D O C U M E N T 5 3 4 M AY 1 9 2 9 4 5 9 534. From Cornel Lanczos Berlin, 23 May 1929 Dear Professor, While I was working over some relativistic lectures, I saw in the proceedings of the Academy an equation given by Weiztenböck that leads to interesting conclusions.[1] He namely had calculated there the ordinary scalar Riemannian cur- vature R on the basis of the h quantities, or rather the invariants formed from them. It turns out that the combination occurs, aside from an invariant of 2nd order.[2] The latter can be decomposed into an ordinary divergence minus . One thus finally obtains: . Since the last term is of no importance for the variation, the invariant that you prefer[3] is thus simply the scalar curvature R, which can already be constructed from the . It follows from this that the underdetermination that occurs in the field equations with the choice of the undefined Hamilton function is precisely of such a kind that only the 10 are determined, and for them, the equations strictly emerge. The metric is thus found generally to be the metric of the gravita- tional field, and the deformation of the action function effects only a further deter- mination of the quantities, without changing anything in the metric. I can see in this the same difficulty that we have seen in the usual theory of rel- ativity, that through the equations , the principle of the geodesic line is al- ready also suggested (at least in the static, spherically symmetric case), so that the derivability of the Lorentz force by this path seems improbable. With many hearty greetings, Yours sincerely, Lanczos 1 2 J 1 1 4 J 2 J 3 + + 2J 3 1 4 R 1 2 J 1 1 4 J 2 J 3 Divergence + + = g ik g ik R ik 0 = h i R ik 0 =
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