The evolution of scientific thought from Newton to Einstein

by A. D'Abro

We have mentioned elsewhere the nature of Planck’s investigations and have seen that they led to the discovery of a universal constant

representing an atom of action. In other words, there appears to exist in nature a definite atom of action, called a quantum of action, just as there appear to exist two definite atoms of electricity, namely, the positive atom, or nucleus of the hydrogen atom, and the negative atom, called electron. It is because this atom of action appears to be of such fundamental importance that we must endeavour to detect its presence in our space-time model of the universe. However, not the slightest suggestion of it can be discovered.

It is not meant to imply that no unit of action can be found. Indeed, the action connected with the totality of the finite universe could be taken as unit. But this unit of action would be enormous, far too great to be identified with Planck’s unit, and it seems impossible to discover a unit of action of any such infinitesimal proportions as is exemplified by Planck’s quantum of action. Nor does it seem likely that any such infinitesimal atom of action will ever be found in our space-time model, whether it be that of Einstein or of Weyl. For, space-time having been assumed from the outset to be a continuous manifold, the only fixed quantities pertaining to volumes in space-time and capable of representing action will always be of cosmic proportions, embracing the whole extension of the finite universe. In order to obtain discontinuities or atoms of infinitesimal proportions, it would seem to be necessary to suppose that this discontinuity was inherent in the texture of space-time; and this would lead us to a granular conception of space-time, as opposed to our present continuous conception. We should have to assume that the apparent continuity of the fundamental manifold was due to our macroscopic study of it; just as a piece of polished marble may appear continuous when we run our fingers over its surface, whereas its discontinuous nature would be revealed were we to study it with the aid of a powerful microscope. This view would imply that the secret of Planck’s quanta of action would only be revealed were we to study space-time on a microscopic scale. Our entire understanding of nature would then be modified, for this atomicity of action might bring in its wake the atomicity of space and of time, proving that space and time, as ordinarily understood, were but approximate concepts.

Also, we should mention that by following another train of thought, de Broglie and Schrödinger have succeeded in throwing new light on the significance of quantum phenomena. For by adopting a wave theory of matter, Schrödinger has proved that the existence of energy levels within the atom (as postulated by Bohr) can be deduced mathematically from the solutions of certain wave equations. Thus our understanding of matter assumes a most revolutionary aspect. In the light of the new investigations, the mechanics of the atom would stand on an entirely different footing from that of classical or even of relativistic science. Just as classical mechanics appears as a first approximation holding good for low velocities, but breaking down for high velocities, in which case the more embracing relativistic mechanics must take its place, so now relativistic mechanics ceases to be applicable when minute regions of atomic dimensions are contemplated. Here the still more embracing wave mechanics of Schrödinger would correspond to reality. We see, then, that these successive scientific structures constitute better and better approximations, each degenerating into its predecessor when certain refinement are neglected.

We may also say that the vicissitudes through which matter is now passing present a striking similarity to those through which our under standing of optics passed during the nineteenth century. Here, also when minute regions of dimensions comparable to those of wave-length were considered, there arose diffraction phenomena which the old-fashioned geometrical optics was unable to account for. Wave optics took it place. But it cannot be stressed too strongly that this new wave mechanic of Schrödinger, which appears to be gaining ground, does not endanger in any sense the main achievement of the relativity theory, namely, the discovery of space-time. Space-time is incorporated into the new mechanics, along with Einstein’s other results. In the present state of these highly abstract investigations, not much positive information is available; and it would be a mere waste of time to guess what the future may hold in store.

CHAPTER XL
THE GENERAL SIGNIFICANCE OF THE THEORY OF RELATIVITY

THE theory of relativity, as we have seen, is one of mathematical physics; and its sole aim has been to co-ordinate the greatest number of natural phenomena and experimental results in as simple and as direct a manner as possible. In common with all other great developments of theoretical physics, it has adhered strictly to scientific methods. But now that the mathematico-physical co-ordination has been completed, it becomes permissible to investigate the changes which the theory may necessitate in our philosophical understanding of nature.

The most interesting aspect of the entire theory for philosophers would appear to be the discovery of space-time, with the paradoxes of feeling to which it leads. Thus, the duration of our life, the distance we cover, have no absolute significance. Two twins might both live seventy years in their own estimation, and yet if they met again before their death one might be younger than the other. Two men starting from the same point and travelling in the same direction might both cover what they would measure as the same distance, and yet might find when they came to a stop that they were many miles apart. The fact is that a distance and a duration are not absolute; they merely express a relation between something that is absolute, and the space-time mesh-system or motion of the observer. There is no more cause to be surprised at the curious results we have mentioned than at the relative character of the length of the shadow cast by a pole, or of the visual angle under which we see the pole.

As an immediate consequence of this relativity of distance and duration, we must accept the relativity of simultaneity. Classical science recognised that no absolute significance could be attached to the concept of the same point of space considered at different times; for since points of space could be determined only with respect to a system of reference, two events occurring in succession at the same point of our system would obviously occur at two different points of some other system, in motion with respect to the first. On the other hand, classical science refused to extend similar relativistic considerations to the concept of the same instant of time at two different points. It was assumed that a change of system of reference could have no effect on the rate of time-flow, which remained absolute, ever the same for all observers. It is this belief in the absolute nature of simultaneity that is shattered by Einstein’s discoveries. Henceforth no greater significance can be attached to the absolute sameness of time in different places than to the absolute sameness of location at different times.