Page:Popular Science Monthly Volume 84.djvu/441

of them be carried to the point B, can not they then be said to be together? Let us examine this relative motion of one clock with respect to another, in the light of the first principle of relativity. Let there be two observers as before with identical clocks, and for simplicity, suppose A is at rest and B moving on the line BX (Fig. 4). Suppose further BX parallel to AY. Let now A send out a light signal which is Fig. 4. reflected on the line BX and returns to A. The signal has then traveled twice the distance between the lines in a certain time. B then repeats the same experiment, for, as far as he knows, he is at rest, and A moving in the opposite direction. The signal traverses twice the distance between the lines, and B's clock must record the same interval of time as A's did. But now suppose B's experiment is visible to A. He sees the signal leave B, traverse the distance between the lines, and return, but not to the point B, but to the point to which B has moved in consequence of his velocity. That is, A sees the experiment as in Fig. 5, where the position of B' depends on B's velocity with respect to A. The state of affairs is to A then simply this: A signal with a certain known velocity has traversed the distance ABA while his (A's) clock has registered a certain time interval. The same signal, moving with the same velocity, has traversed the greater distance BOB' while B's clock registers exactly the same time interval. The only conclusion is that to A, B's clock appears to be running slow as we say, and its rate will depend on the relative velocity of A and B. Thus we are led to a second conclusion regarding time in the relativity mechanics. To an observer on one body the time unit of another body moving relative to the first body varies with this relative velocity. This last conclusion regarding time is certainly staggering, for it takes away from us what we have long Fig. 5. regarded as its most distinguishing characteristic, namely, its steady, inexorable, onward flow, which recognizes neither place nor position nor movement nor anything else. But now in the new mechanics it appears only as a relative notion, just as velocity is. There is no more reason why two beings should be living at the same rate, to coin an expression, than that two railroad trains should be running at the same speed. It is no longer a figure of speech to say that a thousand years are but as yesterday when it is past, but