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Albert Einstein Unified Field Theory AM, 170+ Words & 7 Lines of Equations: "This and the conjugate equation form the 'energy-impulse principle' in its natural form"

A 1p autograph manuscript in German written entirely in the hand of Albert Einstein (1879-1955), the Nobel Prize-winning physicist, comprised of over 170 words and 7 lines of equations relating to the development of his United Field Theory. N.d., n.p. Inscribed in pen on a leaf of watermarked paper numbered "(15)" at upper right, with subsequent numbers in pencil appearing along the right margin. A working document, the manuscript is heavily edited by Einstein, with numerous contemporary cross-outs, insertions, and rewrites appearing throughout the text and formulae. Expected wear including even toning. The upper right hand corner is slightly wrinkled. Else near fine. 8.5" x 11." Accompanied by a German transcription and English translation of all of the legible text excepting the formulae. Previously unpublished.

Translated in part:

"I will now move on to the second approach, which gives us the conservation theorem of impulse and energy in its natural form. If you multiply the field equations (22 a) with ymn and form the usual divergence of the resulting tensor density, you will first obtain


If you consider in the first term the proportion that comes from the usual differentiation after a, it disappears because of the antisymmetry of the contents of the parenthesis with regard to the indices a and n. From the first term, therefore, only the following in the [symbol] square part remains:


in which the two parts with the factor [variables] or [variables] lift away. The third term in the parenthesis also disappears because of the antisymmetry of [variables] in the indices a and l

In the second term, too, only the [symbol] square terms remain, because [variables], k, n or (variables, n), k disappears. The second term therefore takes the form


If this is satisfied, in the above equation after simple rearrangement, you obtain


(Instead of — [variables], you can also write + [variables]) This and the conjugate equation form the 'energy-impulse principle' in its natural form."

In the early 1940s, Einstein began trying to extend the formulation of the General Theory of Relativity for the purpose of Unified Field Theory. Intensely mathematical and highly abstract theoretical investigations, these Unified Field Theories explored the implications of enabling the metric tensor of General Relativity to support both complex manifolds and asymmetric components. As in so many other areas of physics, Einstein was very definitely a pioneer in this mode of research; and because the mathematics of such asymmetric metric tensors was not well understood at the time, Einstein had to “feel his way forward” – repeatedly developing and abandoning different mathematical approaches to the problem. In generalizing the relativistic equations of gravitation by mathematical methods, Einstein hoped that the equations thus obtained would have direct application to the real world (with the symmetric and antisymmetric components of the metric tensor respectively providing the formal support for gravity and electromagnetism), but he was ultimately unable to develop field equations that adequately represented the empirical realities of physics.

Here, Einstein is working through what appears to be extended gravity field equations for the General Theory of Relativity. The present manuscript evidences an early stage of Einstein’s work with asymmetric field theory, and would appear to be a precursory draft for his famous 1945 paper “Generalization of the Relativistic Theory of Gravitation” (Weil 215). Working with a Hermetian tensor, Einstein has here derived a set of field equations, including what he claims are: "This and the conjugate equation form the 'energy-impulse principle' in its natural form." Einstein was perhaps too optimistic in this conclusion, and it appears that Einstein subsequently abandoned this present approach to Unified Field Theory.

This item comes with a Certificate from John Reznikoff, a premier authenticator for both major 3rd party authentication services, PSA and JSA (James Spence Authentications), as well as numerous auction houses.


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