D O C . 1 3 D I A L O G U E A B O U T R E L A T I V I T Y T H E O R Y 6 7

Since I can see your willingness, let us come right to the substance. Since the

special theory of relativity has been formulated, its result of the delaying influence

of motion upon the rate of clocks has elicited protest and, as it looks to me, with

good reason. This result seems necessarily to lead to a contradiction with the very

foundations of the theory. To make things perfectly clear between us, let this

result of the theory be phrased first and precisely enough.

Let be a Galilean coordinate system in the sense of the special theory of

relativity, i.e., a body of reference relative to which isolated material points move

uniformly along straight lines. Furthermore, let and be two exactly identi-

cal clocks, free of any outside influence. They operate at the same rate when

placed immediately side by side, or when placed at an arbitrary distance from each

other and both are at rest relative to . But if one of the clocks, e.g., is in a

state of uniform translatory motion relative to then it shall, according to the

special theory of relativity—judged from the coordinate system —go at a

slower rate than the clock which is still placed at rest relative to . This result

in itself strikes me already as strange. Grave scruples arise if one next considers

the following well-known thought experiment.

Let A and B be two mutually distant points in system . In order to fix the

conditions, let us assume A to be the origin of and B a point on the positive x-

axis. At the beginning, both clocks shall rest at point A. They operate at the same

rate, and their hands shall indicate the same time. Now we shall give clock a

constant velocity along the positive x-axis such that it moves toward B. In B we

imagine its velocity inverted such that the again moves back to A. Upon arrival

in A the clock is braked and brought to rest relative to Since (judged from )

the change in the position of the hands of (which might occur during the

velocity inversion of ) certainly will not exceed a certain amount, and since

during its uniform motion along the distance AB (again as judged form ) runs at

a slower rate than after its return must be late relative to provided the

distance AB is of sufficient length.—Do you agree with this conclusion?

Relativist: I agree, absolutely. It saddened me to see that some authors, who

otherwise stand on the ground of the theory of relativity, wanted to avoid this ines-

capable result.

Krit.: Now comes the snag. According to the principle of relativity, the entire

process must occur in exactly the same way when represented in reference to the

coordinate system which partakes in the movement of the clock Relative

to it is then clock which moves to and fro while clock is at rest all the

time. At the end of the movement, must be late against in contradiction to

the result above. Even the devoutest adherents of the theory cannot claim that of

two clocks, resting side by side, each one is late relative to the other.

[3]

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[p. 698]

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