Tomorrow a Conference on the History of Einstein’s General Theory of Relativity

Space-Time Theories: Historical and Philosophical Contexts. 2015 marks the centenary of Einstein’s General Theory of Relativity (GTR). To celebrate this anniversary, this conference will bring together physicists, historians and philosophers of science, all working from different perspectives on problems inspired by GTR.

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Below I bring Einstein’s derivation of the equations from the right-hand side of the above photo (for further details see my papers on the history of general relativity). Einstein’s conclusion from this derivation is: “A ray of light passing by the sun therefore undergoes a deflection of 1.7”. (Below it should be “on” and not “in”… typo…). The derivation is from 1916, the review paper: The foundation of the general theory of relativity.

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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.

albert-einstein-lg-1

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!

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