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Handwritten manuscript by Albert Einstein for an unpublished scientific work, one page, 8.5 x 11, no date but circa early 1940s. Marked "(12)" in the upper right corner, the page is headed "Die Feldgleichungen [The Field Equations]" and boasts a number of autograph equations with prose text in German. In fine condition.
Einstein quietly pioneered a new approach to Unified Field Theory while World War II was raging. Intending his new Unified Field Theory to be 'a generalization of the relativistic theory of gravitation,' Einstein thought such a theory needed to be written in a new mathematical formalism capable of supporting both complex numbers and an asymmetric composition of the metric tensor.
Representing Einstein’s final approach to Unified Field Theory, Einstein worked on such mathematical considerations for the last 15 years of his life. The present manuscript positions us at the beginning of Einstein’s search for such a UFT extension of General Relativity, and it precedes any published statement of his new approach. In this early effort, Einstein attempts to determine the most natural form of algebraic expression for the 16 complex components of a Hermitian metric tensor—seeking an equation capable of yielding the known conservation law for momentum and energy in the limit case of real coordinates.
Tilman Sauer describes Einstein’s final UFT papers as 'highly abstract and esoteric theoretical investigations…exploring consequences of a generalized mathematics very much like venturing into an uncharted terrain,' and Einstein himself said that these papers were 'hard work…for which [even] a true mathematician would not muster the courage.'
