D O C U M E N T 1 3 J A N U A R Y 1 9 2 2 3 3
Through suitable combination of two of each of these equations, three similarly
structured equations follow, of the type
(6)
From this, by
integration,[12]
(7)
The constant on the right-hand side has to vanish because the left-hand side for
vanishes. That is why, after another integration,
(8)
follows from (7). Likewise follows
(8a)
Within infinite space-time the manifold must be Euclidean and the electrostatic
potential must vanish there. Hence the equations (8) and (8a) require that and
vanish throughout. Therefore, no spatially variable electric potential exists and
hence no electric field, either.
Thus it is proven that Kaluza’s theory possesses no centrally symmetric solution
dependent on the gμν’s alone
that[13]
could be interpreted as a (singularity-free)
electron.
13. To Paul Ehrenfest
[Berlin,] 11 January 1922
Dear Ehrenfest,
I know nothing about a Lenard
Festschrift.[1]
You need not attach any impor-
tance to such trifles, especially to purely interpersonal relations that aren’t based on
cordial feelings. It’s all a mockery, whether good or bad. The light experiment came
r
2
λ
2
g44g′45 g′44g45)]′ ( [
r2λ2(g44g′45
g′44g45)
---------------------------------------------------------------
λ2)′
(
λ2
----------- - .–=
r
2
λ
4
g44g′45 g′44g45) ( const. =
r 0=
g45
g44
------- const. =
[p. 5]
g45
g55
------- const. =
g45
g44
-------
g45
g55
-------
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