ALS in German, signed “A. E.,” three pages on two sheets, 8.5 x 11, May 28, 1950. Lengthy and detailed handwritten letter to his former assistant, the German-American mathematician Ernst G. Straus. Seeking to expand General Relativity into a “Generalized Theory of Gravitation” (as a basis from which the electromagnetic field equations can be derived), Einstein is here wrestling with the problem of finding Bianchi Identities that support a consistent theory of asymmetric fields. (Bianchi Identities are of relevance for both Riemann and Einstein tensors and essentially force the covariant divergence of the Einstein tensor to be 0.) In this highly technical letter to his former assistant, E. G. Straus, Einstein indicates that he is looking for “a complete choice of coordinates”; and he here provides a formula that “corresponds exhaustively to the content of Bianchi Identities” and which he thinks “can be applied to any vector density with an identical vanishing divergence.” The letter suggests, however, that the effort is still a work-in-process: Einstein here admitting to a previous “mistake, which I had made owing to an erroneous consideration of the Bianchi Identities” and pointing at the “ticklish issue” of Straus’ example which cannot be resolved to an identity. In fine to very fine condition.
At the time of this letter’s composition (1950), Einstein was at work on his final version of Unified Field Theory, which explored the use of asymmetric tensor components in equations. In his initial papers (1945-46) on this final version of UFT, Einstein attempted to determine the asymmetric equations by using “a variational principle in close analogy to the symmetric case.” But Einstein subsequently took a new approach to the problem in his 1950 paper “The Bianchi Identities in the Generalized Theory of Gravitation,” Einstein there affirming that “In the theory of symmetric fields there is a second method of ensuring the compatibility of the field-equations (Rik = 0). We must have four identities connecting the equations. These can be derived by contracting the Bianchi Identities which hold for the curvature tensor.” The present letter extends and develops the thinking Einstein articulated in this important 1950 paper.
Einstein letters of this caliber rarely appear on the market. The content is entirely mathematical in nature, and the letter itself has the appearance of a Unified Field Theory manuscript. This letter is both formally unpublished and unknown to scholarship.
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