Physics

"[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."

"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."

"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."

"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..."

"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'."

"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."

"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."

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

"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."

"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."

"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."

"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."

"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."

"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."

"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.""

"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 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."

"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."

"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."

"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.'"

"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..."

"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."

"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."

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

"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."

"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."

"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."

"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."

"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."

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

"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!"

"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."

"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 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."

"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."

"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."

"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."

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

"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."

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

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

"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."

"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."

"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."

"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."

"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.)"

"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."

"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."

"[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."