Since the “Interval” of two events is the same for two observers moving at uniform and different velocities, it is natural to think that it will be the same for a third observer whose velocity increases from that of the first to that of the second—that is to say, whose velocity is uniformly accelerated.
There is, in fact, no reason why the passengers in a train which runs at a uniform speed of sixty miles an hour should observe an “invariant” element in phenomena just as do those in another train moving at half the speed, yet this “invariant” should cease to be such for the passengers in a third train which passes gradually from the velocity of the first train to that of the second. To admit the contrary would be to grant a privileged position in the universe to the first two and others like them. If there is any estate in the world that has had its unjust privileges suppressed by the new physics, it is the study of the material world.
This privilege of observers moving at a uniform velocity would be the less justified as, if we go to the root of the matter, it is very difficult to say exactly what a uniform movement is.
What do we mean when we say that a train has a uniform velocity of sixty miles an hour? We mean that the train has this velocity in reference to the rails or the ground. But in reference to an observer in a balloon, or who passes in another train, the velocity has not the same value, and it may cease to be a uniform velocity. We know only relative movements, or, to be quite accurate, movements relative to some material object or other. According to our choice of this object, this standard of comparison, the same velocity may be uniform or accelerated. In the long run, it is clear, we should have to have recourse to Newton’s hypothesis of absolute space to be able to say whether a given velocity is really uniform or accelerated.
That is the profound reason why the Einsteinian “Interval” of things, the invariable quantity or “Invariant,” must be the same for all observers whatever be their velocity, and in particular for observers moving at velocities equivalent, in a given place, to the effects of gravitation.
But in that case the inferences we draw from the Michelson experiment, in regard to the aspect of phenomena for observers in uniform different movements of translation, no longer suffice to explain to us the whole of reality. They need to be completed in such fashion that the universal invariant, the “Interval” of things, remains the same for an observer who is moving in any way whatever.
If I pass along a street at some unheard-of speed, but with a uniform motion, its general aspect may, on account of the contraction caused by my velocity, be a little different from what it would seem to me if I were stationary.[12] The houses, for instance, will seem narrower in proportion to their height. Nevertheless the general aspect and proportions of objects will be much the same in both cases, and they will have something in common. Thus the gas-lights will seem to me thinner, but they will be straight.
It will be quite otherwise if the observer’s movements are varied: if, for instance, we imagine him a drunken giant, reeling about at a prodigious speed. For such an observer the street will have quite a new aspect. The gas-jets will no longer be straight, but zigzag, reproducing in an inverse way the zigzags which he himself makes as he reels along. This is so true that caricaturists generally represent the trees and lamp-posts and houses seen by a drunken man by ridiculously waving lines.
Our observer will be convinced that objects really have the zigzag forms which he sees, and that the forms change at every step he takes. Try to tell him that it is he who is dancing, not the objects; that it is he who is not walking straight, not the dog he has on leash. He will not believe it—and from the point of view of General Relativity he is neither more nor less right than you.
Yet there is something in the aspect of the world that must be common to the drunkard and the drinker of water.