RELATIVITY RUSSELL. 205 



swered until we have defined the uniformly moving frame of refer- 

 ence with respect to which we are to make our measurements and 

 reasoning. 



With the distance that we have assumed the difference between the 

 two clocks would be only a fraction of a second even if the assumed 

 speed was very great. But if we had taken a distance such as that 

 between the remoter stars, whose light takes thousands of years to 

 travel, then, according to our choice of a frame of reference, we might 

 have been led to the conclusion that A's clock was either in agree- 

 ment with B's or fast or slow by several centuries. 



Once again, the possible difference between the results of different 

 assumptions is immeasurably small for such observations as could be 

 made upon our tiny and slowly moving earth. But for such dis- 

 tances as separate the stars and for greater assumed speeds they may 

 become extremely large. 



I might go on to describe what happens if we imagine two ob- 

 servers, A and B, receding from one another with half the speed of 

 light and exchanging signals by a reflection back and forward from 

 mirrors carried by both. As I have not a blackboard, I will spare you 

 the details, which are not hard for anyone to work out who takes a 

 pencil and piece of paper. 



NEW CONCLUSIONS ABOUT SPACE AND TIME. 



I will simply state the result that, given a certain set of definitely 

 observed facts upon which both observers are entirely and perfectly 

 agreed, it is possible that A, if he considers himself at rest, will say 

 that B is receding from him with half the velocity of light and carry- 

 ing a clock which is running at exactly the same rate as his own; 

 while B, who naturally may prefer to think of himself as at rest and 

 the other fellow moving, will believe that A is receding from him 

 with half the speed of light, but will insist that his clock and A's 

 are not keeping together but are running at different rates. 



The root of this extraordinary discrepancy between their opinions 

 will lie in the fact that they divide up the round trip time interval 

 for the reflected light waves in different manners on account of their 

 different assumptions as to whether the reflecting mirrors are at rest 

 or being chased by the light, thereby introducing a difference into 

 their methods of comparing one another's clocks which continually 

 increases as the distance between them increases, and the round trip 

 time for the light with it. 



I have certainly gone far enough now to show you how we are led, 

 if we stick to these apparently simple and harmless principles of 

 relativity, into the most extraordinary conclusions with respect to 

 space and time. 



As someone has well put it, " when-ness " and " where-ness " are 

 all mixed up together. You can't say just when a thing happened 



