David Hilbert and Albert Einstein independently developed theories of relativity, with Hilbert's action being submitted first but lacking covariant treatment. Einstein formulated the field equations in a fully covariant manner without initially recognizing their derivation from Hilbert's action. The discussion concludes that Hilbert's initial restrictions rendered his theory non-covariant, while Einstein later acknowledged the advantages of deriving field equations from an action. Ultimately, Hilbert's contributions were influenced by Einstein's presentations.
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atyy said:Hmmm, so it seems that there is no debate that the Hilbert action was first (as judged by date of receipt)?
The only debate is about the field equations, which can be derived from the Hilbert action?
PAllen said:That is my understanding. However, it is also my understanding that Einstein initially did not care for derivation from an action, and such an approach had no part in how he derived the field equations. Since the variation of the action is not trivial (though it may seem so decades later), there is also no evidence that Hilbert wrote down field equations before Einstein.
I think a fair summary might be:
1) Hilbert first wrote a correct action, but attached restrictions to it that made it not a covariant theory.
2) Einstein first wrote the field equations (with fully covariant treatment), but did not know, they could be derived from the Hilbert action.
3 Seeing Einstein's final covariant field equations, Hilbert realized they could be derived from his action, and the whole approach made covariant.
4) Later, Einstein accepted the superiority of deriving the field equations form an action.
Also obvious is that Hilbert was able to contribute as he did only by virtue of the presentations Einstein gave him.