x l v i i i I N T R O D U C T I O N T O V O L U M E 1 5 condition” for the gravitational energy-momentum flowing through the three- surface defined previously is fulfilled, then a solution to the linearized field equa- tions will also solve the full non-linear field equations. Assuming this condition, Einstein and Grommer split the metric in the neighborhood of the curve of the ma- terial particle into an “inner metric” (owing to the particle itself) and an “outer metric” (owing to other gravitational sources or the lack thereof). Importantly, the outer metric did not contain any singularities, while the inner metric was taken to be singular. Finally, they calculated the surface integral that is equivalent to the vacuum field equations “around” the curve of the material particle and concluded that this curve is a geodesic of the outer metric. Einstein and Grommer thus con- cluded that the geodesic motion of particles subject only to gravity followed from the field equations.[10] This constituted a significant change. In all of Einstein’s previous publications on relativity he had been careful to stress that the field equations and the equation of motion of particles subject only to gravity—the geodesic equation—needed to be postulated independently. However, he must have asked himself early on wheth- er this was really necessary. For already in the Entwurf theory of 1913, Einstein and Marcel Grossmann had shown that for the special case where all the matter in a giv- en spacetime region is pressureless dust, the condition that the covariant diver- gence of the energy-momentum tensor vanishes implies the equations of motion of dust particles (see Einstein and Grossmann 1913 [Vol. 4, Doc. 13] and the Zurich Notebook [partially published as Vol. 4, Doc. 10]). In a document that was likely a draft for the 1921 Princeton lectures, Einstein stated that the field equation “already contains the divergence equation and with it the laws of motion of material parti- cles” (Vol. 7, Doc. 63). But no such statement is contained in the final Princeton lectures as before, Einstein introduced the field equations and the equations of mo- tion as separate assumptions. The likely reason was that Einstein was unhappy with the role the energy- momentum tensor played in these approaches he had emphasized again and again that the energy-momentum tensor was only a phenomenological representation of matter, to be regarded with caution. In this volume, the clearest case is found in a letter to Besso from 11 August 1926, where he wrote: “But it is questionable whether the equation has any reality left within it in the face of quanta. I vigorously doubt it. In contrast, the left-hand side of the equation surely contains a deeper truth. If the equation really determines the behavior of the singularities, then a law describing this behavior would be justified far more Rik 1 2 -- - gikR – Tik = Rik 0=