation of some deeper fundamental interaction came during the 1940s from experiments which led to the discovery of the . ...A third charged , the tau, and three neutral neutrinos bring the number of family members to six. In addition there are six corresponding antiparticles. It appears that in any interaction a lepton can be created (or can disappear) only together with an antilepton. This empirical rule of 'lepton conservation'... implies... that it is an antineutrino that accompanies the electron in β decay. ...When the decay or capture of a muon was treated in the same way as β decay in Fermi's theory, the s... appeared remarkably similar. ...The agreement between the coupling constants for β decay, muon decay and muon capture led to the idea of a 'universal Fermi interaction' and... experiments began to reveal more and more new particles with similar weak interactions."

"Why can stars do better than the big bang? ...During the big bang, there were only a few minutes when nuclei could form. Very rare processes, or slow ones, played little role. A case in point is the key process from which the sun derives its energy. In this reaction, two protons collide to produce a deuterium nucleus, a neutrino, and a positron. ...This reaction belongs to the family of weak interactions. ...It remains... a remarkable—and for humanity, remarkably fortunate—circumstance that the central reaction that drives the sun is so rare. It is only this extraordinary rarity that allows the average proton in the sun to last so long, billions of years, even though it is colliding with other protons millions of times a second. ...an entertaining example of Treiman's theorem."

"Once helium burning has occurred... the next possible reaction—carbon burning—is not necessarily slow... This reaction involves ...a strong as opposed to a weak interaction. ...Carbon burning results in magnesium. ...Taking a cross section of a highly evolved star would reveal a system of many layers. The inner layers have been subjected to the largest pressures, thereby forced to the highest temperatures, and burned the furthest; the outermost layers, by contrast, have not burned at all. Thus, as we proceed from outside in, there will be an outermost layer with the initial mix of hydrogen and helium, a layer of mostly helium, a layer of carbon, a layer of magnesium, and so on. ...So we arrive at the picture of a star, in the latest stages of its evolution... now composed of mostly carbon nuclei and other explosive material."

"If grand unified theories are correct, we ought to be able to derive the relative power of the strong, weak, and electromagnetic interactions at accessible energies from their presumed equality at much higher energies. When this is attempted, a wonderful result emerges. ...in the form first calculated by Howard Georgi, Helen Quinn, and Steven Weinberg ...The couplings of strong-interaction gluons decrease, those of the [weak interaction] W bosons stay roughly constant, and those of the [electromagnetic interaction] photons increase at short distances [or high energies]—so they all tend to converge, as desired."

"... The way in which string theory addresses the cosmological constant problem can be summarized as follows: • Fundamentally, space is nine-dimensional. There are many distinct ways (perhaps 10500) of turning nine-dimensional space into three-dimensional space by compactifying six dimensions. ... • Distinct compactifications correspond to different three-dimensional metastable vacua with different amounts of vacuum energy. In a small fraction of vacua, the cosmological constant will be accidentally small. • All vacua are dynamically produced as large, widely separated regions in space-time. • Regions with Λ 1 contain at most a few bits of information and thus no complex structures of any kind. Therefore, observers find themselves in regions with Λ ≪ 1."

"The theoretical view of the actual universe, if it is in correspondence to our reasoning, is the following. The curvature of space is variable in time and place, according to the distribution of matter, but we may roughly approximate it by means of a spherical space. ...this view is logically consistent, and from the standpoint of the general theory of relativity lies nearest at hand [i.e. is most obvious]; whether, from the standpoint of present astronomical knowledge, it is tenable, will not be discussed here. In order to arrive at this consistent view, we admittedly had to introduce an extension of the field equations of gravitation, which is not justified by our actual knowledge of gravitation. It is to be emphasized, however, that a positive curvature of space is given by our results, even if the supplementary term [] is not introduced. The term is necessary only for the purpose of making possible a quasi-static distribution of matter, as required by the fact of the small velocity of the stars."

"Most constants are adjusted with a deviation of one percent, which means that if the value differs by one percent everything collapses. Physicists can certainly claim that this is a fluke, but it must be acknowledged that this cosmological constant is adjusted to an accuracy of 1/10120. No one thinks that this is solely a fluke. It is the most extreme example of hyperfine regulation... (Leonard Susskind)"

"Much later, when I was discussing cosmological problems with Einstein, he remarked that the introduction of the cosmological term was the biggest blunder he ever made in his life."

"After putting the finishing touches on general relativity in 1915, Einstein applied his new equations for gravity to a variety of problems. ... Despite the mounting successes of general relativity, for years after he first applied his theory to the most immense of all challenges—understanding the entire universe—Einstein absolutely refused to accept the answer that emerged from the mathematics. Before the work of Friedmann and Lemaître... Einstein, too, had realized that the equations of general relativity showed that the universe could not be static; the fabric of space could stretch or it could shrink, but it could not maintain a fixed size. This suggested that the universe might have had a definite beginning, when the fabric was maximally compressed, and might even have a definite end. Einstein stubbornly balked at this... because he and everyone else "knew" that the universe was eternal and, on the largest scales, fixed and unchanging. Thus, notwithstanding the beauty and successes of general relativity, Einstein reopened his notebook and sought a modification of the equations... It didn't take him long. In 1917 he achieved the goal by introducing a new term... the cosmological constant."

"The miracle of physics that I'm talking about here is something that was actually known since the time of Einstein's general relativity; that gravity is not always attractive. Gravity can act repulsively. Einstein introduced this in 1916... in the form of the cosmological constant, and the original motivation of modifying the equations of general relativity to allow this was because Einstein thought that the universe was static, and he realized that ordinary gravity would cause the universe to collapse if it was static. ...The fact that general relativity can support this gravitational repulsion, still being consistent with all the principles that general relativity incorporates, is the important thing which Einstein himself did discover.."

"In 1917 de Sitter showed that Einstein's field equations could be solved by a model that was completely empty apart from the cosmological constant—i.e. a model with no matter whatsoever, just dark energy. This was the first model of an expanding universe. although this was unclear at the time. The whole principle of general relativity was to write equations for physics that were valid for all observers, independently of the coordinates used. But this means that the same solution can be written in various different ways... Thus de Sitter viewed his solution as static, but with a tendency for the rate of ticking clocks to depend on position. This phenomenon was already familiar in the form of gravitational time dilation... so it is understandable that the de Sitter effect was viewed in the same way. It took a while before it was proved (by Weyl, in 1923) that the prediction was of a redshifting of spectral lines that increased linearly with distance (i.e. Hubble's law). ..."

"Even today, our picture of a world woven together by a gravitational force, and electromagnetic force, a strong force, and a weak force may be incomplete. Astronomers are gathering evidence that an additional fundamental interaction, a repulsive effect opposite to gravity, may be at work over vast distances and possibly changing with time."

"In Einstein's scheme there was no end, no outside. Shoot an arrow or a light beam infinitely far in any direction and it would come back and hit you in the butt. ...But there was a problem with the curved-back universe. Such a configuration was unstable, it would fly apart or collapse. Einstein didn't know about galaxies. He thought, and was reassured as much by the best astronomers of the time, that the universe was a static cloud of stars. To explain why his curved universe didn't collapse like a struck tent, therefore, he fudged his equations with a term he called the cosmological constant, which produced a long-range repulsive force to counteract cosmic gravity. It made the equations ugly and he never really liked it. That was in 1917, twelve years before Hubble showed that the universe was full of galaxies rushing away from each other."

"When the Higgs field froze and symmetry broke, Tye and Guth knew, energy had to be released... Under normal circumstance this energy went into beefing up the masses of particles like the weak force bosons that had been massless before. If the universe supercooled, however, all this energy would remain unreleased... according to Einstein, it was the density of matter and energy in the universe that determined the dynamics of space-time. ...The issue of vacuum energy had been a tricky problem for physics ever since Einstein. According to quantum theory, even the ordinary "true" vacuum should be boiling with energy—infinite energy... due to the the so-called s that produced the transient dense dance of s. This energy... could exert a repulsive force on the cosmos just like the infamous cosmological constant... quantum theories had reinvented it in the form of vacuum fluctuations. The orderly measured pace of the expansion of the universe suggested strongly that the cosmological constant was zero, yet quantum theory suggested it was infinite. Not even Hawking claimed to understand the cosmological constant problem... a trapdoor deep at the heart of physics."

"It's a term that Einstein recognized as allowed by his theory — he threw it in and then, in disgust, threw it out again ... It's back!"

"[Einstein's cosmological constant] is a name without any meaning. ...We have, in fact, not the slightest inkling of what it's real significance is. It is put in the equations in order to give the greatest possible degree of mathematical generality."

"There is no direct observational evidence for the curvature [of space], the only directly observed data being the mean density and the expansion, which latter proves that the actual universe corresponds to the non-statical case. It is therefore clear that from the direct data of observation we can derive neither the sign nor that value of the curvature, and the question arises whether it is possible to represent the observed facts without introducing the curvature at all. Historically the term containing the 'cosmological constant λ' was introduced into the field equations in order to enable us to account theoretically for the existence of a finite mean density in a static universe. It now appears that in the dynamical case this end can be reached without the introduction of λ."

"It was early 1932, when Einstein and I both were at the California Institute of Technology in Pasedena, and we just decided to look for a simple relativistic model that agreed reasonably well with the known observational data, namely, the Hubble recession rate and the mean density of matter in the universe. So we took the space curvature to be zero and also the cosmological constant and the pressure term to be zero, and then it follows straightforwardly that the density is proportional to the square of the Hubble constant. It gives a value for the density that is high, but not impossibly high. That's about all there was to it. It was not an important paper, although Einstein apparently thought that it was. He was pleased to have a simple model with no cosmological constant. That's it."

"String theory seems to be incompatible with a world in which a cosmological constant has a positive sign, which is what the observations indicate."

"The most far-reaching implication of general relativity... is that the universe is not static, as in the orthodox view, but is dynamic, either contracting or expanding. Einstein, as visionary as he was, balked at the idea... One reason... was that, if the universe is currently expanding, then... it must have started from a single point. All space and time would have to be bound up in that "point," an infinitely dense, infinitely small "singularity." ...this struck Einstein as absurd. He therefore tried to sidestep the logic of his equations, and modified them by adding... a "cosmological constant." The term represented a force, of unknown nature, that would counteract the gravitational attraction of the mass of the universe. That is, the two forces would cancel... it is the kind of rabbit-out-of-the-hat idea that most scientists would label ad-hoc. ...Ironically, Einstein's approach contained a foolishly simple mistake: His universe would not be stable... like a pencil balanced on its point."

"Our particular laws are not at all unique. ...they could change from place to place and from time to time. The Laws of Physics are much like the weather... controlled by invisible influences in space almost the same way as that temperature, humidity, air pressure, and wind velocity control how rain and snow and hail form. ...The Landscape... is the space of possibilities... all the possible environments permitted by the theory. ...[T]heoretical physicists ...have always believed that the laws of nature are the unique, inevitable consequence of some elegant mathematical principle. ...the empirical evidence points much more convincingly to the opposite conclusion. The universe has more in common with a Rube Goldberg machine than with a unique consequence of mathematical symmetry. ...Two key discoveries are driving the paradigm shift—the success of inflationary cosmology and the existence of a small cosmological constant."

"At about the time of Malcadena's discovery, physicists started to become convinced (by cosmologists) that we live in a world with a nonvanishing cosmological constant [footnote: 10-23 in Planck units...[t]he incredible smallness... had fooled almost all physicists into believing that it didn't exist.], smaller by far than any other physical constant... the main determinant of the future history of the universe... also known as ... a thorn in the side of physicists for almost a century. ...If \Lambda is positive, the cosomological term creates a repulsive force that increases with distance; if it is negative, the new force is attractive; if \Lambda is zero, there is no new force and we can ignore it."

"The cosmological constant['s]... most important consequence: the repulsive force, acting at cosmological distances, causes space to expand exponentially. There is nothing new about the universe expanding, but without a cosmological constant, the rate of expansion would gradually slow down. Indeed, it could even reverse itself and begin to contract, eventually imploding in a giant cosmic crunch. Instead, as a consequence of the cosmological constant, the universe appears to be doubling in size about every fifteen billion years, and all indications are that it will do so indefinitely."

"The models of Einstein and de Sitter are static solutions of Einstein's modified gravitational equations for a world-wide homogeneous system. They both involve a positive cosmological constant λ, determining the curvature of space. If this constant is zero, we obtain a third model in classical infinite Euclidean space. This model is empty, the space-time being that of Special Relativity. It has been shown that these are the only possible static world models based on Einstein's theory. In 1922, Friedmann... broke new ground by investigating non-static solutions to Einstein's field equations, in which the radius of curvature of space varies with time. This Possibility had already been envisaged, in a general sense, by Clifford in the eighties."

"It is quite easy to include a weight for empty space in the equations of gravity. Einstein did so in 1917, introducing what came to be known as the cosmological constant into his equations. His motivation was to construct a static model of the universe. To achieve this, he had to introduce a negative mass density for empty space, which just canceled the average positive density due to matter. With zero total density, gravitational forces can be in static equilibrium. Hubble's subsequent discovery of the expansion of the universe, of course, made Einstein's static model universe obsolete. ...The fact is that to this day we do not understand in a deep way why the vacuum doesn't weigh, or (to say the same thing in another way) why the cosmological constant vanishes, or (to say it in yet another way) why Einstein's greatest blunder was a mistake."

"De Sitter proposed three types of nonstatic universes: the oscillating universes and the expanding universes of the first or second kiind. The main characteristic of the expanding "family" of the first kiind is that the radius is continually increasing from a definite initial time when it had the value zero. The universe becomes infinitely large after an infinite time. In the second kind... the radius possesses at the initial time a definite minimum value... in the Einstein model... the cosmological constant is supposed to be equal to the reciprocal of R2, whereas de Sitter computed for his interpretation the constant to be equal to 3/R2. Whitrow correctly points out the significant fact that in special relativity the cosmological constant is omitted..."

"A star does not evolve over its lifetime through each spectral type, as Russell once thought; rather, each star experiences its own distinct history, based on its mass at birth. Smaller stars, such as tiny s, will never reach the red-giant stage but just dully burn away like red-hot ovens. Stars that are born with appreciably more mass than our Sun, such as the white-hot O and B stars, will burn swiftly and eventually blow up, leaving behind a city-sized or even a black hole, a gravitational pit from which no light or matter can escape. ...the term black hole wasn't even coined until 1968. Yet the first tentative steps toward understanding this great metamorphosis, the distinct and striking stages in a star's life, were taken at the turn of the century. The elements in the stars themselves were telling the tale in the spectral messages they were telegraphing throughout the cosmos."

"After the nuclear fuel is used up, the star goes into a state of gravitational collapse. All parts of the star fall more or less freely inward... [Y]ou would imagine that the freefall could not continue... because the falling material would... arrive at the center... But Einstein's equations have the peculiar consequence... permanent freefall without ever reaching the bottom... what we call a black hole. ...[T]he space ...is so strongly curved that space and time become interchanged... time becomes space and... space becomes time. More precisely, if you observe... from the outside, you see... motion slow down and stop because the direction of time inside... is perpendicular to the direction of time as seen from the outside. The collapsing star can continue to fall freely forever..."

""Schwarzschild's solution"—revealed a stunning implication of general relativity. He showed that if the mass of a star is concentrated in a small enough spherical region, so that it's mass divided by its radius exceeds a particular critical value, the resulting space-time warp is so radical that anything, including light, that gets too close to the star will be unable to escape its gravitational grip. ...John Wheeler ...called them black holes—black because they cannot emit light, holes because anything getting too close falls into them, never to return. The name stuck."

"Black holes have the universe's most inscrutable poker faces. ...When you've seen one black hole with a given mass, charge, and spin (though you've learned these thing indirectly, through their effect on surrounding gas and stars...) you've definitely seen them all. ...black holes contain the highest possible ...a measure of the number of rearrangements of an object's internal constituents that have no effect on its appearance. ...Black holes have a monopoly on maximal disorder. ...As matter takes the plunge across a black hole's ravenous , not only does the black hole's entropy increase, but its size increases as well. ...the amount of entropy ...tells us something about space itself: the maximum entropy that can be crammed into a region of space—any region of space, anywhere, anytime—is equal to the entropy contained within a black hole whose size equals the region in question."

"A natural guess is that... a black hole's entropy is... proportional to its volume. But in the 1970s and Stephen Hawking discovered that this isn't right. Their... analyses showed that the entropy... is proportional to the area of its event horizon... less than what we'd naïvely guess. ...Berkenstein and Hawking found that... each square being one by one Planck length... the black hole's entropy equals the number of such squares that can fit on its surface... each Planck square is a minimal unit of space, and each carries a minimal, single unit of entropy. This suggests that there is nothing, even in principle, that can take place within a Planck square, because any such activity could support disorder and hence the Planck square could contain more than a single unit of entropy... Once again... we are led to the notion of an elemental spatial entity."

"[F]or a physicist, the upper limit to entropy... is a critical, almost sacred quantity. ...the Bekenstein and Hawking result tells us that a theory that includes gravity is, in some sense, simpler than a theory that doesn't. ...If the maximum entropy in any given region of space is proportional to the region's surface area and not its volume, then perhaps the true, fundamental degrees of freedom—the attributes that have the potential to give rise to that disorder—actually reside on the region's surface and not within its volume. Maybe... the universe's physical processes take place on a thin, distant surface that surrounds us, and all we see and experience is merely a projection of those processes. Maybe... the universe is rather like a hologram."

"The subject of this book is the structure of space-time on length-scales from 10-13 cm, the radius of an elementary particle, up to 1028 cm, the radius of the universe. ...we base our treatment on Einstein's General Theory of Relativity. This theory leads to two remarkable predictions about the universe: first, that the final fate of massive stars is to collapse behind an event horizon to form a 'black hole' which will contain a singularity; and secondly, that there is a singularity in our past which constitutes, in some sense, a beginning to the universe."

"So Einstein was wrong when he said, "God does not play dice." Consideration of black holes suggests, not only that God does play dice, but that he sometimes confuses us by throwing them where they can't be seen."

"I'm sorry to disappoint science fiction fans, but if information is preserved, there is no possibility of using black holes to travel to other universes. If you jump into a black hole, your mass energy will be returned to our universe but in a mangled form which contains the information about what you were like but in a state where it can not be easily recognized. It is like burning an encyclopedia. Information is not lost, if one keeps the smoke and the ashes. But it is difficult to read. In practice, it would be too difficult to re-build a macroscopic object like an encyclopedia that fell inside a black hole from information in the radiation, but the information preserving result is important for microscopic processes involving virtual black holes."

"Black holes ain't as black as they are painted. They are not the eternal prisons they were once thought. Things can get out of a black hole, both to the outside, and possibly to another universe. So if you feel you are in a black hole, don't give up. There's a way out."

"It is hard to understand how this infinitely dense singularity can evaporate into nothing. For matter inside the black hole to leak out into the universe requires that it travel faster than the speed of light."

"Is the reader feeling confused about the status of the black hole information paradox and black holes in general? So am I!"

"Experimentalists dream of some spectacular discovery such as the proof of the existence of black holes to justify the more than eight billion dollars it has cost to build the LHC."

"A large part of the relativity community is in denial - refusing even to contemplate the idea that black holes may not exist in nature, or seriously consider the idea that any kind of new matter such as the new putative dark energy can play a fundamental role in gravity theory."

"Hawking's intitial foray into quantum gravity was more modest than Wheeler's and other[s]... a sneak approach. He first wanted to know what the effect was of an ordinary, classic, curved-space gravitational field on a quantum system. He called this the semiclassical approach. Until that day, most quantum calculations had been done as if gravity didn't exist—they were hard enough without it in normal flat space-time... [Hawking accomplished this by] envisioning an "atom" whose nucleus was a catastrophically powerful black hole... Starobinsky ventured the opinion that rotating black holes would spray elementary particles. ...It was known from Penrose's work, among others, that you could extract energy from the spin of a black hole just like any other dynamo... in particles and radiation just like it did from a particle generator. ...But Hawking ...resolved to redo the calculation for himself ...he decided to warm up first, by calculating the rate of emission from a nonrotating quantum hole. He knew the answer should be no emission. ...his results were embarrassing. His imaginary black hole was spewing matter and radiation... he was reluctant to tell anybody but his closest friends; he was afraid Bekenstein would hear about it. ...It meant that holes had temperatures, just as Bekenstein's work implied."

"Even though a black hole is practically invisible, astronomers can infer its presence from the effects it has on spacetime itself. ...Andrea Ghez... uses s to study the motions of stars near the center of our galaxy. By watching how these stars move, she is really measuring the curvature of spacetime—the strength of gravity—in the heart of the Milky Way. ...Ghez realized that the stars are wheeling about an invisible, supermassive object that weighs more than two and a half million times as much as our sun. The black hole... dubbed ... cannot be seen directly, but Ghez was able to find it because of the effect it has on spacetime, on the stars orbiting it. Ghez's technique is quite similar to what Vera Rubin did when she made the first compelling case for ."

"I was very fortunate to know the great astrophysicist Subrahmanyan Chandrasekhar during his last years. Chandra, as we called him, was the first to discover that general relativity implied that stars above a certain mass would collapse into what we now call a black hole. Much later, he wrote a beautiful book describing the different solutions of the equations of general relativity that describe black holes. As I got to know him, Chandra shocked me by speaking of a deep anger toward Einstein. Chandra was upset that Einstein, after inventing general relativity, had abandoned this masterpiece, leaving it to others to struggle through it."

"There is no shortage of candidates for... baryonic . It may come in many forms—clouds of gas or dust, large planetlike objects, various forms of degraded stars, and black holes. ...MACHOS could include black holes and burned-out stars, such as s or s... Black holes are perhaps the most intriguing, and the most difficult to detect and quantify. As far back as the eighteenth century, scientists speculated about worlds so massive that nothing escaped their gravitational grip, not even light. In the early twentieth century, J. Robert Oppenheimer used Einstein's general theory of relativity to explain how a black hole might form: The black hole would warp adjacent space so deeply that the would exceed the speed of light... hence nothing... could leave... The center of the Milky Way emits intense gamma radiation—the death cry, perhaps, of stars falling into a black hole. Black holes may also be distributed in galactic halos, where they might constitute a substantial fraction of baryonic dark matter."

"According to Newton's law of gravity, every object in the universe attracts every other object... with a gravitational force... F = \frac{m M G}{R^2}... almost as famous as E = mc^2... On the left side is the force, F, between two masses... On the right side, the bigger mass is M and the smaller mass is m. ...The last symbol... G, is a numerical constant called Newton's constant. ...Ironically, Newton never knew the value of his own constant. ...G was too small to measure until the end of the eighteenth century. ...Cavindish found that the force between a pair of one-kilogram masses separated by one meter is approximately 6.6 x 10-11 newtons. (The Newton is... about one-fifth of a pound.) ...Newton had one lucky break... the special mathematical properties of the inverse square law. ...[B]y the miracle of mathematics, you can pretend that the entire mass is located at a single point. This... allowed Newton to calculate the ... Escape \; velocity = \sqrt{2MG/R} ... the bigger the mass [M] and the smaller the radius R, the larger the escape velocity. ...to compute the R_s... plug in the speed of light for the escape velocity... R_s = \frac{2MG}{c^2}... is proportional to the mass. That's all there is to dark stars... at the level that Laplace and Michell were able to understand them."

"[A]round 1967, Wheeler became very interested in the gravitationally collapsed objects that had described in 1917. At the time they were called black stars or dark stars. ...Wheeler began calling them black holes. At first the name was blackballed by the... '. ...the term ...was deemed obscene! But John fought it... Amusingly, John's next coinage was the saying "Black holes have no hair." ...he was making a very serious point about black hole horizons. ...[Each a] smooth ...perfectly regular, featureless sphere. Apart from their mass and rotational speed, every black hole was exactly like every other. Or so it was thought."

"Theory of relativity"

"The light-quantum has the peculiarity that it apparently ceases to exist when it is in one of its stationary states, namely, the zero state, in which its momentum and therefore also its energy, are zero. When a light-quantum is absorbed it can be considered to jump into this zero state, and when one is emitted it can be considered to jump from the zero state to one in which it is physically in evidence, so that it appears to have been created. Since there is no limit to the number of light-quanta that may be created in this way, we must suppose that there are an infinite number of light quanta in the zero state..."

"One hopes will soon demonstrate the incorrectness of the hypothesis of zero-point energy, the theoretical untenability of which became glaringly obvious to me soon after the publication of the paper I coauthored with Mr. Stern."

"Zero-point energy is now dead as a doornail."

"In his Theorie der Wärmestrahlung, Planck emphasized that the existence of a zero-point energy was completely foreign to classical physics. However, it seemed to be a ghost-like entity which it was difficult to connect to experiments."

"I fear that your hatred of the zero-point energy extends to the electrodynamic emission hypothesis that I introduced and that leads to it. But what’s to be done? For my part, I hate discontinuity of energy even more than discontinuity of emission."

"We here face a fundamental problem of outstanding importance. Its solution may still require a radical change in our theories beyond our present imagining."

"From quantum theory there follows the existence of so called zero-point oscillations; for example each oscillator in its lowest is not completely at rest but always is moving about its equilibrium position. Therefore electromagnetic oscillations also can never cease completely. Thus the quantum nature of the electromagnetic field has as its consequence zero point oscillations of the field strength in the lowest energy state, in which there are no light quanta in space... The zero point oscillations act on an electron in the same way as ordinary electrical oscillations do. They can change the eigenstate of the electron, but only in a transition to a state with the lowest energy, since empty space can only take away energy, and not give it up. In this way spontaneous radiation arises as a consequence of the existence of these unique field strengths corresponding to zero point oscillations. Thus spontaneous radiation is induced radiation of light quanta produced by zero point oscillations of empty space."

"The subject of electric oscillation announced in a remarkable paper of Henry in 1842 and threshed out in its main features by Kelvin in 1856, followed by Kirchhoff's treatment of the transmission of oscillations along a wire (1857), has become of discriminating importance between Maxwell's theory of the electric field and the other equally profound theories of an earlier date. These crucial experiments contributed by Hertz (1887, et seq.) showed that electromagnetic waves move with the velocity of light, and like it are capable of being reflected, refracted, brought to interference and polarized. A year later Hertz (1888) worked out the distribution of the vectors in the space surrounding the oscillatory source. ...Some doubt was thrown on the details of Hertz's results by Sarasin and de la Rive's phenomenon of multiple resonance (1890), but this was soon explained away as the necessary result of the occurrence of damped oscillations by Poincaré (1891), by Bjerknes (1891) and others."

"Based on Faraday's earlier work, Maxwell stressed the notion of fields, in contrast to Newton's emphasis on the direct action of bodies on each other across empty space (action at a distance). Faraday and Maxwell regarded the effect of an electrically charged body as giving rise to stresses in its immediate surroundings... [and] in ever widening circles, gradually diminishing... These stresses... [i.e.,] the fields are intermediaries between the material particles and assume the burden of Newton's action at a distance. ...[O]ne set of Maxwell's equations is to the effect that, in the presence of a magnetic field which changes in the course of time, an electric field arises which is not caused by the presence of any electric charge. This [is] the law of ... From his theory, Maxwell... predicted that magnetic fields propogate at... the speed of light. ...The laws of mechanics involve only accelerations, not velocities: the laws of electromagnetism involve a universal velocity [c]..."

"William Gilbert published a famous book on the magnet in 1600 and laid himself open to the gibes of Sir Francis Bacon for being one of those people so taken by their pet subject of research that they could only see the whole universe transposed into terms of it. Having made a spherical magnet called a ', and having found that it revolved when placed in a magnetic field, he decided that the whole earth was a magnet, that gravity was a form of magnetic attraction, and that the principles of the magnet accounted for the workings of the Copernican system as a whole. Kepler and Galileo were both influenced by this view, and with Kepler, it became an integral part of his system, a basis for the doctrine of almost universal gravitation."

"One possibility in this direction is to regard, classically, an electron as the end of a single Faraday line of force. The electric field in this picture from discrete Faraday lines of force, which are to be treated as physical things, like strings. One has then to develop a dynamics for such a string like structure, and quantize it.... In such a theory a bare electron would be inconceivable, since one cannot imagine the end of a piece of string without having the string."

"Classical mechanics has been developed continuously from the time of Newton and applied to an ever-widening range of dynamical systems, including the in interaction with matter. The underlying ideas and the laws governing their application form a simple and elegant scheme, which one would be inclined to think could not be seriously modified without having all its attractive features spout. Nevertheless it has been found possible to set up a new scheme, called quantum mechanics, which is more suitable for the description of phenomena on the atomic scale and which is in some respects more elegant and satisfying than the classical scheme. This possibility is due to the changes which the new scheme involves being of a very profound character and not clashing with the features of the classical theory that make it so attractive, as a result of which all these features can be incorporated in the new scheme."

"We shall therefore assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system."

"If de Sitter's solution were valid everywhere, then it would be thereby shown that the purpose which I pursued with the introduction of the λ-term has not been reached. In my opinion the general theory of relativity only forms a satisfactory system if according to it the physical qualities of space are completely determined by matter alone. Hence no gμv-field must be possible, i.e., no space-time-continuum, without matter that generates it."

"If the idea of physical reality had ceased to be purely atomic, it still remained for the time being purely mechanistic; people still tried to explain all events as the motion of inert masses; indeed no other way of looking at things seemed conceivable. Then came the great change, which will be associated for all time with the names of Faraday, Clerk Maxwell, and Hertz. The lion's share in this revolution fell to Clerk Maxwell. He showed that the whole of what was then known about light and electro-magnetic phenomena was expressed in his well known double system of differential equations, in which the electric and magnetic fields appear as the dependent variables. Maxwell did, indeed try to explain, or justify, these equations by intellectual constructions. But... the equations alone appeared as the essential thing and the strength of the fields as the ultimate entities, not to be reduced to anything else."

"I just want to explain what I mean when I say that we should try to hold on to physical reality. We are … all aware of the situation regarding what will turn out to be the basic foundational concepts in physics: the point-mass or the particle is surely not among them; the field, in the Faraday-Maxwell sense, might be, but not with certainty. But that which we conceive as existing ("real") should somehow be localized in time and space."

"What led me more or less directly to the special theory of relativity was the conviction that the electromotive force acting on a body in motion in a was nothing else but an ."

"During that year in the question came to me: If one runs after a light wave with light velocity, then one would encounter a time-independent wavefield. However, something like that does not seem to exist! This was the first juvenile thought experiment which has to do with the special theory of relativity. Invention is not the product of logical thought, even though the final product is tied to a logical structure."

"The special theory of relativity owes its origins to Maxwell's equations of the electromagnetic field."

"We postulate: It shall be impossible, by any experiment whatsoever performed inside such a box, to detect a difference between an acceleration relative to the nebulae and gravity. That is, an accelerating box in some gravitational field is indistinguishable from a stationary box in some different gravitational field. How much like Einstein this sounds, how reminiscent of his postulate of special relativity! We know the principle of equivalence works for springs, (as we knew special relativity worked for electrodynamics), and we extend it by fiat to all experiments whatsoever. We are used to such procedures by now, but how originally brilliant it was in 1911—what a brilliant, marvelous man Einstein was!"

"From 1916 Einstein and de Sitter corresponded extensively on exactly what kind of universe best fit the relativity equations. De Sitter initially developed a model of a spherical universe, in contrast to the cylindrical one Einstein had envisioned. De Sitter also tried to map out the shape of the spherical universe in absence of all matter. Einstein's reaction to de Sitter's model was strong and negative...de Sitter's sphere described a universe that changed in size instead of remaining nicely constant. ... Einstein saw matter—and its corresponding gravitational field—as what inherently created the shape of the universe. He cited what he dubbed "Mach's principle,"...the movements of any object ...were determined by all other bodies in the universe. ...how a body moves through space is tantamount to what shape space is, the concept of "shape" without matter, Einstein insisted, was meaningless."

"It turns out that the energy of a gravitational field—any gravitational field—is negative. During inflation, as the universe gets bigger and bigger and more and more matter is created, the total energy of matter goes upward by an enormous amount. Meanwhile, however, the energy of gravity becomes more and more negative. The negative gravitational energy cancels the energy in matter, so the total energy of the system remains whatever it was when inflation started—presumably something very small. ...This capability for producing matter in the universe is one crucial difference between the inflationary model and the previous model."

"What it takes to produce a gravitational repulsion is a negative pressure. According to general relativity, it turns out... both pressures and energy densities can produce gravitational fields, unlike Newtonian physics, where it's only mass densities that produce gravitational fields."

"A positive pressure produces an attractive gravitational field... Positive pressures are just sort of normal pressures and attractive gravity is normal gravity, so normal pressures produce normal gravity, but it is possible to have negative pressures, and negative pressures produce repulsive gravity, and that's the secret of what makes inflation possible."

"The universe would have expanded in a smooth way from a single point. As it expanded, it would have borrowed energy from the gravitational field, to create matter. As any economist could have predicted, the result of all that borrowing, was inflation. The universe expanded and borrowed at an ever-increasing rate. Fortunately, the debt of gravitational energy will not have to be repaid until the end of the universe."

"Newton's system was for a long time considered as final and the task... seemed simply to be an expansion.... The first difficulty arose in the discussion of the electromagnetic field in... Faraday and Maxwell. In Newtonian mechanics the gravitational force had been considered as given... In the work of Faraday and Maxwell... the field of force... became the object of the investigation... they tried to set up equations of motion for the fields, not primarily for the bodies... This change led back to a point of view...held... before Newton. An action could... be transferred... only when the two bodies touched... Newton had introduce a very new and strange hypothesis by assuming a force that acted over a long distance. Now in the theory of fields... action is transferred from one point to a neighboring point... in terms of differential equations. ...the description of the s... by Maxwell's equations seemed a satisfactory solution of the problem of force. ...The axioms and definitions of Newton had referred to bodies and their motion; but with Maxwell the fields... seemed to have acquired the same degree of reality as the bodies in Newton's theory. This view... was not easily accepted.; and to avoid such a change in the concept of reality... many physicists believed that Maxwell's equations actually referred to the deformations of an elastic medium... the ether... the medium was so light and thin that it could penetrate into other matter and could not be seen or felt. ...[H]owever ...it could not explain the complete absence of any longitudinal light waves."

"The theory of relativity... showed in a conclusive way that the concept of the ether as a substance, to which Maxwell's equations refer, had to be abandoned. ...the result was that the fields had to be considered as an independent reality."

"He was little interested mathematics or theory; for example, when his ideas on magnetic fields were extensively developed later by [James Clerk Maxwell] (1831-1879), Faraday was little concerned with the results. His own scientific career was characterized by simple ideas and simple experiments."

"The invention of the wheel was perhaps rather obvious; but the invention of an invisible wheel, made of nothing but a magnetic field, was far from obvious, and that is what we owe to Nikola Tesla."

"In view of the facility with which Lorentz's theory explains the dispersion and observation phenomena, a direct proof of its truth was hardly required. But that was also forthcoming. In 1896 a pupil of Lorentz, P. Zeeman, discovered a phenomenon whose existence Faraday had vainly sought for in 1862. If a luminous vapour, say a sodium flame, is brought into a strong magnetic field, the spectrum lines of the vapour show peculiar changes, consisting of a doubling or trebling, according to the line of vision. These changes are predicted by Lorentz's theory. The Zeeman phenomenon further permitted a determination of the inert mass connected with the vibrating charges, and then a striking result was obtained: the vibrating electron is always negatively charged, while the positive charge is stationary. ...The original and almost tacit assumption that the whole ion—i.e., the chemical atom plus its valency charge—was in oscillation must, therefore, be abandoned. We must suppose that the charge, just as is the case in , has also an independent mobility in the light-emitting molecule, and that the mass concerned in the Zeeman phenomenon is that of the electron itself."

"The impressions received by the two observers A0 and A would be alike in all respects. It would be impossible to decide which of them moves or stands still with respect to the ether, and there would be no reason for preferring the times and lengths measured by the one to those determined by the other, nor for saying that either of them is in possession of the "true" times or the "true" lengths. This is a point which Einstein has laid particular stress on, in a theory in which he starts from what he calls the principle of relativity, i.e., the principle that the equations by means of which physical phenomena may be described are not altered in form when we change the axes of coordinates for others having a uniform motion of translation relatively to the original system. I cannot speak here of the many highly interesting applications which Einstein has made of this principle. His results concerning electromagnetic and optical phenomena ...agree in the main with those which we have obtained... the chief difference being that Einstein simply postulates what we have deduced, with some difficulty and not altogether satisfactorily, from the fundamental equations of the electromagnetic field. By doing so, he may certainly take credit for making us see in the negative result of experiments like those of Michelson, Rayleigh and Brace, not a fortuitous compensation of opposing effects, but the manifestation of a general and fundamental principle. Yet, I think, something may also be claimed in favour of the form in which I have presented the theory. I cannot but regard the ether, which can be the seat of an electromagnetic field with its energy and vibrations, as endowed with a certain degree of substantiality, however different it may be from all ordinary matter. ...it seems natural not to assume at starting that it can never make any difference whether a body moves through the ether or not, and to measure distances and lengths of time by means of rods and clocks having a fixed position relatively to the ether. It would be unjust not to add that, besides the fascinating boldness of its starting point, Einstein's theory has another marked advantage over mine. Whereas I have not been able to obtain for the equations referred to moving axes exactly the same form as for those which apply to a stationary system, Einstein has accomplished this by means of a system of new variables slightly different from those which I have introduced."

"The general equations are next applied to the case of a magnetic disturbance propagated through a non-conductive field, and it is shown that the only disturbances which can be so propagated are those which are transverse to the direction of propagation, and that the velocity of propagation is the velocity v, found from experiments such as those of Weber, which expresses the number of electrostatic units of electricity which are contained in one electromagnetic unit. This velocity is so nearly that of light, that it seems we have strong reason to conclude that light itself (including radiant heat, and other radiations if any) is an electromagnetic disturbance in the form of waves propagated through the electromagnetic field according to electromagnetic laws."

"For decades, new-energy researchers talked about the possibility of treating a magnet so that its magnetic field would continuously shake or vibrate. On rare occasions, [Floyd] Sweet saw this effect, called self-oscillation, occur in electric transformers. He felt it could be coaxed into doing something useful, such as producing energy. Sweet thought that if he could find the precise way to shake or disturb a magnet's force field, the field would continue to shake by itself. It would be similar to striking a bell and having the bell keep on ringing. Sweet - who said his ideas came to him in dreams - turned for inspiration to his expertise in magnets. He knew magnets could be used to produce electricity, and wanted to see if he could get power out of a magnet by something other than the standard induction process. What Sweet wanted to do was to keep the magnet still and just shake its magnetic field. This shaking, in turn, would create an electric current. One new-energy researcher compares self-oscillation to a leaf on a tree waving in a gentle breeze. While the breeze itself isn't moving back and forth, it sets the leaf into that kind of motion. Sweet thought that if cosmic energy could be captured to serve as the breeze, then the magnetic field would serve as the leaf. Sweet would just have to supply a small amount of energy to set the magnetic field in motion, and space energy would keep it moving."

"Weyl considered an aspect about general relativity... the nonpreservation of direction in a curved space. ...[He] decided to consider the possibility that length was also not preserved. ...To effect this change mathematically, Weyl had to make a slight modification in the structure of general relativity. He assumed that in addition to the usual metric (set of numbers or variables) that described the gravitational field, there was another one related to length. ...amazingly when the result was analyzed Maxwell's equations mysteriously appeared. It almost seemed as if a bit of magic had occurred and scientists quickly became interested in the miracle. ...but with detailed analysis the theory was shown to be flawed. Einstein was the first to put his finger on the flaw. ...Weyl soon acknowledged the flaw and laid his theory to rest. It may have been a failure (actually it was not an entire failure; a similar idea is used today in modern field theory), but it did accomplish something important: it got people interested in the possibility that the electromagnetic and gravitational field could be unified. Einstein soon began working on an alternative theory, as did others."

"I want to talk about thought experiments and how they can work, and I want to do that by talking about my favorite example which is Maxwell's equations, the laws of electromagnetism. Again, these are more equations, but it's ok because they're on a T-shirt. So these laws govern the behavior of electric and magnetic fields, but actually, when Maxwell was a boy... there was a missing term. ...When Maxwell got into the field these were the equations, and they had been discovered experimentally, and I want to say a little bit about them. So this bit here is Gauss's law\nabla \cdot \mathbf{D} = \rho_\mathrm{v}it says that electric charges produce electric fields. This bit is Ampere's law\mathbf{\nabla} \times \mathbf{H} = \mathbf{J}it says that a electric currents produce magnetic fields. Faraday's law\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}says that oscillating magnetic fields can also produce electric fields... These were discovered and confirmed by a tremendous amount of data. They were consistent with all known measurements/observations of electromagnetism in Maxwell's day, but they have a problem, and the problem was exposed by a thought experiment. The thought experiment is simply to consider a rapidly oscillating current with a break in the circuit, a capacitor... and the problem is that if you use those equations to calculate the magnetic field next to the capacitor you don't get definite answer, you get two different answers, depending on how you use the equations. So there is something wrong. Even without doing this experiment you know that there is something wrong with those equations, and from this clue and a lot more reasoning... Maxwell was able to figure out that he could fix this by adding one more term [to Ampere's law]...\nabla \times \mathbf{H} = \mathbf{J} +\frac{\partial \mathbf{D}} {\partial t}and with this the equations are mathematically and physically well posed. They give unambiguous answers to questions like the one I mentioned. Now, Maxwell got a huge bonus because... Faraday's law says that an oscillating magnetic field produces an electric field. Maxwell's new term says that an oscillating electric field produces a magnetic field. So each can produce the other, and so you can get a disturbance which is self-sustaining, and which doesn't just sustain... but moves... Faraday, Maxwell, Faraday, Maxwell... you get a self-sustaining disturbance which moves at a velocity that you get from the equations, and the velocity is the speed of light. So Maxwell got a huge bonus for understanding the unification of electricity and magnetism. He understood the nature of light! When I first heard about this in high school I thought this was the coolest thing, and I still do. It's what we're all trying to do."

"J. J. Thomson was about to make the most significant find of the late nineteenth century... Thompson had been investigating the nature of cathode rays. He was convinced that they were some kind of electrified particles and, to prove his theory, began testing their behavior in electric or magnetic fields. By measuring both the extent to which such fields deflected them and their electric charge, he discovered that cathode rays consisted of very small negatively charged particles whose mass was about eighteen hundred times smaller than the lightest known substance—the hydrogen atom. ...He initially named these tiny carriers of electricity "corpuscles." Later they would become known as "electrons." The corpuscles were, in fact, the first subatomic particles to be found..."

"There is no direct observational evidence for the curvature [of space], the only directly observed data being the mean density and the expansion, which latter proves that the actual universe corresponds to the non-statical case. It is therefore clear that from the direct data of observation we can derive neither the sign nor that value of the curvature, and the question arises whether it is possible to represent the observed facts without introducing the curvature at all. Historically the term containing the 'cosmological constant λ' was introduced into the field equations in order to enable us to account theoretically for the existence of a finite mean density in a static universe. It now appears that in the dynamical case this end can be reached without the introduction of λ."

"Tesla, with his almost preternatural insight into alternating current phenomenon... enabled him... to revolutionize the art of electric power transmission through the invention of the rotary field motor..."

"If, in the very intense electric field in the neighbourhood of the cathode, the molecules of the gas are dissociated and are split up, not into the ordinary chemical atoms, but into these primordial atoms, which we shall for brevity call corpuscles; and if these corpuscles are charged with electricity and projected from the cathode by the electric field, they would behave exactly like the cathode rays."

"The physicist's definition of a field is the following. It's something that ... is spread everywhere throughout the universe. It's something that takes a particular value at every point in space. And what's more, that value can change in time."

"The conception of lines of force was introduced by Faraday to form a mental picture of the processes going on in the electric field. To him these lines were not mere mathematical abstractions. He ascribed to them properties that gave them a real physical significance. They terminate on opposite charges, are always in a state of tension, tending to shorten themselves, and are mutually repellent. The direction of a line of force at any point gives the direction of the field at that point. With the help of these properties of lines of force it is possible to obtain an idea of the distribution of the intensity of the field surrounding electrically charged bodies."

"In deriving... the energy of the moving electron, it was assumed that the field of the moving electron is the same as that of the stationary electron. This is, however, only the case if the electron moves slowly, because when a Faraday tube is moved it tends to set itself at right angles to the direction of motion. The tubes constituting the electron therefore tend to crowd together in a plane perpendicular to the direction of motion of the electron. The result is an increase in the inertia or mass of the electron, because more work must be done to move a Faraday tube parallel to itself than along its own direction, just as it is harder to move a log of wood in the water parallel to itself than to move it endwise. This increase in the mass of the electron only becomes appreciable when it moves with a speed greater than about one-tenth that of light... The mass of the electron is measured by the ratio of the force to the acceleration to which it gives rise. According to the theory of Abraham and Lorentz the electron has two masses: the longitudinal mass, when it is accelerated in the direction of motion, and the transverse mass, when it is accelerated perpendicular to the direction of motion of the electron. If m represents the mass of the slow moving electron, then the longitudinal and transverse masses m1 and m2 are given by"

"With Mie's view of matter there is contrasted another, according to which matter is a limiting singularity of the field, but charges and masses are force-fluxes in the field. This entails a new and more cautious attitude towards the whole problem of matter."

"First, the physicists in the persons of Faraday and Maxwell, proposed the "electromagnetic field" in contradistinction to matter, as a reality of a different category. Then, during the last century, the mathematicians, … secretly undermined belief in the evidence of Euclidean Geometry. And now, in our time, there has been unloosed a cataclysm which has swept away space, time, and matter hitherto regarded as the firmest pillars of natural science, but only to make place for a view of things of wider scope and entailing a deeper vision. This revolution was promoted essentially by the thought of one man, Albert Einstein."

"From quantum theory there follows the existence of so called zero-point oscillations; for example each oscillator in its lowest is not completely at rest but always is moving about its equilibrium position. Therefore electromagnetic oscillations also can never cease completely. Thus the quantum nature of the electromagnetic field has as its consequence zero point oscillations of the field strength in the lowest energy state, in which there are no light quanta in space... The zero point oscillations act on an electron in the same way as ordinary electrical oscillations do. They can change the eigenstate of the electron, but only in a transition to a state with the lowest energy, since empty space can only take away energy, and not give it up. In this way spontaneous radiation arises as a consequence of the existence of these unique field strengths corresponding to zero point oscillations. Thus spontaneous radiation is induced radiation of light quanta produced by zero point oscillations of empty space."

"Although the Special Theory of Relativity does not account for electromagnetic phenomena, it explains many of their properties. General Relativity, however, tells us nothing about . In Einstein's space-time continuum gravitational forces are absorbed in the geometry, but the electromagnetic forces are quite unaffected. Various attempts have been made to generate the geometry of space-time so as to produce a unified field theory incorporating both gravitational and electromagnetic forces."

"Changing electric fields produce magnetic fields, and changing magnetic fields produce electric fields. Thus the fields can animate one another in turn, giving birth to self-reproducing disturbances that travel at the speed of light. Ever since Maxwell, we understand that these disturbances are what light is."

"String theory is extremely attractive because gravity is forced upon us. All known consistent string theories include gravity, so while gravity is impossible in quantum field theory as we have known it, it is obligatory in string theory."

"It was found [in the 1970s], unexpectedly and without anyone really having a concept for it, that the rules of perturbation theory can be changed in a way that makes relativistic quantum gravity inevitable rather than impossible. The change is made by replacing point particles by strings. Then Feynman graphs are replaced by Riemann surfaces, which are smooth - unlike the graphs, which have singularities at interaction vertices. The Riemann surfaces can degenerate to graphs in many different ways. In field theory, the interactions occur at the vertices of a Feynman graph. By contrast, in string theory, the interaction is encoded globally, in the topology of a Riemann surface, any small piece of which is like any other. This is reminiscent of how non-linearities are encoded globally in twistor theory."

"With the new views advocated by Riemann... the texture, structure or geometry of space is defined by the metrical field, itself produced by the distribution of matter. Any non-homogeneous distribution of matter would then entail a variable structure of geometry for space from place to place. ... Riemann's exceedingly speculative ideas on the subject of the metrical field were practically ignored in his day, save by the English mathematician Clifford, who translated Riemann's works, prefacing them to his own discovery of the non-Euclidean Clifford space. Clifford realised the potential importance of the new ideas and suggested that matter itself might be accounted for in terms of these local variations of the non-Euclidean space, thus inverting in a certain sense Riemann's ideas. But in Clifford's day this belief was mathematically untenable. Furthermore, the physical exploration of space seemed to yield unvarying Euclideanism. ...it was reserved for the theoretical investigator Einstein, by a stupendous effort of rational thought, based on a few flimsy empirical clues, to unravel the mystery and to lead Riemann's ideas to victory. (In all fairness to Einstein... he does not appear to have been influenced directly by Riemann.) Nor were Clifford's hopes disappointed, for the varying non-Euclideanism of the continuum was to reveal the mysterious secret of gravitation, and perhaps also of matter, motion, and electricity. ... Einstein had been led to recognize that space of itself was not fundamental. The fundamental continuum whose non-Euclideanism was fundamental was... one of Space-Time... possessing a four-dimensional metrical field governed by the matter distribution. Einstein accordingly applied Riemann's ideas to space-time instead of to space... He discovered that the moment we substitute space-time for space (and not otherwise), and assume that free bodies and rays of light follow geodesics no longer in space but in space-time, the long-sought-for local variations in geometry become apparent. They are all around us, in our immediate vicinity... We had called their effects gravitational effects... never suspecting that they were the result of those very local variations in the geometry for which our search had been in vain... the theory of relativity is the theory of the space-time metrical field."

"Faraday was the first scientist to realise the enormous importance of the electromagnetic field. He saw in it a reality of a new category differing from matter. It was capable of transmitting effects from place to place, and was not to be likened to a mere mathematical fiction such as the gravitational field was then assumed to be. In his opinion, the phenomena of electricity and magnetism should be approached via the field rather than via the charged bodies and currents. In other words, according to Faraday, when a current was flowing along a wire, the most important aspect of the phenomenon lay not in the current itself but in the fields of electric and magnetic force distributed throughout space in the current's vicinity. It is this elevation of the field to a position of preeminence that is often called the pure physics of the field. Faraday was not a mathematician and was unable to co-ordinate the phenomena he foresaw in a mathematical way, and derive the full benefit from his ideas. Before dying, however, he entrusted this task to his colleague Maxwell; and one of the most astonishing theories of science, eclipsed only in recent years by Einstein's theory of relativity, was the outcome."

"In order to appreciate the nature of Maxwell's contributions, let us recall how matters stood in his day. ...Faraday's law of induction ...states that a variable magnetic field generates an electric field. Maxwell, however, considered that this law, standing alone, lacked symmetry; so he formulated the hypothesis that conversely a variable electric field should generate a magnetic one, and proceeded to construct his theory... no experimental results could be claimed to have justified any such assumption... His celebrated equations of electromagnetics represented, therefore, the results of experiment, supplemented by this additional hypothetical assumption. The advisability of making this hypothesis was accentuated when it was found to ensure the law of conservation of electricity. ...In the particular case of free space in which only fields but no charges or currents are present, Maxwell's equations of electromagnetics, termed field-equations (since they describe the state of the electromagnetic field), can be written:"

"Although experimenters had attempted by various means to submit Maxwell's views to a test, the technical difficulties were so great that no success had been achieved. It appeared clearly from Maxwell's equations that no appreciable effects could be anticipated unless dE/dt was very great; and this meant that the electric intensity E would have to vary with extreme rapidity. The simplest means of obtaining a result of this kind would be to produce an oscillating field of electric intensity in which the oscillations were extremely rapid, say, several millions per second. But no mechanical contrivance could yield such rapid vibrations, and... no other methods suggested themselves. ... In 1885 Helmholtz directed the attention of his pupil, Hertz, to the problem. Hertz was one of the most remarkable experimenters of the nineteenth century; he succeeded in at last vanquishing the technical difficulties and in generating by purely electrical means an oscillating electric field of extremely high frequency. Electromagnetic waves of sufficient intensity were thus produced; and after having been sidetracked for a time by a secondary phenomenon whose nature was elucidated by Poincaré, Hertz verified the fact that the waves advanced with the speed of light and indeed possessed all the essential properties of light waves other than those of visibility to the human eye. Thus, as a result of Hertz's experiments, the foundations were laid for the commercial use of wireless and radio; but, more important still, Maxwell's electromagnetic theory of light establishing the intimate connection between electricity and optics had been at last vindicated."

"The most precise experiments have proved the correctness of the Einsteinian laws of mechanics and...Bucherer's experiment proving the increase in mass of an electron in rapid motion is a case in point. Very important differences distinguish the theory of Einstein from that of Lorentz. Lorentz also had deduced from his theory that the mass of the electron should increase and grow infinite when its speed neared that of light; but the speed in question was the speed of the electron through the stagnant ether; whereas in Einstein's theory it is merely the speed with respect to the observer. According to Lorentz, the increase in mass of the moving electron was due to its deformation or Fitzgerald contraction. The contraction modified the lay of the electromagnetic field round the electron; and it was from this modification that the increase in mass observed by Bucherer was assumed to arise. In Einstein's theory, however, the increase in mass is absolutely general and need not be ascribed to the electromagnetic field of the electron in motion. An ordinary unelectrified lump of matter like a grain of sand would have increased in mass in exactly the same proportion; and no knowledge of the microscopic constitution of matter is necessary in order to predict these effects, which result directly from the space and time transformations themselves. Furthermore, the fact that this increase in mass of matter in motion is now due to relative motion and not to motion through the stagnant ether, as in Lorentz's theory, changes the entire outlook considerably. According to Lorentz, the electron really increased in mass, since its motion through the ether remained a reality. According to Einstein, the electron increases in mass only in so far as it is in relative motion with respect to the observer. Were the observer to be attached to the flying electron no increase in mass would exist; it would be the electron left behind which would now appear to have suffered the increase. Thus mass follows distance, duration and electromagnetic field in being a relative and having no definite magnitude of itself and being essentially dependent on the conditions of observation. Owing to the general validity of the Lorentz-Einstein transformations, it becomes permissible to apply them to all manner of phenomena.. ...temperature, pressure and many other physical magnitudes turned out to be relatives. ...entropy, electric charge and the velocity of light in vacuo were absolutes transcending the observer's motion. ...a number of other entities are found to be absolutes, the most important of which is that abstract mathematical quantity called the Einsteinian interval, which plays so important a part in the fabric of the new objective world of science, the world of four-dimensional space-time."

"In the study of electricity and magnetism we may consider phenomena in which conditions do not vary as time passes by; the electric charges and the magnets remain at rest, and the currents flowing in fixed wires do not vary in intensity. Conditions are then termed stationary [static]; it is as though time played no part. The laws which govern this type of phenomena were discovered empirically over a century ago, and were expressed mathematically in terms of spatial vectors. The problem of ascertaining how electric and magnetic phenomena would behave when conditions ceased to be stationary was one that could not be predicted; further experimental research was necessary before the general laws could be obtained. Even so, the difficulties were considerable, and it needed Maxwell's genius to establish the laws from the incomplete array of experimental evidence then at hand. All this work extended over nearly a century; it was slow and laborious. Yet, had men realised that our world was one of four-dimensional Minkowskian space-time, and not one of separate space and time, things would have been different. By extending the well-known stationary laws to four-dimensional space-time, through the mere addition of time components to the various trios of space ones, we should have written out inadvertently the laws governing varying fields, or, in other words, we should have constructed Maxwell's celebrated equations. Electromagnetic induction, discovered experimentally by Faraday, the additional electrical term introduced tentatively by Maxwell, radio waves, everything in the electromagnetics of the field, could have been foreseen at one stroke of the pen. A century of painstaking effort could have been saved. We are assuming that a four-dimensional vector calculus would have been in existence; but this is purely a mathematical question."

"Let us revert to the metrical field, as defining the space-time structure. Although Riemann had attributed the existence of the structure, or metrical field, of space to the binding forces of matter, there is not the slightest indication in Einstein's special theory that any such view is going to be developed later on; in fact, it does not appear that Einstein was influenced in the slightest degree by Riemann's ideas. ...in the special theory, the problem of determining whence the structure, or field, arises, what it is, what causes it, is not even discussed in a tentative manner. Space-time, with its flat structure, is assumed to be given or posited by the Creator. But in the general theory the entire situation changes when Einstein accounts for gravitation, hence for a varying lay of the metrical field, in terms of a varying non-Euclidean structure of space-time around matter. We are then compelled to recognise not only that the metrical field regulates the behaviour of material bodies and clocks, as was also the case in the special theory, but, furthermore, that a reciprocal action takes place and that matter and energy in turn must affect the lay of the metrical field. But we are still a long way from Riemann's view that the field is not alone affected but brought into existence by matter; and it is only when we consider the cosmological part of Einstein's theory that this idea of Riemann's may possibly be vindicated. And here we come to a parting of the ways with de Sitter and Eddington on one side, Einstein and Thirring on the other, and Weyl somewhere in between the two extremes."

"In electromagnetism... the law of the inverse square had been supreme, but, as a consequence of the work of Faraday and Maxwell, it was superseded by the field. And the same change took place in the theory of gravitation. By and by the material particles, electrically charged bodies, and magnets which are the things that we actually observe come to be looked upon only as "singularities" in the field."

"This is the mathematical formulation of the theory of relativity. The metric properties of the four-dimensional continuum are described... by a certain number (ten, in fact) of quantities denoted by gαβ, and commonly called "potentials." The physical status of matter and energy, on the other hand, is described by ten other quantities, denoted by Tαβ, the set of which is called the "material tensor." This special tensor has been selected because it has the property which is mathematically expressed by saying that its divergence vanishes, which means that it represents something permanent. The fundamental fact of mechanics is the law of inertia, which can be expressed in its most simple form by saying that it requires the fundamental laws of nature to be differential equations of the second order. Thus the problem was to find a differential equation of the second order giving a relation between the metric tensor gαβ and the material tensor Tαβ. This is a purely mathematical problem, which can be solved without any reference to the physical meaning of the symbols. The simplest possible equation (or rather set of ten equations, because there are ten gs) of that kind that can be found was adopted by Einstein as the fundamental equation of his theory. It defines the space-time continuum, or the "field." The world-lines of material particles and light quanta are the geodesics in the four-dimensional continuum defined by the solutions gαβ of these field-equations. The equations of the geodesic thus are equivalent to the equations of motion of mechanics. When we come to solve the field-equations and substitute the solutions in the equations of motion, we find that in the first approximation, i.e. for small material velocities (small as compared with the velocity of light), these equations of motion are the same as those resulting from Newton's theory of gravitation. The distinction between gravitation and inertia has disappeared; the gravitational action between two bodies follows from the same equations, and is the same thing, as the inertia of one body. A body, when not subjected to an extraneous force (i.e. a force other than gravitation), describes a geodesic in the continuum, just as it described a geodesic, or straight line, in the absolute space of Newton under the influence of inertia alone. The field-equations and the equations of the geodesic together contain the whole science of mechanics, including gravitation."

"If we put in the details, the singularities of the field, viz. the galactic systems and the stars, we find that there is... a tendency, called gravitation, to decrease the mutual distances of these "singularities." At short distances, within the confines of a galactic system, this second tendency is by far the strongest, and the galactic systems retain their size independent of the expansion or contraction of the universe..."

"If you wish to learn from the theoretical physicist anything about the methods which he uses... Don't listen to his words, examine his achievements. For to the discoverer in that field, the constructions of his imagination appear so necessary and so natural that he is apt to treat them not as the creations of his thoughts but as given realities."

"I want... to glance... at the development of the theoretical method, and... especially to observe the relation of pure theory to the totality of the data of experience. Here is the eternal antithesis of the two inseparable constituents of human knowledge, Experience and Reason, within the sphere of physics. We honour ancient Greece as the cradle of western science. She for the first time created the intellectual miracle of a logical system, the assertions of which followed one from another with such rigor that not one of the demonstrated propositions admitted of the slightest doubt—Euclid's geometry. This marvellous accomplishment of reason gave to the human spirit the confidence it needed for its future achievements. ...But yet the time was not ripe for a science that could comprehend reality... until a second elementary truth had been realized, which only became the common property of philosophers after Kepler and Galileo. Pure logical thinking can give us no knowledge whatsoever of the world of experience; all knowledge about reality begins with experience and terminates in it."

"Conclusions obtained by purely rational processes are, so far as Reality is concerned, entirely empty. It was because he recognized this, and especially because he impressed it upon the scientific world that Galileo became the father of modern physics and in fact of the whole of modern natural science."

"A complete system of theoretical physics consists of concepts and basic laws to interrelate those concepts and of consequences to be derived by logical deduction."

"[I]f we conceive Euclidean geometry as the science of the possibilities of the relative placing of actual rigid bodies and accordingly interpret it as a physical science, and do not abstract from its original empirical content, the logical parallelism of geometry and theoretical physics is complete."

"We have now assigned to reason and experience their place within the system of theoretical physics. Reason gives the structure to the system; the data of experience and their mutual relations are to correspond exactly to consequences in the theory. On the possibility alone of such a correspondence rests the value and the justification of the whole system, and especially of its fundamental concepts and basic laws. But for this, these latter would simply be free inventions of the human mind which admit of no a priori justification..."

"It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible..."

"The conception... of the purely fictitious character of the basic principles of theory was in the eighteenth and nineteenth centuries still far from being the prevailing one. But it continues to gain more and more ground because of the everwidening logical gap between the basic concepts and laws on the one side and the consequences to be correlated with our experiences on the other—a gap which widens progressively with the developing unification of the logical structure, that is with the reduction in the number of the logically independent conceptual elements required for the basis of the whole system."

"Newton felt by no means comfortable about the concept of absolute space, which embodied that of absolute rest; for he was alive to the fact that nothing in experience seemed to correspond to this latter concept. He also felt uneasy about the introduction of action at a distance. But the enormous practical success of his theory may well have prevented him and the physicists of the eighteenth and nineteenth centuries from recognizing the fictitious character of the principles of his system."

"[S]cientists of those times were for the most part convinced that the basic concepts and laws of physics... were derivable by abstraction, i.e. by a logical process, from experiments. It was the general Theory of Relativity which showed in a convincing manner the incorrectness of this view. ...quite apart from the question of comparative merits, the fictitious character of the principles is made quite obvious by the fact that it is possible to exhibit two essentially different bases, each of which in its consequences leads to a large measure of agreement with experience. This indicates that any attempt logically to derive the basic concepts and laws of mechanics from the ultimate data of experience is doomed to failure."

"Have we any right to hope that experience will guide us aright, when there are theories (like classical mechanics) which agree with experience to a very great extent, even without comprehending the subject in its depths? ...there is the correct path and, moreover... it is in our power to find it. ...in Nature is actualized the ideal of mathematical simplicity. ...pure mathematical construction enables us to discover the concepts and the laws..."

"[E]xperience... remains the sole criterion of the serviceability of a mathematical construction for physics, but the truly creative principle resides in mathematics. ...pure thought is competent to comprehend the real, as the ancients dreamed."

"In the paucity of the mathematically existent simple field-types and of the relations between them, lies the justification for the theorist's hope that he may comprehend reality in its depths. The most difficult point for such a field-theory at present is how to include the atomic structure of matter and energy. For the theory in its basic principles is not an atomic one in so far as it operates exclusively with continuous functions of space, in contrast to classical mechanics whose most important feature, the material point, squares with the atomistic structure of matter."

"The modern quantum theory, as associated with the names of de Broglie, Schrödinger, and Dirac, which of course operates with continuous functions, has overcome this difficulty by means of a daring interpretation, first given in a clear form by Max Born:-the space functions which appear in the equations make no claim to be a mathematical model of atomic objects. These functions are only supposed to determine... the probabilities of encountering those objects in a particular place or in a particular state of motion... This conception... forces us to employ a continuum of which the number of dimensions is not that of previous physics, namely 4, but which has dimensions increasing without limit as the number of the particles... increases. ...I ...accord to this interpretation no more than a transitory significance. I still believe in the possibility of giving a model of reality, a theory, that is to say, which shall represent events themselves and not merely the probability..."

"On the other hand... we have to give up the notion of an absolute localization of the particles in a theoretical model. This seems to me to be the correct theoretical interpretation of Heisenberg's indeterminacy relation. And yet a theory may perfectly well exist, which is in a genuine sense an atomistic one (and not merely on the basis of a particular interpretation), in which there is no localizing of the particles in a mathematical model."

"[I]n order to include the atomistic character of electricity, the field equations only need to involve that a three-dimensional volume of space on whose boundary the electrical density vanishes everywhere, contains a total electrical charge of an integral amount. Thus in a continuum theory, the atomistic character could be satisfactorily expressed by integral propositions without localizing the particles which constitute the atomistic system. Only if this sort of representation of the atomistic structure be obtained could I regard the quantum problem within the framework of a continuum theory as solved."

"[Any] portion of corporeal matter which moves by itself when an impetus has been impressed on it by any external motive force has a natural tendency to move on a rectilinear, not a curved, path."

"Special relativity has this in common with Newtonian mechanics: The laws of both theories are supposed to hold only with respect to certain coordinate sys­tems: those known as "inertial systems. " An inertial system is a system in a state of motion such that "force-free" material points within it are not accelerated with respect to the coordinate system. How­ever, this definition is empty if there is no independent means for recognizing the absence of forces. But such a means of recognition does not exist if gravitation is considered as a "field.""

"[O]ne of the most interesting aspects in Fabri's physics is the wholehearted adoption of the important principle of conservation of rectilinear motion (...CRM) - a direct result of an impetus which... tends to conserve itself in the absence of obstacles or hindrences, and the possibility of motion in a vacuum... CRM is often referred to as "inertia", but this problematic term is both anachronistic and misleading. The word... (...meaning "laziness") was first utilized in a physical sense by Johannes Kepler, to mean a tendency of bodies to come to rest once they are set in motion... It was subsequently used, in a different sense - meaning the reluctance of bodies in rest to be set in motion - by Descartes... and even by Fabri himself. This notion, as... expressed in Newton's first law... could be regarded merely as a "less important aspect of inertia" than in his second law... it is also clear that the classical (or Newtonian) concept cannot be fully expressed and understood without Newton's third law and his concept of force..."

"The law of inertia has no known origin."

"One other test of gravity... is the question of whether the pull is exactly proportional to the ... and changes in velocity are inversely proportional to the mass... That means that two objects of different mass will change their velocity in the same manner in a gravitational field. ...That is Galileo's old experiment from the Leaning Tower of Pisa. ...How accurate is it? It was measured in an experiment by ...Eötvös in 1909 and ...by Dicke, and is known to one part in 10,000,000,000. ...[S]uppose you wanted to know whether the pull is exactly proportional to the inertia. The earth is going around the sun, so the things are thrown out by inertia. But they are attracted by the sun to the extent that they have mass... So if they are attracted to the sun in a different proportion from that thrown out by inertia, one will be pulled towards the sun, and the other away from it, and so, hanging them on opposite ends of a rod on another Cavendish quartz fiber, the thing will twist towards the sun. It does not twist at this accuracy, so we know that the sun's attraction to two objects is exactly proportional to its coefficient of inertia; in other words, its mass."

"The situation of everyday life which Kant used as an analogy to the inertia of matter is the contrast between matter itself and the artisan who operates on the material... The characteristic feature of matter is its complete passivity... responsible for its inertia. ...Although this introduction of the concept of "life" into physical science does make it more "human," it certainly has little to do with the actual law of inertia in mechanics. It even gives the misleading impression that for living organisms the law of inertia would not be valid."

"I tell you that if natural bodies have it from Nature to be moved by any movement, this can only be circular motion, nor is it possible that Nature has given to any of its integral bodies a propensity to be moved by straight motion. I have many confirmations of this proposition, but for the present one alone suffices, which is this. I suppose the parts of the universe to be in the best arrangement, so that none is out of its place, which is to say that Nature and God have perfectly arranged their structure. This being so, it is impossible for those parts to have it from Nature to be moved in straight, or in other than circular motion, because what moves straight changes place, and if it changes place naturally, then it was at first in a place preternatural to it, which goes against the supposition. Therefore, if the parts of the world are well ordered, straight motion is superfluous and not natural, and they can only have it when some body is forcibly removed from its natural place, to which it would then return by a straight line, for thus it appears that a part of the earth does [move] when separated from its whole. I said "it appears to us," because I am not against thinking that not even for such an effect does Nature make use of straight line motion."

"I mentally conceive of some moveable [sphere] projected on a horizontal plane, all impediments being put aside. Now it is evident... that equable motion on this plane would be perpetual if the plane were of infinite extent, but if we assume it to be ended, and [situated] on high, the movable, driven to the end of this plane and going on further, adds on to its previous equable and indelible motion, that downward tendency which it has from its heaviness. Thus, there emerges a certain motion, compounded..."

"It seems to me proper to adorn the Author's thought here with its conformity to a conception of Plato's regarding the determination of the various speeds of equable motion in the celestial motions of revolution. ...he said that God, after having created the movable celestial bodies, in order to assign to them those speeds with which they must be moved perpetually in equable circular motion, made them depart from rest and move through determinate spaces in that natural straight motion in which we sensibly see our moveables to be moved from the state of rest, successively accelerating. And he added that these having been made to gain that degree [of speed] which it pleased God that they should maintain forever, He turned their straight motion into circulation, the only kind [of motion] that is suitable to be conserved equably, turning always without retreat from or approach toward any pre-established goal desired by them. The conception is truly worthy of Plato, and it is to be more esteemed to the extent that its foundations, of which Plato remained silent, but which were discovered by our Author in removing their poetical mask or semblance, show it the guise of a true story."

"Second law of mechanics.—All change of matter has an external cause. (Every body remains in its state of rest or motion in the same direction and with the same velocity, if not compelled by an external cause to forsake this state.) Demonstration. (From universal metaphysics the proposition that all change has a cause, is laid at the foundation; here it only remains to be proved of matter, that its change must always have an external cause. ... this cause cannot be internal for matter has no absolutely internal determinations and grounds of determination. ... Observation. This mechanical law can only be called the law of inertia (lex inertiæ)..."

"The inertia of matter is and means nothing but its lifelessness, as matter in itself. Life means the capacity of a substance, to act from an internal principle, determining a finite substance to change, and a material substance to rest or motion, as change of its state. ...Thus all matter as such is lifeless. The proposition of inertia says so much and no more. If we seek the cause of any change of matter whatsoever in life, we shall have to seek it at once in another substance, distinct from matter, although bound up with it."

"On the law of inertia (next to that of the permanence of substance) the possibility of a natural science proper entirely rests. The opposite of the first, and therefore the death of all natural philosophy, would be hylozoism. From the same conception of inertia as that of mere lifelessness, it follows... that it does not signify a positive effort to maintain its state. Only living beings can be termed inert in this latter sense, inasmuch as they have a conception of another state, which they dread and strive against with all their might."

"Law I. Every body perseveres in its state of rest or of moving uniformly in a straight line, except in so far as it is made to change that state by external forces. ...the motion of a cannon ball is retarded, but this arises from an action between the projectile and the air which surrounds it, whereby the ball experiences a force in the direction opposite to its relative motion, while the air, pushed forward by an equal force, is itself set in motion... But our conviction of the truth of this law may be greatly strengthened by considering what is involved in a denial of it. ...Let us in the first place suppose the law to be that the velocity diminishes at a certain [extremely slow] rate... The velocity referred to in this hypothetical law can only be the velocity referred to a point absolutely at rest... the point of reference. ...If, when referred to a certain point, the body appears to be moving northward with diminishing velocity, we have only to refer it to another point moving northward with a uniform velocity greater than that of the body, and it will appear to be moving southward with increasing velocity. Hence the hypothetical law is without meaning unless we admit the possibility of defining absolute rest and absolute velocity. Even if we admit this as a possibility, the hypothetical law, if found to be true, might be interpreted, not as a contradiction of Newton's law, but as evidence of the resisting action of some medium in space. To take another case. Suppose the law to be that a body, not acted on by any force, ceases at once to move. This is not only contradicted by experience, but it leads to a definition of absolute rest as the state which a body assumes as soon as it is freed from the action of external forces. It may thus be shown that the denial of Newton's law is in contradiction to the only system of consistent doctrine about space and time which the human mind has been able to form."

"The idea that inertia is an acquired property is old, generally going under the name of “”. According to it, inertia is due to the interaction of bodies with some omnipresent medium. Ideas along this line differ on what the medium is, and on the nature of the interaction. But if indeed such is the origin of inertia, then inertia is not some property of ultimate fundamentality, but can take different forms depending on where we are in parameter space of the body with respect to signposts and boundary stones defined by the characteristics of the medium."

"The vis insita, or innate force of matter, is a power of resisting by which every body, as much as in it lies, endeavours to preserve its present state, whether it be of rest or of moving uniformly forward in a straight line."

"The old Greek philosophy, which in Europe in the later middle ages was synonymous with the works of Aristotle, considered motion as a thing for which a cause must be found: a velocity required a force to produce and to maintain it. The great discovery of Galileo was that not velocity, but acceleration requires a force."

"As related by Archimedes in the "sand-counter", Aristarchus advanced the bold hypothesis that the earth rotates in a circle about the sun. Most astronomers rejected this... as Archimedes tells us also. [I]n view of the status of mechanics at the time, there are weighty arguments against the motion of the earth... already found in Aristotle and, developed more fully, in Ptolemy. If the earth had such an enormously rapid motion, says Ptolemy, then everything that was not clinched to and riveted to the earth, would fall behind and would therefore appear to fly off in the opposite direction. Clouds... would be overtaken by the rotation of the earth and would lag behind. ...[T]here is nothing to be said against this since the Greeks did not know the law of inertia and required a force to account for every motion. If the earth does not drag the clouds along, they have to lag behind. We do not know how Aristarchus met these arguments."

"In the history of Science it is possible to find many cases in which the tendency of Mathematics to express itself in the most abstract forms has proved to be of ultimate service in the physical order of ideas. Perhaps the most striking example is to be found in the development of abstract Dynamics. The greatest treatise which the world has seen, on this subject, is Lagrange's Mécanique Analytique, published in 1788. ...conceived in the purely abstract Mathematical spirit ...Lagrange's idea of reducing the investigation of the motion of a dynamical system to a form dependent upon a single function of the of the system was further developed by Hamilton and Jacobi into forms in which the equations of motion of a system represent the conditions for a stationary value of an integral of a single function. The extension by Routh and Helmholtz to the case in which "ignored co-ordinates" are taken into account, was a long step in the direction of the desirable unification which would be obtained if the notion of potential energy were removed by means of its interpretation as dependent upon the kinetic energy of concealed motions included in the dynamical system. The whole scheme of abstract Dynamics thus developed upon the basis of Lagrange's work has been of immense value in theoretical Physics, and particularly in statistical Mechanics... But the most striking use of Lagrange's conception of generalized co-ordinates was made by Clerk Maxwell, who in this order of ideas, and inspired on the physical side by... Faraday, conceived and developed his dynamical theory of the Electromagnetic field, and obtained his celebrated equations. The form of Maxwell's equations enabled him to perceive that oscillations could be propagated in the electromagnetic field with the velocity of light, and suggested to him the Electromagnetic theory of light. Heinrich Herz, under the direct inspiration of Maxwell's ideas, demonstrated the possibility of setting up electromagnetic waves differing from those of light only in respect of their enormously greater length. We thus see that Lagrange's work... was an essential link in a chain of investigation of which one result... gladdens the heart of the practical man, viz. wireless telegraphy."

"Full use of Lagrange's own made the unification of the varied principles of statistics and dynamics possible—in statistics by the use of the principle of virtual velocities, in dynamics by the use of . This led... to generalized coordinates and to the equation of motion in their "Lagrangian" form... Newton's geometrical approach was now fully discarded; Lagrange's book was a triumph of pure analysis."

"The treatment of the kinetics of a material system by the method of generalised coordinates was first introduced by Lagrange, and has since his time been greatly developed by the investigations of different mathematicians. Independently of the highly interesting, although purely abstract science of theoretical dynamics which has resulted from these investigations, they have proved of great and continually increasing value in the application of mechanics to thermal, electrical and chemical theories, and the whole range of ."

"When the position of every point of a material system can be determined in terms of any independent variables n in number, the system is said to possess n degrees of freedom, and the n independent variables are called the generalised coordinates. The choice of the particular independent variables is perfectly arbitrary, and may be varied indefinitely, but the number of degrees of freedom cannot be either increased or diminished."

"In a rigid body free to move in any manner there are six degrees of freedom, and the generalised coordinates most frequently chosen in this case are the three rectangular coordinates of some point in the body and three angular coordinates determining the orientation of the body about that point, generally the angles θ, φ, ψ of ordinary occurrence in rigid dynamical problems."

"When the body degenerates into a material straight line the number of degrees of freedom is reduced to five; and when this straight line is constrained to move parallel to some fixed plane the number of degrees of freedom is still further reduced to four."

"... Where was the particle just before I made the measurement? There are three plausible answers to this question, and they serve to characterize the main schools of thought regarding quantum indeterminacy: ... realist ... orthodox ... agnostic ... Until fairly recently, all three positions (realist, orthodox, and agnostic) had their partisans. But in 1964 John Bell astonished the physics community by showing that it makes an observable difference whether the particle had a precise (though unknown) position prior to the measurement, or not. Bell's discovery effectively eliminated agnosticism as a viable option ..."

"David J. Griffiths, Introduction to Quantum Mechanics (2nd ed., 2016), pp. 3–4"

"One of the fundamental concepts of mechanics is that of a particle. By this we mean a body whose dimensions may be neglected in describing its motion. The possibility of so doing depends, of course, on the conditions of the problem concerned. For example, the planets may be regarded as particles in considering their motion about the Sun, but not in considering their rotation about their axes."

"There were two things that especially attracted me to the ideas of renormalization and quantum field theory. One of them was that the requirement that a physical theory be renormalizable is a precise and rational criterion of simplicity. In a sense, this requirement had been used long before the advent of renormalization theory. When Dirac wrote down the Dirac equation in 1928 he could have added an extra ‘Pauli’ term ... which would have given the electron an arbitrary anomalous magnetic moment. Dirac could (and perhaps did) say ‘I won’t add this term because it’s ugly and complicated and there’s no need for it.’ I think that in physics this approach generally makes good strategies but bad rationales. It’s often a good strategy to study simple theories before you study complicated theories because it’s easier to see how they work, but the purpose of physics is to find out why nature is the way it is, and simplicity by itself is I think never the answer. But renormalizability was a condition of simplicity which was being imposed for what seemed after Dyson’s 1949 papers ... like a rational reason, and it explained not only why the electron has the magnetic moment it has, but also (together with gauge symmetries) all the detailed features of the standard model of weak, electromagnetic, and strong, interactions, aside from some numerical parameters. The other thing I liked about quantum field theory during this period of tremendous optimism was that it offered a clear answer to the ancient question of what we mean by an elementary particle: it is simply a particle whose field appears in the Lagrangian. It doesn’t matter if it’s stable, unstable, heavy, light — if its field appears in the Lagrangian then it’s elementary, otherwise it’s composite."

"I must ask you to go over very old ground, and to turn your attention to a question which has been raised again and again ever since man began to think."

"The question is that of the transmission of force. We see two bodies at a distance from each other exert a mutual influence on each other's motion. Does this mutual action depend on the existence of some third thing, some medium of communication, occupying the space between the bodies, or do the bodies act on each other immediately, without the intervention of anything else?"

"The mode in which Faraday was accustomed to look at phenomena of this kind differs from that adapted by many modern inquirers, and my special aim will be to enable you to place yourselves at Faraday's point of view, and to point out the scientific value of that conception of lines of force which, in his hands, became the key to the science of electricity. ..."

"Why... should we not admit that the familiar mode of communicating motion by pushing and pulling... is the type and exemplification of all action between bodies, even in case in which we can observe nothing between..."

"Here for instance is a kind of attraction which Professor Guthrie has made us familiar. A disk is set in vibtration, and is then brought near a light suspended body, which immediately begins to move towards the disk as if by an invisible cord. ...Sir W. Thomson has pointed out that in a moving fluid the pressure is least where the velocity is greatest. The velocity of the vibratory motion of the air is greatest near the disk. Hence the pressure of the air on the suspended body is less on the side nearest the disk... the body yields to the greater pressuire, and moves toward the disk. The disk, therefore, does not act where it is not. It sets the air next to it in motion by pushing it, this motion is communicated to more and more distant portions of the air in turn, and thus the pressure on opposite sides of the suspended body rendered unequal, and it moves toward the disk in consequence of excess pressure. The force is therefore the force of the old school—a case of vis a tergo—a shove from behind."

"The advocates of the doctrine of action at a distance, however... say... Do we not see an instance of action at a distance in the case of a magnet... Besides this, Newton's law of gravitation... asserts not only that the heavenly bodies act ... across immense intervals of space... on one another with precisely the same force as if the strata beneath which each is buried [were] non-existant. If any medium takes part... it must surely make some difference whether the space... contains nothing but this medium, or whether it is occupied by the dense matter of the earth or of the sun."

"But the advocates... maintain that even when the action is apparently the pressure of contiguous portions of matter... that a space always intervenes between... that so far from action at a distance being impossible, it is the only kind of action which ever occurs, and that the favorite old vis a tergo... exists only in the imagination of schoolmen."

"The best way to prove that when one body pushes another it does not touch it, is to measure the distance between... Here are two glass lenses, one of which is pressed against another... By means of an electric light... a series of coloured rings is formed on the screen... first observed and first explained by Newton. The particular colour of any ring depends on the distance between the surfaces... [W]hat we call optical contact is not real contact. Optical contact indicates only that the distance between... is much less than a wavelength... Now it is possible to bring two pieces of glass so close together, that... they will adhere together so firmly, that when torn asunder the glass will break... Thus... bodies begin to press against each other whilst still at a measurable distance, and that even when pressed together with great force they are not in absolute contact... Why, then, say the advocates... should we continue to maintain the doctrine, founded only in the rough experience of a pre-scientific age, that matter cannot act where it is not, instead of admitting that all... contact essential to action were in reality cases of action at a distance... too small to be measured..."

"[A]s for those who introduce ætherial, or other media... without any direct evidence... or any clear understanding of how the media work... the less these men talk about their philosophical scruples about admitting action at a distance the better."

"The progress of science in Newton's time consisted in getting rid of the celestial machinery with which generations of astronomers had encumbered the heavens, and thus "sweeping cobwebs off the sky." Though the planets had already got rid of their crystal spheres, they were still swimming in the vortices of Descartes. Magnets were surrounded by effluvia, and electrified bodies by atmospheres, the properties of which resembled in no respect those of ordinary effluvias and atmospheres."

"When Newton demonstrated that the force which acts on each of the heavenly bodies depends on its relative position with respect to the other bodies, the new theory met with violent opposition by the advanced philosophers... who described the doctrine of gravitation as a return to the exploded method of explaining everything by occult causes, attractive virtues, and the like. Newton... answered that he made no pretence of explaining the mechanism... To determine the mode in which their mutual action depends on their relative positions was a great step in science, and this Newton asserted he had made."

"But so far was Newton from asserting that bodies really act... over a distance, independently of anything in between them, that in a letter to Bentley... quoted by Faraday... he says:—"It is inconceivable that inanimate brute matter should, without the mediation of something else, which is not material, operate upon and affect other matter without mutual contact, as it must do if gravitation, in the sense of Epicurus, be essential and inherent in it... That gravity should be innate, inherent, and essential to matter, so that one body can act upon another at a distance, through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe that no man who has in philosophical matters a competent faculty of thinking can ever fall into it.""

"Accordingly, we find in his Optical Queries, and in his letters to Boyle, that Newton had very early made the attempt to account for gravitation by means of the pressure of a medium, and that the reason he did not publish these investigations "proceeded from hence only, that he found he was not able, from experiment and observation, to give a satisfactory account of this medium, and the manner of its operation in producing the chief phenomena of nature.""

"The doctrine of direct action at a distance... was first asserted by , in his preface to the Principia... According to Cotes, it is by experience that we learn that all bodies gravitate. We do not learn in any other way that they are extended, movable, or solid. Gravitation, therefore, has as much right to be considered an essential property of matter..."

"And when the Newtonian philosophy gained ground in Europe, it was the opinion of Cotes rather than that of Newton that became most prevalent, till at last Boscovich propounded his theory, that matter is a congeries of mathematical points, each endowed with the power of attracting or repelling the others according to fixed laws. In his world, matter is unextended, and contact is impossible. He did not forget, however, to endow his mathematical points with inertia."

"[I]t was most essential that Newton's method should be extended to every branch of science to which it was applicable—that we should investigate the forces with which bodies act on each other... before attempting to explain how that force is transmitted. No men could be better fitted to apply themselves to the first part of the problem, than those who considered the second part quite unnecessary."

"Accordingly, Cavendish, Coulomb, and Poisson, the founders of the exact sciences of electricity and magnetism, paid no regard to those old notions of "magnetic effluvia" and "electric atmospheres," which had been put forth in the previous century, but turned their undivided attention to the determination of the law of force, according to which electrified and magnetized bodies attract or repel each other. In this way the true laws of these actions were discovered... by men who never doubted that the action took place at a distance, without the intervention of any medium, and who would have regarded the discovery of such a medium as complicating rather than as explaining the undoubted phenomena of attraction."

"We have now arrived at the great discovery of Örsted of the connection between electricity and magnetism, Örsted found that an electric current acts on a magnetic pole, but that it neither attracts nor repels it, but causes it to move round the current. He expressed this by saying that "the electric conflict acts in a revolving manner." The most obvious deduction from this new fact was that the action of the current on the magnet is not a push-and-pull force, but a rotary force, and accordingly many minds were set a-speculating on vortices and streams of æther whirling round the current."

"But Ampère, by a combination of mathematical skill with experimental ingenuity, first proved that two electric currents act on one another, and then analysed this action as a result of a system of push-and-pull forces between the elementary parts of these currents. The formula of Ampère, however, is of extreme complexity, as compared with Newton's law of gravitation, and many attempts have been made to resolve it into something of greater apparent simplicity."

"Let us turn to the independent method of investigation employed by Faraday in those researches in electricity and magnetism which have made this Institution one of the most venerable shrines of science. No man ever more conscientiously and systematically laboured to improve all his powers of mind than did Faraday from the very beginning of his scientific career. But whereas the general course of scientific method then consisted in the application of the ideas of mathematics and astronomy to each new investigation in turn, Faraday seems to have had no opportunity of acquiring a technical knowledge of mathematics, and his knowledge of astronomy was mainly derived from books. Hence, though he had a profound respect for the great discovery of Newton, he regarded the attraction of gravitation as a sort of sacred mystery, which, as he was not an astronomer, he had no right to gainsay or to doubt, his duty being to believe it in the exact form in which it was delivered to him. Such a dead faith was not likely to lead him to explain new phenomena by means of direct attractions. Besides this, the treatises of Poisson and Ampère are of so technical a form, that to derive any assistance from them the student must have been thoroughly trained in mathematics, and it is very doubtful is such a training can be begun with advantage in mature years."

"Thus Faraday, with his penetrating intellect, his devotion to science, and his opportunities for experiments, was debarred from following the course of thought which had led to the achievements of the French philosophers, and was obliged to explain the phenomena to himself by means of a symbolism which he could understand, instead of adapting what had hitherto been the only tongue of the learned."

"This new symbolism consisted of those lines of force extending themselves in every direction from electrified and magnetic bodies, which Faraday in his mind's eye saw as distinctly as the solid bodies from which they eminated."

"The idea of lines of force and their exhibition by means of iron filings was nothing new. They had been observed repeatedly, and investigated mathematically as an interesting curiosity of science. But let us hear Faraday himself... "It would be a voluntary and unnecessary abandonment of most valuable aid if an experimentalist, who chooses to consider magnetic power as represented by lines of magnetic force, were to deny him the use of magnetic filings. By their employment he may make many conditions of the power, even in complicated cases, visible to the eye at once, may trace the varying direction of the lines of force and determine the relative polarity, may observe in which direction the power is increasing or diminishing, and in complex systems may determine the neutral points, or places where there is neither polarity nor power, even when they exist in the midst of powerful magnets. By their use probable results may be seen at once, and many a valuable suggestion gained for future leading experiments.""

"Experiment on Lines of Force. In this experiment each filing becomes a little magnet. The poles of opposite names belonging to different filings attract each other and stick together, and more filings attach themselves to the exposed poles, that is, to the ends of the row of filings. In this way the filings, instead of forming a confused system of dots over the paper, draw together, filing to filing, till long fibres of filings are formed, which indicate by their direction the lines of force in every part of the field."

"The mathematicians saw in this experiment nothing but a method of exhibiting at one view the direction in different places of the resultant two forces, one directed to each pole of the magnet; a somewhat complicated result of a simple law of force."

"But Faraday, by a series of steps as remarkable for their geometrical definiteness as for their speculative ingenuity, imparted to his conception of these lines of force a clearness and precision far in advance of that with which the mathematicians could then invest their new formulæ."

"Faraday's lines of force are not to be considered merely as individuals, but as forming a system, drawn in space in a definite manner so that the number of lines which pass through an area, say of one square inch, indicates the intensity of the force acting through the area. Thus the lines of force become definite in number. The strength of a magnetic pole is measured by the number of lines which proceed from it; the electro-tonic state of a circuit is measured by the number of lines which pass through it."

"[E]ach individual line has a continuous existence in space and time. When a piece of steel becomes a magnet, or when an electric current begins to flow, the lines of force do not start into existence each in its own place, but as the strength increases new lines are developed within the magnet or current, and gradually grow outwards, so that the whole system expands from within, like in our former experiment."

"Thus every line of force preserves its identity during the whole course of its existence, though its shape and size may be altered to any extent."

"[E]very question relating to the forces acting on magnets or currents, or to the induction of currents in conducting circuits, may be solved by the consideration of Faraday's lines of force. In this place they can never be forgotten. By means of this new symbolism, Faraday defined with mathematical precision the whole theory of electro-magnetism, in language free from mathematical technicalities, and applicable to the most complicated and simplest cases."

"He observed that the motion which the magnetic and electric force tends to produce is invariably such a to shorten the lines of force and allow them to spread out laterally from each other. He thus preserved in the medium a state of stress, consisting of a tension, like that of a rope, in the direction of the lines of force, combined with a pressure in all directions at right angles to them."

"This is quite a new conception of action at a distance, reducing it to a phenomenon of the same kind as that action at a distance which is exerted by means of the tension of ropes and the pressure of rods."

"When the muscles of our bodies are excited... the fibres tend to shorten themselves and at the same time expand laterally. A state of stress is produced in the muscle, and the limb moves. This explanation of muscular action is by no means complete..."

"For similar reasons we may regard Faraday's conception of a state of stress in the electro-magnetic field as a method of explaining action at a distance by means of the continuous transmission of force, even though we do not know how the state of stress is produced."

"[O]ne of Faraday's most pregnant discoveries, that of the magnetic rotation of polarised light, enables us to proceed... Of two circularly polarised rays of light, precisely similar in configuration, but rotating in opposite directions, that ray is propagated with greater velocity which rotates in the same direction as the electricity of the magnetizing current."

"It follows... as Sir W. Thomson has shewn by strict dynamical reasoning, that the medium when under the action of magnetic force must be in a state of rotation... [i.e.,] that small portions of the medium, which we may call molecular vortices, are rotating, each on its own axis, the direction of this axis being that of the magnetic force."

"Here, then, we have an explanation of the tendency of the lines of magnetic force to spread out laterally and to shorten themselves. It arises from the of the molecular vortices."

"We have thus found that there are several different kinds of work to be done by the electro-magnetic medium if it exists. We have also seem that magnetism has an intimate relation to light, and we know that there is a theory of light which supposes it to consist of the vibrations of a medium. How is this luminiferous medium related to our electro-magnetic medium?"

"[E]lectro-magnetic measurements have been made from which we can calculate by dynamical principles the velocity of propagation of small magnetic disturbances in the supposed electro-magnetic medium. This velocity is great, from 288 to 314 millions of metres per second... Now the velocity of light, according to Foucault's experiments, is 298... But if the luminiferous and the electro-magnetic media occupy the same place, and transmit disturbances at the same velocity, what reason have we to distinguish the one from the other? By considering them as the same, we avoid at least the reproach of filling space twice over with different kinds of æther."

"[T]he only kind of electro-magnetic disturbance which can be propagated through a non-conducting medium is a disturbance transverse to the direction of propagation, agreeing... with what we know about that disturbance which we call light."

"[T]he electro-magnetic theory of light will agree in every respect with the undulatory theory, and the work of Thomas Young and Fresnel will be established on a firmer basis than ever, when joined with that of Cavindish and Coulomb by the key-stone of the combined sciences of light and electricity—Faraday's great discovery of the electro-magnetic rotation of light."

"The vast interplanetary and interstellar regions will no longer be regarded as waste places in the universe, which the Creator has seen fit to fill with the symbols of the manifest order of His kingdom. We shall find them to be already full of this wonderful medium; so full, that no human power can remove it from the smallest portion of space, or produce the slightest flaw in its infinite continuity. It extends unbroken from star to star; and when a molecule of hydrogen vibrates in the dog-star, the medium receives the impulses of these vibrations; and after carrying it in its immense bosom for three years, delivers them in due course, regular order, and full tale into the spectroscope of Mr Huggins, at ."

"But the medium has other functions and operations besides bearing light from man to man, and from world to world, and giving evidence of the absolute unity of the metric system of the universe. Its minute parts may have rotatory as well as vibratory motions, and the axis of rotation form those lines of magnetic force which extend in unbroken continuity into regions which no eye has seen, and which, by their action on our magnets, are telling us in language not yet interpreted, what is going on in the hidden underworld from minute to minute and from century to century."

"And these lines must not be regarded as mere mathematical abstractions. They are the directions in which the medium is exerting a tension like that of a rope, or rather, like that of our own muscles. The tension of the medium in the direction of the earth's magnetic force is in this country one grain weight on eight square feet. In some of Dr Joule's experiments, the medium has exerted a tension of 200 lbs. per square inch."

"But the medium, in virtue of the very same elasticity by which it is able to transmit undulations of light, is also able to act as a spring. When properly wound up, it exerts a tension, different from the magnetic tension, by which it draws oppositely electrified bodies together, produces effects through the length of telegraph wires, and when of sufficient intensity, leads to the rupture and explosion called lightning."

"These are some of the already discovered properties of that which has been called vacuum, or nothing at all. They enable us to resolve several kinds of action at a distance into actions between contiguous parts of a continuous substance. Whether this resolution is of the nature of explication or complication, I must leave to the metaphysicians."

"The economic transmission of power without wires is of all-surpassing importance to man. By its means he will gain complete mastery of the air, the sea and the desert. It will enable him to dispense with the necessity of mining, pumping, transporting and burning fuel, and so do away with innumerable causes of sinful waste. By its means, he will obtain at any place and in any desired amount, the energy of remote waterfalls — to drive his machinery, to construct his canals, tunnels and highways, to manufacture the materials of his want, his clothing and food, to heat and light his home — year in, year out, ever and ever, by day and by night. It will make the living glorious sun his obedient, toiling slave. It will bring peace and harmony on earth."

"We know what kind of a dance to do experimentally to measure this number very accurately, but we don't what kind of a dance to do on a computer to make this number come out—without putting it in secretly!"

"... an understanding of the numerical value of the fine structure constant may emerge ... charge might be an emergent property generated by a simple interaction mechanism between point-like particles and the electromagnetic vacuum, similar to the process that generates the Lamb shift."

"The theoretical determination of the fine structure constant is certainly the most important of the unsolved problems of modern physics. To reach it, we shall, presumably, have to pay with further revolutionary changes of the fundamental concepts of physics with a still farther digression from the concepts of the classical theories."

"The title of my talk may seem a bit ambitious, but please note the plural “constants”. To calculate the fine structure constant, 1/137, we would need a realistic model of just about everything, and this we do not have. In this talk I want to return to the old question of what it is that determines gauge couplings in general, and try to prepare the ground for a future realistic calculation."

"The hierarchy problem is somewhat unique. ... It's one of a trifecta of problems in the Standard Model that don't come from incontrovertible evidence ... Those three problems are ... the strong CP problem ... the cosmological constant problem ... and the hierarchy problem. ... These .. are ... problems where it's a conflict between our expectations for the size of parameters in quantum field theory and what we see."

"The hierarchy problem is hard to explain. ... Basically, the problem is that there are two main energy (or mass) scales in nature, but that situation shouldn’t be stable. One is the Planck scale, which is defined via fundamental constants: the speed of light, c; Planck’s quantum size, h; and Newton’s gravitational force strength, G. The associated energy scale is about 1019 GeV. The other is the electroweak scale, which is set by the masses of the Higgs and the W and Z bosons, at about 102 GeV. (Protons and atoms have smaller scales, but we understand how to derive those.) It is a conceptual problem, not a conflict with observations."

"Following 't Hooft, we can formulate a technical definition of naturalness: The smallness of a dimensionless parameter η would be considered natural only if a symmetry emerges in the limit η → 0. Thus, fermion masses could be naturally small, since, as you will recall from chapter II.1, a chiral symmetry emerges when a fermion mass is set equal to zero. On the other hand, no particular symmetry emerges when we set either the bare or renormalized mass of a scalar field equal to zero. This represents the essence of the hierarchy problem."

"The discipline of collider physics involves going from the direct collider observables to the underlying lagrangian of the theory. One of the simplest questions one can ask is how to recognize the presence of new particles. In colliders the answer to this question is simple, one collects groups of particles (pairs, for example) and one plots the invariant mass. If a bump is seen in this distribution, one says that there is a new particle. One can also look at the angular distribution of the particles and read off the spin of the new particle."

"Very high energy collisions occur naturally in cosmic ray interactions; they also occurred in the early moments of our universe according to big-bang cosmology. Both these sources provide useful information but they cannot compare with systematic experimentations in accelerator laboratories when this is possible."

"Stephen Hawking and I wrote an essay about future colliders that is relevant to both the CEPC and the FCC. We were encouraged by others to chime in because of discussions that arose in China about physics and economic and cultural issues surrounding building a future collider. The theoretical arguments for building a larger collider with several times the energy of the LHC are thus very strong, particularly in regard to solving the hierarchy problem. What would happen without data? Someone may get or even already have the solution, but no one will be convinced. With data pointing to the solution, we may be able to move on and obtain consensus about a comprehensive theory that incorporates the standard models of particle physics and cosmology and a quantum theory of general relativity, giving us a profound understanding of our universe."

"There is virtually no chance that we will be able to do experiments involving processes at particle energies like 1016 GeV. With current technology the diameter of an accelerator is proportional to the energy given to the accelerated particles. To accelerate particles to an energy of 1016 GeV would require an accelerator a few light-years across."

"... Suppose we take the example of a point charge sitting near the center of a bar magnet, as shown in Fig. 27–6. Everything is at rest, so the energy is not changing with time. Also, E and B are quite static. But the Poynting vector says that there is a flow of energy, because there is an E×B that is not zero. If you look at the energy flow, you find that it just circulates around and around. There isn’t any change in the energy anywhere—everything which flows into one volume flows out again. It is like incompressible water flowing around. So there is a circulation of energy in this so-called static condition. ... Perhaps it isn’t so terribly puzzling, though, when you remember that what we called a “static” magnet is really a circulating permanent current. In a permanent magnet the electrons are spinning permanently inside."

"Richard Feynman:"

"To a considerable extent, one can understand light's momentum properties without reference to photons. A careful analytic treatment of the electromagnetic field gives the total angular momentum of any light field in terms of a sum of spin and orbital contributions. ... In free space, the Poynting vector, which gives the direction and magnitude of the momentum flow, is simply the vector product of the electric and magnetic field intensities. For helical phase fronts, the Poynting vector has an azimuthal component, as shown in figure 1. That component produces an orbital angular momentum parallel to the beam axis. Because the momentum circulates about the beam axis, such beams are said to contain an optical vortex."

"I have in my "Recent Researches on Electricity and Magnetism" calculated the amount of momentum at any point in the electric field, and have shown that if N is the number of Faraday tubes passing through a unit area drawn at right angles to the direction, B the magnetic induction, θ the angle between the induction and the Faraday tubes, then the momentum per unit volume is equal to N B sin θ, the direction of the momentum being at right angles to the magnetic induction and also to the Faraday tubes. Many of you will notice that the momentum is parallel to what is known as Poynting's vector—the vector whose direction gives the direction in which energy is flowing through the field."

"Baryon-number-violating processes, including proton decay, and the existence of superpartners are dramatic, make-or-break predictions ... Either would open new worlds of phenomena to investigation. According to our best estimates, neither proton decay nor superpartners lie beyond the reach of a heroic search. They should be found, well within 100 years."

"It is commonly believed that grand unified theories (GUTs) predict proton decay. This is because the exchange of extra GUT gauge bosons gives rise to dimension 6 proton decay operators. We show that there exists a class of GUTs in which these operators are absent. Many string and supergravity models in the literature belong to this class."

"I expect that sooner or later we will be seeing another departure from the renormalizable Standard Model in the discovery of proton decay, or some other example of baryon nonconservation."

"Besides non-zero neutrino masses, the other classic experimental implication of unification is proton instability, with a very long but perhaps not inaccessible lifetime. That prediction has not yet been verified, despite heroic efforts. The existing limits put significant pressure on the framework. Reading it optimistically: There is an excellent chance that further efforts along this line would be rewarded."

"Proton decays into a positron and neutral pion, p → e+π0, are a dominant decay mode in many GUT models. It also has a very clean experimental signature in a water Cherenkov detector with full reconstruction of the event. After decades of search, the sensitivity is still improving with advancement of detector technology and analysis technique. One of examples for such a technique is the background suppression with the neutron tagging. In the proton decay events, the probability of neutron emission is rather small, while in the atmospheric neutrino events, which is the dominant background of proton decay searches, often neutrons are produced. Thus, neutron tagging can provide an additional handle to suppress the background for the proton decay search and improve the sensitivity."

"Masashi Yokoyama and Proto-collaboration:"

"Tension weakens the bow; the want of it, the mind."

"The approach of Einstein differs from that of Lorentz in two major ways. There is a difference of philosophy, and a difference of style. The difference of philosophy is this. Since it is experimentally impossible to say which of two uniformly moving systems is really at rest, Einstein declares the notions ‘really resting’ and ‘really moving’ as meaningless. For him only the relative motion of two or more uniformly moving objects is real. Lorentz, on the other hand, preferred the view that there is indeed a state of real rest, defined by the ‘aether’, even though the laws of physics conspire to prevent us identifying it experimentally. The facts of physics do not oblige us to accept one philosophy rather than the other. And we need not accept Lorentz’s philosophy to accept a Lorentzian pedagogy. Its special merit is to drive home the lesson that the laws of physics in any one reference frame account for all physical phenomena, including the observations of moving observers. And it is often simpler to work in a single frame, rather than to hurry after each moving object in turn. The difference of style is that instead of inferring the experience of moving observers from known and conjectured laws of physics, Einstein starts from the hypothesis that the laws will look the same to all observers in uniform motion. This permits a very concise and elegant formulation of the theory, as often happens when one big assumption can be made to cover several less big ones. There is no intention here to make any reservation whatever about the power and precision of Einstein’s approach. But in my opinion there is also something to be said for taking students along the road made by Fitzgerald, Larmor, Lorentz and Poincaré. The longer road sometimes gives more familiarity with the country."

"Well, what is not sufficiently emphasized in textbooks, in my opinion, is that the pre-Einstein position of Lorentz and Poincare, Larmor and Fitzgerald was perfectly coherent, and is not inconsistent with relativity theory. The idea that there is an aether, and these Fitzgerald contractions and Larmor dilations occur, and that as a result the instruments do not detect motion through the aether - that is a perfectly coherent point of view."

"Even though the Lorentz theory is no longer generally accepted today, it is worthwhile to study it in some detail, not only because it helps to provide an appreciation of the historical context out of which the theory of relativity arose, but much more because it helps us to understand the essential content of Einstein’s new approach to the problem. Indeed, a critical examination of the Lorentz theory leads one, on the basis of already familiar and accepted physical notions, to see clearly what is wrong with the Newtonian concepts of space and time, as well as to suggest a great many of the changes needed in order to avoid the difficulties to which these concepts lead. Lorentz began by accepting the assumption of an ether. However, his basic new step was to study the dependence of the process of measurement of space and time on the relationship between the atomic constitution of matter and the movement of matter through the ether."

"An experimental decision between Lorentz's and Einstein's theories was thus not possible; it was seen that between them there could fundamentally be no experimentum cruris. The advocates of the new doctrine accordingly had to appeal—an unusual spectacle in the history of physics—to general philosophical grounds, to the advantages over the assumption of Lorentz which the new doctrine possessed in a systematic and epistemological respect."

"Although the contraction hypothesis successfully accounted for the negative result of the experiment, it was open to the objection that it was invented for the express purpose of explaining away the difficulty, and was too artificial. However, in many other experiments to discover an ether wind, similar difficulties arose, until it appeared that nature was in a “conspiracy” to thwart man by introducing some new phenomenon to undo every phenomenon that he thought would permit a measurement of u. It was ultimately recognized, as Poincaré pointed out, that a complete conspiracy is itself a law of nature! Poincaré then proposed that there is such a law of nature, that it is not possible to discover an ether wind by any experiment; that is, there is no way to determine an absolute velocity."

"Lorentz's new theory not only accounted for the negative results of the Michelson-Morley experiment; it also accounted for any conceivable experiment designed to detect changes in the speed of light as a result of an ether wind. Its equations for variations in length and time were worked out in such a way that every possible method of measuring the speed of light, from any frame of reference, would always give the same result. It is easy to understand why physicists were unhappy with this theory. It was ad hoc in the full sense of the word. It seemed little more than a weird effort to patch up the rents that had developed in the ether theory."

"If the ether as an absolute reference system could be demonstrated, the notion of absolute space could be saved. Indeed, one of the most important experiments to this end, the Michelson-Morley experiment, was in 1904 interpreted by Lorentz in this sense. His interpretation fulfilled all physical requirements. As is well known, according to Lorentz every body moving with reference to the motionless ether or absolute space undergoes a certain contraction in the dimension parallel to the motion. However, the Michelson-Morley experiment served as the starting point for the development of the theory of relativity and was interpreted by Einstein on entirely different lines, adverse to the acceptance of absolute space. It was understood that both interpretations give a complete explanation of all observations known at the beginning of the twentieth century. An experimenturn cruris could not decide between these two theories."

"The same point can be made at least equally effectively in reverse: there is no such thing as research without counterinstances. For what is it that differentiates normal science from science in a crisis state? Not, surely, that the former confronts no counterinstances. On the contrary, what we previously called the puzzles that constitute normal science exist only because no paradigm that provides a basis for scientific research ever completely resolves all its problems. The very few that have ever seemed to do so (e.g., geometric optics) have shortly ceased to yield research problems at all and have instead become tools for engineering. Excepting those that are exclusively instrumental, every problem that normal science sees as a puzzle can be seen, from another viewpoint, as a counterinstance and thus as a source of crisis. Copernicus saw as counterinstances what most of Ptolemy’s other successors had seen as puzzles in the match between observation and theory. Lavoisier saw as a counterinstance what Priestley had seen as a successfully solved puzzle in the articulation of the phlogiston theory. And Einstein saw as counterinstances what Lorentz, Fitzgerald, and others had seen as puzzles in the articulation of Newton’s and Maxwell’s theories. Furthermore, even the existence of crisis does not by itself transform a puzzle into a counterinstance. There is no such sharp dividing line. Instead, by proliferating versions of the paradigm, crisis loosens the rules of normal puzzle-solving in ways that ultimately permit a new paradigm to emerge. There are, I think, only two alternatives: either no scientific theory ever confronts a counterinstance, or all such theories confront counterinstances at all times."

"Though a true experimental decision between the theory of Lorentz and the theory of relativity is indeed not to be gained, and that the former, in spite of this, has receded into the background, is chiefly due to the fact that, close as it comes to the theory of relativity, it still lacks the great simple universal principle, the possession of which lends the theory of relativity an imposing appearance."

"That electron-phonon interactions lead to an effective attractive interaction between electrons by exchange of virtual photons was shown by Fröhlich by use of field-theoretic methods. His analysis was extended by Pines and myself to include Coulomb interactions. In second order, there is an effective interaction between the quasi-particle excitations of the normal state which is the sum of the attractive phonon-induced interaction and a screened Coulomb interaction. In the Handbuch article, I suggested that one should take the complete interaction, not just the self-energy tens, and use it for a theory of superconductivity."

"The phonons are well known as the quanta of lattice vibrations. These lattice vibrations are the most understood from successful theories of condensed matter physics and can be considered as a milestone in the comprehension of the properties of condensed materials. Ranging from the infrared, Raman, neutron and in the recent years, synchrotron spectra to the anharmonic properties as well as the electron phonon interactions and superconductivity, there is little left in which the phonons do not play a vital role. In order to understand the material properties, however, the modelling of microscopic interactions intrinsically involved between electrons and ions, remained an ambitious and affordable tool over decades. One of the remarkable developments in physics of phonons is the concept of Rigid Shell Model (RSM) ... derived from the original crystal lattice theory of Born and Huang ..., which includes the microscopic electron-phonon interactions in several classes of non-metallic solids."

"As the concept of a phonon originates from relative motion of the atoms, rather than the motion of their centre of mass, a phonon in a crystal does not carry a momentum. However, for practical purposes we assign a momentum \hbarq to a phonon in the qth mode. For this reason a phonon is called a quasi-particle."

"The Universe is in fact observed not only through the different windows of the electromagnetic spectrum, but also through other cosmic messengers, i.e. through cosmic rays (CRs), neutrinos and gravitational waves (GWs). In general, gamma rays are the perfect companions for multi-messenger astronomy ... gamma-ray production is intimately related to the production of CRs. The latter are charged particles, mainly protons, whose energy spectrum covers a very wide range in energy and flux. Many questions regarding CRs are still open, especially looking at the most energetic ones above 1015 eV (1 PeV). The CR spectrum is approximately described by a power law: dN/dE ∼ E−Γ , where Γ is the spectral index. Γ is not constant, indicating a change in the properties of CRs, like their acceleration sites and chemical composition. For energies around ∼ 4 × 1015 eV, the flux starts to decrease more steeply: Γ changes from about 2.7 to about 3. This feature, marked with the term knee, is thought to indicate the maximum acceleration energy of Galactic sources ..."

"When I began life as a particle physicist fifty years ago, most of the major discoveries were made in Europe by people studying the cosmic rays that bombard the earth from outer space. Particle physics was done by observing the debris produced by cosmic rays as they pass through the atmosphere and the experimental apparatus. The debris consists of particles with short lifetimes and unfamiliar names. ... Three young Italians, Conversi, Pancini, and Piccioni, working with home-made particle counters in the chaos of postwar Italy, discovered that the common cosmic ray particle, later called the muon, had only weak interactions with matter. Cecil Powell, working with microscopes and photographic plates at Bristol in England, discovered the strongly interacting cosmic ray particle, which he called the pion. Other strange new particles were discovered by Rochester and Butler using old-fashioned cosmic ray cloud-chambers in Manchester."

"Why does the atmosphere have conductivity? Here and there among the air molecules there is an ion—a molecule of oxygen, say, which has acquired an extra electron, or perhaps lost one. These ions do not stay as single molecules; because of their electric field they usually accumulate a few other molecules around them. Each ion then becomes a little lump which, along with other lumps, drifts in the field—moving slowly upward or downward—making the observed current. Where do the ions come from? It was first guessed that the ions were produced by the radioactivity of the earth. (It was known that the radiation from radioactive materials would make air conducting by ionizing the air molecules.) Particles like β-rays coming out of the atomic nuclei are moving so fast that they tear electrons from the atoms, leaving ions behind. This would imply, of course, that if we were to go to higher altitudes, we should find less ionization, because the radioactivity is all in the dirt on the ground—in the traces of radium, uranium, potassium, etc. ... To test this theory, some physicists carried an experiment up in balloons to measure the ionization of the air (Hess, in 1912) and discovered that the opposite was true—the ionization per unit volume increased with altitude! ... This was a most mysterious result—the most dramatic finding in the entire history of atmospheric electricity. It was so dramatic, in fact, that it required a branching off of an entirely new subject—cosmic rays."

"If one begins by considering a kind of state or condition for Bose particles which do not interact with each other (we have assumed that the photons do not interact with each other), and then considers that into this state there can be put either zero, or one, or two, ... up to any number n of particles, one finds that this system behaves for all quantum mechanical purposes exactly like a harmonic oscillator. By such an oscillator we mean a dynamic system like a weight on a spring or a standing wave in a resonant cavity. And that is why it is possible to represent the electromagnetic field by photon particles. From one point of view, we can analyze the electromagnetic field in a box or cavity in terms of a lot of harmonic oscillators, treating each mode of oscillation according to quantum mechanics as a harmonic oscillator. From a different point of view, we can analyze the same physics in terms of identical Bose particles. And the results of both ways of working are always in exact agreement. There is no way to make up your mind whether the electromagnetic field is really to be described as a quantized harmonic oscillator or by giving how many photons there are in each condition. The two views turn out to be mathematically identical. So in the future we can speak either about the number of photons in a particular state in a box or the number of the energy level associated with a particular mode of oscillation of the electromagnetic field. They are two ways of saying the same thing. The same is true of photons in free space. They are equivalent to oscillations of a cavity whose walls have receded to infinity."

"Many of the mechanical elements constituting a musical instrument behave approximately as linear systems. By this we mean that the acoustic output is a linear function of the mechanical input, so that the output obtained from two inputs applied simultaneousl is just the sum of the outputs that would be obtained if they were applied separately. For this statement to be true for the instrument as a whole, it must also be true for all of its parts, so that deflections must be proportional to applied forces, flows to applied pressures, and so on. Mathematically, this property is reflected in the requirement that the differential equations describing the behavior of the system are also linear, in the sense that the dependent variable occurs only to the first power. An example is the equation for the displacement y of a simple harmonic oscillator under the action of an applied force F(t): m \frac{\mathrm{d}^2y}{\mathrm{d}t^2} + R\frac{\mathrm{d}y}{\mathrm{d}t} + Ky = F(t), ... where m, R, and K are, respectively, the mass, damping coefficeint, and spring coefficent, all of which are taken to be constants. ... A little consideration shows, of course, that this description must be an over-simplification ..."

"The simple mechanical system of the classical harmonic oscillator underlies important areas of modern physiccal theory. ... The concept of degeneracy arises in the two-dimensional oscillation of a square plate or diaphragm. Three-dimensional harmonic oscillation relates to oscillatory modes in the Rayleigh-Jeans equation ... Vibration of a macroscopic three-dimensional crystal is treated by Debye's theory ... Harmonic oscillator theory is important when it succeeds and also when if fails, as we shall see in the motivation to find a theory of radiation that we now call the quantum theory ..."

"An electronic semiconductor is typically a valence crystal whose conductivity depends markedly on temperature and on the presence of minute amounts of foreign impurities. The ideal crystal at the absolute zero is an insulator. When the valence bonds are completely occupied and there are no extra electrons in the crystal, there is no possibility for current to flow. Charges can be transferred only when imperfections are present in the electronic structure, and these can be of two types: excess electrons which do not fit into the valence bonds and can move through the crystal, and holes, places from which electrons are missing in the bonds, which also behave as mobile carriers. While the excess electrons have the normal negative electronic charge -e, holes have a positive charge, +e. It is a case of two negatives making a positive ; a missing negative charge is a positive defect in the electron structure. The bulk of a semiconductor is electrically neutral; there are as many positive charges as negative. In an intrinsic semiconductor, in which current carriers are created by thermal excitation, there are approximately equal numbers of excess electrons and holes. Conductivity in an extrinsic semiconductor results from impurity ions in the lattice. In n-type material, the negative charge of the excess electrons is balanced by a net positive space charge of impurity ions. In p-type, the positive charge of the holes is balanced by negatively charged impurities. Foreign atoms which can become positively charged on introduction to the lattice are called donors; atoms which become negatively ionized are called acceptors. Thus donors make a semiconductor n-type, acceptors p-type. When both donors and acceptors are present, the conductivity type depends on which is in excess. Mobile carriers then balance the net space charge of the impurity ions."

"One of the remarkable and dramatic developments in recent years has been the application of solid state science to technical developments in electrical devices such as transistors. The study of semiconductors led to the discovery of their useful properties and to a large number of practical applications. ... The semiconductor substances in most common use today are silicon and germanium. These elements crystallize in the diamond lattice, a kind of cubic structure in which the atoms have tetrahedral bonding with their four nearest neighbors. They are insulators at very low temperatures—near absolute zero—although they do conduct electricity somewhat at room temperature. ... somehow put an extra electron into a crystal of silicon or germanium which is at a low temperature ... The electron will be able to wander around in the crystal jumping from one atomic site to the next. Actually, we have looked only at the behavior of electrons in a rectangular lattice, and the equations would be somewhat different for the real lattice of silicon or germanium. All of the essential points are, however, illustrated by the results for the rectangular lattice."

"A consequence of the discovery of electricity was the observation that metals are good conductors while nonmetals are poor conductors. The latter were called insulators. Metallic onductivity is typically between 106 and 104 (Ω cm)–1, while typical insulators have conductivities of less than 10–10 (Ω cm)–1. Some solids with conductivities between 104 and 10–10 (Ω cm)–1 are classified as semiconductors. ... semiconductors have an energy gap while semimetals and metals have no such gap. However, very impure semiconductors show a more or less metallic behavior and with many substances, the art of purification is not so far advanced that a distinction can easily be made. The transition between semiconductors and insulators is even more gradual and depends on the ratio of the energy gap to the temperature of investigation. Very pure semiconductors may become insulators when the temperature approaches the absolute zero."

"[T]he Diffusion of Heat ...invariably transfers heat from a hotter body to a colder one, so as to cool the hotter body and warm the colder... This process would go on till all bodies were brought to the same temperature if it were not for certain other processes..."

"One of the best established facts in thermodynamics is that it is impossible in a system enclosed in an envelope which permits neither change of volume nor passage of heat, and in which both the temperature and the pressure are every where the same, to produce any inequality of temperature or of pressure without the expenditure of work. This is the second law of thermodynamics, and it is undoubtedly true as long as we can deal with bodies only in mass, and have no power of perceiving or handling the separate molecules of which they are made up."

"But if we conceive of a being whose faculties are so sharpened that he can follow every molecule in its course, such a being, whose attributes are as essentially finite as our own, would be able to do what is impossible to us. For we have seen that molecules in a vessel full of air at uniform temperature are moving with velocities by no means uniform, though the mean velocity of any great number of them, arbitrarily selected, is almost exactly uniform."

"Now let us suppose that such a vessel is divided into two portions, A and B, by a division in which there is a small hole, and that a being, who can see the individual molecules, opens and closes this hole, so as to allow only the swifter molecules to pass from A to B, and only the slower molecules to pass from B to A. He will thus, without expenditure of work, raise the temperature of B and lower that of A, in contradiction to the second law of thermodynamics."

"[[Information theory|[I]nformation.]].. does enter into physics and has been in physics for a long time, in the most obvious way with ... [which] is able to use information about the motions of molecules to operate a shutter mechanism and put all the fast-moving ones on the left and the slow-moving ones on the right, thus establishing a temperature difference from which work can be extracted. You can run a heat engine, lift a weight [etc.]"

"It was... just a Gedanken-Experiment... in 1867, but just in recent years, engineers (nanotechnologists) have built real Maxwell demons, and this is now something of a cottage industry."

"[T]he demon... is transferring heat from a colder region to a warmer region in apparent defiance of the second law of thermodynamics. "And hold on," you're thinking, "doesn't my refrigerator do that?" Sure... a refrigerator... costs energy to run... but the demon is operating using information instead... The demon... runs without any energy expenditure."

"So in effect, information serves as a fuel, and this leads to the whole concept of information engines. Engines that will run on information power, and... there is an FQXi initiative on this..."

"Life was onto this... billions of years ago. Life uses many many nano-molecules which are, in effect, Maxwell demons. Our bodies are full of little Maxwell demons... doing the business of life. These little molecular machines are not quite perfect... but they're coming pretty close to the theoretical limit, in terms of energy expenditure."

"s are the way in which, even now, you are thinking and paying attention, because the signals that travel between neurons, down the s, are controlled by the flow of s across the membranes of the axons... [T]hey are, in effect, little demons that sense the incoming signal and open and close the gates; and the ions flow. ...[T]his is so incredibly energy efficient that ...your brain, which is like a megawatt supercomputer, operates with the energy equivalent of a small light bulb."

"[I]n order to investigate this... [I]f you have a Maxwell demon or something like a Szilard engine in , could you use it, as Maxwell envisaged, to use information to extract energy from De Sitter space and lift a weight or do some sort of useful work? ...[T]he answer would seem to be, only if you can create a region of the De Sitter space that is screened out from that horizon, screened out from that thermal nature. If you put a reflective barrier around the demon, you then have De Sitter space, but with the horizon screened out. ...[T]hat's a problem I'm working on now ..."

"Paul Davies"

"Information"

"Information theory"

"James Clerk Maxwell"

"Theory of Heat"

"Thermodynamics"

"The electrical conductivity of biological tissues can be measured through their sonication in a magnetic field: the vibration of the tissues inside the field induces an electrical current by Lorentz force. This current, detected by electrodes placed around the sample, is proportional to the ultrasonic pressure, to the strength of the magnetic field and to the electrical conductivity gradient along the acoustic axis. By focusing at different places inside the sample, a map of the electrical conductivity gradient can be established."

"The interior of a neutron star is likely to be predominantly a mixture of superfluid neutrons and superconducting protons. This results in the quantization of the star’s magnetic field into an array of thin flux tubes, producing a macroscopic force very different from the Lorentz force of normal matter."

"... the Lorentz force law does double service (1) as definer of fields and (2) as predicter of motions. Here and elsewhere in science, as stressed not least by Henri Poincaré, that view is out of date which used to say, "Define your terms before you proceed." All the laws and theories of physics, including the Lorentz force law, have this deep and subtle character, that they both define the concepts they use (here B and E ) and make statements about these concepts. Contrariwise, the absence of some body of theory, law, and principle deprives one of the means properly to define or even to use concepts. Any forward step in human knowledge is truly creative in this sense: that theory, concept, law, and method of measurement—forever inseparable—are born into the world in union."

"The ions of solutions exposed to the propagation of ultrasound in the presence of a magnetic field experience Lorentz force. Their movement gives rise to a local electric current density, which is proportional to the electric conductivity of the medium. In vitro assessment of this current is performed using simple models of biological media."

"Needle-free drug delivery by jet injection is achieved by ejecting a liquid drug through a narrow orifice at high pressure, thereby creating a fine high-speed fluid jet that can readily penetrate skin and tissue. Until very recently, all jet injectors utilized force- and pressure-generating principles that progress injection in an uncontrolled manner with limited ability to regulate delivery volume and injection depth. In order to address these shortcomings, we have developed a controllable jet injection device, based on a custom high-stroke linear Lorentz-force motor that is feed-back controlled during the time-course of an injection."

"δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω."

"One needs occasionally to stand aside from the hum and rush of human interests and passions to hear the voices of God. And it not unfrequently happens that the All-loving gives a great push to certain souls to thrust them out, as it were, from the distracting current for awhile to promote their discipline and growth, or to enrich them by communion and reflection. And similarly it may be woman's privilege from her peculiar coigne of vantage as a quiet observer, to whisper just the needed suggestion or the almost forgotten truth. The colored woman, then, should not be ignored because her bark is resting in the silent waters of the sheltered cove. She is watching the movements of the contestants none the less and is all the better qualified, perhaps, to weigh and judge and advise because not herself in the excitement of the race."

"Make Christianity your own, and it will show you a point outside the world, and by means of this you will move heaven and earth."

"Soweit es sich hier um „Paria"-Intellektualismus handelt, ... beruht dessen Intensität darauf, daß die außerhalb oder am unteren Ende der sozialen Hierarchie stehenden Schichten gewissermaßen auf dem archimedischen Punkt gegenüber den gesellschaftlichen Konventionen, sowohl was die äußere Ordnung wie was die üblichen Meinungen angeht, stehen. Sie sind daher einer durch jene Konvention nicht gebundenen originären Stellungnahme zum „Sinn" des Kosmos und eines starken, durch materielle Rücksicht nicht gehemmten, ethischen und religiösen Pathos fähig."

"Wavelets are everywhere nowadays. Whether in signal or image processing, in astronomy, in fluid dynamics (turbulence), or in condensed matter physics, wavelets have found applications in almost every corner of physics. Furthermore, wavelet methods have become standard fare in applied mathematics, numerical analysis, and approximation theory."

"On the one hand, the concept of wavelets can be viewed as a synthesis of ideas which originated during the last twenty or thirty years in engineering (subbing coding), physics (coherent states, renormalization group), and pure mathematics (study of Calderón-Zygmund operators). As a conseuqence of these interdiscplinary origins, wavelets appeal to scientists and engineers of many different backgrounds. On the other hand, wavelets are a fairly simple mathematical tool with a great variety of possible applications."

"Wavelets were developed independently by mathematicians, quantum physicists, electrical engineers and geologists, but collaborations among these fields during the last decade have led to new and varied applications. What are wavelets, and why might they be useful to you? The fundamental idea behind wavelets is to analyze according to scale. Indeed, some researchers feel that using wavelets means adopting a whole new mind-set or perspective in processing data. Wavelets are functions that satisfy certain mathematical requirements and are used in representing data or other functions."

"Wavelet theory is nowadays a very active field of approximation theory with a wide impact on signal analysis, high-performance imaging applications, and adaptive transversal filter theory. It is concerned with the modeling of univariate and multivariate signals with a set of specific signals. The specific signals are just the wavelets. Families of wavelets are used to approximate a given signal (with respect to the L2 norm, say), and each element in the wavelet set is constructed from the same original window, the mother wavelet."

"Wavelets were introduced at the beginning of the 'eighties by J. Morlet, a French geophysicist at Elf-Aquitaine, as a tool for signal analysis in view of applications for the analysis of seismic data. The numerical success of Morlet prompted A. Grossmann to make a more detailed study of the wavelet transform, which resulted in a paper giving the mathematical foundations (see Grossmann & Morlet ..., where the title of the paper still shows the name wavelets of constant shape. In 1985, the harmonic analyst Y. Meyer became aware of this theory and he recognised many classical results inside it. Meyer pointed out to Grossmann and Morlet that there was a connection between their signal analysis methods and existing, powerful techniques in the mathematical study of singular integral operators. Then Ingrid Daubechies became involved, and all this resulted in the first construction of a special type of frames (see Daubechies, Grossmann & Meyer ..), (the concept frame generalizes the concept basis in a Hilbert space). It was also the start of a cross-fertilization between the signal analysis applications and the purely mathematical aspects of techniques based on dilations and translations."

"A Haar wavelet is the simplest type of wavelet. In discrete form, Haar wavelets are related to a mathematical operation called the Haar transform. The Haar transform serves as a prototype for all other wavelet transforms."

"In my own field of many-body physics, we are, perhaps, closer to our fundamental, intensive underpinnings than in any other science in which non-trivial complexities occur, and as a result we have begun to formulate a general theory of just how this shift from quantitative to qualitative differentation takes place. This formulation called the theory of "broken symmetry," may be of help in making more generally clear the breakdown of the constructive converse of reductionism."

"Explicit symmetry breaking occurs when a dynamical system having a certain symmetry group is perturbed to a system which has strictly less symmetry. We give a geometric approach to study this phenomenon in the setting of Hamiltonian systems. We provide a method for determining the equilibria and relative equilibria that persist after a symmetry breaking perturbation. In particular a lower bound for the number of each is found, in terms of the equivariant Lyusternik–Schnirelmann category of the group orbit."

"... the phenomena of spontaneous symmetry breaking in the radical sense of non-symmetric behaviour is rather related to the fact that, for non-linear infinitely extended systems (therefore involving infinite degrees of freedom), the solutions of the dynamical problem generically fall into classes of "islands" or "phases", stable under time evolution and characterized by the same behaviour at infinity of the corresponding solutions. Since all physically realizable operations have an inevitable localization in space they cannot change such a behaviour at infinity and therefore starting from the configurations of a given islands one cannot reach the configurations of a different island by physically realizable modifications. The different islands can then be interpreted as describing physically disjoint realizations or different phases, or disjoint physical worlds associated with the given dynamics."

"... Broken symmetries in physics go back to work in the 1950s on superconductivity. From the modern perspective (or at least, a modern perspective) a superconductor is nothing but a place where electromagnetic gauge invariance is spontaneously broken to a discrete subgroup, and from this assumption one can derive all the exact properties of superconductors, such as the Meissner effect, persistent currents, flux quantization, and the formula for the Josephson frequency."

"... a solid differs from a liquid because its crystal structure breaks the translational and rotational symmetries of space. Moreover, solids with different crystal structures should be viewed as different phases of matter because they break these symmetries in different ways. Perhaps more surprisingly, liquids and gases break no such symmetries and so should be viewed as the same phase. When you include further symmetries, such as rotations of spins in a magnet or more subtle quantum counterparts, this classification opens up a wide range of possibilities that allows us to understand almost all the known forms of matter... First, we can be sure that any attempt to change a material from one symmetry class to another will necessarily involve a violent phase transition. Second, it turns out that understanding the symmetries of a system will immediately determine many of its properties, especially at low temperature."

"The Einstein–Podolsky–Rosen (EPR) argument has been enormously influential in the debate on the foundations of quantum mechanics. While EPR argue for the incompleteness of quantum mechanics, Bell's 'no-go' theorem, which is in a sense an extension of the EPR argument, appears to support the opposite conclusion."

"The Kochen–Specker theorem has been discussed intensely ever since its original proof in 1967. It is one of the central no-go theorems of quantum theory, showing the non-existence of a certain kind of hidden states models."

"One possibility that comes to mind is that the spin-two graviton might arise as a composite of two spin-one gauge bosons. This interesting idea would seem to be rigorously excluded by a no-go theorem of Weinberg & Witten ... The Weinberg–Witten theorem appears to assume nothing more than the existence of a Lorentz-covariant energy momentum tensor, which indeed holds in gauge theory. The theorem does forbid a wide range of possibilities, but (as with several other beautiful and powerful no-go theorems) it has at least one hidden assumption that seems so trivial as to escape notice, but which later developments show to be unnecessary. The crucial assumption here is that the graviton moves in the same spacetime as the gauge bosons of which it is made!"

"The question of the possibility for a completion of quantum mechanics received its most famous (partial) answer in 1964 by, again, Bell ... He proved what today is known simply as Bell's theorem, to wit, that is such a more complete description exists, it cannot be local, i.e. dependent only on the events in a system's past lightcone, and agree with quantum mechanics in all instances. To this day, this result forms the paradigm example of a 'no-go' theorem."

"... If you start off with switches and gears, or whatever, you can never construct a universe in which you see quantum mechanical phenomena, according to Bell. We call such a thing a 'no-go theorem'. You may already suspect that I still believe in the hidden variables hypothesis. Surely our world must be constructed in such an ingenious way that some of the assumptions that Einstein, Bell and others found quite natural will turn out to be wrong. But how this will come about, I do not know. Anyway, for me, the hidden variables hypothesis is still the best way to ease my conscience about quantum mechanics. And as for 'no-go theorems', we will encounter several of these and discuss their fate."

"Two developments in the late 1960s and early 1970s set the stage for supergravity. First the standard model took shape and was decisively confirmed by experiments. The key theoretical concept underlying this process was gauge symmetry, the idea that symmetry transformations act independently at each point of spacetime. ... The other development was global (also called rigid) supersymmetry ... It is the unique framework that allows fields and particles of different spin to be unified in representations of an algebra system called a superalgebra."

"Supergravity is a theory of gravity which has supersymmetry, a symmetry between bosons and fermions. Supersymmetry in supergravity is a local symmetry like the gauge symmetry in the standard theory of particle physics. The gauge field of the local supersymmetry is the Rarita-Schwinger field, which represents a particle with spin called a graviton. Supersymmetry also has a local symmetry under the general coordinate transformation, whose gauge field is the gravitational field. An important role of supergravity is in its relation to superstring theory. ... Supergravity provides a low energy effective theory of the massless sector of superstring theory and can be used to study its low energy properties."

"Inflation can be caused by the potential energy of a scalar field. Such a potential must be relatively flat in order to guarantee long duration of inflation and small deviation of scale invariance of primordial density fluctuations. However, the flatness of the scalar potential can be easily destroyed by radiative corrections. One of the leading theories to protect a scalar field from radiative corrections is supersymmetry (SUSY), which also gives an attractive solution to the (similar) hierarchy problem of the standard model (SM) of particle physics as well as the unification of the three gauge couplings. In particular, its local version, supergravity, would govern the dynamics of the early Universe, when high energy physics was important. Thus, it is quite natural to consider inflation in the framework of supergravity. However, in fact, it is a non-trivial task to incorporate inflation in supergravity. This is mainly because a SUSY breaking potential term, which is indispensable to inflation, generally gives a would-be inflaton an additional mass, which spoils the flatness of an inflation potential ..."

"In this paper it is shown that a star must experience dynamical friction, i.e., it must suffer from a systematic tendency to be decelerated in the direction of its motion. This dynamical friction which stars experience is one of the direct consequences of the fluctuating force acting on a star due to the varying complexion of the near neighbors. From considerations of a very general nature it is concluded that the coefficient of dynamical friction, \eta, must be of the order of the reciprocal of the time of relaxation of the system. Further, an independent discussion based on the two-body approximation for stellar encounters leads to the following explicit formula for the coefficient of dynamical friction: \eta = 4\pi m_1 (m_1 + m_2)G^2/v^3 log_e [D_0\overline {|u|^2}/G(m_1+m_2)] \int_{0}^{v} N(v_1) \,dv_1, where m_l and m_2 denote the masses of the field star and the star under consideration, respectively; G, the constant of gravitation; D_0 the average distance between the stars; \overline {|u|^2}, the mean square velocity of the stars; N(v_1) dv_1, the number of field stars with velocities between v_1 and v_1 + dv_1; and, finally, v, the velocity of the star under consideration. It is shown that the foregoing formula for η is in agreement with the conclusions reached on the basis of the general considerations. Finally, some remarks are made concerning the further development of these ideas on the basis of a proper statistical theory."

"We investigate dynamical friction on a test object (such as a bar or satellite) which rotates or revolves through a spherical stellar system. We find that frictional effects arise entirely from near-resonant stars and we derive an analog to Chandrasekhar's dynamical friction formula which applies to spherical systems. We show that a formula of this type is valid so long as the angular speed of the test object changes sufficiently rapidly. If the angular speed is slowly changing two new effects appear: a reversible dynamical feedback which can stabilize or destabilize the rotation speed, and permanent capture of near-resonant stars into librating orbits. We discuss orbital decay of satellites in the light of these results."

"A test particle traveling through a collisionless gravitating background suffers a dissipative drag force known as dynamical friction. As with other dissipative forces, this friction must be related to fluctuations in the underlying medium (fluctuation-dissipation theorem). However, this long recognized aspect of the force did not easily yield to analysis until now, and Chandrasekhar’s celebrated formula was obtained by considering momentum exchanges resulting from encounters between a test particle and field particles which were ideal- ized as occurring sequentially. In this paper we return to the underlying basic physics and develop a theory of the interaction of the test particle with the stochastic force of the background. This enables us to derive in a unified way the Chandrasekhar formula for the friction (for the full range of m/M) and the heating of the particle by background fluctuations."

"... It was impossible, on first witnessing an appearance so similar to a sudden conflagration, not to expect a considerable result in the way of alteration of the details of the group in which it occurred; and I was certainly surprised, on referring to the sketch which I had carefully and satisfactorliy (and I may add fortunately) finished before the ocurrence, at finding myself unable to recognise any change whatever as having taken place. The impression left upon me is, that the phenomenon took place at an elevation considerably above and over the great group in which it was seen projected."

"Without warning, two beads of searing white light, bright as forked lightning but rounded rather than jagged and persistent instead of fleeting, appeared over the monstrous sunspot group. Momentarily taken by surprise, Carrington assumed that a ray of sunlight had found its way through the shadow-screen attached to the telescope. He reached out and jiggled the instrument, expecting the errant ray to zip wildly across the image. Instead, it stayed doggedly fixed in its position on the sunspot group. Whatever it was, it was not some stray reflection; it was coming from the Sun itself. As he stared, dumfounded, the two spots of light intensified and became kidney shaped."

"... In the case of the Carrington event of 1859, the most severe coronal mass ejection known to have occurred, the propagation time between the Sun and the Earth, at a speed of 2,300 kilometres per second, was seventeen and a half hours. The way to avert the most serious impacts would be to make adjustments to the operation of the electricity grids before the storm struck (see Space Studies Board 2008, Chapter 7). The necessary actions would have to be taken very quickly and in a coordinated way in order to be effective, so they would have to be carefully planned in advance, preferably in an international context."

"Hari Seldon devised psychohistory by modeling it upon the kinetic theory of gases. Each atom or molecule in a gas moves randomly so that we can't know the position or velocity of any one of them. Nevertheless, using statistics, we can work out the rules governing their overall behavior with great precision. In the same way, Seldon intended to work out the overall behavior of human societies even though the solutions would not apply to the behavior of the individual human beings."

"In this book I have tried... to make clearly comprehensible the path-breaking works of Clausius and Maxwell. The reader may not think badly of me for finding also a place for my own contributions. These were cited respectfully in Kirchhoff's lectures [on Maxwell's kinetic theory] and in Poincare’s Thermodynamique at the end, but were not utilized where they would have been relevant. From this I concluded that a brief presentation, as easily understood as possible, of some of the principal results of my efforts might not be superfluous. Of great influence on the content and presentation was what I have learned at the unforgettable meeting of the British Association in Oxford and the subsequent letters of numerous English scientists, some private and some published in Nature. I intend to follow Part I by a second part, where I will treat the van der Waals theory, gases with polyatomic molecules, and dissociation. ...Unfortunately it was often impossible to avoid the use of long formulas to express complicated trains of thought, and... to many who do not read over the whole work, the results will perhaps not seem to justify the effort expended. Aside from many results of pure mathematics which, though likewise apparently fruitless at first, later become useful in practical science as soon as our mental horizon has been broadened, even the complicated formulas of Maxwell’s theory of electromagnetism were often considered useless before Hertz’s experiments. I hope this will not also be the general opinion concerning gas theory!"

"Boltzmann decided to publish his lectures, in which the most important parts of the theory, including his ...contributions, were carefully explained. ...[H]e included his mature reflections and speculations on such questions as the nature of irreversibility and the justification for using statistical methods in physics. His Vorlesungen über Gastheorie was... the standard reference... for advanced researchers, ...[and] a popular textbook ...for the first quarter of the [20th] century ...The reason why the classical theory works is that, while the internal structure of molecules must be described by quantum mechanics, the interaction between two molecules can be fairly well described by a classical model which ignores this structure and simply uses a postulated force law whose parameters can be chosen to fit experimental data. ...Aside from phenomena at very high densities or very low temperatures, the only property that the classical theory fails to account for is the ratio of specific heats. ...Boltzmann ...simply concludes that for some unknown reason all the possible internal motions of a molecule do not have an equal share in the total energy, and takes this into account as an empirical fact."

"Boyle... proposed a theoretical explanation for the elasticity of air... "a heap of little bodies, lying upon one another"... The atoms are said to behave like springs... Boyle also tried the "crucial experiment" which was to help overthrow his own theory in favor of the kinetic theory two centuries later, though he did not realize its significance... Experiment No. 26... places a pendulum in the evacuated chamber... [A]bsence of air makes hardly any difference to the period of the swings or the time... to come to rest. In 1859, James Clerk Maxwell deduced from the kinetic theory that the viscosity of a gas should be independent of its density... which would be very hard to explain on the basis of Boyle's theory. ...Neither Boyle nor Newton claimed that the hypothesis of repulsive forces between atoms is the only correct explanation for gas pressure; both were willing to leave the question open. Boyle mentions the Descartes theory of vortices (1644)... somewhat closer in spirit to the kinetic theory since it relies more heavily on the rapid motion of the parts of the atom as a cause of repulsion. (Though Descartes did not believe in "atoms" in the classical sense.) Nevertheless, the Boyle-Newton theory of gases was apparently accepted by most scientists until about the middle of the 19th century, when the kinetic theory finally managed to overcome Newton's authority."

"It is difficult to understand the relative lack of progress in gas theory during the 18th century ...[T]here was little interest in the properties of freely moving atoms. The atoms in gas were... conceived as... suspended in the ether, although they could vibrate or rotate enough to keep other atoms from coming too close. This model was... awkward... mathematically, as... seen from an... attempt by Leonhard Euler in 1727. ...[O]ne contribution from this period has been... recognized as the first kinetic theory of gases. This is Daniel Bernoulli's derivation of the gas laws from a "billiard ball" model—in 1738... [H]is kinetic theory is... a small part of a treatise [Hydrodynamica (1738)] on hydrodynamics... Bernoulli's formulation and... applications of the principle of conservation of mechanical energy (...' ..."living force" ...) were ...more important than the fact that he proposed a kinetic theory ...a century ahead of its time ...Heat was still regarded as a substance ...Bernoulli's assumption that heat was nothing but atomic motion was unacceptable, especially to scientists interested in... radiant heat. The assumption that atoms could move freely through space until they collided like billiard balls... neglected the drag of the ether and oversimplified the interaction between atoms. ...When physics reached the stage of development at which the kinetic theory no longer conflicted with established principles, ...[it] had almost been forgotten and had to be rediscovered. ...In a very real sense, the man who persuades the world to adopt a new idea has accomplished as much as the man who conceived that idea."

"The influence of Quetelet's ideas spread throughout the sciences, even to the physical sciences. The two primary founders of the modern kinetic theory of gases, based on considerations of probability, were James Clerk Maxwell and Ludwig Boltzmann. Both acknowledged their debt to Quetelet. ...[H]istorians generally consider the influence of the natural sciences on the social sciences, whereas in the case of Maxwell and Boltzmann, there is an influence of the social sciences on the natural sciences, as Theodore Porter has shown."

"It will be shown in this paper that, according to the molecular-kinetic theory of heat, bodies of microscopically visible size suspended in liquids must, as a result of thermal molecular motions, perform motions of such magnitude that these motions can easily be detected by a microscope. It is possible that the motions to be discussed here are identical with the so-called "Brownian molecular motion"; however, the data available to me on the latter are so imprecise that I could not form a definite opinion on this matter. If it is really possible to observe the motion to be discussed here, along with the laws it is expected to obey, then classical thermodynamics can no longer be viewed as strictly valid even for microscopically distinguishable spaces, and an exact determination of the real size of atoms becomes possible. Conversely, if the prediction of this motion were to be proved wrong, this fact would provide a weighty argument against the molecular-kinetic conception of heat."

"In 1909 Perrin suspended particles of in a liquid of slightly lower density, and found that the heavy particles did not sink to the bottom of the lighter liquid; they were prevented from doing so by their own Brownian movements. If the liquid had been infinitely fine-grained, with molecules of infinitesimal size and weight, every solid particle would have had as many impacts from above as below; these impacts, coming in a continuous stream, would have just cancelled one another out, so that each particle would have been free to fall to the bottom under its own weight. But when they were bombarded by molecules of finite size and weight, the solid particles were hit, now in one direction and now in another, and so could not lie inertly on the bottom of the vessel. From the extent to which they failed to do this, Perrin was able to form an estimate of the weights of the molecules of the liquid... and this agreed so well with other estimates that there could be but little doubt felt as to the truth either of the kinetic theory of liquids, or of the associated explanation of the Brownian movements."

"Now, although the plans of the edifice of the electromagnetic theory of light were laid in 1880 by H. A. Lorentz, and even indicated much earlier by W. Weber, a full 10 years were required before the discoveries of Heinrich Hertz gave the impetus to collect the building stones and work them into shape. In the years 1890-93 a number of works appeared by F. Richarz, H. Ebert and G. Johnstone Stoney, mostly dealing with the mechanism of the emission of luminous vapours, and in which attempts are made, on the basis of the kinetic theory of gases, to determine the magnitude of the elementary electrical quantity, called by Stoney by the now universally accepted name of electron. ...H. Ebert proved that the amplitude of an electron in luminous sodium vapour need only be a small fraction of a molecular diameter in order to excite a radiation of the absolute intensity determined by E. Wiedemann. The way of determining the amount of electricity contained in the electron is very simple. The quantity of electricity required for the electrolytic evolution of 1 cubic cm. of any monatomic gas is divided by Loschmidt's number—i.e., the number of gas molecules contained in 1 cubic cm."

"One of the most important and interesting aims of is to explain the properties of matter in terms of the motions and spatial arrangements of atoms and molecules. This aim has been more nearly achieved in the physical chemical study of gases at low pressures [below a few atmospheres at ordinary temperatures] than the study of matter in any other conditions. ... The structure of gases at these pressures is particularly simple: such gases are collections of molecules which move randomly in space and which collide with each other relatively infrequently—that is, the molecules are so far apart that much of the time they exert little influence on each other. ...[T]he properties of the gaseous state play a role in many important practical processes, such as [in]... the internal combustion engine, the function of the lungs, the motions of the winds across the earth and the flight of airplanes. Gases... provide a useful and pedagogically attractive starting point for the introduction of students to physical chemistry."

"The kinetic theory of gases is a small branch of physics which has passed from the stage of excitement and novelty into staid maturity. ...Formerly it was hoped that the subject of gases would ultimately merge into a general kinetic theory of matter; but the theory of condensed phases... today, involves an elaborate and technical use of wave mechanics, and for this reason it is best treated as a subject in itself. The scope of the present book is, therefore, the traditional kinetic theory of gases. ...[A]n account has been included of the wave-mechanical theory, and especially of the degenerate Fermi-Dirac case... There is also a concise chapter on , which... may be of use as an introduction... [T]he discussion of electrical phenomena has been abbreviated... the latter voluminous subject is best treated separately. ...[F]undamental parts have been explained... [as] to be within the reach of college juniors and seniors. The... wave mechanics and statistical mechanics... are of graduate grade. ...[A] number of carefully worded theorems have been inserted in the guise of problems, without proof... to give... a chance to apply... lines of attack exemplified in the text. To facilitate use as a reference book, definitions have been repeated freely, I hope not ad nauseam. ...Ideas have been drawn freely from ...books such as ...of Jeans and Loeb..."

"The last thirty years have seen the beginning and development of a new period in physics and chemistry, namely the atomic period. In contrast to the period preceding it where nature's processes were described in terms of continua, recent developments have emphasized the discrete structure of the submicroscopic universe. Thus, today one hears of the atoms of matter, the atoms of electricity, and even the atoms of energy, the quanta. ...[T]he atomic theory of matter is the oldest and perhaps the most complete. ...[B]ecause of its relative simplicity the problem of the atomic theory of gases, in the form of the kinetic theory of gases, has attained the highest degree of perfection in this field. Its admirable methods of analysis are therefore indispensable... This book... endeavors to develop the various concepts... independently...Besides a simple introduction of each concept it gives derivations... elementary ones, using little or no calculus; more advanced classical derivations; and in some cases the most recent developments available. It also contains the comparison of the theoretical deductions with modern experiment and a critique of the theories."

"The science of Thermodynamics, founded by the labors of these three illustrious men [Nicolas Léonard Sadi Carnot, William Thomson & Rudolf Clausius], has led to the most important developments in all departments of physical science. It has pointed out relations among the properties of bodies which could scarcely have been anticipated in any other way; it has laid the foundation for the Science of Chemical Physics; and, taken in connection with the , as developed by Maxwell and Boltzmann, it has furnished a general view of the operations of the universe which is far in advance of any that could have been reached by purely dynamical reasoning."

"The first edition of this book appeared in 1877, at the time of the most rapid and beautiful development of the kinetic theory of gases. About twenty years before, the founders... Kronig and Clausius, had explained the expansive tendency of gases, and had calculated their pressure on the assumption that the smallest particles of gases do not repel each other, but are in rapid motion. From the theory based on this supposition not only were the laws of gases... deduced... but also new laws, hitherto undreamt of, were discovered... [and] afterwards confirmed... by experiment. These results, which we owe to Maxwell and Clausius, quickly won to the theory many friends and adherents. ...I undertook ...to exhibit the ...theory ...such ...as to be more easily intelligible ...especially to chemists and other natural philosophers to whom mathematics are not congenial. ...I endeavoured ...not only to develop the theory by calculation, but ...to support it by observation and found it on experiment. I... collected... and summarised, the observations by which the admissibility of the theory might be tested and its correctness proved. ...The mathematical discussions form ...an Appendix which ...need not be studied by every reader ..."

"The researches of Galileo, followed up by Huygens and others, led to those modern conceptions of Force and Law, which have revolutionized the intellectual world. The great attention given to mechanics in the seventeenth century soon so emphasized these conceptions as to give rise to the Mechanical Philosophy, a doctrine that all the phenomena of the physical universe are to be explained upon mechanical principles. Newton's great discovery imparted a new impetus to this tendency. The old notion that heat consists in an agitation of corpuscles was now applied as an explanation to the chief properties of gases. The first suggestion in this direction was that the pressure of gases is explained by the battering of the particles against the walls of the containing vessel, which explained Boyle's law of the compressibility of air. Later, the expansion of gases, Avogadro's chemical law, the diffusion and viscosity of gases, and the action of Crooke's radiometer were shown to be consequences of the same kinetical theory; but other phenomena, such as the ratio of the specific heat at constant volume to that at constant pressure, require additional hypotheses, which we have little reason to suppose are simple, so that we find ourselves quite afloat. In like manner with regard to light..."

"The first constant... is connected with the definition of temperature. If temperature were defined as the mean of a molecule in a , which is a minute energy indeed, this constant would have the value ⅔. But in the conventional scale of temperature the constant ...[instead] assumes an extremely small value... intimately connected with the energy of a single molecule... [I]ts accurate determination would lead to the calculation of the mass of a molecule and... associated magnitudes. This constant is frequently termed Boltzmann's constant, although to the best of my knowledge Boltzmann... never introduced it (...he, as appears from... his statements, never believed it would be possible to determine this constant accurately)..."

"If we study the history of science we see happen two inverse phenomena, so to speak. Sometimes simplicity hides under complex appearances; sometimes it is the simplicity which is apparent, and which disguises extremely complicated realities. ...What is more complicated than the confused movements of the planets? What simpler than Newton's law? ...In the kinetic theory of gases, one deals with molecules moving with great velocities, whose paths, altered by incessant collisions, have the most capricious forms... The observable result is Mariotte's simple law. ...The law of great numbers has reestablished simplicity in the average. ...No doubt, if our means of investigation should become more and more penetrating, we should discover the simple under the complex, then the complex under the simple, then again the simple under the complex, and so on, without our being able to foresee what will be the last term. We must stop somewhere, and that science may be possible, we must stop when we have found simplicity. This is the only ground on which we can rear the edifice of our generalizations."

"The old mechanical and atomic hypotheses have, during recent years, become so plausible that they have ceased to seem like hypotheses; atoms are no longer just a convenient fiction. It seems almost as if we could see them, now that we know how to count them. ...The kinetic theory of gases has thus received unexpected corroboration. ...The remarkable counting of the number of atoms by Perrin completed the triumph of the atomic theory. ...In the processes used with the Brownian phenomenon, or in those used for the law of radiation, we do not deal directly with the number of atoms, but with their degrees of freedom of movement. In that process where we consider the blue of the sky, the mechanical properties of the atoms come into play; the atoms are looked upon as producing an optical discontinuity. ...The atom of the chemist is now a reality. But that does not mean that we have reached the ultimate limit of the divisibility of matter. When Democritus invented the atom he considered it as the absolutely indivisible element within which there would be nothing further to distinguish. That is what the word meant in Greek. ... the atom of the chemist would not have satisfied him since that is not indivisible; it is not a true element; it is not free from mystery, from secrets. The chemist's atom is a universe. Democritus would have considered, even after so much trouble in finding it, that we were still only at the beginning of our search—these philosophers are never satisfied. ...This atom disintegrates into yet smaller atoms. What we call is the perpetual breaking up of atoms. ...Each atom is like a sort of solar system where the small negative electrons play the role of planets revolving around the great... sun. ...the atom of a radioactive body is a universe within itself and a world subject to chance."

"The idea of a Kinetic Theory of Gases originated with J. Bernouilli about the middle of the last century, but the first establishment of the theory on a scientific basis is due to Professor Clausius. During the last few years the theory has been greatly developed by many physicists, especially by Professor Clerk Maxwell in England and Professor Clausius and Dr. Ludwig Boltzmann... and although still beset by formidable difficulties, it has succeeded in explaining most of the established laws of gases in so remarkable a manner as to render it well worthy of the attentive consideration of scientific men. ...For the most part I have followed the method of treatment adopted by Dr. Ludwig Boltzmann in some very interesting memoirs ..."

"The quantum mechanics of two identical particles with spin S in three dimensions is reformulated by employing not the usual fixed spin basis but a transported spin basis that exchanges the spins along with the positions. Such a basis, required to be smooth and parallel-transported, can be generated by an ‘exchange rotation’ operator resembling angular momentum. This is constructed from the four harmonic oscillators from which the two spins are made according to Schwinger's scheme. It emerges automatically that the phase factor accompanying spin exchange with the transported basis is just the Pauli sign, that is (−1)2S. Singlevaluedness of the total wavefunction, involving the transported basis, then implies the correct relation between spin and statistics. The Pauli sign is a geometric phase factor of topological origin, associated with non-contractible circuits in the doubly connected (and non-orientable) configuration space of relative positions with identified antipodes. The theory extends to more than two particles."

"One of the reasons for being interested in the geometric phase is that it connects a number of different areas."

"Whenever a quantum system undergoes a cyclic evolution governed by a slow change of parameters, it acquires a phase factor: the geometric phase. Its most common formulations are known as the Aharonov–Bohm phase and the Pancharatnam and Berry phase, but both earlier and later manifestations exist. Although traditionally attributed to the foundations of quantum mechanics, the geometric phase has been generalized and become increasingly influential in many areas from condensed-matter physics and optics to high-energy and particle physics and from fluid mechanics to gravity and cosmology. Interestingly, the geometric phase also offers unique opportunities for quantum information and computation. In this Review, we first introduce the Aharonov–Bohm effect as an important realization of the geometric phase. Then, we discuss in detail the broader meaning, consequences and realizations of the geometric phase, emphasizing the most important mathematical methods and experimental techniques used in the study of the geometric phase, in particular those related to recent works in optics and condensed-matter physics."

"One of the simplest chemical exchange reactions involves a system of three hydrogen atoms: H+H2→H2+H. Surely, chemists have felt, one should be able to calculate the cross sections for this reaction from first principles. But the computations have not been easy. Only in the last six years or so have theorists, aided by efficient methodologies and access to supercomputers, been able to predict the cross sections in sufficient detail for comparison with experiments, which themselves have evolved in precision. The agreement has been good—well, almost. Small discrepancies, especially at higher total energies, stubbornly refused to yield to adjustments in either the calculations or the experiments. Now Yi‐Shuen Mark Wu and Aron Kuppermann of Caltech have erased these pesky discrepancies by including a topological effect known as the geometric phase. Michael Berry (University of Bristol) has called attention to the presence of this phase, which now bears his name, in a wide variety of physical systems."

"The geometric phase acquired by the eigenstates of cycled quantum systems is given by the flux of a two-form through a surface in the system’s parameter space. We obtain the classical limit of this two-form in a form applicable to systems whose classical dynamics is chaotic. For integrable systems the expression is equivalent to the Hannay two-form. We discuss various properties of the classical two-form, derive semiclassical corrections to it (associated with classical periodic orbits), and consider implications for the semiclassical density of degeneracies."

"Examples of geometric phases abound in many areas of physics. Many familiar problems that we do not ordinary associate with geometric phases may be phrased in terms of them. Often, the result is a clearer understanding of the structure of the problem, and of its solution."

"Here as he walked by, on the 16th of October 1843 Sir William Rowan Hamilton in a flash of genius discovered the fundamental formula for quaternion multiplication i^2 = j^2 = k^2 = ijk = -1 & cut it on a stone of this bridge."

"Quantum theory may be formulated using s over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. ...[P]roblems can be resolved if we treat real, complex and quaternionic quantum theory as part of a unified structure. Dyson called this structure the "three-fold way". ... This three-fold classification sheds light on the physics of time reversal symmetry, and it already plays an important role in particle physics. ...There are precisely four 'normed division algebras': the real numbers \mathbb{R}, the complex numbers \mathbb{C}, the quaternions \mathbb{H} and the octonions \mathbb{O}. Roughly speaking, these are the number systems extending the reals that have an ‘absolute value’ obeying the equation |xy| = |x| |y|. Since the octonions are nonassociative [their use] proves difficult... except in a few special cases. ...[I]nstead of being distinct alternatives, real, complex and quaternionic quantum mechanics are three aspects of a single unified structure."

"The real numbers are the dependable breadwinner of the family, the complete ordered field we all rely on. The complex numbers are a slightly flashier but still respectable younger brother: not ordered, but algebraically complete. The quaternions, being noncommutative, are the eccentric cousin who is shunned at important family gatherings. But the octonions are the crazy old uncle nobody lets out of the attic: they are nonassociative."

"It is a curious fact in the history of mathematics that discoveries of the greatest importance were made simultaneously by different men of genius. The classical example is the... development of the infinitesimal calculus by Newton and Leibniz. Another case is the development of vector calculus in Grassmann's Ausdehnungslehre and Hamilton's Calculus of Quaternions. In the same way we find analytic geometry simultaneously developed by Fermat and Descartes."

"[Q]uaternions form the appropriate algebraic basis for a description of nature whenever we have to deal either with pseudoreal group representations or with co-representations of Wigner's Type II. The context in which quaternions arose historically, in a study of the three-dimensional rotation group, can now be seen to be an extremely special case of this general principle. Every group which admits pseudoreal representations equally admits a natural description in terms of real quaternions."

"The history of geometry may be conveniently divided into five periods. The first extends from the origin of the science to about A. D. 550, followed by a period of about 1,000 years during which it made no advance, and in Europe was enshrouded in the darkness of the middle ages; the second began about 1550, with the revival of the ancient geometry; the third in the first half of the 17th century, with the invention by Descartes of analytical or modern geometry; the fourth in 1684, with the invention of the differential calculus; the fifth with the invention of by Monge in 1795. The quaternions of Sir William Rowan Hamilton, the Ausdehnungslehre of Dr. Hermann Grassmann, and various other publications, indicate the dawn of a new period. Whether they are destined to remain merely monuments of the ingenuity and acuteness of their authors, or are to become mighty instruments in the investigation of old and the discovery of new truths, it is perhaps impossible to predict."

"Frobenius' Theorem. Over the real number field there exist precisely three associative s, namely the real numbers, the complex numbers, and the real quaternions."

"More than a third part of a century ago, in the library of an ancient town, a youth might have been seen tasting the sweets of knowledge to see how he liked them. He was of somewhat unprepossessing appearance, carrying on his brow the heavy scowl that the "mostly-fools" consider to mark a scoundrel. In his father's house were not many books, so it was like a journey into strange lands to go book-tasting. Some books were poison; theology and metaphysics in particular they were shut up with a bang. But scientific works were better; there was some sense in seeking the laws of God by observation and experiment, and by reasoning founded thereon. Some very big books bearing stupendous names, such as Newton, Laplace, and so on, attracted his attention. On examination, he concluded that he could understand them if he tried, though the limited capacity of his head made their study undesirable. But what was Quaternions? An extraordinary name! Three books; two very big volumes called Elements, and a smaller fat one called Lectures. What could quaternions be? He took those books home and tried to find out. He succeeded after some trouble, but found some of the properties of vectors professedly proved were wholly incomprehensible. How could the square of a vector be negative? And Hamilton was so positive about it. After the deepest research, the youth gave it up, and returned the books. He then died, and was never seen again. He had begun the study of Quaternions too soon."

"My own introduction to quaternionics took place in quite a different manner. Maxwell exhibited his main results in quaternionic form in his treatise. I went to Prof Tait's treatise to get information, and to learn how to work them. I had the same difficulties as the deceased youth, but by skipping them, was able to see that quaternionics could be employed consistently in vectorial work. But on proceeding to apply quaternionics to the development of electrical theory, I found it very inconvenient. Quaternionics was in its vectorial aspects antiphysical and unnatural, and did not harmonise with common scalar mathematics. So I dropped out the quaternion altogether, and kept to pure scalar and vectors, using a very simple vectorial algebra in my papers from 1883 onward. The paper at the beginning of vol. 2 of my Electrical Papers may be taken as a developed specimen; the earlier work is principally concerned with the vector differentiator ∇ and its applications, and physical interpretations of the various operations. Up to 1888 I imagined that I was the only one doing vectorial work on positive physical principles; but then I received a copy of Prof. Gibbs's Vector Analysis (unpublished, 1881-4)."

"Mr. McAulay asks: "What is the first duty of the physical vector analyst quâ physical vector analyst?" The answer is... to present the subject in such a form as to be most easily acquired, and most useful when acquired. ...What then is the cause of the fact ...all of us deplore? ...We need only a glance at the volumes in which Hamilton set forth his method. No wonder that physicists and others failed to perceive the possibilities of simplicity, perspicuity, and brevity... in a system presented... in ponderous volumes of 800 pages. ...[I]f we turn to his earlier papers on Quaternions in the Philosophical Magazine... we find... "On Quaternions; or on a New System of Imaginaries in Algebra," and in them we find a great deal about imaginaries and very little of a vector analysis. To show how slowly the system of vector analysis developed itself in the quaternionic nidus, we need only say that the symbols S, V, and ∇ do not appear until two or three years after the discovery of quaternions. In short it seems to have been only a secondary object with Hamilton to express the geometrical relations of vectors... it was never allowed to give shape to his work. ...[I]s it not discouraging to be told that in order to use the quaternionic method one must give up the progress which he has already made in the pursuit of his favourite science and go back to the beginning and start anew on a parallel course? ...Whatever is special, accidental, and individual, will die, as it should; but that which is universal and essential should remain as an organic part of the whole intellectual acquisition. If that which is essential dies with the accidental, it must be because the accidental has been given the prominence which belongs to the essential. ...In Italy they say all roads lead to Rome. In mechanics, , astronomy, physics, all study leads to the consideration of certain relations and operations. These are the capital notions; these should have the leading parts in any analysis suited to the subject."

"If I wished to attract the student of any of these sciences to an algebra for vectors, I should tell him that the fundamental notions of this algebra were exactly those with which he was daily conversant. ...I should call his attention to the fact that Lagrange and Gauss used the notation (αβγ) to denote precisely the same as Hamilton by his S(αβγ) except that Lagrange limited the expression to s, and Gauss to vectors of which the length is the secant of the latitude, and I should show him that we have only to give up these limitations, and the expression (in connection with the notion of geometrical addition) is endowed with an immense wealth of transformations. I should call his attention to the fact that the notation [r_1r_2], universal in the theory of orbits, is identical with Hamilton's V(\rho_1\rho_2) except that Hamilton takes the area as a vector... I confess that one of my objects was to show that a system of vector analysis does not require any support from the notion of the quaternion, or... of the imaginary in algebra."

"Prof. Tait has spoken of the calculus of quaternions as throwing off in the course of years its early Cartesian trammels. I wonder that he does not see how well the progress in which he has led may be described as throwing off the yoke of the quaternion. A characteristic example is seen in the use of the symbol ∇. Hamilton applies this to a vector to form a quaternion, Tait to form a linear vector function. ...Now I appreciate and admire the generous loyalty toward one whom he regards as his master which has always led Prof. Tait to minimise the originality of his own work in regard to quaternions and write as if everything was contained in the ideas which flashed into the mind of Hamilton at the classic . But... we owe duties to our scholars as well as to our teachers, and the world is too large, and the current of modern thought is too broad, to be confined by the ipse dixit [he says] even of a Hamilton"

"I certainly admit that vectors may be used in connection with and to represent rotations. I have no objection to calling them in such cases versorial. In that sense Lagrange and Poinsot... used versorial vectors. But what has this to do with quaternions? Certainly Lagrange and Poinsot were not quaternionists. ...Does it follow that I have used a quaternion? Not at all. A quaternionic expression may represent a number. Does everyone who uses any expression for that number use quaternions? A quaternionic expression may represent a vector. Does everyone who uses any expression for that vector use quaternions? A quaternionic expression may represent a linear vector operator. If I use expression for that linear vector operator do I therefore use quaternions? My critic is so anxious to prove that I use quaternions that he uses arguments which would prove that quaternions were in common use before Hamilton was born."

"I have not been exclusively occupied by my Quaternions, but confess that they have been growing in interest upon me, and that I more and more believe they will one day justify a hope which I ventured to express... that they will constitute nothing less than "a new algebraical geometry.""

"I had been wishing for an occasion of corresponding a little with you on Quaternions: and such now presents itself, by your mentioning in your note... that you "have been reflecting on several points connected with them"... "particularly on the Multiplication of Vectors. ...No more important, or ...fundamental question, in the whole theory of Quaternions, can be proposed than that which thus inquires What is such Multiplication? What are its Rules, its Objects, its Results? What Analogies exist between it and other Operations, which have received the same general Name? And finally, what is (if any) its Utility? ...[R]eferring to an ante-quaternionic time, when you were a mere child, but had caught from me the conception of a Vector, as represented by a Triplet... I happen to be able to put the finger of memory upon the year and month—October, 1843—when... the desire to discover the laws of the multiplication referred to regained with me a certain strength and earnestness, which had for years been dormant, but was then on the point of being gratified, and was occasionally talked of with you. Every morning in the early part of the... month, on my coming down to breakfast, your (then) little brother William Edwin, and yourself, used to ask me, "Well, Papa, can you multiply triplets"? Whereto I was always obliged to reply, with a sad shake of the head: "No, I can only add and subtract them." But on the 16th day of the same month… I was walking… and your mother was walking with me, along the … and although she talked with me now and then, yet an under-current of thought was going on in my mind, which gave at last a result, whereof... I felt at once the importance. An electric circuit seemed to close; and a spark flashed forth, the herald (as I foresaw, immediately) of many long years to come of definitely directed thought and work, by myself if spared, and at all events on the part of others, if I should even be allowed to live long enough distinctly to communicate the discovery. Nor could I resist the impulse—unphilosophical as it may have been—to cut with a knife on a stone of , as we passed it, the fundamental formula with the symbols, i, j, k; namely,i^2 = j^2 = k^2 = ijk = -1,"

"all the numbers that have been derived from the genus are four; but number is the indefinite genus, from which was constituted, according to them, the perfect number, viz. the decade. For one, two, three, four, become ten, if its proper denomination be preserved essentially for each of the numbers. Pythagoras affirmed this to be a sacred quaternion, source of everlasting nature, having, as it were, roots in itself; and that from this number all the numbers receive their originating principle."

"The familiar proposition that all A is B, and all B is C, and therefore all A is C, is contracted in its domain by the substitution of significant words for the symbolic letters. The A, B, and C, are subject to no limitation for the purposes and validity of the proposition; they may represent not merely the actual, but also the ideal, the impossible as well as the possible. In Algebra, likewise, the letters are symbols which, passed through a machinery of argument in accordance with given laws, are developed into symbolic results under the name of formulas. When the formulas admit of intelligible interpretation, they are accessions to knowledge; but independently of their interpretation they are invaluable as symbolical expressions of thought. But the most noted instance is the symbol called the impossible or imaginary, known also as the square root of minus one, and which, from a shadow of meaning attached to it, may be more definitely distinguished as the symbol of semi-inversion. This symbol is restricted to a precise signification as the representative of perpendicularity in quaternions, and this wonderful algebra of space is intimately dependent upon the special use of the symbol for its symmetry, elegance, and power."

"[O]f possible quadruple algebras the one... by far the most beautiful and remarkable was practically identical with quaternions, and... it [is] most interesting that a calculus which so strongly appealed to the human mind by its intrinsic beauty and symmetry should prove to be especially adapted to the study of natural phenomena. The mind of man and that of Nature’s God must work in the same channels."

"[T]he common solution, using three Euler's angles interpolated independently, is not ideal. The more recent (1843) notation of quaternions is proposed instead, along with interpolation on the quaternion unit sphere. Although quaternions are less familiar, conversion to quaternions and generation of in-between frames can be completely automatic, no matter how key frames were originally specified, so users don't need to know—or care—about inner details. The same cannot be said for Euler's angles, which are more difficult to use."

"While translations are well animated by using vectors, rotation animation can be improved by using the progenitor of vectors, quaternions. ...By an odd quirk of mathematics, only systems of two, four, or eight components will multiply as Hamilton desired; triples had been his stumbling block."

"Closely akin to his third and fourth propositions is Riemann's fifth proposition, that continuous quantities are coördinate with discrete quantities, both being in their nature multiples or aggregates, and therefore species of the same genus. This pernicious fallacy is one of the traditional errors current among mathematicians, and has been prolific of innumerable delusions. It is this error which has stood in the way of the formation of a rational, intelligible, and consistent theory of irrational and imaginary quantities, so called, and has shrouded the true principles of the doctrine of "complex numbers" and of the calculus of quaternions in an impenetrable haze."

"The next grand extensions of mathematical physics will, in all likelihood, be furnished by quaternions."

"I do think... that you would find it would lose nothing by omitting the word "vector" throughout. It adds nothing to the clearness or simplicity of the geometry, whether of two dimensions or three dimensions. Quaternions came from Hamilton after his really good work had been done; and, though beautifully ingenious, have been an unmixed evil to those who have touched them in any way, including Clerk Maxwell."

"Symmetrical equations are good in their place, but "vector" is a useless survival, or offshoot, from quaternions, and has never been of the slightest use to any creature. Hertz wisely shunted it, but unwisely he adopted temporarily Heaviside’s nihilism. He even tended to nihilism in dynamics, as I warned you soon after his death. He would have grown out of all this, I believe, if he had lived. He certainly was the opposite pole of nature to a nihilist in his experimental work, and in his Doctorate Thesis on the impact of elastic bodies."

"I see no possible objection to your now publishing the deferred "scrap" if you yourself approve of what is said in it in favour of quaternions. I think you are right in your use of the word "Volapuk," but I don't think you should confine it to the vector part of quaternions. The whole affair has in respect to mathematics a value not inferior to that of "Volapuk" in respect to language."

"I first became personally acquainted with Tait a short time before he was elected Professor in Edinburgh… It must have been either before his election or very soon after it that we entered on the project of a joint treatise on Natural Philosophy. He was then strongly impressed with the fundamental importance of Joule’s work… We incessantly talked over the mode of dealing with energy which we adopted in the book, and we went most cordially together in the whole affair. … We have had a thirty-eight years’ war over quaternions. He had been captivated by the originality and extraordinary beauty of Hamilton’s genius in this respect; and had accepted, I believe, definitely from Hamilton to take charge of quaternions after his death, which he has most loyally executed. Times without number I offered to let quaternions into Thomson and Tait if he could only show that in any case our work would be helped by their use. You will see that from beginning to end they were never introduced."

"Yet, though few, if any—Clerk-Maxwell perhaps only excepted—ever possessed the same almost magical quality of physical insight, none could be more strict than Lord Kelvin in requiring demonstration freed from untenable assumptions or undemonstrable hypotheses. Daring as he was, at least in his earlier days, in the application of analytical methods to the phenomena of nature, he was in several ways very conservative. For example, he never would countenance the use in physics of the method of quaternions. At the British Association Meeting at Cambridge in 1845, he had met Hamilton, who there read his first paper on Quaternions. One might have thought that the young enthusiast would have readily welcomed a new and ingenious method of symbolic analysis: but it was not so. He would not use quaternion notation or quaternion methods himself, nor did he admit the into his work."

"'(1). The word "Quaternion" requires no explanation, since... it occurs in the Scriptures and in Milton. Peter was delivered to "four quaternions of soldiers" to keep him; Adam, in his morning hymn, invokes air and the elements, "which in quaternion run." The word (like, the Latin "quaternio," from which it is derived) means simply a set of four, whether those "four" be persons or things."

"'(2). But the question arises, what special connexion has the number Four with mathematics generally, or with that branch of mathematical science in particular, to which the "Lectures on Quaternions" relate?"

"'(3). One general form of answer... is... that in the mathematical quaternion is involved a peculiar synthesis, or combination, of the conceptions of space and time; and that while TIME is usually pictured or represented by metaphysicians under the figure of a line—a single stream with its ONE current—an unique axis of progression, SPACE is, on the contrary, imagined or conceived in connexion with THREE distinct axes, three lines at right angles to each other... height, length, and breadth. In time, we have only the forward and the backward, looking before and after. In space, there is not merely the contrast between the directions of upward and downward, but also between those of southward and northward, and again between westward and eastward. Time is said to have only one dimension, and space to have three dimesions. The former is an unidimensional, the latter a tridimensional progression. The mathematical quaternion partakes of both these elements; in technical language it may be said to be "time plus space," or "space plus time": and in this sense it has, or at least it involves a reference to, four dimensions. In an unpublished sonnet to Sir John Herschel, entitled "The "(...Greek ...equivalent to the Latin Quaternio), the author of the Lectures introduced the two following lines... an expression of the view... in the foregoing remarks..:"And how the One of Time, of Space the Three, Might in the Chain of Symbol girdled be.""

"'(4). Those who are entirely unacquainted with mathematical science may yet derive, from what has been above remarked, a sufficient preliminary insight into the nature of the speculations and inquiries to which the "Lectures on Quaternions" relate. A philosophical, if not a technically scientific, knowledge of the author's general aim, and of the idea which has guided him, may in this way be easily attained. But a very moderate acquaintance with the conceptions of geometry will suffice to render intelligible, from another point of view, the importance which the author attaches to the number Four in mathematics."

"(5). As early as the first book of Euclid's Elements, an attentive student is (or may be) led to consider the relative length, and also the relative direction, of one straight line as compared with another. Thus when Euclid shows, in his very first proposition, how to construct on a given base AB an equilateral triangle ABC, he virtually teaches how, when one line AB is proposed or given, to draw a new line BC (or AC), which shall in length be equal to the given one, and in direction shall make with it an angle of sixty degrees, namely, the angle ABC (or BAC), which is the third part of 180 degrees, or of two right angles."

"'(6). In this elementary example, if the length of the given base AB be taken as the standard of length, and be on that account called unity, or one, then the length of the side BC (or AC) of the triangle must also be denoted by the same number, ONE; and these TWO NUMBERS, one, and sixty, serve in this view to define, or to describe, the length and direction of the new or constructed line BC; at least if the latter number (sixty) be combined with the consideration of a certain hand, or direction of rotation, towards which the old line BA may be conceived to turn, in the plane of the triangle (or of the paper)..."

"'(7). The foregoing view, although not precisely the same with that adopted by Euclid himself, in his exposition of the elements of geometry, is at least consistent therewith; and has been made the basis of an important and modern method of calculation, respecting directed lines in one plane, which seems to have been first introduced about the commencement of the present century, by Argand in France, and for which Professor De Morgan... has lately proposed the name of Double Algebra: because it recognises and employs two numerical elements (such as the numbers 1 and 60 in the foregoing example), as required for the joint determination of the length and direction of a straight line. And it is now to be shown what is the nature of the passage that has been made, by the author of the Lectures on Quaternions, from such a double system of algebraic geometry, to what may be called, by analogy and contrast, a quadruple system of calculations respecting directed lines, or a system of QUADRUPLE ALGEBRA."

"'(8). This passage from the one system to the other may be said to consist mainly in the consideration of the variable plane of an angle. If, after tracing the equilateral triangle ABC on a card, which at first rests on a horizontal table, we then lift up that card, with the figure traced thereon, and lay it on a sloping desk, the triangle in its new position takes also a new aspect; it faces a different region of space, and may be conceived to look at, or be looked at by, a new point of the heavens, which is not now the vertical point (or ), as before. This new aspect of the figure, or of the plane (or desk) on which it is now situated, is the new circumstance introduced, in the transition from Double to Quadruple Algebra. And in fact it is easy to see that this new circumstance, of the varied position of the figure, namely, of the triangle, or simply (if we choose) of the ANGLE ABC, requires the consideration of two new numerical elements. For we have now two new questions to answer, or two new things to determine: namely, 1st, the slope of the desk (or inclination of the plane), suppose forty-five degrees, conducting to a first new number, 45 ; and 2nd, the direction of the edge (or, technically speaking, the line of the nodes), where that slope meets the table, and which may deviate from the line of north and south by any other number of degrees, suppose seventy, giving thus a second new number, in this case 70.'"

"In the Green-function treatment of particle motion, a unit impulse is represented by a force F(t) = δ(t–t′) and is the analogue of the unit point source in spatial problems. The initial conditions play the role of boundary conditions."

"Inflation has attracted cosmologists because of its potential to free the standard big bang model from its worst flaw, the need for special initial conditions and, in particular, the requirement of initial acausal homogeneity. Naturally one must check whether inflation itself depends critically on initial conditions. Several “no hair” theorems and perturbation calculations have indicated that inflation is stable, and that it will take place when the initial conditions are perturbed. This has led to the belief that inflation will start in any generic universe."

"The surprising discovery of Newton’s age is just the clear separation of laws of nature on the one hand and initial conditions on the other. The former are precise beyond anything reasonable; we know virtually nothing about the latter. ,,, … how can we ascertain that we know all the laws of nature relevant to a set of phenomena? If we do not, we would determine unnecessarily many initial conditions in order to specify the behavior of the object."

"Since 1974, the guiding principle for building extensions of the standard model has been the so-called desert hypothesis. ... Its premise is that there is no new physics between the energy scales of electroweak unification (109 GeV or 1 TeV) and the vicinity of the Planck mass MPl (1019 GeV). That implies an enormous "desert," 16 orders of magnitude wide, where one would expect to encounter nothing new. MPl is the mass at which a particle's Compton wavelength becomes equal to its Schwarzschild radius—a realm where one can't do without a quantum theory of gravity. ... The leading contender for the elaboration of the desert picture has been the supersymmetric extension of the standard model ..."

"Let me come finally to the question that is of more direct interest to the audience here: ‘what are the scales of string unification?’ or put more provocatively, ‘will we see strings and extra dimensions at the LHC?’ (this is also discussed in Peskin’s talk ...) The conventional (and conservative) hypothesis is that the string, compactification and Planck scales lie all to within two or three orders of magnitude from each other, and are hence far beyond direct experimental reach. The non-gravitational physics at lower energies is thus described by a 4d supersymmetric quantum field theory (SQFT), which must at least include in it the MSSM. This conventional hypothesis is supported by the following three solid facts : (i) Softly broken SQFTs can indeed be extrapolated consistently to near-Planckian energies without destabilizing the electroweak scale ; (ii) the hypothesis is (almost) automatic in the weakly-coupled heterotic string theory, and (iii) the minimal (or ‘desert’) string-unification assumption is in remarkable agreement with some of the measured low-energy parameters of our world."

"The most natural expectation away from asymptotic limits in moduli space of supergravity theories is the desert scenario, where there are few states between massless fields and the quantum gravity cutoff. In this paper we initiate a systematic study of these regions deep in the moduli space, and use it to place a bound on the number of massless modes by relating it to the black hole species problem. There exists a consistent sub-Planckian UV cutoff (the species scale) which resolves the black hole species problem without bounding the number of light modes. We reevaluate this in the context of supersymmetric string vacua in the desert region and show that even though heuristically the species scale is compatible with expectations, the BPS states of the actual string vacua lead to a stronger dependence of the cutoff scale on the number of massless modes. We propose that this discrepancy, which can be captured by the “BPS desert conjecture”, resurrects the idea of a uniform bound on the number of light modes as a way to avoid the black hole species problem. This conjecture also implies a stronger form of the Tadpole Conjecture, which leads to an obstruction in stabilizing all moduli semi-classically for large number of moduli in flux compactifications."

"If our geometry is to resemble differential geometry we must adjoin some uniqueness properties. Now in those geometries the geodesics, and more generally the externals in the calculus of variations, are given by differential equations of the second order, and under the hypotheses usually made in those fields, there is just one solution through a given line element. Thus a geodesics has a unique prolongation, though the shortest geodesic are joining two points even on simple surfaces such as the sphere, need not be unique."

"A geodesic that is not a null geodesic has the property that ∫ds, taken along a section of the track with the end points P and Q, is stationary if one makes a small variation of the track keeping the end points fixed."

"String topology has been used to study closed geodesics on Riemannian manifolds through Morse theory on the energy functional ..."

"We begin by recalling that geodesics can be obtained as solutions of the Euler-Lagrange equation of a Lagrangian given by the kinetic energy. We define symplectic and contact manifolds and we set up the basic geometry of the tangent bundle; we introduce the connection map, horizontal and vertical subbundles, the Sasaki metric, the symplectic form and the contact form. We describe the main properties of these objects and we show that the geodesic flow is a Hamiltonian flow. Also, when we restrict the geodesic flow to the unit sphere bundle of the manifold, we obtain a contact flow. The contact form naturally induces a probability measure that is invariant under the geodesic flow and is called the Liouville measure."

"The idea of a parallel displacement along some given curve in a two-dimensional surface can be given an intuitive interpretation. Suppose the surface is developable. Then we can unroll it on to a plane and parallel-displace vectors in the plane. The surface is then rolled back and we have the required parallel-transported vector. If a given surface is not developable, we must first select a path for parallel transport, then erect a tangent plane at each point of the path. These tangent planes will envelope a developable surface. This new developable surface can then be unrolled and the operations of parallel transport and rerolling carried out. If the curve along which the parallel displacement is to be carried out happens to be a geodesic, it becomes a straight line when unrolled on to a plane. It is then clear that the angle between a geodesic and a vector remains unchanged in a parallel displacement."

"The choice (or accident) of s creates a sense of time directionality in a physical environment. The 'arrow' of entropy increase is a reflection of the improbability of those initial conditions which are entropy-decreasing in a closed physical system. ... Everywhere... in the Universe, we discern that closed physical systems evolve in the same sense from ordered states towards a state of complete disorder called . This cannot be a consequence of known laws of change, since... these laws are time symmetric—they permit... time-reverse... The initial conditions play a decisive role in endowing the world with its sense of temporal direction. ...some prescription for initial conditions is crucial if we are to understand... A Theory of Everything needs to be complemented by some such independent prescription which appeals to simplicity, economy, or some other equally metaphysical notion to underpin its credibility. The only radically different alternative... a belief that the type of mathematical description of Nature... —that of causal equations with starting conditions—is just an artefact of our own preferred categories of thought and merely an approximation... At a deeper level, a sharp divide between those aspects of reality that we habitually call 'laws' and... 'initial conditions' may simply not exist."

"The first step came from W. Wien, whose displacement law of 1893 is embodied in the shift of the maximum of spectrum energy density, from red to violet, with increasing temperatures. Wien showed that a universal function of the ratio of temperature to frequency must here be in question. The determination of this universal function was the culmination of the insight and consistent labors of Planck (1900), who by postulating the energy quantum, became the creator of modern thermodynamics; for this energy element is a saucy reality, whose purpose is to stay. It not only tells us all we know of the distribution of energy in the black body spectrum in its thermal relations, but it gives us, indirectly, perhaps the most accurate data at hand of the number of molecules per normal cubic centimeter of the gas, of the mean translational energy of its molecules, of the molecular mass, of the Boltzmann entropy constant, even of the charge of the electron or electric atom itself."

"Of the Planck molecular oscillators... If operating continuously under the established electromagnetic laws they lead to the impossible distributions of energy in the spectrum investigated by Rayleigh and Jeans. But if emitting only, when their energy content is a whole number of energy elements, a case thus involving the entropy probability of Boltzmann, Wien's law and the numerical data referred to are deducible with astounding precision."

"We show that it is natural to introduce the concept of black-hole entropy as the measure of information about a black-hole interior which is inaccessible to an exterior observer. Considerations of simplicity and consistency, and dimensional arguments indicate that the black-hole entropy is equal to the ratio of the black-hole area to the square of the Planck length times a dimensionless constant of order unity. A different approach making use of the specific properties of Kerr black holes and of concepts from information theory leads to the same conclusion, and suggests a definite value for the constant."

"For well over a hundred years, a basic antithesis was noticed between inanimate and animate nature. The direction of physical events is prescribed by the second principle of thermodynamics... the general trend of physical happenings is toward most probable states, that is, maximum entropy and progressive destruction of differentiation and order. ...The system will tend toward thermal equilibrium ...a state of most probable distribution of molecules ...disappearance of the temperature gradient and uniform distribution ...maximum entropy. "Higher," directed forms of energy (e.g., mechanical, electric, chemical) are dissipated... progressively converted into the lowest form of energy, i.e., undirected heat movement of molecules; chemical systems tend toward equilibria with maximum entropy; machines wear out owing to friction; in communication channels, information can only be lost by conversion of messages into noise but not vice versa, and so forth."

"If for the entire universe we conceive the same magnitude to be determined, consistently and with due regard to all circumstances, which for a single body I have called entropy, and if at the same time we introduce the other and simpler conception of energy, we may express in the following manner the fundamental laws of the universe which correspond to the two fundamental theorems of the mechanical theory of heat. 1. The energy of the universe is constant. 2. The entropy of the universe tends to a maximum."

"All this prompts the question of why, from the infinite rage of possible values that Nature could have selected for the fundamental constants, and from the infinite variety of initial conditions that could have characterized the primeval universe, the actual values and conditions conspire to produce the particular range of special features that we observe. For clearly the universe is a very special place: exceedingly uniform on a large scale, yet not so precisely uniform that galaxies could not form; extremely low entropy per , and hence cool enough for chemistry to happen; almost zero cosmic propulsion and an expansion rate tuned to that energy content to unbelievable accuracy; values for the strengths of its forces that permit nuclei to exist, yet do not burn up all the cosmic , and many more apparent accidents of fortune."

"The fundamental problem about trying to define life in terms of physics is easily explained. If you go to a physics department... you'll be given a definition in terms of matter... force... energy... entropy... free energy, molecular binding affinities, and so on. If you go to a biology department... you'll be given a very different narrative in terms of... instructions, transcription, , translation, coding, signals... Biologists use information-speak... informational qualities... physicists define life in terms of physical quantities."

"Paul Davies, The Demon in the Machine (Sep. 7, 2019) 6th International FQXi Conference, "Mind Matters: Intelligence and Agency in the Physical World." A YouTube video source, 4:31."

"I know of no theorem that tells you... the maximum amount of change that agency can achieve in the universe, and what interests me... is agency at the end of the universe. If you end up in , which has a temperature and a horizon entropy, can you do anything with... those thermal fluctuations? Can you mine them... to extract energy?"

"Paul Davies, The Demon in the Machine (Sep. 7, 2019) 6th International FQXi Conference, "Mind Matters: Intelligence and Agency in the Physical World." A YouTube video source, 17:22."

"In the year 1900 Max Planck wrote... E = hv, where E is the energy of a light wave, v is its , and h is... . It said that energy and frequency are the same thing measured in different units. Plank's constant gives you a rate of exchange for for converting frequency into energy... But in the year 1900 this made no physical sense. Even Plank himself did not understand it. ...Now Hawking has written down an equation which looks rather like Plank's equation... S = kA, where S is the entropy of a black hole, A is the area of its surface, and k is... Hawking's constant. Entropy means roughly the same thing as the of an object. ...Hawking's equation says that entropy is really the same thing as area. The exchange rate... is given by Hawking's constant... But what does it really mean to say that entropy and area are the same thing? We are as far away from understanding that now as Planck was of understanding quantum mechanics in 1900. ...[T]his equation will emerge as a central feature of the still unborn theory which will tie together gravitation and quantum mechanics and thermodynamics."

"If I took a heavy weight on the floor here and pushed it, it would slide and stop. ... So, a frictional effect seems to be irreversible. ... a frictional effect ... is the result of enormous complexity of the interaction of the block with the wood ... the jiggling of the atoms inside the wood of the block is changed into disorganized irregular wiggle-waggles of the atoms in the wood."

"Newton and his theories were a step ahead of the technologies that would define his age. Thermodynamics, the grand theoretical vision of the nineteenth century, operated in the other direction with practice leading theory. The sweeping concepts of energy, , work and entropy, which thermodynamics (and its later form, statistical mechanics) would embrace, began first on the shop floor. Originally the domain of engineers, thermodynamics emerged from their engagement with machines. Only later did this study of heat and its transformation rise to the heights of abstract physics and, finally, to a new cosmological vision."

"Black holes have the universe's most inscrutable poker faces. ...When you've seen one black hole with a given mass, charge, and spin (though you've learned these thing indirectly, through their effect on surrounding gas and stars...) you've definitely seen them all. ...black holes contain the highest possible entropy ...a measure of the number of rearrangements of an object's internal constituents that have no effect on its appearance. ...Black holes have a monopoly on maximal disorder. ...As matter takes the plunge across a black hole's ravenous , not only does the black hole's entropy increase, but its size increases as well. ...the amount of entropy ...tells us something about space itself: the maximum entropy that can be crammed into a region of space—any region of space, anywhere, anytime—is equal to the entropy contained within a black hole whose size equals the region in question."

"A natural guess is that... a black hole's entropy is... proportional to its volume. But in the 1970s and Stephen Hawking discovered that this isn't right. Their... analyses showed that the entropy... is proportional to the area of its ... less than what we'd naïvely guess. ...Berkenstein and Hawking found that... each square being one by one Planck length... the black hole's entropy equals the number of such squares that can fit on its surface... each Planck square is a minimal unit of space, and each carries a minimal, single unit of entropy. This suggests that there is nothing, even in principle, that can take place within a Planck square, because any such activity could support disorder and hence the Planck square could contain more than a single unit of entropy... Once again... we are led to the notion of an elemental spatial entity."

"[F]or a physicist, the upper limit to entropy... is a critical, almost sacred quantity. ...the Bekenstein and Hawking result tells us that a theory that includes gravity is, in some sense, simpler than a theory that doesn't. ...If the maximum entropy in any given region of space is proportional to the region's surface area and not its volume, then perhaps the true, fundamental degrees of freedom—the attributes that have the potential to give rise to that disorder—actually reside on the region's surface and not within its volume. Maybe... the universe's physical processes take place on a thin, distant surface that surrounds us, and all we see and experience is merely a projection of those processes. Maybe... the universe is rather like a hologram."

"Just like a computer, we must remember things in the order in which entropy increases. This makes the second law of thermodynamics almost trivial. Disorder increases with time because we measure time in the direction in which disorder increases. You can’t have a safer bet than that!"

"The homeostatic principle does not apply literally to the functioning of all complex living systems, in that in counteracting entropy they move toward growth and expansion."

"Because entropy is not really a classical quantity, we must build quantum mechanics into the definition. ... It suffices to define entropy as the logarithm of the number of quantum states accessible to a system."

"As the natural sciences have developed to encompass increasingly complex systems, scientific rationality has become ever more statistical, or probabilistic. The deterministic classical mechanics of the enlightenment was revolutionized by the near-equilibrium statistical mechanics of late 19th century atomists, by quantum mechanics in the early 20th century, and by the far-from-equilibrium complexity theorists of the later 20th century. Mathematical , information theory, and quantitative social sciences compounded the trend. Forces, objects, and natural types were progressively dissolved into statistical distributions: heterogeneous clouds, entropy deviations, s, gene frequencies, noise-signal ratios and redundancies, dissipative structures, and complex systems at the edge of chaos."

"So if we're going to ask... What is life? ...Erwin Schrödinger wrote a famous book on that theme ...Two famous ideas ...emerged ...one ...was ...that genes are a code-script, and that was the first time anybody had used the word "code-script" or really thought in terms of information, in biology. ...This was before DNA was discovered. He was a direct inspiration to Watson and Crick and many others. The second theme... was how life maintains its organization over time, and why don't we just fall to pieces as entropy would tend to suggest... He talked about life feeding on negative entropy, or "negentropy"... [H]e talked about continually sucking order... from its environment. ...[I]t's a wonderful book. ...[H]e said, "If I had been catering for physicists alone I should have let the discussion turn on free energy instead." ...In more modern terms he's saying something like life is the harnessing of in such a way that the energy-harnessing device makes a copy of itself. ...[H]e's linking the two key themes of biology ...information and energy together."

"The new information technologies can be seen to drive societies toward increasingly dynamic high-energy regions further and further from thermodynamical equilibrium, characterized by decreasing specific entropy and increasingly dense free-energy flows, accessed and processed by more and more complex social, economic, and political structures."

"There is nothing supernatural about the process of to states of higher entropy; it is a general property of systems, regardless of their materials and origin. It does not violate the Second Law of thermodynamics since the decrease in entropy within an open system is always offset by the increase of entropy in its surroundings."

"After the invention of the steam-engine... by James Watt, the attention of engineers and of scientific men was directed to... its further improvement. ...Sadi Carnot, in 1824, published Réflexions sur la Puissance Motrice du Feu... [which] examined the relations between and the work done by heat used in an ideal engine, and by reducing the problem to its simplest form and avoiding...questions relating to details, he succeeded in establishing the conditions upon which the economical working of all heat-engines depends. ...Though the proof was invalid, the proposition remained true... Carnot's memoir remained for a long time unappreciated, and it was not until use was made of it by William Thomson... in 1848, to establish an absolute scale of temperature, that the merits of the method proposed in it were recognized. ...[H]e found that Carnot's proposition could no longer be proved by denying the possibility of "the ," and was led to lay down a second fundamental principle... now called the Second Law of Thermodynamics. ...It was published in March, 1851. In the previous year Clausias published a discussion of the same question... in which he lays down a principle for use in the demonstration of Carnot’s proposition, which, while not the same in form as Thomson’s, is the same in content, and ranks as another statement of the Second Law of Thermodynamics. Clausius followed up this paper by others, and subsequently published a book in which the subject of Thermodynamics was given a systematic treatment, and in which he introduced and developed the important function called by him the ."

"The most common way to describe entropy is as disorder... associated with things becoming more mixed, random and less ordered, but... the best way to think about entropy is as the tendency of energy to spread out. ...Most of the laws of physics work... the same... forwards or backwards in time. ...So how does this clear time dependence arise? ...[T]his is where Ludwig Boltzmann made an important insight. Heat flowing from cold to hot is not impossible, it's just improbable. ...In everyday solids there are about 100 trillion trillion atoms and even more energy packets, so heat flowing from cold to hot is just so unlikely that it never happens. ...[I]f the ...tendency is to spread out and for things to get messier, then how is it possible to have ...air conditioning, where the cold interior gets cooler and the hot exterior gets hotter? Energy is going from cold to hot, decreasing the entropy of the house. ...[T]his ...is only possible by increasing the entropy a greater amount ...at a power plant ...heating up the environment ...and creating waste heat in the fans and compressor [of the air conditioner]. ...How is there any structure left on earth? ...[I]f the earth were a the energy would spread out completely, meaning all life would cease, everything would decay and mix, and ...reach the same temperature. But luckily the earth is not a closed system, because we have the sun."

"You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, no one really knows what entropy really is, so in a debate you will always have the advantage."

"The equations of Newtonian mechanics are reversible in time and Poincaré proved that if a mechanical system is in a given state it will return infinitely often to a state arbitrarily close to the given one. Zermelo deduced that the Second Law of Thermodynamics is impossible in a mechanical system. Boltzmann asserted that entropy increases almost always, rather than always. However he believed that Poincaré's result, although correct in theory, was in practice impossible to observe since the time before a system returns to near its original state was too long."

"Let's talk some energy transfer principles. ...My Grandpappy always used to say "hot goes to cold." ...Things of a higher energy intensity state tend to equalize with things at a lower intensity energy state. ...Where there's differences, things tend towards equilibrium... You put a ball on top of a hill and you give it a chance to roll down the hill, that's what's going to happen... If you leave a big pile of sand outside long enough, it's going to flatten out. ...You take an ice cube and hold it in your hand ...heat goes out of your hand and melts the ice cube until that water becomes the same temperature as your hand. ...[V]oltage tends toward equilibrium ...If you have this ...high voltage [or current] ...stored in a battery ...[T]ake a wire and hook it from one side to the other ...It's going to equalize ...and the battery's going to be dead ..."

"Energy in the universe is constant and it can't be destroyed or created. [1st Law of Thermodynamics] ...You've got what's you've got. You've got entropy, which is a state of disorder, so things tend [from] order to disorder, but you're not going to destroy [the energy]. • Energy goes from organized and usable to disorganized and unusable, and it seeks equilibrium. That's the 2nd law and discusses entropy, which is just decay and disorder and death and destruction and... all that good stuff! All the happy stuff! When you get to be my age, you kind of look forward to it so it's not necessarily that bad. • Molecular motion stops, as does entropy, at . [3rd law] So when you get to absolute zero... nothing moves, which is why we can't really get there... because... we always take heat out of things by putting it into something else [at a lower temperature]... • Hot goes to cold. (Energy moves from higher temperature to lower temperature.) • High voltage goes to lower voltage. (Electrical current moves from high potential to low potential.) • High pressure goes to low pressure."

"Investigations of the entropy of substances at low temperatures have produced very important information regarding the structure of crystals, the work of Giauque and his collaborators being particularly noteworthy. For example, the observed entropy of crystalline hydrogen shows that even at very low temperatures the molecules of orthohydrogen in the crystal are rotating about as freely as in the gas; ... subsequent to this discovery the phenomenon of rotation of molecules in crystals was found to be not uncommon."

"Use "entropy" and you can never lose a debate, von Neumann told Shannon - because no one really knows what "entropy" is."

"My colleague Paul Glansdorff and I have investigated the problem as to if the results of near-equilibrium can be extrapolated to those of far - from-equilibrium situations and have arrived at a surprising conclusion: Contrary to what happens at equilibrium, or near equilibrium, systems far from equilibrium do not conform to any minimum principle that is valid for functions of free energy or entropy production."

"The functional order maintained within living systems seems to defy the Second Law; nonequilibrium thermodynamics describes how such systems come to terms with entropy."

"In an isolated system, which cannot exchange energy and matter with the surroundings, this tendency is expressed in terms of a function of the macroscopic state of the system: the entropy."

"Entropy is the price of structure."

"As far as we know, entropy increases throughout the portion of the universe observable from Earth. It does not seem probable to us, but in any case nothing excludes, that beyond the particle horizon which marks the maximum limit of observations there exist regions in which the arrow of time is reversed compared to ours and in which entropy decreases. I dare not think of the theoretical and observational complications that would arise if the matter contained in one of these anomalous regions began to interact with ours."

"My greatest concern was what to call it. I thought of calling it 'information,' but the word was overly used, so I decided to call it 'uncertainty.' When I discussed it with John von Neumann, he had a better idea. Von Neumann told me, 'You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, no one really knows what entropy really is, so in a debate you will always have the advantage.'"

"Prigogine was also concerned with the broader philosophical issues raised by his work. In the 19th century the discovery of the second law of thermodynamics, with its prediction of a relentless movement of the universe toward a state of maximum entropy, generated a pessimistic attitude about nature and science. Prigogine felt that his discovery of self-organizing systems constituted a more optimistic interpretation of the consequences of thermodynamics. In addition, his work led to a new view of the role of time in the physical sciences."

"Entropy... we shall use this property in a specific and limited manner. ...The following are two implications of this property: 1. If a gas or vapor is compressed or expanded frictionlessly without adding or removing heat during the process, the entropy of the substance remains constant. 2. In the process implied in implication 1, the change in represents the amount of work per unit mass required by the compression or delivered by the expansion. Possibly the greatest possible use we shall have for entropy is to read lines of constant entropy on graphs in computing the work of compression in cycles."

"Why is entropy at the beginning of time so low, and the entropy in a black hole so high? ...We ...don't know that the entropy was low ...We don't even know if there was a beginning of time. ...[E]ntropy ...is the physicist's measure of how messy things are, so my room ...tends to get higher and higher entropy, messier and messier. Why... eggs fall on the floor and break, and not... fly up and unbreak? People argued about that for a very long time until the shocking insight... that it was very low 13.4 billion years ago at the time when those... baby pictures of our universe were given off... the cosmic microwave background. ...So somehow, our flow of time towards greater messiness has something to do with our origin of our universe? That... we have learned. ...But now the question of why was that is something where many of my colleagues disagree violently... I have written a paper... which... has very little support... anyway, ...if you take seriously the idea of inflation and also this theory that the does not collapse, according to Hugh Everett, you can do some math and get an explanation... but... it's a wonderful mystery, and I'm open to all ideas... and black holes... is something else we know very little... ultimately where there are great truths yet to be discovered."

"One could... safely declare that 'Physics... can be defined as that subject which treats of the transformation of energy.' The philosophical version of Herakleitos and Empedokles... a continual cycle of changes and exchanges, had... crystallized into a quantitative physical theory. But this... picture... was... incomplete. For... there was a second, equally general and fundamental element in Nature—a directional one. This had first been formulated in the 1820s by the Mozart of modern physics, Sadi Carnot. ...Carnot started with the question: What proportion of the in any system is 'available' as a means of producing ? ...Carnot demonstrated ...a one-hundred-per-cent-efficient engine could exploit only a fraction of the heat supplied to it... A 'super-efficient' machine which could exploit all the heat supplied, would be (as Carnot's mathematics proved) a machine... one could get out of it more energy than was supplied... In an ... physical changes could at most be perfectly reversible; [but] in normal cases they would result in the progressive... 'degradation' of mechanical energy by the production of unavailable heat. To characterize this... Clausius coined the word ... [T]he directional principle of Carnot and Clausias (which gave precise expression to Newton's insight that 'motion is more easily lost than got, and is continually upon the decrease') became the Second Law of Thermodynamics."

"The third model regards mind as an information processing system. This is the model of mind subscribed to by cognitive psychologists and also to some extent by the ego psychologists. Since an acquisition of information entails maximization of negative entropy and complexity, this model of mind assumes mind to be an open system."

"It is my thesis that the physical functioning of the living individual and the operation of some of the newer communication machines are precisely parallel in their analogous attempts to control entropy through . Both of them have sensory receptors as one stage in their cycle of operation: that is, in both of them there exists a special apparatus for collecting information from the outer world at low energy levels, and for making it available in the operation of the individual or of the machine. In both cases these external messages are not taken neat, but through the internal transforming powers of the apparatus, whether it be alive or dead. The information is then turned into a new form available for the further stages of performance. In both the animal and the machine this performance is made to be effective on the outer world. In both of them, their performed action on the outer world, and not merely their intended action, is reported back to the central regulatory apparatus. This complex of behavior is ignored by the average man, and in particular does not play the role that it should in our habitual analysis of society; for just as individual physical responses may be seen from this point of view, so may the organic responses of society itself. I do not mean that the sociologist is unaware of the existence and complex nature of communications in society, but until recently he has tended to overlook the extent to which they are the cement which binds its fabric together."

"Progress imposes not only new possibilities for the future but new restrictions. It seems almost as if progress itself and our fight against the increase of entropy intrinsically must end in the downhill path from which we are trying to escape."

"He sat in the window thinking. Man has a for order. Keys in one pocket, change in another. Mandolins are tuned G D A E. The physical world has a tropism for disorder, entropy. Man against Nature . . . the battle of the centuries. Keys yearn to mix with change. Mandolins strive to get out of tune. Every order has within it the germ of destruction. All order is doomed, yet the battle is worth while."

"Revolution is everywhere, in everything. It is infinite. There is no final revolution, no final number. The social revolution is only one of an infinite number of numbers: the law of revolution is not a social law, but an immeasurably greater one. It is a cosmic, universal law—like the laws of the and of the dissipation of energy (entropy). Some day, an exact formula for the law of revolution will be established. And in this formula, nations, classes, stars—and books—will be expressed as numerical quantities."

"[M]y previous studies on the second law of thermodynamics served me here... in that my first impulse was to bring not the temperature but the entropy of the resonator into relation with its energy, more accurately not the entropy itself but its second derivative with respect to the energy... [T]his differential coefficient... has a direct physical significance for the irreversibility of the exchange of energy between the resonator and the radiation."

"But as I was... too much devoted to pure phenomenology to inquire more closely into the relation between entropy and probability, I felt compelled to limit myself to the available experimental results. Now, at that time... 1899, interest was centred on the law of the distribution of energy... proposed by W. Wien... On calculating the relation following from this law between the entropy and energy of a resonator the remarkable result is obtained that the reciprocal value of the above differential coeffcient... R, is proportional to the energy. This extremely simple relation can be regarded as an adequate expression of Wien's law..."

"I was... occupied with the task of giving it a real physical meaning, and this... led me, along Boltzmann's line... to the consideration of the relation between entropy and probability... after some weeks of the most intense work of my life clearness began to dawn... and an unexpected view revealed itself..."

"Entropy, according to Boltzmann, is a measure of a physical probability, and the meaning of the second law of thermodynamics is that the more probable a state is, the more frequently will it occur in nature."

"[W]hat one measures are only the differences of entropy, and never entropy itself, and consequently one cannot speak... of the absolute entropy of a state. But nevertheless the introduction of an appropriately defined absolute magnitude of entropy is... recommended... by its help certain general laws can be formulated with great simplicity."

"The significant part played in the origin of the classical thermodynamics by mental experiments is now taken over in the quantum theory by P. Ehrenfest's hypothesis of the adiabatic invariance; and just as the principle introduced by R. Clausius, that any two states of a material system are mutually interconvertible on suitable treatment by reversible processes, formed the basis for the measurement of entropy, just so do the new ideas of Bohr show a way into the midst of the wonderland he has discovered."

"Entropy continually increases. We can, by isolating parts of the world and postulating rather idealized conditions... arrest the increase, but we cannot turn it into a decrease. ...The law that entropy always increases—the second law of thermodynamics—holds... the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is... found to be against the second law... I can give you no hope; there is nothing for it but to collapse in deepest humiliation."

"I wish I could convey to you the amazing power of this conception of entropy in scientific research. From the property that entropy must always increase, practical methods of measuring it have been found. The chain of deductions from this simple law have been almost illimitable... equally successful in... theoretical physics and the practical tasks of the engineer. ...It is not concerned with the nature of the individual; it is interested in him only as a component of the crowd. ...[T]he method is applicable in fields of research where our ignorance has scarcely begun to lift ..."

"Thermodynamical Equilibrium. Progress of time introduces more of the random element into the constitution of the world. ...[T]he world contains both chance and design, or... antithesis of chance. ...[O]ur method of measurement of entropy: we assign to the organization or non-chance element a measure... proportional to the strength of our disbelief in a chance origin of it. ...The scientific name for a fortuitous concourse of atoms is "thermodynamic equilibrium". ...Thermodynamic equilibrium is the... case... in which no increase in the random element can occur... [i.e.] shuffling is... as thorough as possible. ...In such a region we lose time's arrow. ...[T]he arrow points in the direction of increase of the random element. ...The arrow does not know which direction to point."

"Is the random element... the only feature of the physical world which can furnish time with an arrow? ...Nothing in the statistics of an assemblage can distinguish a direction of time when entropy fails to distinguish one. ...[T]his law was only discovered in the last few years ...It is accepted as fundamental in ...atoms and radiation and had proved to be one of the most powerful weapons of progress in such researches. It does not seem to be... deducible from the second law..."

"Whilst the physicist would... say that the matter of this... [dining] table... is really a curvature of space, and its colour is really an electromagnetic wavelength, I do not think that he would say that the familiar moving on of time is really an entropy-gradient. ...[T]here is something as yet ungrasped behind the notion of entropy—some mystic interpretation... not apparent in the definition... [W]e strive to see that entropy-gradient may really be the moving on of time (instead of vice-versa)."

"The more closely we examine the association of entropy with "becoming" the greater do the obstacles appear. If entropy were one of the elementary indefinables of physics there would be no difficulty. Or if the moving on of time were something of which we were made aware through our sense organs there would be no difficulty. ...Suppose that we had to identify "becoming" with an electrical potential-gradient ...through the readings of a voltmeter."

"[S]uppose that we had to identify force with entropy-gradient. That would only mean that entropy-gradient is a condition which stimulates a nerve, which thereupon transmits an impulse to the brain, out of which the mind weaves its own peculiar impression of force. ...It is absurd to pretend that we are in ignorance of the nature of organisation in the external world in the same way that we are ignorant of the intrinsic nature of potential. It is absurd to pretend that we have no justifiable conception of "becoming"... That dynamical quality... has to do much more than pull the trigger of a nerve. ...a moving on of time is a condition of consciousness. ...It is the innermost Ego of all which is and becomes."

"Consciousness, besides detecting time's arrow, also roughly measures the passage of time. ...but is a bit of a bungler in carrying it out. ...Our consciousness somehow manages to keep ...record of the flight of time ...reading some kind of clock in the material brain ...a better analogy would be an entropy-clock ...primarily for measuring the rate of disorganisation of energy, and only roughly keeping pace with time. ...[I]n forming our ideas of duration and of becoming... [e]ntropy-gradient is... the direct equivalent of the time of consciousness in both... aspects. Duration measured by physical clocks (time-like interval) is only remotely connected."

"[T]he conception associated with entropy... marked a reaction from the view that everything to which science must pay attention is discovered by a microscopic dissection of objects. ...[T]he centre of interest is shifted from the entities reached by the customary analysis (atoms, electric potentials, etc.) to qualities possessed by the system as a whole... The artist... resorts to an impressionist painting. ...[T]he physicist has found ...his impressionist scheme is just as much exact science and even more practical ...than his microscopic scheme."

"Entropy... was discovered and exalted because it was essential to practical applications of physics... But by it science has been saved from a fatal narrowness. ...[T]here would have been nothing to represent "becoming" in the physical world."

"Entropy was not in the same category as the other physical quantities ...and the extension ...was in a very dangerous direction. ...But entropy had secured a firm place in physics before it was discovered that it was a measure of the random element in arrangement. It was in great favour with the engineers. ...[A]t that time it was the general assumption that the Creation was the work of an engineer (not of a mathematician, as is the fashion nowadays)."

"Suppose that we are asked to arrange the following in two categories— distance, mass, electric force, entropy, beauty, melody. [T]here are the strongest grounds for placing entropy alongside beauty and melody... Entropy is only found when the parts are viewed in association... [as are] beauty and melody. All three are features of arrangement. ...The reason why this [entropy] stranger can pass itself off among the aborigines of the physical world is... the language of arithmetic. It has... measure-number... at home in physics."

"It had become the regular outlook of science... that constellations are not to be taken seriously, until the constellation of entropy made a solitary exception. When we analyze the picture into a large number of particles of paints, we lose the aesthetic significance of the picture. The particles... go into the scientific inventory, and it is claimed that everything that there really was in the picture is kept. But this way of keeping... may be... losing ... The essence of a picture... is arrangement."

"I cannot read any significance into a physical world that is held... upside down. For that reason I am interested in entropy not only because it shortens calculations which can be made by other methods, but because it determines an orientation which cannot be found by other methods. ...[T]ime makes a dual entry and thus forms an intermediate link between the internal and the external. This is shadowed partially by the scientific world of primary physics (which excludes time's arrow), but fully when we... include entropy. ...[It] has generally been assumed that the object of the quest is to find out all that really exists. There is another quest... to find out all that really becomes."

"The discrimination between cause and effect depends on time's arrow and can only be settled by reference to entropy."

"Except for action and entropy (which belongs to an entirely different class of physical conceptions) all the quantities prominent in pre-relativity physics refer to the three-dimensional sections which are different for different observers."

"I am standing on the threshold about to enter a room. ...I must make sure of landing on a plank travelling twenty miles a second around the sun—a fraction of a second too early or too late, the plank would be miles away. I must do this whilst hanging from a round planet head outward into space, and with a wind of aether... I ought really to look at the problem four-dimensionally as concerning the intersection of my world-line with that of the plank. Then again it is necessary to determine in which direction the entropy of the world is increasing in order to make sure that my passage over the threshold is an entrance, not an exit. Verily, it is easier for a camel to pass through the eye of a needle than for a scientific man to pass through a door. And whether... barn... or church door it might be wiser that he should consent to be an ordinary man... rather than wait til all the difficulties in... scientific ingress are resolved."

"I was interested in the concept introduced by Clausius, entropy.., (in addition to energy,) one of the most important variables of nature."

"Energy remains constant and entropy always grows and can never be reduced... the essence of the second law of thermodynamics... [i.e.,] the entropy of a system of bodies can... only increase."

"In the limiting case, [entropy] stays the same. If it increases.., the process is irreversible. If it remains the same.., the process is reversible... [i.e.,] you can let it run backwards."

"When occurs, entropy has reached... maximum. If entropy can no longer grow.., no change can occur. This... I applied to physical-chemical and to radiation equilibria."

"I did not find the entropy of heat radiation... purely theoretically in the beginning. I only found it by reference to experimental measurements... To interpret these laws... found experimentally.., I was guided by the thoughts of Ludwig Boltzmann.., who was able to interpret the entropy of a from... atomic theory, as the logarithm of the probability of the state of the gas."

"When is a piece of matter said to be alive? When it goes on... moving, exchanging material with its environment... When a system... is not alive... all motion usually comes to a standstill... as a result of friction... [T]he whole system fades away into a dead, inert lump of matter. A permanent state is reached, in which no observable events occur. The physicist calls this the state of thermodynamic equilibrium, or of 'maxiumum entropy'."

"What is entropy? ...a measurable physical quantity just like the length ...temperature ...the heat of fusion ...or the specific heat of any given substance. At ... ...the entropy of any substance is zero. When you bring the substance into any other state by slow, reversible little steps ...the entropy increases by an amount computed by dividing every little portion of heat you had to supply ...by the absolute temperature at which it was supplied ...and by summing up all these small contributions."

"[T]he statistical concept of order and disorder... was revealed by... Boltzmann and Gibbs... This too is an exact quantitative connection...entropy = k\log Dwhere k is the... and D is... the atomistic disorder of the body... The disorder... is partly... heat of motion, partly... atoms and molecules being mixed at random... e.g., sugar and water molecules... The gradual 'spreading out' of the sugar over all the water... increases the disorder D, and hence (since the logarithm of D increases with D) the entropy. ...[A]ny supply of heat increases the turmoil of heat motion, that is ...increases D... [W]hen you melt a crystal... you... destroy the neat and permanent arrangement of... atoms or molecules and turn the crystal lattice into a continually changing random distribution."

"If D is a measure of disorder... 1/D... can be regarded as a... measure of order. Since the logarithm of 1/D is... minus the logarithm of D...-(entropy) = k\log 1/D"

"[T]he device by which an organism maintains itself stationary at a fairly high level of orderliness (...low level of entropy) ...consists in continually sucking orderliness from its environment."

"[H]igher animals... feed upon... the extremely well-ordered state of... foodstuffs. After utilizing it they return it in a... degraded form—not entirely degraded... for plants can... use... it. (...[Plants] have their most powerful supply of 'negative entropy' in the sunlight)."

"The remarks on negative entropy have met with doubt and opposition from physicist colleagues. ...[I]f I had been catering for them alone I should have let the discussion turn on free energy instead. It is the more familiar notion... [b]ut seemed linguistically too near energy for... the average reader... the concept is a rather intricate one, whose relation to Boltzmann's order-disorder principle is less easy to trace... '[E]ntropy with a negative sign'... is not my invention. It... [is] precisely the thing on which Boltzmann's original argument turned."

"Energy is needed to replace not only the mechanical energy of our bodily exertions, but also the heat we continually give off... And that we give off heat is not accidental, but essential. For this is precisely the manner in which we dispose of the surplus entropy we continually produce in our... life process."

"Nernst's discovery was induced by the fact that even at room temperature entropy plays an astonishingly insignificant role in many chemical reactions."

"Carnot was... wrong about his perception of the steam engine, but... the essence... shone through... his fundamental misconception... that heat is a fluid—caloric—that flows from a hot reservoir [source] to a cold sink... [to] turn an engine... as [does] a waterwheel... by water. ...He ...considered heat ...neither created not destroyed as it flowed ...[H]e was able to prove ...efficiency of an idealized steam engine ...that ignores friction, leaks ...[etc.] is determined only by the temperatures of the ...source and ...sink ...independent of ...pressure and ...working substance [e.g., water, steam or air]. ...[T]he hot reservoir should be as hot as possible and the cold... as cold as possible. All other variables were fundamentally irrelevant."

"Kelvin... formed... the view that... the essential component of the steam engine is the cold sink—the surroundings into which waste heat is discarded. The crucial part of the engine... didn't have to be designed or constructed... inverting common sense. ...Kelvin's conceptual somersault led him to promote ...the central ...cold sink to a universal principle ...all viable engines have a cold sink ...not ...[in] those words but ...[in] essence ...Take away the cold sink and the engine stops ..."

"All viable engines have a cold sink is one statement of the Second Law of thermodynamics. ...[T]his form of words captures its essence."

"Rudolph Clausius... noticed a common feature of nature and had the stature... to publish [in 1850, Über die bewegende Kraft der Wärme (On the motive force of heat)] what others might think a simpleton's observation: heat does not flow from a cooler to a hotter body... [I]n this and subsequent papers he developed this... into a quantitative principle..."

"[T]he law does not prohibit the transfer of heat from cold to hot... [T]o achieve , we have to do work... Clausius's... process... refers to 'natural' or 'spontaneous' changes ...without ...[being] driven by an external agency."

"The quality of stored energy is measured by... entropy. ...[T]he lower the entropy the higher the quality."

"The concept of entropy was... rendered quantitatively precise by Rudolph Clausius in 1856... by defining the change... when energy is transferred to a system as heat. Specifically...Change\;in\;entropy = \frac{energy\;supplied\;as\;heat}{temperature\;at\;which\;the\;transfer\;occurs}[N]ote... temperature... is on the absolute scale..."

"If the same amount of energy is supplied as heat...at a lower temperature... the change in entropy is greater."

"If energy leaves a body as heat... 'energy supplied as heat' is negative, so the change in entropy is negative... the entropy of the body decreases..."

"Work itself does not generate or reduce entropy."

"Clausius proposed... The entropy of an isolated system increases in any spontaneous change."

"[T]he Kelvin statement is equivalent to... 'your engine will work only if you waste some energy'..."

"Suppose we claim... heat flowing in the wrong direction, such as... ice forming in a glass of water... in an oven. ...Energy left the cool... water as heat, so the entropy went down. Because the temperature is low... in the denominator... that decrease in entropy is large. The same energy enters the hot region (...oven), so the entropy of that region increases. However... its temperature is high, [so] that increase in entropy is small. The net effect... a net decrease overall. ...[But] entropy never decreases, so heat cannot flow spontaneously... hot to cold..."

"Clausius... summarized... the First and Second Laws: ...[T]he energy of the world is constant; the entropy strives towards a maximum."

"There was considerable opposition... the Second Law... offended the sensibilities of the age... [H]ow can something increase in abundance? ...Who or what is pouring entropy into the universe..?"

"The [Second] law is... used to predict whether a chemical reaction will run in one direction or another..."

"Ludwig Boltzmann... saw further into the nature of matter than any... contemporaries until... he hanged himself in the face of their incomprehension and rejection of his ideas. Entropy, he showed, is a measure of disorder... A solid... has a lower entropy that the liquid into which it melts. A gas... has a higher entropy than the liquid from which it evaporates. ...When a gas expands to fill an enlarged volume, its disorder and therefore its entropy increases even though we keep its temperature the same... [W]e become less confident... [that] a molecule will be found in a given small region. ...Entropy [also] increases as the thermal disorder of a substance becomes more vigorous, with increasing thermal motion of... atoms... [and] as... positional disorder increases... [the] available positions of... atoms."

"Boltzmann...was driven to his death by the inability of scientists... to come to terms with this profoundly simple insight."

"'[E]nergy supplied as heat' appears in the numerator of Clausius' expression, for the greater the energy... as heat, the greater... increase in disorder and therefore... entropy. The... temperature in the denominator fits... this analogy too... for a given supply of heat... [added to] a cool [little thermal motion] object... will introduce a... [relatively large] disturbance, corresponding to a big rise in entropy... [and the same heat added to a] hot [lots of thermal motion] object has relatively little effect, and the increase in entropy is small."

"The statement that entropy never decreases in any natural change is the same as saying... molecular order never increases on its own... Molecules... will not form... spontaneously into the Statue of Liberty. A gas will not collect spontaneously in one corner of a container."

"...attributes may be maintained because of deformations in fields. Such conservation laws are called topological. Thus, it may happen that a knot in a set of field lines, called a soliton, cannot be smoothed out. As a result, the soliton is prevented from dissipating and behaves much like a particle. A classic example is a magnetic monopole, which has not been found in nature but shows up as twisted configurations in some field theories. In the traditional view, then, particles such as electrons and quarks (which carry Noether charges) are seen as fundamental, whereas particles such as magnetic monopoles (which carry topological charge) are derivative. In 1977, however, Claus Montonen, now at the Helsinki Institute of Physics in Finland, and David I. Olive, now at the University of Wales at Swansea, made a bold conjecture. Might there exist an alternative formulation of physics in which the roles of Noether charges (like electrical charge) and topological charges (like magnetic charge) are reversed? In such a “dual” picture, the magnetic monopoles would be the elementary objects, whereas the familiar particles—quarks, electrons and so on—would arise as solitons."

"A method is proposed to calculate quantum numbers on solitons in quantum field theory. The method is checked on previously known examples and, in a special model, by other methods. It is found, for example, that the fermion number on kinks in one dimension or on magnetic monopoles in three dimensions is, in general, a transcendental function of the coupling constant of the theories."

"While J. Scott Russell first observed solitons in water waves in Augst 1834, a full-fledged theory of solitons has only come of age in the last decade. This advance is due primarily in the discovery of a generalization of the , the . While this method can be used to solve exactly only a certain number of nonlinear equations, many of these are relevant to broad areas in physics."

"The idea that in some sense the ordinary proton and neutron might be solitons in a non-linear sigma model has a long history. The first suggestion was made by Skyrme more than twenty years ago ... David Finkelstein and Rubinstein showed that such objects could in principle be fermions ... in a paper that probably represented the first use of what would now be θ vacua in quantum field theory. A gauge invariant version was attempted by Faddeev ... Some relevant miracles are known to occur in two space-time dimensions ... ; there also exists a different mechanism by which solitons can be fermions ..."

"The general problem of Celestial Mechanics consists in the determination of the relative motions of p bodies attracting one another according to the Newtonian law. This problem is not able to be solved directly: in order to deal with it, certain limitations must be made. ... Again, owing to the conditions under which the bodies of our solar system move, we are further able to divide the problem of p bodies into several others, each of which may be treated as a case of the problem of three particles, or, as it is generally called, the Problem of Three Bodies. The greater part of the Lunar Theory is a particular case of the Problem of Three Bodies; it involves the determination of the motion of the Moon relative to the Earth, when the mutual attraction of the Earth, Moon and Sun, considered as particles, are the only forces under consideration. When this has been found, the effects produced by the actions of the planets, the non-spherical forms of the bodies etc., can be be exhibited as small corrections to the coordinates."

"In Book I, Prop. LXVI of the first edition of Philosophiae naturalis principia mathematica, Newton (1687) discussed the dynamical problem of three bodies in a general way, and then in Book III he asserted that the vagaries of the Moon's motion could be accounted for by the gravitational attraction of the Sun. He recognized that he needed to develop the theory further, and summarized his later results in The theory of the Moon's motion of 1702 (Cohen 1975). He continued to refine his treatment up to the publication of the second edition of Principia (Newton 1712), some sections of which differ greatly from the first edition. He made almost no further changes of his own in the third edition, but added a scholium by Machin (1726) on the motion of the nodes. The published account of the rotation of the apse line, much the same in all versions, was seriously wrong, but even before 1690 Newton had developed a somewhat more satisfactory treatment, with which, however, he remained dissatisfied and never published (Whiteside 1976). (Since this article was prepared, the new English translation of the Principia by Cohen and Whitman (1999) has appeared. It is a translation of the third edition of 1726, which differs significantly in a few places from the first and second editions, as will be indicated.)"

"There are three essentially different types of lunar theory — that of de Pontécoulant, that of Delaunay, and that first developed by Hill, to which may perhaps be added that of Hansen as containing many features of more or less importance different from the others. That of de Pontécoulant and most of his predecessors consists in developing certain coordinates in periodic series of assumed form with the time or true anomaly as argument and determining the coefficients step by step as powers of the small parameters involved ; that of Delaunay consists in applying the method of the variation of parameters in the canonical form over and over in such a way as to remove the most important parts of the perturbative function ; that of Hill consists in finding very accurate particular solutions of the differential equations after the parts depending on the parallax of the sun, the eccentricity of the earth's orbit, and the latitude of the moon have been neglected, and then finding the deviations from this orbit due to general initial conditions and the neglected part of the perturbative function."

"Perhaps the best-known giant resonance in nuclei is the giant dipole resonance (GDR). The GDR is described in classical hydrodynamics as a class of nuclear motion in which the neutrons and protons within a nucleus move collectively against one another, providing a separation between the centers of mass and charge, thus creating a dipole moment."

"Nuclei interact with the external environment through a number of different fields—electromagnetic, weak and hadronic. The collective excitations induced by these interactions are known as giant resonances. The best known example is the giant dipole resonance, which is stimulated when the electric field of an incident gamma ray exerts a force on the positively charged protons in a nucleus, moving them relative to the uncharged neutrons ... Other giant resonances that have been studied are the monopole, quadrupole and spin-isospin modes of oscillation. The spin-isospin mode involves charge-changing processes, in particular beta decay. The quadrupole and monopole giant resonances are most easily seen with fields that act equally on neutrons and protons, because in these modes the neutrons and protons oscillate in the same mode. The giant resonances are collective oscillations and the various modes of oscillation depend on specific aspects on the nuclear force to sustain them. In the monopole mode, the motion is radial and the frequency depends on the compressibility of the nucleus. In the dipole and spin-isospin resonances, the protons and neutrons are excited out of phase, and the proton-neutron interaction provide the restoring force."

"The spectrum of gamma-radiation emitted by a highly excited nucleus can be calculated in two ways. In the first method the transition probability for gamma emission is related to the photon absorption cross-section by detailed balance. The second method relies on the fact that an excited hot nucleus has thermal fluctuations. In particular it has a fluctuating dipole moment which produces thermal radiation. The two methods are closely related and in both cases the spectrum of the radiation emitted is dominated by the giant dipole resonance. The equivalence of the detailed balance and thermal radiation theories can be demonstrated explicitly for a coupled oscillator model of the giant resonance."

"A powerful method to study the properties of a system is to subject it to a weak external perturbation and to examine its response. For the atomic nucleus subjected to the absorption of a photon or to the scattering of a particle (electron, proton, etc.) the response is ... a function of the energy and linear momentum transferred to the system. ... Up to about 10 MeV the nucleus responds through the excitation of relatively simple states often involving only one or a few particles. In the energy range between 10 and 30 MeV the system response exhibits broad resonances. These are the giant resonances ... Giant resonances correspond to a collective motion involving many if not all the particles in the nucleus. The occurrence of such a collective motion is a common feature of many-body quantum systems. In quantum-mechanical terms the resonance corresponds to a transition between the ground state and the collective state and its strength is described by a transition amplitude. Intuitively it is clear that the strength of the transition will depend on the basic properties of the system such as the number of particles participating in the response and the size of the system. This implies that the total transition strength should be limited by a sum rule which depends 'only' on ground-state properties. If the transition strength of an observed resonance exhausts a major part, say greater than 50%, of the corresponding sum rule we call it a giant resonance."

"Maurice Goldhaber has emphasized that the situation with respect to possible nuclear resonances in (γ,n) or (γ,fission) reactions was quite unclear at the time of George C. Baldwin and G. Stanley Klaiber’s papers on these reactions. ... This was because the rapid rise of their yield to a prominent peak with increasing energy, followed by a slower fall off was then thought to have been due to the competition between the rapidly rising density of nuclear states and the eventual domination of other reaction channels at higher energies. Goldhaber realized, however, that there could be an analogy between a possible collective nuclear resonance and the restrahl resonance (essentially the transverse optical phonon mode) in polar crystals. Goldhaber sought out Teller because of his paper with Russell Lyddane and Robert Sachs, ... relating the restrahl frequency to the asymptotic behavior of the crystal’s dielectric function. Goldhaber and Teller, in their paper together, went on to predict universal, giant photo-nuclear resonances. ..."

"To know the quantum mechanical state of a system implies, in general, only statistical restrictions on the results of measurements. It seems interesting to ask if this statistical element be thought of as arising, as in classical statistical mechanics, because the states in question are averages over better defined states for which individually the results would be quite determined. These hypothetical 'dispersion free' states would be specified not only by the quantum mechanical state vector but also by additional 'hidden variables' - 'hidden' because if states with prescribed values of these variables could actually be prepared, quantum mechanics would be observably inadequate."

"In contemplating the papers Einstein wrote in 1905, I often find myself wondering which of them is the most beautiful. It is a little like asking which of Beethoven’s symphonies is the most beautiful. My favorite, after years of studying them, is Einstein’s paper on the blackbody radiation. [...] Part of being a great scientist is to know—have an instinct for—the questions not to ask. Einstein did not try to derive the Wien law. He simply accepted it as an empirical fact and asked what it meant. By a virtuoso bit of reasoning involving statistical mechanics (of which he was a master, having independently invented the subject over a three-year period beginning in 1902), he was able to show that the statistical mechanics of the in the cavity was mathematically the same as that of a dilute gas of particles. As far as Einstein was concerned, this meant that this radiation was a dilute gas of particles—light quanta. But, and this was also characteristic, he took the argument a step further. He realized that if the energetic light quanta were to bombard, say, a metal surface, they would give up their energies in lump sums and thereby liberate electrons from the surface in a predictable way, something that is called the photoelectric effect. [...] In the first place, not many physicists were even interested in the subject of blackbody radiation for at least another decade. Kuhn has done a study that shows that until 1914 less than twenty authors a year published papers on the subject; in most years there were less than ten. Planck, who was interested, decided that Einstein’s paper was simply wrong."

"Newton and his theories were a step ahead of the technologies that would define his age. Thermodynamics, the grand theoretical vision of the nineteenth century, operated in the other direction with practice leading theory. The sweeping concepts of energy, heat, work and entropy, which thermodynamics (and its later form, statistical mechanics) would embrace, began first on the shop floor. Originally the domain of engineers, thermodynamics emerged from their engagement with machines. Only later did this study of heat and its transformation rise to the heights of abstract physics and, finally, to a new cosmological vision."

"The Schrödinger equation, which is at the heart of quantum theory, is applicable in principle to both microscopic and macroscopic regimes. Thus, it would seem that we already have in hand a non-classical theory of macroscopic dynamics, if only we can apply the Schrödinger equation to the macroscopic realm. However, this possibility has been largely ignored in the literature because the current statistical interpretation of quantum mechanics presumes the classicality of the observed macroscopic world to start with. But the Schrödinger equation does not support this presumption. The state of superposition never collapses under Schrödinger evolution."

"Ludwig Boltzmann, who spent much of his life studying statistical mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics. Perhaps it will be wise to approach the subject cautiously."

"In the consistent-histories approach, the classical limit can be studies by using appropriate subspaces of the quantum as a "coarse graining," analogous to dividing up into nonoverlapping cells in classical statistical mechanics. This coarse graining can then be used to construct quantum histories. It is necessary to show that the resulting family of histories is consistent, so that the probabilities assigned by make good quantum mechanical sense. Finally, one needs to show that the resulting quantum dynamics is well approximated by appropriate classical equations."

"[I]n the nineteenth century, even the could be reduced to mechanics by the assumption that heat really consists of a complicated statistical motion of the smallest parts of matter. By combining the concepts of the mathematical theory of probability with the concepts of Newtonian mechanics Clausius, Gibbs and Boltzmann were able to show that the fundamental laws in the theory of heat could be interpreted as statistical laws following from Newton's mechanics when applied to very complicated mechanical systems."

"In the history of Science it is possible to find many cases in which the tendency of Mathematics to express itself in the most abstract forms has proved to be of ultimate service in the physical order of ideas. Perhaps the most striking example is to be found in the development of abstract Dynamics. The greatest treatise which the world has seen, on this subject, is Lagrange's Mécanique Analytique, published in 1788. ...conceived in the purely abstract Mathematical spirit ...Lagrange's idea of reducing the investigation of the motion of a dynamical system to a form dependent upon a single function of the of the system was further developed by Hamilton and Jacobi into forms in which the equations of motion of a system represent the conditions for a stationary value of an of a single function. The extension by Routh and Helmholtz to the case in which "ignored co-ordinates" are taken into account, was a long step in the direction of the desirable unification which would be obtained if the notion of were removed by means of its interpretation as dependent upon the of concealed motions included in the dynamical system. The whole scheme of abstract Dynamics thus developed upon the basis of Lagrange's work has been of immense value in theoretical Physics, and particularly in statistical Mechanics... But the most striking use of Lagrange's conception of generalized co-ordinates was made by Clerk Maxwell, who in this order of ideas, and inspired on the physical side by... Faraday, conceived and developed his dynamical theory of the , and obtained his celebrated equations. The form of Maxwell's equations enabled him to perceive that oscillations could be propagated in the electromagnetic field with the velocity of light, and suggested to him the Electromagnetic theory of light. Heinrich Herz, under the direct inspiration of Maxwell's ideas, demonstrated the possibility of setting up electromagnetic waves differing from those of light only in respect of their enormously greater length. We thus see that Lagrange's work... was an essential link in a chain of investigation of which one result... gladdens the heart of the practical man, viz. ."

"In the history of sciences, important advances often come from... the recognition that two hitherto separate observations can be viewed from a new angle and seen to represent nothing but different facets of one phenomenon. Thus, terrestrial and celestial mechanisms became a single science with Newton's laws. Thermodynamics and mechanics were unified through statistical mechanics, as were optics and electromagnetism through Maxwell's theory of magnetic field, or chemistry and through quantum mechanics. Similarly different combinations of the same atoms, obeying the same laws, were shown by biochemists to compose both the inanimate and animate worlds. ... Despite such generalizations, however, large gaps remain... Following the line from physics to sociology, one goes from simpler to the more complex objects... from the poorer to the richer empirical content, as well as from the harder to the softer system of hypotheses and experimentation. ...Because of the hierarchy of objects, the problem is always to explain the more complex in terms and concepts applying to the simpler. This is the old problem of reduction, emergence, whole and parts... an understanding of the simple is necessary to understand the more complex, but whether it is sufficient is questionable. ...the appearance of life and later of thought and language—led to phenomena that previously did not exist... To describe and to interpret these phenomena new concepts, meaningless at the previous level, are required. ...At the limit total reductionism results in absurdity. ...explaining democracy in terms of the structure and properties of elementary particles... is clearly nonsense."

"The kinetic theory of gases is a small branch of physics which has passed from the stage of excitement and novelty into staid maturity. ...Formerly it was hoped that the subject of gases would ultimately merge into a general kinetic theory of matter; but the theory of condensed phases... today, involves an elaborate and technical use of wave mechanics, and for this reason it is best treated as a subject in itself. The scope of the present book is, therefore, the traditional kinetic theory of gases. ...[A]n account has been included of the wave-mechanical theory, and especially of the degenerate Fermi-Dirac case... There is also a concise chapter on statistical mechanics, which... may be of use as an introduction... [T]he discussion of electrical phenomena has been abbreviated... the latter voluminous subject is best treated separately. ...[F]undamental parts have been explained... [as] to be within the reach of college juniors and seniors. The... wave mechanics and statistical mechanics... are of graduate grade. ...[A] number of carefully worded theorems have been inserted in the guise of problems, without proof... to give... a chance to apply... lines of attack exemplified in the text. To facilitate use as a reference book, definitions have been repeated freely, I hope not ad nauseam. ...Ideas have been drawn freely from ...books such as ...of Jeans and Loeb..."

"The rapid development of quantum mechanics stimulated research in and theory. Initiated during the mid-twenties, intensive study of s and their representations led to Haar's discovery of the basic construction of invariant integration on a topological group. Bohr's theory of s influenced the work of Wiener, Bochner and many other analysts. They enriched the technical arsenal of harmonic analysis and the scope of its applications (statistical mechanics, ergodic theory, , etc.) The new notion of the generalized made it possible to consider Plancherel's theory simultaneously with Bohr's theory, the continuous spectrum with the discrete. The Pontrjagin-van Kampen duality opened the way for an unobstructed development of on locally compact s, allowing , Fourier integrals and expansions via numerical characters to be viewed as objects of the same kind. The Peter–Weyl theory made it possible for von Neumann to analyze almost periodic functions on groups by connecting them to group representation theory. Along with the many other discoveries of that period, this led to the inclusion of group theorethical methods into the tool kit of harmonic analysis."

"The need for a fundamentally different approach to the study of physical processes at the molecular level motivated the development of relevant statistical methods, which turned out to be applicable not only to the study of molecular processes (statistical mechanics), but to a host of other areas such as the actuarial profession, design of large telephone exchanges, and the like. In statistical methods, specific manifestations of microscopic entities (molecules, individual telephone sites, etc.) are replaced with their statistical averages, which are connected with appropriate macroscopic variables. The role played in Newtonian mechanics by the calculus, which involves no uncertainty, is replaced in statistical mechanics by ', a theory whose very purpose is to capture uncertainty of a certain type."

"As the natural sciences have developed to encompass increasingly s, scientific rationality has become ever more statistical, or probabilistic. The deterministic classical mechanics of the enlightenment was revolutionized by the near-equilibrium statistical mechanics of late 19th century atomists, by quantum mechanics in the early 20th century, and by the far-from-equilibrium complexity theorists of the later 20th century. Mathematical , information theory, and quantitative social sciences compounded the trend. Forces, objects, and natural types were progressively dissolved into statistical distributions: heterogeneous clouds, entropy deviations, s, gene frequencies, noise-signal ratios and redundancies, dissipative structures, and complex systems at the edge of chaos."

"The path integral is a formulation of quantum mechanics equivalent to the standard formulations, offering a new way of looking at the subject which is, arguably, more intuitive than the usual approaches. Applications of path integrals are as vast as those of quantum mechanics itself, including the quantum mechanics of a single particle, statistical mechanics, condensed matter physics and quantum field theory. ... It is in quantum field theory, both relativistic and nonrelativistic, that path integrals (functional integrals is a more accurate term) play a much more important role, for several reasons. They provide a relatively easy road to quantization and to expressions for s, which are closely related to amplitudes for physical processes such as scattering and decays of particles. The path integral treatment of gauge field theories (non-abelian ones, in particular) is very elegant: and ghosts appear quite effortlessly. Also, there are a whole host of nonperturbative phenomena such as solitons and that are most easily viewed via path integrals. Furthermore, the close relation between statistical mechanics and quantum mechanics, or and quantum field theory, is plainly visible via path integrals."

"There is an interesting analogy... with the philosophy of the natural sciences, which has flourished under the combined influence of both general methodology and classical metaphysical questions (realism vs. antirealism, space, time, causation, etc.) interacting with detailed case studies in... (physics, biology, chemistry, etc.)... [C]ase studies both historical (studies of Einstein's relativity, Maxwell's electromagnetic theory, statistical mechanics, etc.). By contrast, with few exceptions, philosophy of mathematics has developed without the corresponding detailed case studies."

"The idea behind the Feynman path integral goes back to a paper by P. A. M. Dirac published in 1933 in Physikalische Zeitschrift der Sowjetunion. It formed the core of Richard Feynman’s space–time approach to quantum mechanics and quantum electrodynamics. Although the path integral was not mathematically well defined, it was widely used in quantum field theory, statistical mechanics, and string theory. Recently, path integrals have been the guide to spectacular developments in pure mathematics."

"Another crucial point is that MOND as we know it now is arguably only an approximate 'effective field theory' that approximates some more fundamental scheme at a deeper stratum — some 'FUNDAMOND' — conceptually, in a similar way to thermodynamics being an approximation of the statistical-mechanics, microscopic description."

"With the growing importance of models in statistical mechanics and in field theory, the path integral method of Feynman was soon recognized to offer frequently a more general procedure of enforcing the instead of the Schrödinger equation. To what extent the two methods are actually equivalent, has not always been understood... [T]here are few nontrivial models which permit deeper insight into their connection. However, the exactly solvable cases... the Coulomb potential and the harmonic oscillator... point the way: For scattering problems the path integral seems particularly convenient, whereas for the calculation of discrete eigenvalues the Schrödinger equation [is preferable]. ...[P]otentials with degenerate vacua ...arise ...in recently studied models of large spins."

"You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, no one really knows what entropy really is, so in a debate you will always have the advantage."

"Carnot's Principle. ...If physical phenomena were due exclusively to the movements of atoms whose mutual attraction depended only on the distance, it seems that all these phenomena should be reversible; if all the initial velocities were reversed, these atoms, always subjected to the same forces, ought to go over their trajectories in the contrary sense, just as the earth would describe in the retrograde sense this same elliptic orbit which it describes in the direct sense, if the initial conditions of its motion had been reversed. On this account, if a physical phenomenon is possible, the inverse phenomenon should be equally so, and one should be able to reascend the course of time. Now, it is not so in nature, and this is precisely what the principle of Carnot teaches us; heat can pass from the warm body to the cold body; it is impossible afterward to make it take the inverse route and to reestablish differences of temperature which have been effaced. Motion can be wholly dissipated and transformed into heat by friction; the contrary transformation can never be made except partially. We have striven to reconcile this apparent contradiction. If the world tends toward uniformity, this is not because its ultimate parts, at first unlike, tend to become less and less different; it is because, shifting at random, they end by blending. For an eye which should distinguish all the elements, the variety would remain always as great; each grain of this dust preserves its originality and does not model itself on its neighbors; but as the blend becomes more and more intimate, our gross senses perceive only the uniformity. This is why for example, temperatures tend to a level, without the possibility of going backwards. A drop of wine falls into a glass of water; whatever may be the law of the internal motion of the liquid, we shall soon see it colored of a uniform rosy tint, and however much from this moment one may shake it afterwards, the wine and the water do not seem capable of again separating. Here we have the type of the irreversible physical phenomenon : to hide a grain of barley in a heap of wheat, this is easy; afterwards to find it again and get it out, this is practically impossible. All this Maxwell and Boltzmann have explained; but the one who has seen it most clearly, in a book too little read because it is a little difficult to read, is Gibbs, in his 'Elementary Principles of Statistical Mechanics.’"

"The only important variables of interest must involve averaging over many of the degrees of freedom. Statistical mechanics is the formalization of this intuitive concept. The problems to be addressed... are threefold: under what circumstances can the properties of a physical system be defined by the behavior of an appropriate small set of variables, what are the appropriate sets of relevant variables, and how can one calculate the properties of the system in terms of these variables."

"I thought of calling it 'information,' but... Von Neumann told me, 'You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, no one really knows what entropy really is, so in a debate you will always have the advantage.'"

"[[Game theory|[G]ame theory]] has already established itself as an essential tool in the , where it is widely regarded as a unifying language for investigating human behavior. Game theory's prominence in evolutionary biology builds a natural bridge between the life sciences and the behavioral sciences. And connections have been established between game theory and the two most prominent pillars of physics: statistical mechanics and quantum theory. ...[M]any physicists, neuroscientists, and social scientists... are... pursuing the dream of a quantitative science of human behavior. Game theory is showing signs of... an increasing important role in that endeavor. It's a story of exploration along the shoreline separating the continent of knowledge from an ocean of ignorance... a story worth telling."

"Maxwell, and then Boltzmann, and then... J. Willard Gibbs consequently expended enormous intellectual effort in devising... statistical mechanics, or... . The uses... extend far beyond gases... describing electric and magnetic interactions, chemical reactions, phase transitions... and all other manner of exchanges of matter and energy. The success... has driven the belief among many physicists that it could be applied with similar success to society. ...[E]verything from the flow of funds in the stock market to the flow of traffic on interstate highways ..."

"The way he taught statistical mechanics and electromagnetic theory, you got the feeling of a growing science that emerged out of conflict and debate. It was alive, like his lectures, which were full of personal references to men like Boltzmann, Klein, Ritz, Abraham, and Einstein. He told us at the beginning that we should teach ourselves in a fortnight—no babying. Ehrenfest's students all acknowledge how much his method of exposition has influenced their own teaching."

"Thermodynamics is more like a mode of reasoning than a body of physical law. ...we can think of thermodynamics as a certain pattern of arrows that occurs again and again in very different physical contexts, but, wherever this pattern of explanation occurs, the arrows can be traced back by the methods of statistical mechanics to deeper laws and ultimately to the principles of elementary particle physics. ...the fact that a scientific theory finds applications to a wide variety of different phenomena does not imply anything about the autonomy of this theory from deeper physical laws."

"As Oliver Cromwell said to the General Assembly of the Church of Scotland, "I beseech you, in the bowels of Christ, think it possible that you might be mistaken." Life and the affairs of the living are so tangled, the world not only stranger than we imagine but stranger than we can imagine, that all questions are conundrums, no answers "correct." Is it certain that parallel lines never meet? No. Does water freeze at 32 degrees Fahrenheit? Only probably. Shall I marry? Who can say? And yet the world's work must be done. One Oblomov is enough. Thus we learn a conventional certitude, acting as though all were light by blinking the shadow. A simple proof demonstrates that parallel lines do meet, but, on the assumption that they do not, the architect builds the skyscraper. Despite his knowledge of statistical mechanics, the engineer designs the refrigerator to maintain a constant temperature of 31 degrees. Le cœur a ses raisons que la raison ne connait pas [the heart has its reasons that reason does not know], and families are raised."

"… once a healthy cell sort of abandons ship and decides that it's going to just be, like, a ravenous, invasive cancer cell, its voltage changes radically. And what you can do with an ion channel drug is change the electrical state of that cell by messing with the ion channels. And in tadpole experiments — and this is early days, but this is moving really fast. In tadpole experiments, they were able to use ion channel drugs to keep cells that had been genetically engineered to be tumors from changing their electrical voltage, right? And without doing any kind of genetic mucking around, they kept these tumors from forming in tadpoles that had been genetically engineered to express tumors."

"The plasma membrane is a heterogeneous structure whose thickness ia around 75 Å and which bounds the cell. An important constituent is lipid, which often represents as much as 70% of the membrane volume (depending on cell type). The membrane lipid readily excludes the passage of ions; it remains for imbedded proteins to form the channels which permit exchange of ions between intracellular and extracellular space. For nerve and muscle, electrical activation is associated with the movement of sodium and potassium (and other) ions across membranes by means of these channels; the proteins not only facilitate the flow of each ion but they control the flow of each giving rise to the ' of the membrane."

"Waste biomass is a cheap and relatively abundant source of electrons for microbes capable of producing electrical current outside the cell. Rapidly developing microbial electrochemical technologies, such as microbial fuel cells, are part of a diverse platform of future sustainable energy and chemical production technologies. We review the key advances that will enable the use of exoelectrogenic microorganisms to generate biofuels, hydrogen gas, methane, and other valuable inorganic and organic chemicals. Moreover, we examine the key challenges for implementing these systems and compare them to similar renewable energy technologies. Although commercial development is already underway in several different applications, ranging from wastewater treatment to industrial chemical production, further research is needed regarding efficiency, scalability, system lifetimes, and reliability."

"Bioelectricity is about the electrical phenomena of life processes, and is a parallel to the medical subject electrophysiology. One basic mechanism is the energy consuming cell membrane ion pumps polarising a cell, and the action potential generated if the cell is excited and ion channels open. The dipolarisation process generates current flow also in the extracellular volume, which again results in measurable biopotential differences in the tissue. An important part of the subject is intracellular and extracellular single cell measurements with microelecroeds. Single neuron activity and signal transmission can be studied by recording potentials with multiple microelectrode arrays. In addition to measure on endogenic sources, bioelectricty also comprises the use of active stimulating current carrying (CC) electrodes. Since bioelectricity is about life processes the experiments are per definition in vivo or ex vivo."

"The winter solstice has always been special to me as a barren darkness that gives birth to a verdant future beyond imagination, a time of pain and withdrawal that produces something joyfully inconceivable, like a monarch butterfly masterfully extracting itself from the confines of its cocoon, bursting forth into unexpected glory."

"Each solstice shows us that we can choose. We cannot stop the winter or the summer from coming. We cannot stop the spring or the fall or make them other than they are. They are gifts from the Universe that we cannot refuse. But we can choose what we will contribute to Life when each arrives."

"I remember a lunch in which Schwinger began by saying to Weisskopf, “Now I will make you a world.” The “world” was written down on a few paper napkins, one of which I saved. In any event, one of the things that he said, which has stuck with me ever since, was that scalar particles were the only ones that could have nonvanishing vacuum expectation values. He then went on to say that if you couple one of these to a fermion \Psi by a of the form \Phi \overline \Psi\Psi, then this vacuum expectation value would act like a mass. This sort of coupling is how mass generation is done in principle for the fermions. All particles in this picture would acquire their masses from the vacuum."

"A new conceptual foundation for Tμν on locally flat —to obtain the so-called Casimir effect—is presented. The Casimir ground state is viewed locally as a (nonvacuum) state on Minkowski space-time and the expectation value of the normal-ordered is taken. The same ideas allow us to treat, for the first time, self-interacting fields for arbitrary mass in —using traditional flat-space-time renormalization theory. First-order results for zero-mass λφ4 theory agree with those recently announced by . We point out the crucial role played by the simple renormalization condition that the vacuum expectation value of Tμν must vanish in Minkowski space-time, and in a critical discussion of other approaches, we clarify the question of renormalization ambiguities for Tμν in curved space-times."

"Vacuum expectation values of products of neutral operators are discussed. The properties of these distributions arising from , the absence of states and the of the scalar product are determined. The vacuum expectation values are shown to be s of s. Local commutativity of the field is shown to be equivalent to a symmetry property of the analytic functions. The problem of determining a theory of a neutral scalar field given its vacuum expectation values is posed and solved."

"It is a basic fact of life that Nature comes to us in many scales. Galaxies, planets, aardvarks, molecules, atoms and nuclei are very different sizes, and are held together with very different binding energies. Happily enough, it is another fact of life that we don’t need to understand what is going on at all scales at once in order to figure out how Nature works at a particular scale. Like good musicians, good physicists know which scales are relevant for which compositions. The mathematical framework which we use to describe nature — — itself shares this basic feature of Nature: it automatically limits the role which smaller distance scales can play in the description of larger objects. This property has many practical applications, since a systematic identification of how scales enter into calculations provides an important tool for analyzing systems which have two very different scales, m ≪ M. In these systems it is usually profitable to expand quantities in the powers of the small parameter, m/M, and the earlier this is done in a calculation, the more it is simplified."

"... Imagine you have an image with enormous resolution, but all you really need to know is whether a giant gorilla sits at the center of the image. To that end, a low-resolution picture would suffice. Effective-field theory is the tool a nuclear physicist would use to controllably blur the picture, reduce its complexity, and make the problem computationally tractable. Effective-field theory averages out interactions’ short-range components not relevant to the physics of nuclei, and it provides a form of the force using parameters that can be determined directly from QCD. The resulting NN force can then be used to solve the nuclear many-body problem and calculate all relevant nuclear properties"

"What makes a field theory effective? We shall argue in this book that the way s are set up in EFTs makes them the most natural and convenient tools to address multi scale problems. Problems with separated scales often appear in Nature, and we intuitively know that it is most convenient to only work with degrees of freedom that are relevant for a particular scale — otherwise the problem quickly becomes intractable! You never worry about physics of the atoms when designing bridges, nor try to track each and every molecule of a gas through ; you instead define some "macroscopic" variables, and once you know how to relate those variables to the more "fundamental" laws, you can stop thinking about those cases and focus only on the relevant large-scale physics. EFT techniques codify this principle when working with problems in quantum field theory."

"Standard cosmological models rely on an approximate treatment of gravity, utilizing solutions of the linearized Einstein equations as well as physical approximations. In an era of precision cosmology, we should ask: are these approximate predictions sufficiently accurate for comparison to observations, and can we draw meaningful conclusions about properties of our Universe from them? In this work we examine the accuracy of linearized gravity in the presence of collisionless matter and a cosmological constant utilizing fully general relativistic simulations. We observe the gauge dependence of corrections to linear theory, and note the amplitude of these corrections. For perturbations whose amplitudes are in line with expectations from the standard , we find that the full, general relativistic metric is well described by linear theory in Newtonian and harmonic gauges, while the metric in comoving-synchronous gauge is not. For the most extreme observed structures in our Universe, such as supervoids, our results suggest that corrections to linear gravitational theory can reach or surpass the percent level in all gauges."

"Both classical and quantum corrections can be analyzed by a perturbative approach based on the so-called weak field approximation. The heart of Einstein’s theory is represented by its ten coupled partial differential equations. The solutions of these equations, i.e., the gravitational potentials, are the metric tensor components. In the weak field approximation, the metric tensor can be decomposed in two terms: the flat Minkowski metric and the small perturbation multiplied by the gravitational constant. The solution of the non-linear equations can be considered the sum of infinite terms, and Newton’s theory emerges in the linear order. ... used this approximation to investigate the infinities that emerge by applying the early QFT techniques to quantize the gravitational interaction (Rosenfeld, 1930). Different kinds of divergent quantities had already appeared in the context of QED at the end of the 1920s: their correct treatment will be clarified only after the Second World War."

"The fundamental scientific purpose of the LHC is to explore the inner structure of matter and the forces that govern its behavior, and thereby understand better the present content of the Universe and its evolution since the Big Bang, and possibly into the future. The unparalleled high energy of the LHC, which is designed to be 7 TeV per proton in each colliding beam, and its enormous collision rate, which is planned to attain about a billion collisions per second, will enable the LHC to examine rare processes occurring at very small distances inside matter. It will be a microscope able to explore the inner structure of matter on scales an order of magnitude smaller than any previous collider. The energies involved in the proton-proton collisions will be similar to those in particle collisions in the first trillionth of a second of the history of the Universe. By studying these processes in the laboratory, the LHC experiments will, in a sense, be looking further back into time than is possible with any telescope."

"… The relied not on the detection of photon pairs with a certain energy but on the detection of more of those pairs than expected. That reliance on probabilities is why the L.H.C. and other major collider experiments often have independent teams, working with separate detectors, analyzing the same types of collisions—to avoid biasing each other. It is also the reason for the ."

"With the discovery of the Higgs boson, the next burning question at the LHC is why its mass is so low. Nobody knows the answer to that question, but it is definitely the next hot topic for LHC physicists ..."

"On July 4, scientists working with data from ongoing experiments at the Large Hadron Collider (LHC) announced the discovery of a new particle "consistent with" the Higgs boson — a subatomic particle also colloquially referred to as the "God particle." After years of design and construction, the LHC first sent protons around its 27 kilometer (17 mile) underground tunnel in 2008. Four years later, the LHC's role in the discovery of the Higgs boson provides a final missing piece for the Standard Model of Particle Physics — a piece that may explain how otherwise massless subatomic particles can acquire mass. Gathered here are images from the construction of the massive $4-billion-dollar machine that allowed us peer so closely into the subatomic world."

"The last few decades have provided abundant evidence for physics beyond the two standard models of particle physics and . As is now known, the by far largest part of our universe's matter/energy content lies in the `dark' and consists of and . Despite intensive efforts on the experimental as well as the theoretical side, the origins of both are still completely unknown. Screened scalar fields have been hypothesized as potential candidates for dark energy or dark matter. Among these, some of the most prominent models are the , , and environment-dependent ."

"2. Are there any new elementary scalars not yet discovered with masses below the mass of the -like Higgs boson? For example, do -like particles exist? ... 8. If additional scalars are discovered, how will these discoveries impact the question of the stability of the ? 9. Do neutral (inert) scalars comprise a significant fraction of the dark matter?"

"When you pick the string just right, a higher pitch other than the fretted note is sounded. This higher pitch is an overtone, or harmonic, that stems from the overtone series related to that note. Indicated by the abbreviation P.H., the pinch harmonic is a fantastic expressive device to use when playing a solo or melody. Much beloved by rock, blues, country and metal guitarists alike, the pinch harmonic has been used to great effect by such legendary axemen as Roy Buchanan, Billy Gibbons, Eddie Van Halen and Zakk Wylde."

"There has always been a good deal of mystery surrounding the pinch harmonic, or, as hip players like to call it, “pick squeal.” A pick squeal is simply an artificial harmonic, or high-pitched sound, produced by choking up on the pick and allowing the thumb or thumbnail to catch the string in just as it is picked. The result, of course, resembles a squeal. Or a squawk. Or a scream. (It could take several tries before you get the desired "s" word.) Anyhow, what was once the domain of blues-rock string benders is now a staple for most metal guitarists."

"In short, pick squealing, or pinch harmonics is part of the reason why a lot of people started using copious amounts of hairspray and dressing in very tight clothing during the '80s. However, pick squeals, or, in less cool words, pinch harmonics, can be used in a much broader spectrum of ways than just heavy metal, and the technique was originally probably first used by blues players of old."

"The way I and most guitarists produce a pinch harmonic is to grasp the pick close to its pointed tip with your thumb and index finger. You then pick a downstroke, intentionally allowing a bit of the fleshy part of the thumb to graze the string at the same time."