October 3, 1913] 



SCIENCE 



471 



miles; or that the sun miles are shorter in the 

 ratio of 3 to 4. 



This apparent paradox is due to the fact 

 that we are not accustomed to establishing 

 simultaneity by accurate instruments of time, 



Pig. 13 



but rather by a vague " now " which can be 

 established neither by clear thought nor by 

 experiment. We have been thinking absolute 

 time which can not be measured, hence is 

 meaningless; the only time that has meaning 

 is the time we can measure with nature's in- 

 struments of time, her uniform processes. 



Let us study for a moment the clocks on the 

 moving system; to an observer outside the 

 moving system, the two clocks will be out of 

 synchronism; viewed from the sun (Fig. 14), 



Fig. 14 



B"s clock will be five and one third hours 

 behind the clock of A': If, however, A"s clock 

 be moved to 5"s station, it will no longer be 

 five and one third hours ahead of B"s clock, 

 but will record the time of that station in 

 perfect agreement with B"s. In the process of 

 moving from its own station at zero to jB"s 

 station at 60, ^"s clock must therefore have 

 gradually slowed up. Vice versa, if B"s clock 

 .be moved to A"s station, it will on arrival no 



longer be five and one third hours behind A"s 

 clock, but in agreement with it; in moving 

 against the direction of the moving system it 

 has gained five and one third hours in time. 



Since the clocks are all nature's timepieces, 

 all the clocks in one system (and we can 

 imagine an infinite number of them) move in 

 perfect uniformity. Each point or station on 

 the system has its own particular local or 

 place time (Eigenzeit). If a clock be moved 

 from one station to another, on reaching its 

 new station it records the place-time of that 

 station. It would seem therefore that the im- 

 pulse which sets the clock in motion in the 

 direction of the moving system acts upon the 

 balance wheel, — or whatever may be the clock 

 regulator, to retard it; and the impulse which 

 sets the clock in motion counter to the moving 

 system acts upon the balance wheel to accel- 

 erate it. 



The logical deductions that follow from 

 these facts are so startling to the lay mind 

 that I prefer to translate from Einstein him- 

 self:" 



Give the watch a very large velocity (approxi- 

 mating the velocity of light) so that it travels 

 with uniform speed; after it has gone a long dis- 

 tance give it an impulse in the opposite direction 

 so that it returns to its starting point. We then 

 observe that the hand of this watch during its 

 entire journey to and fro has remained practically 

 at a standstill, while the hand of an exactly sim- 

 ilar watch which did not move with respect to the 

 coordinate system (the sun or earth) has changed 

 its position considerably. 



We must add: what is true for our watch with 

 respect to time must also be true of any other 

 enclosed physical system, whatever its nature, be- 

 cause in all our thinking the watch was introduced 

 simply as a representative of all physical actions 

 or occurrences. Thus, for example, we could sub- 

 stitute for the watch a living organism enclosed 

 in a box. Were it hurled through space like the 

 watch, it would be possible for the organism, after 

 a flight of whatever distance, to return to its 

 starting point practically unchanged, while an 

 exactly similar organism which remained motion- 



" Zurich, Fierteljahressohrift d. Natf. Gesell., 

 56: 1-230, 1911. Reprinted in Berlin; Naturw. 

 Sundshau, 28: 285, 1912. 



