At any rate, once the existence of a semi-material ether was accepted, it was natural to suppose that the motion of our optical and electrical apparatus through its substance should exert a perceptible influence on the results of experiment. Just as the velocity of the wind adds itself to the velocity of sound waves propagated through the atmosphere, so was it logical to anticipate, in view of our understanding of light waves and of electrical phenomena, that an ether wind should carry the light waves and ether strains along with it. Optical and electrical experiments conducted with sufficient refinement should therefore be susceptible of detecting the velocity of our planet through the ether; so that in contradistinction to the relativity of Galilean motion for mechanical phenomena with which the ether was not concerned, Galilean motion would be anything but relative were electromagnetic or optical experiments to be attempted.
Now this duality which was thus assumed to exist in the nature of Galilean motion or velocity, making it relative for mechanical phenomena and absolute for electrodynamic ones, was perfectly acceptable, provided it was permissible to draw a sharp distinction between mechanics and electrodynamics, between space and the ether. But the entire trend of recent research had been to show that this distinction was unjustified. In the first place, matter seemed to be constituted by electrons and protons, hence to be reducible to phenomena of an electromagnetic nature. Then again, electromagnetic phenomena were known to develop mechanical forces. Where, then, was the essential difference between mechanical and electromagnetic phenomena? Under the circumstances how could we account for this anticipated duality in the palpable effects caused by a velocity through the ether, relative or physically meaningless for mechanical experiments, and capable of producing physical effects in electromagnetic ones?
It appeared as though mechanical and electromagnetic phenomena should be susceptible of being placed on the same footing. We should then have to assume that mechanical phenomena together with electromagnetic ones would be affected by velocity through the ether, hence through space, or else to recognise that both electrodynamic and mechanical phenomena could never be influenced by this type of motion. If we should accept the first hypothesis, the Newtonian or mechanical principle of relativity would be overthrown, and with it the entire structure of Newtonian mechanics; and if we should accept the second hypothesis, our understanding of electromagnetic processes and of the ether would have to be modified profoundly. In either case, whether or not electromagnetic and optical experiments succeeded in detecting absolute Galilean motion, science seemed to be faced with a difficult situation.
Classical physicists held to the view that optical and electromagnetic experiments would surely reveal absolute Galilean motion, and they were not perturbed by the fact that as a result Newtonian mechanics might have to be abandoned. Indeed, doubts as to the validity of Newtonian mechanics already presented themselves when Kaufmann and Bucherer showed that electrons in very rapid motion appeared to increase in mass—a phenomenon which was of course incompatible with the Newtonian belief in the invariance of mass, unless some hypothesis ad hoc was to be invoked. It is true that Michelson’s very refined test attempted in 1887 failed to detect any influence of absolute Galilean motion in a certain optical experiment; but it was always assumed that an explanation for this failure would be forthcoming sooner or later, and that other experiments would be successful where Michelson’s had failed. When, therefore, Einstein suggested as a principle of nature that, regardless of whether or not the ether was a necessary hypothesis, Galilean motion through the ether or through space would never be detected by any type of experiment, whether optical or electromagnetic or mechanical, the majority of physicists paid little heed to the new doctrine.
It must not be thought that this hostility of classical physicists to the Einstein theory in its initial stages was due solely to their belief in the absolute and objective nature which it appeared inevitable to credit to the ether. It was due also to other reasons which we shall now proceed to investigate.
From a mathematical point of view, a physical phenomenon reduces to the systematic variation in intensity and in orientation from place to place and from time to time of a number of magnitudes. A physical phenomenon as referred to some arbitrary frame of reference can therefore be expressed by mathematical equations in which the space and time co-ordinates with respect to the frame figure as variables. Now a fundamental problem of theoretical physics is to determine how the equation of a phenomenon referred to a frame
, which is in motion with respect to a frame
, can be obtained from its equation referred to the frame