The Road to Relativity and Dishonesty in Scientific Research

Prof. Hanoch Gutfreund, the former president of the Hebrew University of Jerusalem, has been plagiarizing my papers and book. To call prof. Gutfreund prolific in plagiarizing my work would be an understatement. The serious damages I sustain from this in Israel are enormous, actually it is far more damaging than I previously thought. I wrote to the president of the Hebrew University in Jerusalem but the latter has not even answered my email. Hence it seems he fails to take responsibility for damage caused by plagiarism. I am not surprised.

In the book, The Road to Relativity: The History and Meaning of Einstein’s “The Foundation of General Relativity” (an annotated facsimile of Einstein’s original handwritten manuscript on general relativity and explanation of Einstein’s manuscript and equations), co-authored by prof. Jürgen Renn, prof. Gutfreund writes:

cosmo

Prof. Gutfreund has picked this passage with only slight changes from 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.

My name is not mentioned in note 4:

notes

Compare the above paragraph from prof. Gutfreund’s book, The Road to Relativity: The History and Meaning of Einstein’s “The Foundation of General Relativity, to the abstract of my paper, “George Gamow and Albert Einstein: Did Einstein say the cosmological constant was the ‘biggest blunder’ he ever made in his life”:

gamow2

gamow

And compare the penultimate paragraph from prof. Gutfreund’s book, The Road to Relativity: The History and Meaning of Einstein’s “The Foundation of General 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?”:

blunder1

blunder2

In 2016 I received this message from ResearchGate:

gate

My paper gained traffic but no citations, but prof. Gutfreund, who plagiarized 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”.

Gamow

It is quite obvious the Prof. Gutfreund has effectively paraphrased the passage from my paper. On November 30, 2015,  Prof. Gutfreund said in his plenary lecture, “100 years of General Relativity – What are we Celebrating?” At the Berlin Conference: A Century of General Relativity:

“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”.

My second bookGeneral Relativity Conflict and Rivalries. Einstein’s Polemics with Physicists (published on December 1, 2015) has a whole chapter dedicated to Einstein’s “biggest blunder”. This chapter is based on my 2013 ArXiv paper: “George Gamow and Albert Einstein: Did Einstein say the cosmological constant was the ‘biggest blunder’ he ever made in his life?”:

gut3

Hence, plagiarism of my 2013 paper on Albert Einstein and George Gamow causes damage to my second book and to my academic status.

In addition, Prof. Gutfreund writes in The Road to Relativity: The History and Meaning of Einstein’s “The Foundation of General Relativity”:

gut

A circle around the origin of coordinates is a rotating disk (in his 1916 paper “The Foundation of General Relativity”, Einstein calls the disk “a circle around the origin”).

In the preceding passage prof. Gutfreund have paraphrased a 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:

disk1

 

disk2

and from my 2014 paper, “Einstein, Schwarzschild, the Perihelion Motion of Mercury and the Rotating Disk Story”, ArXiv, 1411.7370v [physics.hist-ph], 26 Nov, 2014 [Equation (70) is my equation (6) and equation (71) is my equation (11)]:

gut2

Towards the end of his 1916 paper, “The Foundation of General Relativity”, Einstein demonstrates that the gravitational field changes spatial dimensions and the clock period. However, nowhere does Einstein directly relate the rotating disk story to the  above derivation. I have invoked this interpretation of Einstein’s paper. Einstein writes:

Ein5 Ein4

Digital Einstein

On November 30, 2015, Prof. Gutfreund lifted another passage from my paper, “Einstein, Schwarzschild, the Perihelion Motion of Mercury and the Rotating Disk Story” and changed a word here and there, in his plenary lecture, “100 years of General Relativity – What are we Celebrating? at the Berlin Conference: A Century of General Relativity:

“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”.

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, I wrote:

“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).”

He could have though picked the idea from my 2012 paper, Weinstein, Galina, “From the Berlin ‘Entwurf’ Field equations to the Einstein Tensor III: March 1916”, ArXiv: 1201.5358v1 [physics.hist-ph], 25 January, 2012:

Scwarzschild.jpg

Einstein’s equations in his 1916 paper, “The Foundation of General Relativity”:

Schwartz1

Schwartz2

Schwartz3

In my book, General Relativity Conflict and Rivalries. Einstein’s Polemics with Physicists  I have also developed my previous ideas from my paper, “Einstein, Schwarzschild, the Perihelion Motion of Mercury and the Rotating Disk Story”.

 

 

 

 

 

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

conference Berlin

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

רן

קוראים 10000

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

ג2

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”.

ג3

ג4

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

Scwarzschild

Einstein’s 1916 Equations:

Schwartz1

Schwartz2

Schwartz3

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

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

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

שוורצשילד1

שוורצשילד2

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

ג1

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”.

ג6

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

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

2012-1

2012-2

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

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

stachel

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

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

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

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

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

Prof. Gutfreund explained in his lecture:

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

And Professor Gutfreund showed the following slide:

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

snake3

I see phrases here that come from my work and Prof. Stachels’ bookEinstein from B to Z, 2002, for which there is no attribution. I recognize my own words: “but a physical significance can hardly be ascribed to them”.

Prof. Stachel wrote: “to which a physical significance can hardly be ascribed”. Hence, prof. Gutfreund did not even bother to read prof. Stachel’s original paper; he simply lifted phrases from my paper. His above citation and slide contain exact words from my own published paper but he does not give attribution to me. I wrote in my paper, “The Mythical Snake which Swallows its Tail: Einstein’s matter world” the following:

פרידמן

snake

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

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

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:

snake1

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:

Friedmann

Prof. Stachel writes:

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

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

The bracketed portion being crossed out in the manuscript”.

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

גוטפרוינד

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

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

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

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

In his lecture Prof. Gutfreund explained:

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

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

finger

Mach3

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

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

And he showed the following slide:

Mach's ideas

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

Mach's idea

I Therefore write:

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

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

Mach2

I therefore write:

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

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

Machbook

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

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

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

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

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

Besso3

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

Besso0

 

Besso1

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

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

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

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

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

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

Besso

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

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

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

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

6. Cosmological Constant Biggest blunder

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

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

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

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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:

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

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In 2016 I received this message from ResearchGate:

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

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

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Gamow

cheers

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

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

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

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

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“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.

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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):

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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):

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

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

Mach's principle

I therefore write in my book:

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

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

8. Einstein and Poincare.

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

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

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

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

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

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

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The prediction of gravitational waves emerged as early as 1913

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

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

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

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

A summary was published in German:

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

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

and also in English:

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

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

And here as well.

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

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

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

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

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

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

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

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

I start with Einstein’s childhood and school days.

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

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Young Einstein, Aarau Class 1896

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

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Albert Einstein at the Patent office

Mileva Marić and Einstein

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Eduard Tete, Mileva Marić and Hans Albert

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

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

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

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

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My books

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

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The back cover of my book:

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

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

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

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Grossmann and Einstein

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From Zurich to Berlin

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

General Relativity between 1912 and 1916

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

General Relativity after 1916

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

 

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Einstein 1916

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

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

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

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

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

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

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Max Abraham

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

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Gunnar Nordström

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

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Marcel Grossmann

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

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Elwin Bruno Christoffel

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Gregorio Curbastro Ricci

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Bernhard Riemann

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

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

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

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

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Michele Besso

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

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Tulio Levi-Civita

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

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

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

Einstein and Hilbert

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David Hilbert

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

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

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

Schwarzschild

Karl Schwarzschild

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

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Ernst Mach

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

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

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

Lemaitre

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

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

 

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Einstein in America.

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

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

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

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

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

Cover

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

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

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

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My first book:

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

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

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Review of Arch and Scaffold Physics Today

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

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

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

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

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

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

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

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

Einstein

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

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

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

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

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

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

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

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

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

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

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

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The Publisher uploaded the contents and intro.

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I hope you like my drawing on the cover:

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

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

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Have a very happy Einstein year!

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

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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”.

The centenary of Einstein’s General Theory of Relativity

Einstein’s first big project on Gravitation in Berlin was to complete by October 1914 a summarizing long review article of his Einstein-Grossmann theory. The paper was published in November 1914. This version of the theory was an organized and extended version of his works with Marcel Grossmann, the most fully and comprehensive theory of gravitation; a masterpiece of what would finally be discovered as faulty field equations.

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On November 4, 1915 Einstein wrote his elder son Hans Albert Einstein, “In the last days I completed one of the finest papers of my life; when you are older I’ll tell you about it”. The day this letter was written Einstein presented this paper to the Prussian Academy of Sciences. The paper was the first out of four papers that corrected his November 1914 review paper. Einstein’s work on this paper was so intense during October 1915 that he told Hans Albert in the same letter, “I am often so in my work, that I forget lunch”.

Einstein

In the first November 4 1915 paper, Einstein gradually expanded the range of the covariance of his field equations. Every week he expanded the covariance a little further until he arrived on November 25 1915 to fully generally covariant field equations. Einstein’s explained to Moritz Schlick that, through the general covariance of the field equations, “time and space lose the last remnant of physical reality. All that remains is that the world is to be conceived as a four-dimensional (hyperbolic) continuum of four dimensions” (Einstein to Schlick, December 14, 1915, CPAE 8, Doc 165) John Stachel explains the meaning of this revolution in space and time, in his book: Stachel, John, Einstein from ‘B’ to ‘Z’, 2002; see p. 323).

Albert Einstein as a Young Man

These are a few of my papers on Einstein’s pathway to General Relativity:

http://xxx.tau.ac.il/abs/1201.5352

http://xxx.tau.ac.il/abs/1201.5353

http://xxx.tau.ac.il/abs/1201.5358

http://xxx.tau.ac.il/abs/1202.2791

http://xxx.tau.ac.il/abs/1202.4305

http://xxx.tau.ac.il/abs/1204.3386

http://xxx.tau.ac.il/abs/1309.6590

http://xxx.tau.ac.il/abs/1310.1033

http://xxx.tau.ac.il/abs/1205.5966

http://xxx.tau.ac.il/abs/1310.2890

http://xxx.tau.ac.il/abs/1310.6541

Stay tuned for my next centenary of GTR post!