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).

 

 

 

 

 

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My work has been plagiarized at the Century of General Relativity conference

conference Berlin

You often think that if your papers and books are good, conferences all around the world will invite you to present them. How can you measure how influential your work is? The answer is simple: The more your papers are interesting, the greater the odds become you will not be invited to conferences, and your papers will be plagiarized at a conference by a professor extraordinarius. He will present your work as his own and use your ideas without mentioning your name in his conference speech. Can you imagine your reaction to later hearing his lecture on the web site of the Max Planck Institute for the History of Science in Berlin? “Oh my, these are my words! This cannot be true!” The organizers of the Berlin Century of General Relativity and MPIWG conference  failed to invite me to lecture at this international conference to celebrate 100 years of general relativity, a conference I should have gone to. But it turns out that my work on Einstein is so influential that professor Hanoch Gutfreund from the Hebrew University of Jerusalem gave the main or plenary evening lecture at the Century of General Relativity conference, “100 years of General Relativity – What are we Celebrating?”, and he made use in his lecture of passages I wrote two and four years ago and failed to mention my name. He has plagiarized content from my papers for his lecture. “O human race, born to fly upward, wherefore at a little wind dost thou so fall?” Dante Alighieri. I always felt there was something special in my papers because 10,000 people have downloaded my work. However, I don’t exactly feel flattered. I’m grossed out! I am completely disappointed. People have their head in the sand when my work is plagiarized in a big conference.

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קוראים 10000

The comparison between the original, my work, and citations from Prof. Gutfreund’s talk will speak for itself.

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Professor Hanoch Gutfreund’s lecture presented Einstein’s road to general relativity (the genesis of general relativity) and the formative years of general relativity (a term coined by Prof. Gutfreund and Prof. Jürgen Renn). Six times he lifted ideas, phrases and lines from my work.

1. Einstein does not use the Schwarzschild Solution in his 1916 Review Paper.

Professor Gutfreund speaks about things Einstein could have done: “He could have done it… we know that he could have done it”. In this respect he mentions Einstein and the Schwarzschild solution:

“Another thing which he could have done. So he already knew the Schwarzschild solution, because the Schwarzschild correspondence is in December. He wrote this paper [review paper, 1916] later. He submitted it only in March. So he could have used this Schwarzschild solution who showed a simpler derivation of the motion of the perihelion and of the bending of light and he did not do it”.

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It seems Prof. Gutfreund have picked the above passage from my 2012 paper, “From the Berlin ‘Entwurf’ Field equations to the Einstein Tensor III: March 1916”, ArXiv: 1201.5358v1 [physics.hist-ph], 25 January, 2012:

Scwarzschild

Einstein’s 1916 Equations:

Schwartz1

Schwartz2

Schwartz3

In addition, the above passage from prof. Gutfreund’s speech had been previously explained in great detail in my paper, “Einstein, Schwarzschild, the Perihelion Motion of Mercury and the Rotating Disk Story”, published in 2014. A year before Prof. Gutfreund’s lecture at the Century of General Relativity conference in Berlin, I wrote in the abstract of my paper, “Einstein, Schwarzschild, the Perihelion Motion of Mercury and the Rotating Disk Story”, ArXiv: 1411.7370v [physics.hist-ph], 26 Nov, 2014:

“On November 18, 1915 Einstein reported to the Prussian Academy that the perihelion motion of Mercury is explained by his new General Theory of Relativity: Einstein found approximate solutions to his November 11, 1915 field equations. Einstein’s field equations cannot be solved in the general case, but can be solved in particular situations. The first to offer such an exact solution was Karl Schwarzschild. Schwarzschild found one line element, which satisfied the conditions imposed by Einstein on the gravitational field of the sun, as well as Einstein’s field equations from the November 18, 1915 paper. On December 22, 1915 Schwarzschild told Einstein that he reworked the calculation in his November 18 1915 paper of the Mercury perihelion. Subsequently Schwarzschild sent Einstein a manuscript, in which he derived his exact solution of Einstein’s field equations. On January 13, 1916, Einstein delivered Schwarzschild’s paper before the Prussian Academy, and a month later the paper was published. In March 1916 Einstein submitted to the Annalen der Physik a review article on the general theory of relativity. The paper was published two months later, in May 1916. The 1916 review article was written after Schwarzschild had found the complete exact solution to Einstein’s November 18, 1915 field equations. Einstein preferred in his 1916 paper to write his November 18, 1915 approximate solution upon Schwarzschild exact solution (and coordinate singularity therein).”

I demonstrate in my paper that in his 1916 review paper, “The Foundation of the General Theory of Relativity”, Einstein used Huygens principle and the first order approximate solution to his vacuum field equations from the November 18, 1915 perihelion of Mercury paper to derive bending of light, the deflection of a ray of light passing by the sun. I end my paper by saying: “Einstein ended his paper with the final equation from his November 18 paper, the equation for the perihelion advance of Mercury in the sense of motion after a complete orbit. And he only mentioned in a footnote, ‘With respect to the calculation, I refer to the original treatments’: Einstein’s November 18 paper and Schwarzschild’s 1916 paper”. Here are two paragraphs from my own paper:

שוורצשילד1

שוורצשילד2

I wrote above: “In March 1916 Einstein submitted to the Annalen der Physik a review article on the general theory of relativity, “The Foundation of the General Theory of Relativity”. The paper was published two months later, in May 1916. The 1916 review article was written after Schwarzschild had found the complete exact solution (8) to Einstein’s November 18, 1915 field equations. Even so, in his 1916 paper, Einstein preferred not to base himself on Schwarzschild’s exact solution… and he returned to his first order approximate solution (6) from his November 18, 1915 paper”.

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Einstein preferred in his 1916 review paper to write his November 18, 1915 approximate solution upon the Schwarzschild exact solution because he objected to the “Schwarzschild singularity”. Einstein repeatedly spoke against the Schwarzschild singularity and stated the impossibility of the Schwarzschild singularity.

2. Einstein and the Riemann tensor.

In his talk Professor Gutfreund concentrated on Einstein’s mistakes. In describing Einstein’s mistakes prof. Gutfreund said:

“The Riemann tensor is not a tensor of curvature. There is no affine connection. There is no parallel transport, all that, all the geometrization that is the trademark of the whole theory, that was not a presupposition that led him to the final results. He could have done it, maybe in another step. How could we know that he could have done it?

In 1914 he wrote another review article that was the review article of the Entwurf theory, a long article, he wrote it when he was confident that this was the correct theory; and there where he gets to the point where he has to explain covariant differentiation, he makes a remark: I know that Levi-Civita told us how to do it this way, but I prefer to do it differently, and this differently is abominable. I can tell you. If you look at the text how it is done, and when he did his 1916 review [article] he followed almost word by word except in that chapter where the new Lagrangian has to appear, except there he followed exactly what he did, so he could have done it”.

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To begin with, this explanation combines two unrelated elements. The second part of the above passage seems to represent incorrectly a paragraph from my 2012 paper, “From the Berlin ‘Entwurf’ Field equations to the Einstein Tensor II: November 1915 until March 1916”, ArXiv: 1201.5353v1 [physics.hist-ph], 25 January, 2012. In 2012 I sent this paper to prof. Gutfreund.

The opening remarks of my paper, “From the Berlin ‘Entwurf’ Field equations to the Einstein Tensor II: November 1915 until March 1916” (pp. 1-2), deal with Einstein’s 1914 review article and the comment he later made. Einstein had published a comprehensive review article dealing with his Entwurf  theory. On page 1041, he presented the Ricci tensor. On pages 1042 he found a problem with the Ricci tensor. Evidently he did not yet realize that the solution was to restrict himself to unimodular transformations. On page 1053 he presented the Riemann-Christoffel tensor. He did not use this tensor in his 1914 Entwurf field equations. That was the reason why the presentation of this tensor in 1914 was very brief. Of course the reason was also page 1041. In his first talk on the general theory of relativity (November 4, 2015), Einstein postulated that only unimodular transformations were allowed. This solved the problem with the 1914 Ricci tensor (page 1041). He wrote the Riemann-Christoffel tensor, obtained the Ricci tensor G and a gravitational tensor R. The field equations were restricted to unimodular transformations. He then wrote the following remark: the Ricci and Levi-Civita fundamental tensor of page 1041 could be written in a different form, it could be obtained from the Riemann-Christoffel tensor. He explained that he had given this proof in his 1914 paper on page 1053 and had followed this root in 1912 in the Zurich Notebook. Hence, Einstein made the remark (comment) – not in the 1914 Entwurf paper – but rather in the November 4, 1915 paper; and the remark referred to the field equations formulated in a non-Lagrangian form. I explain this in my 2012 paper:

2012-1

2012-2

The first part of Prof. Gutfreund’s explanation represents Prof. John Stachel’s memorable phraseology, the importance of “the affine connection”. Prof. Stachel explains that until 1912, Einstein lacked the Riemanian geometry and the tensor calculus as developed by the turn of the century, i.e., based on the concept of the metric tensor; and after 1912 when he was using these, he then lacked more advanced mathematical tools (the affine connection); these could be later responsible for inhibiting him for another few years. Judged from the historical point of view of his time, Einstein did not make a mistake, because he lacked the appropriate mathematical tools. Actually with hindsight the story is more complicated. What was eventually mere coincidence for Einstein would later turn to be a consequence derived by new mathematical tools, the affine connection, which was invented after Einstein had arrived at generally covariant field equations. (See Stachel, John, Einstein from ‘B’ to ‘Z’, 265, 304-306.

The above explanation is from my paper: “Einstein’s 1912-1913 struggles with Gravitation Theory: Importance of Static Gravitational Fields Theory”, ArXiv: 1202.2791v1 [physics.hist-ph], 13 February, 2012, p. 20):

stachel

Finally, following the November 4, 1915 field equations, Einstein wrote the 1914 Entwurf Lagrangian and adjusted in 1915 and in 1916 his Entwurf 1914 variational formalism. In section 12 of the 1916 review article, Einstein started from the 1914 equations he had written on page 1053, he contracted the Riemann-Christoffel tensor and obtained the Ricci tensor and the field equations in unimodular coordinates; he also wrote the field equations in Lagrangian form.

In my 2012 paper, “From the Berlin ‘Entwurf’ Field equations to the Einstein Tensor III: March 1916”, ArXiv: 1201.5358v1 [physics.hist-ph], 25 January, 2012, I pinpoint the differences and similarities between Einstein’s first 1914 review paper and second 1916 review paper, “The Foundation of the General Theory of Relativity”. I discuss the differences and similarities among Einstein’s 1914 and 1916 formulations and Einstein’s 1916 manuscript “The Foundation of the General Theory of Relativity” and 1916 review paper, “The Foundation of the General Theory of Relativity”.

3. Friedmann’s model and Einstein’s reaction to it.

Towards the end of his lecture, “100 years of General Relativity – What are we Celebrating?”, prof. Gutfreund lifted phrases from my 2013 paper, “The Mythical Snake which Swallows its Tail: Einstein’s matter world”, ArXiv: 1309.6590v [physics.hist-ph], 26 Sep. 2013.

In 1922, Alexander Friedman published a model of an expanding universe. Einstein was not satisfied with this model and replied by a note; he thought he found a mistake in Friedmann’s results, which when corrected Friedmann’s solution would give Einstein’s good old static model. Friedmann sent Einstein his calculations and asked him to publish a correction to his statement. Einstein was willing to correct the slip in his previous note. Prof. John Stachel discovered that in the draft to the note to the editor Einstein wrote something quite different.

Prof. Gutfreund explained in his lecture:

“But here we have you see the letter, the letter to the editor, the angry letter. You see the last sentence is crossed out. So I will tell you what is it the last sentence. The last sentence says ‘It follows that the field equations, besides the static solution’, there are such static solution and so on. But then what is crossed out is ‘but a physical significance can hardly be attributed to them’.”.

And Professor Gutfreund showed the following slide:

“It follows that the field equations, besides the static solutions, permit dynamic (that is varying with time coordinates) spherically symmetric solutions for the spatial structure. He added the words: ‘but a physical significance can hardly be ascribed to them’, which he crossed out before sending the note to the editor”.

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I see phrases here that come from my work and Prof. Stachels’ bookEinstein from B to Z, 2002, for which there is no attribution. I recognize my own words: “but a physical significance can hardly be ascribed to them”. Prof. Stachel wrote: “to which a physical significance can hardly be ascribed”. Hence, prof. Gutfreund did not even bother to read prof. Stachel’s original paper; he simply lifted phrases from my paper. His above citation and slide contain exact words from my own published paper but he does not give attribution to me. I wrote in my paper, “The Mythical Snake which Swallows its Tail: Einstein’s matter world” the following:

פרידמן

snake

Therefore, in my paper, “The Mythical Snake which Swallows its Tail: Einstein’s matter world”, I wrote the following (pp. 39-40):

“Einstein was willing to correct the slip in his previous note: ‘In my previous note I have criticized the cited work [Friedmann’s 1922 work, ‘On the curvature of Space’], but my objection, as I became convinced by Friedmann’s letter communicated to me by Mr. Krutkov, rested on an error in my calculations. I consider that Mr. Friedmann’s results are correct and shed new light. It follows that the field equations, besides the static solution, permit dynamic (that is, varying with the time coordinate) spherically symmetric solutions for the spatial structure’. 126

In fact, Einstein was little impressed by Friedmann’s mathematical models. In Einstein’s draft of the second note to the Zeitschrift für Physik, in which he withdrew his earlier objection to Friedmann’s dynamical solutions to the field equations, he crossed-out the final last section of the sentence, ‘a physical significance can hardly be ascribed to them’, before sending the note to the editor of the Zeitschrift für Physik, thus Einstein originally wrote in the draft: ‘It follows that the field equations, besides the static solution, permit dynamic (that is, varying with the time coordinate) spherically symmetric solutions for the spatial structure, but a physical significance can hardly be ascribed to them’.127”.

I placed the endnotes at the end of my paper. Footnotes and endnotes are a bother to read and are rarely read. People abstain from reading endnotes. However, endnote 126 refers to Einstein’s (German) paper and endnote 127 in the above passage refers to the paragraph from Prof. Stachel’s paper, “Eddington and Einstein”, Einstein from ‘B’ to ‘Z’, p. 469:

Friedmann

Prof. Stachel writes:

“Friedmann’s paper came to Einstein’s attention. He thought he had found a mathematical flow in Friedmann’s argument, and said so in print. When he became convinced that the error was his not Friedmann’s, he retracted his mathematical objection, but stuck to his static cosmological model. How little impressed he was by Friedmann’s models can be seen from the final clause of his draft retraction, which (fortunately for him) Einstein deleted before it was printed:

It follows that the field equations, besides the static solution, permit dynamic (that is, varying with the time coordinate) spherically symmetric solutions for the spatial structure, [to which a physical significance can hardly be ascribed.],

The bracketed portion being crossed out in the manuscript”.

Compare prof. Gutfreund’s slide to the passage from my 2013 paper. Professor Gutfreund uses my phrases verbatim in his slide with no citation:

גוטפרוינד

Surely prof. Gutfreund did not read my endnote 127, otherwise he would have mentioned prof. John Stachel’s paper in his lecture, because when there is acknowledgment in prof. Gutfreund’s talk, the impression is of a wholesale attribution to prof. Jürgen Renn and other notable Einstein scholars. This is far from being the only sources for professor Gutfreund’s lecture. Indeed, in his lecture he mentions prof. John Stachel’s paper on Hilbert’s competition with Einstein (priority dispute) written with prof. Jürgen Renn and prof. Leo Corry, while discussing Einstein’s competition with David Hilbert:

“He was concerned that he will be outrun, and was concerned that he will be outrun by David Hilbert; and the question is who gets there first. Now had Einstein read the article by Jürgen Renn, and John Stachel and Leo Corry, he wouldn’t have to worry”.

Hilbert2 4. Demarcation between “Mach’s idea” and ‘Mach’s principle”

After presenting the genesis of general relativity, prof. Gutfreund briefly reviewed Mach’s principle. Here I highlight what I see as plagiarized demarcation between “Mach’s idea” and “Mach’s principle”. This demarcation is found in my 2013 paper, “The Mythical Snake which Swallows its Tail: Einstein’s matter world” and in my 2012 paper “Einstein’s 1912-1913 struggles with Gravitation Theory: Importance of Static Gravitational Fields Theory”. I also briefly discuss this matter in my first book, Einstein’s Pathway to the Special Theory of Relativity.

In his lecture Prof. Gutfreund explained:

“So this is a great Challenge, this is what happens, so he talks about the general theory of relativity and that he writes after visiting De Sitter in Leiden. Now at the outset I want to tell you that everything that Einstein did in those years in this context and in other until 1929, and maybe over, it was a little longer, was to defend his strong belief in Mach’s criticism of Newton. Mach’s criticism, I mean there is no absolute space, all inertial effects are due to all the masses in the universe, there is no inertia, except determined by all the masses of the universe. This is Mach’s idea. I am not calling it a principle yet. This is Mach’s idea ….”

When prof. Gutfreund explained the difference between Mach’s idea and Mach’s principle, he raised his hand and pointed his finger to the audience:

finger

Mach3

Professor Gutfreund then spoke about Einstein’s exchange of letters with de Sitter, Felix Klein and Hermann Weyl and said:

“And then Einstein makes a bold step. He elevates Mach’s idea into a principle. No longer a property of the theory, but a property of an acceptable solution. Only solutions which satisfy Mach are physically acceptable”.

And he showed the following slide:

Mach's ideas

In my 2013 paper, “The Mythical Snake which Swallows its Tail: Einstein’s matter world”, I demarcated between “Mach’s ideas” and “Mach’s Principle”:

Mach's idea

I Therefore write:

“Einstein desired to eliminate what he called the “epistemological weakness” [“erkenntnistheoretischen Schwächen”] of Newtonian mechanics, the absolute space, from physics; he invented a world, finite and spatially closed static universe, bounded in space, according to the idea of inertia having its origin in an interaction between the mass under consideration and all of the other masses in the universe, which he called “Mach’s ideas” (obviously not Ernst Mach’s ideas as has been generally recognized and as Mach himself pronounced them). This would be later called by Einstein “Mach’s principle” (more precisely Mach-Einstein principle)”.

In my 2012 paper “Einstein’s 1912-1913 struggles with Gravitation Theory: Importance of Static Gravitational Fields Theory”, I explain on page 22 the difference between “Mach’s idea” and Mach’s principle”:

Mach2

I therefore write:

“Einstein ended section §1 with the conclusion that the momentum and kinetic energy are inversely proportional to c. Or, the inertial mass is m/c and independent of the gravitational potential.116 This conforms to Mach’s idea that inertia has its origin in an interaction between the mass point under consideration and all of the other mass points. Einstein explained that if other masses are accumulated in the vicinity of the mass point, the gravitational potential c decreases. And then the quantity m/c increases which is equal to the inertial mass. In the static fields theory Einstein presented the predecessor to Mach’s principle.117“.

In my book, Einstein’s Pathway to the Special Theory of Relativity I again say:

Machbook

Prof Gutfreund says: “So this is a great Challenge, this is what happens, so he talks about the general theory of relativity and that he writes after visiting De Sitter in Leiden. … And then Einstein makes a bold step. He elevates Mach’s idea into a principle. No longer a property of the theory, but a property of an acceptable solution. Only solutions which satisfy Mach are physically acceptable”. And he presents the above slide.

In my paper, “The Mythical Snake which Swallows its Tail: Einstein’s matter world” I wrote the following:

Mach's ideas3.jpg 5. Besso as Einstein’s Sounding Board

Quite at the beginning of his lecture, “100 years of General Relativity – What are we Celebrating?”, prof. Gutfreund borrowed passages from my 2012 paper, “Albert Einstein’s Methodology”. Prof Gutfreund said in his lecture:

“Einstein with his very good friend usually a sounding board, in this case, a collaborator, in this case when they worked together. Usually he was Einstein’s sounding board. They wrote… the Einstein-Besso manuscript… and in that document they calculated the perihelion motion”.

Besso3

My own words in “Albert Einstein’s Methodology” are:

Besso0

 

Besso1

The Philosophy of Science Portal added a link to my paper, “Albert Einstein’s Methodology”.

Hence, in my 2012 paper, “Albert Einstein’s Methodology”, ArXiv: 1209.5181v1 [physics.hist-ph], 25 September, 2012, I write:

“Later in 1913 Besso came to Zurich and actively participated in solving the Einstein-Grossman (‘Entwurf’) gravitation equations with Einstein. They both tried to find solutions to the problem of the advance of the perihelion of Mercury. The young Einstein may have considered Besso as his sounding board, but was Besso still Einstein’s sounding board in 1913?”

I explain in my paper that in 1913, Besso still functioned as Einstein’s sounding board while they were both working on the Einstein-Besso manuscript:

“Indeed when Einstein wrote Besso a series of letters between 1913 and 1916, and described to him step by step his discoveries of General Relativity, Besso indeed functioned again as the good old sounding board as before 1905”.

I also wrote about Besso in my book, Einstein’s Pathway to the Special Theory of Relativity, April 2015:

Besso

Therefore, in my book, Einstein’s Pathway to the Special Theory of Relativity (Newcastle, UK: Cambridge Scholars Publishing), April 2015, I have dedicated a whole chapter to Einstein’s “sounding boards”. In the section explaining Michele Besso’s role as Einstein’s sounding board I write:

“Even in 1913, Besso was still Einstein’s sounding board. In June 1913, Besso visited Einstein in Zurich and actively participated in solving the Einstein-Grossmann Entwurf gravitation equations with Einstein. They both tried to find solutions to the problem of the advance of mercury’s perihelion in the field of a static sun. Their join work is known as the Einstein-Besso manuscript”.

Prof. John Stachel was the first to show that Michele Besso acted as Einstein’s sounding board. The need to put ideas into communicable form led Einstein to search throughout his early life for people to act as sounding boards for his ideas. See his book: Einstein’s Miraculous Year. Five Papers that Changed the Face of Physics (Princeton: Princeton University Press). Following discussions with prof. Stachel I have extended his ideas into the above expression.

I really hoped that some conference would ask me to give a talk about my work, “Albert Einstein’s Methodology”. I thought I had a philosophical paper worth talking about at a conference. Obviously, now that prof. Gutfreund lifted my unique expression of prof. Stachel’s idea of sounding boards from this paper there is no point presenting it at a conference.

6. Cosmological Constant Biggest blunder

A thread that runs through Professor Gutfreund’s entire talk is that Einstein had made many mistakes on his road to general relativity and cosmological model. Towards the end of his talk prof. Gutfreund mentions Einstein’s biggest mistake:

“But you know there is this Myth that Einstein when he abandoned the cosmological constant he said this is the worst error that I made. There is no evidence for that. Probably he never said that”.

In prof. Gutfreund’s book with prof. Jürgen Renn, The Road to Relativity, prof. Gutfreund further explains this:

cosmo

notes

Compare the above paragraph from prof. Gutfreund’s book The Road to Relativity to the abstract of my 2013 paper, “George Gamow and Albert Einstein: Did Einstein say the cosmological constant was the “biggest blunder” he ever made in his life?”, ArXiv: 1310.1033v [physics.histph], 03 Oct, 2013:

gamow

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And compare the penultimate paragraph from prof. Gutfreund’s book The Road to Relativity to two paragraphs from my paper, “George Gamow and Albert Einstein: Did Einstein say the cosmological constant was the ‘biggest blunder’ he ever made in his life?”:

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blunder2

In 2016 I received this message from ResearchGate:

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My paper gained traffic but no citations, but prof. Gutfreund, who plagiarized the abstract of my paper, received the citations. Allen I. Janis writes in his review: “The Road to Relativity: The History and Meaning of Einstein’s ‘The Foundation of General Relativity’.” American Journal of Physics 84, 2016:

“An interesting sideline in this chapter has to do with the frequently heard story that Einstein called his introduction of the cosmological constant the biggest mistake of his life. It seems there is no evidence that Einstein ever said or wrote this, and that it is in fact an invention of George Gamow”.

cite

Gamow

cheers

The audience of prof. Gutfreund’s lecture, “100 Years of General Relativity – What Are We Celebrating?”, consisted of top experts and known professors in my field. They clapped and cheered when he finished to speak. They seemed to like his lecture. I wish they knew that parts of professor Hanoch Gutfreund’s lecture were based on my papers and I worked so hard to write them.

7. David Hume and Ernst Mach’s influence on Einstein

At the Thursday round table speech Prof. Gutfreund seems to also lifted something from my 2013 paper, “The Mythical Snake which Swallows its Tail: Einstein’s matter world”. At the Berlin MPIWG conference round table discussion about general relativity, professor Gutfreund explained:

“But then in his [Einstein’s] Autobiographical Notes his most, I mean this is for the philosophers of science here, may be his most blant [blatant], most explicit departure from empiricism, you know until almost end he always mentions Mach together with Hume. The two of them who showed him the way to general relativity. I quote”.

manspla

“I mean this is for the philosophers of science here”, Prof. Gutfreund said while pointing to where the philosopher of science prof. Yemima Ben Menahem was sitting.

Mach and HUme

It is fairly obvious that the explanation about Hume and Mach showing Einstein the way to general relativity was either lifted from my 2013 paper, “The Mythical Snake which Swallows its Tail: Einstein’s matter world” or from my book, Einstein’s Pathway to the Special Theory of Relativity.

Hume and Mach showing Einstein the way to general relativity is a mistake in my 2013 paper which prof. Gutfreund seems to have reproduced in his round table discussion. Actually, in 1949 Einstein explicitly expressed in his Autobiographical Notes an intellectual debt to Hume and Mach’s philosophical writings in his discovery of special relativity. However, in my 2013 paper, “The Mythical Snake which Swallows its Tail: Einstein’s matter world”, I wrote about Hume’s influence on the elder Einstein and I said that Hume’s influence on Einstein was greater than Mach’s ideas (general relativity and cosmology):

Hume

I thus write:

“The elder Einstein could not remember how far Mach’s writings have influenced his work in the same way as could the young Einstein who was inspired by Mach’s ideas when creating the general theory of relativity. Indeed the elder Einstein often wrote that the influence of David Hume was greater on him. Finally, a year before his death Einstein silently dropped Mach’s principle in itself”.

The philosophy of Hume and Mach had an important influence on Einstein’s development and discovery of special relativity. Mach’s ideas about the relativity of inertia influenced Einstein on his road to general relativity. If Professor Gutfreund “quotes”, then I shall quote as well. Einstein writes in his Autobiographical Notes (1949, p. 53):

Einst

“One sees that in this paradox [of Einstein chasing a light beam] the germ of the special relativity theory is already contained. Today everyone knows, of course, that all attempts to clarify this paradox satisfactorily were condemned to failure as long as the axiom of the absolute character of time, or of simultaneity, was rooted unrecognized in the unconscious. To recognize clearly this axiom and its arbitrary character already implies the essentials of the solution of the problem. The type of critical reasoning required for the discovery of this central point was decisively furthered, in my case, especially by the reading of David Hume’s and Ernst Mach’s philosophical writings”.

However, in my first book, Einstein’s Pathway to the Special Theory of Relativity, on page 292, I tried to correct my mistake in my 2013 paper, and I combined the influence of David Hume’s and Ernst Mach’s philosophy on Einstein with Mach’s ideas and Mach’s principle:

Mach's principle

I therefore write in my book:

“The older Einstein could not remember how far Mach’s writings influenced his work in the same way as could the young Einstein who was inspired by Mach’s ideas when creating the theory of relativity. Indeed, the older Einstein often wrote that David Hume was a greater influence on him. We should remember that in 1948 Einstein saw Mach’s weakness in his belief more or less that science consists in the mere “ordering” of empirical material. Mach, according to Einstein, misjudged the free constructive element in the formation of concepts. He believed that in some sense theories arise by discovery and not invention (Einstein to Besso, January 6, 1948, Einstein and Besso 1971, Letter 153; see Section 1.1). Finally, a year before his death, Einstein silently dropped Mach’s principle in itself…”.

Prof. Gutfreund seems to have combined in his round table discussion my mistake from 2013 and the above so-called correction.

8. Einstein and Poincare.

Finally, it is not the first time that prof. Gutfreund has endorsed my ideas and presented them as his own. In August 2015, at the World Science Conference – Israel (WSCI), young students from all around the world and 15 Nobel laureates were invited to the WSCI conference. Prof. Gutfreund was part of a panel discussion at the WSCI conference on “Eureka moment!”. He happened to be sitting next to Nobel Laureates prof. Arieh Warshel, prof. Harold Kroto and prof. Sidney Altman. Later the Lectures and panels were uploaded to the website of the homepage of the WSCI conference.

I heard prof. Gutfreund speaking about Einstein’s 1916 interview (“exchange of readers” [letters]) with Max Wertheimer. He told the audience about Einstein describing to Wertheimer how the theory of general relativity occurred to him. Actually Wertheimer discussed with Einstein the development of his special theory of relativity and not the genesis of general relativity and the road to general relativity. Prof. Gutfreund spoke about Einstein’s creativity and Poincaré’s creativity and his Eureka moment, something he had read in my book, Einstein’s Pathway to the Special Theory of Relativity. He told the story of Poincaré who could not find the solution to his problem. Poincaré then took part in an excursion. The events of the trip made him forget his mathematical work. He entered a bus; the moment he put his foot on the step, the idea came to him, without anything in his former thoughts seeming to have prepared him for it.

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Prof. Gutfreund told the audience the following, here is the citation from his lecture:

“Einstein had a very close friendly relationship with Max Wertheimer. Max Wertheimer is one of the founding fathers of gestalt psychology, and they exchanged readers [letters]. Max Wertheimer even wrote a book about creativity and they explored this idea of creativity and debation [debated] time, and then this ha-moment according, so I mean the classical example of an ha-moment again according to his, to Einstein’s testimony is this happiest thought in retrospect. There is another ha-moment, because you see, a ha-moment and Eureka does not have always to be something which turns out to be correct. Einstein had an ha-moment in something which turned out completely wrong at the end, that is something I refer to, one day he writes to Lorentz and this I have a theory which is a dark spot there and the next day he writes I am now completely satisfied that this is true. But that was completely wrong. But the person who really discussed it is another physicist, a polyglot of science and that is Poincaré, and Poincaré describes an ha-moment he was troubling with his idea whether it should be Lobachevski’s geometry, this kind of geometry, Euclidean geometry, and suddenly he gets on a bus and he describes the moment when he puts his foot on the step of the bus and suddenly it all comes to him and he runs home and writes it all. So you don’t have to run naked in the streets in an ha-moment. There are all kind of…”.

Compare this to the following several paragraphs from my own book, Einstein’s Pathway to the Special Theory of Relativity, April 2015. Prof. Gutfreund has lifted the Einstein-Wertheimer-creativity-Poincaré bus story discussion from my own book:

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Fools had ne’er less wit in a year, For wise men are grown foppish. They know not how their wits to wear, Their manners are so apish. King Lear, Act 1, scene 4.

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Some of the topics discussed in my first book, Einstein’s Pathway to the Special Theory of Relativity

People ask questions about Einstein’s special theory of relativity: How did Einstein come up with the theory of special relativity? What did he invent? What is the theory of special relativity? How did Einstein discover special relativity? Was Einstein the first to arrive at special relativity? Was Einstein the first to invent E = mc2?

Did Poincaré publish special relativity before Einstein? Was Einstein’s special theory of relativity revolutionary for scientists of his day? How did the scientific community receive Einstein’s theory of special relativity when he published it? What were the initial reaction in the scientific community after Einstein had published his paper on special relativity?

In my book, Einstein’s Pathway to the Special Theory of Relativity, I try to answer these and many other questions.The topics discussed in my book are the following:

I start with Einstein’s childhood and school days.

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I then discuss Einstein’s student days at the Zurich Polytechnic. Einstein the rebellious cannot take authority, the patent office, Annus Mirabilis, University of Bern and University of Zurich, Minkowski’s space-time formalism of special relativity.

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Young Einstein, Aarau Class 1896

Additional topics treeated in my book are the following: Fizeau’s water tube experiment, Fresnel’s formula (Fresnel’s dragging coefficient), stellar aberration, and the Michelson and Michelson-Morley Experiments.

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Albert Einstein at the Patent office

Mileva Marić and Einstein

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Eduard Tete, Mileva Marić and Hans Albert

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Einstein’s road to the special theory of relativity: Einstein first believes in the ether, he imagines the chasing a light beam thought experiment and the magnet and conductor thought experiment. Did Einstein respond to the Michelson and Morley experiment? Emission theory, Fizeau’s water tube experiment and ether drift experiments and Einstein’s path to special relativity; “The Step”.

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Henri Poincaré’s possible influence on Einstein’s road to the special theory of relativity.

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Einstein’s methodology and creativity, special principle of relativity and principle of constancy of the velocity of light, no signal moves beyond the speed of light, rigid body and special relativity, the meaning of distant simultaneity, clock synchronization, Lorentz contraction, challenges to Einstein’s connection of synchronisation and Lorentz contraction, Lorentz transformation with no light postulate, superluminal velocities, Laue’s derivation of Fresnel’s formula, the clock paradox and twin paradox, light quanta, mass-energy equivalence, variation of mass with velocity, Kaufmann’s experiments, the principles of relativity as heuristic principles, and Miller ether drift experiments.

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The book also briefly discusses general relativity: Einstein’s 1920 “Geometry and Experience” talk (Einstein’s notion of practical geometry), equivalence principle, equivalence of gravitational and inertial mass, Galileo’s free fall, generalized principle of relativity, gravitational time dilation, the Zurich Notebook, theory of static gravitational fields, the metric tensor, the Einstein-Besso manuscript, Einstein-Grossmann Entwurf theory and Entwurf field equations, the hole argument, the inertio-gravitational field, Einstein’s general relativity: November 1915 field equations, general covariance and generally covariant field equations, the advance of Mercury’s perihelion, Schwarzschild’s solution and singularity, Mach’s principle, Einstein’s 1920 suggestion: Mach’s ether, Einstein’s static universe, the cosmological constant, de Sitter’s universe, and other topics in general relativity and cosmology which lead directly to my second book, General Relativity Conflict and Rivalries.

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My books

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Some of the topics discussed in my new book General Relativity Conflict and Rivalries

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The back cover of my book:

General Relativity Conflict and Rivalries: Einstein’s Polemics with Physicists:

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This book focuses on Albert Einstein and his interactions with, and responses to, various scientists, both famous and lesser-known. It takes as its starting point that the discussions between Einstein and other scientists all represented a contribution to the edifice of general relativity and relativistic cosmology. These scientists with whom Einstein implicitly or explicitly interacted form a complicated web of collaboration, which this study explores, focusing on their implicit and explicit responses to Einstein’s work.

This analysis uncovers latent undercurrents, indiscernible to other approaches to tracking the intellectual pathway of Einstein to his general theory of relativity. The interconnections and interactions presented here reveal the central figures who influenced Einstein during this intellectual period. Despite current approaches to history presupposing that the efforts of scientists such as Max Abraham and Gunnar Nordström,  which differed from Einstein’s own views, be relegated to the background, this book shows that they all had an impact on the development of Einstein’s theories, stressing the limits of approaches focusing solely on Einstein. As such, General Relativity Conflict and Rivalries proves that the general theory of relativity was not developed as a single, coherent construction by an isolated, brooding individual, but, rather, that it came to fruition through Einstein’s conflicts and interactions with other scientists, and was consolidated by his creative processes during these exchanges.

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Grossmann and Einstein

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From Zurich to Berlin

  1. Einstein and Heinrich Zangger (Einstein and Michele Besso)
  2. From Zurich to Prague.
  3. Back to Zurich (Einstein and Marcel Grossmann).
  4. From Zurich to Berlin (Einstein and Max Planck, Erwin Freundlich and others in Berlin) .

General Relativity between 1912 and 1916

  1. The Equivalence Principle.
  2. Einstein’s 1912 Polemic with Max Abraham: Static Gravitational Field
  3. Einstein’s 1912 Polemic with Gunnar Nordström: Static Gravitational Field
  4. Einstein’s 1912-1913 Collaboration with Marcel Grossmann: Zurich Notebook to Entwurf Theory.
  5. Einstein’s 1913-1914 Polemic with Nordström: Scalar Theory versus Tensor Theory (Einstein and Adriaan Fokker).
  6. Einstein’s Polemic with Gustav Mie: Matter and Gravitation.
  7. 1914 Collaboration with Grossmann and Final Entwurf Theory.
  8. Einstein’s Polemic with Tullio Levi-Civita on the Entwurf Theory.
  9. Einstein’s 1915 Competition with David Hilbert and General Relativity
  10. Einstein Answers Paul Ehrenfest‘s Queries: 1916 General Relativity.
  11. The Third Prediction of General Relativity: Gravitational RedShift
  12. Erich Kretschmann‘s Critiques of Einstein’s Point Coincidence Argument (Einstein and Élie Cartan).
  13. Einstein and Mach‘s Ideas.
  14. Einstein’s Reaction to Karl Schwarzschild‘s Solution (Einstein and Nathan Rosen and Leopold Infeld and others in Princeton).
  15. The Fourth Classic Test of General Relativity: Light Delay.

General Relativity after 1916

  1. Einstein’s 1916 Polemic with Willem de Sitter, Levi-Civita and Nordström on Gravitational Waves (Einstein and Nathan Rosen and Leopold Infeld and Howard Percy Robertson).
  2. Einstein’s Polemic with de Sitter: Matter World and Empty World.
  3. Bending of Light and Gravitational Lens: Einstein and Arthur Stanley Eddington
  4. Einstein’s Interaction with Hermann Weyl and the Cosmological Constant
  5. Einstein’s 1920 Matter World, Mach’s Ether and the Dark Matter
  6. Einstein’s 1920 Polemic with Eddington on de Sitter’s World.
  7. Einstein’s Reaction to the Aleksandr Friedmann Solution.
  8. Einstein’s Reaction to the Georges Lemaître Solution.
  9. Edwin Hubble‘s Experimental Results.
  10. The Lemaître-Eddington Model
  11. Einstein and the Matter World: the Steady State Solution.
  12. Einstein’s Collaboration with de Sitter.
  13. Einstein’s Reaction to Lemaître‘s Big Bang Model
  14. Einstein’s Interaction with George Gamow: Cosmological Constant is the Biggest Blunder
  15. Einstein, Gödel and Backward Time Travel

 

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Einstein 1916

People ask many questions about Einstein’s general theory of relativity. For instance: How did Einstein come up with the theory of general relativity? What did he invent? What is the theory of general relativity? How did Einstein discover general relativity? How did he derive his theory? Why was Einstein the first to arrive at generally covariant field equations even though many lesser-known scientists worked on the gravitational problem?

Did David Hilbert publish the field equations of general relativity before Einstein? Was Einstein’s theory of relativity revolutionary for scientists of his day? How did the scientific community receive Einstein’s theory of general relativity when he published it? What were the initial reaction in the scientific community after Einstein had published his paper on relativity?

Why did Einstein object so fiercely to Schwarzschild’s’ singularity (black holes)? Why did Einstein introduce the cosmological constant? Was it his biggest blunder? Why did Einstein suggest Mach’s principle? Is Mach’s principle wrong? And so forth.

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In my book General Relativity Conflict and Rivalries: Einstein’s Polemics with Physicists I try to answer these and many other questions.

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Between 1905 and 1907, Einstein first tried to extend the special theory of relativity and explain gravitational phenomena. This was the most natural and simplest path to be taken. These investigations did not fit in with Galileo’s law of free fall. This law, which may also be formulated as the law of the equality of inertial and gravitational mass, was illuminating Einstein, and he suspected that in it must lie the key to a deeper understanding of inertia and gravitation. He found “the happiest thought of my life”. He imagined an observer freely falling from the roof of a house; for the observer there is during the fall – at least in his immediate vicinity – no gravitational field. 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”. Newton realized that Galileo’s law of free fall is connected with the equality of the inertial and gravitational mass; however, this connection was accidental. Einstein said that Galileo’s law of free fall can be viewed as Newton’s equality between inertial and gravitational mass, but for him the connection was not accidental. Einstein’s 1907 breakthrough was to consider Galileo’s law of free fall as a powerful argument in favor of expanding the principle of relativity to systems moving nonuniformly relative to each other. Einstein realized that he might be able to generalize the principle of relativity when guided by Galileo’s law of free fall; for if one body fell differently from all others in the gravitational field, then with the help of this body an observer in free fall (with all other bodies) could find out that he was falling in a gravitational field.

In June 1911, Einstein published his paper, “On the Influence of Gravitation on the Propagation of Light”. An important conclusion of this paper is that the velocity of light in a gravitational field is a function of the place. In December 1911, Max Abraham published a paper on gravitation at the basis of which was Einstein’s 1911 conclusion about a relationship between the variable velocity of light and the gravitational potential. In February 1912, Einstein published his work on static gravitational fields theory, which was based on his 1911 June theory. In March 1912, Einstein corrected his static gravitational fields paper, but Abraham claimed that Einstein borrowed his equations; however, it was actually Abraham who needed Einstein’s ideas and not the other way round. Einstein thought that Abraham converted to his theory of static fields while Abraham presumed exactly the opposite. Einstein then moved to Zurich and switched to new mathematical tools, the metric tensor as representing the gravitational potential. He examined various candidates for generally covariant field equations, and already considered the field equations of his general theory of relativity about three years before he published them in November 1915. However, he discarded these equations only to return to them more than three years later. Einstein’s 1912 theory of static fields finally led him to reject the generally covariant field equations and to develop limited generally covariant field equations.

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Max Abraham

The Finnish physicist Gunnar Nordström developed a competing theory of gravitation to Einstein’s 1912-1913 gravitation theory. The equivalence principle was valid in his theory and it also satisfied red shift of the spectral lines from the sun. However, it was unable to supply the advance of the Perihelion of Mercury, such as Einstein’s theory; it led to a Perihelion like the one predicted by Newton’s law of gravity, and, it could not explain the deflection of light near the sun, because in Nordström’s theory the velocity of light was constant. Einstein’s 1913-1914 Entwurf theory of gravitation, the field equations of which were not generally covariant, remained without empirical support. Thus a decision in favor of one or the other theory – Einstein’s or Nordström’s – was impossible on empirical grounds. Einstein began to study Nordström’s theory from the theoretical point of view and he developed his own Einstein-Nordström theory on the basis of his conception of the natural interval. Eventually, in a joint 1914 paper with Lorentz’s student Adrian Fokker, Einstein showed that a generally covariant formalism is presented from which Nordström’s theory follows if a single assumption is made that it is possible to choose preferred systems of reference in such a way that the velocity of light is constant; and this was done after Einstein had failed to develop a generally covariant formulation for his own Entwurf theory.

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Gunnar Nordström

After arriving back to Zurich in summer 1912, Einstein was looking for his old student friend Marcel Grossmann, who had meanwhile become a professor of mathematics in the Swiss Federal Polytechnic institute. He was immediately caught in the fire. So he arrived and he was indeed happy to collaborate on the problem of gravitation. Einstein’s collaboration with Marcel Grossmann led to two joint papers, the first entitled, “Entwurf einer verallgemeinerten Relativitätstheorie und einer Theorie der Gravitation” (“Outline of a Generalized Theory of Relativity and of a Theory of Gravitation”) is called by scholars the Entwurf paper.

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Marcel Grossmann

The Entwurf theory was already very close to Einstein’s general theory of relativity that he published in November 1915. The gravitational field is represented by a metric tensor, the mathematical apparatus of the theory is based on the work of Riemann, Christoffel, Ricci and Levi-Civita on differential covariants, and the action of gravity on other physical processes is represented by generally covariant equations (that is, in a form which remained unchanged under all coordinate transformations). However, there was a difference between the two theories, the Entwurf and general relativity. The Entwurf theory contained different field equations that represented the gravitational field, and these were not generally covariant.

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Elwin Bruno Christoffel

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Gregorio Curbastro Ricci

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Bernhard Riemann

Indeed at first though – when Einstein first collaborated with Grossmann – he considered (in what scholars call the “Zurich Notebook) field equations that were very close to the ones he would eventually choose in November 1915:

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(See visual explanation of the Zurich Notebook on John Norton’s website).

In 1913, Einstein thought for a while – or persuaded himself – that generally covariant field equations were not permissible; one must restrict the covariance of the equations. He introduced an ingenious argument – the Hole Argument – to demonstrate that generally covariant field equations were not permissible. The Hole Argument seemed to cause Einstein great satisfaction, or else he persuaded himself that he was satisfied. Having found the Hole argument, Einstein spent two years after 1913 looking for a non-generally covariant formulation of gravitational field equations.

Einstein’s collaboration with his close friends included Michele Besso as well. During a visit by Besso to Einstein in Zurich in June 1913 they both tried to solve the Entwurf field equations to find the perihelion advance of Mercury in the field of a static sun in what is known by the name, the Einstein-Besso manuscript. Besso was inducted by Einstein into the necessary calculations. The Entwurf theory predicted a perihelion advance of about 18” per century instead of 43” per century.

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Michele Besso

Towards the end of 1915 Einstein abandoned the Entwurf theory, and with his new theory got the correct precession so quickly because he was able to apply the methods he had already worked out two years earlier with Besso. Einstein though did not acknowledge his earlier work with Besso.

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Tulio Levi-Civita

Tullio Levi-Civita from Padua, one of the founders of tensor calculus, objected to a major problematic element in the Entwurf theory, which reflected its global problem: its field equations were restricted to an adapted coordinate system. Einstein proved that his gravitational tensor was a covariant tensor for adapted coordinate systems. In an exchange of letters and postcards that began in March 1915 and ended in May 1915, Levi-Civita presented his objections to Einstein’s above proof. Einstein tried to find ways to save his proof, and found it hard to give it up. Finally, Levi-Civita convinced Einstein about a fault in his arguments. Einstein realized that his Entwurf field equations of gravitation were entirely untenable. He discovered that Mercury’s perihelion’s motion was too small. In addition, he found that the equations were not covariant for transformations which corresponded to a uniform rotation of the reference system. Thus he came to the conviction that introducing the adapted coordinate system was a wrong path and that a more far-reaching covariance, preferably a general covariance, must be demanded.

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Sometime in October 1915, Einstein dropped the Einstein-Grossman Entwurf theory. He adopted the postulate that his field equations were covariant with respect to arbitrary transformations of a determinant equal to 1 (unimodular transformations), and on November 4, 1915, he presented to the Prussian Academy of Sciences these new field equations. Einstein gradually expanded the range of the covariance of the field equations until November 25, 1915. On that day, Einstein presented to the Prussian Academy his final version to the gravitational field equations.

Einstein’s biographer Albrecht Fölsing explained: Einstein presented his field equations on November 25, 1915, but six days earlier, on November 20, Hilbert had derived the identical field equations for which Einstein had been searching such a long time. On November 18 Hilbert had sent Einstein a letter with a certain draft, and Fölsing asked about this possible draft: “Could Einstein, casting his eye over this paper, have discovered the term which was still lacking in his own equations, and thus ‘nostrified’ Hilbert?” Historical evidence support a scenario according to which Einstein discovered his final field equations by “casting his eye over” his own previous works. In November 4, 1915 Einstein wrote the components of the gravitational field and showed that a material point in a gravitational field moves on a geodesic line in space-time, the equation of which is written in terms of the Christoffel symbols. Einstein found it advantageous to use for the components of the gravitational field the Christoffel symbols. Einstein had already basically possessed the field equations in 1912, but had not recognized the formal importance of the Christoffel symbols as the components of the gravitational field. Einstein probably found the final form of the generally covariant field equations by manipulating his own (November 4, 1915) equations. Other historians’ findings seem to support the scenario according to which Einstein did not “nostrify” Hilbert.

Einstein and Hilbert

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David Hilbert

In March 1916 Einstein submitted to the Annalen der Physik a review article on the general theory of relativity, “The Foundation of the General Theory of Relativity”. The paper was published two months later, in May 1916. In this paper Einstein presented a comprehensive general theory of relativity. In addition, in this paper Einstein presented the disk thought experiment. Einstein’s first mention of the rotating disk in print was in his paper dealing with the static gravitational fields of 1912; and after the 1912 paper, the rotating-disk thought experiment occurred in Einstein’s writings only in a 1916 review article on general relativity: He now understood that in the general theory of relativity the method of laying coordinates in the space-time continuum (in a definite manner) breaks down, and one cannot adapt coordinate systems to the four-dimensional space.

Further, Einstein avoided the Hole Argument quite naturally by the Point Coincidence Argument. The point being made in the 1916 Point-Coincidence Argument is, briefly, that unlike general relativity, in special relativity coordinates of space and time have direct physical meaning. Since all our physical experience can be ultimately reduced to such point coincidences, there is no immediate reason for preferring certain systems of coordinates to others, i.e., we arrive at the requirement of general covariance. In 1918 Einstein saw the need to define the principles on which general relativity was based. In his paper, “Principles of the General Theory of Relativity”, he wrote that his theory rests on three principles, which are not independent of each other. He formulated the principle of relativity in terms of the Point Coincidence Argument and added Mach’s principle.

On November 18, 1915 Einstein reported to the Prussian Academy that the perihelion motion of Mercury is explained by his new General Theory of Relativity: Einstein found approximate solutions to his November 11, 1915 field equations. Einstein’s field equations cannot be solved in the general case, but can be solved in particular situations. The first to offer such an exact solution was Karl Schwarzschild. Schwarzschild found one line element, which satisfied the conditions imposed by Einstein on the gravitational field of the sun, as well as Einstein’s field equations from the November 18, 1915 paper. On December 22, 1915 Schwarzschild told Einstein that he reworked the calculation in his November 18 1915 paper of the Mercury perihelion. Subsequently Schwarzschild sent Einstein a manuscript, in which he derived his exact solution of Einstein’s field equations. On January 13, 1916, Einstein delivered Schwarzschild’s paper before the Prussian Academy, and a month later the paper was published. Einstein though objected to the Schwarzschild singularity in Schwarzschild’s solution.

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Karl Schwarzschild

In 1917 Einstein introduced into his 1915 field equations a cosmological term having the cosmological constant as a coefficient, in order that the theory should yield a static universe. Einstein desired to eliminate absolute space from physics according to “Mach’s ideas”.

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Ernst Mach

Willem De Sitter objected to the “world-matter” in Einstein’s world, and proposed a vacuum solution of Einstein’s field equations with the cosmological constant and with no “world-matter”. In 1920 the world-matter of Einstein’s world was equivalent to “Mach’s Ether”, a carrier of the effects of inertia.

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Einstein, Paul Ehrenfest and De Sitter; Eddington and Hendrik Lorentz. Location: office of W. de Sitter in Leiden (The Netherlands). Date: 26 Sept. 1923

De Sitter’s 1917 solution predicted a spectral shift effect. In 1923 Arthur Stanley Eddington and Hermann Weyl adopted De Sitter’s model and studied this effect. Einstein objected to this “cosmological problem”. In 1922-1927, Alexander Friedmann and Georges Lemaitre published dynamical universe models.

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Friedmann’s model with cosmological constant equal to zero was the simplest general relativity universe. Einstein was willing to accept the mathematics, but not the physics of a dynamical universe.

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In 1929 Edwin Hubble announced the discovery that the actual universe is apparently expanding. In 1931 Einstein accepted Friedmann’s model with a cosmological constant equal to zero, which he previously abhorred; he claimed that one did not need the cosmological term anymore. It was very typical to Einstein that he used to do a theoretical work and he cared about experiments and observations.

 

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Einstein in America.

In Princeton in 1949, Kurt Gödel found an exact solution to Einstein’s field equations. Gödel’s solution was a static and not an expanding universe. Gödel’s universe allows the existence of closed timelike curves (CTCs), paths through spacetime that, if followed, allow a time traveler to interact with his/her former self.

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The book also discusses other topics: for instance,  gravitational lensing, gravitational waves, Einstein-Rosen bridge, unified field theory and so forth.

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My new book on Einstein and the history of the general theory of relativity

Here is the dust jacket of my new scholarly book on the history of general relativity, to be released on… my Birthday:

General Relativity Conflict and Rivalries: Einstein’s polemics with Physicists.

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The book is illustrated by me and discusses the history of general relativity, gravitational waves, relativistic cosmology and unified field theory between 1905 and 1955:

The development of general relativity (1905-1916), “low water mark” period and several results during the “renaissance of general relativity” (1960-1980).

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Conversations I have had more than a decade ago with my PhD supervisor, the late Prof. Mara Beller (from the Hebrew University in Jerusalem), comprise major parts of the preface and the general setting of the book. However, the book presents the current state of research and many new findings in history of general relativity.

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My first book:

Einstein’s Pathway to the Special Theory of Relativity (April, 2015)

includes a wide variety of topics including also the early history of general relativity.

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Review of Arch and Scaffold Physics Today

Arch and scaffold: How Einstein found his field equations” by Michel Janssen and Jürgen Renn. Physics Today 68(11), 30 (2015). The article is published in November 2015, which marks the centenary of the Einstein field equations. (Renn co-authored with Gutfreund The Road to Relativity, Princeton Press)

This is a very good article. However, I would like to comment on several historical interpretations. . Michel Janssen and Jürgen Renn ask: Why did Einstein reject the field equations of the first November paper (scholars call them the “November tensor”) when he and Marcel Grossmann first considered them in 1912–13 in the Zurich notebook?

They offer the following explanation: In 1912 Albert Einstein gave up the November tensor (derived from the Ricci tensor) because the rotation metric (metric of Minkowski spacetime in rotating coordinates) did not satisfy the Hertz restriction (the vanishing of the four-divergence of the metric). Einstein wanted the rotation metric to be a solution of the field equations in the absence of matter (vacuum field equations) so that he could interpret the inertial forces in a rotating frame of reference as gravitational forces (i.e. so that the equivalence principle would be fulfilled in his theory).

However, the above question – why did Einstein reject the November tensor in 1912-1913, only to come back to it in November 1915 – apparently has several answers. It also seems that the answer is Einstein’s inability to properly take the Newtonian limit.

Einstein’s 1912 earlier work on static gravitational fields (in Prague) led him to conclude that in the weak-field approximation, the spatial metric of a static gravitational field must be flat. This statement appears to have led him to reject the Ricci tensor, and fall into the trap of Entwurf limited generally covariant field equations. Or as Einstein later put it, he abandoned the generally covariant field equations with heavy heart and began to search for non-generally covariant field equations. Einstein thought that the Ricci tensor should reduce in the limit to his static gravitational field theory from 1912 and then to the Newtonian limit, if the static spatial metric is flat. This prevented the Ricci tensor from representing the gravitational potential of any distribution of matter, static or otherwise. Later in the 1920s, it was demonstrated that the spatial metric can go to a flat Newtonian limit, while the Newtonian connection remains non-flat without violating the compatibility conditions between metric and (affine) connection (See John Stachel).

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Phys. Today 68, 11, 30 (2015).

As to the “archs and scaffolds” metaphor. Michel Janssen and Jürgen Renn demonstrate that the Lagrangian for the Entwurf field equations has the same structure as the Lagrangian for the source-free Maxwell equations: It is essentially the square of the gravitational field, defined as minus the gradient of the metric. Since the metric plays the role of the gravitational potential in the theory, it was only natural to define the gravitational field as minus its gradient. This is part of the Entwurf scaffold. The authors emphasize the analogy between gravity and electromagnetism, on which Einstein relied so heavily in his work on the Entwurf theory.

However, I am not sure whether in 1912-1913 Einstein was absolutely aware of this formal analogy when developing the Entwurf field equations. He first found the Entwurf equations, starting from energy-momentum considerations, and then this analogy (regarding the Lagrangian) lent support to his Entwurf field equations. Anyway, I don’t think that this metaphor (analogy between gravity and electromagnetism) persisted beyond 1914. Of course Einstein came back to electrodynamics-gravity, but I think that he discovered his 1915 field equations in a way which is unrelated to Maxwell’s equations (apart from the 1911 generally covariant field equations, influenced by Hilbert’s electromagnetic-gravitational unified theory, but this is out of the scope of this post and of course unrelated to the above metaphor).

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As to the November 4, 1915 field equations of Einstein’s general theory of relativity: When all was done after November 25, 1915, Albert Einstein said that the redefinition of the components of the gravitational field in terms of Christoffel symbols had been the “key to the solution”. Michel Janssen and Jürgen Renn demonstrate that if the components of the gravitational field – the Christoffel symbols – are inserted into the 1914 Entwurf Lagrangian, then the resulting field equations (using variational principle) are the November tensor. In their account, then, Einstein found his way back to the equations of the first November paper (November 4, 1915) through considerations of physics. Hence this is the interpretation to Einstein’s above “key to the solution”.

I agree that Einstein found his way back to the equations of the first November paper through considerations of physics and not through considerations of mathematics. Mathematics would later serve as heuristic guide in searching for the equations of his unified field theory. However, it seems to me that Michel Janssen and Jürgen Renn actually iterate Einstein’s November 4, 1915 variational method. In November 4, 1915, Einstein inserted the Christoffel symbols into his 1914 Entwurf Lagrangian and obtained the November 4, 1915 field equations (the November tensor). See explanation in my book, General Relativity Conflict and Rivalries, pp. 139-140.

Indeed Janssen and Renn write: There is no conclusive evidence to determine which came first, the redefinition of the gravitational field (in terms of the Christoffel symbols) or the return to the Riemann tensor.

Hence, in October 1915 Einstein could have first returned to the November tensor in his Zurich Notebook (restricted to unimodular transformations) and only afterwards in November 1915, could he redefine the gravitational field components in terms of the Christoffel symbols. Subsequently, this led him to a redefinition of the Entwurf Lagrangian and, by variational method, to a re-derivation of the 1912 November tensor.

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Van Gogh had nostrified Hilbert (Hilbert visited Van Gogh, closed time-like loops…. ….)

Finally, Michel Janssen and Jürgen Renn write: Despite Einstein’s efforts to hide the Entwurf scaffold, the arch unveiled in the first November paper (November 4, 1915) still shows clear traces of it.

I don’t think that Einstein tried to hide the Entwurf scaffold. Although later he wrote Arnold Sommerfeld: “Unfortunately, I have immortalized the last error in this struggle in the Academy-papers, which I can send to you soon”, in his first November paper Einstein had explicitly demonstrated equations exchange between 1914 Entwurf and new covariant November ones, restricted to unimodular transformations.

Stay tuned for my book release, forthcoming soon (out by the end of 2015) on the history of general relativity, relativistic cosmology and unified field theory between 1907 and 1955.

My book: Einstein’s Pathway to the Special Theory of Relativity

2015 marks several Albert Einstein anniversaries: 100 years since the publication of Einstein’s General Theory of Relativity, 110 years since the publication of the Special Theory of Relativity and 60 years since his passing.

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What is so special about this year that deserves celebrations? My new book on Einstein: Einstein’s Pathway to the Special Theory of Relativity has just been returned from the printers and I expect Amazon to have copies very shortly.

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The Publisher uploaded the contents and intro.

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I hope you like my drawing on the cover:

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Einstein, 1923: “Ohmmm, well… yes, I guess!”

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The book is dedicated to the late Prof. Mara Beller, my PhD supervisor from the Hebrew University of Jerusalem who passed away ten years ago and wrote the book: Quantum Dialogue (Chicago University Press, 1999):

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Have a very happy Einstein year!

Celebrating the centennial of Einstein’s general relativity. (next year)…

“Shaken to its depths by the tragic catastrophe in Palestine, Jewry must now show that it is truly equal to the great task it has undertaken. It goes without saying that our devotion to the cause and our determination to continue the work of peaceful construction will not be weakened in the slightest by any such set-back. But what has to be done to obviate any possibility of a recurrence of such horrors?

The first and most important necessity is the creation of a modus vivendi with the Arab people”.

Albert Einstein, August 1929. (here)

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Einstein attends a concert with Helen Dukas at the Great Synagogue in Berlin, 1930.

On December 10, 1915 Einstein told his best friend Michele Besso that his wildest dreams have now come true: general covariance and the perihelion of Mercury. Einstein wished Besso best regards and signed “your satisfied kaput Albert”.

Sometime in October 1915 Einstein dropped his old Einstein-Grossman theory, but he realized that the key to the solution lies in his 1914 review article “The Formal Foundation of the General Theory of Relativity”. He was finally led to general covariance. Starting on November 4 1915, Einstein gradually expanded the range of the covariance of his field equations.

Between November 4 and November 11, 1915, Einstein simplified the field equations, and was able to write them in general covariant form in an addendum to the November 4 paper, published on November 11. But there still remained difficulties.

On Thursday, November 18, Einstein presented to the Prussian Academy his solution to the longstanding problem of the precession of the perihelion of Mercury, on the basis of his November 11 general theory of relativity. Today, exactly one year from now the world will celebrate one hundred years to this achievement. Mazal Tov.

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Between November 18 and November 25 Einstein found that he could write the field equations with an additional term on the right hand side of the field equations involving the trace of the energy-momentum tensor, which now need not vanish. Hence, Einstein resolved the final difficulties of his November 11 1915 theory of gravitation in his final November 25 1915 paper. These were the November 25 1915 field equations.

How did Einstein do this? Read my two papers (one and two) and see how Einstein solved the problem.

 

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In winter 1916 Einstein exchanged letters with his friend from Leiden Paul Ehrenfest and rederived the November 25, 1915 field equations. How did Einstein do this? Read my two papers (one and two) and find out.

Einstein elaborated his 1912 Disk thought experiment, and his 1914 thought experiment, originally suggested by Newton in the Principia, the Two Globes thought experiment. After presenting the 1905 magnet and conductor thought experiment, Einstein wrote, “Examples of this sort … lead to the conjecture that the phenomena of electrodynamics as well as those of mechanics possess no properties corresponding to the idea of absolute rest”. The globes thought experiment was intended to demonstrate that this could be extended to accelerated motions and to the theory of gravitation using Mach’s principle (still not defined as a principle).

 

Einstein and 1915 General Relativity

My new paper shows that a correction of one mistake was crucial for Einstein’s pathway to the first version of the 1915 general theory of relativity, but also might have played a role in obtaining the final version of Einstein’s 1915 field equations. In 1914 Einstein wrote the equations for conservation of energy-momentum for matter, and established a connection between these equations and the components of the gravitational field. He showed that a material point in gravitational fields moves on a geodesic line in space-time, the equation of which is written in terms of the Christoffel symbols. By November 4, 1915, Einstein found it advantageous to use for the components of the gravitational field, not the previous equation, but the Christoffel symbols. He corrected the 1914 equations of conservation of energy-momentum for matter. Einstein had already basically possessed the field equations in 1912 together with his mathematician friend Marcel Grossman, but because he had not recognized the formal importance of the Christoffel symbols as the components of the gravitational field, he could “not obtain a clear overview”. Finally, considering the energy-momentum conservation equations for matter, an important similarity between equations suggests that, this equation could have assisted Einstein in obtaining the final form of the field equations (the November 25, 1915 ones) that were generally covariant.

My new paper on general relativity

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שנים לטנסור המטרי 100 Years of Metric Tensor

 לפני מאה שנים ב-2012 איינשטיין לראשונה אימץ את הטנסור המטרי. באחד ממאמריו איינשטיין סיפר לקורא שלו:”הדרך שבה אני עצמי עברתי, הייתה עקיפה ופתלתלה למדי, כי אחרת אינני יכול לקוות שהוא יתעניין יותר מידי בתוצאה של סוף המסע”, תורת היחסות הכללית. למטה מובאת רשימה של ספרים ומאמרים שנכתבו על ידי חוקרים מהעולם על דרכו של איינשטיין לתורת היחסות הכללית והפילוסופיה של היחסות הכללית.

A hundred years ago, in 1912, Einstein adopted the metric tensor. In one of his later papers Einstein told his reader about “the road that I have myself travelled, rather an indirect and bumpy road, because otherwise I cannot hope that he will take much interest in the result at the end of the journey”: the General theory of Relativity

Relatively speaking

The following  list of books and papers discussing Einstein’s Pathway to General Relativity and Philosophy of General Relativity covers the period 1912-1916, and beyond

Corry, Leo, Renn, Jürgen and John Stachel, “Belated Decision in the Hilbert-Einstein Priority Dispute”, 1997, in Stachel 2002, pp. 339-346

Corry, Leo, Renn, Jürgen and John Stachel, “Response to F. Winterberg ‘On Belated Decision in the Hilbert-Einstein Priority Dispute'”, 2004, Z. Naturforsen 59a, pp. 715-719

Earman, John, Janis, Allen, I., Massey, Gerald. I., and Rescher, Nicholas, Philosophical Problems of the Inertial and External Worlds, Essays of the philosophy of Adolf Grünbaum, 1993, University of Pittbsbutgh/ Universitätswerlag Konstanz

Earman, John, Janssen, Michel, Norton, John (ed), The Attraction of Gravitation, New Studies in the History of General Relativity, Einstein Studies Vol 5, 1993, Boston: Birkhäuser

Earman, John and Janssen, Michel, “Einstein’s Explanation of the Motion of Mercury’s Perihelion”, in Earman, Janssen, and Norton, John, 1993, pp. 129-172

Goener, Hubert, Renn Jürgen, Ritter, Jim, Sauer, Tilman (ed), The Expanding Worlds of General Relativity, 1999, Boston: Brikhäser

Howard, Don, “Point Coincidences and Pointer Coincidences: Einstein on Invariant Structure in Spacetime Theories”, in Goener et al, 1999, pp. 463-500

Howard, Don and Norton, John, “Out of the Labyrinth? Einstein, Hertz, and the Göttingen Answer to the Hole Argument”, in Earman, Janssen, Norton (ed), 1993, pp. 30-61

Howard, Don and Stachel, John (eds.), Einstein and the History of General Relativity: Einstein Studies, Volume 1, 1989, New York: Birkhauser

Janssen, Michel, “The Einstein-De Sitter Debate and its Aftermath”, lecture, pp. 1-8, based on “The Einstein-De Sitter-Weyl-Klein Debate” in CPAE, Vol. 8, 1998, pp. 351-357

Janssen, Michel, “Rotation as the Nemesis of Einstein’s Entwurf Theory”, in Goener, Renn, Ritter and Sauer (ed), 1999, pp. 127-157

Janssen, Michel, “The Einstein-Besso Manuscript: A Glimpse Behind the Certain of a Wizard”, Freshman Colloquium: “Introduction to the Arts and Sciences”, Fall 2002

Janssen, Michel, “Of Pots and Holes: Einstein’s Bumpy Road to General Relativity”, in Renn, 2005, pp-58-85; reprinted as “Einstein’s First Systematic Exposition of General Relativity”, pp, 1-39

Janssen Michel and Renn, Jürgen, “Untying the Knot: How Einstein Found His Way Back to Field Equations Discarded in the Zurich Notebook”, in Renn et all, Vol. 1, 2007, pp. 839-925

Janssen, Michel, “What did Einstein know and When did he Know It?” in Renn et all, Vol. 2, 2007, pp. 786-837

Janssen, Michel, “‘No Success Like Failure’: Einstein’s Quest for General Relativity”, The Cambridge Companion to Einstein, 2009

Alfred Eisenstaedt, Einstein Life Magazine

Norton, John, “How Einstein Found His Field Equations: 1912-1915”, Historical Studies in the Physical Sciences 14, 1984, pp. 253-315. Reprinted in Howard, Don and Stachel, John (eds.), 1989, pp 101-159

Norton, John, “General Covariance and the Foundations of General Relativity: Eight Decades of Dispute,” Reports on Progress in Physics 56, 1993, pp.791-858

Norton, John, “Einstein and Nordström: Some Lesser-Known Thought Experiments in Gravitation”, Archive for History of Exact Sciences 45, 1993, pp.17-94

Norton, John, “Nature in the Realization of the Simplest Conceivable Mathematical Ideas: Einstein and the Canon of Mathematical Simplicity”, Studies in the History and Philosophy of Modern Physics 31, 2000, pp.135-170

Norton, John, “Einstein, Nordström and the early Demise of Lorentz-covariant, Scalar Theories of Gravitation,” in Renn et all, Vol. 3, 2007, pp. 413-487

Renn, Jürgen and Tilman Sauer, “Heuristics and mathematical Representation in Einstein Search for a Gravitational Field Equation”, Preprint 62, Max Planck Institute for the History of Science, 1997

Renn, Jürgen, (ed.) Einstein’s Annalen Papers. The Complete Collection 1901-1922, 2005, Germany: Wiley-VCH Verlag GmbH & Co

Renn, Jürgen, “The Summit Almost Scaled: Max Abraham as a Pioneer of a Relativistic Theory of Gravitation”, in Renn et all, Vol.3, 2007, pp. 305-330

Renn, Jürgen, Norton, John, Janssen, Michel and Stachel John, ed., The Genesis of General Relativity. 4 Vols., 2007, New York, Berlin: Springer

Renn, Jürgen and Stachel, John, “Hilbert’s Foundation of Physics: From a Theory of Everything to a Constituent of General Relativity”, in Renn et all, Vol. 4, 2007, pp. 857-974

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Stachel, John, “The Genesis of General Relativity”, Physics 100, 1979, pp. 428-442; reprinted in Stachel, 2002, pp. 233-244

Stachel, John, “The Rigidity Rotating Disk as the ‘Missing Link’ in the History of General Relativity”, General Relativity and Gravitation one Hundred Years After the Birth of Albert Einstein, Vol. 1, 1980, pp. 1-15; reprinted in Stachel, 2002, pp. 245-260

Stachel, John, “‘Subtle is the Lord'”… The Science and Life of Albert Einstein” by Abraham Pais”, Science 218, 1982, pp. 989-990; reprinted in Stachel, 2002, pp. 551-554

Stachel, John, “Albert Einstein: The Man beyond the Myth”, Bostonia Magazine 56, 1982, pp. 8–17; reprinted in Stachel, 2002, pp. 3-12

Stachel, John, “Einstein and the ‘Research Passion'”, Talk given at the Annual Meeting of the American Associates for the Advancement of Science in Detroit, May 1983; reprinted in Stachel, 2002, pp. 87-94

Stachel, John, “The Generally Covariant Form of Maxwell’s Equations”, in J.C. Maxwell, the Sesquicentennial Symposium, M.S. Berger (ed), 1984, Elsevier: Amsterdam, pp. 23-37.

Stachel, John, “What a Physicist Can Learn From the Discovery of General Relativity”, Proceedings of the Fourth Marcel Grossmann Meeting on General relativity, ed. R. Ruffini, Elsevier: Amsterdam, 1986, pp.1857-1862

Stachel, John, “How Einstein Discovered General Relativity: A Historical Tale With Some Contemporary Morals”, in MacCallum, M.A.H., General Relativity and Gravitation Proceedings of the 11th International Conference on General Relativity and Gravitation, 1987, pp. 200-209, reprinted in Satchel, 2002, pp. 293-300

Stachel, John, “Einstein’s Search for General Covariance 1912-1915”, in Howard, Don and Stachel John (eds), 1989, pp. 63-100; reprinted in Stachel, 2002, pp. 301-338

Stachel, John, “Albert Einstein (1897-1955), The Blackwell Companion to Jewish Culture, ed Glenda Abramson, Oxford: Blackwell, pp. 198-199; reprinted in Stachel, 2002, pp. 19-20

Stachel, John, “the Meaning of General Covariance. The Hole Story”, in Earman, John, Janis, Allen, et all, 1993, pp. 129-160.

Stachel, John, “The Other Einstein: Einstein Contra Field Theory”, Science in Context 6, 1993, pp. 275-290; reprinted in Stachel, 2002, pp. 141-154

Stachel, John, “Changes in the Concept of Space and Time Brought About by Relativity”, Artifacts, Representations and Social Practice: Essays for Marx Wartofsky, eds Carol Gould and Robert S. Cohen., Dordrecht/Boston/London: Kluwer Academic, pp. 141-162

Stachel, John, “History of relativity,” in Brown, Laurie M., Pais, Abraham, and Sir Pippard, Brian (eds.), Twentieth century physics, 1995, New York: American Institute of Physics Press, pp. 249-356

Stachel, John, “Albert Einstein: A Biography by Albert Fölsing”, Review of Albrecht Fölsing, Albert Einstein: A Biography, in Physics Today, January, 1998; reprinted in Stachel, 2002, pp. 555-556

Stachel, John, “New Light on the Einstein-Hilbert Priority Question”, Journal of Astrophysics 20, 1999, pp. 90-91; reprinted in Stachel, 2002, pp. 353-364

Stachel, John, “Einstein and Infeld: Seen through Their Correspondence”, Acta Physica Polonica B 30, 1999, pp. 2879–2904; reprinted in Stachel, 2002, pp. 477–497

Stachel, John, “The First-two Acts”, in Renn et all, 2007, Vol. 1, pp. 81-112; appeared first in Stachel, 2002, pp. 261-292

Stachel, John, Einstein from ‘B’ to ‘Z’, 2002, Washington D.C.: Birkhauser

Stachel, John, “Albert Einstein”, The 2005 Mastermind Lecture, Proceedings of the British Academy 151, 2007, pp.423-458

Stachel, John, “Where is Creativity? The example of Albert Einstein”, Invited Lecture at the Congresso International de Filosophia, Pessoa & Sociadade (Person and Society), Braga, 17-19 November 2005, to appear in 2012

Stachel, John, “Einstein and Hilbert”, invited lecture in March 21, 2005 Session: Einstein and Friends, American Physical Society, Los Angeles; and response to Questions from FAZ on Hilbert and Einstein

Stachel, John, “Einstein’s Intuition and the Post-Newtonian Approximation”, World Scientific, 2006, pp. 1-15

Stachel, John, “The Story of Newstein: Or is Gravity Just Another Pretty Force?”, in Renn, et all, Vol. 4, 2007, pp. 1041-1078

Stachel, John, “A world Without Time: the Forgotten Legacy of Gödel and Einstein”, Notices of the American Mathematical Society 54, 2007, pp. 861-868/1-8

Stachel, John, “Albert Einstein”, The New Dictionary of Scientific Biography, Vol. 2, Gale 2008, pp. 363-373

Stachel, John, “The Hole Argument”, Living Reviews in Relativity, June 25, 2010, to appear in 2012

Stachel, John, “The Rise and Fall of Einstein’s Hole Argument”, pp. 1-15 to appear in 2012

Stachel, John, “The Scientific Side of the Einstein-Besso Relationship”, to appear in 2012

Torretti, Roberto, Relativity and Geometry, 1983/1996, Ney-York: Dover

Prime Minister of Israel Ben Gurion visits Albert Einstein in Princeton. Here