D O C U M E N T 1 3 2 S E P T E M B E R 1 9 2 0 2 5 9
I asked Grebe to show his exposures in [Bad] Nauheim. He is going to do so. For
the discussion, this issue seems to me to be the most important now. You are going
to be coming to Nauheim for sure, aren’t
you?[10]
132. To Edouard Guillaume
4 September 1920
Dear Guillaume,
The conclusion about the rate of the moving clock cannot be derived from the
formula[1]
. . . . . (1)
It rather results directly from the inverse Lorentz transformation:
For the pointlike events that correspond to the ticking of a clock indicating seconds
positioned at the origin of K , is
The result is therefore
.
From this, one may not by any means conclude that “the clock that indicates t is
running more slowly than the one that indicates t .” Rather, t is indicated by many
clocks and, to be precise, by each clock at rest relative to K that just coincides with
the nth tick of the clock positioned at the origin of K . I see from this statement of
yours that you have still not fully grasped the special theory of relativity, i.e., the
theory of 1905, misunderstandings prevail instead. A single clock can only mea-
sure the time at a single location (of the frame of reference). In time evaluations in
which many locations (with reference to the coordinate system) are involved, a sys-
tem of set clocks is always necessary.
t t 1 cos + =
t
t
v-x
c2
---- +
1
v2
c2
---- -–
------------------- -=
t n ( whole number = =
x 0.=
t
n
1
v2
c2
---- -–
------------------ =