Page:Popular Science Monthly Volume 84.djvu/442

438 thousand years and yesterday are actually the same time interval provided the bodies on which these two times are measured have a sufficiently high relative velocity.

It is to be noted that in the above discussion, use was made of the fact that the light signal sent out by B appeared to A to have the same velocity as one sent out by A himself. This stated in general terms, the velocity of light in free space appears the same to all observers, regardless of the motion of the source of light or of the observer, is the second fundamental postulate of relativity. It is an assumption pure and simple, reasonable on account of the analogy between sound and light, and does not contradict any known facts.

Now there is a second fundamental concept of mechanics, very much resembling time in that we are unable to define it, namely, space. Instead of being one-dimensional, as is time, it is three-dimensional, which is not an essential difference. From the days of Newton and Galileo, physicists have agreed that space like time is everywhere the same, and that it too is independent of any motion or external object. To fix the ideas, consider any one of the units in measuring length, the yard, for example. To be sure, the bar of wood or iron, which in length more or less nearly represents this yard, may vary, as every one knows, in its dimensions, on account of varying temperature or pressure or humidity, or what not, but the yard itself, this unit of linear space which we have arbitrarily chosen, according to all our preconceived notions, neither depends on place nor position, nor motion, nor any other thinkable thing. But let us follow through another imaginary experiment in the light of the two fundamental postulates of relativity. Consider again our two observers A and B (Fig. 6), each furnished with a clock and a yardstick, A at rest, B moving in the direction indicated by the arrow. Suppose A sends out a light signal and adjusts a mirror at C say, so that a ray of light goes from A to C and returns in say one second. A then measures the distance AC with his yardstick and finds a certain number. Then B, supposing that he himself is at rest and A in motion, sends out a light signal and adjusts a mirror at D so that a ray travels the distance BD and back again in one second of his time. B then measures the distance BD with his yardstick, and since the velocity of light is the same in any system, B comes out with the same number of units of length in BD as A found in AC But A watching Bs experiment sees two remarkable facts: first, that the light has not traversed the distance BDB at all, but the greater distance BD'B (Fig. 7), where D and B are the points, respectively, to which D and B