3 6 8 D O C U M E N T 2 1 6 M A R C H 1 9 2 6 Nehmen Sie an, man hätte bei dem Lichtkegel K des Punktes P a priori zwischen Vorkegel V und Nachkegel N unterschieden —was man bisher in Wahrheit nicht nötig hatte—so kann man festsetzen: σ ist positiv, wenn der (zeitartige) Stromvektor ( ) des Punktes P in N liegt, negativ dagegen, wenn er in V liegt. Ich habe versucht, Feldgesetze aufzustellen, in welche eine nicht symmetrische Funktion von σ eingeht. Aber ich hatte dabei keinen guten Erfolg.[3] Ihre Notiz in der „Nature“ hat mich sehr interessiert. Denn sie liefert eine ma- thematische Interpretation des Tensors , dessen Einführung in die all- gemeine Rel. Theorie durch das kosmologische Problem nahe gelegt wird. Ich habe dies in einer Arbeit ausgeführt, welche in der Riemann-Festschrift erscheinen wird.[4] Es grüsst Sie freundlich Ihr A. Einstein. ALSX. [79 686]. [1]Rainich had sent the manuscript of Rainich 1926b to Einstein on 21 February 1926 (see Abs. 326). He starts by summarizing the main result of Einstein 1925w (Doc. 92) as having proven that ‘‘if there exists a solution of the field equations of general relativity which gives an electron with the charge and the mass m there must exist another solution which gives an electron with the charge +e and the mass m.” Einstein’s argument, however, concerned all theories in which the elec- tromagnetic field is represented by an antisymmetric second-rank tensor this includes the Einstein- Maxwell equations as a special case. In his paper, Rainich argues that Einstein’s result would imply a contradiction with experiment only if the field equations were linear, for only then would the exis- tence of a and a +e solution imply that there is a solution with both particles as well. He goes on to argue that, while in a linear theory the existence of a solution that represents one particle at rest implies the existence of a solution corresponding to two particles at rest with respect to one another, this is generally not so in a theory such as general relativity. The reason is that the nonlinearity of the field equations implies that in general the superposition of two solutions to the field equations is not itself a solution. For more reflections on what follows from the nonlinearity of the Einstein-Maxwell equations, see Rainich 1925a, sec. 11. [2]Einstein had made the same argument in the addendum to Einstein 1925w (Doc. 92). Repeating it here seems to suggest that Einstein thought that Rainich had missed his main concern in Rainich 1926b (see the preceding note). For even in the absence of a solution that describes negatively and positively charged particles with mass m, Einstein’s result seems to show that the theory predicts that if particles with charge and mass m exist, then particles with charge +e and mass m should also exist. This, in turn, is in contradiction with experimental results of the time, where the only known positively charged particle (the proton) was much heavier than the only known negatively charged particle (the electron). [3]In Einstein 1925w (Doc. 92), after the preceding arguments, Einstein had stated that it would be “easily possible” (“leicht möglich”) to find such laws. [4]Einstein 1927a (Doc. 158). Rik 1 4 -- - gikR –e –e –e
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