An Einsteinian Experiment

Einstein's Theories of Relativity and Gravitation by Albert Einstein, is part of the HackerNoon Books Series. You can jump to any chapter in this book here. An Einsteinian Experiment

An Einsteinian Experiment

Let us imagine an indefinitely long, straight railroad track, with an observer located somewhere along it at the point M. According to the convention suggested above, he has determined points A and B in opposite directions from him along the

track, and equally distant from him. We shall imagine, further, than a beneficent Providence supplies two lightning flashes, one striking at A and one at B, in such a way that observer M finds them to be simultaneous.

While all this is going on, a train is passing—a very long train, amply long enough to overlap the section AMB of the track. Among the passengers [87]there is one, whom we may call M′, who is directly opposite M at the instant when, according to M, the lightning strikes. Observe he is not opposite M when M sees the flashes, but a brief time earlier—at the instant when, according to M’s computation, the simultaneous flashes occurred. At this instant there are definitely determined the points A′ and B′, on the train; and since we may quite well think of the two systems—train-system and track-system—as in coincidence at this instant, M′ is midway between A′ and B′, and likewise is midway between A and B.

Now if we think of the train as moving over the track in the direction of the arrow, we see very easily that M′ is running away from the light from A and toward that from B, and that, despite—or if you prefer because of—the uniform velocity of these light signals, the one from B reaches him, over a slightly shorter course, sooner than the one from A, over the slightly longer course. When the light signals reach M, M′ is no longer abreast of him but has moved along a wee bit, so that at this instant when M has the two signals, one of these has passed M′ and the other has yet to reach him. The upshot is that the events which were simultaneous to M are not so to M′.

It will probably be felt that this result is due to our having, somewhat unjustifiably and inconsistently, localized on the train the relative motion between train and track. But if we think of the track as sliding back under the train in the direction opposite to the arrow, and carrying with it the points A and B; and if we remember that this in no way [88]affects M’s observed velocity of light or the distances AM and BM as he observes them: we can still accept his claim that the flashes were simultaneous. Then we have again the same situation: when the flashes from A and from B reach M at the same moment, in his new position a trifle to the left of his initial position of the diagram, the flash from A has not yet reached M′ in his original position while that from B has passed him. Regardless of what assumption we make concerning the motion between train-system and track-system, or more elegantly regardless of what coordinate system we use to define that motion, the event at B precedes that at A in the observation of M′. If we introduce a second train moving on the other track in the opposite direction, the observer on it will of course find that the flash at A precedes that at B—a disagreement not merely as to simultaneity but actually as to the order of two events! If we conceive the lightning as striking at the points A′ and B′ on the train, these points travel with M′ instead of with M; they are fixed to his coordinate system instead of to the other. If you carry out the argument now, you will find that when the flashes are simultaneous to M′, the one at A precedes that at B in M’s observation.

A large number of experiments more or less similar in outline to this one can be set up to demonstrate the consequences, with regard to measured values of time and space, of relative motion between two observers. I do not believe that a multiplicity of such demonstrations contributes to the intelligibility of the subject, and it is for this reason that I have cut loose from immediate dependence upon [89]the essayists in this part of the discussion, concentrating upon the single experiment to which Einstein himself gives the place of importance.

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This book is part of the public domain. Albert Einstein (2020). Einstein's Theories of Relativity and Gravitation. Urbana, Illinois: Project Gutenberg. Retrieved October 2022.

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