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Autograph manuscript, 'Naheliegende Modifikation der allgemeinen Relativitätstheorie' (An obvious modification of the general theory of relativity), [c.1932-34]
細節
Albert Einstein (1879-1955)
Autograph manuscript, 'Naheliegende Modifikation der allgemeinen Relativitätstheorie' (An obvious modification of the general theory of relativity), [c.1932-34]
Four pages, 279 x 214mm, including 16 numbered and 6 unnumbered mathematical formulae, on paper with watermark 'CARAVAN BOND / RAG CONTENT'.
An unpublished draft on unified field theory. Einstein proposes modifying the metric tensor gµν of standard general relativity by the addition of a new mathematical object, the scalar density f, which together will fully describe the gravitational field. He then seeks to demonstrate that the resulting displacement field and the scalar density can be assigned a vector 'in a truly natural way': the result, crucial to a unified field theory, is that 'the electromagnetic terms do not vanish, as is unsatisfactorily the case in the original theory'. The equations can be simplified by making the scalar density f equal to 1, although Einstein admits that the result is that the equations lose their general covariance.
'The relativistic theory of the gravitational field assumes that the latter is described by a metric (gµν) alone. We now want to show that, for formal reasons, it is obvious to introduce, alongside the metric, a scalar density f, initially independent of it, which together with the gµν fully characterizes the gravitational field ...'.
Although undated, the manuscript fits most closely into Einstein's approach to unified field theory using 'semi-vectors' between November 1932 and January 1934 (Einstein and Mayer 1932b, 1933a, 1933b, 1934). The American-made paper of the present manuscript may suggest that it was produced during the winter of 1932-33, which Einstein spent at the California Institute of Technology, or after his arrival at Princeton in late 1933. '[T]he incentive came from Paul Ehrenfest, Einstein’s Leyden colleague and one of his closest personal friends. Ehrenfest had closely studied recent investigations of a relativistic quantum theory by Wolfgang Pauli and Paul Dirac, and had introduced the term “spinor” for the two-component complex vector representation of the Lorentz group. Since spinors have somewhat counterintuitive transformation properties, e.g. a full rotation of 360o changes the sign of the spinor, Ehrenfest was uncomfortable with the formalism and urged his colleagues to provide a more natural and intuitive mathematical representation. Einstein and Mayer picked up on this problem in four papers, published between November 1932 and January 1934 (Einstein and Mayer 1932b, 1933a, 1933b, 1934). / In essence, what Einstein and Mayer investigated in these papers was the Dirac equation in a different representation. They introduced what they called “semi-vectors,” essentially a four-dimensional real vector representation of the Lorentz group. They argued that semi-vectors were a more natural concept than the suspicious spinors, most likely because of their similarity to ordinary four-dimensional space-time vectors. As it turned out, however, the field equations for semi-vectors turned out to be decomposable into equations that were equivalent to field equations using the spinors, which in hindsight is not surprising since semi-vectors are not an irreducible representation of the Lorentz group, whereas spinors are' (Tilman Sauer, 'Einstein’s Unified Field Theory Program', 2007, 19).
Autograph manuscript, 'Naheliegende Modifikation der allgemeinen Relativitätstheorie' (An obvious modification of the general theory of relativity), [c.1932-34]
Four pages, 279 x 214mm, including 16 numbered and 6 unnumbered mathematical formulae, on paper with watermark 'CARAVAN BOND / RAG CONTENT'.
An unpublished draft on unified field theory. Einstein proposes modifying the metric tensor gµν of standard general relativity by the addition of a new mathematical object, the scalar density f, which together will fully describe the gravitational field. He then seeks to demonstrate that the resulting displacement field and the scalar density can be assigned a vector 'in a truly natural way': the result, crucial to a unified field theory, is that 'the electromagnetic terms do not vanish, as is unsatisfactorily the case in the original theory'. The equations can be simplified by making the scalar density f equal to 1, although Einstein admits that the result is that the equations lose their general covariance.
'The relativistic theory of the gravitational field assumes that the latter is described by a metric (gµν) alone. We now want to show that, for formal reasons, it is obvious to introduce, alongside the metric, a scalar density f, initially independent of it, which together with the gµν fully characterizes the gravitational field ...'.
Although undated, the manuscript fits most closely into Einstein's approach to unified field theory using 'semi-vectors' between November 1932 and January 1934 (Einstein and Mayer 1932b, 1933a, 1933b, 1934). The American-made paper of the present manuscript may suggest that it was produced during the winter of 1932-33, which Einstein spent at the California Institute of Technology, or after his arrival at Princeton in late 1933. '[T]he incentive came from Paul Ehrenfest, Einstein’s Leyden colleague and one of his closest personal friends. Ehrenfest had closely studied recent investigations of a relativistic quantum theory by Wolfgang Pauli and Paul Dirac, and had introduced the term “spinor” for the two-component complex vector representation of the Lorentz group. Since spinors have somewhat counterintuitive transformation properties, e.g. a full rotation of 360o changes the sign of the spinor, Ehrenfest was uncomfortable with the formalism and urged his colleagues to provide a more natural and intuitive mathematical representation. Einstein and Mayer picked up on this problem in four papers, published between November 1932 and January 1934 (Einstein and Mayer 1932b, 1933a, 1933b, 1934). / In essence, what Einstein and Mayer investigated in these papers was the Dirac equation in a different representation. They introduced what they called “semi-vectors,” essentially a four-dimensional real vector representation of the Lorentz group. They argued that semi-vectors were a more natural concept than the suspicious spinors, most likely because of their similarity to ordinary four-dimensional space-time vectors. As it turned out, however, the field equations for semi-vectors turned out to be decomposable into equations that were equivalent to field equations using the spinors, which in hindsight is not surprising since semi-vectors are not an irreducible representation of the Lorentz group, whereas spinors are' (Tilman Sauer, 'Einstein’s Unified Field Theory Program', 2007, 19).
榮譽呈獻
Eugenio Donadoni
Senior Specialist, Medieval & Renaissance Manuscripts