714 PROCEEDINGS OF THE AMERICAN ACADEMY. 



which is reflected back to the starting point. He measures the time 

 taken by the light in transit. 



A, assuming that his system is at rest (and the other in motion), 

 considers that the light passes over the path opo, but he believes that 

 if a similar experiment is conducted by an observer, B, in the moving 

 system, the light must pass over the longer path mum' in order to 

 return to the starting point ; for the point m moves to the position m' 

 while the light is passing. He therefore predicts that the time required 

 for the return of the reflected beam will be longer than in his own ex- 

 periment. A, however, having established communication with B, learns 

 that the time measured is the same as in his own experiment. 8 



a o n < — <~ & 



1 ft 



i 

 I 



I / 



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/ 



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\ 



\ 

 \ 



\ 

 \ 



\ 

 \ 



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b P ml m ^j^ & 



Figure 1. 



The only explanation which A can offer for this surprising state of 

 affairs is that the clock used by B for his measurement does not keep 

 time with his own, but runs at a rate which is to the rate of his own 

 clock as the lengths of the paths opo to mum'. 



B, however, is equally justified in considering his system at rest and 

 A's in motion, and by identical reasoning has come to the conclusion 

 that A's clock is not keeping time. Thus to each observer it seems that 

 the other's clock is running too slowly. 



This divergence of opinion evidently depends not so much on the 

 fact that the two systems are in relative motion, but on the fact that 

 each observer arbitrarily assumes that his own system is at rest. If, 

 however, they both decide to call A's system at rest, then both will 

 agree that in the two experiments the light passes over the paths opo 



8 This is evidently required by the principle of relativity, for contrary to 

 A's supposition the two systems are in fact entirely symmetrical. Any differ- 

 ence in the observations of A and B would be due to a difference in the abso- 

 lute velocity of the two systems, and would thus offer a means of determining 

 absolute velocity. 



