8 0 8 D O C . 5 1 5 C A L C U L A T I O N S ALSX. [24 088]. [1]Doc. 473. [2]As presented in Weyl 1923, sec. 38. [3]The term “Kanal” refers to what Weyl calls “Schlauch” in Doc. 473. In Weyl 1923, the term is also used. [4]In Einstein and Grommer 1927 (Doc. 443), the authors only hint at this possible connection between a quantum theory of matter on the one hand and the project of deriving geodesic motion from the gravitational field equations, albeit they make the connection in the final sentence of the paper. As in the present letter to Weyl, Einstein was more open about the motivation of producing results that would be helpful for a quantum theory of matter in a letter to Michele Besso (Doc. 348) and to Paul Ehrenfest (Doc. 450). 515. Calculations [Berlin, on or before 5 May 1927] unter Bedingung oder _____________________________________________________________ Für δ( G M) + τ) d ³( 0= δ( –gdτ) ³ 0. = δ( M + λ g)(dτ) –+ ³G 0. = G giκ{ ΓiαβΓκα β ΓiακΓαβ} β – –g = M giκTiκ = Tiκ giαgκβ –g® ρ ds dxαdxβ ds pgαβ – ¯ ¿ ¾ ­ ½ = giκp – giαgκβρdsαdsβ¹ · dx dx + © § · –g = ds2 f 2dt2 dσ2 – f 2dr2 dr2 – –U2dϑ2– U2sin2ϑdϕ2 + = = 0 1 2 3 g00 g1 dσ2 dr2 U2( dϑ2 sin2ϑdϕ2) + += g00 f 2 = g11 1–= g22 U2 –= g33 U2sin2ϑ –= g00 1- f 2 --- = g11 1–= g22 U 2– –= g33 U 2– sin 2– ϑ –= –g f 2U2sin2ϑ = r 0 und r M: dσ2 dr2 M r)2( – ( dϑ2 sin2ϑ)dϕ2 + + = = =