Reverting to the motives which had driven Einstein to suspect that matter must modify the space-time structure, we have seen that they were of a totally different nature. The rotating-disk argument was exclusively mathematical; the equivalence of the two masses was based on a fact of experience. Neither of these two arguments was suggested by philosophy, theosophy or theology. To assert, then, that Einstein was influenced by the philosophy of Descartes or Leibnitz or Mme. Blavatsky or any one else would indicate a very poor knowledge of scientific method. Although the new views entail a marked change in our understanding of the relationships between extension and matter, yet there is no irresponsible guesswork in Einstein’s procedure. In particular, there is no desire to impose some special matter-moulding philosophy. If the theory is drifting towards certain philosophical conclusions, it is drifting with the current; and the current is represented by a rational co-ordination of the facts of experience.
We now come to the third argument advanced by Einstein in favour of his matter-modifying space-time theory. We have left it to the last, as it is more philosophical than the two preceding ones. We may condense it into the statement that where there is action there must also be reaction. Now, in rigidly flat space-time, the courses of free bodies must be conceived of as directed by the geometry or structure of space-time. Hence there exists an action of the space-time structure on the bodies. But then there should also exist a reciprocal action of the bodies on the structure. In much the same way, the electron affects the electromagnetic field and, inversely, the field affects the electron. Einstein expresses, in the following words, his dislike for a conception which would conflict with the reciprocity of action:
“In the first place, it is contrary to the mode of thinking in science to conceive of a thing (the space-time continuum) which acts itself, but which cannot be acted upon. This is the reason why E. Mach was led to make the attempt to eliminate space as an active cause in the system of mechanics. According to him, a material particle does not move in unaccelerated motion relatively to space, but relatively to the centre of all the other masses in the universe; in this way the series of causes of mechanical phenomena was closed, in contrast to the mechanics of Newton and Galileo. In order to develop this idea within the limits of the modern theory of action through a medium, the properties of the space-time continuum which determine inertia must be regarded as field properties of space analogous to the electromagnetic field. The concepts of classical mechanics afford no way of expressing this. For this reason Mach’s attempt at a solution failed for the time being.”
If we review the position of the theory as it now stands, we may summarise it as follows: Space-time is primarily an absolute four-dimensional continuum of events. When devoid of matter and energy, its structure is flat. When matter is present, the flat structure yields gently both around matter and in its interior. The yielding, however, is exceedingly slight. Though sufficient to account for gravitation, it is far too insignificant to be detected through direct measurements with rods (this holds at least in the case of the space around the sun). Disturbances of structure, caused by the sudden arrival or passage of matter, are propagated from place to place with the velocity of light, so that gravitation manifests itself as a continuous action through a medium, just like the action of the electromagnetic field. Action at a distance is thus avoided.
And now, what is the bearing of these discoveries on the problem of absolute rotation and absolute space-time? We see that space-time, by yielding slightly in the presence of matter, has lost that absolute rigidity which characterised Newton’s space. Owing to these varying distortions of the space-time background, brought about by variations in the matter distribution, the rotational velocity of a body suffers from a certain measure of indeterminateness. To this extent rotation is no longer absolute.[153] But when we review the sequence of deductions that has led us to this partial rejection of Newton’s belief in absolute rotation, we see that our discoveries have become possible only through the medium of space-time. Had space-time never been discovered, had we remained content with a separate space and time, it would have been quite impossible to establish this indeterminateness of rotation; for it would have been impossible to account for gravitation in terms of the variations in the structure of space alone. As a result, the spatial background would have remained rigid, and Newton’s position would have stood secure.
Even now, though the fluctuating space-time background has been discovered, the absolute nature of rotation has not been fully disproved. For in an empty universe, space-time would still preserve a well-defined rigid structure; hence, if we conceive of one single body introduced into this otherwise empty world, an absolute rotation of this body could always be detected. It would be betrayed by centrifugal forces; and these forces would arise because the particles of the body would be following world-lines which departed from the geodesics, or lines of least resistance, of the space-time structure. For this reason, rotation would still be absolute, since it would preserve a real meaning in a world devoid of matter. In short, it would have nothing to do with a rotation relative to the star-masses. Obviously we are still a long way from having vindicated Mach’s mechanics.
But when it is considered that Einstein’s theory is based on the relativity of velocity, then that it establishes, in a partial way at least, the relativity of acceleration, it cannot be denied that a logical extension of its triumphs would be for it to succeed in establishing the complete relativity of all motion and of inertia. Although Einstein never conceals his hope that this will be the ultimate outcome, there is no desire on his part to force the issue in defiance of facts.
It may, however, be of interest to ascertain what modifications in the theory would be required for the relativity of all motion and of inertia to be established. Inasmuch as it is the inherent structure of space-time persisting even in the absence of matter which is responsible for centrifugal force in an empty world, hence for absolute rotation and inertia, a vindication of Mach’s ideas would entail the following condition: It would be necessary to assume that in the absence of all matter, space-time would lose all trace of a structure and become amorphous. In other words, matter would have to create space-time and its structure (i.e., the
-distribution, or the metrical field), and not merely modify locally a pre-existing structure. It is interesting to note that the relativity of rotation is thus leading us to a concept of space which could not have been anticipated a priori. Mach himself, when defending the relativity of motion, does not appear to have realised that the abandonment of Newton’s absolute space would entail a matter-created universe.