Belated Decision in the Hilbert-Einstein Priority Dispute

Abstract

According to the commonly accepted view, David Hilbert completed the general theory of relativity at least 5 days before Albert Einstein submitted his conclusive paper on this theory on 25 November 1915. Hilbert's article, bearing the date of submission 20 November 1915 but published only on 31 March 1916, presents a generally covariant theory of gravitation, including field equations essentially equivalent to those in Einstein's paper. A close analysis of archival material reveals that Hilbert did not anticipate Einstein. The first set of proofs of Hilbert's paper shows that the theory he originally submitted is not generally covariant and does not include the explicit form of the field equations of general relativity.

Arch and scaffold: How Einstein found his field equations

“…13 Page proofs of Hilbert's paper, which was not published until March 1916, surfaced in the late 1990s. An analysis of them 14 shows that Einstein need not have worried about Hilbert in November 1915. In important ways, the theory presented in the page proofs is closer to the Entwurf theory than to general relativity in its final form.…”

Selected Solutions of Einstein’s Field Equations: Their Role in General Relativity and Astrophysics

“…Although it would not be inappropriate to 4 David Hilbert submitted his paper on these field equations five days before Einstein, though it was published only on March 31, 1916. Recent analysis [17] of archival materials has revealed that Hilbert made significant changes in the proofs. The originally submitted version of his paper contained the theory which is not generally covariant, and the paper did not include equations (III).…”

“…Now when a slightly nonspherical star starts to collapse, the perturbations become dynamical and propagate as waves. Their evolution can be determined by solving the wave equation (17). Because of the potential barrier (18) the waves get backscattered and produce slowly decaying radiative tails, as shown in the classical papers by Price [108,109], and generalized to the Reissner-Nordström case in [107,110].…”

“…I recall how during my visits to Moscow in the middle of the 1970s Zel'dovich and his colleagues were somewhat regretfully admitting that they were on the edge of discovering the Hawking effect. They realized that an analogue of the Penrose process occurs with the waves (in so called superradiant scattering) which get amplified if their energy per unit angular momentum is smaller than the angular velocity 17 Relativists often consider the effects produced by moving mass currents as "the dragging of inertial frames", but the concept of the gravomagnetic field, or gravomagnetism has some advantages, as has been stressed recently [148]. The gravomagnetic viewpoint, however, has also been used in many works in the pastsee, e.g.…”

How were the Hilbert – Einstein equations discovered?

“…Einstein. In 1997 an article appeared in the journal "Science" under the title "Belated Decision in the Hilbert-Einstein Priority Dispute" [2], the authors of which claim that "...knowledge of Einstein's result may have been crucial to Hilbert's introduction of the trace term into his field equations". On this ground they push forward their point of view "that radically differs from the standard point of view" and which is exposed in a many-page ref.…”