There being no longer any reason to subordinate one frame to another, the descriptions of all phenomena in terms of space and time are on the same footing in all Galilean frames; and there is no longer any reason to follow Lorentz in limiting the validity of the transformations to the sole case of electromagnetic phenomena. Henceforth, these transformations appear of universal application, holding for mechanics, for the composition of velocities, and indeed for the entire universe of physical phenomena. This belief is not dependent on the fact that, matter being constituted electronically, all mechanical experiments must be regarded as electrodynamic experiments viewed microscopically. Rather is it due to the fact that these changes in space and time are absolutely general. They arise from the relative motion of the observer and not from the peculiar microscopic constitution of the phenomena observed.
The method of presentation of Einstein’s theory we have followed up to this stage is not the one usually adhered to, but it has appeared preferable to proceed as we have done in order to bring into prominence certain important features which are obscured in the customary presentation (these features will be better understood later). We will now fall in with the usual procedure.
As Maxwell proved many years ago, a necessary consequence of the laws of electromagnetics was that light waves in vacuo in the stagnant ether should travel with a velocity of 186,000 miles per second. This was the celebrated law of light propagation of classical science. Now we have seen that the laws of electromagnetics (and with them their immediate consequence, the law of light propagation) held only for privileged observers, those situated in any frame at rest in the stagnant ether. As referred to all other Galilean observers situated in frames moving through the ether, an application of the classical transformations showed that the equations of electromagnetics, and with them the velocity of light propagation, would be modified. But since the essence, of the relativity of Galilean motion is to deprive any particular Galilean observer of his privileged position, the laws of electromagnetics must now maintain the same form for all Galilean observers. Hence the law of light propagation, which is a mathematical consequence of these electromagnetic laws, must likewise hold in exactly the same way for all Galilean observers. Whence the new result: “Light waves must travel with the same invariant speed of 186,000 miles through any Galilean frame when this speed is measured by the observer located in the frame.” It is this statement which Einstein has called the principle or the postulate of the invariant velocity of light.
If we combine this principle with the relativity of the ether for Galilean motion and endeavour to construct the transformations which will be compatible with these two principles, we are again led to the Lorentz-Einstein transformations.[46] This should not surprise us since, as we have seen, the principle of the invariant velocity of light is but a direct consequence of the invariance of the electrodynamical equations; so that the transformations ensuring invariance will be the same in either case.
In short, we see that without appealing directly to the equations of electrodynamics, we can deduce the Lorentz-Einstein transformations merely by taking one of their consequences into consideration, namely, the invariant velocity of light, and combining it with the relativity of Galilean motion. From a mathematical point of view, this procedure is the simpler. Hence, Einstein posits as his fundamental assumptions:
1. The relativity of space or of the ether for Galilean motion, or, more simply, the relativity of Galilean motion without particular reference to the ether or to space.
2. The postulate or principle of the invariant velocity of light.
This procedure followed by Einstein offers a number of advantages. In the first place, as we have said, the mathematical discovery of the Lorentz-Einstein transformations is considerably simplified. Secondly, as the classical law of light propagation, though a consequence of the laws of electromagnetics, insusceptible of being tested by direct experiment without any reference to the laws of electromagnetics, there is no necessity for dragging in these highly complex laws. In fact, even had the laws of electromagnetics been unknown, the relativity of velocity and the classical law of light propagation are all that would have been required to construct the theory. Hence, from the standpoint of mathematical elegance, the procedure is certainly one of extreme simplicity. Furthermore, inasmuch as in Einstein’s theory the Lorentz-Einstein transformations are of general application and do not concern only electromagnetic phenomena, it is preferable to avoid conferring on them an exclusively electromagnetic aspect. This aim is achieved by deducing them from a general law of propagation, such as that of light.
On the other hand, this method of presentation, by appealing to the propagation of light, is likely to confuse the beginner, who is apt to assume that Einstein postulated the invariant velocity of light as a hypothesis ad hoc for the sole purpose of accounting for Michelson’s negative experiment. In this way the entire theory is supposed to hinge on Michelson’s experiment, and the critic assumes that could Michelson’s experiment be explained in some other way, Einstein’s theory would be obviated. This assumption appears all the more natural to the critic as Michelson’s experiment is, nine times out of ten, the only negative experiment he is acquainted with. The result is that he assumes Einstein’s theory to be nothing but a wild guess grafted on one of those highly delicate experiments where the chances of error are always great. As a matter of fact, by reasoning in this way, the critic loses sight of the entire raison d’être of the theory. It is safe to say that even had Michelson’s experiment never been performed, Einstein’s theory would have been forthcoming just the same (though, of course, had Michelson’s experiment given a positive result, enabling us to measure our velocity through the ether, the theory of relativity would have been untenable).
This explains why, in presenting the theory, we started by showing how it arose as a necessary consequence of the irrelevance of absolute velocity in all electromagnetic experiments, hence sprang from the invariance of the equations of electrodynamics, which expresses mathematically the aggregate of all the negative results. If the reader has grasped the significance of these Lorentz-Einstein transformations, we may proceed to examine certain of their particular consequences, and to show how, quite apart from the negative experiments, the theory of relativity has cleared up a number of obscure points in our understanding of electromagnetics.