The purpose of this piece is to review Hanoch Gutfreund’s and Jürgen Renn’s new book The Formative Years of Relativity: The History and Meaning of Einstein’s Princeton Lectures, Princeton University Press and Oxford University Press. I have found two problems in the book the first of which is Poincaré’s influence on Einstein and the second problem is related to gravitational waves. The first part of the review deals with Poincaré’s influence on Einstein. In this part I discuss the problem related to gravitational waves.
Gravitational waves have won the 2017 Nobel Prize in Physics. The prize is awarded to Kip Thorne, Rainer Weiss, Barry Barish for their work on Ligo experiment. Actually, Kip Thorne’s interesting work is on wormholes: the Einstein-Rosen bridges, the Schwarzschild (non-traversable) wormholes and traversable wormeholes converted into time machines. Wormholes spark our imagination because of the possibility of travelling backwards in time and sending signals through the throat in space-time with causality violation.
However, let us concentrate on gravitational waves.
I have ordered the book from Amazon together with The Asshole Survival Guide: How to Deal with People who Treat you Like Dirt written by Robert Sutton, a Stanford University professor:
It seems that the book, The Formative Years of Relativity has mistakes and also errors in English (the book needs proofreading). I therefore ask the second writer: Are you living in a fool’s paradise?
Right at the beginning Gutfreund argues that gravitational waves is the only major topic debated during the formative years that has no trace in Einstein’s book The Meaning of Relativity. He writes: “Had we restricted our commentaries to the contents of Einstein’s book, there would be no reason to mention gravitational waves; however, it would be inconceivable to talk about the formative years without thoroughly discussing them. What is worth emphasizing in this context is how Einstein’s predominant interest in this phenomenon which developed immediately after the completion of his general theory, had faded away completely by the time he delivered the Princeton lectures” (Gutfreund’s book, page 8):
And the above conclusion is mentioned in the New York Times book review section:
Gutfreund and Renn “note, however, a conspicuous absence. There is ‘no trace’ in Einstein’s lectures of what is today considered a key topic in relativity: gravitational waves”.
In fact quite the opposite is true. Einstein’s mathematical derivations in his 1916 and 1918 two gravitational waves papers play a central role in The Meaning of Relativity of 1922. It therefore appears that Einstein’s interest in this topic had not faded away by the time he delivered the Princeton lectures.
Consider Einstein’s gravitational waves paper of 1916:
And here is the same equation in his 1921 book, The Meaning of Relativity (Gutfreund’s book, page 240):
Equation (92) represents the metric of general relativity , which is the sum of the Minkowski flat metric of special relativity and a very small disturbance.
And again, Einstein’s gravitational waves paper of 1916:
And his book, The Meaning of Relativity (Gutfreund’s book, page 246):
We write the field equations in terms of . Equation (96b) below is the linearized approximation of Einstein’s field equations. Then we can solve the field equations in the same way that we solve Maxwell’s electromagnetic field equations (Gutfreund’s book, page 247):
Equations (101) above from the book The Meaning of Relativity, which are exactly like equations (9) from the gravitational waves paper of 1916, are the method of retarded potentials.
In his review paper of 1916, The Foundation of the General Theory of Relativity, Einstein’s field equations were valid for systems in unimodular coordinates, i.e. he chose the coordinates so that .
However, in his gravitational waves paper of 1916, Einstein thanked de Sitter for sending him the following metric, the one below: “Herr [Willem] de Sitter sent me these values by letter”:
And in the book, The Meaning of Relativity he writes the the same metric (Gutfreund’s book, page 249):
Indeed, in the book, The Formative Years of Relativity, Gutfreund writes: “On 22 June 1916, Einstein wrote to Willem de Sitter […] ‘For I found that the gravitation equations in first-order approximation [i.e. equations (96b) the linearized approximation of Einstein’s field equations] can be solved exactly by means of retarded potentials, if the condition of is abandoned. Your solution for the mass point is then the result upon specialization to this case'” (Gutfreund’s book, page 97):
Daniel Kennefick explains Einstein’s letter to de Sitter in his book, Traveling at the Speed of Thought: Einstein and the Quest for Gravitational Waves (page 51):
By the way I highly recommend Kennefick’s book.
That being said, Gutfreund begins the chapter on gravitational waves with Max Born. Born asked Einstein how fast does the effect of gravitation propagates according to his theory? Einstein replied to him that it is simple to write down the equation for the case where the disturbances one places into the field are infinitesimal. In that case the metric differs only infinitesimally () from the values () that would be present without that disturbance; and the disturbance propagates with the velocity of light (Gutfreund’s book, page 94):
I wrote in my 2015 book General Relativity Conflict and Rivalries and in other places as well that the first time Einstein mentioned gravitational waves was in the discussion after the Vienna lecture in 1913:
However, Gutfreund does not cite my 2015 book.
In 2016 Gutfreund wrote a blog post and added Jürgen Renn and Diana Buchwald as co-authors:
They told the story of the origin of gravitational waves:
They briefly summarize the history of gravitational waves: “The first debates about the existence of gravitational waves even preceded the completion of general relativity by Einstein in November, 1915”. They only mention Max Abraham but don’t write that the first time that Einstein had mentioned gravitational waves was after the Vienna lecture in 1913, in the discussion, Max Born asked Einstein how fast does the effect of gravitation propagates according to his Entwurf theory.
Finally, in the same book, General Relativity Conflict and Rivalries, of 2015 I wrote:
And I read in Gutfreund’s book of 2017 and discover that he writes exactly the same thing but does not cite my book (Gutfreund’s book, page 35):