EINSTEIN, Albert (1879-1955). Autograph scientific manuscript signed ("A. Einstein," in pencil on verso of p.6), UNPUBLISHED, a working draft with extensive revisions, deletions and addition, in which Einstein explores the construction of a Unified Field Theory based on a Hermitean metric tensor field in a space of four complex, or equivalently eight real, dimensions. The experiment seeks to derive field equations "analogous to the gravitational equations of the General Theory of Relativity." No place, no date [circa 1941-45?].
EINSTEIN, Albert (1879-1955). Autograph scientific manuscript signed ("A. Einstein," in pencil on verso of p.6), UNPUBLISHED, a working draft with extensive revisions, deletions and addition, in which Einstein explores the construction of a Unified Field Theory based on a Hermitean metric tensor field in a space of four complex, or equivalently eight real, dimensions. The experiment seeks to derive field equations "analogous to the gravitational equations of the General Theory of Relativity." No place, no date [circa 1941-45?]. 4to (8½ x 11 in.), 19 pages, blue fountain-pen ink (2pp. in pencil) on paper watermarked "Whiting Mutual Bond Rag Content," irregularly paginated in four groups: pp.1-7, 13-18, 21-22, plus equations and text on versos of 6, 13 and 16 (the latter two pp. lined out). Tiny rust stain from paperclip, otherwise in very fine condition. In German. A NEW APPROACH TO THE UNIFIED FIELD THEORY: SEEKING "FIELD EQUATIONSANALOGOUS TO THE GRAVITATIONAL EQUATIONS OF THE GENERAL THEORY OF RELATIVITY" From roughly 1923 until the end of his life Einstein dedicated his work in theoretical physics to the study of the Unified Field Theory, seeking a single mathematical path defined on the four-dimensional space-time manifold from which to effect a unification of the gravitational and electromagnetic fields. By applying this structure to the simplest possible field equations, Einstein sought to derive a field theory applicable both to the gravitational field equations of the General Theory of Relativity and Maxwell's electromagnetic field equations. A Unified Field Theory, he hoped, would explain the existence and nature of elementary particles including the electron and would also express the quantum nature of radiation that he had first proposed in 1905. Despite the development of theories of quantum mechanics in the 1920s, Einstein continued to seek a Unified Field Theory that would offer an alternative explanation of quantum phenomena. In this investigation, Einstein considered and tested several different mathematical structures, one of which is embodied in this manuscript, that might furnish a basis for the Unified Field Theory. Einstein began work on a class of field theories based on a Hermitean metric tensor field in 1941. Early work on this include item 2-135 in the Einstein Archive-- an unpublished manuscript entitled "Metrische Geometri komplexer Raume" ("Metric Geometry of Complex Spaces"), and Item 2-136, an unpublished manuscript entitled "Der metrische komplexe Raum" ("Metric Complex Space"), both of which appear to date from about 1941. Letters from a collaborator, Valentine Bargmann, also refer to this work (see Items 6-211, 6- 212, 6-213 and 6-215, 15 May 1941 and 22 July [1942]). By August 1942, Einstein had made considerable progress, and he detailed his efforts in a letter to his lifelong friend and collaborator Michele Besso (1873-1955). Einstein expressed dissatisfaction with the quantum mechanical probabilistic treatment of microphysics as an ultimate theory of physical, and wrote: "What I am working on now, will appear rather crazy to you, and perhaps it is...I consider a space, the four coordinates of which x1...x4 are complex, so that it really is an 8-dimentional space. To each coordinate x1, therefore, there is associated a complex conjugate x1. Every vector A1 has these four complex components and the conjugate ones A1. The Riemannian metric is replaced by one of the form glk dxl dxk...This is supposed to be real, which requires that glk = gkl (Hermitean metric) The glk are analytic functions of the x1 and xlk . The question is now quite analogous to the Riemannian case. What are the differential equations of second order that are to be postulated for glk. Instead of covariance with respect to arbitrary continuous transformations of real coordinates xl, here there enters (essentially) covariance with respect to transformations of the type xxi= fl (x5) x^xii = fl (x5) The difficulty lies in
EINSTEIN, Albert (1879-1955). Autograph scientific manuscript signed ("A. Einstein," in pencil on verso of p.6), UNPUBLISHED, a working draft with extensive revisions, deletions and addition, in which Einstein explores the construction of a Unified Field Theory based on a Hermitean metric tensor field in a space of four complex, or equivalently eight real, dimensions. The experiment seeks to derive field equations "analogous to the gravitational equations of the General Theory of Relativity." No place, no date [circa 1941-45?].
EINSTEIN, Albert (1879-1955). Autograph scientific manuscript signed ("A. Einstein," in pencil on verso of p.6), UNPUBLISHED, a working draft with extensive revisions, deletions and addition, in which Einstein explores the construction of a Unified Field Theory based on a Hermitean metric tensor field in a space of four complex, or equivalently eight real, dimensions. The experiment seeks to derive field equations "analogous to the gravitational equations of the General Theory of Relativity." No place, no date [circa 1941-45?]. 4to (8½ x 11 in.), 19 pages, blue fountain-pen ink (2pp. in pencil) on paper watermarked "Whiting Mutual Bond Rag Content," irregularly paginated in four groups: pp.1-7, 13-18, 21-22, plus equations and text on versos of 6, 13 and 16 (the latter two pp. lined out). Tiny rust stain from paperclip, otherwise in very fine condition. In German. A NEW APPROACH TO THE UNIFIED FIELD THEORY: SEEKING "FIELD EQUATIONSANALOGOUS TO THE GRAVITATIONAL EQUATIONS OF THE GENERAL THEORY OF RELATIVITY" From roughly 1923 until the end of his life Einstein dedicated his work in theoretical physics to the study of the Unified Field Theory, seeking a single mathematical path defined on the four-dimensional space-time manifold from which to effect a unification of the gravitational and electromagnetic fields. By applying this structure to the simplest possible field equations, Einstein sought to derive a field theory applicable both to the gravitational field equations of the General Theory of Relativity and Maxwell's electromagnetic field equations. A Unified Field Theory, he hoped, would explain the existence and nature of elementary particles including the electron and would also express the quantum nature of radiation that he had first proposed in 1905. Despite the development of theories of quantum mechanics in the 1920s, Einstein continued to seek a Unified Field Theory that would offer an alternative explanation of quantum phenomena. In this investigation, Einstein considered and tested several different mathematical structures, one of which is embodied in this manuscript, that might furnish a basis for the Unified Field Theory. Einstein began work on a class of field theories based on a Hermitean metric tensor field in 1941. Early work on this include item 2-135 in the Einstein Archive-- an unpublished manuscript entitled "Metrische Geometri komplexer Raume" ("Metric Geometry of Complex Spaces"), and Item 2-136, an unpublished manuscript entitled "Der metrische komplexe Raum" ("Metric Complex Space"), both of which appear to date from about 1941. Letters from a collaborator, Valentine Bargmann, also refer to this work (see Items 6-211, 6- 212, 6-213 and 6-215, 15 May 1941 and 22 July [1942]). By August 1942, Einstein had made considerable progress, and he detailed his efforts in a letter to his lifelong friend and collaborator Michele Besso (1873-1955). Einstein expressed dissatisfaction with the quantum mechanical probabilistic treatment of microphysics as an ultimate theory of physical, and wrote: "What I am working on now, will appear rather crazy to you, and perhaps it is...I consider a space, the four coordinates of which x1...x4 are complex, so that it really is an 8-dimentional space. To each coordinate x1, therefore, there is associated a complex conjugate x1. Every vector A1 has these four complex components and the conjugate ones A1. The Riemannian metric is replaced by one of the form glk dxl dxk...This is supposed to be real, which requires that glk = gkl (Hermitean metric) The glk are analytic functions of the x1 and xlk . The question is now quite analogous to the Riemannian case. What are the differential equations of second order that are to be postulated for glk. Instead of covariance with respect to arbitrary continuous transformations of real coordinates xl, here there enters (essentially) covariance with respect to transformations of the type xxi= fl (x5) x^xii = fl (x5) The difficulty lies in
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