In his very first(!) published work as a Nobel Prize recipient, Einstein incorporates a variant of his General Theory of Relativity.
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Handwritten manuscript in German (signed "Einstein’schen" in the title). 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 very first paper, published after he received the Nobel Prize on December 10, 1922.
CLICK HERE for a full transcript of the manuscript (in German).
CLICK HERE for a full translation of the manuscript (in English).
In total, the following equations are written in the manuscript.
1. Rik –1/4gikR = 0
1a. (Rik – 1/2gikR) – λgik = 0
2. ds2 = f4(x)dt2 – [dx2 + f2(x)(dθ2 + sin2θdφ2)]
3. x = ∫ dw / √1 + A/w + Bw2
f2 = w2
f4 =C2 (1+A/w+Bw2)
4. (2+3) ds2 =(1+A/w+Bw2)dt2 –dw2/1+A/w+Bw2 – w2 (dθ2 + sin2θdφ2)
5. dw/dx=√1+A/w+Bw2 =0
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) – λgik = 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)(dθ2 + sin2θdφ2)] (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.
Most significantly, this manuscript contains a handwritten version of Einstein's General Theory of Relativity, incorporating a cosmological constant: “(Rik – 1/2gikR) – λgik = 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 λ 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) – λgik = 0," which is the equation cited as "(1a)" in the present manuscript. By a mathematical operation called contraction, equation "(1a)" implies that λ = - R/4 in the case of a vacuum. Substituting this expression for λ 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.
The manuscript was presented on November 23 1922 by Albert Einstein and was later published on December 21 1922 by the Royal Prussian Academy of Sciences (German: Königlich-Preußische Akademie der Wissenschaften). The Royal Prussian Academy of Sciences was an academic academy established in Berlin on 11 July 1700; Albert Einstein became a member of the academy in 1914.
Max von Laue, German physicist who won the Nobel Prize in Physics in 1914 for his discovery of the diffraction of X-rays by crystals, became a corresponding member of the Royal Prussian Academy of Sciences in 1919. Two years later von Laue became regular member of the academy. In other words, von Laue was highly involved in the academy. It is truly remarkable that this manuscript has been owned by two Nobel Prize winners in Physics (von Laue in 1914 and Einstein in 1921).
There are many attributes that makes this manuscript truly high-end and remarkable. The very important scientific content, and the enormously significant date within the context of Einstein's career makes this item stands out from all other Einstein manuscripts. This is arguably one of the most important Einstein papers in existence!
Size: Approximately 8.1 x 10.2 inches / 20,5 x 26 cm each, unframed.
Condition: Fine condition; folded, both horizontal and vertical, with some separation along the folds of the horizontal fold on the first page; impression of a paperclip mark in the upper left corner of both pages; overall scattered staining.
Provenance: Albert Einstein, 1922; Max von Laue, Royal Prussian Academy of Sciences, 1922–1948; Alexander Dingas, 1948–1964; G. Schrupf, 1964–1980s; Private collection, Germany, 1980s–2016. 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". Letter of authenticity from Universal Archives/John Reznikoff. Letter of authenticity from Alexander Bitar History.