ALS in German, signed “A. Einstein,” one page both sides, 8.5 x 11, December 13, 1928. Handwritten letter to German mathematician Chaim Herman Muntz, in part (translated): "The identity for the Λ can be found as follows: one starts with the identity for [the case of] curvature ≡ 0. -Δikl,m +Δikm,l +Δiσl +Δσkm -ΔiσmΔσkl. By the cyclic permutations of k, l, m, one obtains two other equations. Then all three are added…We combine the third term together with the fourth, twice cyclically permutated." Einstein gives the mathematical result of these permutations, observing: "This is still not a genuinely covariant form of the identity, since differentiating with regard to m does not give a 'covariant' derivative." He goes on to provide the final result: "The final result is thus (Λikl;m + . + .) + (ΛikσΛσlm + . + .) ≡ 0. In particular, the equation resulting from a single contraction of this equation should be quite useful for our purposes." In fine condition, with small edge separations to the horizontal fold. An exceptional, highly technical letter boasting numerous mathematical equations in Einstein's own hand.
Published as part of The Collected Papers of Albert Einstein, Volume 16: The Berlin Years: Writings & Correspondence, June 1927-May 1929 (English Translation Supplement), Document 333, p. 318.
Einstein began his correspondence with Muntz in 1927, and in 1928 was writing to him on 'distant parallelism,' an extension of Riemannian geometry in which new mathematical objects, called 'tetrads' are introduced, which allow for the comparison of the direction of vectors at distant points of the spacetime. This letter relates to those investigations, which Einstein felt to be important as a mathematical attempt at a unified field theory—the incorporation of electromagnetism and gravitation in a single field theory. Although he published a number of papers on the subject from 1928 to 1931, the work is considered inaccurate and not recognized by physicists of today.
During this period Einstein was working closely with colleagues Herman Muntz and Cornelius Lantz on formalizing the 'Unified Field Theory of Gravitational Force and Electromagnetism.' Einstein’s article 'On Unified Field Theory' was presented on January 10, 1929, and published on January 30, 1929, by the Prussian Academy of Sciences. In the article he discloses the final stages of the development of this theory, and it reveals critical stages in the solution that he presents. The theory tried to achieve one unified formula that would unite the electromagnetic and gravitational fields and present them as different manifestations of a single universal force. At the article's close, Einstein expresses appreciation for Muntz's assistance: 'It is my pleasant duty to thank Dr. H. Müntz for his laboriously precise calculation of the centrally symmetric problem on the basis of Hamilton’s principle the results of his calculation suggested to me the method used here.'
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