The evolution of scientific thought from Newton to Einstein

by A. D'Abro

We may recall that all these so-called paradoxes of relativity are by no means antinomies of reason or of logic, which the theory could not possibly survive. They are merely paradoxes of feeling, which arise when from force of habit we continue to be haunted by the classical concepts of absolute duration and distance, and to credit these erroneously with some a priori inevitable virtue of logical necessity.

When we consider that there is scarcely a single field in our understanding of the physical universe upon which relativity has failed to throw some new light, we can realise that as yet the full significance of its discoveries is far from being established. Nevertheless, sufficient positive information has been gathered with respect to the concepts of space and time for certain philosophical conclusions to appear legitimate. What the theory has proved conclusively is that real space and real time can be approached only by empirical methods, and in particular by ultra-refined experiment.

We mentioned, when discussing space, that Kant’s philosophy of the a priori nature of three-dimensional Euclidean space as representing the form of pure sensibility was exploded years ago by the mathematicians from Gauss onwards. So far as scientists were concerned, the matter was definitely settled. The theory of relativity merely confirms these views by justifying them no less on physical than on mathematical grounds. Henceforth, four-dimensional space-time, which, though flat, is non-Euclidean (in the extended sense), owing to the negative dimensionality of time, constitutes the fundamental continuum of the universe. Had it not been for the general theory, it might have been argued that space-time possessed no deep significance, and that it reduced to a mere convenient mode of mathematical representation, like the graph of a barometer needle. Though we may state (even confining ourselves to the special theory) that this opinion would have been untenable, the use which Einstein has made of space-time in the general theory excludes this view completely. With space-time we are in the presence of a new continuum which has exactly the same measure of reality as was formerly attributed to three-dimensional space.

Now we have seen that with the rejection of the a priori Kantian attitude, mathematicians long before the advent of Einstein’s theory were thrown back on the empirical philosophy of space as arising from the simplest co-ordination of our sensory impressions. In particular, the apparent inevitability of Euclidean space was assumed to result from the co-ordination of sensory experience, whether that of the individual or that of the species. In other words, it was the behaviour of material bodies and of light rays which was held to be the fundamental source of our natural belief in the Euclideanism of space. But here an objection might be urged, for it might be contended with perfect truth that according to Einstein the behaviour of material bodies and light rays is such as to yield space-time, and not separate space and time. How, then, could we account for space-time having failed to impose itself ages ago; and why had it been necessary to await the arrival of Minkowski and Einstein?

The reason is, of course, obvious. Theoretically, there is a great difference in structure between space-time and separate space and time, and this difference arises, as we know, from the finiteness of the invariant velocity in space-time as contrasted with its infinite magnitude in separate space and time. The higher the relative speeds of bodies, and, in particular, the nearer they approximate to the critical speed of light, the more marked will become the physical discrepancies between the two worlds. And as the velocities of those bodies which enter into our daily experience are exceedingly small in contrast to that of light, crude perception cannot enable us to detect the minute differences which are theoretically present. To all intents and purposes, therefore, the world of common experience is one of separate space and time, and not one of space-time. In much the same way, the mere survey of a landscape would be incapable of revealing the rotundity of the earth. And so we understand why it was that the discovery of space-time had to await the performance of ultra-refined physical experiments. We might, of course, conceive of beings whose senses were so far developed as to detect the minute differences that escape us. If such beings existed, there is every reason to suppose that their sensibility would accept space-time as a matter of course, just as ours accepts three-dimensional Euclidean space and time. In the words of Eddington: “It is merely the accident that we are not furnished with a pair of eyes in rapid relative motion, which has allowed our brains to neglect to develop a faculty for visualising this four-dimensional world as directly as we visualise its three-dimensional section.” Being so poorly equipped as to sensory organs, being unable to discern the minute discrepancies that arise when

is very large though finite and when

is infinite, we have got into a rut and have believed from ages immemorial in a world of separate space and time. There is no reason to marvel at the paradoxes of feeling which we suffer when told of the strange disclosures that would ensue were relative velocities to become very great or our senses to become more acute. In much the same way, quite apart from the disclosures of relativity, were our eyes to be suddenly gifted with microscopic vision, our familiar world would become so terrifying as to baffle description.

Now the essential characteristic of space-time is that it exhibits no absolute separation between space and time which would hold for all observers, regardless of their motion. Each and every observer will split it up in a different way, so that the totality of space at an instant for one becomes a successive spread of points throughout space at a succession of times for another. Of course, so long as we are considering only our immediate perceptions, we shall always split up space-time into a separate space and time; and this fact has been construed by some as implying that the space-time amalgamation is obviously artificial, since it can be so easily separated into space and time. Needless to say, the argument is faulty. For the space and time that we obtain as a result of a splitting up of the space-time continuum correspond to a private view of the world, and it is never the private views considered in isolation that give us the objective world. It is solely a certain construct or synthesis of the private views which can be deemed to represent objective reality. To revert to an illustration from classical science, it is not the shape of the rock as seen from here or there that yields us a knowledge of the rock’s shape, but solely a synthesis of the appearances of the rock as seen from here, there and anywhere. In relativity we must also consider the perceptions of observers moving with various relative motions Then it is found that objective shape, size and duration can no longer be constructed by a synthesis of private views, in contrast to what classical science had erroneously supposed. For this reason, distance and time separation, or, what comes to the same thing, space and time though remaining real from the standpoint of the private view, can no longer be claimed to constitute the scaffolding of the common objective world. From an objective point of view, such concepts are ambiguous and we must substitute for them a space-time world and space-time configurations. In short, it must be realised that space-time is an entirely new concept, new both in science and in philosophy, and it must not be confused with the mere artificial representation of time and space directions in graphs such as classical science had often made use of.