D O C . 4 4 3 G E N E R A L R E L A T I V I T Y A N D M O T I O N 6 9 5 Published 24 February 1927 in Preußische Akademie der Wissenschaften (Berlin). Physikalisch- mathematische Klasse. Sitzungsberichte (1927): 2–13. An ADft is also available [1 065]. [1]Rainich 1926b had argued that only a linear theory with a one-electron solution would get into conflict with experience because in such a theory the existence of a solution describing one electron at rest would imply a solution describing two electrons at rest, despite the forces acting between them. Rainich further pointed out that in a nonlinear theory like general relativity, the existence of a solution representing two bodies at rest does not follow from the existence of a one-body solution. Rainich had sent the paper to Einstein attached to Abs. 326 see Doc. 216, note 1 for a summary of the paper and its context. Einstein himself had long looked for one-electron solutions to nonlinear field equa- tions see Einstein 1925w (Doc. 92), note 2, for a summary of this line of thought. He connected the question of finding electron solutions to the question of deriving the equations of motions of electrons in Doc. 245. For detailed analysis of this development see Lehmkuhl 2017b. [2]Havas 1989, p. 239, argues that Einstein overstates his case here. Even though a linear field the- ory cannot describe interactions between particles described by a solution of superposed one-particle states (see the previous note), it is possible for linear field equations to constrain the motion of a par- ticle subject to the field. [3]Einstein had first written about the program of expanding general relativity to a field theory encompassing both gravity and matter in Einstein 1919a (Vol. 7, Doc. 17). In this earlier article, as in the present one, he sees this research program in the tradition of Mie and Weyl in 1919 he also men- tioned Hilbert. In Einstein and Grommer 1923a, 1923b (Vol. 13, Doc. 12), the authors first formulated the criterion that a satisfactory (unified) field theory must overcome the dualism between field and particles subject to the field by allowing to derive particle solutions to the field equations (see Vol. 13, Doc. 12, note 9). For an analysis of the three ways (“Betrachtungsweisen”) of relating the gravita- tional field equations to the equations of motion of material particles subject to gravitational fields, see Havas 1989, Kennefick 2005, and Tamir 2012. [4]Einstein had already argued for seeing the geodesic equation as the equation of motion of parti- cles subject to arbitrary gravitational fields in Einstein and Grossmann 1913 (Vol. 4, Doc. 13). See Lehmkuhl 2014, sec. 3.1, for an overview and analysis of Einstein’s reasoning. [5]Einstein writes the field equations in a purely affine form here, using a Kronecker delta instead of a metric tensor in the second term. This is akin in spirit to Eddington’s affine theory that Einstein had abandoned after Einstein 1925t (Doc. 17). In his papers on affine field theory, Einstein did not introduce a Kronecker delta for this purpose, as he took the vacuum field equations without energy- momentum tensor to describe the purely gravitational limit, in which the Einstein tensor reduces to the Ricci tensor. [6]Einstein had originally thought of the energy-momentum tensor as fundamental in the sense that it was expected to determine the metric tensor throughout spacetime (see especially Einstein 1918e [Vol. 7 Doc. 4] for the culmination of this line of thought). At the same time, he believed that general relativity should not constrain the possibilities for a theory of matter more than special relativity does (see Einstein 1916o [Vol. 6 Doc. 41] and in Einstein to Hendrik A. Lorentz, 13 November 1916 [Vol. 8, Doc. 276]). In Einstein 1922c (Vol. 7, Doc. 71), Einstein further comments that the energy- momentum tensor only amounts to a “phenomenological” description of matter that has to be delivered by theories other than general relativity, in particular fluid dynamics and classical electro- dynamics see also Einstein and Grommer 1923a (Vol. 13, Doc. 12) and Doc. 348 for similar remarks. Instead, the sought-after theory was supposed to allow the derivation of corpuscular matter and its properties directly from field equations, without a theory-external source term (see note 3). Einstein had presented a general framework of how this might be achieved in Einstein 1924d (Vol. 14, Doc. 170). [7]Einstein here refers to the contracted Bianchi identities see Einstein 1927a (Doc. 158), note 2, for details. [8]The idea of deriving from gravitational field equations that the covariant divergence of the energy-momentum tensor vanishes, and deriving from this, in turn, that point masses move on geo- desics, already appears in Einstein and Grossmann 1913, sec. 4. The derivation depends on assuming that the energy-momentum tensor is that of a pressureless relativistic fluid, and on integrating over