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Re: Arch and scaffold: How Einstein found his field equations

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On 11/2/2015 10:31 AM, Sam Wormley wrote:
> Arch and scaffold: How Einstein found his field equations


>
>
>> In his later years, Einstein often claimed that he had obtained the
>> field equations of general relativity by choosing the mathematically
>> most natural candidate. His writings during the period in which he
>> developed general relativity tell a different story.
>


more in depth with equations, and references here;

http://arxiv.org/pdf/1201.5353


"There are differences between the proofs and the printed version of the 
paper from March 1916. In the November 20 proofs Hilbert asserted that 
the theory he was developing could not be generally covariant. He based 
his assertion on a slightly more sophisticated version of Einstein's 
Hole Argument, and he cites Einstein's 1914 discussion of this argument.

Hilbert was adopting Einstein's line of reasoning from 1913-mid 1915 
just at the time that Einstein was abandoning it, in favor of a return 
to general covariance.251 In addition, in Hilbert's proofs of November 
20 the gravitational field equations do not appear explicitly. 252 In 
the published version of March 1916 – after Einstein had published the 
final form of his field equations – the expression equivalent in form to 
Einstein's November 25 equations (2a) and (6) is written down 
explicitly. Corry, Renn and Stachel indeed claim that knowledge of 
Einstein's result [equations (2a) and (6)] may have been crucial to 
Hilbert's introduction of the second term in his equation, which was 
equivalent in form to these equations of Einstein. 253 And thus 
Einstein's 63 papers helped Hilbert in putting his November 20 paper in 
a malleable form containing generally covariant field equations.

Finally, in the proofs of 6 December, Hilbert supplemented his reference 
to the gravitational potentials gin handwriting with the phrase 
"first introduced by Einstein".254 However, Renn and Stachel found 
lately that, in the December 6 proofs in handwriting Hilbert not only 
acknowledged Einstein's priority but attempted to placate him.

In the introduction to his paper Hilbert wrote,255 "In the following – 
in the sense of the axiomatic method – I would like to develop, 
essentially from three axioms a new system of basic equations of 
physics, of ideal beauty, concerning, I believe, the solution of the 
problems presented". Hilbert deleted the word "new", and this is a clear 
indication that he had read Einstein's November 25 paper and recognized 
that his own equations are formally equivalent (because of where the 
trace term occurs) to Einstein's.

On December 20, 1915 Einstein wrote Hilbert,256 "There has been certain 
resentment between us, the cause of which I do not want to analyze. I 
have fought against the associated feeling of bitterness, and this with 
complete success. I think of you again with unmixed kindness, and I ask 
you to try to do the same with me. It is objectively a shame when two 
real guys that have emerged from this shabby world do not give each 
other a little pleasure".

In the March 1916 printed version of his November 20 paper Hilbert added 
a reference to Einstein's November 25 paper and wrote, "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 last papers".257

On May, 27, 1916 Hilbert replied to Einstein's letter, and then only in 
response to a post card from Einstein with some questions about 
Hilbert's first paper on his new theory, which has just been published.

Hilbert invited Einstein to visit Göttingen again and stay with him; but 
in spite of several invitations over the next few years, Einstein never 
came, perhaps because of Einstein's poor health in the last years of 
World War I. However, they continued to correspond over issues connected 
with Hilbert's paper.258

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Arch and scaffold: How Einstein found his field equations Sam Wormley <swormley1@gmail.com> - 2015-11-02 10:31 -0600
  Re: Arch and scaffold: How Einstein found his field equations gilber34 <fafa@invalid.com> - 2015-11-02 10:57 -0600
  Re: Arch and scaffold: How Einstein found his field equations Jeffrey Bannister <jbann@highadvancedscience.org> - 2015-11-02 19:41 +0000
  Re: Arch and scaffold: How Einstein found his field equations Fabian Russell <root@localhost.localdomain> - 2015-11-02 20:07 +0000
    Re: Arch and scaffold: How Einstein found his field equations xxein1@att.net - 2015-11-04 18:11 -0800
      Psalms 46 noTthaTguY <abu.kuanysh05@gmail.com> - 2015-11-05 20:08 -0800
  Re: Arch and scaffold: How Einstein found his field equations "Y.Porat" <y.y.porat@gmail.com> - 2015-11-06 05:23 -0800
    languages of the mother tongue(s noTthaTguY <abu.kuanysh05@gmail.com> - 2015-11-07 18:17 -0800

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