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Autograph manuscript, 'Verallgemeinerung der relativistischen Gravitationstheorie II' (A generalisation of the relativistic theory of gravity), [1946]
Details
Albert Einstein (1879-1955)
Autograph manuscript, 'Verallgemeinerung der relativistischen Gravitationstheorie II' (A generalisation of the relativistic theory of gravity), [1946]
In German. A partial manuscript, with cancellations and emendations, four pages, 280 x 216mm (paginated), including 29 distinct mathematical equations; on paper with watermark 'WHITING / MUTUAL BOND / RAG CONTENT'.
The autograph manuscript for the first half of this important late paper on unified field theory. The paper, co-written with Ernst Gabor Straus, was submitted to Annals of Mathematics on 24 January 1946 and published (in English) in October that year (vol. 47, no. 4): the translated text closely follows the original German of this manuscript. The paper sought to correct an error in Einstein's 1945 paper of the same title, which had 'asserted ... that there exist identities which allow us to adjoin these equations [Γi = ½ (Γaia - Γaai) = 0.] without introducing an impermissible overdetermination. This assertion was, however, based on an error. The introduction of equation (1) implies a different derivation of the field equations from the original one and a (slight) deviation of the latter from the field equations of the first paper'. Einstein and Straus go on to re-state the propositions of their previous paper, with this modification. The present draft comprises section 1, 'The dependence of the infinitesimal parallel translation of the fundamental tensor. Absolute differentiation of densities ... Absolute differentiation of tensor densities' and part of section 2, 'Hamiltonian. Field equations', concluding with the equation numbered 6.1 in the published text.
The paper and its predecessor laid the foundations for Einstein's last approach to unified field theory, in which he extended the symmetric metric tensor of general relativity into a non-symmetric, complex Hermitian tensor which would cover both gravitation and electromagnetism. Its approach incorporated both real and imaginary components within a unified geometric framing, but its formidably complex mathematics and stern refusal to incorporate quantum mechanics meant that it ultimately proved inconclusive. Nevertheless, Einstein continued to work on it until his death, still firm in his conviction that the world could be explained purely by the beauties of mathematics. After a lifetime of trying alternative approaches, Einstein ultimate conclusion was that his own theory of general relativity remained the best basis on which to build a unified field theory.
Autograph manuscript, 'Verallgemeinerung der relativistischen Gravitationstheorie II' (A generalisation of the relativistic theory of gravity), [1946]
In German. A partial manuscript, with cancellations and emendations, four pages, 280 x 216mm (paginated), including 29 distinct mathematical equations; on paper with watermark 'WHITING / MUTUAL BOND / RAG CONTENT'.
The autograph manuscript for the first half of this important late paper on unified field theory. The paper, co-written with Ernst Gabor Straus, was submitted to Annals of Mathematics on 24 January 1946 and published (in English) in October that year (vol. 47, no. 4): the translated text closely follows the original German of this manuscript. The paper sought to correct an error in Einstein's 1945 paper of the same title, which had 'asserted ... that there exist identities which allow us to adjoin these equations [Γi = ½ (Γaia - Γaai) = 0.] without introducing an impermissible overdetermination. This assertion was, however, based on an error. The introduction of equation (1) implies a different derivation of the field equations from the original one and a (slight) deviation of the latter from the field equations of the first paper'. Einstein and Straus go on to re-state the propositions of their previous paper, with this modification. The present draft comprises section 1, 'The dependence of the infinitesimal parallel translation of the fundamental tensor. Absolute differentiation of densities ... Absolute differentiation of tensor densities' and part of section 2, 'Hamiltonian. Field equations', concluding with the equation numbered 6.1 in the published text.
The paper and its predecessor laid the foundations for Einstein's last approach to unified field theory, in which he extended the symmetric metric tensor of general relativity into a non-symmetric, complex Hermitian tensor which would cover both gravitation and electromagnetism. Its approach incorporated both real and imaginary components within a unified geometric framing, but its formidably complex mathematics and stern refusal to incorporate quantum mechanics meant that it ultimately proved inconclusive. Nevertheless, Einstein continued to work on it until his death, still firm in his conviction that the world could be explained purely by the beauties of mathematics. After a lifetime of trying alternative approaches, Einstein ultimate conclusion was that his own theory of general relativity remained the best basis on which to build a unified field theory.
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