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,

I have received your manuscript for the

Academy.[1]

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

0α

β

⎩ ⎭

⎨ ⎬

⎧ ⎫

0α

β

–

α

---fαβ,2 = =

α

x4 it] = [

gμν⎨

μα

β

⎩ ⎭⎩

⎬⎨

⎧ ⎫⎧

νβ

α

⎭

⎬

⎫

g00⎨

0α

β

⎩ ⎭⎩

⎬⎨

⎧ ⎫⎧

0β

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–