The Formative Years of Relativity. Gravitational waves go in one ear and out the other

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:

formative1

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):

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And the above conclusion is mentioned in the New York Times book review section:

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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:

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And here is the same equation in his 1921 book, The Meaning of Relativity (Gutfreund’s book, page 240):

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Equation (92) represents the metric of general relativity Picture1 - Copy, which is the sum of the Minkowski flat metric Picture1 - Copy - Copy of special relativity and Picture1 - Copy (2) a very small disturbance.

And again, Einstein’s gravitational waves paper of 1916:

Picture4

And his book, The Meaning of Relativity (Gutfreund’s book, page 246):

Picture3 - Copy

We write the field equations in terms of Picture1 - Copy (2). 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):

Picture3

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 Picture1111.

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”:

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And in the book, The Meaning of Relativity he writes the the same metric (Gutfreund’s book, page 249):

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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 Picture1111is abandoned. Your solution for the mass point is then the result upon specialization to this case'” (Gutfreund’s book, page 97):

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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):

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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 Picture1 - Copy differs only infinitesimally (Picture1 - Copy (2)) from the values (Picture1 - Copy - Copy) that would be present without that disturbance; and the disturbance propagates with the velocity of light (Gutfreund’s book, page 94):

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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:

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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:

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They told the story of the origin of gravitational waves:

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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:

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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):

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The Formative Years of Relativity and a Prejudice on Poincaré’s Conventionalism

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 find two problems in the book the first of which is Poincaré’s influence on Einstein. This is the first part of the review which deals with Poincaré’s influence on Einstein. Since the book has mistakes and also errors in English and Jürgen Renn is considered a notable scholar, I assume that Gutfreund is probably responsible for the mistakes and for the errors in English.

Let us begin with page 26 of the book The Formative Years of Relativity. Gutfreund is apparently much attracted by “the painstaking analysis by the philosopher of science Yemima Ben-Menachem” in her book Conventionalism: From Poincaré to Quine. Cambridge University Press, Cambridge (2006):

Yemima 1921

Gutfreund writes that “Until 1921, Einstein did not mention Poincaré explicitly”.

Einstein obviously mentioned Poincaré before 1921. For instance, after the first Solvay congress in 1911, Einstein wrote to Heinrich Zangger (see the Collected Papers of Albert Einstein, CPAE):

Zangger1

……

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Einstein says that Poincaré was in general simply antagonistic and for all his acuity showed little understanding of the situation.

There was then great excitement among philosophers and historians of science when they discovered, as Gutfreund writes on page 26 above that “We know that he [Einstein] read Science and Hypothesis with his friends in the Akademie Olympia in 1902″.

Poincaré’s publisher Flammarion published La science et l’hypothèse (Science and Hypothesis) in Paris in 1902. How do we know that Einstein read this book in 1902 and not in 1903 or 1904? Take a look at Gutfreund’s words: “We know that he [Einstein] read Science and Hypothesis with his friends in the Akademie Olympia in 1902″. It means that Einstein rushed to the local bookstore in Bern the day the book was out, dodged people in the crowd waiting outside the bookstore and found the first French edition of Poincaré’s book. But maybe Einstein read the 1904 German translation of Poincaré’s 1902 book? This could be quite different from the original 1902 French edition.

Subsequently,  on page 26 Gutfreund writes: “Einstein’s biographer Abraham Pais quotes one of the members, Maurice Solovine, as saying: ‘This book profoundly impressed us and kept us breathless for weeks on end'”:

Pais

Gutfreund simply takes the Pais paragraph from Yemima Ben-Menahem’s book, Conventionalism, see footnote 80 below (page 134):

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This is a mistake: We cannot cite Einstein’s biographer Abraham Pais quoting one of the members of the Akademie Olympia (Olympia Academy). The biography of Pais is not a primary source. We have to check a primary source and see whether Maurice Solovine himself said: “This book profoundly impressed us and kept us breathless for weeks on end”.

Here is the original primary source:

soloving

Lettres à Maurice Solovine. Paris: Gauthier-Villars, 1956.

Here luck plays an important role because in the above book Solovine writes in French that Poincaré’s book “profoundly impressed us and kept us breathless for many weeks”. One should, however, check the original quote in French.

On page 30 Gutfreund tells the story of Einstein who explored “a famous example that goes back Poincaré”. There are several typos in the book.

Poincare typo

It is interesting, however, to look at the following sentence, several sentences below the above one on page 30:

He typo

“Without the distinction between axiomatic Euclidean geometry and practical rigid-body geometry, we arrive at the view advanced by Poincaré”. And then Gutfreund adds an end-note 15: “For an extensive analysis of Poincaré’s conventionalism, see Yemima Ben-Menachem, […]” Her book Conventionalism.

Yemima 1921-2

You might, of course, be tempted to suppose that Ben-Menahem has said the above words in her book. But this is by no means the case. Einstein says this in his 1921 talk, “Geometry and Experience” (see CPAE):

geometry and experience

After the words: “Without the distinction between axiomatic […]” Gutfreund writes: “He suggested that […]”

He typo

Who is “He”? Einstein or Poincaré?

Let us then examine Yemima Ben-Menahem’s book, Conventionalism.

I am quoting from Yemima Ben-Menahem’s book Conventionalism, page 84:

“… as both GR [general relativity] and the special theory of relativity originated in insights about equivalence, an element of conventionality might seem to be built right into the theory.  It is important to recognize, however, that Einstein’s use of equivalence arguments differs fundamentally from that of the conventionalist”.

And on page 134 Ben-Menahem writes: “The preceding discussion should alert us to the traces of Poincaré’s equivalence argument in Einstein’s work on GR as well. […] The centrality of equivalence arguments and their geometric implications is too obvious in Science and Hypothesis to be missed by a reader such as Einstein, who, we know, was familiar with the book. Beginning with the hypothesis of equivalence in 1907, Einstein makes use not only of the general idea of equivalent descriptions, but also of the types of examples Poincaré used”.

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and on page 135, Yemima Ben Menahem argues that “Einstein was deeply influenced by the idea of equivalence, and to that extent could concede that Poincaré was right”:

page 135

I have found no historical evidence (primary documents, i.e. correspondence of Einstein with others, manuscripts, and also interviews with Einstein) supporting the claim that Einstein makes use of Poincaré’s equivalent descriptions.

In the 1920 unpublished draft of a paper for Nature magazine, “Fundamental Ideas and Methods of the Theory of Relativity, Presented in Their Development”, Einstein explained how he arrived at the principle of equivalence (see CPAE):

happiest happiest2

(Original in German). “When I (in Y. 1907) [in Bern] was busy with a comprehensive summary of my work on the special theory relativity for the ‘Jahrbuch für Radioaktivität und Elektronik’, I also had to try to modify Newton’s theory of gravitation in such a way that its laws fitted into the theory. Attempts in this direction showed the feasibility of this enterprise, but did not satisfy me, because they had to be based upon unfounded physical hypotheses. Then there came to me the happiest thought of my life in the following form:

The gravitational field is considered in the same way and has only a relative existence like the electric field generated by magneto-electric induction. Because for an observer freely falling from the roof of a house there is during the fall – at least in his immediate vicinity – no gravitational field. Namely, if the observer lets go of any bodies, they remain relative to him, in a state of rest or uniform motion, regardless of their particular chemical and physical nature. The observer is therefore justified in interpreting his state as being ‘at rest’.

The extremely strange experimental law that all bodies fall in the same gravitational field with the same acceleration, immediately receives through this idea a deep physical meaning. If there were just one single thing that fell differently in a gravitational field from the others, the observer could recognize with its help that he was in a gravitational field and that he was falling in the latter. But if such a thing does not exist – as experience has shown with great precision – then there is no objective reason for the observer to regard himself as falling in a gravitational field. Rather, he has the right to consider his state at rest with respect to gravitation, and his environment as field-free.

The experimental fact of independence of the material of acceleration, therefore, is a powerful argument for the extension of the relativity postulate to coordinate systems moving nonuniformly relative to each other”.

Isaac Newton had already recognized that Galileo’s law of free fall was connected with the equality of the inertial and gravitational mass. In approximately 1685, Newton realized that there was an (empirical) equality between inertial and gravitational mass (Newton 1726, Book I, 9). For Newton, however, this connection was accidental. Einstein, on the other hand, said that Galileo’s law of free fall could be viewed as Newton’s equality between inertial and gravitational mass, but for him the connection was not accidental.

Hence, Einstein made use of Newton’s equality (accidental equivalence) between inertial and gravitational mass and Galileo’s law of free fall and in his 1907 paper, “On the Relativity Principle and the Conclusions Drawn from It”, he invoked a new principle, the equivalence principle or hypothesis. He assumed the complete physical equivalence of a homogeneous gravitational field and a corresponding (uniform) acceleration of the reference system. Acceleration in a space free of homogeneous gravitational fields is equivalent to being at rest in a homogeneous gravitational field.

Ernst Mach criticized Newton’s bucket experiment. He said that we cannot know which of the two, the water or the sky, are rotating; both cases produce the same centrifugal force. Mach thus expressed a kind of equivalence principle: Both explanations lead to the same observable effect. Einstein could have been influenced by Mach’s idea that we cannot know which of the two, the water or the sky, are rotating. Indeed Charles Nordmann interviewed Einstein and wrote: “Perhaps even more than Poincaré, Einstein admits to have been influenced by the famous Viennese physicist Mach”.

On page 31, Gutfreund writes in his book:

disk

“Had he [Einstein] instead accepted the conventionalist position […]” and then Gutfreund writes: “This in fact is exactly the situation in which Einstein introduced the mental model of a rotating disk, which he used as early as 1912 to show that the new theory of ravitation requires a new framework for space and time”.

Another typo: it should be the new theory of gravitation.

The rotating disk story starts with a problem in special relativity, with Max Born’s notion of rigidity and not with Poincaré! Einstein never mentioned any influence Poincaré had had on him when inventing the disk thought experiment.

At the annual eighty-first meeting of the German Society of Scientists and Physicians in Salzburg on 21-25 September 1909, Born first analyzed the rigid body problem and showed the existence of a class of rigid motions in special relativity.

John Stachel describes this state of affairs in his seminal paper of 1980: “The Rigidly Rotating Disk as a ‘Missing Link’ in the History of General Relativity”. It seems that Gutfreund is unacquainted with Stachel’s paper.

On September 29, 1909 the Physikalische Zeitschrift received a short note from Paul Ehrenfest. In his note Ehrenfest demonstrated that according to Born’s notion of rigidity, one cannot bring a rigid body from a state of rest into uniform rotation about a fixed axis. Ehrenfest had pointed out that a uniformly rotating rigid disk would be a paradoxical object in special relativity; since, on setting it into motion its circumference would undergo a contraction whereas its radius would remain uncontracted.

Born noted: “Mr. Ehrenfest shows that the rigid body at rest can never be brought into uniform rotation; I have discussed the same fact with Mr. Einstein in the meeting of natural scientists in Salzburg”. Born discussed the subject with Einstein and they were puzzled about how the rigid body at rest could never be brought into uniform motion. Born and Einstein discovered in that discussion that setting a rigid disk into rotation would give rise to a paradox: the rim becomes Lorenz-contracted, whereas the radius remains invariant. This problem was discussed almost simultaneously by Ehrenfest in the above short note.

Later in 1919, Einstein explained to Joseph Petzoldt why it was impossible for a rigid disk in a state of rest to gradually set into rotation around its axis:

PetoltzPetoltz2

On page 32 Gutfreund mentions the 10th German edition of Einstein’s popular book Relativity the Special and General Theory. He says that in a copy of this book there is a sheet of paper in the handwriting of Einstein’s stepdaughter containing a remark:

disk2

As you can see this remark is quite similar to Einstein’s letter to Petzoldt. Thus, it is preferable to quote Einstein’s own words, his letter to Petzhold. It seems that Gutfreund is unacquainted with the history of the rotating disk, because according to his book he is unaware of Stachel’s paper and the letter to Petzhold.

At the end of October 1909 Born submitted an extended version of his Salzburg talk to Physikalische Zeitschrift. In December 1909 Gustav Herglotz published a paper in which he noted that according to Born’s notion of rigidity, a “rigid” body with a fixed point can only rotate uniformly about an axis that goes through it, like an ordinary rigid body. Several months later, Einstein mentioned Born’s and Herglotz’s papers in a letter from March 1910 to Jakob Laub, in which he said that he was very much interested in their then recent investigations on the rigid body and the theory of relativity.  A month later, in conversations with Vladimir Varičak Einstein explained that the great difficulty lies in bringing the “rigid” body from a state of rest into rotation. In this case, each material element of the rotating body must Lorentz contract. See my new book Einstein’s Pathway to the Special Theory of Relativity 2Ed for full details.

In his paper from February 1912, Einstein considered a system K with coordinates x, y, z in a state of uniform rotation (disk) in the direction of its x-coordinate and referred to it from a non-accelerated system. Einstein wrote that K‘s uniform rotation is uniform “in Born’s sense”, namely, he considered a rotating disk already in a state of uniform rotation observed from an inertial system and reproduced his conversations with Varičak. Einstein then extended the 1907–1911 equivalence principle to uniformly rotating systems as promised in conversations with Sommerfeld in 1909.

All we know according to primary sources is that the origin of the rotating disk story is in a problem in special relativity, Max Born’s notion of rigidity and Ehrenfest’s paradox, which Einstein mentioned many times before 1912. Einstein never mentioned any influence Poincaré had had on him when inventing the disk thought experiment. Writing that Einstein was influenced by Poincaré’s conventionalism and equivalent arguments is speculating about the influence of the later on the former.

Gutfreund’s mistake about Poincaré’s influence on Einstein and Einstein’s so-called failure to acknowledge Poincaré’s work in connection with the equivalence principle and the rotating disk thought experiment in general relativity comes from Yemima Ben-Menahem’s book, Conventionalism. However, this misconception or prejudice on the part of Ben-Menahem comes from my PhD thesis which was submitted to the Hebrew University of Jerusalem back in 1998. I was a PhD student in the program for the history and philosophy of science and Yemima Ben-Menahem was a professor there. Here for example are several paragraphs from my PhD thesis:

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thesis

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And Poincaré’s disk thought experiment:

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…..

thesis5

……

thesis6

…..

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I have thus written in my thesis about Poincaré’s disk thought experiment and the equivalence of Euclidean and non-Euclidean geometries. I then mentioned Einstein’s rotating disk thought experiment and said that we eliminate absolute motion of the disk by assuming the equivalence of gravity and inertia. I then spoke about conventionalism and Einstein’s equivalence principle.

After the PhD I corrected and edited my PhD but then I was horrified to discover what looked like a magnification of the prejudice of Poincaré’s conventionalism and equivalence argument and his disk thought experiment influencing Einstein when creating general relativity: In 2006 Yemima Ben-Menahem said exactly the same thing in her book, Conventionalism. You might say that it is even a more unfortunate instance to write about Poincaré’s influence on Einstein in connection with the equivalence principle and the disk thought experiment in general relativity over and over again in a single book… (see now for instance her book, pages 64-65):

diskyemima

…….

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……

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Going on to Hanoch Gutfreund, in his new book of 2017, The Formative Years of Relativity, he has simply brought this incidence to the surface when he told the whole story of this prejudice all over again.