My new paper on Einstein and general relativity

didMy new paper on Einstein and the general theory of relativity:

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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.

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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.

100 GTR: Uniformly Rotating Disk and the Hole Argument

The “Ehrenfest paradox“: Ehrenfest imagined a rigid cylinder set in motion from rest and rotating around its axis of symmetry. Consider an observer at rest measuring the circumference and radius of the rotating cylinder. The observer arrives at two contradictory requirements relating to the cylinder’s radius:

  1. Every point in the circumference of the cylinder moves with radial velocity ωR, and thus, the circumference of the cylinder  should appear Lorentz contracted to a smaller value than at rest, by the usual “relativistic” factor γ: 2πR‘ < 2πR.
  2. The radius R’ is always perpendicular to its motion and suffers no contraction at all; it should therefore be equal to its value R: R’ = R.

Einstein wrote to Vladimir Varićak either in 1909 or in 1910 (Febuary 28): “The rotation of the rigid body is the most interesting problem currently provided by the theory of relativity, because the only thing that causes the contradiction is the Lorentz contraction”.  CPAE 5, Doc. 197b.

Ehrenfest imagined a rigid cylinder gradually set into rotation (from rest) around its axis until it reaches a state of constant rotation.

In 1919 Einstein explained why this was impossible: (CPAE 9, Doc. 93)

“One must take into account that a rigid circular disk at rest would have to snap when set into rotation, because of the Lorentz shortening of the tangential fibers and the non-shortening of the radial ones. Similarly, a rigid disk in rotation (made by casting) would have to shatter as a result of the inverse changes in length if one attempts to bring it to the state of rest. If you take these facts fully into consideration, your paradox disappears”.

Assuming that the cylinder does not expand or contract, its radius stays the same. But measuring rods laid out along the circumference 2πR should be Lorentz-contracted to a smaller value than at rest, by the usual factor γ. This leads to the paradox that the rigid measuring rods would have to separate from one another due to Lorentz contraction; the discrepancy noted by Ehrenfest seems to suggest that a rotated Born rigid disk should shatter. According to special relativity an object cannot be spun up from a non-rotating state while maintaining Born rigidity, but once it has achieved a constant nonzero angular velocity it does maintain Born rigidity without violating special relativity, and then (as Einstein showed in 1912) a disk riding observer will measure a circumference.

Hence, in 1912, Einstein discussed what came to be known as the uniformly rotating disk thought experiment in general relativity. Thinking about Ehrenfest’s paradox and taking into consideration the principle of equivalence, Einstein considered a disk (already) in a state of uniform rotation observed from an inertial system.

We take a great number of small measuring rods (all equal to each other) and place them end-to-end across the diameter 2R and circumference 2πR of the uniformly rotating disk. From the point of view of a system at rest all the measuring rods on the circumference are subject to the Lorentz contraction. Since measuring rods aligned along the periphery and moving with it should appear contracted, more would fit around the circumference, which would thus measure greater than 2πR. An observer in the system at rest concludes that in the uniformly rotating disk the ratio of the circumference to the diameter is different from π:

circumference/diameter = 2π(Lorentz contracted by a factor…)/2R = π (Lorentz contracted by a factor….).

According to the equivalence principle the disk system is equivalent to a system at rest in which there exists a certain kind of static gravitational field. Einstein thus arrived at the conclusion that a system in a static gravitational field has non-Euclidean geometry.

Soon afterwards, from 1912 onwards, Einstein adopted the metric tensor as the mathematical respresentation of gravitation.

Indeed 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: “The Foundation of the General Theory of 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.

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My new paper deals with Einstein’s 1912 and 1916 rotating disk problem, Einstein’s hole argument, the 1916 point coincidence argument and Mach’s principle; a combined-into-one deal (academic paper) for the readers of this blog.

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Sitting: Sir Arthur Stanley Eddington and Hendrik Antoon Lorentz. Standing: Albert Einstein, Paul Ehrenfest and Willem de Sitter. September 26, 1923.

Further reading: Ehrenfest paradox

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

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Max Abraham

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Gunnar Nordström

Einstein’s Pathway to his Equivalence Principle 1905-1907

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1912 – 1913 Static Gravitational Field Theory

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1913 – 1914 “Entwurf” theory

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Berlin “Entwurf” theory 1914

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The Einstein-Nordström Theory

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Dawn of “Entwarf theory”

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1915 Relativity Theory

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1916 General Theory of Relativity

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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

Einstein’s Pathway to the Special Theory of Relativity and the General Theory of Relativity

Einstein’s Pathway to the Special Theory of Relativity

Einstein’s Pathway to the Special Theory of Relativity

Einstein’s discovery of Special Relativity

Einstein Believes in the Ether

Einstein Chases a Light Beam

Einstein recounts the Aarau thought experiment in his Autobiographical Notes, 1949

Magnet and Conductor Thought Experiment, Faraday’s magneto-electric induction

Föppl’s book on Maxwell’s theory

Ether drift and Michelson and Morley’s experiment

The Role of the Michelson-Morley Experiment on the Discovery of Relativity

The Dayton Miller Experiments

Emission theory and ether drift experiments

Paul Ehrenfest and Walter Ritz. Ritz’s Emission Theory

“The Step”

Einstein defined distant simultaneity physically; relativity of simultaneity

The Kyoto lecture notes – Einstein could have visited and consulted his close friend Michele Besso, whom he thanked at the end of his relativity paper. The Patent Office brought them together – their conversations on the way home. Besso was always eager to discuss the subjects of which he knew a great deal – sociology, medicine, mathematics, physics and philosophy – Einstein initiated him into his discovery

Joseph Sauter – Before any other theoretical consideration, Einstein pointed out the necessity of a new definition of synchronization of two identical clocks distant from one another; to fix these ideas, he told him, “suppose one of the clocks is on a tower at Bern and the other on a tower at Muri (the ancient aristocratic annex of Bern)” – synchronization of clocks by light signals.

Did Poincaré have an Effect on Einstein’s Pathway toward the Special Theory of Relativity? Einstein’s reply to Carl Seelig

Poincaré

Einstein’s pathway to the General Theory of Relativity

Entwurf theory – Einstein-Grossmann theory, Hole argument, field equations and the Einstein-Besso manuscript

Grossmann

Gunnar Nordström develops a competing theory of gravitation to Einstein’s 1912-1913 gravitation theory. Einstein begins to study Nordström’s theory and develops his own Einstein-Nordström theory. In a joint 1914 paper with Lorentz’s student Adrian Fokker – a generally covariant formalism is presented from which Nordström’s theory follows if the velocity of light is constant Here

Nordström

The three problems that led to the fall of the entwurf theory –

The gravitational field on a uniformly rotating system does not satisfy the field equations.

Covariance with respect to adapted coordinate system was a flop.

In the Entwurf theory the motion of Mercury’s perihelion came to 180 rather than 450 per century

The General Theory of Relativity – 1915

David Hilbert Enters the Game, the priority dispute – Einstein and Hilbert

In November 18 1915 Einstein calculated rapidly the precession of Mercury’s

Perihelion

Geodesic Equation. Metric tensor. Einstein’s November 4, 11, and 25 field equations.The Riemann-Christoffel Tensor; the Ricci tensor; the Einstein tensor

von Deinem zufriedenen aber ziemlich kaputen

General Theory of Relativity – 1916

Mid December to Mid January 1915: Exchange of letters between Einstein and Ehrenfest

The disk thought experiment; coordinates have no direct physical meaning Euclidean Geometry breaks down; two Globes Thought Experiment; Mach’s Principle; the principle of general relativity; the Equivalence Principle; the principle of general covariance

The Summation Convention

Motion of the Perihelion of the Planetary Orbit; Redshift; Deflection of light in a gravitational field of the sun

Einstein in the Patent Office:

Michele Besso, Joseph Sauter, and Lucian Chavan – Patent Office, Maurice Solovine and Conrad Habicht – the Olympian Academy

Annus mirabilis papers

On a Heuristic Viewpoint Concerning the Generation and Transformation of Light – It argues a heuristic manner for the existence of light quanta and derives the photoelectric law

On a New Determination of Molecular Dimensions – doctoral thesis submitted to the mathematical and natural science branch of Zürich University

On the Movement of Particles Suspended in Fluids at Rest, as Postulated by the Molecular Theory of Heat. The Brownian motion paper

On the Electrodynamics of Moving Bodies. The Relativity Paper

Does the Inertia of a Body Depend on its Energy Content? The first derivation of the mass energy equivalence

German Scientists Responded to Einstein’s Relativity Paper – Max Planck wrote Einstein. Max von Laue met Einstein

Einstein teaches his 3 friends from the Patent Office at the University of Bern

Finally Einstein leaves the Patent Office to his first post in the University of Zürich

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