768 



SCIENCE 



[N. S. Vol. XXXI. No. 803 



pressed that such an idea was clearly 

 against common sense. 



The whole principle of relativity may be 

 based on an answer to the question : When 

 are two events which happen at some 

 distance from each other to be considered 

 simultaneous? The answer, "When they 

 happen at the same time," only shifts the 

 problem. The question is, how can we 

 make two events happen at the same time 

 when there is a considerable distance be- 

 tween them. 



Most people will, I think, agree that one 

 of the very best practical and simple ways 

 would be to send a signal to each point 

 from a point half-way between them. 

 The velocity with which signals travel 

 through space is of course the characteristic 

 "space velocity," the velocity of light. 



Two clocks, one at A and the other at 

 B, can therefore be set running in unison 

 hy means of a light signal sent to each 

 from a place midway between them. 



Now suppose both clock A and clock B 

 are on a kind of sidewalk or platform 

 moving uniformly past us with velocity 

 V. In Fig. 1 (2) is the moving platform 

 and (1) is the fixed one, on which we con- 

 sider ourselves placed. Since the observer 

 on platform (2) is moving uniformly he 

 can have no reason to consider himself 

 moving at all, and he will use just the 

 method we have indicated to set his two 

 clocks A and B in unison. He will, that is, 



C 



B 



send a light flash from C, the point mid- 

 way between A and B, and when this flash 

 reaches the two clocks he will start them 

 with the same reading. 



To us on the fixed platform, however, it 



will of course be evident that the clock B 

 is really a little behind clock A, for, since 

 the whole system is moving in the direc- 

 tion of the arrow, light will take longer to 

 go from C to B than from C to A. Thus 

 the clock on the moving platform which 

 leads the other will be behind in time. 



Now it is very important to see that the 

 two clocks are in unison for the observer 

 moving with them (in the only sense in 

 which the word "unison" has any mean- 

 ing for him), for if we adopt the first pos- 

 tulate of relativity, there is no way in 

 which he can know that he is moving. In 

 other words, he has just as much funda- 

 mental right to consider himself station- 

 ary as we have to consider ourselves sta- 

 tionary, and therefore just as much right 

 to apply the midway signal method to set 

 his clocks in unison as we have in the 

 setting of our "stationary clocks." "Sta- 

 tionary" is, therefore, a relative term and 

 anything which we can say about the mov- 

 ing system dependent on its motion, can 

 with absolutely equal right be said by the 

 moving observer about our system. 



We are, therefore, forced to the conclu- 

 sion that, unless we discard one of the two 

 relativity postulates, the simultaneity of 

 two distant events means a different thing 

 to two different observers if they are mov- 

 ing with respect to each other. 



The fact that the moving observer dis- 

 agrees with us as to the reading of his two 

 clocks as well as to the reading of two sim- 

 ilar clocks on our "stationary" platform, 

 gives us a complete basis for all other dif- 

 ferences due to point of view. 



A very simple calculation will show that 

 the difference in time between the two 

 moving clocks is^ 



* The time it takes light to go from C to B is 

 J/(F — v) and the time to go from (7 to A is 

 i/(V + v). The difference in these two times is 

 the amount by which the clocks disagree and this 



