We must be careful not to confuse the present situation with that entailed by atomism, for example. Even to-day we can scarcely say that atoms have been observed in the same sense that stones and tables have been observed; nevertheless, the majority of scientists accepted the existence of atoms years ago, because by postulating their presence a number of phenomena could be co-ordinated with simplicity. Thus, though eluding direct detection, atoms were demanded by indirect mathematical reasoning. Nothing similar is observed in the case of absolute velocity. We insist on this point because it is sometimes thought that the theory of relativity is essentially phenomenological. In a wide sense this is true, but it is most certainly not true if by phenomenalism we understand the word in its narrower sense. An out-and-out phenomenologist, such as Mach, would go so far as to deny the existence of atoms merely because they had never been observed by human eyes, regardless of whether it was useful to conceive of them for the purpose of co-ordinating empirical facts. This is not the attitude of science. But if by phenomenalism we mean the desire to free our understanding of things from unnecessary metaphysical notions which are in no wise demanded by experiment, then we are undoubtedly justified in claiming that not only the theory of relativity, but modern science itself, is essentially phenomenological. If these points are clearly understood, we see why it was that Einstein considered it necessary to rid physics of absolute velocity. In short, the exclusion of absolute velocity from science appears to be imposed by experiment; and the only course to adopt is to pursue this train of enquiry in a logical way and see where it will lead us.
We remember that the relativity of velocity, taken in conjunction with the equations of electromagnetics, indicated the invariance of the velocity of light in vacuo, as measured in any Galilean frame. From this, the Lorentz-Einstein transformations followed with mathematical logic. It is these transformations that entail, as we know, the relativity of duration, length and simultaneity. We cannot, therefore, regard the new notions as the result of some pipe dream or some divine inspiration; they were forced on Einstein by his transformation equations, and these, in turn, were derived from the initial principles, hence from ultra-refined experiment. Needless to say, it would have been highly arbitrary, and in fact absurd, to lay down the special principle of relativity before such time as the negative experiments had driven us to it. To proceed on the strength of some divine inspiration prior to the disclosures of experiment would have been to start out on a wild-goose chase. Here it cannot be emphasised too strongly that a belief in the relativity of velocity through the ether does not impose itself a priori; quite the reverse. To put it differently, there is no a priori reason why the equations of electromagnetics should preserve the same form regardless of the velocity of our frame of reference. We may feel more sympathetic towards one doctrine or another, but in the last analysis it is experiment, and experiment alone, which can guide science in such matters.
It is important to understand that at this stage Einstein had discovered only the Lorentz-Einstein transformations together with their inevitable relativistic consequences. There is not the slightest hint, in his writings, of a world of space-time. This great discovery is due to the mathematician Minkowski, who, in the year 1908, proved that the Lorentz-Einstein transformations connoted the existence of a four-dimensional space-time continuum of events. From then on, those concepts of classical science, a space of points and a time of instants, considered by themselves, faded into shadows. Here again, Minkowski’s discovery was purely mathematical. It issued from a simple application of the theory of groups, and no trace of philosophical prejudice can be found in his work.
In short, it was the mathematical equations, hence the ultra-precise experiments, that had rendered inevitable the new outlook of the world. As Minkowski tells us himself in his inaugural address: “The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength.” As for space-time, that amalgamated continuum, it had never even been suggested in the speculations either of scientists or of philosophers. To Einstein himself, the discovery of the four-dimensional space-time world was probably quite as much of a surprise as it was to the world at large; but there was no gainsaying the correctness of Minkowski’s arguments, which any one with an elementary knowledge of mathematics could verify. Thus, although space-time constitutes one of the most astounding philosophic revolutions ever witnessed, yet the procedure which led to its discovery reduces to the customary mathematical treatment of the empirical facts yielded by the experimenters.
Let us examine what bearing these new ideas will have on Newton’s absolute space and motion. Of course, to begin with, space-time taking the place of separate space and time, our outlook of the world is considerably modified. It is modified in the sense that distance, duration and simultaneity are no longer absolute. If, however, we view the problem of space from the standpoint of motion, that cornerstone of the Newtonian synthesis, we find very little change.
The same dynamical facts that had compelled Newton to recognise rotationary motion as absolute drove Einstein once more to the same conclusion. Hence, just as Newton, arguing from the standpoint of space, was compelled to accept absolute space, so now Einstein, arguing from the standpoint of space-time, was driven to absolute space-time. In short, whether we argue in terms of space or of space-time, the dynamical facts of motion appear to impose an absolute background in either case.
Yet, even when confining ourselves to the problem of motion, absolute space-time presents a great advantage over Newtonian absolute space. With absolute space, the difficulty was to account for the elusiveness, relativity or mythical nature of velocity through empty space (embodied in the Newtonian principle of relativity). But with absolute space-time this difficulty is overcome. For absolute space-time, while necessitating the absolute nature of rotation and acceleration, necessitates with equal inevitableness the relativity of velocity. And so the introduction of space-time has served to eliminate that displeasing dualistic feature which was characteristic of Newton’s space. From all this, we see that the fundamental characteristic of the Newtonian synthesis, namely, the presence of a suprasensible absolute frame with respect to which rotation and acceleration would be measured (the inertial frame), remained unaffected. A vindication of Mach’s ideas seemed to be as remote as ever.
Einstein, in the following words, summarises the situation as it stood before the general theory was elaborated:
“The principle of inertia, in particular, seems to compel us to ascribe physically objective properties to the space-time continuum. Just as it was necessary from the Newtonian standpoint to make both the statements, tempus est absolutum, spatium est absolutum, so from the standpoint of the special theory of relativity we must say, continuum spatii et temporis est absolutum. In this latter statement, absolutum means not only ‘physically real,’ but also ‘independent in its physical properties,’ having a physical effect, but not itself influenced by physical conditions.
“As long as the principle of inertia is regarded as the keystone of physics, this standpoint is certainly the only one which is justified.” [150]