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ALS in German, signed “A. Einstein,” one page, 8.5 x 11, May 27, 1929. Handwritten letter to German mathematician Chaim Herman Muntz, mentioning the 'gauge problem'—an important concept in modern physics that Einstein was working on with his assistant Cornelius Lanczos. In part (translated): "I thank you for sending these calculations. It will be important to know how many equations are equivalent to the condition Sauv = 0; that is still unclear to me. Regarding the problem as a whole, Lanczos's discovery changes the situation fundamentally. My opinion is now oriented around the following considerations: It is impossible that the equations Rik = 0 hold in general, since these equations alone already satisfy causality. Therefore E1 = E2 = 0 cannot be the case. I begin with the field equations and decompose them into [mathematical equations]…(symmetric)…[mathematical equations]…(antisymmetric)."
Following much more math, Einstein writes: "It is quite natural to consider (I) as the 'gravitational equations,' (III) as the electromagnetic field equations. The parenthesis in (III) is then the electric field strength Fua. Then, however, we cannot set the antisymmetric equations (II), since they would require the vanishing of the field (pure gravitational field). (III) is—this is the important point—derived from (I) alone. There are, however, only 10 independent equations. We would still certainly have to add the equations Sauv=0, if that is permitted, i.e. if there is no overdetermination. I am not sure about that. Then, the terms with E1 would vanish, while E2 would be a temporarily unknown constant. The gravitational equations (in vacuum) would then differ from the Rik = 0 only in terms of second order, which should be permissible. It would in any case be essential that E2 ≠ 0." In fine condition. Accompanied by the original mailing envelope, addressed in Einstein's hand to Muntz.
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 537, p. 461.
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.'
It is significant that, in this letter, Einstein pens his "gravitational equations," "electromagnetic field equations," and one of the fundamental equations of his General Relativity Theory: "Rik = 0," the equation for a vanishing Ricci Curvature Tensor. The Ricci Curvature Tensor measures the deviation of a curved spacetime from a Euclidean framework, and it is a concept of central importance for Einstein's General Relativity and Unified Field Theories. When the Ricci Curvature Tensor is equal to a zero value, the equation betokens a spacetime that is stable and static (neither expanding nor contracting). “Rik = 0 ” has been called 'Einstein’s favorite equation' and Einstein spent the second half of his life and career attempting to fine tune the precise value of this equation.
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