The logic of modern physics

by P. W. Bridgman

The question now for us is whether we shall regard this as a mere invention, made for convenience in thinking, or shall go further and ascribe physical reality to it, that is, shall we think of light as capable of independent physical existence in the space between the matter that constitutes the source and the mirror? Now in spite of the resemblances pointed out above, there is at least one universal and fundamental difference between a thing that travels and light. We have independent physical evidence of the continued existence of the ball, for example, at all intermediate points of space; we can see it, or hear it, or feel the wind in the air as it passes, or even touch it. All these phenomena are independent of the initial and terminal phenomena, and hence by our criterion for the physical reality of an invention, we are justified in ascribing physical reality to the ball in transit. But with the beam of light it is entirely different; the only way by which we can obtain physical evidence of the intermediate existence of the beam is by interposing some sort of a screen, and this act destroys just that part of the beam whose existence we have thereby detected. There is no physical phenomenon, whatever by which light may be detected apart from the phenomena of the source and the sink (understanding that a mirror is included in the idea of, sink); that is, no phenomenon exists independent of the phenomenon which led us to the invention of a thing travelling. Hence from the point of view of operations it is meaningless or trivial to ascribe physical reality to light in intermediate space, and light as a thing travelling must be recognized to be a pure invention.

The status of light is exactly the same as that of an electric field; there is not the slightest warrant for ascribing physical reality to either at points of empty space—light and field-at-a-point have no meaning until we go there and make experiments with some material thing. Of course the electromagnetic theory of light makes this resemblance inevitable, provided the theory and our views of the nature of light and the field are correct.

It cannot be denied that there are some phenomena which uncritically considered appear to justify thinking of light as a thing that travels; these will now be discussed. Probably the argument to which most significance is usually ascribed is derived from the phenomena of energy. The passing of light from source to sink is accompanied by the transfer of energy. But energy is conserved, so that we have to ask where the energy is in the time interval between the emission of light from the source and its absorption by the sink. There is an obvious answer: the energy is in transit, of course, somewhere in the intermediate space between source and sink. If we think of light as propagated through a medium, then the medium is such that energy may reside in it, as in the electromagnetic theory of light, or if light is more material and ballistic in character, the thing that travels has itself energy. We notice in the first place that the conservation principle involves the time concept, because what we mean by conservation is that the total energy of the universe, at a fixed instant of time, is constant. That is, we have to integrate over all space the local energy at a definite instant of time, and this involves spreading the time concept over all space. It is further evident that unless we spread the time concept over space in the right way we shall not get conservation. The proof that it is possible to spread the time concept over space in such a way as to give conservation involves a knowledge of the properties of light. It would seem, then, that we ought not to assume conservation in deducing the properties of light, when a knowledge of the properties of light is necessary to establish conservation. These considerations cannot be accepted as final, however, until a detailed analysis has been made, and this would be most complicated. But there is a more important consideration derived from our previous critique of the energy concept, namely, that there is no basis for asserting that energy is localized in space at all; energy is not a physical thing, but rather what we would call a property of a system as a whole. If this view of energy be granted, the whole energy argument for light as a thing travelling, and also for the existence of a medium, falls. I believe that similar considerations apply to any arguments from the conservation of momentum.

The possibility of detecting light in apparently empty space by a screen constitutes perhaps the most immediate reason for considering light as a thing that travels. This point of view I believe is characteristic of the entire attitude of Einstein in deducing the theorems of the special theory of relativity. Einstein's light signal is for the purposes of the deduction thought of as a simple spherical wave spreading from the source and capable of being watched as it spreads by an observer outside the system, in much the same way that a water wave can be watched. Of course the light signal cannot actually be watched in transit, but we can come fairly close to this ideal by placing screens at any point we please to make the wave visible. It is true that the mere act of showing the existence of the light destroys that part of the beam whose existence is detected, but the screen needs only an infinitesimal amount of light to make it visible, and so by the usual physical argument we may suppose that the detecting screen produces only an infinitesimal modification of the total original light.

Our satisfaction with this picture evaporates if our present quantum views of the nature of light are correct. We can no longer think of the spherical light pulse as of irreducible simplicity, but it is an exceedingly complicated thing, perhaps more complicated than a gas from the point of view of kinetic theory, and simulates simplicity by some sort of averaging of the effects of the elementary quantum processes of which it is composed. If the principles of relativity are to continue to be regarded as fundamental, or even if they are to remain intelligible, we must apply our reasoning, not to spherical wavelets, but to the elementary process of which these wavelets are composed. Now the elementary quantum act is essentially a twofold thing: there is a discrete act of emission at some discrete material particle, and the act is consummated by another discrete act (absorption or scattering) at some other discrete particle. We cannot yet fully characterize the details of this twofold process, but have to connect the place at which absorption takes place with the place of emission by statistical considerations. It is evident, however, that to think of emission as starting some process like a spherical wavelet travelling like a thing through space presents an entirely incorrect view, because in the wave there is no hint of the discrete place which is to terminate it. We may say crudely that there is no way by which the wave can know what discrete material particle is to complete the emission process. We may perhaps try to save the situation by remembering that a spherical wave is polarized and so has a unique direction associated with it; but further examination shows that this does not help, because the unique direction is that of no energy flow, and absorption can take place in any direction except this. It appears then that instead of being a help, the thing travelling point of view is a positive embarrassment when we try to picture by means of it the essentially twofold nature of the elementary quantum act.

Another plausible argument for light as a thing travelling may be deduced from our principle of connectivity. Imagine a dark lantern with a shutter that can be opened or closed so as to emit a momentary flash of light, a distant mirror, and a receiving instrument near the source. One of the properties of light that we always assume is that no permanent trace of the act of emission is left behind in the source. The most minute examination of all the details of the lantern and its surroundings at some time after the emission of the flash has not yet shown any phenomenon that betrays a remembrance of the emission of the flash, unless perhaps we measure the total energy or momentum and have some way of knowing what the energy or momentum would have been if the flash had not been emitted, and in any event we cannot specify the moment in past time when the signal was emitted. In the same way we cannot tell from an examination of a mirror whether it has at any time in the past reflected a beam of light. Consider now two systems, each consisting of a source and a mirror distant 3 x 10¹⁰ cm., identical in all respects, except that in one a light signal was flashed from the source 1.5 seconds ago, and in the other only 0.5 seconds ago. According to our hypothesis, the most complete examination of source and mirror in either system fails to show the slightest difference, but nevertheless there is something essentially different about the two systems, for in one a light signal arrives at the screen in 0.5 seconds, and in the other not until 1.5 seconds. This violates what we have suggested might be regarded as the cardinal and most general principle of all physics, the principle of essential connectivity, which states that differences between two systems must be associated with other differences. A most obvious and simple way of maintaining our principle is merely to point out that the system really included more than we investigated: the system properly consists of source, mirror, screen, and all intermediate space, so that if we had examined intermediate space we should have found light there in transit in different positions in the two systems, thus correlating with the differences in subsequent history. This argument appeals to me as perhaps the strongest that can be advanced for the view of light as a thing travelling. But it seems in no way conclusive. Our principle of essential connectivity made no mention of the time concept, but we have somehow smuggled it in making the application above. We sought to give a complete description of our system at some one instant of time, and this involved spreading the time concept over space. This itself is a questionable operation and may be done in different ways. But, more important, what is the justification for supposing that the system can be completely described by giving a complete description of all the measurable parts of it at some one epoch? We have seen that in the most general case the principle of essential connectivity must recognize that the concept of "initial condition" of a system involves all the past history, and we may have here a case in point. The answer can be given only by experiment. In dealing with ordinary experience, when we do not have to distinguish between local and extended time, and are not dealing with optical phenomena, there can be little question that experience at least approximately justifies the expectation that future behavior is determined in terms of the present condition and that present condition may be specified in terms of the results of present operations performed in the system. But before extending this principle to phenomena in which we have to distinguish between local and extended time, we have to answer just that question which we are now considering; namely, whether there are physical phenomena taking place in apparently empty space, and whether therefore empty space has to be included in the system. We find ourselves again treading the vicious circle. Perhaps experience will show that the extension of the principle of connectivity to optical phenomena involves something like this: namely, the future at any point in a material system is determined by a complete description of the present state of the system in the immediate vicinity, and by a history of the behavior at more distant points, this history extending over longer and longer intervals of time as the point becomes more remote.

I believe, however, that these possibilities will not seem very satisfactory, and that most physicists will discover in themselves a very strong disposition to feel that the future is determined in terms of a complete description of some sort of instantaneous configuration, time being extended in some suitable way over space. This instinctive demand that the future be determined in terms of the present may easily be consistent with the optical phenomena in our two systems consisting of source, mirror, and screen, without involving the material existence of light in empty space, provided that our assumption that the emission of light leaves behind it no permanent record in the source was incorrect. It may be that detailed examination of a source after emission will disclose permanent traces, from which the instant of emission may be found by extrapolation. If the conviction of determinism of the future is strong, the physicist may well be impelled to search here for new phenomena indicating such a memory of emission.

Let us now inquire how our physical structure might be affected if we should give up the identification of light with a thing travelling. One consequence is that light need no longer be thought of as having the property of velocity, since velocity, in terms of immediate experience, is a property of things moving from place to place. Giving up the concept of light as a thing travelling would enable us, then, to adopt an alternative method of describing nature with a different concept of velocity; we have seen that it is possible to define velocity in terms of operations different from the usual ones, in such a way as to give the usual numerical results at small velocities, but different results at high velocities, and in particular to give an infinite velocity for light.[26]

[26]No difficulty arises from the asymmetric character of light in assigning an infinite velocity to light because those physical operations by which we discover which is the source and which the sink are entirely distinct from the operations by which a velocity is measured; or in other words, even in the limit, it still has meaning to say that an infinite velocity has a direction associated with it.

There is now no objection to an infinite number associated with light, if we no longer think of light as having physical velocity. We may, if we like, continue for the sake of convenience to talk of the velocity of light, clearly understanding that the infinite value which must be ascribed to this velocity corresponds to the fact that the physical concept of velocity does not apply in all respects to light. We should now have to revise our process for extending the time concept over space, because this was formerly so done as to give light a finite velocity. We are now to make this velocity infinite, which is obviously to be done simply by setting a distant clock on zero at the instant it receives a light signal flashed from our clock at its zero. The behavior of material things now takes on a simple aspect—there is no longer a finite upper limit to the velocity that can be given a material thing, and light has no longer the paradoxical property of bearing the same finite relation to each of two material systems which differ from each other by a finite amount (that is, the first postulate of relativity that the velocity of light is 3 x 10¹⁰ in all reference systems). Light instead now bears the relation of infinitude to each of two systems which differ from each other by only a finite amount, and this is natural from the mathematical point of view.