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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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.

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!

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

My new paper on Einstein and Schwarzschild

My new paper on General Relativity: Einstein and Schwarzschild.

Sometime in October 1915 Einstein dropped the Einstein-Grossman theory. Starting on November 4, 1915, Einstein gradually expanded the range of the covariance of his field equations. On November 11, 1915 Einstein was able to write the field equations of gravitation in a general covariant form, but there was a coordinate condition (there are no equations here so I cannot write it down here).

On November 18, 1915, Einstein presented to the Prussian Academy his paper, “Explanation of the Perihelion Motion of Mercury from the General Theory of Relativity”. Einstein reported in this talk that the perihelion motion of Mercury is explained by his theory. In this paper, Einstein tried to find approximate solutions to his November 11, 1915 field equations. He intended to obtain a solution, without considering the question whether or not the solution was the only possible unique solution.

Einstein’s field equations are non-linear partial differential equations of the second rank. This complicated system of equations cannot be solved in the general case, but can be solved in particular simple situations. The first to offer an exact solution to Einstein’s November 18, 1915 field equations was Karl Schwarzschild, the director of the Astrophysical Observatory in Potsdam. On December 22, 1915 Schwarzschild wrote Einstein from the Russian front. Schwarzschild set out to rework Einstein’s calculation in his November 18 1915 paper of the Mercury perihelion problem. He first responded to Einstein’s solution for the first order approximation from his November 18, 1915 paper, and found another first-order approximate solution. Schwarzschild told Einstein that the problem would be then physically undetermined if there were a few approximate solutions. Subsequently, Schwarzschild presented a complete solution. He said he realized that there was only 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.

“Raffiniert ist der Herrgott, aber boshaft ist er nicht” (Einstein might have already said….), because the problem with Schwarzschild’s line element was that a mathematical singularity was seen to occur at the origin! Oh my, Einstein abhorred singularities.

Actually, Schwarzschild “committed another crime”: he did not satisfy the coordinate condition from Einstein’s November 11 or November 18, 1915 paper. Schwarzschild admitted that his coordinates were not “allowed” coordinates, with which the field equations could be formed, because these spherical coordinates did not have determinant 1. Schwarzschild chose then the non-“allowed” coordinates, and in addition, a mathematical singularity was seen to occur in his solution. But Schwarzschild told Einstein: Don’t worry, “The equation of [Mercury’s] orbit remains exactly as you obtained in the first approximation”! See my paper from 2012.

Einstein replied to Schwarzschild on December 29, 1915 and told him that his calculation proving uniqueness proof for the problem is very interesting. “I hope you publish the idea soon! I would not have thought that the strict treatment of the point- problem was so simple”. Subsequently Schwarzschild sent Einstein a manuscript, in which he derived his solution of Einstein’s November 18, 1915 field equations for the field of a single mass. Einstein received the manuscript by the beginning of January 1916, and he examined it “with great interest”. He told Schwarzschild that he “did not expect that one could formulate so easily the rigorous solution to the problem”. On January 13, 1916, Einstein delivered Schwarzschild’s paper before the Prussian Academy with a few words of explanation. Schwarzschild’s paper, “On the Gravitational Field of a Point-Mass according to Einstein’s Theory” was published a month later.

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Karl Schwarzschild

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 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 from his November 18, 1915 paper.

A comment regarding Einstein’s calculations in his November 18, 1915 paper of the Mercury perihelion problem and Einstein’s 1916 paper. In his early works on GTR, in order to obtain the Newtonian results, Einstein used the special relativistic limit and the weak field approximation, and assumed that space was flat (see my paper). Already in 1914 Einstein had reasoned that in the general case, the gravitational field was characterized by ten space-time functions of the metric tensor. g were functions of the coordinates. In the case of special relativity this reduces to g44 = c2, where c denotes a constant. Einstein took for granted that the same degeneration occurs in the static gravitational field, except that in the latter case, this reduces to a single potential, where g44 = c2 is a function of spatial coordinates, x1, x2, x3. 

Later that year David Hilbert (with a vengeance from 1915?…) arrived at a line-element similar to Schwarzschild’s one, and he concluded that the singularity disappears only if we accept a world without electricity. Such an empty space was inacceptable by Einstein who was apparently much attracted by Mach’s ideas! (later termed by Einstein “Mach’s Principle”). Okay, Einstein, said Hilbert: If there is matter then another singularity exists, or as Hilbert puts it: “there are places where the metric proves to be irregular”…. (See my paper from 2012).

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Strange Days at Blake Holsey High: a student is sucked into the black hole…

 

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”.

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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’s cosmological model

I find the following new paper “Einstein’s steady-state model of the universe” very interesting. The authors present a translation and analysis of an unpublished manuscript by Albert Einstein in which he proposed a “steady-state” model of the universe. They show that the manuscript appears to have been written in early 1931, and demonstrate that Einstein once considered a cosmic model in which the mean density of matter in an expanding universe remains constant due to a continuous creation of matter from empty space, a process he associated with the cosmological constant. x

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Einstein, Hubble, Michelson, Campbell, Adams, and others. Einstein wrote the equation: Is Ricci tensor zero in all components? on the blackboard in the library of the Mount Wilson Observatory in Pasadena, California, Jan. 1931. Here

In 1922, Aleksandr Friedmann published a dynamical universe model. Friedmann discovered non-static models with a cosmological constant equal to zero or not equal to zero. This was a prediction of an expanding or a contracting universe of which Einstein’s (static) and de Sitter worlds were special cases. Friedmann’s model with a cosmological constant equal to zero was the simplest general relativity universe. See my paper

In 1929 Edwin Hubble announced the discovery that the actual universe is apparently expanding. In the years beyond 1930, the tide turned in favor of dynamical models of the universe. The discovery was hailed as fulfilling the prediction of general relativity. In January 1931 Einstein became aware of this revolution during a visit to Caltech in Pasadena. Einstein discussed his general theory of relativity and cosmological model at length with Richard Tolman and Hubble, and viewed the skies through the colossal telescope at Mount Wilson. Hubble accompanied Einstein while he examined evidence that demonstrated that the universe was expanding. Upon his return to Berlin the new experimental and theoretical findings have led Einstein to drop his old suggestions in favor of new ones, the dynamical universe. x

Einstein found that models of the expanding universe could be achieved without any mention of the cosmological constant. In April 1931 Einstein published his new findings in a short paper, “On the Cosmological problem of General Relativity”; in this paper he studied Friedmann’s non-static solution of the field equations of the general theory of relativity, of which the line element corresponded to a cosmological constant equal to zero. x

In an August 1931 paper De Sitter adopted this line element with a cosmological constant equal to zero. A few months later, on January 1932, when both De Sitter and Einstein were visiting Mount Wilson Observatory, they wrote a joint paper in which they presented the Einstein-De Sitter universe following Einstein’s lead without the cosmological term. See my paper

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Einstein writes the equation: Is Ricci tensor zero in all components? on the blackboard in the library of the Mount Wilson Observatory, Pasadena, California, Jan. 1931. here

The authors of the paper “Einstein’s steady-state model of the universe” found a new manuscript, according to which, in early 1931 Einstein proposed a ‘steady-state’ model of the universe. They claim that this model is in marked contrast to previously known Einsteinian models of the cosmos (both static and dynamic) but anticipates the well-known steady-state theories of Hoyle, Bondi and Gold. x

Hence, I assume that perhaps sometime between January 1931 (Einstein’s visit to Caltech) and March 1931, Einstein embarked on developing a “steady-state” model, but eventually renounced this idea; in April 1931 he adopted the line element with a cosmological constant equal to zero, Friedmann’s non-static solution. x

The authors of the paper, “Einstein’s steady-state model of the universe”, write that Einstein’s steady-state model contains a fundamental flaw and suggest it was discarded for this reason. x

It is reasonable to assume that Einstein had renounced the “steady-state” model before April 1931, and then he was ready to publish his April 1931 paper. Einstein dropped the cosmological term publicly and returned to the unmodified field equations of general relativity, and accepted Friedmann’s model with a cosmological constant equal to zero. x

Why did Einstein consider a “steady-state” model of the universe? it seems that the authors do not consider Mach’s principle. Einstein invented a finite and spatially closed static universe, bounded in space (and introduced the cosmological constant for this purpose), 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”, later called, “Mach’s principle”.

Mach’s Principle was of utmost importance to Einstein. Later Hermann Bondi and Thomas Gold came up with the idea of a steady-state theory of the expanding universe. They were fascinated by Mach’s principle, and spoke about the difficulties “concerned with the absolute state of rotation of a body. Mach examined this problem very thoroughly and all the advances in theory which have been made have not weakened the force of his argument. According to ‘Mach’s Principle’ inertia is an influence exerted by the aggregate of distant matter which determines the state of motion of the local frame of reference by means of which rotation of acceleration is measured…. …. The stationary character of the universe permits us to assume very strong interactions and yet to have permanent laws of nature. Only in this way can Mach’s principle be truly satisfied…” See my paper 

Albert Einstein Traveling with His Wife

(Iranian piece on Einstein)

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

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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

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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

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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

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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