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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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    $\begingroup$ Does the picture of the document make this question more clear? $\endgroup$
    – DanielSank
    Commented Feb 11, 2016 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
    Commented Feb 11, 2016 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
    Commented Feb 11, 2016 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
    Commented Feb 11, 2016 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 ♦
    Commented Feb 11, 2016 at 20:43

1 Answer 1

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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
    Commented Feb 20, 2016 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
    Commented Feb 21, 2016 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
    Commented Feb 28, 2016 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
    Commented Feb 29, 2016 at 22:54

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