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Autograph manuscript, 'Feldgleichungen' (field equations), a summary of his paper 'Systematic investigations of compatible field equations ...', [April 1931]
細節
Albert Einstein (1879-1955)
Autograph manuscript, 'Feldgleichungen' (field equations), a summary of his paper 'Systematic investigations of compatible field equations ...', [April 1931]
In German. One page, 267 x 219mm, including 9 numbered equations, the paper with perforations at upper margin where extracted from a pad. Housed in a custom cloth box. Provenance: Sotheby's New York, 27 June 1989, lot 39 (part: one of ten related manuscripts in the sale, all drafts on unified field theory, chiefly the distant parallelism approach); Harvey Plotnick Library of Quantum Physics, Christie's New York, 4 October 2002, lot 97.
Einstein's summary of his last attempt on a unified field theory based on distant parallelism. The summary begins with the Ansatz (assumed mathematical form) for the field equations of the theory and for the divergence identity which is to be satisfied, numbered (1) and (2), both of which contain a series of unspecified constants: the next steps are to 'Substitute (1) into (2) and determine the constants such that identity is maintained'. A further transformation is to take place, taking into account three further identities which Einstein numbers (3) to (5). 'Performing the calculation yields 20 equations for the 10 constants ... A more detailed examination of the results ... yields 4 types of equations, which can be characterized as follows ...'. He then sets out the four field equations which result, and ends with the notes 'I and II contain earlier gravitational equations as a special case. / II appears as the most natural singularity-free solutions!'.
This unusually technical paper, written jointly with Einstein's mathematical collaborator Walther Mayer, was his last contribution to the theory of distant parallelism, which had been the basis of his attempts on a unified field theory (one that would account for both electromagnetism and gravity) since 1928. This theory substituted the mathematical language of curvature used in general relativity with one based on torsion: in this version of gravity based on 'distant parallelism' or 'teleparallelism', matter and energy work on spacetime by twisting rather than curving it, and this twisting ripples outwards to affect everything else. In the present paper, Einstein and Mayer attempt to find and classify all the field equations compatible with a divergence-like identity, leading to a classification of the four types of field equation which emerge. Ultimately, Einstein abandoned the distant parallelism approach on the basis, as he explained later, that it was impossible to find a tensor-like representation of electromagnetism, and that the theory left 'too large a freedom for the choice of the field equations'. However, the richer, more complicated mathematics of distant parallelism have attracted recent interest as a basis for solving the mysteries of dark matter and dark energy.
The paper was presented to the Prussian Academy of Sciences on 23 April 1931, and published as 'Systematic investigations of compatible field equations that are possible in a Riemannian space with distant parallelism' (Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-mathematische Klasse, 1931, 257–265). Schilpp 250.
Autograph manuscript, 'Feldgleichungen' (field equations), a summary of his paper 'Systematic investigations of compatible field equations ...', [April 1931]
In German. One page, 267 x 219mm, including 9 numbered equations, the paper with perforations at upper margin where extracted from a pad. Housed in a custom cloth box. Provenance: Sotheby's New York, 27 June 1989, lot 39 (part: one of ten related manuscripts in the sale, all drafts on unified field theory, chiefly the distant parallelism approach); Harvey Plotnick Library of Quantum Physics, Christie's New York, 4 October 2002, lot 97.
Einstein's summary of his last attempt on a unified field theory based on distant parallelism. The summary begins with the Ansatz (assumed mathematical form) for the field equations of the theory and for the divergence identity which is to be satisfied, numbered (1) and (2), both of which contain a series of unspecified constants: the next steps are to 'Substitute (1) into (2) and determine the constants such that identity is maintained'. A further transformation is to take place, taking into account three further identities which Einstein numbers (3) to (5). 'Performing the calculation yields 20 equations for the 10 constants ... A more detailed examination of the results ... yields 4 types of equations, which can be characterized as follows ...'. He then sets out the four field equations which result, and ends with the notes 'I and II contain earlier gravitational equations as a special case. / II appears as the most natural singularity-free solutions!'.
This unusually technical paper, written jointly with Einstein's mathematical collaborator Walther Mayer, was his last contribution to the theory of distant parallelism, which had been the basis of his attempts on a unified field theory (one that would account for both electromagnetism and gravity) since 1928. This theory substituted the mathematical language of curvature used in general relativity with one based on torsion: in this version of gravity based on 'distant parallelism' or 'teleparallelism', matter and energy work on spacetime by twisting rather than curving it, and this twisting ripples outwards to affect everything else. In the present paper, Einstein and Mayer attempt to find and classify all the field equations compatible with a divergence-like identity, leading to a classification of the four types of field equation which emerge. Ultimately, Einstein abandoned the distant parallelism approach on the basis, as he explained later, that it was impossible to find a tensor-like representation of electromagnetism, and that the theory left 'too large a freedom for the choice of the field equations'. However, the richer, more complicated mathematics of distant parallelism have attracted recent interest as a basis for solving the mysteries of dark matter and dark energy.
The paper was presented to the Prussian Academy of Sciences on 23 April 1931, and published as 'Systematic investigations of compatible field equations that are possible in a Riemannian space with distant parallelism' (Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-mathematische Klasse, 1931, 257–265). Schilpp 250.
榮譽呈獻
Eugenio Donadoni
Senior Specialist, Medieval & Renaissance Manuscripts