The evolution of scientific thought from Newton to Einstein

by A. D'Abro

So much for the scientific understanding of the word. But if, on the other hand, when discussing “reality” we are referring to the reality of the metaphysicians, as happens to be the case with Poincaré, then it appears quite impossible to dispute his stand; at least it is scarcely credible that any scientist would feel inclined to do so. For, assuming even that such a thing as metaphysical reality has any meaning at all, why should it be connected with simplicity of co-ordination? At any rate, Einstein himself, whose entire theory centres round a definite geometry being ascribed to the spatio-temporal background, writes: “Sub specie œternitatis, Poincaré in my opinion is right.”

If any criticism is to be directed against Poincaré’s stand, it should be on the ground that he showed himself a poor prophet when he claimed that it would always be simpler to retain Euclidean geometry. Einstein has proved the contrary. At all events, in what is to follow, we will concern ourselves solely with the real space of the physicist, that is, with the space to which he is led when he seeks to co-ordinate phenomena with the maximum of simplicity. With this understanding of space in our minds, a first reason for rejecting the concept of an amorphous space arises when we find that a large number of different methods of investigation all point to the same definite metrics for space. Thus, the various material bodies we encounter are by no means identical in nature; some are light, others are heavy, and their chemical and molecular constitutions are certainly not the same. And yet in every case, whether our rods be of wood, of stone, or of steel, we obtain the same Euclidean results provided we operate as far as possible under the same conditions of temperature and pressure. In other words, there appears to be a sameness in our determinations of congruence regardless of the material bodies to which we appeal.

This uniqueness of the geometry of space is still further exemplified in the following example: Here are two totally different methods of exploring space, one with material rods giving us a physical definition of congruence, and one with light-ray triangulations giving us a physical definition of geodesics. In either case we are led to the same Euclidean geometry, and this concordance appears rather strange, for we might have expected that if the geometry we credited to space were irrelevant to space, the type of geometry obtained would have varied according to the physical exploration method considered. Besides, if space were amorphous, hence possessed no geodesics, it would be inconceivable that a free body or a light pulse should know how and where to move. The very definiteness and Euclidean straightness of the paths of free bodies and light rays, when referred to a certain frame of reference, would seem to indicate that space had a structure and was not amorphous.

To be sure, in view of modern discoveries there is nothing very strange in the fact that the courses of free bodies should coincide with the paths of light waves, since light has been proved to possess momentum just as matter does. But even so, it appears strange that the courses defined by moving bodies should yield the same geometry as measurements conducted with bodies at rest.

Then again, there are the dynamical properties of space, which we cannot afford to neglect. If physical space were amorphous, all paths through space should be equivalent, and yet centrifugal force and forces of inertia manifest themselves for certain paths and motions and not for others. Whence could these forces arise if not from the structure of space itself? Such was indeed Newton’s contention.

In view of all these occurrences, difficult to account for if we believe in the amorphous nature of space, unless we appeal to some miraculous pre-established harmony, it appears as though space must be credited with a definite structure or metrics which, in the light of experiment, turns out to be Euclidean, at least to a first approximation. Expressed in a different way, real space appears to be permeated by an invisible field, the Metrical Field, endowing it with a metrics or structure.

Now, in view of the fact that the mathematical requirements of that void we call empty space preclude it from having a metrical field (i.e., a structure or a metrics per se), the simplest way out of the difficulty is to assume that real space is not truly empty, but is filled with some mysterious physical medium, which we may call the “ether,”[15] and that it is this physical medium and not space itself which possesses a Euclidean structure. Henceforth it will be this ether structure which will be responsible for the apparent metrics or metrical field of space, which will cause material bodies to settle into definite shapes, and which will regulate the courses of light rays and free bodies far from matter.

For the physicist, however, this ether will be inseparable from real space; so that, to all intents and purposes, when the physicist discusses real space he will be referring to space together with its ether content. Were this ether structure to vanish, space would become amorphous, bodies would not know what shape to take, and light rays would not know where and how to move.

At this stage we must mention the premonitions of Riemann on the subject of the metrical field of real space. Riemann did not attribute this structure of space to the presence of some invisible medium, the ether, possessing a structure of its own. According to him the origin of the metrical field should be sought elsewhere. He felt that the metrical field of space should be compared to a magnetic or an electric field pervading space. And just as a magnetic field exists in the space surrounding a magnet, Riemann searched for the physical cause of the metrical field. With characteristic boldness, he found it in the matter of the universe; the metrical field thus became a species of material field. If Riemann’s ideas are accepted we can understand how a redistribution of the star matter in the universe, altering as it would the lay of the metrical field, would produce deformations in the shape of a given body and variations in the paths of light rays. As Weyl tells us, a spherical ball of clay compressed into any other form might again be made to appear spherical were all the matter in the universe to be redistributed in a suitable way.

It would also follow that were all the matter in the universe to be annihilated, and as a result the metrical field to vanish, space (assuming that any physical meaning were left the term) would become completely amorphous, just like mathematical space; light rays would not know where to move, all geodesics having disappeared; and were one lone material body to be introduced into otherwise empty space, it would not know what shape to take. Without the metrical field, physical space would be unthinkable.