THE THEORY OF RELATIVITY 437 



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 re- o X>. 



fleeted on the line BX and returns i 



to A. The signal has then trav- | , 



eled twice the distance between 



the lines in a certain time. B i 



then repeats the same experi- /\ "Y 



ment, for, as far as he knows, he Fig. 4. 



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 ap- 

 pears to be running slow as we say, and its rate will depend on the rela- 

 tive velocity of A and B. Thus we are led to a second conclusion regard- 

 ing 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 

 J3 d' - staggering, for it takes away 



f\ / from us what we have long 



regarded as its most distinguish- 

 \ / ing characteristic, namely, its 



\ /' steady, inexorable, onward flow, 



i 



A f* which recognizes neither place 



FlQ> 5 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 









