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.


קוראים 10000

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


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”.



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:


Einstein’s 1916 Equations:




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:



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”.


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”.


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:



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):


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”.


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:



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

Endnote 126 sends the reader to Einstein’s original paper in German and to the following reference: Tropp, Eduard A., Frenkel, Viktor Ya. and Chernin, Artur D., Alexander A Friedmann: The Man who Made the Universe Expand, Cambridge: Cambridge University Press, 1993. In this book one finds a translation of the relevant paragraph of Einstein’s paper into English:


However, in my paper, “The Mythical Snake which Swallows its Tail: Einstein’s matter world”, I have changed this translation. For instance I make a mistake and write: “In my previous note I have criticized”… Prof. Gutfreund reproduces my awkward translation and not the above translation.

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 to the above said translation 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:


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:


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:



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”:


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:


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”.


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




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:


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:



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:



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?”:



In 2016 I received this message from ResearchGate:


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”.




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”.


“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):


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):


“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.


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:






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.









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.


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”.

George Gamow and Albert Einstein

Here is my new paper about George Gamow and Albert Einstein (here) x

Mr. Newton once said, momentum conservation
Teach einStein acceleration
If it is in empty space,
Moving straight on a trace,
And flies, never to return,
Then nothing remained of it again. x

Albert Einstein

There was a young fellow from Trinity,
Who took the square root of infinity.
But the number of digits, gave him the fidgets;
He dropped Math and took up Divinity. x

George Gamow, One, Two, Three… Infinity


Mr. Tomkins was in a world where the speed of light was about 30 km/h


George Gamow and Albert Einstein and the “biggest blunder” x

Einstein’s cosmological constant

The year 2013 is Israel’s “Space Year”. Here

Read my new Paper discussing Einstein’s cosmological model and the cosmological constant:

The Mythical Snake which Swallows its Tail: Einstein’s matter world

In 1917 Einstein introduced into his field equations a cosmological term having the cosmological constant as a coefficient; he invented a 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 (Mach’s Principle).

In 1931 new experimental findings led Einstein to drop his cosmological constant.

We usually characterize Einstein’s renouncement of the cosmological constant and coming up with new ideas as Einstein’s mistake. Perhaps we rather say that Einstein’s old and new ideas link up with the same good old Mach’s principle that brought him to introduce the cosmological constant.

Later cosmological models of Einstein are either compatible or incompatible with Einstein’s understanding of Mach’s principle.

In 1931 Einstein dropped the cosmological constant and later also dropped Mach’s principle.


Einstein and Willem de Sitter in 1932

מסיבת התה של הכובען המטורף: הקבוע הקוסמולוגי של איינשטיין

ב-1917 אלברט איינשטיין החליט להוסיף איבר למשוואות השדה של תורת היחסות הכללית שלו. הוא הכניס את האיבר הקוסמולוגי בעל המקדם שקרוי “הקבוע הקוסמולוגי”, כדי שתורת היחסות הכללית תניב יקום סטטי. איינשטיין טען שהאיבר הקוסמולוגי לא ישנה את הקוואריינטיות של משוואות השדה וגם לא את שאר ניבויי התיאוריה.

באותו הזמן תורת היחסות של איינשטיין עדיין לא אומתה ניסויית, אבל איינשטיין היה נחוש בדעתו להשמיט את שאריות המרחב המוחלט שלכאורה אולי נותרו בתורתו. לשם כך הוא המציא “טירה יפיפה שתלוי באוויר”, כפי שאיינשטיין עצמו תאר זאת, עולם סופי וסגור בממדיו המרחביים ובייחוד עולם סטטי. עולם זה תאם לרעיונות של מאך, לפיהם האינרציה מקורה באינטראקציה שבין המסה לשאר המסות ביקום. שנה אחר כך איינשטיין היה כה בטוח ברעיונותיו של מאך עד כי הוא קרא לרעיון זה עקרון מאך.

מבחינה פיזיקאלית, הקבוע הקוסמולוגי בהיותו גדול מאפס פירושו היה הקיום של דחייה קוסמית וכך היקום הסטטי של איינשטיין הוא כזה שבו הדחייה בכל מקום מאזנת את משיכת הכבידה.

והנה ידידו של איינשטיין מלידן, וילהם דה סיטר, הגה פיתרון לאותן משוואות שדה של איינשטיין עם הקבוע הקוסמולוגי, אבל שמניבות יקום ריק לחלוטין. היקום של דה סיטר היה כדורי בממדיו המרחביים, אבל פתוח לאינסוף כאילו היה היפרבולואיד. דה סיטר שמע על עבודתו הניסויית של וסטו סליפר שחקר את המהירויות של 25 ערפיליות ספיראליות (מה שיותר מאוחר כונה גלקסיות). דה סיטר גילה אפקט הסחה לאדום בעולם ההיפרבולואידי שלו.

דה סיטר החליט להשוות בין העולם שלו לעולם של איינשטיין. כדי לעשות זאת הוא ביצע לעולם שלו טרנספורמציה לצורה סטטית, כך שעתה שני העולמות, שלו ושל איינשטיין, היו בעלי עקמומיות חיובית; עולם דה סיטר היה האנלוגיה הארבע-ממדית של העולם התלת-ממדי של איינשטיין. אבל בעולם של דה סיטר הזמן הוא לגמרי יחסי ושווה-ערך במעמדו לשלושת הקואורדינאטות המרחביות ואילו בעולם של איינשטיין הזמן באינסוף היה שונה כאילו היה זה זמן דמוי-מוחלט. לפיכך, המערכת של איינשטיין מספקת את עקרון היחסות רק אם פוסטולט זה תקף לשלושת ממדי המרחב ולא לממד הזמן. מכאן, טען דה-סיטר, איינשטיין השיב במו-ידיו את המרחב המוחלט של ניוטון, אותו חלל מוחלט שהוא כה התאמץ לגרש!

אבל איינשטיין לא השתכנע מהטיעונים של דה סיטר; ולא זאת בלבד, איינשטיין טען שהעולם של דה סיטר מפר את עקרון מאך. איינשטיין ניסה במקום זאת להדגים שהפתרון של דה סיטר מכיל סינגולאריות בדיוק בקו המשווה. במקום הזה שבו מצויה הסינגולאריות מתחבא לו החומר הנעלם ולכן עולם דה סיטר אינו ריק כלל. הטיעון של איינשטיין היה כזה: לפי תורת היחסות הכללית, ככל ששעונים הם קרובים יותר למקור חומרי, כך הם נעים לאט יותר. מכיוון שהשעונים הולכים ומאטים ככל שמתקרבים ל”קו המשווה” בעולם דה סיטר בצורה הסטטית, כל החומר של עולם דה סיטר מרוכז שם בקו המשווה.

ארתור אדינגטון הגדיר זאת בצורה ציורית ב-1920: ביקום דה סיטר “כאשר אנחנו מגיעים למחצית הדרך לנקודה הנגדית, הזמן עומד מלכת. בדיוק כמו מסיבת התה של הכובען המטורף, השעה היא תמיד 6 אחר הצהריים; ושום דבר לא יכול בכלל להתרחש ולא משנה כמה נחכה”.

ולכן איינשטיין הסיק שבפתרון דה סיטר ישנה סינגולאריות אינהרנטית, שהיא חלק מהפיתרון עצמו; ואם כך הדבר, מתחבא לו חומר שם בקו המשווה.

איינשטיין התווכח עם דה סיטר ולא קיבל את עובדת קיום יקומו הריק שסותר את עקרון מאך; ואז נכנס לויכוח המתמטיקאי הדגול פליקס קליין. קליין הסביר לאיינשטיין שקו המשווה בצורה הסטטית של יקום דה סיטר היא תופעת לוואי של הצורה הסטטית. למעשה זו לגמרי מקריות שיקום דה סיטר יכול להיכתב בצורה סטטית. וזו הסיבה שאנחנו אף פעם לא יכולים להגיע לקו המשווה, בגלל שהוא אירוע שנמצא מחוץ להישג ידינו; מערכת הקואורדינאטות שבה העולם של דה סיטר הוא סטטי מכסה רק חלק ממרחב-זמן דה סיטר השלם. לכן הסינגולאריות בקו-המשווה היא סינגולאריות לא אינהרנטית.

איינשטיין בהתחלה התקשה לקבל את הטיעון, אבל בסוף הוא הסכים לקבל שפתרון דה סיטר הוא אכן פתרון למשוואות השדה שלו המתוקנות עם הקבוע הקוסמולוגי, יקום ריק מחומר שמפר את עקרון מאך. אבל הוא עדיין האמין שזהו לא פתרון אפשרי מבחינה פיזיקאלית, אין כזה יקום פיזיקאלי; איינשטיין האמין שכל מודל קוסמולוגי אפשרי צריך להיות סטטי והרי המודל של דה סיטר מבחינה גלובאלית הוא אינו סטטי.

ב-1922 אלכסנדר פרידמן וב-1927 ג’ורג’ למטר פרסמו באופן נפרד זה מזה מודלים דינמיים ליקום. פרידמן גילה מודלים לא-סטטיים מעניינים בעלי קבוע קוסמולוגי שהוא אינו אפס או שווה לאפס. הוא ניבה יקום מתפשט או מתכווץ, שהניב את העולמות של איינשטיין ודה סיטר כמקרה פרטי. המודל של פרידמן עם קבוע קוסמולוגי שווה לאפס היה היקום הפשוט ביותר במסגרת תורת היחסות הפרטית. אבל ב-1922 איינשטיין חשב שהוא מצא טעות בתוצאות של פרידמן, שאם תתוקן, תיתן את היקום הסטטי של איינשטיין. פרידמן שלח לאיינשטיין את החישובים שלו ואיינשטיין השתכנע שהתוצאות של פרידמן אכן נכונות מתמטית, אבל סירב לקבל את הפתרון של פרידמן כמודל פיזיקאלי אפשרי.

ב-1927 למטר פרסם פחות או יותר את אותו המודל כמו זה של פרידמן, כאשר המודל של למטר היה יותר אסטרונומי מאשר המודל המתמטי של פרידמן. אבל כאשר למטר פגש את איינשטיין בכנס סולביי ב-1927, תגובתו של איינשטיין לעבודתו של למטר לא הייתה שונה מתגובתו למודל של פרידמן. איינשטיין היה מוכן לקבל את המתמטיקה אבל לא את הפיזיקה של היקום הדינמי המתפשט.

ב-1929 אדווין האבל הכריז על תגליתו הניסויית לפיה דומה שהיקום למעשה מתפשט. בשנים שאחרי 1930 הנטייה של הקוסמולוגים הייתה לעבור מתמיכה במודלים סטטיים כמתארים את היקום למודלים דינמיים. הגילוי של האבל נחשב לגילוי מרעיש.

ב-1931 איינשטיין ביקר בפסדינה ובהר וילסון והאבל וד”ר אדמס ליוו אותו למצפה כדי שיצפה בשמיים באמצעות הטלסקופ. איינשטיין הביט בגרמי השמיים והתפעם ולא רצה לעזוב את המקום. הוא בחן את התצפיות של האבל ועדויות אחרות שאיששו שאכן היקום מתפשט. איינשטיין שמע מהאבל עצמו אודות התצפיות שלו שהובילו למסקנה שהיקום מתפשט.

בשובו לברלין איינשטיין החליט לנטוש את הקבוע הקוסמולוגי לטובת יקום פרידמן עם הקבוע הקוסמולוגי ששווה לאפס. איינשטיין שב למשוואות השדה שלו מ-1916 ללא הקבוע הקוסמולוגי. איינשטיין פרסם מאמר קצר ב-1931 בו הוא מציג מודל קוסמולוגי עם קבוע קסמולוגי ששווה לאפס. מיד אחר כך דה סיטר הציג מודל קוסמולוגי זהה וב-1932 איינשטיין ודה סיטר חברו יחד וכתבו מאמר משותף שבו הם הציגו את מודל איינשטיין-דה סיטר.

למטר נותר נאמן לקבוע הקוסמולוגי והציע ב-1933 את ההיסטוריה המודרנית הראשונה של העולם. אבל בגלל השפעתו העצומה של איינשטיין שויתר על הקבוע הקוסמולוגי, קוסמולוגים לא שמו לב בהתחלה לרעיונות של למטר.

למטר הניח שהקבוע הקוסמולוגי גדול מאפס. הוא גילה שעבור יקום הומוגני איזוטרופי מתפשט, בזמן אפס בהיסטוריה הייתה סינגולאריות (והרי אנחנו זוכרים שלאיינשטיין הייתה בעיה עם סינגולאריות). בעקבות הסינגולאריות הזו הייתה התפשטות. כאשר בוחרים את הערך של הקבוע הקוסמולוגי בצורה מתאימה, מתחילה התפשטות מואצת, תחת דחייה קוסמית שאחר כך מואטת על ידי כבידה-עצמית מגיעים לכמעט עצירה במצב של יקום איינשטיין סטטי, שהוא בלתי תלוי בזמן. לפי למטר היקום המוקדם מאוד היה אטום קדום, גרעין אטומי קוסמי, כאשר הוא התפרק רדיואקטיבית בצורה ספונטאנית בצורת המפץ הגדול. ולכן היקום המאוד קדום נשלט על ידי חלקיקים בעלי אנרגיה מאוד גבוהה שיצרו יקום קדום הומוגני. למטר הסיק את קיומן של הקרניים הקוסמיות, השריד הקדום ביותר מההתפרקות הזו, חלקיקים אנרגטיים המרכיבים קרינת רקע למודל.

סטודנט של למטר סיפר, שמרבית האסטרונומים בתקופתו חשדו בתורת המפץ הגדול של למטר ובייחוד איינשטיין חשד בה, כי מי שהציע אותה היה כומר קתולי ותמך בה קווייקר [זרם דתי נוצרי] אדוק (ארתור אדינגטון).

אחרי שהוא ויתר על הקבוע הקוסמולוגי, איינשטיין המבוגר גם ויתר על עקרון מאך; וכך הוא נותר בלי קבוע קוסמולוגי, בלי עקמומיות מרחבית ובלי עקרון מאך… ג

Did Einstein ever say “biggest blunder”?

Astrophysicist and author Mario Livio publishes a new book Brilliant Blunders.

George Gamow reports about Einstein telling him: “Einstein’s original gravity equation was correct, and changing it was a mistake. Much later, when I was discussing cosmological problems with Einstein, he remarked that the introduction of the cosmological term was the biggest blunder he ever made in his life. But this ‘blunder,’ rejected by Einstein is still used by cosmologists even today, and the cosmological constant denoted by the Greek letter Λ rears its ugly head again and again and again. (Gamow, George My World Line, 1970, Viking Press, pp. 149-150; see quote in Janssen below).

In his new book “Brillianat Blundders”, Livio doubts that Einstein said “biggest blunder” to Gamow. Livio can find no documentation that Einstein said this. Instead, claims Livio, all references eventually lead back only to Gamow, who reported Einstein’s use of the phrase in two sources: his posthumously published autobiography My World Line (1970) and a Scientific American article from September 1956.

Yet from the reported evidence Livio was unable to demonstrate that Einstein have never  uttered the phrase “biggest blunder.” See reference here. And here.

In an interview with Livio, reporter of the Atlantic writes that Livio “looked at almost every single paper that Einstein ever wrote” including making a trip to the Einstein archive in Jerusalem to look at the collection personally. “And nowhere did I ever find the phrase ‘biggest blunder’” said Livio.

Already in 1999 John Stachel told the authors of this paper that “The comment [‘biggest blunder’] doesn’t appear in Einstein’s writings”.

The phrase “biggest blunder” perfectly suits Einstein’s sense of humor.

On September 30, 1915, Einstein was completely excited. He wrote an astrophysicist friend from Berlin Erwin Freundlich about his 1914 general theory of relativity: He thought the latter might help him:

“I am writing you now  about a scientific matter that electrifies me enormously. I have come upon a logical contradiction of a quantitative nature in the theory of gravitation, which proves to me that there must be a calculational error somewhere within my framework”. Einstein spoke about “a blatant contradiction” [ein flagranter Widerspruch].

Einstein asked for help from Freundlich: “I do not think that I myself am in the  position to find the error, because my mind is locked in the same rut in this matter. Rather, I must depend on a person being with unspoiled brain matter to find the error. If you have time, do not forget to be occupied with the topic”.

On November 28, 1915 Einstein wrote Arnold Sommerfeld: “I realized, namely, that my existing field equations of gravitation were entirely untenable! […] This showed that covariance with respect to ‘adapted’ coordinate system was a flop [ein Schlag ins Wasser war]”. And Einstein explained to Sommerfeld: “Once every last bit of confidence in result and method of the earlier theories had given away, I saw clearly that only through a link with general covariance theory, i.e., with Riemann’s covariant, that a satisfactory solution could be found. Unfortunately, I have immortalized the last error in this struggle in the Academy-papers, which I can send to you soon”.

On April 8, 1915 Einstein wrote Tulio Levi-Civita: “Hoch geehrter und lieber Herr Kollege!” In a long an tiering correspondence with Levi-Civita Einstein stubbornly tried to save his limited covariant gravitational tensor. Einstein was hard to give up, but then finally wrote his “Kollege” Levi-Civita: “My proof of the invariant nature of ΔJ fails with such infinitesimal transformations”, (which he called the sorest spot) “in which the gμν‘s of the original system are constant, because then the quantities Aμν cannot be chosen freely, but vanish altogether”.

On May 23, 1923 Einstein wrote a postcard to Herman Weyl, and towards the end of the postcard he wrote (Archives ETH, Zurich):

“Wenn schon keine-quasistatische Welt, dann fort mit dem kosmologischen Glied.”

Abraham Pais translated this in the following way (Subtle is the Lord, 1983, p. 288): “If there is no quasi-static world, then away with the cosmological term”.


Postcard to Herman Weyl. Archives ETH, Zurich.

Einstein replied to an article by Lemaître (the latter trying to persuade Einstein that the cosmological term is necessary in the equations of gravitation):

“I must admit that these arguments do not appear to me as sufficiently convincing in view of the present state of our knowledge.

The introduction of such a constant implies a considerable renunciation of the logical simplicity of theory, a renunciation which appeared to me unavoidable only so long as one had no reason to doubt the essentially static nature of space. After Hubble’s discovery of the ‘expansion’ of the stellar system, and since Friedmann’s discovery that the unsupplemented equations involve the possibility of the existence of an average (positive) density of matter in an expanding universe, that introduction of such a constant appears to me, from the theoretical standpoint, at present unjustified”.

Indeed Einstein’s main object in the 1916 general theory of relativity was to develop a theory that the chosen path entered to it was psychologically the natural one, and its underlying assumptions would appear to have been secured experimentally.

Einstein abandoned his cosmological constant when he gradually understood that it was untenable; but did he say it was a blunder or his biggest blunder?

In his paper “Mathematical theory of the origin of matter” Fred Hoyle describes cosmologists as “umpires” and he tells the following anecdote: “[Vesto Melvin] Slipher was the first important umpire. In effect, he had the temerity to give Einstein out leg before the wicket. A story tells us that Einstein did not enjoy the experience. For quite a while he glared at the umpire and even complained to the crowd as he walked back to the pavilion. When in later years Martin Ryle, dressed in the umpires white coat, somewhat joyously gave me out caught behind I did not hesitate to follow Einstein’s excellent example, and indeed a TV rerun of the situation has shown that the ball actually hit my boot not my bat”.

In the same paper Hoyle also wrote about Gamow: “would shout from the other end: ‘the elements were made in less time than you could cook a dish of duck and roast potatoes”. Indeed Gamow was known of his sense of Humor.

In 1949, in his paper, “On relativistic Cosmology”, Gamow wrote:

“Another important group of studies based on the general theory of relativity is presented by the work on relativistic cosmology, which is an attempt to understand the development of various characteristic features of our universe as the result of its expansion from the originally homogeneous state. This includes essentially the theory of the origin of atomic species, which presumably took place during the very early epoch when the material forming the universe was in highly compressed and very hot state, and the theory of the formation of galaxies which must have occurred during the later revolutionary period. The neutron-capture theory of the origin of atomic speciaes recently developed by Alpher, Bethe, Gamow, and Delter suggests that different atomic nuclei were formed by the successive aggregation of neutrons and protons which formed the original hot ylem during the early highly compressed stages in the history of the universe”.

And in the footnote the reference appearing are: G. Gamow, Phys. Rev. 70, 572 (1946); Alpher, Bethe, and Gamow, Phys. Rev. 73, 803 (1948); R. A. Alpher, Phys. Rev. 74, 1577 (1948); R.A. Alpher and R. C. Herman, Phys. Rev. 74, 1737 (1948).

The αβγ paper was created by Ralph Alpher under the supervision of Gamow. Livio says, “that if he were to add as a co-author another known astrophysicist, whose name was Hans Bethe, then the three names would be Alpher Bethe Gamow, like alpha beta gamma, even though Hans Bethe had nothing to do with that paper.”

In his 1949 paper Gamow even humorously added a new “Mr. Tompkins” by the name: Deltor…

However, it is possible that Einstein was fond of Gamow’s sense of humor. He owned Gamow’s humorous popular science books in his personal library.

For instance one can find two of Gamow’s popular books in Einstein’s personal library kept in the Einstein Archives:

Gamow, George, Mr. Tompkins in Wonderland: or stories of c, G, and h, illustrated by John Hookham, 1940, New York : Macmillan. Gamow, George, One, two, three… infinity: facts & speculations of science, illustrated by the author, 1947, New York: Viking Press.

George Gamow told the following anecdote in his autobiography My World Line:

“There is very little to say about my consultation work for the armed forces of the United States during World War II. It would have been, of course, natural for me to work on nuclear explosions, but I was not cleared for such work until 1948, after Hiroshima. The reason was presumably my Russian origin and the story I had told freely to my friends of having been a colonel in the field artillery of the Red Army at the age of about twenty.

Thus I was very happy when I was offered a consultantship in the Division of High Explosives in the Bureau of ordnance of the US navy Department.

A more interesting activity during that time was my periodic contact with Albert Einstein, who along with other prominent experts such as John von Neumann, served as a consultant for the High Explosive Division. Accepting this  consultantship, Einstein stated that because of his advanced age he would be unable to travel periodically from Princeton to Washington, D.C., and back, and that somebody must come to his home in Princeton, bringing the problems with him. Since I happened to have known Einstein earlier, on non-military grounds, I was selected to carry out this job. Thus on every other Friday I took a morning train to Princeton, carrying a briefcase tightly packed with confidential and secret Navy projects. […]

After the business part of the visit was over, we had lunch either at Einstein’s home or at the cafeteria of the Institute for Advanced Study, which was not far away, and the conversation would turn to the problems of astrophysics and cosmology. In Einstein’s study there were always many sheets of paper scattered over his desk and on a nearby table, and I saw that they were covered with tensor formulae which seemed to pertain to the unified-field theory, but Einstein never spoke about that. However, in discussing purely physical and  astronomical problems he was very refreshing, and his mind was as sharp as ever”.

Livio discovered an article by a scientist: “I discovered a small article published in some obscure journal of the Navy by somebody named Stephen Brunauer,” a scientist who had recruited both Einstein and Gamow to the Navy. In that article, Brunauer wrote, “Gamow, in later years, gave the impression that he was the Navy’s liaison man with Einstein, that he visited every two weeks, and the professor ‘listened’ but made no contribution—all false [emphasis added]. The greatest frequency of visits was mine, and that was about every two months.” Clearly, Livio says, Gamow exaggerated his relationship with the famous physicist.

It is not surprising. Einstein’s fame led people who knew him to write about their personal acquaintance with him. Brunauer was probably one of them… And indeed Gamow probably also exaggerated his friendship with Einstein. Einstein had a friend, a Hungarian Jewish physician named János Plesch.  Jeremy Bernstein writes of Plesch autobiography, “indicates it was there that he began collecting people both as patients and friends. If we can believe his autobiography, he knew everybody”, and above all Albert Einstein. Plesch starts the chapter of his autobiography presenting Einstein with the following description, “Among the many scientific men who are, or have been, my friends there is one who out-tops all the others in stature, and that is Albert Einstein”. Yet Einstein told him many valuable typical Einstein anecdotes.

How do we know whether Plesch’s reports are authentic or not? We cross-reference them with letters, unpublished talks, etc., written by Einstein himself!

We know from Einstein’s own writings that it was typical of Einstein to tell his friends that he made errors and found blatant contradiction in his work. With his usual sense of humor, Einstein used to laugh about his difficulties in inventing the most beautiful and genius theory ever created: the general theory of relativity.

It is possible that Einstein said something in German to Gamow, and the latter might have translated it to one of the classical apercus attributed to Einstein.

Albert Einstein and Willem de Sitter discussing the Universe.

Further reading:

Michel Janssen, “Why Einstein Introduced the Cosmological Constant”.

John Stachel, Einstein from B to Z.

Abraham Pais, Subtle is the Lord.