David Rowe reviews my book and the Gutfreund Renn book in ISIS. My reply.

Prof. David E. Rowe has published a review of my third book, Einstein’s Pathway to the Special Theory of Relativity, Second edition:

Galina Weinstein. Einstein’s Pathway to the Special Theory of Relativity. Second edition. xv + 642 pp., bibl., notes, index. Newcastle upon Tyne: Cambridge Scholars Publishing, 2017. £80.99 (cloth). ISBN 9781443895125.

and Hanoch Gutfreund’s and Jürgen Renn’s book, The Formative Years of Relativity: The History and Meaning of Einstein’s Princeton Lectures, Princeton University Press under the title:

Hanoch Gutfreund; Jürgen Renn. The Formative Years of Relativity: The History and Meaning of Einstein’s Princeton Lectures.; Galina Weinstein. Einstein’s Pathway to the Special Theory of Relativity.

I will speak as if the book, The Formative Years of Relativity was written by an author Gutfreund to emphasize that the main author of the book is Gutfreund without forgetting about Renn’s important contributions to the book.

Rowe’s book review compares the two books, mine and Gutfreund’s. But there is nothing common between my third book, Einstein’s Pathway to the Special Theory of Relativity, Second Edition, and Gutfreund’s book, The Formative Years of Relativity. Indeed, the first thing that strikes the reader is Rowe’s choice to compare two books that have nothing to do with one another in one review simply because the titles of the two books have the word “relativity”. My book discusses the genesis of special and general relativity (1905-1918) and Gutfreund’s book encompasses the period after 1918, especially the 1920s which he calls “the formative years of relativity”. These are two completely different topics and periods of time. Gutfreund discusses the “debates and developments characterizing the early reception and spread of Einstein[‘s] ideas in the late 1910s and 1920s” (preface, Gutfreund and Renn 2017). The main theme of my book Einstein’s Pathway to the Special Theory of Relativity, Second Edition is Einstein’s own intellectual path to relativity.

The second thing that catches the eye of the reader is that Rowe is mentioned in the acknowledgements section in the preface of Gutfreund’s book (preface, Gutfreund and Renn 2017):

Special thanks are due to our colleagues and friends Alexander Blum, Yemima Ben-Menachem, […], David E. Rowe, Donald Salisbury, and Robert Schulmann”.

In such circumstances, it seems that Rowe cannot write an objective review. Indeed, Rowe praises with much insincerity Gutfreund’s and Renn’s book but gives what seems like an unfair review of my third book, which should be rectified. I first comment on Rowe’s criticism in his book review of the editing process of my book and then correct his errors in reviewing my book (I am following Rowe’s order of presentation).

My intention in this piece is only to explain the reasoning behind the editing process of my book and to correct the errors in Rowe’s review.

The editing process of my book:

Firstly, Rowe writes (Isis —Volume 110, Number 1, March 2019, 203):

“While she sings the praise of the CSP stuff, the lapses in layout and copyediting begin with the table of contents. The cover design, produced by the author, shows a drawing entitled ‘Einstein is wearing the Patent Office Suit,’ which should bring to mind one of the most iconic of all photographs of the young genius. Inside one finds a great deal of rambling, barely edited prose in six chapters […].”

I drew the cover design by myself because the Einstein Archives and the Hebrew University of Jerusalem would not give me permission to use Einstein’s quotations in my first book: Between 2012 and 2014 the Einstein Archives and the Hebrew University refused to give me permission to use quotations from Einstein’s manuscripts and papers in my first book. I chased for two years the Hebrew University and only after two years, did I receive the permission. In this state of affairs, I realized that I would neither get any permission to use photos of Einstein nor would I be able to reproduce any photo of an Einstein document in my book. I thus had no other choice but to draw Einstein on the front cover. At least I am capable of drawing.

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Major parts of my book were edited by Prof. John Stachel. Stachel wanted to publish the book by Springer as part of the Einstein Studies series. However, the Hebrew University put a spoke in the wheels of this plan. Stachel stepped down a few times from editing the Einstein Studies series and the Hebrew University delayed the permission, as said above, and the end result was that I missed the opportunity to publish by Springer, the Einstein Studies series. Finally, I published my first book by CSP. The third book is a second edition of the first book and this is the reason why the title of the book remained the same (it’s the publisher’s decision).

Secondly, Rowe writes in his review (Isis —Volume 110, Number 1, March 2019, 203):

“A reader might wonder what Weinstein means by ‘critical biography,’ but since she offers no explanation I will demur from giving an opinion. In fact, I am at a loss to explain why she included Chapter A in her book at all, since its contents have virtually no bearing on Einstein’s paths to special and general relativity. At any rate, what she delivers is nothing but strings of information about his life […]. In Chapter F (“The Sources”) she distinguishes between documentary and nondocumentary biographies, noting that both can be unreliable. Here she shows no hesitation to criticize earlier work, but usually just by making flippant remarks rather than cogent arguments. She also writes as if no one before her has ever reviewed the literature bearing on Einstein and relativity. Her book makes no reference to Klaus Henschel’s monumental 1990 study of the reception of relativity among philosophers (cited several times by Gutfreund and Renn). Nor does she cite my own more recent discussion of the biographical literature in ‘Einstein and Relativity: What Price Fame?’ (Science in Context, 2012, 25: 197-246). Even more glaring than these omissions is another: she never points out that several of the biographies she writes about are blatantly hagiographic”.

John Stachel who edited my book thought that the book should have a short biography of Einstein, and this would be the first chapter of the book. He edited the sources chapter: documentary and non-documentary biographies and in the third edition, I extended it. Finally, I don’t “criticize earlier work”. What seems like a criticism of earlier work is actually an attenuated version of Stachel’s review (see Stachel, John, Einstein from B to Z, Springer, 2002, 556). The purpose of the “sources” chapter is not to review the literature bearing on Einstein and relativity, rather it is meant to provide complementary information on the sources used in the book.

As to “Klaus Hentschel’s monumental 1990 study of the reception of relativity among philosophers” (Interpretationen und Fehlinterpretationen der speziellen und der allgemeinen Relativitätstheorie durch Zeitgenossen Albert Einsteins). It is not so relevant for my third book which discusses the history of Einstein’s intellectual journey to special and general relativity until 1918, i.e. Einstein’s path to the special and general theory of relativity until 1918. I need not here dwell on Hentschel’s book but its theme is fully pertinent to the topics dealt with in Gutfreund’s book. Nonetheless, I do mention Klaus Hentschel in my book (see the reference list of my book):

Hentschel, Klaus (1992). “Einstein’s Attitude towards Experiments: Testing relativity theory 1907–1927.” Studies in History and Philosophy of Science 23, 593-624.

And I also mention two of Prof. Rowe’s works in my book (see my reference list):

Rowe, David E. (2008). “Max von Laue’s Role in the Relativity Revolution.” The Mathematical Intelligencer 30, 54-60.

Rowe, David E. and Schulmann Robert (2007). Einstein on Politics: His Private Thoughts and Public Stands on Nationalism, Zionism, War, Peace, and the Bomb. Princeton: Princeton University Press.

The above professors, however, don’t mention my papers in their works…

The errors in Rowe’s book review:

Now I would like to correct Rowe’s embarrassingly blatant errors in his book review of my book.

Firstly, Prof. Rowe writes: “she never points out that several of the biographies she writes about are blatantly hagiographic” (Isis 2019, 203).

This is not true. I do point out that the biographies are hagiographic. I even say this on the back cover of my Book. See the back cover of my book which says: “The first chapter provides a narrative of Einstein’s early life until 1914 without resorting to hagiography”.

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Back cover of my book.

Secondly, Prof Rowe writes (Isis —Volume 110, Number 1, March 2019, 203-204):

“Chapter D deals with the period preceding the formative years. Those familiar with the work of John Stachel, the doyen of modern Einstein scholarship, will likely find little new to contemplate in this survey, which forthrightly adopts Stachel’s ‘drama in three acts’. In sharp contrast with Gutfreund and Renn, who identify over fifty other actors during the formative years, Weinstein’s account puts Einstein alone in the limelight. She writes that her aim, “the simplification of the history of physics” (p. xv), was achieved with minimal reliance on mathematical formulas. Yet a cursory glance at this new chapter reveals that nearly every page contains formulas, many of them surely intelligible only to specialists, Gutfreund and Renn wrote their commentary using virtually none; they wisely left technicalities for Einstein to explain. Moreover, their lucid and compelling writing is packaged in a book that is not only readable but beautifully designed and affordable!”

I don’t forthrightly adopt Stachel’s drama in three acts! Prof. Rowe easily fell into the trap of the three-act drama because Stachel edited major parts of my book! In fact, after presenting Stachel’s three-act drama, I adopt quite the opposite point of view. I write on page 279 in my book:

“There is, however, the objection by Jürgen Renn that the genesis of general relativity did not quite unfold in the form of a classic three-act drama between 1907 and 1915. The story begins before 1907 and continues well beyond 1915. An additional problem of this portrait as a classic three-act drama is that it leaves out what is usually considered ‘a villain’ in this story, namely a theory on which Einstein worked between 1913 and 1915, in Zurich mostly but later also in Berlin, where he discarded it. It is called the preliminary or the draft, outline, in German, the Entwurf theory (Renn, 2016; Janssen, Norton, Renn, Sauer and Stachel, “Introduction to Vol. 1 and 2” in Renn et al 2007, 16)”.

And I follow this line of reasoning in my book rather than the three-act drama!
In fact, I dedicated a whole big section (pages 321-398) to the Entwurf theory and to all the intricacies of the Entwurf theory from 1913 to 1915.

Thirdly, Prof. Rowe then says that my account puts Einstein alone in the limelight. This is not quite true because I explicitly write that Chapter D of my third book complements the text of my second book General Relativity Conflict and Rivalries, which focuses on Einstein’s interaction with other scientists.

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Indeed, in my third book, the one reviewed by Rowe, I write in the preface:

“My primary goal in writing this second edition of Einstein’s Pathway to the Special Theory of Relativity, is the following: Firstly, I have updated and made corrections and minor revisions in many places in the text. I have also simplified explanations. Secondly, I have added a chapter (Chapter D) on Einstein’s route to the General Theory of Relativity (1905 – 1918) that will complement the text in my book, General Relativity Conflict and Rivalries, in which I focus on the work of Albert Einstein and his interaction with and response to many eminent and not-so-eminent scientists (1905 – 1945). In General Relativity Conflict and Rivalries I demonstrate that the ongoing discussions between Einstein and other scientists have all contributed to the edifice of general relativity and relativistic cosmology. In this edition of Einstein’s Pathway to the Special Theory of Relativity, I centralize on Einstein’s own creativity, invention and inner struggles on his route to general relativity, rather than on his interactions with other scientists”.

Gutfreund even read my book General Relativity Conflict and Rivalries but failed to cite it in his book, The Formative Years of Relativity: The History and Meaning of Einstein’s Princeton Lectures. He writes on page 94 in Chapter 6 of his book The Formative Years of Relativity:

“Questions about the nature of this propagation [gravitational waves] and its velocity already naturally led to a discussion of gravitational waves. Such questions did in fact arise in connection with the Entwurf theory […] after Einstein presented it in 1913 in Vienna. In the discussion period Max Born asked [a quotation…] and Einstein responded [a quotation]” and so forth.

I wrote on pages 242-243 of my second book, General Relativity Conflict and Rivalries, in 2015 (and I also wrote this in other pieces as well) that the first time Einstein mentioned gravitational waves was in the discussion after the Vienna lecture in 1913:

“In the discussion after Einstein’s 1913 Vienna talk, Max Born asked Einstein about the speed of propagation of gravitation, whether the speed would be that of the velocity of light. Einstein replied that it is extremely simple to write down the equations for the case in which the disturbance in the field is extremely small […] In 1916 Einstein followed these steps and studied gravitational waves.

Gutfreund does not cite my works. In the same book, General Relativity Conflict and Rivalries, published in 2015, I write on pages 287-288:

“Einstein later explains this in his 1938 book with Infeld in the following thought experiment. Although Infeld wrote the book, it is reasonable to assume that the thought experiment came from Einstein.

Consider a great elevator at rest at the bottom of a building much higher than any real one. […] We thus have two observers, K’ and K’’ and two opposite points of view: the phenomenon is different for the two. There would be no equivalence of K and K’’ and from the behaviour of the light ray we could say that K’ is in absolute motion: whenever an observer on Earth finds a bent light ray in an accelerated elevator, he knows that the reference frame under consideration is in absolute motion. Here then we have a version of Newton’s bucket Experiment”.

And on page 35 of his 2017 book, The Formative Years of Relativity: The History and Meaning of Einstein’s Princeton Lectures, Gutfreund writes the same thing but does not cite my book:

“In this sense, the uniformly accelerated frame of reference introduced by Einstein and later often described in terms of the elevator thought experiment was nothing but a simplified version of the bucket thought experiment of Newton and Mach”.

Rowe writes (Isis —Volume 110, Number 1, March 2019, 202):

“Gutfreund and Renn show, in 1921–1922 Einstein was still struggling to defend his views regarding Mach’s principle and its cosmological implications, ideas that Willem de Sitter had challenged directly (see p. 70 for de Sitter’s notes from a conversation with him in Leiden in September 1916). Yet in the years that followed Einstein seems to have fallen silent when it came to cosmological matters, even when faced with Hermann Weyl’s open heresy (to which he reacted only briefly in a letter; see p. 78). Weyl had initially defended Einstein’s arguments against de Sitter’s matter-free model of the universe, but he gradually drifted over to the other side, arguing instead for a field-theoretic ether as the primary agent accounting for inertia (as opposed to distant masses à la Mach). Weyl also cited Vesto Slipher’s early observations of redshift effects among distant nebulae as further support for de Sitter’s model. Still, as noted by the authors, serious consideration of nonstatic models of the universe came only later. In the wake of Hubble’s findings, Einstein and de Sitter could agree they had both been wrong, and in 1932 they tossed out Einstein’s cosmological constant and introduced a new model, the Einstein–de Sitter universe”.

In my second book, General Relativity Conflict and Rivalries, 2015, on pages 242-359 (more than hundred pages) I extensively discuss the above-mentioned historical milestones: Einstein’s efforts to defend Mach’s ideas and principle, Einstein’s 1920 “Mach’s Ether”, Einstein’s discussions and correspondence with Willem de Sitter, Einstein’s interaction with Hermann Weyl. Weyl’s position first corresponded exactly to Einstein’s when he criticised de Sitter’s solution and then Weyl crossed the lines, as I extensively discuss in my book. Weyl found that spectral lines show redshift to a first-order approximation proportional to their distances in de Sitter’s world. I also present this matter in my book and say that these considerations were suggested in connection with Slipher’s observations. I perform historical analysis of Hubble’s findings, Eddington’s cosmological model, Einstein’s cosmological constant, Einstein’s steady-state model, the Einstein-de Sitter model, etc.

Rowe writes (Isis —Volume 110, Number 1, March 2019, 203): “Weinstein’s idiosyncratic book is already her third in as many years published by Cambridge Scholars Publishing”.

Having mentioned my three books published by CSP and comparing my work and Gutfreund’s, Rowe should also have mentioned that I had discussed the aforementioned topics.

Fourthly, Rowe notes that I write in my preface that I promise “minimal reliance on mathematical formulas. Yet a cursory glance at this new chapter reveals that nearly every page contains formulas, many of them surely intelligible only to specialists. Gutfreund and Renn wrote their commentary using virtually none; they wisely left the technicalities for Einstein to explain”.

However, I write in my preface (p. xv):

“Einstein also thought that a scientist should not attempt to popularize his theories. It is the duty of a scientist to remain obscure (Douglas Vibert 1956, 99-100). I thus have attempted to make Chapter D as intriguing as possible to readers with strong physics and historiography backgrounds. With this objective in mind, the explanations in Sections 3-7 of Chapter D are, understandably, less general. The mathematical background needed to read these sections corresponds to the level of a college student graduating in science”.

Surprisingly, therefore, Einstein sided with me!

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The Genesis and ‘Renaissance’ of General Relativity: Jürgen Renn’s talk

All the Berlin Century of General Relativity and MPIWG conference talks and discussions are on the web site of the Max Planck Institute for the History of Science in Berlin.

I shall begin by presenting the opening remarks of prof. Jürgen Renn’s talk, “The ‘Renaissance’ of General Relativity: Social and Epistemic Factors”, and thereafter I shall list my various comments on this talk. I shall present my views at the end regarding the term “Renaissance” describing the period from 1955 to the end of 1964.

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Prof. Jürgen Renn:

“This talk is about explaining historical change; how we preliminary see the various stages of the history of general relativity: there was the genesis of general relativity [the period from 1907 to 1916] where Einstein worked not quite but almost alone with a few helpers. There were the formative years [the period from 1916 to 1925], in which the theory was discussed among a group of experts; there was then what Jean Eisenstaedt has epically termed the low-water mark period [the period from 1925 to 1955]; and then comes the renaissance [the period from 1955 to 1964]. Clifford Will gave the name to this period; and for us historians then came the golden ages [the period from 1964 to the mid 1970s] and today and the future, but I will not talk about that.

So the main challenge is to explain how development went from the low-water mark period to the renaissance; how what we today see as the basic theory of cosmology and astrophysics came back into the mainstream of physics after the low-water mark period. There were many factors of course and we have concentrated on several scenarios, examining them in preliminary ways to try to come up with what we think as a convincing explanation.

Let me start to outline the thesis. We think that the renaissance was mainly due to two factors:

One was the discovery of the untapped potential of general relativity as it has been created as a tool for theoretical physics. Hidden secrets that were discovered in this period, hidden potential of application, these would not have been explored and actively developed had it not been within a community that was just forming in this period.

[The second factor] We think that the renaissance is also very much history of a community, in which for the first time a real community of relativists and cosmologists emerged. We have kind of loosely been talking of relativists and cosmologists, even when referring to the twenties and the thirties [1920s and 1930s]. This is a somewhat anachronistic use of terms, because the real community only emerged as we see it during the period of the renaissance.

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So you see already that the general approach is one that combines epistemological aspects with sociological aspects, and that is very much the spirit of our thinking. Robert Schulmann [a speaker in the conference] used the terminology of internalist and externalist. So we see this very much as a development that can only be understood if you combine the cognitive, the epistemological side, with the sociological developments parallel to it”.

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My comments on this talk:

Prof. Jürgen Renn says: “There was the genesis of general relativity where Einstein worked not quite but almost alone with a few helpers. There were the formative years, in which the theory was discussed among a group of experts; there was then what Jean Eisenstaedt has epically termed the low-water mark period”.

I think that even during the genesis of general relativity, between 1912 and 1916, Einstein’s interaction with and response to eminent and non-eminent scientists and his ongoing discussions with other scientists contributed to the formation of general relativity. The efforts invested by physicists like Max Abraham, Gunnar Nordström, Gustav Mie, David Hilbert and others, which presented differing outlooks and discussions revolving around the theory of gravitation, were relegated to the background. Those works that did not embrace Einstein’s overall conceptual concerns – these primarily included the heuristic equivalence principle and Mach’s ideas (later called Mach’s principle) – were rejected, and authors focused on Einstein’s prodigious scientific achievements. However, one cannot discard Einstein’s response to the works of Abraham, Nordström, Mie, Tullio Levi-Civita, Hilbert and others. On the contrary, between 1912 and 1915 (the so-called genesis of general relativity) Einstein’s response to these works, and corrections made by these scientists to his work, constitutes a dynamic interaction that assisted him in his development (so-called genesis) of the general theory of relativity. In my book, General Relativity Conflict and Rivalries I show that general relativity was not developed as a single, coherent construction by an isolated individual, brooding alone. Instead, general relativity was developed through Einstein’s conflicts and interactions with other scientists, and was consolidated by his creative process during these exchanges.

Indeed, performing a historical research and also applying comparative research in a sociological context, we can emphasize the limits and associated problems tracing Einstein’s “odyssey”, i.e. intellectual road to the general theory of relativity. An intellectual approach emphasizes the simplistic hero worship narrative. In addition, some philosophers embrace externalist theories of justification and others embrace internalist theories of justification. There are many different versions of internalism and externalism, and philosophers offered different conceptions of internalism and externalism.

I would like to comment on the “formative years” and the “low-water mark” period. I show in my book General Relativity Conflict and Rivalries that between 1916 and 1955, Einstein was usually trusted as the authority on scientific matters. His authority in physics is revealed even on first-rate mathematicians and physicists. For example, in 1918 Felix Klein demonstrated to Einstein that the singularity in the de Sitter solution to the general relativity field equations was an artefact of the way in which the time coordinate was introduced. Einstein failed to appreciate that Klein’s analysis of the de Sitter solution showed that the singularity could be transformed away. In his response to Klein, Einstein simply reiterated the argument of his critical note on the de Sitter solution. In 1917-1918 the physicist-mathematician Hermann Weyl’s position corresponded exactly to Einstein’s when he criticized de Sitter’s solution; Weyl’s criticism revealed the influence of Einstein’s authority in physics even on first-rate mathematicians like Weyl.

Two other examples from the introduction of my book:

In March 1918, before publishing the book Space-Time-Matter, Weyl instructed his publisher to send Einstein the proofs of his book. In the same month, Weyl also instructed his publisher to send David Hilbert the proofs of his book. Hilbert looked carefully at the proofs of Weyl’s book but noticed that the latter did not even mention his first Göttingen paper from November 20, 1915, “Foundations of Physics”. Though Weyl mentioned profusely Einstein’s works on general relativity, no mention was made of Hilbert’s paper. Einstein received the proofs page-by-page from the publisher and read them with much delight and was very impressed. However, Einstein, an initial admirer of the beauty of Weyl’s theory, now raised serious objections against Weyl’s field theory. Einstein’s objection to Weyl’s field theory was Weyl’s attempt to unify gravitation and electromagnetism by giving up the invariance of the line element of general relativity. Weyl persistently held to his view for several years and only later finally dropped it.

Einstein also seemed to influence Sir Arthur Stanley Eddington when he objected to what later became known as “black holes”. In his controversy during the Royal Astronomical Society meeting of 1935 with Subrahmanyan Chandrasekhar, Eddington argued that various accidents may intervene to save a star from contracting into a diameter of a few kilometres. This possibility, according to Eddington, was a reductio ad absurdum of the relativistic degeneracy formula. Chandrasekhar later said that gravitational collapse leading to black holes is discernible even to the most casual observer. He, therefore, found it hard to understand why Eddington, who was one of the earliest and staunchest supporters of the general theory of relativity, should have found the conclusion that black holes may form during the natural course of the evolution of stars, so unacceptable. However, it is very reasonable that Eddington, who was one of the earliest and staunchest supporters of Einstein’s classical general relativity, found the conclusion that “black holes” were so unacceptable, because he was probably influenced by Einstein’s objection to the Schwarzschild singularity.

Prof. Jürgen Renn explained in his talk: “We think that the renaissance is also very much a history of a community, in which for the first time a real community of relativists and cosmologists emerged. We have kind of loosely been talked of relativists and cosmologists, even when referring to the twenties and the thirties. This is a somewhat anachronistic use of terms, because the real community only emerged as we see it during the period of the renaissance”.

I would like to comment on the proposal to call the period from 1955 to 1964 the “renaissance” of general relativity. Clearly, in the atmosphere of cinquecento Florence or Milan, a scientist and artist needed a community. Actually for the first time in history, in renaissance Italy there were concentrations of scientists, writers, artists and patrons in close communities and courts. There were communication and interaction between those communities. Historians have reconstructed what went in these communities and how these communities functioned. Hence renaissance is a suitable historical term to describe the period from 1955 to 1964.

Updated July 2016, another talk by Jürgen Renn: the sixth biennial Francis Bacon Conference, “General Relativity at 100”, Bacon Award Public Lecture: (I did not attend this conference but the talk was uploaded to YouTube):

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In 1907 in the patent office, Einstein was sitting down to write a review article in which he reviewed all the phenomena of physics in order to adapt them to the new framework of space and time established by special relativity. It was a routine task and dealing with gravitation in that context was also a routine task, so it seemed at the beginning.

[My comment: Einstein said in 1933, in the Glasgow lecture: “I came a step closer to the solution of the problem for the first time, when I attempted to treat the law of gravity within the framework of the special theory of relativity.” Apparently, sometime between September 1905 and September 1907 Einstein had already started to deal with the law of gravity within the framework of the special theory of relativity. When did he exactly start his work on the problem? Einstein did not mention any specific date, but in the Glasgow lecture he did describe the stages of his work presumably prior to 1907].

But then Einstein had to deal with the principle that was already established by Galileo hundreds of years ago, namely, the universality of free fall, the fact that all bodies fall with the same acceleration. How can these two be reconciled? When two people, one on the moving train and one on the platform each drop a stone, will the two stones hit the ground simultaneously? According to classical, Newtonian physics yes, but according to special relativity no. That is surprising. Was there any way to impose the universality of free fall and maintain Galileo’s principle?

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The following is what inspired Einstein. Later he recalled in 1920: “Then came to me the happiest thought of my life in the following form. In an example worth considering the gravitational field only has a relative existence in a manner similar to the electric field generated by electromagnetic induction. Because for an observer in free-fall from the roof of a house, there is during the fall – at least in his immediate vicinity – no gravitational field”. Now the great thing is that this allowed Einstein to simulate gravity by acceleration and he could now treat accelerated frames of reference with the help of relativity, so he had a handler in the framework of special relativity, but in a new way that preserved universality of free fall. He could now predict that light bends in a gravitational field. The principle of equivalence (elevator experiments – linear acceleration, a heuristic guide).

Where did the idea of a generalization of the special relativity principle to accelerated motion actually come from? Einstein was particularly fascinated by Ernst Mach’s historical critical analysis of mechanics. What could Einstein learn from Mach? Mach had reconsidered Newton’s bucket experiment. Why does the water rise when it stars rotating? Newton’s answer was the following: because it moves with respect to absolute space. Mach’s answer was different: he claimed that it moves because it moves with respect to the fixed stars. That would make it a relative motion, an inertia, an interaction of bodies in relative motion with respect to each other: the water and the stars.

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Rotation – heuristic guide

Besides Mach’s critique of mechanics, there is another element which can be identified in what Einstein called the happiest thought of his life. Einstein said (1920): “Then came to me the happiest thought of my life in the following form. In an example worth considering the gravitational field only has a relative existence in a manner similar to the electric field generated by electromagnetic induction. Because for an observer in free-fall from the roof of a house, there is during the fall – at least in his immediate vicinity – no gravitational field” (not italicized in the original). Use electromagnetic field theory as a mental model. We can see that it was the analogy of the gravitational field theory with the well-known theory of the electromagnetic field, on which Einstein of course was a specialist, that inspired him to the happiest thought as well, alongside the influence of Mach.

Now with the help of Mach, Einstein was in the position to complete the analogy between electromagnetic theory on the one hand and gravitational theory on the other hand by conceiving gravitation and inertia together as corresponding to the electromagnetic field. This analogy will guide him all these years from 1907 till 1915 to the completion of general relativity.

Let us look at the milestones of the genesis of general relativity. Usually this is portrayed as a drama in three acts:

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[My comment: John Stachel wrote in his paper “The First Two Acts”, Einstein from B to Z, p. 261, that in 1920 Einstein himself wrote a short list of “my most important scientific ideas” in a letter to Robert Lawson (April 22, 1920):

1907 Basic idea for the general theory of relativity

1912 Recognition of the non-Euclidean nature and its physical determination by gravitation

1915 Field equations of gravitation. Explanation of the perihelion motion of Mercury.

Einstein’s words provide the warrant for comparing the development of general relativity to a three-act drama]:

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According to Jürgen Renn: The problem here is that this portrait, this drama here leaves out the villain in this story, what is usually considered a villain, namely a theory on which Einstein worked between 1913 and 1915, in Zurich mostly but later also in Berlin, where he discarded it. It is called the preliminary or the draft and in German, the Entwurf theory. Now the point is what for other accounts is the villain of the story, a theory that was discarded, in my account, my book [? not yet published?] is the actual hero.

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[My comment: I see what Jürgen Renn means, but I don’t think that for other historical accounts the Entwurf theory is a so-called villain of the story, a theory that is discarded in accounts of historians. Jürgen Renn even mentions these historians in his talk – Michel Janssen and John Stachel. What he jokingly calls the “villain”, the Entwurf theory, is a major part of my book, General Relativity Conflict and Rivalries, December 2015 and it is spread over many pages of it].

But let us proceed in order. At the begging of 1911 Einstein became the chair of physics at the German university of Prague, his first full professorship. Parague: What did Einstein achieve in 1912? He knew that the field had to be a combination of gravitation and inertia, but he did not know how to represent it mathematically. Fortunately the problem had two parts: equation of motion – the field tells matter how to move, and field equation – matter tells the field how to behave. He thus first tried to solve the problem of the equation of motion. And in particular the simple case how does a body move when no other forces, other than gravitation and inertia, act on it. Again the analogy with electromagnetism came to his rescue. It made sense that other special cases of dynamic gravitational fields such as the forces acting in a rotating frame of reference… [?] It should be possible to consider such a system at rest and the centrifugal forces acting there as dynamical gravitational forces. That’s what Einstein took from Mach. But the clue is a combination of gravity and inertia. So what could he learn?

Let us look at a rotating disk and try to measure its circumference with little roods. The disk is set into motion. Because of the length contraction predicted by special relativity, the rods would be shrunk, so that we need more of them to cover the circumference. In other words, the ratio between the circumference and the diameter would be larger than pi. This simple thought experiment gave Einstein the idea that, to describe general dynamical gravitational fields one needs to go beyond Euclidean geometry.

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Non-Euclidean geometries were known. Einstein himself was not too familiar with non-Euclidean geometries. He had some courses at the ETH, he had skipped some courses at the ETH, but he did know that a straight line in such a geometry corresponds to a straightest line, or a geodesic. That solved for him the problem of the equation of motion, because when no other forces act in such a geometry, a particle would just follow the straightest possible line. Now the program of the new theory was clear. (John A, Wheeler: “matter tells space-time how to curve; curved space-time tells matter how to move”).

In the summer of 1912, Einstein returned to Zurich. He knew that he could describe a curved space-time by the metric tensor. He knew that he could define the deviation of space-time from Euclidean flat geometry in terms of the metric tensor.  A metric tensor is a complicated object:

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The metric tensor replaces the one Newtonian gravitational potential with ten gravitational potentials. He could even write down the equation of motion in terms of the metric tensor, he achieved that relatively quickly. But he had no clue as how to find a field equation for this complicated object, the metric tensor, these ten gravitational potentials.

One of the most important sources for our story is a notebook in which Einstein entered his calculations, in the winter of 1912-1913, the so-called Zurich Notebook.

The following fraternity of scholars provided historical-critical-mathematical-physical interpretation of the Zurich Notebook (it took them 10 years to interpret Einstein’s calculations):

Einstein scholars

Einstein’s first attempts to deal with the mathematics of the metric tensor look rather pedestrian. He tried to bring together the metric tensor with what he knew about the gravitational field equation, which was also relatively little.

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When Einstein was desperate he called his old friend Marcel Grossmann: “Grossman you have got to help me or I will go crazy!” Grossman had helped Einstein to survive his exams and he got him his job at the patent office. Now he helped him master the problem of gravitation. Indeed, one immediately recognizes Grossman’s intervention in the notebook. His name appears next to the Riemann tensor, the crucial object for building a relativistic field equation. Einstein immediately used it to form what he considered a candidate to the left hand-side of the field equation.

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Einstein and Grossmann found that these field equations do not match their physical expectations. It turned out to be difficult to reconcile Einstein’s physical expectations with the new formalism. Groping in the dark, Einstein and Grossmann essentially hit upon the correct field equations, in the winter of 1912-1913, three years before the final paper, in the weak field limit:

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But Einstein and Grossmann found that these field equations do not match their physical expectations. Eventually they had to learn how to adapt these physical expectations to the implications of the new formalism: we are talking about a learning experience that took place between a mathematical formalism and new physical concepts that were being shaped during the process.

Jürgen Renn then gives the following metaphor [a machine] to explain the mechanism behind a field equation (the Einstein-Grossmann Entwurf gravitational field equation): Einstein started out with a hand made mathematical formalism, at least before Grossmann came into the game, but it did the job. Extracting from the source of the field (mass and energy) a gravitational field. That’s what a field equation is all about. Of course it was most crucial that the familiar special case of Newtonian gravity would also come out in the appropriate circumstances. And Einstein had to make sure that this machine was firmly grounded in basic physical principles and in particular in the conservation of energy and momentum. But he also wanted to generalize the principle of relativity to accelerated motions and he looked for a machine that worked in more general coordinate systems, but at that point he didn’t know quite at which. The later point was unclear to Einstein.

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The problem was that it was not clear whether that machine would actually deliver the requested physical results. With Grossmann came the dream for a much more sophisticated machine, a machine that worked for all coordinate systems because it was generally covariant:

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Here the starting point was a sophisticated mathematical formalism based on the Riemann tensor, and then of course the machine had to work in the same way: the source makes a field, but does the Newtonian limit come out right? And is the machine firmly grounded in the principles of energy and momentum conservation? It certainly doesn’t look that quite way. In any way it was generally covariant, working in all coordinate systems. The problem was that it was not entirely clear whether that machine would actually deliver the requested physical results and what kind of tweaking it would take to get them. In short, the mechanism was great but the output was uncertain. Given this situation, Einstein could now peruse two different strategies:

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*physical requirements: the Newtonian limit and the energy momentum conservation.

In the winter of 1912-1913, Einstein and with him Grossmann constantly oscillated between these two strategies. At the end of the winter he decided for one of them: the physical strategy. Well not quite, but rather a physical strategy tweaked and adapted to match the requirements of energy-momentum conservation and a generalized principle of relativity. So it was a home made extension of the original machine.

[My comment: The “physical strategy” and the “mathematical strategy” and the “oscillation” between them are memorable phraseology of Jürgen Renn. These had already been invented by Jürgen Renn several years ago. You can find it in many papers by Jürgen Renn. For instance Renn, Jürgen and Sauer, Tilman, “Pathways out of Classical Physics”, The Genesis of General Relativity 1, 2007, 113-312].

The result of the collaboration between Einstein and Grossmann in the winter of 1912-1913 was a hybrid theory, the so-called Entwurf or draft theory, the villain or hero mentioned before. Why was the theory, “Draft of a Generalized Theory of Relativity and a Theory of Gravitation” a hybrid theory? It was a hybrid theory because the equation of motion (the field tells matter how to move) is generally covariant (retaining its form in all coordinate systems), but the field equation (matter tells the field how to behave) is not generally covariant. It was not even clear in which coordinate system the field equation would be covariant. Nevertheless, Einstein was quite proud. To his future wife Elsa he wrote: “I finally solved the problem a few weeks ago. It is a bold extension of the theory of relativity together with the theory of gravitation. Now I must give myself some rest, otherwise I will go kaput”. But was it worth the effort? Wasn’t the Entwurf theory just a blind alley and a waste of time (for more than two and a half years)? Most accounts say yes and speak of a comedy of errors.

[My comment: As I mentioned previously, I am afraid I don’t really agree with this conclusion. Other historians don’t say yes. In my account, for instance, in my book General Relativity Conflict and Rivalries, I demonstrate that the Entwurf theory plays a crucial role in Einstein’s development of the November 1915 theory. I refrain, however, from using the terms “bridges”, “scaffolding” and other metaphors Einstein did not use (see below) because I think that, these terms and metaphors embed constraints that impact the understanding of the historical narrative. I rather prefer Einstein’s own terms, for instance, “heuristic guide”. Hence, Einstein was guided by the 1913 calculation of the perihelion of Mercury. So was he guided by the 1914 variational principle, formalism].

But if the Entwurf theory was important, what was its role? What function did it have for the creation of the general theory of relativity, if it turned out to be a wrong theory at the end? To answer that question we shall use another metaphor: the Entwurf theory as a scaffolding for building an arch or a bridge between physics and mathematics (Michel Janssen’s metaphor). The building of a bridge between physics and mathematics. On its basis, Einstein first calculated the Mercury perihelion motion, and working out its mathematical structure, and by “its”, meaning the preliminary Entwurf draft theory. Einstein worked out its mathematical structure and set up a variational formalism for it.

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The Mercury calculation eventually helped him to solve the problem of the Newtonian limit and the variational formalism helped him to solve the other problem he had encountered with the mathematical strategy, that is, the conservation of energy and momentum. All this prepared the situation of November 1915, when it eventually came to a situation when the scaffolding was torn down.

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Let us look at the first issue, the issue of the Mercury perihelion motion (a problem studied in detail by Michel Janssen). In 1913 Einstein together with Michele Besso calculated the Mercury perihelion motion on the basis of the Entwurf theory and the value which they miscalculated came out too small.  The theory predicated only 18″per century. This did not shatter, however, Einstein’s confidence in that theory. Einstein never mentioned this unsatisfactory result until 1915 but he reused this method developed under the auspices of the Entwurf theory in November 1915. The method of calculation,  the scaffolding, could be used in the final November theory. The creation of general relativity was a team effort. Besso had a role in the perihelion calculation in building a scaffolding for the transition to the final theory. The Mercury calculation helped Einstein understand the problem of Newtonian limit and accept the field equation he had earlier discarded. The Mercury (perihelion) calculation of 1913 really did act as a scaffolding for what Einstein achieved in November 1915, when he redid this calculation now on the basis of the correct theory.

Einstein’s colleagues were amazed how quickly he could calculate. David Hilbert wrote in a postcard just a day after Einstein had submitted the paper: “Congratulations on conquering the perihelion motion. If I could calculate as fast as you can, the electron would be forced to surrender to my equations and the hydrogen atom would have to bring a note from home to be excused for not radiating”. However, all Einstein had to do is to redo the calculations for the perihelion motion in the Entwurf theory that he had done with Besso in 1913 but never published. Einstein did not bother to tell Hilbert about this earlier work. Apparently he wanted to give Hilbert a dose of his own medicine, seeing Hilbert as somebody who gave the impression of being superhuman by obfuscating his methods (Einstein to Ehrenfest, May 24, 1916).

In November 1915 the building of a scaffolding (Besso’s assistance) helped Einstein to overcome his earlier problems with extracting the Newtonian limit from the field equation found along the mathematical strategy.

But what about the second problem? The conservation laws of energy and momentum? Again the Entwurf theory served as a scaffolding. In 1914 Einstein and Grossmann set up a variational formalism for the Entwurf theory from which it was easy to derive the conservation laws. That formalism was general enough to allow the derivation of the conservation laws also for other theories, including the ones Einstein had discarded in the winter of 1912-1913.  You can use the variational formalism to make a candidate field equation for the physical strategy or you can change the settings, and then you get a different machine, a candidate field equation for the mathematical strategy.

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Having constructed such a formalism, the variational formalism, is what allowed Einstein to switch from the Entwurf theory to the theory he presented on November 4, 1915.

Einstein had resolved his two major problems that had prevented him in Zurich to accept candidate field equations along the mathematical strategy; namely the requirement to get out the Newtonian limit in the special case and the conservation laws. That confronts us with a puzzle: Why did Einstein not come back to the mathematical strategy right away once he had resolved these problems at the end of 1914?  He firmly believed in the Entwurf theory and had concocted all kinds of arguments in its favor, for instance the hole argument.

[My comment: I am afraid I don’t agree with this conclusion: I don’t think that at the end of 1914 Einstein had already resolved his two major problems (Newtonian limit and conservation laws). He was only able to resolve them in November 1915].

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But by October 1915, his perspective was gradually changing because problems with the Entwurf theory were gradually accumulated:

1) It did not explain the perihelion problem well, we have seen that. Einstein could live with it. He just put it under the rug and did not mention it in his publications.

2) It did not allow him to conceive rotation at rest. It was a major blow, considering his Machian vision.

3) And, it did not follow uniquely, as he had hoped, from the variational formalism that he had set up. But this failure was actually a blessing in disguise. It meant that the formalism was actually more general and not just tailor-made for the Entwurf theory. So he could use it.

So these problems were the prelude to the drama of November 1915 when Einstein published week after week his four conclusive publications on general relativity. On the 4th of November that is the transition from the Entwurf theory to the new mathematical objects; with an addendum on the 11th of November; the Mercury paper on the 18th of November, and the final field equations on the 25th. The first paper contains an interesting hint at what Einstein considered the “fatal prejudice” that had hindered him so far and also what was the key to the solution. The subsequent papers successively straighten out a logical structure of the theory, show that now the Mercury problem works and the final paper completes the logical structure of the theory.

In order to understand what the fatal prejudice was and what the key to the solution was, we have to once more time look at the mechanism at work here:

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There is indeed not just the source and the field. There is also the gravitational potential represented by the metric tensor and its connection with the gravitational field. That connection is expressed by a differential operator. One way to express this differential operator turned out to be a fatal prejudice, the other a key to the solution. As it turned out, it was essentially sufficient to change one element in the variational formalism developed for the Entwurf field equations, in order to get the theory from November the 4th, 1915. Namely, redefine the gravitational field.

Here are two ways in which Einstein expressed the connection between the field and the potential: One in the 1913 Entwurf theory and the other in the theory of November 4th. In the paper itself he speaks of the first way as a fatal prejudice and in a letter to Sommerfield he characterizes the second option as the key to the solution:

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In the end the transition from the Entwurf theory, based on the physical strategy, to the November 1915 theory, based on the sophisticated math of the Riemann tensor, seems to have been a rather simple step. But what made this step possible was the scaffolding represented by the variational formalism Einstein had built for the Entwurf theory.

[My comment: In my book, General Relativity Conflict and Rivalries, I demonstrate an additional element. Einstein wrote to Sommerfeld the following:

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“scalar derived from the energy tensor of matter, for which I write T in the following”.

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In my book I show how one can derive the second term on the right-hand side of the above November 25, 1915 equation on the basis of the variational formalism and on the basis of Einstein’s 1914 Entwurf theory and November 4th, 1915 paper. I connect between this latter derivation and the derivation of the November 4, 1915 field equation from the 1914 variation principle].

A variational formalism is a machine for making machines: It made it simpler to pass from a machine based on the fatal prejudice:

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to a machine that represented the key to the solution:

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Einstein had to revise the architecture of his theory step by step and that is what happened in the final publication of November 1915. To Arnold Sommerfeld he wrote: “unfortunately I have immortalized my final errors in the academy papers” (November 28, 1915). And to his friend Paul Ehrenfest he wrote: “It is convenient with that fellow Einstein: every year he retracts what he wrote the year before” (December 26, 1915).

In Einstein’s defense one had to remember that what contributed to the drama was that the mathematical David Hilbert was or at least seemed to have been hot on Einstein’s trail. Hilbert presented his field equations in Göttingen on November 20, 1915, five days before Einstein. He used the Riemann curvature scalar in his variational formalism. He did not explicitly write down the field equation but he could have easily calculated it of course. In the late 1990s, page proofs of Hilbert paper, which itself was not published until March 1916, turned up. These page proofs carry a date of December 6, 1915, after Einstein’s publication.

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Did Hilbert beat Einstein to the punch? His page proofs show that the original version of Hilbert’s theory was conceptually closer to the Entwurf theory than to Einstein’s final version. Hilbert’s theory of December 6, 1915 was just as the Entwurf theory, a hybrid theory with extra conditions on the coordinate systems. This restriction on the coordinate systems was later dropped in the published version appearing in March 1916. Hence, the moral is: Einstein could have taken his time in November 1915 and need not have worried about Hilbert stealing his thunder. Hilbert did not build a bridge between mathematics and physics as Einstein had done. In fact he didn’t worry about these problems of Newtonian limit and energy momentum conservation in the way that Einstein had done. So on November 25, 1915, the edifice of general relativity seemed complete.

This is the first part of Jürgen Renn’s lecture, it deals with the genesis of general relativity (until approximately 49 minutes after the YouTube video start time). The second part of the lecture, not given here, is quite disappointing compared to the first part. In the first part of the lecture, Jürgen Renn is inspired by great scholars, notably John Stachel. Unfortunately, the second part of the lecture lacks the inspiration and sensation of the greatness of the fraternity of Einstein scholars (see photo further above).

 

 

 

 

 

The prediction of gravitational waves emerged as early as 1913

On February 11, 2016, The Max Planck Institute for the History of Science in Berlin published the following announcement: “One Hundred Years of Gravitational Waves: the long road from prediction to observation”:

“Collaborative work on the historiography 20th century physics by the Einstein Papers Project at Caltech, the Hebrew University of Jerusalem, and the Max Planck Institute for the History of Science carried out over many years has recently shown that the prediction of gravitational waves emerged as early as February 1916 from an exchange of letters between Albert Einstein and the astronomer Karl Schwarzschild . In these letters Einstein expressed skepticism about their existence. It is remarkable that their significant physical and mathematical work was carried out in the midst of a devastating war, while Schwarzschild served on the Eastern Front”.

Collaborative work by experts on the physics of Einstein from the Einstein papers Project, from the Max Planck Institute for the History of Science in Berlin: Prof. Jürgen Renn, Roberto Lalli and Alex Blum; and from the Hebrew University of Jerusalem the only representative is Prof. Hanoch Gutfreund, the academic director of the Albert Einstein Archives. Their main finding is therefore:

The prediction of gravitational waves emerged as early as February 1916 from an exchange of letters between Albert Einstein and the astronomer Karl Schwarzschild. However, from a historical point of view this is not quite accurate because Einstein reached the main idea of gravitational waves three years earlier, as I demonstrate below. Any way the group published two summaries of the study.

A summary was published in German:

“Als Einstein dann seine abschließende Arbeit zur allgemeinen Relativitätstheorie am 25. November 1915 der Preussischen Akademie in Berlin vorlegte, war die Frage, ob solche Wellen tatsächlich aus seiner Theorie folgen, noch offen. Einstein erwähnte das Thema zum ersten Mal in einem Brief, den er am 19. Februar 1916 an Karl Schwarzschild schickte. Nach einigen obskuren technischen Bemerkungen, stellte er lakonisch fest: „Es gibt also keine Gravitationswellen, welche Lichtwellen analog wären”.”

“Gravitationswellen – verloren und wiedergefunden” von Diana K. Buchwald, Hanoch Gutfreund und Jürgen Renn.

and also in English:

“When Einstein presented his theory of general relativity on Nov. 25, 1915 in Berlin, the question of whether such waves would constitute a consequence of his theory remained untouched. Einstein mentioned gravitational waves for the first time in a letter of 19 February 1916 to Karl Schwarzschild, a pioneer of astrophysics. After some obscure technical remarks, he laconically stated: “There are hence no gravitational waves that would be analogous to light waves”.”

“Gravitational Waves: Ripples in the Fabric of Spacetime Lost and Found” by Hanoch Gutfreund, Diana K. Buchwald and Jürgen Renn.

And here as well.

Hence, according to the three above authors Einstein mentioned gravitational waves for the first time in a letter of 19 February 1916 to Karl Schwarzschild. However, this is wrong . Einstein reached the main idea of gravitational waves three years earlier, which is not when the above group of scholars had thought the gravitational waves were mentioned for the first time. As early as  1913, Einstein started to think about gravitational waves when he worked on his Entwurf gravitation theory.

In the discussion after Einstein’s 1913 Vienna talk on the Entwurf theory, Max Born asked Einstein about the speed of propagation of gravitation, whether the speed would be that of the velocity of light. Here is Einstein’s reply:

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In 1916, Einstein followed these steps and studied gravitational waves.

See my papers on gravitational waves (one and two) and my book for further information.

Review: The Cambridge Companion to Einstein

I recommend this recent publication, The Cambridge Companion to Einstein, edited by Michel Janssen and Christoph Lehner.
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It is a real good book: The scholarly and academic papers contained in this volume are authored by eminent scholars within the field of Einstein studies.

The first paper introduces the term “Copernican process”, a term invented by scholars to study scientists’ and Einstein’s achievements. The Copernican process describes a complex revolutionary narrative and the book’s side of the divide.

First, Einstein did not consider the relativity paper a revolutionary paper, but rather a natural development of classical electrodynamics and optics; he did regard the light quantum paper a revolutionary paper.

Carl Seelig wrote, “As opposed to several interpreters, Einstein would not agree that the relativity theory was a revolutionary event. He used to say: ‘In the [special] relativity theory it is no question of a revolutionary act but of a natural development of lines which have been followed for centuries'”.

Why did Einstein not consider special relativity a revolutionary event? The answer was related to Euclidean geometry and to measuring rods and clocks. In his special theory of relativity Einstein gave a definition of a physical frame of reference. He defined it in terms of a network of measuring rods and a set of suitable-synchronized clocks, all at rest in an inertial system.

The light quantum paper was the only one of his 1905 papers Einstein considered truly revolutionary. Indeed Einstein wrote Conrad Habicht in May 1905 about this paper, “It deals with the radiation and energy characteristics of light and is very revolutionary”.

A few years ago Jürgen Renn introduced a new term “Copernicus process”: […] “reorganization of a system of knowledge in which previously marginal elements take on a key role and serve as a starting point for a reinterpretation of the body of knowledge; typically much of the technical apparatus is kept, inference structures are reversed, and the previous conceptual foundation is discarded. Einstein’s achievements during his miracle year of 1905 can be described in terms of such Copernican process” (p. 38).

For instance, the transformation of the preclassical mechanics of Galileo and contemporaries (still based on Aristotelian foundations) to the classical mechanics of the Newtonian era can be understood in terms of a Copernican process. Like Moses, Galileo did not reach the promised land, or better perhaps, like Columbus, did not recognize it as such. Galileo arrived at the derivation of results such as the law of free fall and projectile motion by exploring the limits of the systems of knowledge of preclassical mechanics (p. 41).

Einstein preserved the technical framework of the results in the works of Lorentz and Planck, but profoundly changed their conceptual meaning, thus creating the new kinematics of the theory of special relativity and introducing the revolutionary idea of light quanta. Copernicus as well had largely kept the Ptolemaic machinery of traditional astronomy when changing its basic conceptual structure.

Although Einstein did not consider his relativity paper a revolutionary paper, he explained the new feature of his theory just before his death: “the realization of the fact that the bearing of the Lorentz transformation transcended its connection with Maxwell‘s equations and was concerned with the nature of space and time in general. A further new result was that the ‘Lorentz invariance’ is a general condition for any theory. This was for me of particular importance because I had already previously recognized that Maxwell‘s theory did not represent the microstructure of radiation and could therefore have no general validity”.

Planck assumed that oscillators interacting with the electromagnetic field could only emit and/or absorb energy in discrete units, which he called quanta of energy. The energy of these quanta was proportional to the frequency of the oscillator.

Planck believed, in accord with Maxwell’s theory that, the energy of the electromagnetic field itself could change continuously. Einstein first recognized that Maxwell’s theory did not represent the microstructure of radiation and could have no general validity. He realized that a number of phenomena involving interactions between matter and radiation could be simply explained with the help of light quanta.

Using Renn and Rynasiewicz phraseology, Planck “did not reach the promised land”, the light quanta. Moreover, he even disliked this idea. Einstein later wrote about Planck, “He has, however, one fault: that he is clumsy in finding his way about in foreign trains of thought. It is therefore understandable when he makes quite faulty objections to my latest work on radiation”.

In an essay on Johannes Kepler Einstein explained Copernicus’ discovery (revolutionary process): Copernicus understood that if the planets moved uniformly in a circle round the stationary sun (one frame of reference), then the planets would also move round all other frames of reference (the earth and all other planets): “Copernicus had opened the eyes of the most intelligent to the fact that the best way to get a clear group of the apparent movements of the planets in the heavens was to regard them as movements round the sun conceived as stationary. If the planets moved uniformly in a circle round the sun, it would have been comparatively easy to discover how these movements must look from the earth”.

Therefore Einstein’s revolutionary process was the following: Einstein was at work on his light quanta paper, but he was busily working on the electrodynamics of moving bodies too. Einstein understood that if the equation E = hf holds in one inertial frame of reference, it would hold in all others. Einstein realized that the ‘Lorentz invariance’ is a general condition for any theory, and then he understood that the Lorentz transformation transcended its connection with Maxwell’s equations and was concerned with the nature of space and time in general.