The evolution of scientific thought from Newton to Einstein

by A. D'Abro

First in order among these tests we must mention the well-known phenomenon of astronomical aberration, according to which the direction of incidence of a ray of starlight varies annually as the earth circumnavigates the sun. The obvious analogy of this phenomenon is the slanting direction followed on the window pane of a moving train by raindrops which to an observer stationed on the embankment would appear to be falling vertically. This analogy might tempt us to assume that inasmuch as the slant of the raindrops on the pane permits us to deduce the speed of our train through the stagnant atmosphere, so now the slant of the ray of starlight resulting from the earth’s motion should yield us our velocity through the stagnant ether. But the conclusion would be faulty; for if we reflect we shall see that we were able to deduce our motion through the atmosphere, solely because we had reason to assume that had our train stood motionless in the atmosphere the raindrops would have appeared to fall vertically. But in the case of astronomical aberration we have no means of basing our deductions on any such preliminary information. We cannot tell from what directions the rays of starlight would appear to issue were we at rest in the ether; for we ignore the true positions of the stars. And so all that astronomical aberration can yield us is the annual variation in our velocity through the ether, hence our velocity relative to the sun.[39] In short, astronomical aberration does not enable us to detect our absolute speed through the ether, and we must rely on other means.

In all the experiments we shall have occasion to mention, the velocity through the ether which we shall seek to determine will be that of our earth; for, attached as we are to the earth’s surface, this will be the speed we shall best be in a position to determine. Unfortunately, the earth does not constitute a truly Galilean frame on account of its acceleration or rotation round its axis. However, this acceleration of the points on the earth’s surface is very small and the centrifugal force to which it gives rise is scarcely perceptible. Calculation shows that, so far as optical and electromagnetic experiments are concerned, we may regard a frame attached to the earth as constituting a Galilean frame, possessing velocity but no acceleration, at least as a first approximation. Nevertheless this statement is not altogether correct. Experiments can be devised both in mechanics and in optics which would reveal the earth’s acceleration or rotation. Of course this is only natural, since acceleration, in contradistinction to velocity through space, is known to be absolute.

A proper understanding of Einstein’s theory requires that this point be fully understood, so we must be excused for repeating once more that all we are concerned with at present is to reach a decision on the relativity or the absoluteness of velocity or Galilean motion through the ether. In the case of the earth there is no danger of our confusing any possible effects of acceleration with those due to velocity because, owing to the comparative slowness of the earth’s rotationary motion, any effects that might arise from acceleration would in any case be far feebler than those arising from velocity through the ether.

Summarising, we may say that a veritable ether hurricane must be blowing over the earth, varying both in intensity and in direction at the different points of the earth’s surface and also at the various times of the day and year. It is this ether hurricane or ether drift that we must proceed to detect. Now all experiments, whether optical or electrical, obstinately refused to detect the slightest trace of this ether drift; so that one of two things was obvious. Either there was no drift; or else, if drift there was, it was completely concealed by compensating phenomena of which as yet nothing was known. Stokes adopted the first alternative and suggested that the earth in its motion round the sun might possibly drag the ether along with it, in its immediate vicinity at least. It would follow that there could never be any drift on the earth’s surface; and all the negative experiments which had failed to detect the drift would be explained. The obvious objection to Stokes’ hypothesis was the existence of astronomical aberration, which seemed to imply that the earth was moving through a stagnant ether. Stokes, however, proved mathematically that aberration was no argument against his hypothesis; that this phenomenon would still be in order, provided the earth’s motion did not set up whirlpools in the convected ether.

In addition to a number of other difficulties to be explained shortly, we may mention that for the motion of the ether to be such as to satisfy Stokes’ requirements, hence the observed phenomenon of astronomical aberration, calculation proved that the ether could not be incompressible. In fact, Planck showed that on the earth’s surface the ether would have to be 60,000 times denser, and thus correspondingly more compressed than in distant regions; and it would seem strange indeed that this considerable increase in the density of the ether should fail to manifest itself when we compared the results of optical experiments performed on the summit of a high mountain and at sea level. Moreover, light vibrations being transversal, the hypothesis of a rigid ether appeared to be inevitable, so long as we wished to conceive of light as due to vibrations in the ether. Here again the Stokes-Planck theory was difficult to accept.

Lodge endeavoured to subject Stokes’ hypothesis to a direct experimental test. He argued that if the earth were capable of dragging the ether along with it in its motion, the same should be true of other moving bodies. But when he investigated this anticipated drag effect in the case of rapidly revolving disks of steel, he found it entirely absent.

Even if we ignore these contradictions and assume that the terrestrial atmosphere is able to drag the ether along bodily, a new series of difficulties awaits us. A total drag of this sort would be incompatible with a general phenomenon predicted by Fresnel and verified by Fizeau according to which dielectrics in motion (electrical non-conductors), such as water, glass and air, drag the ether along only in a partial way; the percentage of drag increasing with the refractivity of the dielectric. Inasmuch as the refractivity of the atmosphere is comparatively feeble it would be impossible to credit the total drag of the ether to the atmosphere.

A quite recent experiment of Michelson (not to be confused with the celebrated experiment of Michelson and Morley) also renders Stokes’ hypothesis extremely unlikely. The essence of this particular experiment is to send two light rays round the earth in opposite directions. Its result was to prove that the ray travelling eastward required a longer time to complete its circuit than the one travelling westward. Such would not be the case were the earth to drag the ether around with it in its rotation on its axis. True, this experiment did not prove that the ether was not dragged along by the earth’s motion along its orbit, but, on the other hand, it did prove that the earth’s rotationary motion produced no such drag. This, of course, rendered extremely improbable the hypothesis that the earth’s motion along its orbit should be any more successful in producing an ether drag. The aforementioned experiment of Michelson is an apt illustration of the type of experiment which enables us to detect by optical means the earth’s rotation or acceleration through the ether, and is therefore irrelevant to the problem we are here investigating, namely, that of its velocity through the ether. The only reason we mentioned the experiment was because of its bearing on Stokes’ hypothesis.

Stokes’ hypothesis was thus discarded, and the most satisfactory explanation of all negative experiments that had been suggested was given by Fresnel. It must be realised that up to this stage all the experiments attempted were of an optical nature, and related to the transmission of light rays through dielectrics (glass, water, etc.). Such experiments had been performed by Foucault, Airy, and Arago. Fresnel succeeded in proving by mathematical analysis that if dielectrics carried the ether along in their interior in a partial manner, increasing in a definite degree with their refractive power, all the negative results attained up to his day would be explained, provided they were not pursued to too high an order of accuracy. This required percentage of drag of the ether by dielectrics was called Fresnel’s convection coefficient.

Fresnel’s hypothesis was subjected to a direct experimental test. Fizeau discovered, exactly as had been anticipated by Fresnel, that when a ray of light was propagated through running water, the total speed of the light ray with respect to the tube was equal to its speed through the water, when the water was stagnant, plus only a fraction of the water’s velocity in the tube; and that this fraction was precisely equal to the convection coefficient predicted by Fresnel.