Einsteinian Optics

Abstract

Relativity provided an ideally simple solution to a problem that had considerably exercised the ingenuity of theoreticians before. The question is, to what extent a flowing liquid will “drag” light along with it. Flowing air, of course, drags sound along totally, but the optical situation is different: on the basis of an ether theory, it would be conceivable that there is no drag at all, since light is a disturbance of the ether and not of the liquid. Yet experiments indicated that there was a drag: the liquid seemed to force the ether along with it, but only partially. If the speed of light in the liquid at rest is u’, and the liquid is set to move with velocity v, then the speed of light relative to the outside was found to be of the form

$$u = u' + kv,\;\;k = 1 - 1/{n^2}$$

((3.1))

where k is the “drag coefficient,” a number between zero and one indicating what fraction of its own velocity the liquid imparts to the ether within, and n is the refractive index c/u’ of the liquid. Fifty years before Einstein, Fresnel succeeded in giving a plausible ether-based explanation of this. From the point of view of special relativity, however, the result (3.1) is nothing but the relativistic velocity addition formula!