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 Special Theory and Its Surprising Consequences
The Special Theory and Its Surprising Consequences
It was upon these facts that Einstein based his original, or “special” theory of Relativity. He assumed boldly that the universe is so constituted that uniform straight-ahead motion of an observer and all his apparatus will not produce any difference whatever in the result of any physical process or experiment of any kind. Granting this, it follows that if all objects in the visible universe were moving uniformly together in any direction, no matter how fast, we could not find this out at all. We cannot [310]determine whether the universe, as a whole, is at rest or in motion, and may as well make one guess as another. Only the relative motions of its parts can be detected or studied.
This seems simple and easy enough to understand. But the consequences which follow from it are extraordinary, and at first acquaintance seem almost absurd.
Similar complications arise in the measurement of time. Suppose that we have two observers, A and B, provided with clocks which run with perfect uniformity, and mirrors to reflect light signals to one another. At noon exactly by his clock, A sends a [311]flash of light towards B. B sees it come in at 12:01 by his clock. The flash reflected from B’s mirror reaches A at 12:02 by A’s clock. They communicate these observations to one another.
If A and B regard themselves as being at rest, they will agree that the light took as long to go out as it did to come back, and therefore that it reached B at just 12:01 by A’s clock, and that the two clocks are synchronized. But they may, if they please, suppose that they (and the whole universe) are moving in the direction from A towards B, with half the speed of light. They will then say that the light had a “stern chase” to reach B, and took three times as long to go out as to come back. This means that it got to B at 1½ minutes past noon by A’s clock, and that B’s clock is slow compared with A’s. If they should assume that they were moving with the same speed in the opposite direction, they would conclude that B’s clock is half a minute fast.
Hence their answer to the question whether two events at different places happen at the same time, or at different times, will depend on their assumption about the motion of the universe as a whole.
Once more, let us suppose that A and B, with their clocks and mirrors, are in relative motion, with half the speed of light, and pass one another at noon by both clocks. At 12:02 by A’s clock, he sends a flash of light, which reaches B at 12:04 by his clock, is reflected, and gets back to A’s clock at 12:06. They signal these results to each other, and sit down to work them out. A thinks that he is at rest, and B moving. He therefore concludes that the light had the same distance to go out as to return [312]to him and took two seconds each way, reaching B at 12:04 by A’s clock, and that the two clocks, which agreed then, as well as at noon, are running at the same rate.
B, on the contrary, thinks that he is at rest and A in motion. He then concludes that A was much nearer when he sent out the flash than when he got it back, and that the light had three times as far to travel on the return journey. This means that it was 12:03 by A’s clock at the instant when the light reached B and B’s clock read 12:04. Hence A’s clock is running slow, compared with B’s.
Hence the answer to the question whether two intervals of time, measured by observers who are in motion relative to one another, are of the same or of different durations, depends upon their assumptions about the motion of the universe as a whole.
Now we must remember that one assumption about the motion of the universe as a whole is exactly as good—or bad—as another. No possible experiment can distinguish between them. Hence on the Principle of Relativity, we have left no absolute measurement of time or space. Whether two distances in different directions are to be called equal or not—whether two events in different places are to be called simultaneous or not—depends on our arbitrary choice of such an assumption, or “frame of reference.” All the various schemes of measurement corresponding to these assumptions will, when applied to any imaginable experiment, predict exactly the same phenomena. But, in certain important cases, these predictions differ from those of the old familiar theory, and, every time that such experiments [313]have been tried, the result has agreed with the new theory, and not with the old.
We are therefore driven to accept the theory of relativity, strange as it is, as being more nearly “true to nature” than our older ideas. Fortunately, the difference between the results of the two become important only when we assume that the whole visible universe is moving together much faster than any of its parts are moving relatively to one another. Unless we make such an unwarranted assumption, the differences are so small that it takes the most ingenious and precise experiments to reveal them.
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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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