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Rare and important unpublished AMS signed "A. Einstein," one page (enumerated "(2)"), 8.5 x 11, no date. Handwritten leaf of Einstein's work toward a Unified Field Theory (UFT), offering a grand statement explaining how his new UFT equations are compatible with 'the complete system of field equations' for General Relativity and Maxwell’s theory of electromagnetism. Einstein pens a remarkable nine equations on the page, numbering them "(2)" through "(4a)," and makes several editorial corrections throughout the page.
In 1929 Einstein published 'On Unified Field Theory' (Weil 165), a publication that made headlines around the world and rocketed Einstein to the greatest height of his fame. Seeking to unify gravity and electromagnetism in a mathematical set of field equations, Einstein proposed a new vision of spacetime based in the geometrical concept of teleparallelism (or: distant parallelism): a spacetime that supported the vanishing of the curvature tensor while asymmetrically sustaining a non-vanishing 'torsion' (representing the 'spin' of spacetime). The work was highly mathematical in its tone and detail: employing a 'tetrad field' of vectors, Einstein was able to construct and compare tangent vectors at any point of spacetime; and the nonsymmetric affine connections constructible with this mathematical formalism could both assign a displacement to any arbitrary vector and also conserve parallelism at a distance.
Even the great Einstein, however, was challenged by the mathematical complexities of his work. He had difficulty formulating a uniquely determined set of field equations compatible with the established field equations of General Relativity and Maxwell’s Electromagnetism—his theory could only work to a first approximation of such compatibility, beyond which it could not provide accurate solutions—and within a year’s time of publishing 'On Unified Field Theory,' Einstein saw the necessity to publish a further article on 'The Compatibility of Field Equations in Unified Field Theory' (Weil 169).
This present leaf of manuscript is thought to be a preparatory draft for 'The Compatibility of Field Equations in Unified Field Theory.' This remarkable document superbly conveys the concept of mathematically reducing the central formulas of Unified Field Theory to the firmly established equations of General Relativity and Electromagnetism. Working at a very high level of generalization—there is an almost 'archetypal' quality to this manuscript—this document would appear to reflect an early stage of Einstein’s thinking on the topic of Compatibility, the actual article presenting a more specific and articulated mode of statement.
Einstein was ever the pioneer in theoretical physics—always breaking through to new theoretical heights of idea. Einstein’s 1929 paper 'On Unified Field Theory' marked the beginning of his own original efforts to find an adequate mathematical framework for merging gravity and electromagnetism—a quest he would pursue through a series of mathematical variations for the remainder of his life. Realistically viewed, Compatibility is necessarily a central concern of Unified Field Theory; and while 'The Compatibility of Field Equations in Unified Field Theory' is Einstein’s first explicit examination of this critical issue, it was hardly his last: Einstein repeatedly returning to the issue of Compatibility, both privately and publicly, right up until his death.
Signed leaves of Unified Field Theory are extremely rare. This present manuscript is unpublished. In fine condition, with a trivial light stain to the top edge.
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