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PROPERTY OF A LADY AND A GENTLEMAN
EINSTEIN, Albert (1879-1955). Autograph manuscript, n.p., [c. 1940-1945].
Details
EINSTEIN, Albert (1879-1955). Autograph manuscript, n.p., [c. 1940-1945].
In German, two pages on a single leaf, 275 x 213mm (lightly creased at two corners).
Einstein sketches calculations in preparation for his landmark 1945 paper proposing a new approach to a unified field theory. A series of calculations relating to Einstein's approach towards a unified field theory that he pursued from about 1945 to his death in 1955 – based on a generalization of the mathematical framework he had used when he formulated the general theory of relativity in 1915, namely pseudo-Riemannian geometry. Einstein took the fundamental mathematical object of general relativity, the metric tensor, and, firstly, allowed it to have not only real numbers as components but imaginary numbers as well; and secondly, he allowed it to be asymmetric in its indices. Thus, in contrast to the metric tensor of general relativity, the metric tensor in the new theory could be split into a symmetric and an antisymmetric part. Since in his 1915 theory the gravitational field was represented by a symmetric tensor and the electromagnetic field by an antisymmetric tensor, Einstein hoped that this new approach would allow him to give a unified theory of both gravity and electromagnetism. As far as we know as of today, Einstein’s methodology in these years was characterized by trying out ever new symmetry requirements and ever new fundamental field equations for the metric tensor and the second fundamental object of the theory, the affine connection ?ikl . Einstein's pioneering 1945 paper, “Generalization of the Relativistic Theory of Gravitation” (Annals of Mathematics 46, 1945, pp. 578–584), introduced a so-called “Hermitian symmetry”, which we see used here.
On the first page of this manuscript, Einstein investigates the properties of a mathematical object, first publicly introduced in his 1945 paper: the novel vector ?i that is formed by contracting the difference between the affine connection of the theory from its Hermitian conjugate. But the page also features the properties of the third-rank tensorial object Uiak that Einstein likewise first introduced in 1945. All in all, the manuscript exhibits key thoughts and concepts that would form the foundations of what was to become the 1945 paper. On the verso Einstein investigates the asymmetric metric tensor of the theory using the calculus of variations. These calculations are exemplary examples of Einstein’s search for a unified field theory within the approach he followed passionately during the last decade of his life.
Christie's thanks Dr. Dennis Lehmkuhl, Scientific Editor of the Einstein Papers Project, for lending his expertise.
In German, two pages on a single leaf, 275 x 213mm (lightly creased at two corners).
Einstein sketches calculations in preparation for his landmark 1945 paper proposing a new approach to a unified field theory. A series of calculations relating to Einstein's approach towards a unified field theory that he pursued from about 1945 to his death in 1955 – based on a generalization of the mathematical framework he had used when he formulated the general theory of relativity in 1915, namely pseudo-Riemannian geometry. Einstein took the fundamental mathematical object of general relativity, the metric tensor, and, firstly, allowed it to have not only real numbers as components but imaginary numbers as well; and secondly, he allowed it to be asymmetric in its indices. Thus, in contrast to the metric tensor of general relativity, the metric tensor in the new theory could be split into a symmetric and an antisymmetric part. Since in his 1915 theory the gravitational field was represented by a symmetric tensor and the electromagnetic field by an antisymmetric tensor, Einstein hoped that this new approach would allow him to give a unified theory of both gravity and electromagnetism. As far as we know as of today, Einstein’s methodology in these years was characterized by trying out ever new symmetry requirements and ever new fundamental field equations for the metric tensor and the second fundamental object of the theory, the affine connection ?ikl . Einstein's pioneering 1945 paper, “Generalization of the Relativistic Theory of Gravitation” (Annals of Mathematics 46, 1945, pp. 578–584), introduced a so-called “Hermitian symmetry”, which we see used here.
On the first page of this manuscript, Einstein investigates the properties of a mathematical object, first publicly introduced in his 1945 paper: the novel vector ?i that is formed by contracting the difference between the affine connection of the theory from its Hermitian conjugate. But the page also features the properties of the third-rank tensorial object Uiak that Einstein likewise first introduced in 1945. All in all, the manuscript exhibits key thoughts and concepts that would form the foundations of what was to become the 1945 paper. On the verso Einstein investigates the asymmetric metric tensor of the theory using the calculus of variations. These calculations are exemplary examples of Einstein’s search for a unified field theory within the approach he followed passionately during the last decade of his life.
Christie's thanks Dr. Dennis Lehmkuhl, Scientific Editor of the Einstein Papers Project, for lending his expertise.