אודיסאת איינשטיין ליחסות הכללית Einstein’s Odyssey to General Relativity

מאמר שלי על דרכו של איינשטיין לתורת היחסות הכללית: אודיסאת איינשטיין ליחסות הכללית

סיינטיפיק אמריקן ישראל

“Einstein’s Odyssey to General Relativity”, Scientific American Israel

את המונח “אודיסאה” ליחסות הכללית טבע פרופ’ ג’ון סטצ’ל מאוניברסיטת בוסטון והוא מייצג את המסע המפרך של איינשטיין בדרכו ליחסות הכללית. ראו המאמר של סטצ’ל למטה

Odyssey to general relativity is John Stachel’s memorable phraseology. See:

Stachel, John (1979). “Einstein’s Odyssey: His Journey from Special to General Relativity”. In Einstein from B to Z, 2002.

I am sorry but this piece is in Hebrew. You can read my book General Relativity Conflict and Rivalries, my papers on Einstein and general relativity and a short summary below.

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מפייסבוק: מארחים את ד”ר גלי וינשטיין לדבר על איינשטיין

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My drawing of Einstein:      האיור שלי של איינשטיין

איינשטיין צעיר

And the original (I tried as hard as I could to draw a young Einstein…):       המקור

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The article discusses the following topics:

1907. The Happiest thought of my life.

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1907-1911. The equivalence principle and elevator experiments.

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1911. Deflection of light and explaining deflection of light using an elevator thought experiment.

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1911-1912 (1916). The disk thought experiment, gravitational time dilation and gravitational redshift.

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1912. The disk thought experiment and non-Euclidean geometry.

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1912. Einstein to Marcel Grossmann: “Grossmann, you must help me or else I’ll go crazy!”. Grossmann searched the literature, and brought the works of Bernhard Riemann, Gregorio Curbastro-Ricci, Tullio Levi-Civita and Elwin Bruno Christoffel to Einstein’s attention. With Grossmann’s help Einstein searched for gravitational field equations for the metric tensor in the Zurich Notebook.

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1913-1914. The Entwurf theory. In 1913, Einstein and Michele Besso both tried to solve the new Entwurf field equations to find the perihelion advance of Mercury.

2October 1915. Einstein realizes there are problems with his 1914 Entwurf theory. November 1915. Einstein’s competition with David Hilbert.

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November 1915. Four ground-breaking papers: Einstein presents the field equations of general relativity, finds the advance of the perihelion of Mercury and predicts that a ray of light passing near the Sun would undergo a deflection of amount 1.7 arc seconds.

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.

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.

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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).

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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.