Einstein’s Magnificent Equations Forming His Final Unified Field Theories, a “Coda” to His Life’s Work with Gravity and Relativity
A truly spectacular unpublished autograph manuscript produced by German physicist Albert Einstein (1879-1955), exploring his celebrated Unified Field Theory. Looking to extend his relativistic theory of gravity, Einstein specifies the tensor and field equations defining the spacetime curvature of a new Unified Field Theory in the 1940s. A prime leaf from Einstein’s sketchbook superbly exemplifying Einstein’s final idea of physics, and enriched with more than 10 formulae and equations!
The single leaf of paper features 19 lines of text in German, or nearly 200 words (we counted approximately 189 words excluding the mathematical formulae.) A full 11 lines are devoted to Einstein's mathematical calculations. The manuscript testifies to a nearly seamless work process, but Einstein did make five editorial changes including several cross-outs and additions. The page is numbered 13 at upper right. Near fine. 8.375" x 10.875." Accompanied by a complete translation of the words; we left the advanced math to the scientists among you.
Then (16) takes the form
Now we specialise the vector field in the considered point further through the relationship
where v is a complex scalar. Then the first one disappears and fourth bracket of the expression above, and it can be the second and the third link after the conversion of the summation indices into the latter. After omitting the factor ( - ), one obtains the expression
So, this one has a vector character, so you can infer the vector character of
where the cn are any complex coefficients, but the factor is any tensor a^ts. Hence the tensor character of the bracket. We have thereby eliminated the auxiliary vectors a and b and from the vector field Ai derived by differentiation a tensor existing in the sense of §5.
Now first of all
This is a tensor for each choice of the vector Ai. We now choose the considered points the vector Ai according to the condition: For each choice of the auxiliary vector ls should
Then the last two links of the above expression disappear, and the tensor character of the first term follows and thus also the tensor character of
This tensor is an expression for the "curvature" of the complex space."
In the 1940s, the ever-pioneering Einstein began to explore “the question of whether the most fundamental equations of physics might have a structure other than the familiar partial differential equations” (Abraham Pais, "Subtle is the Lord: The Science and the Life of Albert Einstein" (Oxford: Oxford University Press, 1982), 347). Einstein began conceptualizing new asymmetric forms of Unified Field Theory after abandoning standard Riemanian metric. In creating such asymmetric theories, Einstein would variously compose the metric tensor (and even spacetime itself) from different mixtures of real and complex (“imaginary”) components, and then develop the mathematical properties of his prospective field equations. Only afterwards would Einstein then check to see if the result had a consistent physical interpretation, and depending on that, Einstein might elect either to continue or to abandon his investigations along the laid-down lines.
Products of Einstein’s mature thought, these “Thought Experiments” in asymmetric Unified Field Theory are “highly abstract and esoteric theoretical investigations, mostly of a mathematical character, exploring consequences of a generalized mathematics very much like venturing into an uncharted terrain” (Sauer, 23). The "Thought Experiments" are “hard work,” Einstein said, “for which [even] a true mathematician would not muster the courage” (1947 letter to Romanian mathematician Maurice Solovine).
The present manuscript is an early example of Einstein’s 1940s work with asymmetric Unified Field Theories. It functions as a prelude to Einstein’s major Unified Field Theory statements of the 1940s: “Generalization of the relativistic theory of gravitation” (1945-46, in 2 parts) and “A Generalized Theory of Gravitation” (1948). The page numbering on this leaf clearly evidences that it is part a larger concept and score, but no complete source manuscript is known to exist. Though the existence of unpublished manuscripts such as the present has been known to scholarship, they have never been formally published or studied, and the full particulars of their content remain unknown. This manuscript appears to treat a complex metric not treated elsewhere in Einstein’s published work.
Einstein’s late Unified Field Theories form a “coda” to his life’s work with gravity and relativity. Einstein undoubtedly took as much pleasure in their creation as he did in playing Mozart on his violin. From a musical perspective, these late theories resemble “études” or meditational “jazz exercises” in which Einstein improvises on a theme of his own creation: the relativistic theory of gravity. Heady flights of unfettered genius – Einstein in mathematical nirvana! These late Unified Field Theories are Einstein’s “swan song” and final gift to the world.
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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