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 -------
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