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Albert Einstein

Currency:USD Category:Collectibles / Autographs Start Price:NA Estimated At:175,000.00 - 200,000.00 USD
Albert Einstein

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Auction Date:2018 Jun 13 @ 18:00 (UTC-5 : EST/CDT)
Location:236 Commercial St., Suite 100, Boston, Massachusetts, 02109, United States
ALS - Autograph Letter Signed
ANS - Autograph Note Signed
AQS - Autograph Quotation Signed
AMQS - Autograph Musical Quotation Signed
DS - Document Signed
FDC - First Day Cover
Inscribed - “Personalized”
ISP - Inscribed Signed Photograph
LS - Letter Signed
SP - Signed Photograph
TLS - Typed Letter Signed
Important handwritten manuscript in German, unsigned (but incorporating "Einstein" in the title), two pages, 8 x 10.25, no date but circa late 1922. Headed (translated), "Comment on E. Trefftz's Paper: 'The Static Gravitational Field of Two Mass Points in Einstein's Theory,'" the paper was presented on November 23, 1922, to the Berlin-based Royal Prussian Academy of Sciences, who published the work on December 21, 1922. The present manuscript was probably a draft used for typesetting, as it contains several handwritten editor's annotations in pencil which were executed in the published version. This was Einstein's first paper published after he received the Nobel Prize on December 10, 1922.

The manuscript is Einstein's criticism of a paper in which the author, Erich Trefftz, claimed to have found a static solution of the equations of general relativity for two point masses; Einstein points out that such a conclusion is based on an error. Featuring several mathematical equations—including a modified form of his General Theory of Relativity—Einstein's manuscript reads, in part (translated): "The author grounds his analysis on the field equations in vacuo, Rik –1/4gikR = 0 (1), which are equivalent to the equations: (Rik – 1/2gikR) – ?gik = 0 (1a), as is easily proved by reducing (1a). The author believes he has found a solution that has a spherical connection in space and except for the two masses no singularity, also not containing any other masses.

In view of the importance of the problem to the cosmological issue, i.e., the question of the large-scale geometrical structure of the universe, I was interested to know whether the equations really did yield as a physical possibility a static universe whose material mass was concentrated in just two celestial bodies. It became apparent, however, that Trefftz's solution does not permit this physical interpretation at all. This will be demonstrated in the following.

Mr. Trefftz sets out the assumption for the (four-dimensional) line element: ds2 = f4(x)dt2 – [dx2 + f2(x)(d?2 + sin2?df2)] (2). This assumption corresponds to a space of spherical symmetry around the origin. The special case f4 = const; f2 = x2 would correspond to the Euclidean-Galilean isotropic and homogeneous space." Einstein goes on to identify that, according to a general solution proposed by Trefftz, "for negative A and vanishing B this yields the well-known Schwarzschild solution for the field of a material point." The manuscript breaks off mid-sentence at the end of the second page, and is missing three-and-a-half concluding lines found in the published version; copies of the paper as published, in both German and English, are included.

In very good to fine condition, with scattered light creasing, paperclip impressions to the upper left corner of each page, a semicircular area of spilled wax on the top edge of the first page, and separations along the central horizontal fold of each page (the second page repaired with old tape on the reverse). Accompanied by a full letter of authenticity from University Archives. Provenance: Albert Einstein, 1922; Max von Laue, Royal Prussian Academy of Sciences, 1922–1948; Alexander Dingas, 1948–1964; G. Schrupf, 1964–1980s; private collector, Berlin, 1980s–2016. Includes a letter of provenance by Dingas, dated April 12, 1964, in part (translated): "Einstein – Manuscript, given by Mr. v. Laue, 1948 in Gottingen, Alex. Dingas. For Miss G. Schrupf. To be used in any way, possibly even for sale." Notably, Max von Laue was himself a Nobel Prize–winning physicist and a member of the Prussian Academy of Sciences.

Most significantly, this manuscript contains a handwritten version of Einstein's General Theory of Relativity, incorporating a cosmological constant: "(Rik – 1/2gikR) – ?gik = 0." In 1915, Einstein made his groundbreaking achievement with the introduction of the General Theory of Relativity. The heart of the theory, where the generally covariant field equations of gravitation, is written in the form: 'Rik – 1/2gikR = - kTik.' In 1917, Einstein applied his equations to the problem of explaining the structure of the cosmos on a large scale and found that he would need to modify his equations by adding another term, containing a constant, which he denoted ? and called 'cosmological.' This cosmological constant relied on a static universe; upon the later discovery that the universe was expanding, Einstein reportedly called this the greatest blunder of his career.

With the famous cosmological constant and for the special case of a vacuum, where the energy-momentum tensor 'Tik' vanishes, Einstein’s gravitational field equations read "(Rik – 1/2gikR) - ?gik = 0," which is the equation cited as "(1a)" in the present manuscript. By a mathematical operation called contraction, equation "(1a)" implies that ? = - R/4 in the case of a vacuum. Substituting this expression for ? into equation (1a), one obtains the equation "Rik – 1/4 gikR = 0," which is given as equation "(1)" in the present manuscript. It was advanced by Einstein in a 1919 paper as a candidate for a slightly modified field equation to account both for the structure of matter and for cosmological structure. With important scientific content—and an enormously significant date within the context of Einstein's career—this is a truly remarkable piece which stands as the most spectacular Einstein manuscript we have ever offered.