May 20, 1910] 



SCIENCE 



769 



i/y^/(i-^=) 

 where 



Z = distance between clocks A and B; 

 V = velocity of moving system ; 

 y = velocity of light ; 

 ^ = v/V. 



The way in which this difference of opin- 

 ion with regard to time between the moving 

 ing observer and ourselves leads to a differ- 

 ence of opinion with regard to length also 

 may very easily be indicated as follows: 



A -» B B' 



M 



E N 



Suppose the moving observer desires to 

 let us know the distance between his clocks 

 and says he will have an assistant sta- 

 tioned at each clock and each of these, at a 

 given instant, is to make a black line on 

 our platform. He will, therefore, he says, 

 be able to leave marked on our platform 

 an exact measure of the length between his 

 clocks and we can then compare it at leis- 

 ure with any standard we choose to apply. 



"We, however, object to this measure left 

 with us, on the ground that the two assist- 

 ants did not make their marks simultane- 

 ously and hence the marks left on our 

 platform do not, we say, represent truly 

 the distance between his clocks. The dif- 

 ference is readily shown in Fig. 2, where 

 M represents the black mark made on our 

 platform at a certain time by the assistant 

 at A, and N that made by the assistant at 

 5 at a later time. The latter assistant 

 waited, we say, until his clock read the 

 same as clock A, waited, that is, until B 

 was at B'; and then made the mark N. 

 The moving observer declares, therefore, 

 that the distance MN is equal to the dis- 



difference becomes, on simplification, the expres- 

 sion given above. 



taace AB, while we say that MN is greater 

 than AB. 



Again it must be emphasized that, be- 

 cause of the first fundamental postulate, 

 there is no universal standard to be ap- 

 plied in settling such a difference of opin- 

 ion. Neither the standpoint of the "mov- 

 ing" observer nor our standpoint is wrong. 

 The two merely represent two different 

 sides of reality. Any one could ask: 

 What is the "true" length of a metal 

 rod? Two observers working at different 

 temperatures come to different conclu- 

 sions as to the "true length." Both are 

 right. It depends on what is meant by 

 "true." Again, asking a question which 

 might have been asked centuries ago, is a 

 man walking toward the stern of an east- 

 bound ship really moving west 1 We must 

 answer "that depends" and we must have 

 knowledge of the questioner's view-point 

 before we can answer yes or no. 



A similar distinction emerges from the 

 principle of relativity. What is the dis- 

 tance between the two clocks? Answer: 

 that depends. Are we to consider our- 

 selves with the clock system when we 

 answer, or passing the cloclvs with a hun- 

 dredth the velocity of light or passing the 

 clocks with a tenth the velocity of light? 

 The answer in each case must be different, 

 but in each ease may be true. 



It must be remembered that the results 

 of the principle of relativity are as true 

 and no truer than its postulates. // future 

 experience bears out these postulates then 

 the length of the tody, even of a geomet- 

 rical line, in fact the very meaning of 

 "length," depends on the point of view, 

 that is, on the relative motion of the ob- 

 server and the object measured. The rea- 

 son this conclusion seems at first contrary 

 to common sense is doubtless because we, 

 as a race, have never had occasion to ob- 

 serve directly velocities high enough to 



