The Einstein Legacy Project

Happy Birthday Albert Einstein!

Einstein once wrote to his close friend: “With fame I became more and more stupid, which of course, is a very common phenomenon”.

Bingo. This exactly describes the spirit of a new project called, “The Einstein Legacy Project”.

Here is “the official Einstein Legacy Project video. It tells the story of how and WHY this project was born”.

However, the people in the official Einstein Legacy Project video use Einstein’s name in order to throw lavish parties. Entire fortunes are spent for celebrations and demonstrations of pomp and power. Einstein was not a Sun king, Louis le Grand.

The Einstein Legacy Project consists of two lavish projects and two (I hope so) less lavish projects (I will present 3 of them):

1) Dinner of the Century: (here)

“To celebrate the centennial of Einstein’s Relativity theory and to launch the publication of Genius: 100 Visions of the Future, the Einstein Legacy Project will be holding the ‘Dinner of the Century’; a star studded event that will bring together our Genius contributors, along with young Einsteins and dignitaries from around the world”.

While we celebrate and launch the grandiose 3D book, in the presence of Hollywood actors and other dignitaries from around the world, and mid all the pomp and ceremony, we receive Einstein’s response to the “Dinner of the Century” as told to his biographer Carl Seelig (see full story in my book Einstein’s Pathway to the Special theory of Relativity, 2015):

“The celebration ended with the most opulent banquet that I have ever attended in my life. So I said to a Genevan patrician who sat next to me, ‘Do you know what Calvin would have done if he were still here?’ When he said no and asked what I thought, I said: ‘He would have erected a large pyre and had us all burned because of sinful gluttony’. The man uttered not another word, and with this ends my recollection of that memorable celebration”.

In September 2017 the Einstein Legacy Project will throw an opulent banquet, a parodic dinner, a celebration of sinful gluttony.

2) 3D printed book: Genius: 100 Visions of the Future: (here)

“To celebrate the 100th anniversary of the publication of Einstein’s General Theory of Relativity, the Einstein Legacy Project is embarking on a publishing milestone: collecting the visions of the 100 greatest innovators, artists, scientists and visionaries of our time in the world’s first 3D-printed book – Genius: 100 Visions of the Future. It’s the creation of world renowned designer Ron Arad, formed in the likeness of Einstein himself in a 3D limited edition book for the ages”.

Here is Einstein’s response to the 3D book formed in the likeness of his head:

“Generally I find it tasteless… I have also prohibited …[this] book from appearing in the German language, but allowed the book to appear in foreign languages, I also hold the latter [author] to be quite tasteless. … [He] need[s] to earn money, which serves as an excuse for and for that […he] cannot wait until I’m dead. Is the mention of such a basic fact an accusation?”

I agree with you Einstein, I also find it tasteless.

Who are contributing to this book? For instance, Barbra Streisand, Deepak Chopra and others.

I would like to ask the contributors a question: A uniformly moving train could as well be seen at rest and the tracks, including the landscape, as uniformly moving. Will the common sense of the locomotive engineer allow this? He will object that he does not go on to heat and grease the landscape but rather the locomotive, and that consequently it must be the latter whose motion shows the effect of his labor. Why? Can you explain why? After all you are “genius contributors”…. If you can explain this, then I can pose questions about general relativity.

3) Einstein’s Archives and Visitor Center: (here)

“The first and only institution to celebrate the life, history and vision of Einstein. Built around the unique collection of The Hebrew University of Jerusalem, where Einstein bequeathed his entire personal archive, the Einstein Archive and Visitor Center will be a global attraction dedicated to science and humanitarian ideals”.

This is the only project that Einstein probably would have approved. However, in light of the above two projects (pomp “Dinner of the Century” and 3D book), I am very doubtful that the people who are organizing the Einstein’s Legacy Project really care about Einstein, his legacy and his writings.

Stay tuned. More to come…. … ….

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.


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.


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”.


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):


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?


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.


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:


[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]:


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.


[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.


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:


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.


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.


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:


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.


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:


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:


*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.


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.


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.


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].


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:


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:


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:


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


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:


to a machine that represented the key to the solution:


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.



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).






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.


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.


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.


Albert Einstein at the Patent office

Mileva Marić and Einstein




Eduard Tete, Mileva Marić and Hans Albert


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”.


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


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.


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.


My books


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


The back cover of my book:

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


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.


Grossmann and Einstein


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



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.


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


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.


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.


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.


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.


Elwin Bruno Christoffel


Gregorio Curbastro Ricci


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:



(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.


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.

Levi-Civita (2)

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.


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


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.


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”.


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.


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.


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.


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.




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.



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.


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).


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.


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.


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).


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).


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.


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.


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.


The Publisher uploaded the contents and intro.


I hope you like my drawing on the cover:


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



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):


Have a very happy Einstein year!

100 GTR: Uniformly Rotating Disk and the Hole Argument

The “Ehrenfest paradox“: Ehrenfest imagined a rigid cylinder set in motion from rest and rotating around its axis of symmetry. Consider an observer at rest measuring the circumference and radius of the rotating cylinder. The observer arrives at two contradictory requirements relating to the cylinder’s radius:

  1. Every point in the circumference of the cylinder moves with radial velocity ωR, and thus, the circumference of the cylinder  should appear Lorentz contracted to a smaller value than at rest, by the usual “relativistic” factor γ: 2πR‘ < 2πR.
  2. The radius R’ is always perpendicular to its motion and suffers no contraction at all; it should therefore be equal to its value R: R’ = R.

Einstein wrote to Vladimir Varićak either in 1909 or in 1910 (Febuary 28): “The rotation of the rigid body is the most interesting problem currently provided by the theory of relativity, because the only thing that causes the contradiction is the Lorentz contraction”.  CPAE 5, Doc. 197b.

Ehrenfest imagined a rigid cylinder gradually set into rotation (from rest) around its axis until it reaches a state of constant rotation.

In 1919 Einstein explained why this was impossible: (CPAE 9, Doc. 93)

“One must take into account that a rigid circular disk at rest would have to snap when set into rotation, because of the Lorentz shortening of the tangential fibers and the non-shortening of the radial ones. Similarly, a rigid disk in rotation (made by casting) would have to shatter as a result of the inverse changes in length if one attempts to bring it to the state of rest. If you take these facts fully into consideration, your paradox disappears”.

Assuming that the cylinder does not expand or contract, its radius stays the same. But measuring rods laid out along the circumference 2πR should be Lorentz-contracted to a smaller value than at rest, by the usual factor γ. This leads to the paradox that the rigid measuring rods would have to separate from one another due to Lorentz contraction; the discrepancy noted by Ehrenfest seems to suggest that a rotated Born rigid disk should shatter. According to special relativity an object cannot be spun up from a non-rotating state while maintaining Born rigidity, but once it has achieved a constant nonzero angular velocity it does maintain Born rigidity without violating special relativity, and then (as Einstein showed in 1912) a disk riding observer will measure a circumference.

Hence, in 1912, Einstein discussed what came to be known as the uniformly rotating disk thought experiment in general relativity. Thinking about Ehrenfest’s paradox and taking into consideration the principle of equivalence, Einstein considered a disk (already) in a state of uniform rotation observed from an inertial system.

We take a great number of small measuring rods (all equal to each other) and place them end-to-end across the diameter 2R and circumference 2πR of the uniformly rotating disk. From the point of view of a system at rest all the measuring rods on the circumference are subject to the Lorentz contraction. Since measuring rods aligned along the periphery and moving with it should appear contracted, more would fit around the circumference, which would thus measure greater than 2πR. An observer in the system at rest concludes that in the uniformly rotating disk the ratio of the circumference to the diameter is different from π:

circumference/diameter = 2π(Lorentz contracted by a factor…)/2R = π (Lorentz contracted by a factor….).

According to the equivalence principle the disk system is equivalent to a system at rest in which there exists a certain kind of static gravitational field. Einstein thus arrived at the conclusion that a system in a static gravitational field has non-Euclidean geometry.

Soon afterwards, from 1912 onwards, Einstein adopted the metric tensor as the mathematical respresentation of gravitation.

Indeed 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: “The Foundation of the General Theory of 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.


My new paper deals with Einstein’s 1912 and 1916 rotating disk problem, Einstein’s hole argument, the 1916 point coincidence argument and Mach’s principle; a combined-into-one deal (academic paper) for the readers of this blog.


Sitting: Sir Arthur Stanley Eddington and Hendrik Antoon Lorentz. Standing: Albert Einstein, Paul Ehrenfest and Willem de Sitter. September 26, 1923.

Further reading: Ehrenfest paradox

My new paper on Einstein and Schwarzschild

My new paper on General Relativity: Einstein and Schwarzschild.

Sometime in October 1915 Einstein dropped the Einstein-Grossman theory. Starting on November 4, 1915, Einstein gradually expanded the range of the covariance of his field equations. On November 11, 1915 Einstein was able to write the field equations of gravitation in a general covariant form, but there was a coordinate condition (there are no equations here so I cannot write it down here).

On November 18, 1915, Einstein presented to the Prussian Academy his paper, “Explanation of the Perihelion Motion of Mercury from the General Theory of Relativity”. Einstein reported in this talk that the perihelion motion of Mercury is explained by his theory. In this paper, Einstein tried to find approximate solutions to his November 11, 1915 field equations. He intended to obtain a solution, without considering the question whether or not the solution was the only possible unique solution.

Einstein’s field equations are non-linear partial differential equations of the second rank. This complicated system of equations cannot be solved in the general case, but can be solved in particular simple situations. The first to offer an exact solution to Einstein’s November 18, 1915 field equations was Karl Schwarzschild, the director of the Astrophysical Observatory in Potsdam. On December 22, 1915 Schwarzschild wrote Einstein from the Russian front. Schwarzschild set out to rework Einstein’s calculation in his November 18 1915 paper of the Mercury perihelion problem. He first responded to Einstein’s solution for the first order approximation from his November 18, 1915 paper, and found another first-order approximate solution. Schwarzschild told Einstein that the problem would be then physically undetermined if there were a few approximate solutions. Subsequently, Schwarzschild presented a complete solution. He said he realized that there was only 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.

“Raffiniert ist der Herrgott, aber boshaft ist er nicht” (Einstein might have already said….), because the problem with Schwarzschild’s line element was that a mathematical singularity was seen to occur at the origin! Oh my, Einstein abhorred singularities.

Actually, Schwarzschild “committed another crime”: he did not satisfy the coordinate condition from Einstein’s November 11 or November 18, 1915 paper. Schwarzschild admitted that his coordinates were not “allowed” coordinates, with which the field equations could be formed, because these spherical coordinates did not have determinant 1. Schwarzschild chose then the non-“allowed” coordinates, and in addition, a mathematical singularity was seen to occur in his solution. But Schwarzschild told Einstein: Don’t worry, “The equation of [Mercury’s] orbit remains exactly as you obtained in the first approximation”! See my paper from 2012.

Einstein replied to Schwarzschild on December 29, 1915 and told him that his calculation proving uniqueness proof for the problem is very interesting. “I hope you publish the idea soon! I would not have thought that the strict treatment of the point- problem was so simple”. Subsequently Schwarzschild sent Einstein a manuscript, in which he derived his solution of Einstein’s November 18, 1915 field equations for the field of a single mass. Einstein received the manuscript by the beginning of January 1916, and he examined it “with great interest”. He told Schwarzschild that he “did not expect that one could formulate so easily the rigorous solution to the problem”. On January 13, 1916, Einstein delivered Schwarzschild’s paper before the Prussian Academy with a few words of explanation. Schwarzschild’s paper, “On the Gravitational Field of a Point-Mass according to Einstein’s Theory” was published a month later.


Karl Schwarzschild

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 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 from his November 18, 1915 paper.

A comment regarding Einstein’s calculations in his November 18, 1915 paper of the Mercury perihelion problem and Einstein’s 1916 paper. In his early works on GTR, in order to obtain the Newtonian results, Einstein used the special relativistic limit and the weak field approximation, and assumed that space was flat (see my paper). Already in 1914 Einstein had reasoned that in the general case, the gravitational field was characterized by ten space-time functions of the metric tensor. g were functions of the coordinates. In the case of special relativity this reduces to g44 = c2, where c denotes a constant. Einstein took for granted that the same degeneration occurs in the static gravitational field, except that in the latter case, this reduces to a single potential, where g44 = c2 is a function of spatial coordinates, x1, x2, x3. 

Later that year David Hilbert (with a vengeance from 1915?…) arrived at a line-element similar to Schwarzschild’s one, and he concluded that the singularity disappears only if we accept a world without electricity. Such an empty space was inacceptable by Einstein who was apparently much attracted by Mach’s ideas! (later termed by Einstein “Mach’s Principle”). Okay, Einstein, said Hilbert: If there is matter then another singularity exists, or as Hilbert puts it: “there are places where the metric proves to be irregular”…. (See my paper from 2012).








Strange Days at Blake Holsey High: a student is sucked into the black hole…


A Century of General Relativity מאה שנה ליחסות הכללית

Hebrew University of Jerusalem celebrates the anniversary of Einstein’s General Theory of Relativity (GTR) in a four-day conference:

Space-Time Theories: Historical and Philosophical Contexts

Monday-Thursday, January 5-8, 2015, in Jerusalem, the van Leer Jerusalem Institute. The conference brings together physicists, historians and philosophers of science from Israel and the world, all working from different perspectives on problems inspired by GTR. It is the first among three conferences planned to celebrate the centenary of Einstein’s General Theory of Relativity, the last of which will take place in the Max Planck Institute in Berlin on December 5, 2015, my next birthday. I am not on the list of speakers of the conference, but it says that admission is free.

בין ה-5-8 לינואר 2015 יתקיים כנס לציון 100 שנה להולדת תורת היחסות הכללית של איינשטיין. הכנס יתקיים במכון ואן ליר בירושלים ליד בית הנשיא. בכנס יישאו דברים היסטוריונים ופילוסופים של המדע שעוסקים בתחום וכן פיסיקאים. הוא הכנס הראשון מבין שלושה שמאורגנים בתחום. הראשון מאורגן באוניברסיטה העברית והאחרון במכון מקס פלאנק: יתקיים בדיוק בעוד שנה ביום ההולדת הבא שלי ב-5 לדצמבר, 2015. אני אמנם לא ברשימת הדוברים של הכנס בירושלים, אבל המודעה מציינת שהכניסה חופשית. בכנס הקודם מ-2005, שציין מאה שנים להולדת תורת היחסות הפרטית של איינשטיין במכון ואן ליר, זכורים היטב דברי הפתיחה של הנשיא ד’אז משה קצב


Einstein wrote Max Born on May 12, 1952:

“The generalization of gravitation is now, at last, completely convincing and unequivocal formally unless the good Lord has chosen a totally different way of which one can have no conception. The proof of the theory is unfortunately far too difficult for me. Man is, after all, only a poor wretch… Even if the deflection of light, the perihelial movement or line shift were unknown, the gravitation equations would still be convincing because they avoid the inertial system (the phantom which affects everything but is not itself affected). It is really rather strange that human beings are normally deaf to the strongest arguments while they are always inclined to overestimate measuring accuracies”.

What did Einstein mean by saying “the gravitation equations would still be convincing…”? “In June 9, 1952 Einstein wrote an appendix to the fifteenth edition of his popular 1917 book Über die spezielle und die allgemeine Relativitätstheorie Gemeinverständlich (On the Special and the General Theory of Relativity). In this appendix he explained:

“I wished to show that space-time is not necessarily something to which one can ascribe a separate existence, independently of the actual objects of physical reality. Physical objects are not in space, but these objects are spatially extended. In this way the concept “empty space” loses its meaning”.