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 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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