Einstein's Theories of Relativity and Gravitation / A selection of material from the essays submitted in the competition for the Eugene Higgins prize of $5,000

by J. Malcolm Bird

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, is the greater will therefore depend on his assumption about the motion of the universe as a whole.

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 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 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.