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I came across the original handwritten papers in which Einstein predicted gravitational waves1:

enter image description here

and since LIGO announced they've detected a signal confirming the predictions I was wondering if someone can briefly describe the equations and possibly explain the mechanism of the experiment?


1. Full original manuscript http://alberteinstein.info/vufind1/Digital/EAR000000025#page/1/mode/1up

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closed as too broad by Norbert Schuch, John Rennie, ACuriousMind, user36790, mpv Feb 29 '16 at 10:39

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ Does the picture of the document make this question more clear? $\endgroup$ – DanielSank Feb 11 '16 at 19:23
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    $\begingroup$ @DanielSank If you would like I could use the text editor to rewrite the field equation for clarity, as for the picture, I think it provides sufficient context for the question. $\endgroup$ – Ziezi Feb 11 '16 at 19:34
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    $\begingroup$ Do you happen to have a higher resolution version of that page? And could you give us some links to where you got it? Thank you :-) $\endgroup$ – Giorgio Comitini Feb 11 '16 at 19:48
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    $\begingroup$ Great, thank you! I may be able to explain the mathematics of gravitational waves (though I need to consult the manuscript in order to follow Einstein's notation). I'll see what I can do. $\endgroup$ – Giorgio Comitini Feb 11 '16 at 20:03
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    $\begingroup$ DanielSank's point is that the picture of the handwriting and the field equation are wholly irrelevant to asking how the LIGO experiment works $\endgroup$ – ACuriousMind Feb 11 '16 at 20:43
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The paper referred to above as the "Full original manuscript" is the "Die Grundlagen der allgemeinen Relativitatstheorie" paper - the original paper on General Relativity published in March 1916 in Annalen der Physik. As far as I know that makes no reference to gravitational waves. The first of Einstein's papers to explicitly refer to Gravitational waves was "Naherungsweise Integration der Feldgleichungen der Gravitation" published a few months later in May 1916 in the Sitzung of the Prussian Academy (pp 688-696): http://articles.adsabs.harvard.edu/cgi-bin/get_file?pdfs/SPAW./1916/1916SPAW.......688E.pdf (See the very last page.)

However, that paper was flawed and Einstein had to write THE paper on gravitational waves: "Uber Gravitationswellen", published in February 1918 in the same journal (pp.154-167). (See Steinicke, "Einstein and the gravitational waves", @Astron. Nach. 2005 vol. 326, p640).

What happened next when in 1937 he wrote the paper with Rosen is well documented in the paper by Kennefick referred to above by @Dargscisyhp.

Much of this reflects the difficulty people had in coming to terms with the incredible coordinate freedom that General Relativity had to offer. Even interpreting something as simple as de Sitter's metric caused long-term confusion, particularly with regard to the question of the red-shift. GR is a wonderful theory, albeit somewhat abstruse and even, at times, abstruse for its great inventor!

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  • $\begingroup$ around the last event, I heard that it was a 1911 or 1912 paper, published before the GR $\endgroup$ – user46925 Feb 20 '16 at 21:37
  • $\begingroup$ I'd heard that too but could not trace a reference. The first version of GR was the Einstein-Grossmann "Entwurf" paper of 1913 (Zeit. Math. Phys. 62, 1-38. This was the paper written in Zurich at the time Einstein was learning about Riemannian Geometry (see the Zurich notebook) and gave vacuum field equations. So it's hard to imagine anything before that coming up with gravitational waves as we understand them now. The "Entwurf" equations were in fact solved in 1914 by Droste, a student of Lorentz, to give the Schwarzschild solution (Kon. Ned. Akad. Weten. Ser. B. 17, 998-1011)! $\endgroup$ – JonesTheAstronomer Feb 21 '16 at 0:01
  • $\begingroup$ Isn't it true that Einstein didn't predict gravitational waves, but argued with Rosen that they don't exist? $\endgroup$ – user7348 Feb 28 '16 at 18:27
  • $\begingroup$ As I said, the story is in Kennefick's paper, Physics Today, 2005, 58, 43. But that is not open access. So, briefly, Einstein and Rosen did submit a paper saying that gravitational waves did not exist. Robertson found an error and rejected the paper. Einstein got annoyed and resubmitted to the J. Franklin Institute. While correcting proofs, Infeld, his research assistant explained Robertson's critique to Einstein. Einstein corrected the paper thanking Robertson. Ironically, Rosen submitted what must have been the original paper to a Russian journal - Einstein was not a co-author on that. $\endgroup$ – JonesTheAstronomer Feb 29 '16 at 22:54

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