D O C U M E N T 2 8 3 O C T O B E R 1 9 2 1 3 3 3
Es ist
und somit oder , was gibt const.
= 1. Es [wir]d
In sind die erste zwei Glieder rein räum-
lich, dagegen das dritte enthält nur Glieder mit . Andererseits ist
wobei , die zweite Erweiterung bedeu-
tet. (Vergl. Weyl
1te
Aufl. S.
193)[6]
Es ist somit
,
da aus folgt
. setzt man ,
so wird ,
ALS. [11 411].
[1]The following argument provides proof that the five-dimensional theory of Kaluza 1921 does
not allow for nonsingular, spatially spherically symmetric and static vacuum solutions that may be
interpreted as elementary electric charges (electrons). For further explanation, see the more explicit
version of the same argument published as Einstein and Grommer 1923. The word “scheinbar” is
interlineated. For Einstein’s interest in Kaluza’s five-dimensional unified field theory, see also
Doc. 270.
[2]The following equation is the same as eq. (4) in Einstein and Grommer 1923.
[3]Since Einstein left Berlin on 15 October for a trip to Italy and the Netherlands from which he
R11
g11
4
-------R – T11 – + g00--------
12
2
= =
R00
g00
4
-------R – T00 – + g11--------
12
2
= =
R11g11 R00g00 = R1212g11 R0202g00 = g00g11 =
H2323 2R0202g00
R
6
--- + =
R22 R1212g11 R2323g33 R0202g00 + + =
g
00
R22 ds2 R22 d 2
f22
f
----- -+ = f
2
g00 = fik
R0202 .=f22f
H2323
6 f
-+=22-----2Rf---
f22
x2 2
2
f
2 2
1
f1 –
f-
r
--
lr
h2
---- -f –
f
h2r
------- -
f f-
2
r
------- = = = =
gik
ik
– lxixk
h2
– 1
lr2
+ = =
g00R00 g11R11
=
g00h2
=
const 1 g00 f
2f 2
f
2h2
= = = =
H2323
R
6
---
2f f
r
-------- += s f
2
1–=
R s –
4s
r
------- –
2s
r2
----- – = H2323
–s
6
------- -
s
3r
-----
s
3r2
------- -–+ = const. =
s
6?
----------
s
r2
---- – 12 =