Physics

"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."

"[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..."

"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."

"[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."

"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."

"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..."

"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."

"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..."

"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."

"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..."

"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..."

"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."

"[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."

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"The special theory of relativity owes its origins to Maxwell's equations of the electromagnetic 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."

"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."

"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."

"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!"

"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."

"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:"

"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."

"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."

"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."

"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"

"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."

"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."

"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 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."

"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."

"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..."

"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."

"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."