204 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1921. 



MEASUREMENT OF TIME ALSO ONLY RELATIVE. 



Now how about measuring times? 



Let us go back to our observer with his mirror and call him A, and 

 suppose that at the mirror there is a second observer whom we will 

 call B, and that both observers have clocks which run with perfect 

 accuracy, and are able to observe the time of anything with the aid 

 of their clocks as precisely as you please. 



Now let us suppose that exactly at 12 noon A sends a flash of light 

 out toward B. B perceives it at the instant when it is reflected by 

 his mirror and notes the time as exactly one second past 12 o'clock. 

 A observes the reflected signal at two seconds past 12 o'clock. 



Repetitions of this signal on successive days give exactly the same 

 result. A and B will conclude that the distance between them does 

 not change (since it always takes light the same time to make the 

 round trip) and that their clocks are running at the same rate. 



Now suppose that A and B regard themselves as at rest. They 

 will then agree that the distance between them is 186,000 miles, since 

 it takes light one second to go each way, and they will also agree that 

 their clocks are not merely running at the same rate but are exactly 

 synchronized, because the light must have reached B just one second 

 after it left A. 



But now suppose that A and B agree in the belief that they are 

 moving through space with half the speed of light, so that they are 

 following the same track with B preceding A. 



Using the same principle of the stern chase of which we have 

 spoken before, they will now figure out their distance apart is not 

 186,000 miles, but just three-fourths as much, or 139,500 miles, and 

 also that the light in going outward over this distance from A to B 

 on the stern chase took one and a half seconds, whereas in coming 

 back it occupied only one-half second. 



This change in the distance amounts to exactly the same thing 

 which we described a few moments ago; but there will be a second 

 interesting change with respect to their measurement of time. For 

 since they now believe that the light took one and a half seconds to 

 go out, the time when it reached B was one and a half seconds past 

 noon by A's clock and only one second past noon by B's clock. 



Hence they will agree that B's clock is half a second fast. 



On the other hand, it is easy to see that, if they had supposed them- 

 selves to be going along the same line, and at the same rate of speed, 

 but in the opposite direction, they would have concluded that B's 

 clock was half a second slow. 



We reach, therefore, the still more picturesque conclusion that the 

 question whether or not two events which take place at different points 

 of space are simultaneous or occur at different times cannot be an- 



