General relativity priority dispute

Albert Einstein presented the theories of special relativity and general relativity in publications that either contained no formal references to previous literature, or referred only to a small number of his predecessors for fundamental results on which he based his theories, most notably to the work of Henri Poincaré and Hendrik Lorentz for special relativity, and to the work of David Hilbert, Carl F. Gauss, Bernhard Riemann, and Ernst Mach for general relativity. Subsequently, claims have been put forward about both theories, asserting that they were formulated, either wholly or in part, by others before Einstein. At issue is the extent to which Einstein and various other individuals should be credited for the formulation of these theories, based on priority considerations.
In general relativity, there is a controversy about the amount of credit that should go to Einstein, Marcel Grossmann, and David Hilbert. Many others (such as Gauss, Riemann, William Kingdon Clifford, Ricci, Gunnar Nordström and Levi-Civita) contributed to the development of the mathematical tools and geometrical ideas underlying the theory of gravity. Also polemics exist about alleged contributions of others such as Paul Gerber.
It was noted by Sir Edmund Whittaker in his 1954 book that David Hilbert had derived the theory of General Relativity from an elegant variational principle "almost simultaneously" with Einstein's discovery of the theory. Hilbert's derivation of the theory predated that of Einstein by five days.
Undisputed facts.
The following facts are well established and referable:
Disputed claims.
The following things seem to be unclear, unknown or disputed:
There are a large number of opinions related to these involving questions of "who should get the credit" - these are not enumerated here.
Did Hilbert claim priority for parts of General Relativity?
Kip Thorne concludes, in remarks based on Hilbert's 1924 paper, that Hilbert regarded the General Theory of relativity as Einstein's: "Quite naturally, and in accord with Hilbert's view of things, the resulting law of warpage was quickly given the name the Einstein field equation rather than being named after Hilbert. Hilbert had carried out the last few mathematical steps to its discovery independently and almost simultaneously with Einstein, but Einstein was responsible for essentially everything that preceded those steps...". However, Kip Thorne also stated, "Remarkably, Einstein was not the first to discover the correct form of the law of warpage [. . . .] Recognition for the first discovery must go to Hilbert."
Arguments have been made that Hilbert claimed priority for the field equations themselves; the sources cited for this are:
Hilbert's article (dated 20 November 1915), when it appeared in 1916, contained the text "Die so zu Stande kommenden Differentialgleichungen der Gravitation sind, wie mir scheint, mit der von Einstein in seinen späteren Abhandlungen aufgestellten großzügigen Theorie der allgemeinen Relativität in gutem Einklang." In translation, "The differential equations of gravity arrived at in this way are, I think, in good agreement with those of Einstein in his later papers in which he presented his comprehensive theory of general relativity." Hilbert refers here to the "later papers" of Einstein, obviously to distinguish them from the Entwurf theory of 1913 and the preliminary papers prior to the end of November 1915 when Einstein published the equations of general relativity in their final form.
Wuensch points out that Hilbert refers to the field equations of gravity as "meine Theorie" ("my theory") in his February 6, 1916 letter to Schwarzschild. This, however, is not at issue, since no one disputes that Hilbert had his own "theory", which Einstein criticized as naive and overly ambitious. Hilbert's theory was based on the work of Mie combined with Einstein's principle of general covariance, but applied to matter and electromagnetism as well as gravity.
Mehra and Bjerknes point out that Hilbert's 1924 version of the article contained the sentence "... und andererseits auch Einstein, obwohl wiederholt von abweichenden und unter sich verschiedenen Ansätzen ausgehend, kehrt schließlich in seinen letzten Publikationen geradenwegs zu den Gleichungen meiner Theorie zurück" - "Einstein [...] in his last publications ultimately returns directly to the equations of my theory.". These statements of course do not have any particular bearing on the matter at issue. No one disputes that Hilbert has "his" theory, which was a very ambitious attempt to combine gravity with a theory of matter and electromagnetism along the lines of Mie's theory, and that his equations for gravitation agreed with those that Einstein presented beginning in his, Einstein's, Nov 25 paper (which Hilbert refers to as Einstein's later papers to distinguish them from previous theories of Einstein). None of this bears on the precise origin of the trace term in the Einstein field equations (a feature of the equations that, while theoretically significant, does not have any effect on the vacuum equations, from which all the empirical tests proposed by Einstein were derived).
Sauer says "the independence of Einstein's discovery was never a point of dispute between Einstein and Hilbert ... Hilbert claimed priority for the introduction of the Riemann scalar into the action principle and the derivation of the field equations from it, " (Sauer mentions a letter and a draft letter where Hilbert defends his priority for the action functional) "and Einstein admitted publicly that Hilbert (and Lorentz) had succeeded in giving the equations of general relativity a particularly lucid form by deriving them from a single variational principle". Sauer also stated, "And in a draft of a letter to Weyl, dated 22 April 1918, written after he had read the proofs of the first edition of Weyl's 'Raum-Zeit-Materie' Hilbert also objected to being slighted in Weyl's exposition. In this letter again 'in particular the use of the Riemannian curvature [scalar] in the Hamiltonian integral' ('insbesondere die Verwendung der Riemannschen Krümmung unter dem Hamiltonschen Integral') was claimed as one of his original contributions. SUB Cod. Ms. Hilbert 457/17."
Einstein wrote to Hilbert on 20 December 1915 that there was an "ill-feeling between us" and it has been suspected that this ill feeling was the result of Einstein's bitterness over Hilbert's "nostrification" of his (Einstein's) theory. Others have suggested that Hilbert might have felt that Einstein had derived some benefit or hints from his (Hilbert's) letters, and that those had helped him to arrive at the trace term of the field equations, and if so, that Einstein should have acknowledged this in his paper. But this is pure speculation, aside from Einstein's comment that he believed others (presumably Hilbert) had tried to "nostrify" his theory.
So far, there seems to be no consensus that these statements form a clear claim by Hilbert to have published the field equations first.
Did Einstein develop the field equations independently?
For a long time it was believed that Einstein and Hilbert found the field equations of gravity independently. While Hilbert's paper was submitted somewhat earlier than Einstein's, it only appeared in 1916, after Einstein's field equations paper had appeared in print. For this reason there was no good reason to suspect plagiarism on either side. In 1978, a November 18, 1915 letter from Einstein to Hilbert resurfaced, in which Einstein thanked Hilbert for sending an explanation of Hilbert's work. This was not unexpected to most scholars, who were well aware of the correspondence between Hilbert and Einstein that November, and who continued to hold the view expressed by Albrecht Fölsing in his Einstein biography:
In the very next sentence, after asking the rhetorical question, Folsing answers it with "This is not really probable...", and then goes on to explain in detail why
In their 1997 "Science" paper, Corry, Renn and Stachel quote the above passage and comment that "the arguments by which Einstein is exculpated are rather weak, turning on his slowness in fully grasping Hilbert's mathematics", and so they attempted to find more definitive evidence of the relationship between the work of Hilbert and Einstein, basing their work largely on a recently discovered pre-print of Hilbert's paper. A discussion of the controversy around this paper is given below.
Those who contend that Einstein's paper was motivated by the information obtained from Hilbert have referred to the following sources:
Those who contend that Einstein's work takes priority over Hilbert's, or that both authors did their work independently have used the following arguments:
Scholars.
This section cites notable publications where people have expressed a view on the issues outlined above.
Albrecht Fölsing on the Hilbert-Einstein interaction (1993).
From Fölsing's 1993 (English translation 1998) Einstein biography " Hilbert, like all his other colleagues, acknowledged Einstein as the sole creator of relativity theory."
Cory/Renn/Stachel and Friedwardt Winterberg (1997/2003).
In 1997, Cory, Renn and Stachel published a 3-page article in "Science" entitled "Belated Decision in the Hilbert-Einstein Priority Dispute" , concluding that Hilbert had not anticipated Einstein's equations.
Friedwardt Winterberg, a professor of physics at the University of Nevada, Reno, disputed these conclusions, observing that the galley proofs of Hilbert's articles had been tampered with - part of one page had been cut off. He goes on to argue that the removed part of the article contained the equations that Einstein later published, and he wrote that "the cut off part of the proofs suggests a crude attempt by someone to falsify the historical record". "Science" declined to publish this; it was printed in revised form in "Zeitschrift für Naturforschung", with a dateline of June 5, 2003. Winterberg criticized Corry, Renn and Statchel for having omitted the fact that part of Hilbert's proofs were cut off. Winterberg wrote that the correct field equations are still present on the existing pages of the proofs in various equivalent forms. In this paper Winterberg asserted that Einstein "sought the help of" Hilbert and Klein to help him find the "correct field equation", without mentioning the research of Fölsing (1997) and Sauer (1999) according to which Hilbert "invited" Einstein to Göttingen to give a week of lectures on general relativity in June 1915, which however does not necessarily contradict Winterberg. Hilbert at the time was looking for physics problems to solve.
A short reply to Winterberg's article could be found at ; the original long reply can be accessed via the Internet Archive at . In this reply, Winterberg's hypothesis is called "paranoid" and "speculative". Cory et al. offer the following alternative speculation: "it is possible that Hilbert himself cropped off the top of p. 7 to include it with the three sheets he sent Klein, in order that they not end in mid-sentence."
As of September 2006, the Max Planck Institute of Berlin has replaced the short reply with a note saying that the Max Planck Society "distances itself from statements published on this website [...] concerning Prof. Friedwart Winterberg" and stating that "the Max Planck Society will not take a position in [this] scientific dispute".
Ivan Todorov, in a paper published on ArXiv, says of the debate:
In the paper recommended by Todorov as calm and non-confrontational, Tilman Sauer concludes that the printer's proofs show conclusively that Einstein did not plagiarize Hilbert, stating
Max Born's letters to David Hilbert, quoted in Wuensch, are quoted by Todorov as evidence that Einstein's thinking towards general covariance was influenced by the competition with Hilbert.
Todorov ends his paper by stating:
Anatoly Alexeevich Logunov on general relativity (2004).
Anatoly Logunov (a former vice president of the Soviet Academy of Sciences and currently the scientific advisor of the Institute for High Energy Physics), is author of a book about Poincaré's relativity theory and coauthor, with Mestvirishvili and Petrov, of an article rejecting the conclusions of the Corry/Renn/Stachel paper. They discuss both Einstein's and Hilbert's papers, claiming that Einstein and Hilbert arrived at the correct field equations independently. Specifically, they conclude that:
Wuensch and Sommer (2005).
Daniela Wuensch, a historian of science and a Hilbert and Kaluza expert, responded to Bjerknes, Winterberg and Logunov's criticisms of the Corry/Renn/Stachel paper in a book which appeared in 2005, wherein she defends the view that the cut to Hilbert's printer proofs was made in recent times. Moreover, she presents a theory about what might have been on the missing part of the proofs, based upon her knowledge of Hilbert's papers and lectures.
She defends the view that knowledge of Hilbert's November 16, 1915 letter was crucial to Einstein's development of the field equations: Einstein arrived at the correct field equations only with Hilbert's help ("nach großer Anstrengung mit Hilfe Hilberts"), but nevertheless calls Einstein's reaction (his negative comments on Hilbert in the November 26 letter to Zangger) "understandable" ("Einsteins Reaktion ist verständlich") because Einstein had worked on the problem for a long time.
According to her publisher, Klaus Sommer, Wuensch concludes though that:
In 2006, Wuensch was invited to give a talk at the annual meeting of the German Physics Society (Deutsche Physikalische Gesellschaft) about her views about the priority issue for the field equations.
Wuensch's publisher, Klaus Sommer, in an article in "Physik in unserer Zeit", supported Wuensch's view that Einstein obtained some results not independently but from the information obtained from Hilbert's November 16 letter and from the notes of Hilbert's talk. While he does not call Einstein a plagiarist, Sommer speculates that Einstein's conciliatory December 20 letter was motivated by the fear that Hilbert might comment on Einstein's behaviour in the final version of his paper. Sommer claimed that a scandal caused by Hilbert could have done more damage to Einstein than any scandal before ("Ein Skandal Hilberts hätte ihm mehr geschadet als jeder andere zuvor").
David E. Rowe (2006).
The contentions of Wuensch and Sommer have been strongly contested by the historian of mathematics and natural sciences David E. Rowe in a detailed review of Wuensch's book published in "Historia Mathematica" in 2006. Rowe argues that Wuensch's book offers nothing but tendentious, unsubstantiated, and in many cases highly implausible, speculations.