Remarkable scientific AMS in German, signed "A. Einstein," one page, 8.5 x 11, no date but circa 1938 or earlier. An important working manuscript apparently representing Einstein's notes for a paper entitled 'On a Generalization of Kaluza's Theory of Electricity,' co-authored with Peter Bergmann and published in Annals of Mathematics, vol. 39, no. 3, July 1938. This manuscript details part of Einstein's attempt to construct a unified theory of electromagnetism, gravitation and quantum mechanics based on a curved five dimensional spacetime with five spacetime coordinates x1, x2, x3, x4, x0 and four spatial coordinates, one of which, x0, is periodic. Through every point it is assumed that there passes a closed geodesic given by x1, x2, x3, x4 constant. In fine condition, with scattered light toning and faint show-through from old adhesive on reverse. Einstein presented this manuscript page to the daughter of Luther P. Eisenhart, chairman of the Mathematics Department at Princeton University.
Although the final paper appeared in English, correspondences in the wording and equations used in this manuscript and in the section of the published article headed 'The Space Structure' suggest that they are linked. The approach taken in this paper is sometimes referred to as 'Projective Relativity' and is a type of unified theory pioneered by Theodor Kaluza and later by Oskar Klein in the 1920s; their underlying ideas form the basis for modern superstring theory and studies on these subjects continue to be pursued by theoretical physicists today.
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