D O C U M E N T 1 7 8 D E C E M B E R 1 9 2 3 1 7 9
178. To Paul Ehrenfest
[Amsterdam, 13 December
1923][1]
Dear Ehrenfest,
You are a loyal letter-writing
husband.[2]
Don’t tell my wife! Today was the cer-
emony in Amsterdam, trusting and fine, afterwards a cosy dinner among a closer
circle.[3]
These really are an endearing, good little folk, among whom one’s life
laps softly by. But now to my theory, or what would like to become
one.[4]
Goal. Translation through differential equations whose solutions should also sat-
isfy the grav[itational] and Maxwellian ones, and among whose solutions should
be the point-shaped electron. Special equations of motion for these singularities
should be made unnecessary through overdetermination.
Method:
Equations up to now
…(I)
yield the spherically symmetric solution
…(2)
which is symbolically denoted by L(mε).
If one initially assumes (II)
one achieves that has the same symmetry character as , namely for
every constant . [---] (II) itself cannot be the sought-after system, how-
ever. Because, with a vanishing electric field the manifold would be Euclidean, i.e.,
without a gravitational field, which does not agree with experience. But L(o,ε) turns
Rik Φik
1
4
-–=--gikϕαβϕαβ ϕiαϕk
α·
+
© ¹
§
=
f2 g44 1
2m
r
------- –
ε2
r2
---- -+ = =
ϕ4
ε±
r
----- -=
II
Riklm Φik,lm =
Φik,lm A′Φ′… A″Φ″… A′″Φ′″… + + =
Φ′ik,lm ϕikϕlm
1
2
--( - ϕilϕkm ϕimϕkl) – += Φ′il gkmΦ′ik,lm =
Φ″iklm gilΦ′km gkmΦ′il gimΦ′kl – gklΦ′im – +=
Φ′″ gilgkm gimgkl)Φ′, – ( = Φ″ rilΦ′il =
Φik
lm ,
Rik,
lm
A′A″A″′