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. Relativity and Reality

Relativity and Reality

[A simple computation shows that this effect is exactly the amount suggested by Lorentz and Fitzgerald to explain the Michelson-Morley experiment.]188 [This ought not to surprise us, since both that explanation and the present one are got up with the same purpose. If they both achieve that purpose they must, numerically, come to the same thing in any numerical case. It is, however, most emphatically to be insisted that the present “shortening” of lengths]* [no longer appears as a “physical” shortening caused by absolute motion through the ether but is simply a result of our methods of measuring space and time.]188 [Where Fitzgerald and Lorentz had assumed that a body in motion has its dimensions shortened in the direction of its motion,]220 [this very form of statement ceases to possess significance under the relativity assumption.]* [For if we cannot tell which of two bodies is moving, which one is shortened? The answer is, both—for the other fellow. For each frame of reference there is a scale of length and a scale of time, and these scales for different frames are related in a manner involving both the length and the time.]220 [But we must not yield to the temptation to say that all this is not real; the confinement of a certain scale of length and of time to a single observation system does not in the least make it unreal.]* [The situation [96]is real—as real as any other physical event.]165

[The word physical is used in two senses in the above paragraph. It is denied that the observed variability in lengths indicates any “physical” contraction or shrinkage; and on the heels of this it is asserted that this observed variability is of itself an actual “physical” event. It is difficult to express in words the distinction between the two senses in which the term physical is employed in these two statements, but I think this distinction ought to be clear once its existence is emphasized. There is no material contraction; it is not right to say that objects in motion contract or are shorter; they are not shorter to an observer in motion with them. The whole thing is a phenomenon of observation. The definitions which we are obliged to lay down and the assumptions which we are obliged to make in order, first, that we shall be able to measure at all, and second, that we shall be able to escape the inadmissible concept of absolute motion, are such that certain realities which we had supposed ought to be the same for all observers turn out not to be the same for observers who are in relative motion with respect to one another. We have found this out, and we have found out the numerical relation which holds between the reality of the one observer and that of the other. We have found that this relation depends upon nothing save the relative velocity of the two observers. As good a way of emphasizing this as any is to point out that two observers who have the same velocity with respect to the system under examination (and whose mutual relative velocity is therefore zero) will always get [97]the same results when measuring lengths and times on that system. The object does not go through any process of contraction; it is simply shorter because it is observed from a station with respect to which it is moving. Similar remarks might be made about the time effect; but the time-interval is not so easily visualized as a concrete thing and hence does not offer such temptation for loose statement.

The purely relative aspect of the matter is further brought out if we consider a single example both backwards and forwards. Systems S and S′ are in relative motion. An object in S which to an observer in S is L units long, is shorter for an observer in S′—shorter by an amount indicated through the “correction factor” K. Now if we have, in the first instance, made the objectionable statement that objects are shorter in system S′ than they are in S, it will be quite natural for us to infer from this that objects in S must be longer than those in S′; and from this to assert that when the observer in S measures objects lying in S′, he gets for them greater lengths than does the home observer in S′. But if we have, in the first instance, avoided the objectionable statement referred to, we shall be much better able to realize that the whole business is quite reciprocal; that the phenomena are symmetric with respect to the two systems, to the extent that we can interchange the systems in any of our statements without modifying the statements in any other way.

Objects in S appear shorter and times in S appear longer to the external “moving” observer in S′ than they do to the domestic observer in S. Exactly in the same way, objects in S′ appear shorter to observers [98]in the foreign system S than to the home observer in S′, who remains at rest with respect to them. I think that when we get the right angle upon this situation, it loses the alleged startling character which has been imposed upon it by many writers. The “apparent size” of the astronomer is an analogy in point. Objects on the moon, by virtue of their great distance, look smaller to observers on the earth than to observers on the moon. Do objects on the earth, on this account, look larger to a moon observer than they do to us? They do not; any suggestion that they do we should receive with appropriate scorn. The variation in size introduced by distance is reciprocal, and this reciprocity does not in the least puzzle us. Why, then, should that introduced by relative motion puzzle us?

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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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