Science & Natural History
EINSTEIN, ALBERT. 1879-1955.
Autograph Manuscript Signed ("A.E."), 2 pp recto and verso, folio, [Berlin], December 25, 1925, creases where previously folded, a few very small marginal tears, else fine.
EINSTEIN DRAFTS BOTH A LETTER TO THE FEDERATION OF JEWISH FOREIGN STUDENTS AND GRAVITATIONAL FIELD EQUATIONS. ALL IN A DAY'S WORK: CHRISTMAS, 1925.
At the head of the first page, Einstein drafts an address to the Federation of Foreign Jewish Students in Germany on the occasion of their upcoming conference. In full, translated: "To the Union of Jewish Student Societies in Germany, I wish your conference much success. I myself would gladly have attended, but am unfortunately prevented from doing so because of urgent work. I will always do whatever is possible in order to promote your goals. A.E."
After 1919, Einstein increasingly devoted his energy to the alleviation of the plight of Eastern European Jewish students, many of whom were denied access to university in both their home countries and in Germany, where many found themselves in the aftermath of the population displacements caused by World War I and the Russian Revolution. Einstein subsequently wrote a clean copy of the above draft, in which he replaced "urgent work" with "urgent matters." (Albert Einstein Archives, 44-056).
On the rest of the page and continued on the verso, Einstein proceeds to work, possibly on some of those "urgent matters" he had in mind. There are calculations pertaining to the relationship of the Riemann curvature tensor to the field equations of gravitation, calculations that Einstein first presented in a session of the Prussian Academy of Sciences on January 7, 1926 ("Über die Anwendung einer von Rainich gefundenen Spaltung des Riemannschen Krümmungstensors in der Theorie des Gravitationsfeldes") and subsequently published as a complete paper, submitted on January 9, 1926 to the journal Mathematische Annalen: "Über die formale Beziehung des Riemannschen Krümmungstensors zu den Feldgleichungen der Gravitation", Math. Ann., 97, pp 99–103, (1927). The paper was written as part of Einstein's ongoing program of unifying the electromagnetic and gravitational field theories. By 1925, Einstein had developed further the work of Arthur S. Eddington and H. Weyl on a unified theory. He employed a mixed geometry (a metric-affine theory) to generate the vacuum field equations of general relativity for a vanishing electromagnetic field, and in a first order approximation, to also generate Maxwell's field equations. But by the end of the year, he had become dissatisfied with his earlier work, in particular after having become aware of further work by G.Y. Rainich on the algebraic properties of the curvature tensor and the electromagnetic field tensor.
The manuscript deals with the field equations of relativity, usually written as R_{im} -R/2 g_{im} = -kT_{im} where T_{im} is the energy tensor of matter and of the electromagnetic field and the left side of the equation represents the Riemannian curvature tensor. In his paper, Einstein introduces a new tensor, R_{im} - R/4 g_{im}, which he considers of deeper significance for the understanding of the law of gravitation, leading through calculation to equations of the form:
R_{im} - R/4 g_{im} = - kT_{im}(seen written out on the verso in pencil)(1). He writes that this second set of equations has "received only little attention" due to "two circumstances. First, all our attempts, along the path taken by Weyl and Eddington or a similar one, have been directed at arriving at a theory that amalgamates the gravitational field and the electromagnetic field into a formal unity." But, he continued, "through multiple failures I have now driven myself to the conviction that one cannot come closer to the truth in this manner."^{1} Einstein proceeds, on the basis of Rainich's paper, to show that the anti-symmetric component of the Riemannian curvature tensor R_{ik,lm} will also vanish when the tensor R_{im} - R/4 g_{im} vanishes. Most of the calculations in the current document pertain to this proof. Einstein then proceeds to construct from the electromagnetic Tensor (φ_{ik}) a new energy tensor whose symmetry properties are the same as the Riemannian curvature tensor. He thus produces an "electromagnetically enhanced curvature tensor" (AE's quotation marks) and shows that the equations (1) of the gravitational field "explained through the cosmological problem and the electromagnetic energy tensor allow for a simple mathematical interpretation." The published paper contains, in a more formalized shape, the present calculations. A few months later, Einstein was dissatisfied again, because his latest equations above do not "allow for electrical masses free from singularities," as he wrote to his friend Michele Besso.
The manuscript sheet is significant in that it shows us the "shorthand" Einstein used for his calculations with gravitational field equations. It also contains a graphic representation of field lines and vectors. Bonhams is grateful to Diana K. Buchwald, Einstein Papers Project, Caltech for her assistance in cataloguing this lot.
^{1}_{"Über die formale Beziehung des Riemannschen Krümmungstensors zu den Feldgleichungen der Gravitation.", Math. Ann., 97, pp. 99–103, (1927), p. 100. See Hubert Goenner, "On the History of the Unified Field Theories", Living Reviews in Relativity, 7 (2004), 2, pp. 48-61 and references therein.}