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.
U1 U2
U2 U2
U1, U2 U1,
[p. 698]
U1 U2
U1 U2
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