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Did Hilbert publish general relativity field equation before Einstein?

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up vote 32 down vote accepted


On November 25, nearly ten years after the foundation of special relativity, Einstein submitted his paper The Field Equations of Gravitation for publication, which gave the correct field equations for the theory of general relativity (or general relativity for short). Actually, the German mathematician David Hilbert submitted an article containing the correct field equations for general relativity five days before Einstein. Hilbert never claimed priority for this theory. [Bold mine.]

The Official Web Site of the Nobel Prize

Edit 1. But...

Many have claimed that in 1915 Hilbert discovered the correct field equations for general relativity before Einstein but never claimed priority. The article [11] however, shows that this view is in error. In this paper the authors show convincingly that Hilbert submitted his article on 20 November 1915, five days before Einstein submitted his article containing the correct field equations. Einstein's article appeared on 2 December 1915 but the proofs of Hilbert's paper (dated 6 December 1915) do not contain the field equations.

As the authors of [11] write:-

In the printed version of his paper, Hilbert added a reference to Einstein's conclusive paper and a concession to the latter's priority: "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 in his later papers". If Hilbert had only altered the dateline to read "submitted on 20 November 1915, revised on [any date after 2 December 1915, the date of Einstein's conclusive paper]," no later priority question would have arisen.

[11] L Corry, J Renn and J Stachel, Belated Decision in the Hilbert-Einstein Priority Dispute, Science 278 (14 November, 1997).


Edit 2. Haha, butbut... :)

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Edit 3. Roundup.

Recent controversy, raised by a much publicized 1997 reading of Hilbert's proof-sheets of his article of November 1915, is also discussed [on pp. 11-13; presumed included in this answer].

Einstein and Hilbert had the moral strength and wisdom - after a month of intense competition, from which, in a final account, everybody (including science itself) profited - to avoid a lifelong priority dispute (something in which Leibniz and Newton failed). It would be a shame to subsequent generations of scientists and historians of science to try to undo their achievement.

Einstein and Hilbert: The Creation of General Relativity

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"It would be a shame to subsequent generations of scientists and historians of science to try to undo their achievement." These words sound utterly manipulative. Like somebody dislikes the truth and for that bad reason inclines us to believe the nonsense that historical research can undermine the achievements made. – Val Apr 25 '13 at 19:28
@Val I think the author meant something different than "undermine" with his "undo", perhaps more like "under-appreciate". In my reading, he emphasises that the near-simulteneity wasn't because GR was there for the taking ("low-hanging fruit"), but rather that the development of GR was a huge effort. – Keep these mind Apr 25 '13 at 20:00
This is an excellent collection of quotes, thanks! It does seem to me, though, that Hilbert was quite fond of his way of deriving the equations and behind all the politeness was a feeling of superiority. Because in one of his "Lectures on the Foundations of Physics" that Hilbert gave a few days after Einstein's article surfaced he speaks of the work of Civita, Weyl, Schouten, Eddington and culminating in Einstein as a "colossal detour" and concludes that Einstein's equations confirm his variational computation is a "nice consistency check" (German: "schöne Gewähr"). See the citations listed.. – Urs Schreiber Feb 5 '14 at 0:11

Gugg's answer is thorough (+1 :-), and the answer to your question is probably "yes". However Hilbert acknowledged that he had merely added the last step to a long process and therefore that he had no claim to have invented General Relativity.

It's tempting to think of GR being revealed to the world in a single stunning paper, but this isn't the way it happened. Hilbert was only able to write down the correct action because of the previous publications by Einstein on his work leading up to that point.

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Edit: Hilbert Derived the EFE before Einstein, but using the EH Action as a postulate. Einstein took the EFE as a postulate.

I think the matter is only the formulation of General Relativity; the postulates made.

Hilbert's postulate was elegantly simple. It was only that

$$\mathcal L_G=\lambda R$$

I.e. that the Lagrangian Density of Gravity was proportional to the Ricci Scalar. From then on, he applied the Hamilton's principle to this's equation and found that the field equations for gravity are $$G_{\mu\nu}=\kappa T_{\mu\nu}$$ And then, he showed how this is a better theory of gravity etc. etc.

Einstein's postulate was not so elegant or simple, in my opinion. However, many hold that it was simpler. His postulate was the field equation itself! I.e that

$$G_{\mu\nu}=\kappa T_{\mu\nu}$$

The reason why people hold this to be very elegant is that $\nabla^\mu G_{\mu\nu}=0$ and $\nabla^\mu T_{\mu\nu}=0$.

So, it is no different than whether Einstein or Minkowski should get the credit. Minkowski did it the elegant way.

Similarly, Hilbert did it the elegant way.


Note: That Einstein's postulate was the EFE has its reference in Einstein's original GR paper "On the Foundations of the General Theory of Relativity". As for Hilbert's postulate being the EH Action, I think it was from some book... Can't remember.

P.S. The fact that Einstein's postulate itself was the EFE means that he first wrote down the EFE. The fact that Hilbert's postulate itself was the EH Action means that he first wrote down the EH Action, (that is, 5 days before Einstein wrote down the EFE).

P.P.S. By "wrote down", I mean "published", who knows wheter Einstein/Hilbert actually wrote down the action/FE, or forced someone else to write it for them? Who knows...

P.P.P.S. Another important point of this answer is that there is no controversy, since it is just the formulation that matters, like Einstein&Minkowski, Newton&Leibniz, Heisenberg&Schrodinger&Feynman&somerandompersonwhodiscoveredthevariationalformulation&..., etc. Because the OP seems to think there's a big controversy... But there's not, at least there shouldn't be.

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This doesn't answer the question though. – Larry Harson Jul 3 '13 at 14:17
@LarryHarson: It does. They formulate General Relativity in different ways, both of them contributed to GR in enormous ways, like Ein&Mink, New&Lei etc. and the EFE was postulated and first published by Einstein, but the EH Action was first published by Hilbert. – centralcharge Jul 3 '13 at 14:20
Where in your answer does it say who published what before who, and whether the papers contained the field equations? – Larry Harson Jul 3 '13 at 14:49
The fact that I stated that Einstein's postulate was EFE, and Hilbert's was EH, was enough. AAnd that there's no controversy. – centralcharge Jul 3 '13 at 15:13
Read the question. – Larry Harson Jul 3 '13 at 15:21

People are still asking this? This is revisionist nonsense. Hilbert did NOT publish the correct field equations before Einstein. Research done between 97 and 2002 discovered that field equations published by Hilbert were NOT generally co-variant, Einstein's were. (Ironically it was Einstein who pointed this mathematical fact out to Hilbert - arguably one the top 3 most gifted mathematicians of all-time).

Moreover, if you read the letters between Einstein and Levi-Civita, it is very apparent that it was Einstein who had done most of the mathematical and conceptual work for GR. It was Einstein that had tutored Hilbert - who had invited Einstein to perform a series of lectures in Gottingen on GR in 1913 and 1914. And Einstein, after publishing his failed Entwurf theory (which was a necessary step in clarifying which tensors held primacy), actually wrote down the correct field equations in a previous paper he had discarded in 1914 but returned to once he discovered Hilbert was on his ass. Without Einstein's papers published in 12 through 14 Hilbert doesn't even stand a chance at coming up with the proper FE.

Remember, the most difficult element of GR wasn't the differential equations, it was the translation of very, very difficult kinematic concepts into mathematics. This is why many physicists-cum-historians tend to say that it may have taken another 100 years to discover General Relativity had Einstein never came along. GR is laden with very subtle but highly complex conceptual nuances that defy easy explanation.


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