4 7 8 D O C U M E N T 4 8 0 K A L U Z A S T H E O R Y : P A R T 2 Now one separates in the sum of (16a) the index 0 from the other indices. This gives us . (21) This in turn gives, in connection with (20) and (17), . (22) With the exception of the sign of the second term, this is the usual expression of the Hamiltonian function of the gravitational field and the electromagnetic field. Regarding the sign of the second term it should be noted that it is determined by us having made the arbitrary choice , whereas we could just as well have set then the sign of the second term would have come out positive. The same is achieved by reversing the sign of , which means that one chooses time- like line elements to be negative instead of positive. Both choices are united by the sentence: In order for the field equations of the total field to appear in the usual form, one must presume the 0-direction to be spacelike. In conclusion, one can say that Kaluza’s idea within the framework of the gen- eral theory of relativity delivers a rational justification for Maxwell’s electromagnetic equations, and it unifies them with the gravitational equations to a formal whole. ________________ Addendum to the Foregoing Two Communications[10] Mr. H. Mandel has pointed out to me that the findings communicated by me here are not new. The entire content is found in the paper by O. Klein (Zeitschr. f. Physik 37, 12, 1926, p. 895). Compare, furthermore, Foch’s paper (Zeitschr. f. Physik 39, 226, 1926). 481. Statement on Charlie Chaplin [Berlin, after 18 February 1927] [See Doc. 482 in documentary edition for English translation.] H γ ------ γmn( Γmb a Γna b 2Γmb 0 Γn0 b Γm0 0 Γn0 0 + + ) = + 2γm0( Γmb a Γ0a b Γmb 0 Γ00 b Γm0 a Γ0a 0 + + ) + γ00( Γ0b a Γ0a b 2Γ0b 0 Γ00 b + ) –Γab b γmnΓmn a 2γm0Γm0 a γ00Γ00 a + + ( ) H γ[ gmn( Γmb a Γna b Γmn a Γab b ) φb aφa b] = γ00 +1 = γ00 –1 = gmn [p. 30]
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