Now we have said that when submitted to the classical space and time transformations, the invariance of the equations of electrodynamics does, not hold. It appeared then that, contrary to the negative results of experiment and contrary to Lorentz’s principle of correlation, velocity through the ether should be detectible by electromagnetic experiments. Science was thus placed in an exceedingly difficult position; the equations of electrodynamics had been so strongly confirmed by extremely accurate experiment that we could scarcely question their accuracy. There remained, but one alternative, namely, to suspect the accuracy of the classical transformations.
This was indeed the course followed by Lorentz. He succeeded in establishing the transformations which would be in harmony with the invariance of the electrodynamic equations, and he found these to differ perceptibly from the classical ones; although reducing to the latter in the case of low velocities. The new transformations constitute the celebrated Lorentz transformations.[44]
Translated into ordinary language, these transformations expressed the existence of two separate phenomena: first, the FitzGerald contraction of bodies moving through the ether, a phenomenon with which we are already acquainted; and, secondly, a new phenomenon consisting in the slowing down (with increase of velocity through the ether) of the rate of time-flow as applying to electromagnetic processes. Thus, contrary to the classical transformations, where time was absolute (
), we see that in the Lorentz transformations this absoluteness of time begins to be questioned. For psychological reasons, however, imbued as he was with the spirit of classical science, Lorentz was unable to realise the importance of his discovery; and he never, succeeded in ridding himself of his belief in the absoluteness of time. For him, as also for Larmor, who contributed to these discoveries, this new species of variable duration, depending as it did on the motion through the ether of the Galilean frame, was not real time. It was a species of “local time”—a distortion of real time—and it was not assumed that this local time corresponded in any way to the time which the observer in the moving frame would live and sense.
And so Lorentz assumed that these new transformations applied only to purely electromagnetic quantities, and no reference was made to their being applicable to mechanical phenomena as well. Though, as a result of these transformations, the velocity of light proved to have always the same invariant value through all Galilean frames when measured by the observer in the frame, no suspicion was cast on the classical formula for the composition of the velocities of material bodies; and this in spite of the fact that these two circumstances were mutually incompatible.
It appeared then as if Lorentz still considered the classical transformation-formulæ to be the real ones, the new transformations being merely of limited application and referring solely to the electromagnetic quantities. When, therefore, in such experiments as that of Trouton and Noble, mechanical and purely electromagnetic effects were indissolubly connected, a large measure of obscurity was involved. Lorentz, however, succeeded in extricating himself from his difficulties and in accounting for all the negative experiments; but he was compelled to appeal to additional hypotheses, such as a modification in those elastic forces which cause the electrons to vibrate in transparent bodies (Rayleigh and Brace experiments). In a similar way it was possible to explain the negative result of the Trouton and Noble experiment. Nevertheless, we can understand the numerous difficulties into which Lorentz’s theory was leading us. We knew very little about the constitution of matter, and here, in Lorentz’s theory, we were compelled to account for negative experiments by taking this unknown constitution of matter into consideration.
Taking Lorentz’s theory as it stands, one cannot help but recognise that this accumulation of hypotheses postulated ad hoc makes it painfully artificial. According to the theory, the ether must be regarded as stagnant and the earth as moving through it with some definite velocity. This velocity must, however, remain eternally unknowable to us. Its elusiveness arises from the slowing down of time and the FitzGerald contraction, in the case of the simplest electromagnetic experiments; in the case of experiments dealing with dielectrics and conductors, we have to appeal to still more complicated adjustments pertaining to the constitution of matter. But although forever indiscernible, our velocity through the ether was a reality; it was there, and had it not been for all these compensating effects, it would have been observed. All the forces of the cosmos appeared to have conspired to deprive us of a knowledge we were so anxious to obtain, namely, the velocity of our planet through the ether.
The existence of the FitzGerald contraction, holding in exactly the same degree for all bodies, was an instance of this marvellous conspiracy of nature. Even if we admitted that all matter were electronically constituted, and that the constituent electrons became flattened as a result of their motion through the ether, it was still impossible to conceive of an identical flattening for all bodies, whether rigid or soft, unless we assumed that an appropriate adjustment had also taken place in the other factors entering into the constitution of matter (elastic forces, etc.). The whole theory was unsatisfactory in the extreme. If Nature was blind, by what marvellous coincidence had all things been so adjusted as to conceal a velocity through the ether? And if Nature was wise, she had surely other subjects to attend to, more worthy of her consideration, and would scarcely be interested in hampering our feeble attempts to philosophise. In Lorentz’s theory, Nature, when we read into her system all these extraordinary adjustments ad hoc, is made to appear mischievous; it was exceedingly difficult to reconcile one’s self to finding such human traits in the universal plan.
Possibly more space than was needed has been devoted to a discussion of these difficulties of pre-Einsteinian physics, but the purpose of these lengthy explanations has been to show that science was confronted with an exceedingly difficult situation. Before proceeding to a study of Einstein’s solution, we must mention a tentative hypothesis put forward by the Swiss physicist Ritz.