“I know that it will be said that we are not measuring its absolute velocity, but its velocity in relation to the ether. That is scarcely satisfactory. Is it not clear that, if we conceive the principle in this fashion, we can make no deductions whatever from it?”
From this it is evident that Poincaré, in spite of himself and all his efforts to avoid it, was disposed to find the distinction between space and ether “scarcely satisfactory.”
I must admit that Poincaré’s own argument seems to me not wholly satisfactory, or at least not convincing. “Nature,” says Fresnel, “cares nothing about analytical difficulties.” I imagine that it cares just as little about philosophical or purely physical difficulties. It is hardly an incontestable criterion to suppose that a conception of phenomena is so much nearer to reality the more “satisfactory” it is to us, or the better it is found adapted to the weakness of the human mind. Otherwise we should have to hold, whether we liked or no, that the universe is necessarily adapted to the categories of the mind; that it is constituted with a view to giving us the least possible intellectual trouble. That would be a strange return to anthropocentric finalism and conceit! The fact that vehicles do not pass there, and that pedestrians have to turn back, does not prove that there are no such things as no-thoroughfares in our towns. It is possible, even probable, that the universe also, considered as an object of science, has its no-thoroughfare.
Clearly one may reply to me that it is not the universe that is adapted to our mind, but the mind that has become adapted to the universe in the evolutionary course of their relations to each other. The mind needs in its evolution to adapt itself to the universe, in conformity with the principle of minimum action formulated by Fermat: perhaps the most profound principle of the physical, biological, and moral world. In that respect the simplest and most economical ideas are the nearest to reality.
Yes, but what proof is there that our mental evolution is complete and perfect, especially when we are dealing with phenomena of which our organism is insensible?
Experiment alone has proved, and had the right to prove, that it is impossible to measure the velocity of an object relatively to the ether. At all events, this is now settled. After all, since it is evidently in the very nature of things that we cannot detect an absolute movement, is it not because the velocity of the earth in relation to the ether is an absolute velocity that we have been unable to detect it? Possibly; but it cannot be proved. If it is so—which is not at all certain—it is in the last resort experience, the one source of truth, which thus tends to prove, indirectly, that the ether is really identical with space. In that case, however, a space devoid of ether, or one containing spheres of ether, would no longer be conceivable, and there can be nothing but a single mass of ether with stars floating in it. In a word, the negative result of Michelson’s experiment could not be deduced a priori from the problematical identity of absolute space and the ether; but this negative result does not justify us in denying the identity a posteriori.
Let us return to our proper subject, the Fitzgerald-Lorentz hypothesis which explains the issue of the Michelson experiment, and which was in a sense the spring-board for Einstein’s leap. The hypothesis is as follows.
The result of the experiment is that, whereas when the path of a ray of light between two mirrors is transverse to the earth’s motion through ether, and it is then made parallel to the earth’s motion, the path ought to be longer, we actually find no such lengthening. According to Fitzgerald and Lorentz, this is because the two mirrors approached each other in the second part of the experiment. To put it differently, the frame in which the mirrors were fixed contracted in the direction of the earth’s motion, and the contraction was such in magnitude as to compensate exactly for the lengthening of the path of the ray of light which we ought to have detected.
When we repeat the experiment with all kinds of different apparatus, we find that the result is always the same (no displacement of the fringes). It follows that the character of the material of which the instrument is made—metal, glass, stone, wood, etc.—has nothing to do with the result. Therefore all bodies undergo an equal and similar contraction in the direction of their velocity relatively to the ether. This contraction is such that it exactly compensates for the lengthening of the path of the rays of light between two points of the apparatus. In other words, the contraction is greater in proportion as the velocity of bodies relatively to the ether becomes greater.