3 6 D O C . 4 0 M A Y 1 9 1 9
40. To Theodor Kaluza
[Berlin,] 14 May 1919
Highly esteemed Colleague,
Now, however, upon more
careful reflection about the consequences of your interpretation, I did hit upon an-
other difficulty, which I have not been able to resolve until
now.[2]
In short, what is
involved is that would have to have a catastrophically great influence on the
motion of matter. I would like to sketch my train of thought briefly for you.
1. If I set in first approximation[3]
then of interest next is the order of magnitude of the constant . This I find as fol-
lows. The Hamilton function (for g = 1
)[4]
should
be[5]
.
μ = ν = 0 contributes
or .
As this must be the electromagnetic term of the dualistic theory, then its order of
magnitude is accordingly
.
Since we obviously propose to set , therefore
.
2. Now I look at the field equation with indices 00 and find to first approximation[6]
is hence of the same order of magnitude as the potential , the derivatives of
in the Earth’s field [are] thus of order of magnitude (time unit, light-
second).[7]
g00

β

β

α
---fαβ,2 = =
α
x4 it] = [
gμν⎨
μα
β
⎭⎩
⎬⎨
⎫⎧
νβ
α

g00⎨

β
⎭⎩
⎬⎨
⎫⎧

α

g00⎛
α⎞
2⎠
---

2
fαβ f
αβ
g00α2
κ 10
28–
=
g00
1
α 10 14–
1
2
-- - g00
α
2⎠
---⎞

2
fαβ
fαβ
+ 0. =

κ2
g00 g44
g00 10
18–
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