![EINSTEIN, Albert (1879-1955) Autograph manuscript, [New York, 25-26 June 1945].](https://www.christies.com/img/LotImages/2018/NYR/2018_NYR_16082_0183_001(einstein_albert_autograph_manuscript_new_york_25-26_june_1945033131).jpg?w=1)
![EINSTEIN, Albert (1879-1955) Autograph manuscript, [New York, 25-26 June 1945].](https://www.christies.com/img/LotImages/2018/NYR/2018_NYR_16082_0183_002(einstein_albert_autograph_manuscript_new_york_25-26_june_1945033146).jpg?w=1)
![EINSTEIN, Albert (1879-1955) Autograph manuscript, [New York, 25-26 June 1945].](https://www.christies.com/img/LotImages/2018/NYR/2018_NYR_16082_0183_000(einstein_albert_autograph_manuscript_new_york_25-26_june_1945033116).jpg?w=1)
PROPERTY OF A LADY AND A GENTLEMAN
EINSTEIN, Albert (1879-1955) Autograph manuscript, [New York, 25-26 June 1945].
Details
EINSTEIN, Albert (1879-1955) Autograph manuscript, [New York, 25-26 June 1945].
In German, three pages, 213 x 170mm in pencil and ink on lined paper in a spiral-bound composition book (light toning at margins).
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.
In this manuscript, Einstein explores an alternative strategy to that found in lot 182. Here he allows not only for complex (i.e. partly imaginary) components of the metric tensor but also for complex coordinates. He had first played with this idea in 1942, as we know from a letter to his close friend Michele Besso from 1942. This most likely places these three pages as calculations leading up to the 1945 paper as well; for by the time he wrote the paper, Einstein had abandoned the idea that the coordinates might be complex numbers as well. However, it is possible that Einstein came back to this idea in the years that followed his1945 paper. All in all these calculations are exemplary for 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, three pages, 213 x 170mm in pencil and ink on lined paper in a spiral-bound composition book (light toning at margins).
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.
In this manuscript, Einstein explores an alternative strategy to that found in lot 182. Here he allows not only for complex (i.e. partly imaginary) components of the metric tensor but also for complex coordinates. He had first played with this idea in 1942, as we know from a letter to his close friend Michele Besso from 1942. This most likely places these three pages as calculations leading up to the 1945 paper as well; for by the time he wrote the paper, Einstein had abandoned the idea that the coordinates might be complex numbers as well. However, it is possible that Einstein came back to this idea in the years that followed his1945 paper. All in all these calculations are exemplary for 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.