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

-------