Albert Einstein 3pp of Unified Field Theory Equations: "I want to try to show that a truly natural choice for field equations exists" -- Formalizing His Final Approach to the Theory of Relativity

3pp, measuring 8.5" x 11", no place, n.d. [Ca, 1940s]. A German scientific manuscript, written in Einstein's hand. The pages are seemingly from a larger work, as they are numbered p. 9-11. Full translation of the pages can be viewed in the accompanying images. Einstein begins with outlining "some formal formations and relationships", writing in part: "The decisive formal difference of the spatial structure considered here compared to the Riemann structure, lies in the existence of tensors of the first order of differentiation…" He then goes on to outline various components and derivations of the tensor with numerous equations. He concludes his work (on the third page) with the statement:

"…The tensor character of Γi ḷ k (or Γi ị ḳ) implies that the spatial structure considered here is much richer in tensors and invariants (which can be formed from the g i k) than the Riemannian Theory. Except for the formations that algebraically result from it Γ and the absolute derivatives and the g, there are also formations, which are based on the tensor character of (lg g), i, ḳ . . . . . (21) Those tensors to be obtained in the manner of the curvature of space are already included in this scheme. This wealth of tensors means that the choice of field equations in the considered manifold are not prescribed by purely formal aspects. In the following, however, I want to try to show that a truly natural choice for field equations exists." Pages have light toning, more so at the edges. Minor chipping at the lower corners. Ink is bold and clear.

Einstein here appears to be at an early stage of his work with such asymmetric Unified Field Theories. This is evidenced both by the very nature of the manuscript’s contents and by the fact that Einstein here uses the pronoun “I” in this manuscript (suggesting that its composition precedes his 1945-48 collaboration with E. G. Straus.) There is a pristine and expansive quality to this composition which one does not find in later versions of Einstein’s Unified Field Theory: it is as if Einstein were here first thinking through the necessary steps and structure such a “thought experiment” requires. Proposing to detail “some formal structures and relationships” of the tensor logic he will be using in his field formulas, Einstein here announces with a straightforward simplicity that the spatial structure he is considering will formally differ from Riemann Space with regard to its internal differentiability. Einstein then proceeds to articulate at considerable length the mathematical nature of his tensor components; but insofar as Einstein’s developed formalism supports a rich variety of outcomes, Einstein concludes that the sought-after field equations cannot be prescribed by purely formal criteria alone, and he suggests that natural conditions will impose a constraint on the supportable outcomes. As the text itself evidences – with its deletions, additions, and emendations – this manuscript is a work in progress. Much of what we see detailed here will later become standardized or routinized or taken for granted in later versions of Einstein’s asymmetric field theory, and Einstein’s almost naïve suggestion here that natural reality will impose a “compatibility” constraint on admissible formulations will later become a dominant concern of his work with such unified field formalisms. Though Einstein ultimately abandoned his work on this paper – we do not find a similar text among his published works -- it appears to represent an early approach to what would become his famous 1945 UFT paper “Generalization of the Relativistic Theory of Gravitation” (Weil 215).

In the early 1940s, Einstein began trying to formulate Unified Field Theory in a manner "analogous to the gravitational equations of the General Theory of Relativity." Returning to a 4-dimensional basis for Unified Field theory, Einstein sought to extend the mathematical framework of General Relativity and thus evidence electromagnetism as a derivative subfield of gravity. Einstein began working on a class of covariant field theories where the metric tensor supported both complex and asymmetric components. (It was Einstein’s hope that the symmetric and antisymmetric components of the metric would somehow provide the formal support for gravitational and electromagnetic forces respectively.) Beginning with a natural generalization of Riemannian symmetric space from real manifolds to complex manifolds (preserving an inversion symmetry at every point), Einstein successively tried out increasingly asymmetric versions of the metric tensor. As the mathematics of asymmetric metric tensors was less well understood than the standard Riemannian metric of General Relativity, Einstein had to “feel his way forward” as he learned how to work with such asymmetric metrics and what to expect from them. Einstein’s late efforts at Unified Field Theory are extremely abstract “thought experiments” – intensely mathematical works composed in the hope of finding a correlate physical connection – and many of them foundered or were abandoned either because of problems with their formalism or because they were ultimately found to be incompatible with empirical reality.

Einstein significantly reduced the number of articles he wrote during WWII and basically published nothing on Unified Field Theory during the period. But as the present manuscript demonstrates, Einstein was actively at work developing a new approach to UFT during these war years. Einstein’s late work with asymmetric field theories has been underexplored by scholars, and no full record exists of the different versions of the theory he tried out. Though the present manuscript was abandoned, it nonetheless evidences some of Einstein’s earliest thinking and works on asymmetric unified field theory, and it is therefore of considerable historical importance. Einstein manuscripts of such caliber and scientific importance are now very rare on the market, and its WWII dating makes it especially desirable.

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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