6 9 8 D O C U M E N T 4 4 4 J A N U A R Y 1 9 2 7 tensor and the tensor density of the gravitational energy-pseudotensor. On p. 281, Weyl defines a four-force as . Then is equal to the spatial current through the three-surface. Hence, Einstein and Grommer’s equilibrium condition, namely, the condition that the integral of their eq. (17) vanishes, corresponds to the demand that the four-force as defined by Weyl vanishes. [32]Einstein had been convinced of this through his correspondence with Rainich see especially Doc. 300 and also note 1 above. However, the justification of the claim that static two-particle solu- tions (or, relatedly, a single static particle subject to an external field) do not exist by appeal to the equilibrium condition does not appear in the correspondence. [33]A demand that the metric does not deviate “too much” from flatness, which Einstein and Grommer take to be a necessary, but not a sufficient, condition for solutions to the linearized Einstein equations. [34]A similar split between the metric field inside the three-surface that encloses the body (see notes 28 and 31) and the metric outside is introduced by Weyl 1922, pp. 278–281. Weyl calls the inner metric “fictitious” and, in contrast to Einstein, does not postulate any particular inner metric (apart from demanding it to be static and smoothly connecting to the outer metric), and indeed argues that no particular choice for the “fictitious” inner metric is needed. See Lehmkuhl 2017a for an argument that Einstein and Grommer’s derivation in the present document likewise does not depend on the choice of any particular inner metric, and hence does not depend on seeing the particle as represented by a singularity. [35]Eq. (20) corresponds to Einstein and Grommer’s earlier claim (p. 6) that the field strength of the external field had to vanish at the location of the particle. However, on p. 6, they use a particular exact solution to the nonlinear Einstein equations (the Curzon-Chazy solution, modified by addition of an external field see notes 17 and 20). Here, on the other hand, they look at a class of solutions to the linearized field equations for interpretation of their equilibrium condition, see note 31. [36]In the manuscript, “Falle des Gleichgewichts im stationären Felde bei der von uns angewende- ten Approximation” replaces “von uns betrachteten speziellen Falle.” [37]In the manuscript, the paragraph starting with “Wir gehen zu dem Falle über…” replaces the following paragraph: “Wir gehen nun zu dem allgemeinen Falle des nicht stationären Feldes über. Die angewendete Methode ist hier dieselbe. Auch hier werden die Gleichungen (15)–(16) angewendet, und der singuläre Punkt auf Ruhe transformiert. Aber die angestellte Betrachtung ist dadurch kom- pliziert, dass es hier nicht.” [38]See note 34 for the question of whether the choice of any inner metric is ever necessary. [39]See Weyl 1922, pp. 283–285, for a similar derivation (note 31 discusses Weyl’s starting point) that does not depend on linearizing the field equations. Weyl gives a derivation of the equations of motion of charged particles, including the influence of electromagnetic fields on them. However, in the absence of electromagnetic fields, his derivation results in the geodesic equation as the equation of motion of the particle. 444. To Hedwig Born [Berlin,] 6. I. 27. Liebe Frau Born! Ich habe Ihr Stück mit vielem Vergnügen gelesen und denke, dass es als Satyre der Zeit guten Erfolg haben kann.[1] Es ist durch und durch witzig und amüsant. Als Kunstwerk allerdings scheint es mir nicht gerade viel zu taugen in Bestätigung der vielbestätigten Wahrheit, dass Männer und Weibsen an verschiedenen Stellen ν dJμ dt -------- –= Uμ, 1 Uμ, 2 3 ( ) gμν
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