The Relativity of Time and Space

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. The Relativity of Time and Space

The Relativity of Time and Space

[The degree to which distance and time become relative instead of absolute quantities under the Special Theory of Relativity can be stated very definitely. In the first place, we must point out [92]that the relativity of lengths applies with full force only to lengths that lie parallel to the direction of relative motion. Those that lie exactly perpendicular to that direction come out the same for both observers; those that lie obliquely to it show an effect, depending upon the angle, which of course becomes greater and greater as the direction of parallelism is approached.

[The argument that these formulae are contradicted by human experience can be refuted by examining a concrete instance. If a train is 1,000 feet long at rest, how long will it be when running a mile a minute?]232 [I have quoted this question exactly as it appears in the essay from which it is taken, because it is such a capital example of the objectionable way in which this business is customarily put. For the statement that lengths decrease and time-intervals increase “with velocity” is not true in just this form. The velocity, to have meaning, must be relative to some external system; and it is the observations from that external system that are affected. So long as we confine ourselves to the system in which the alleged modifications of size are stated as having taken place, there is nothing to observe that is any different from what is usual; there is no way to establish that we are enjoying a velocity, and in fact within the intent of the relativity theory we are not enjoying a velocity, for we are moving with the objects which we are observing. It is inter-systemic observations, and these alone, that show the effect. When we travel with the system under observation, we get the same results as any [94]other observer on this system; when we do not so travel, we must conduct our observations from our own system, in relative motion to the other, and refer our results to our system.

Now when no particular observer is specified, we must of course assume an observer connected with the train, or with whatever the body mentioned. To that observer it doesn’t make the slightest difference what the train does; it may stand at rest with respect to some external system or it may move at any velocity whatsoever; its length remains always 1,000 feet. In order for this question to have the significance which its propounder means it to have, I must restate it as follows: A train is 1,000 feet long as measured by an observer travelling with it. If it passes a second observer at 60 miles per hour, what is its length as observed by him? The answer is now easy.]* [According to the formula the length of the moving train as seen from the ground will be

feet, a change entirely too small for detection by the most delicate instruments. Examination of the expression K shows that in so far as terrestrial movements of material objects are concerned it is equal to 1]232 [within a far smaller margin than we can ever hope to make our observations. Even the diameter of the earth, as many of the essayists point out, will be shortened only 2½ inches for an outside observer past whom it rushes with its orbital speed [95]of 18.5 miles per second. But slight as the difference may be in these familiar cases, its scientific importance remains the same.]*

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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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