General relativity priority dispute

Albert Einstein's discovery of the gravitational field equations of general relativity and David Hilbert's almost simultaneous derivation of the theory using an elegant variational principle, during a period when the two corresponded frequently, has led to numerous historical analyses of their interaction. The analyses came to be called a priority dispute.

The events of interest to historians of the dispute occurred in late 1915. At that time Albert Einstein, now perhaps the most famous modern scientist, had been working on gravitational theory since 1912. He had "developed and published much of the framework of general relativity, including the ideas that gravitational effects require a tensor theory, that these effects determine a non-Euclidean geometry, that this metric role of gravitation results in a redshift and in the bending of light passing near a massive body." While David Hilbert never became a celebrity, he was seen as a mathematician unequaled in his generation, with an especially wide impact on mathematics. When he met Einstein in the summer of 1915, Hilbert had started working on an axiomatic system for a unified field theory, combining the ideas of Gustav Mie's on electromagnetism with Einstein's general relativity. As the historians referenced below recount, Einstein and Hilbert corresponded extensively throughout the fall of 1915, culminating in lectures by both men in late November that were later published. The historians debate consequences of this friendly correspondence on the resulting publications.

The following facts are well established and referable:

Historians have discussed Hilbert's view of his interaction with Einstein.

Walter Isaacson points out that Hilbert's publication on his derivation of the equations of general relativity included the text: “The differential equations of gravitation that result are, as it seems to me, in agreement with the magnificent theory of general relativity established by Einstein.”

Wuensch points out that Hilbert refers to the field equations of gravity as "meine Theorie" ("my theory") in his 6 February 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 had "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 Einstein's 25 November 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"^{[citation needed]}. 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."