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THE GRAVITATIONAL EQUATIONS FROM A VARIATIONAL PRINCIPLE. First editions, extremely rare author s presentation offprint (not to be confused with the much more common trade separate see below), from the library of the great German physicist Arnold Sommerfeld, of Einstein s derivation of the field equations of gravitation from a variational principle. This was the first time Einstein had derived the field equations of gravitation in arbitrary coordinates in his celebrated 1915 papers he derived the equations in generally-covariant form, but only in special unimodular coordinates. In the early 19th century William Rowan Hamilton (1805-65) showed that Newton s equations of motion for a classical mechanical system were equivalent to the statement that the action of the system (now called the Lagrangian) has a stationary value (generally a minimum). A first variational approach to the gravitational field equations of general relativity was unsuccessfully sketched by Einstein and Marcel Grossmann in 1913-1914, and subsequently by Einstein himself in 1914 (the so-called Entwurf Theory). But Einstein s 1914 theory was invalidated by a misconception related to the physically unjustified requirement of restricting the covariance of the gravitational field equations and by some mathematical errors in a crucial proof in the theory. Between March and May 1915, the Italian mathematician Tullio Levi-Civita (1873-1941), in his private correspondence with Einstein, singled out the mathematical flaws of the Entwurf theory, setting Einstein back on the path of general covariance, which eventually brought him, in November 1915, to the correct formulation of the gravitational field equations. Also in November 1915, the great German mathematician David Hilbert (1862-1943) published an article in which he correctly showed that Einstein s gravitational field equations could be obtained from a variational principle, at least in the presence of an electromagnetic field. Five days later, independently of Hilbert, Einstein obtained in the present paper the same results, thus obtaining the definitive variational formulation of the field equations. Einstein considered his approach to be more general than Hilbert s as Hilbert had made some hypotheses about matter which Einstein dispensed with (Einstein also refused to accept the electromagnetic origin of matter which Hilbert had assumed). In the course of this paper, Einstein also proved a special case of Emmy Noether s second theorem on the relation between symmetry and conservation laws, which she published in full generality two years later. The only author s presentation offprint listed on RBH is that is the collection of Einstein s son Hans Albert (Christie s 2006); it was not in Einstein s own collection of his offprints (Christie s 2008). Provenance: Arnold Sommerfeld (1868-1951) (his characteristic numbering in red pencil ( 33 ) on front cover). "The son of a physician, Sommerfeld was educated at the University of Königsberg. After teaching briefly at the universities of Göttingen, Clausthal, and Aachen he was appointed professor of physics at the University of Münich in 1906. Sommerfeld should have retired in 1936 in favour of his pupil, Werner Heisenberg. Opposition from the Nazi party to Heisenberg s appointment prolonged Sommerfeld s tenure and it was not in fact until late 1939 that he finally retired, to be succeeded not by Heisenberg but by Wilhelm Müller, a Nazi aerodynamicist without a single publication in physics to his credit. Although Sommerfeld and Heisenberg were not Jewish, they were regarded by the Nazis as Jewish sympathizers. Sommerfeld, however, survived the war and returned to his Münich chair in 1945, continuing to work at physics until he died in a car accident in 1951" (Oxford Reference). "Arnold Sommerfeld was one of the most distinguished representatives of the transition period between classical and modern theoretical physics. The work of his youth was still firmly.
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