A few last days we were bombarded by questions from friends who were sending us links to numerous articles on the gravitational waves discovery. Most of these articles look like a continuation of press release, but one of them attracted our attention, because it presented hard evidence of Einstein’s involvement. Our friend, a bureaucrat, sent us the link to Business Insider (BI) and asked whether Einstein really predicted gravitational waves and what equation is shown on the pictures in the BI article. We have already posted discussion on the first topic (whether Einstein really predicted gravitational waves) in a few our posts in 2012. Maybe, it’s time to return to this question, repeat our arguments or reconsider some of them. This we will do in our incoming posts.

Today we want to talk about the article in BI and the pictures there. After the announcement of discovery of gravitational waves on February 11, 2016 (LIGO, press release ) we observe the overflow of articles, interviews, press releases, advertisements, etc. dedicated to this ‘important discovery’. The article in BI is one more zilch in the predictable sequence of events. Business as usual… However, this article looks very convincing: with two documents shown and with a finger pointing on Einstein’s fateful equation as the final proof of Einstein’s invincible predictions.

**Picture #1.** The curator for Einstein’s archives, Roni Grosz, is holding two documents. It is written above the picture:

“Here’s his original hand-written logic (on left), which the genius later converted into a typed manuscript (on right)”.

**This statement is wrong! The manuscript (on right) has nothing to do with the hand-written document (on left).**

It is easy to see that the hand-written document differs from the published manuscript. On the bottom of the hand-written document there is the archival call number 120-788. Let us look at the Einstein Archives Online at the Herbew University of Jerusalim: http://www.albert-einstein.org/. Here is the link to this paper: Einstein’s paper, 20 March 1916 .

Unfortunately, there is nothing on this page about whether this document was later converted to a published manuscript or not, but we can see the title “Die Grundlage der allgemeinen Relativitätstheorie” and scroll the whole document (for free, which is a very rare fortunate opportunity in nowadays world). The page presented on the picture is 33; please compare to Albert Einstein, the hand-written manuscript . Now the question is how to find a published manuscript. On the page Einstein’s paper, 20 March 1916 there is the link to the Einstein Papers Project . Let’s go to this page and look at volume 6 (here is this manuscript): The collected papers of Albert Einstein, volume 6 . Oops, you have to buy this volume for $160. But we need only one paper:

30.”The Foundation of the General Theory of Relativity,” 20 March 1916 283

“Die Grundlage der allgemeinen Relativitätstheorie”

Annalen der Physik 49 (1916)

Fortunately, this manuscript in German is available for free: “Die Grundlage der allgemeinen Relativitätstheorie” Annalen der Physik 49 (1916) . The formulas on the pictures correspond to those on pages 807-808 in the manuscript.

By the way, an English translation of this paper is also available online for free Albert Einstein “The Foundation of the Generalised Theory of Relativity” . We don’t need to buy the Princeton collection.

The paper on the right of this picture ( Business Insider ) is Einstein’s paper (which is also listed in volume 6 of the Einstein Papers Project ):

32.”Approximative Integration of the Field Equations of Gravitation,” 22 June 1916 347

“Näherungsweise Integration der Feldgleichungen der Gravitation”

Königlich Preuáische Akademie der Wissenschaften (Berlin).

Sitzungsberichte (1916)

It is also available online (in German!): Albert Einstein, “Näherungsweise Integration der Feldgleichungen der Gravitation” Königlich Preuáische Akademie der Wissenschaften (Berlin) . Einstein’s manuscript started at p. 688 and continues up to p. 696. Here, on p. 696 is the formula, to which a finger is pointing on Picture 2 in Business Insider .

We would like to note that we were not able to find English translation of this manuscript, which is freely available online. We would very much appretiate if somebody finds it and send us the link. It is an interesting fact that the discovery paper PhysRevLett.116.061102 is available for everybody, and the first reference there is Einstein’s paper “Näherungsweise Integration der Feldgleichungen der Gravitation”, but people should know German to read it!

Luckily, we have it in our possession this translation, as well as translation of all Einstein’s scientific papers in Russian (we have already written about this in our posts, and also discussed possible reasons why Einstein’s papers are translated into English in such a slow pace). Let us see what is there.

**Picture #2.** What is shown on this picture? The equation on this page is what will be left from Einstein’s equations of General Relativity (GR) after linearization. i.e. after a certain assumption is imposed: the gravitational field is considered weak (is it a correct assumption for two black holes?). Moreover, this equation is similar to the wave equation of the Maxwell theory that (after some additional manipulations) describes propagation of electromagnetic waves in the absence of sources (absence of any source, including a system of two black holes!).

Einstein pointed out in this paper that its result is not general, it is valid only under assumption that the gravitational field is weak and only linear coordinate transformations (a linearized version of the general coordinate transformations of GR) can be applied to these (linearized) equations. Einstein also did not predict in this paper “that two celestial bodies in orbit will generate invisible ripples in spacetime that experts call gravitational waves”, as BI claims. He was talking about “the system” that radiates energy, without specifying what kind of system it is.

Eintein returned to the question whether gravitational waves exist many times during his life. We have already wrote about that on our blog and also in our scientific papers, and will continue to do this with hope to attract attention of (at least) the general public to Einstein and to the ‘discovery’ that now is attached to his name.