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EINSTEIN, Albert (1879-1955). Autograph manuscript, comprising calculations and arguments from the Einheitliche theorie von Gravitation un Elektrizitt (Unified Theory of Gravitation and Electricity), n.p., n.d. [1931], including equations numbered 34-42 [from Part 5, Die Krmmung bezglich des V5 (The Curvature relating to V5)], one page (numbered '15'), 283 x 224mm (a few cancellations and corrections, 2 tiny red pencil marks, slight wear to edges).
EINSTEIN, Albert (1879-1955). Autograph manuscript, comprising calculations and arguments from the Einheitliche theorie von Gravitation un Elektrizitt (Unified Theory of Gravitation and Electricity), n.p., n.d. [1931], including equations numbered 34-42 [from Part 5, Die Krmmung bezglich des V5 (The Curvature relating to V5)], one page (numbered '15'), 283 x 224mm (a few cancellations and corrections, 2 tiny red pencil marks, slight wear to edges).

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EINSTEIN, Albert (1879-1955). Autograph manuscript, comprising calculations and arguments from the Einheitliche theorie von Gravitation un Elektrizitt (Unified Theory of Gravitation and Electricity), n.p., n.d. [1931], including equations numbered 34-42 [from Part 5, Die Krmmung bezglich des V<->5 (The Curvature relating to V<->5)], one page (numbered '15'), 283 x 224mm (a few cancellations and corrections, 2 tiny red pencil marks, slight wear to edges).

The manuscript is from the paper written in collaboration with Walther Mayer, which Einstein submitted to the Prussian Academy of Science at its session on 22 October 1931, published in Sonderausgabe den Sitzungberichten der Preussischen Akademie der Wissenschaft, Physikalische-Mathematische Klasse, 1931, XXV (the text of Part 5, which begins with equation 29, is on pages 551-553).

The Unified Field Theory, probably Einstein's most visionary project, was intended to solve one of the outstanding problems of fundamental theoretical physics, that of how to fit gravity into a Quantum field theory. Einstein spent the latter part of his life trying to bring together the general theory of relativity, which was concerned with gravity, and James Clerk Maxwell's theory of electro-magnetism. All his attempts, produced, as he wrote to a friend, 'in an agony of mathematical torment', were abandoned, and the problem has continued to defy solution.

Einstein's outline of a unified field theory was published by the Prussian Academy of Sciences in 1928. In January 1929 he submitted a new paper for examination. From the end of 1929 he worked in collaboration with his Austrian assistant, Walther Mayer (1887-1948), on a unified theory of gravity and electricity. Mayer accompanied Einstein to America from December 1930 to March 1931. Sailing from Southampton on the Belgeland, they worked throughout the voyage in three flower-filled staterooms, permanently guarded from intrusion (R.W. Clark, Einstein, 1978, 402). Their first joint paper was submitted to the Academy on 23 April 1931. The present manuscript represents part of another attempt, in which they used the ideas, published in 1921, of Theodore Kaluza, who had introduced a five-dimensional space-time in order to unify gravitation and electro-magnetism.

The equations in the manuscript form part of the discovery of the relation between the fivefold curvature with which the paper works and Bernhard Riemann's fourfold curvature, and the demonstration that Bianchi's Identity (equation 38) holds true for tensors (generalised vectors) in fivefold curvature, enabling the production of the antisymmetrical tensor in equation 42.
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