Lot 381

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Einstein “General Theory of Relativity” Superb Equations In His Long Manuscript; He Explains Unified Filed Theory Reconciled To Gravity & Relativity

A 1p mathematical manuscript in German entirely inscribed in the hand of Nobel Prize-winning physicist Albert Einstein (1879-1955). The manuscript is paginated "14" at upper right and consists of approximately 366 words and two mathematical equations on watermarked paper. A working document, with several contemporaneous cross-outs, additions, and editorial or typographical reworkings in Einstein's hand. Expected wear including light even toning and isolated edge darkening along the bottom edge. A gentle wrinkle and two isolated stains affect the top and right edges respectively, else near fine. 8.375" x 11." Includes a full transcript in German as well as a complete English translation.

This piece is one of the finest Einstein items we have ever offered. While there have been Einstein manuscripts appearing on the market, very, very few feature direct quotes within the text of “General Theory of Relativity” [allgemeinen Relativitätstheorie] (line 25) and “theory of gravity” [Gravitationstheorie] (line 24), all the while reconciling them to Einstein's famous “field theory,” that is, Unified Field Theory. That there is more than one equation also speaks to the rarity of this item and enhances its value. An important 54pp Einstein manuscript recently sold in Paris for approximately $240,000 per page.

Translated in part:

"A characteristic trait of the theory presented above is that the field equations fulfil identities corresponding to the Bianchi identities to a first approximation but not in a strict manner. This circumstance has the following consequence. For example, one would think that an approximation method for solving the field equations was based on the splitting of the field according to (24). For the sake of simplicity, we limit ourselves to the determination of the field to the first approximation, that is, we approximate the quadratic terms in [ỽ] to the linear. Then we initially have the linear differential equations to determine the [ỽ [k m].
L km = 0 (28)
… In the case of the theory of gravity of real space of the previous General Theory of Relativity, quite analogous calculations can be made. Here, too, the solution of the (28) of the corresponding linear equations leaves a vector [?] and quadratic equations which correspond to equations (27) also apply there. However, the existence of the strict Bianchi identities means that each solution of the linear system of equations (with any choice of vector?) corresponds to the quadratic equations according to (27). Herein lies a profound difference between the two theories, which is based on the diversity of the underlying transformation groups…"

Most famous for developing his General Theory of Relativity, Einstein devoted the later part of his life to the development of Unified Field Theory (UFT). Seeking a coherent set of equations that could elegantly explain both gravity and electromagnetism, Einstein explored a number of different approaches to Unified Field Theory over the years – variously investigating the application of affine geometry, teleparallelism, and 5-dimensional spacetime to the problem – before finally concluding (in the early 1940s) that the equations of General Relativity were in fact the optimal basis on which to build Unified Field Theory. Einstein himself called this groundbreaking approach a “generalization of the relativistic theory of gravitation” (or, alternatively, “a generalized theory of gravitation”), and the present unpublished manuscript superbly examples Einstein’s thinking about the field equations needed for such a UFT generalization of the General Theory of Relativity.

Einstein's manuscript extensively discusses the mathematical concept of Bianchi identities, that is, differential equations satisfied by curvature data. The manuscript refers to several variables including L, k, and m, and uses the lowercase Delta symbol denoting change or difference. Einstein considers vectors, linear equations, and quadratic equations in his quest for a tidy explanation of fundamental laws.

In the manuscript, Einstein also praises the work of "Mr Bargmann" (line 37). This was Valentine "Valya" Bargmann (1908-1989), a German-Jewish physicist who served as Einstein's longtime assistant at Princeton University's Institute for Advanced Study from 1937-1946. Einstein, Bargmann, and another of Einstein's research assistants, Peter Bergmann (1915-2002), co-authored work exploring the Kaluza-Klein 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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March 15, 2023 11:00 AM EDT
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Bid Increments
From: To: Increments:
$0 $99 $10
$100 $299 $20
$300 $499 $25
$500 $999 $50
$1,000 $1,999 $100
$2,000 $2,999 $200
$3,000 $4,999 $250
$5,000 $9,999 $500
$10,000 $19,999 $1,000
$20,000 $49,999 $2,500
$50,000 + $5,000