438 THE POPULAR SCIENCE MONTHLY 



thousand years and yesterday are actually the same time interval pro- 

 vided the bodies on which these two times are measured have a suffi- 

 ciently high relative velocity. 



It is to be noted that in the above discussion, use was made of the 

 fact that the light signal sent out by B appeared to A to have the same 

 velocity as one sent out by A himself. This stated in general terms, the 

 velocity of light in free space appears the same to all observers, regard- 

 less of the motion of the source of light or of the observer, is the second 

 fundamental postulate of relativity. It is an assumption pure and 

 simple, reasonable on account of the analogy between sound and light, 

 and does not contradict any known facts. 



Now there is a second fundamental concept of mechanics, very much 

 resembling time in that we are unable to define it, namely, space. 

 Instead of being one-dimensional, as is time, it is three-dimensional, 

 which is not an essential difference. From the days of Newton and 

 Galileo, physicists have agreed that space like time is everywhere the 

 same, and that it too is independent of any motion or external object. 

 To fix the ideas, consider any one of the units in measuring length, the 

 yard, for example. To be sure, the bar of wood or iron, which in length 

 more or less nearly represents this yard, may vary, as every one knows, 

 in its dimensions, on account of varying temperature or pressure or 

 humidity, or what not, but the yard itself, this unit of linear space which 

 we have arbitrarily chosen, according to all our preconceived notions, 

 neither depends on place nor position, nor motion, nor any other think- 

 able thing. But let us follow through another imaginary experiment in 

 the light of the two fundamental postulates of relativity. Consider 

 again our two observers A and B (Fig. 6), each furnished with a clock 



and a yardstick, A at rest, B mov- 

 £s *ri ^ ing in the direction indicated by 



the arrow. Suppose A sends out a 



hr h\ light signal and adjusts a mirror 



FlG> 6 at C say, so that a ray of light goes 



from A to C and returns in say one 

 second. A then measures the distance AC with his yardstick and finds 

 a certain number. Then B, supposing that he himself is at rest and A 

 in motion, sends out a light signal and adjusts a mirror at D so that a 

 ray travels the distance BD and back again in one second of his time. 

 B then measures the distance BD with his yardstick, and since the veloc- 

 ity of light is the same in any system, B comes out with the same num- 

 ber of units of length in BD as A found in AC But A watching B's 

 experiment sees two remarkable facts: first, that the light has not 

 traversed the distance BDB at all, but the greater distance BD'B' 

 (Fig. 7), where D' and B' are the points, respectively, to which D and B 



