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

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


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


The Publisher uploaded the contents and intro.


I hope you like my drawing on the cover:


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



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


Have a very happy Einstein year!

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”.

Einstein and 1915 General Relativity

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

My new paper on general relativity



Einstein’s pathway to his General Theory of Relativity

Einstein thought that when dealing with gravity high velocities are not so important. So in 1912 he thought about gravity in terms of the principle of relativity and not in terms of the constant-speed-of-light postulate (special relativity). But then he engaged in a dispute with other scholars who claimed that he gave up the central postulate of his special theory of relativity. x

File:Max abraham.png

Max Abraham

File:Gunnar Nordström.jpg

Gunnar Nordström

Einstein’s Pathway to his Equivalence Principle 1905-1907


1912 – 1913 Static Gravitational Field Theory


1913 – 1914 “Entwurf” theory


Berlin “Entwurf” theory 1914


The Einstein-Nordström Theory


Dawn of “Entwarf theory”


1915 Relativity Theory


1916 General Theory of Relativity


How many scientists did it take to make the discovery of Relativity – Special and General Theories? x

 Albert Einstein? or Albert Einstein, Michele Besso, Marcel Grossmann?… Read my latest paper

Besso, Special Relativity: Einstein ends his 1905 relativity paper by saying that he is indebted to Besso for several valuable suggestions. What could Besso’s valuable suggestions have been? Einstein’s biographer, Carl Seelig, wrote: “Later Besso […] used the following analogy: Einstein the eagle has taken Besso the sparrow under his wing. Then the sparrow fluttered a little higher: ‘I could not have found a better sounding-board in the whole of Europe’, Einstein remarked when the conversation turned one day to Besso. This way Einstein and Besso became inseparable”. x

In 1952 Besso recounted, “Another little fairy tale of mine concerning my view that I had participated in [the formulation of] the special theory of relativity. It seemed to me, as an electrical engineer, I must have brought up, in conversations with you, the question, within the context of Maxwell’s theory, of what is induced in the inductor of an alternator […]”: the Magnet and Conductor thought experiment that opens Einstein’s 1905 Relativity Paper. Maxwell’s theory was not yet on the official program of the Polytechnic School ETH (Einstein’s and Besso’s collage). It was probably Einstein’s self-reading about Maxwell’s theory, who explained to Besso about this theory. Only after such explanation could Besso within the context of Maxwell’s theory refer to his technical work and speak with Einstein or remind him about induction of which Einstein had already read about in books

Einstein and his closest friend, Michele Besso

Grossmann, General Relativity: When Einstein came back to Zurich in 1912 Marcel Grossmann looked through the literature, and discovered that the mathematical problem was already solved by Riemann, Ricci and Levi-Civita. Einstein collaborated with Grossmann and this led to the Einstein-Grossmann theory published in two joint papers. Just before writing the first paper with Grossmann, Einstein had struggled with these new tools in the Zurich Notebook. Einstein wrote Grossmann’s name and considered candidate field equations he would come back to in the first 1915 paper on General Relativity

In this paper Einstein wrote in the introduction, “I completely lost trust in my established field equations [of the Einstein-Grossmann theory], […]. Thus I arrived back at the demand of a broader general covariance for the field equations, from which I parted, though with a heavy heart, three years ago when I worked together with my friend Grossmann. As a matter of fact, we then have already come quite close to the solution of the problem given in the following”. x

Marcel Grossmann, Albert Einstein, Gustav Geissler and Marcel’s brother Eugen
during their time as students at the ETH- here

Besso, General Relativity: During a visit by Besso to Einstein in Zurich in June 1913 they both tried to solve the Einstein-Grossmann theory field equations to find the perihelion advance of Mercury in the “Einstein-Besso manuscript”. Besso was inducted by Einstein into the necessary calculations. Besso collaborated with Einstein on the wrong gravitational Einstein-Grossmann theory, and their calculation based on this theory gave a wrong result. In October 1915 Einstein abandoned the Einstein-Grossmann theory; he transferred the basic framework of the calculation from the Einstein-Besso manuscript, and corrected it according to his new 1915 General Relativity Theory with which he 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, and did not mention his name in his 1915 paper that explains the anomalous precession of Mercury

Einstein considered his best friend Michele Besso as a sounding board and his class-mate from the Polytechnic Marcel Grossman – as his active partner. Yet, Einstein wrote that Grossman will never claim to be considered a co-discoverer of the Einstein-Grossmann theory – a theory very close to Einstein’s general theory of relativity that he published in November 1915. He only helped in guiding Einstein through the mathematical literature, but contributed nothing of substance to the results of the theory. Hence, Einstein neither considered Besso or Grossmann as co-discoverers or co-inventors of the relativity theory which he himself invented

Read also this paper, “How many scientists does it take to make a discovery? The era of the lone genius , as epitomised by Albert Einstein, has long gone”. Prof. Athene Donald, the author of the paper writes, “Ask people to conjure up an image of a scientist and Albert Einstein is most likely to pop into their head. The iconic image is of a lone genius beavering away in some secluded room until that familiar equation – E=mc2 – crystallised in his brain sufficiently to be written down. I very much doubt doing science was ever quite like that, but it is even more unlikely to apply now”. What do you think? x

שנים לטנסור המטרי 100 Years of Metric Tensor

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

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

Relatively speaking

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Alfred Eisenstaedt, Einstein Life Magazine

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

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

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

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

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

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

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

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

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

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

Time Magazine Photo

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Albert Einstein and David Hilbert – Einstein’s General Relativity

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, and on November 4, 1915 he presented to the Prussian Academy these new field equations. Starting on November 4, 1915, Einstein gradually expanded the range of the covariance of his field equations

On November 7, 1915, Einstein sent David Hilbert the proofs to his first paper of November 4, and he wanted Hilbert to look at this work. Hilbert alsoreadEinstein’s1914reviewpaper discussing his “Entwurf” theory: Hilbert found some mistake in this paper; Einstein wrote that his colleague Arnold Sommerfeld wrote him that Hilbert had objected to the 1914 “Entwurf” foundations paper

By November 10, 1915 Hilbert probably answered Einstein’s letter, telling him about his system of electromagnetic theory of matter, the unified theory of gravitation and electromagnetism, in which the source of the gravitational field is the electromagnetic field. Hilbert’s goal was to develop an electromagnetic theory of matter, which would explain the stability of the electron

Between November 4 and November 11 it seems that Einstein was influenced by Hilbert’s physical attitude towards a field theory of matter. In his addendum to the first note, published on November 11 Einstein directly referred to the supporters of the electrodynamic worldview, “One now has to remember that, in accord with our knowledge, ‘matter’ is not to be conceived as something primitively given, or physically simple. There even are those, and not just a few, who hope to be able to reduce matter to purely electrodynamic processes, which of course would have to be done in a theory more complete than Maxwell’s electrodynamics”. Einstein probably discussed the electrodynamic worldview with Hilbert and felt that he was now in competition with the latter

In the addendum to the November 4 paper, the November 11 paper, Einstein added a coordinate condition (determinant equal to 1), which allowed him to take the last step and to write the field equations of gravitation in a general covariant form. He then dropped his November 4 postulate and adopted it as a coordinate condition

The day afterwards Einstein wrote Hilbert again. He told him about the progress in his work. Hilbert replied and invited Einstein to come to Göttingen. Hilbert explained to Einstein the main points of his new unified theory of gravitation and electromagnetism, and told Einstein that he had already discussed his discovery with Sommerfeld. He wanted next to explain it to Einstein. He thus invited him to come to hear his talk on November 16. Hilbert told Einstein that the latter’s November 4 paper was entirely different from his own work

With hindsight Hilbert’s work was different from Einstein’s November 4 paper in that, Hilbert eventually endeavored to derive generally covariant field equations for the combined gravitational and electromagnetic fields without explicitly writing down these equations. Hilbert accepted Einstein’s 1914 Hole Argument against general covariance (after Einstein had silently dropped it). Hilbert was thus finally obliged to supplement his generally covariant field equations by four non-generally covariant field equations based on rather dubious energy considerations, which Hilbert would eventually drop later when he would publish his paper (after Einstein presented his final form of field equations to the Prussian Academy on November 25). Einstein replied and told Hilbert he could not come, but requested a copy of his work. In response, Hilbert perhaps sent a copy of the lecture he had given on the subject on November 16, or else a copy of a manuscript of the paper he would present five days later on November 20 to the Royal Society in Göttingen

Einstein was already less patient after he had received Hilbert’s work. He replied to Hilbert on November 18 telling him that his work agrees – as far as he could see – exactly with what he had found in the last few weeks and have already presented to the Prussian Academy. Einstein was in competition with Hilbert and appeared to have been still influenced by his unified theory of matter, gravitation and electromagnetism until November 18. Indeed on Thursday, November 18, Einstein presented to the Prussian Academy his solution to the longstanding problem of the precession of the perihelion of Mercury, on the basis of his November 11 General theory of relativity

The day afterwards Hilbert sent a polite letter in which he congratulated Einstein on overcoming the perihelion motion. He was quite astonished that Einstein calculated so rapidly the precession of Mercury’s perihelion. In fact the basic calculation has already been done two years earlier with Michele Besso in the Einstein-Besso manuscript. Einstein transferred the basic framework of the calculation from the Einstein-Besso manuscript, and corrected it according to his November field equations

In November 1915 Einstein could calculate so rapidly the precession of Mercury’s perihelion for another reason. Einstein’s November 11 field equations for the metric tensor are the field equations for the gravitational field in the November 18 paper. The added coordinate condition, determinant equal to 1 (from Einstein’s November 11 paper), implied by the assumption of an electromagnetic origin of matter, was essential for Einstein’s calculation of the precession of Mercury’s perihelion

The November 11 field equations are non-linear partial differential equations of the second rank, and there is no general solution to these equations. Solving the field equations give the components of the metric tensor. In his November 18 paper Einstein tried to find approximate solutions

What happened during the week of November 18–25, 1915? After or while working on the solution of the problem of the Perihelion of Mercury, Einstein could resolve the final difficulties in his November 11 theory. It took him an extra week to arrive at the November 25 field equations. On November 26 Einstein wrote his close friend Heinrich Zangger, however, only one colleague has really understood it [his theory], and he is seeking to clearly “nostrify” it (Abraham’s expression).This colleague was David Hilbert

Recall that on November 19 Hilbert sent Einstein a letter in which he congratulated him on overcoming the perihelion motion. Hilbert ended his letter by asking Einstein to continue and keep him up to date on his latest advances. Hilbert did not tell Einstein about the important talk he was giving the day afterwards. Hilbert presented on November 20 a paper to the Göttingen Academy of Sciences, “The Foundations of Physics”, including his version to the gravitational field equations of general relativity. Five days later on November 25, Einstein presented to the Prussian Academy his version to the gravitational field equations

At the end of the day it appears that Einstein did not “nostrify” Hilbert. After November 18 Einstein was no more influenced by Hilbert’s theory of matter, and he was thus not in competition with him anymore. His new field equations of November 25 with the new trace term are related to his work of November 4, and appear to have sprung from it

In two papers (here and here) I derive Einstein’s November 25, 1915 field equations from Einstein’s November 4, 1915 field equations and connect between the two. In his 1916 review paper, “The Foundation of the General Theory of Relativity” Einstein connected between his  November 4 and November 25 field equations and I follow his derivation

Update December 5, 2014. It took me two years to formulate the above ideas, to write them down and get them onto a scholarly paper. But finally I found a way to do this and yesterday I uploaded the paper.

Here it is: “Did Einstein ‘Nostrify’ Hilbert’s Final Form of the Field Equations for General Relativity?”

Albert Einstein as a Young Man