## General Relativity without the Equivalence principle?

I have skimmed through this book Handbook of Spacetime:

The following represents my impressions formulated after reading the sections about the equivalence principle.

However, Einstein did not write this wonderful passage in the letter to Robert Lawson. Here is the letter to Lawson (Einstein to Lawson, 22 January 1920):

Einstein writes to Lawson in the above letter: “The article for Nature is almost finished, but it has unfortunately become so long that I very much doubt whether it could appear in Nature“. Indeed, in a 1920 unpublished draft of a paper for Nature, “Fundamental Ideas and Methods of the Theory of Relativity, Presented in Their Development”, Einstein wrote the above long paragraph describing him in 1907 sitting in the Patent Office. He was brooding on special relativity, and suddenly there came to him the happiest thought of his life:

Let us analyze this passage. The man in free fall (elevator experiments): Special relativity is incorporated into general relativity as a model of space-time experienced by an observer in free fall, over short times and distances (locally):

Between 1905 and 1907, Einstein tried to extend the special theory of relativity so that it would explain gravitational phenomena. He reasoned that the most natural and simplest path to be taken was to correct the Newtonian gravitational field equation. Einstein also tried to adapt the Newtonian law of motion of the mass point in a gravitational field to the special theory of relativity. However, he found a contradiction with Galileo’s law of free fall, which states that all bodies are accelerated in the gravitational field in the same way (as long as air resistance is neglected). Einstein was sitting on a chair in my patent office in Bern and then suddenly a thought struck him: If a man falls freely, he would not feel his weight. This was the happiest thought of his life. He imagined an observer freely falling from the roof of a house; for the observer there is during the fall – at least in his immediate vicinity – no gravitational field. If the observer lets go of any bodies, they remain relative to him, in a state of rest or uniform motion, regardless of their particular chemical and physical nature. The observer is therefore justified in interpreting his state as being (locally) at rest. Einstein’s 1907 breakthrough was to consider Galileo’s law of free fall as a powerful argument in favor of expanding the special principle of relativity to systems moving non-uniformly relative to each other. Einstein realized that he might be able to generalize and extend special relativity when guided by Galileo’s law of free fall. The Galilean law of free fall (or inertial mass is equal to gravitational mass) became known as the weak principle of equivalence.

Lewis Ryder explains: “Some writers distinguish two versions of the equivalence principle: the weak equivalence principle, which refers only to free fall in a gravitational field and is stated… as The worldline of a freely falling test body is independent of its composition or structure; and the strong equivalence principle, according to which no experiment in any area of physics should be able, locally, to distinguish a gravitational field from an accelerating frame”.

There are several formulations of the weak and the strong principles of equivalence in the literature. By far the most frequently used formulation of the strong principle of equivalence is Einstein’s 1912 local principle of equivalence: In a local free falling system special relativity is valid. (See my book General Relativity Conflict and Rivalries. Einstein’s Polemics with Physicists, 2015, for further details).

Nick Woodhouse explains:

in the chapter:

Hence Joshi says:

in the chapter:

Lewis Ryder

writes in the above paper:

(i.e. Einstein 1911 paper: “On the Influence of Gravitation on the Propagation of Light”). He formulates the equivalence principle in the following way: “In a freely falling (non-rotating) laboratory occupying a small region of spacetime, the local reference frames are inertial and the laws of physics are consistent with special relativity”. He then writes:

The equivalence principle enables us to find just one component g00 – of the metric tensor gmn. All components can be found (at least in principle) from the Einstein field equations. Ryder thus concludes that the equivalence principle is dispensable. I don’t quite agree with Ryder.

In my 2012 paper, “From the Berlin ‘Entwurf’ Field equations to the Einstein Tensor III: March 1916”, ArXiv: 1201.5358v1 [physics.hist-ph], 25 January, 2012 and also in my 2014 paper,  “Einstein, Schwarzschild, the Perihelion Motion of Mercury and the Rotating Disk Story”, ArXiv: 1411.7370v [physics.hist-ph], 26 Nov, 2014, I demonstrate the following:  On November 18, 1915, Einstein found approximate solutions to his November 11, 1915 field equations and explained the motion of the perihelion of Mercury. Einstein’s field equations cannot be solved in the general case, but can be solved in particular situations. Indeed, the first to offer an exact solution was Karl Schwarzschild. Schwarzschild found 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 11, 1915 paper. Schwarzschild sent Einstein a manuscript, in which he derived his exact solution of Einstein’s field equations. In January, 1916, Einstein delivered Schwarzschild’s paper before the Prussian Academy, and a month later the paper was published. In March 1916 Einstein submitted to the Annalen der Physik a review article, “The Foundation of the General Theory of Relativity”, on 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, Einstein preferred not to base himself on Schwarzschild’s exact solution, and he returned to his first order approximate solution from November 18, 1915. In the final part of the 1916 review paper Einstein demonstrated that a gravitational field changes spatial dimensions and the clock period:

This equation is further explained in my 2012 paper (page. 56):

Neither did Einstein use the Schwarzschild solution nor was he guided by the  equivalence principle. He was rather using an approximate solution and the metric, the line element to arrive at the same factor he had obtained by assuming the heuristic equivalence principle. He thus demonstrated that the equivalence principle was a fundamental principle of his theory, because in 1912 he formulated an equivalence principle valid only locally  (see my book: General Relativity Conflict and Rivalries. Einstein’s Polemics with Physicists, 2015, p. 184). I further explain it below.

Ryder then explains: The equivalence principle is local (a complete cancelation of a gravitational field by an accelerating frame holds locally). However, over longer distances two objects in free fall at different places in a realistic gravitational field move toward each other and this does not happen in an accelerating elevator. The cancelation of the gravitational field by an accelerating field is thus not complete. According to general relativity this effect (tidal effect) is a consequence of the curvature of space-time:

Although the equivalence principle might have been a heuristic guide to Einstein in his route to the fully developed theory of general relativity, Ryder holds that it is now irrelevant.

I don’t agree with Ryder’s conclusion which resembles that of John Lighton Synge (and Hermann Bondi). Indeed the equivalence principle is not valid globally (i.e. for tidal effects). Although the strong equivalence principle can at best be valid locally, it is still crucial for the general theory of relativity:

1. Einstein formulated an equivalence principle which is valid only locally. Special relativity is valid locally and space-time is locally the Minkowski space-time.
2. The principle of equivalence is fundamental for a metric theory and for our understanding of curved space-time: Freely falling test bodies move along geodesic lines under the influence of gravity alone, they are subject to an inertio-gravitational field . The metric determines the single inertio-gravitational field (affine connection), and there is breakup into inertia and gravitation relative to the acceleration. According to the equivalence principle, the components of the affine connection vanish in local frames. John Stachel quotes a passage from Einstein’s letter to Max von Laue:

Stachel, John, “How Einstein Discovered General Relativity: A Historical Tale with Some Contemporary Morals”, Einstein B to Z, 2002.

Indeed Ryder quotes J. L. Synge :

Einstein’s equivalence principle was criticized by Synge:

Synge, J. L. (1960). Relativity: The General Theory (Amsterdam, The Netherlands: North Holland Publishing Co).

And Hermann Bondi reacted to Einstein’s principle of equivalence:

Bondi also said (‘NO SUCCESS LIKE FAILURE …’: EINSTEIN’S QUEST FOR GENERAL RELATIVITY, 1907–1920, Michel Janssen):

Other authors contributing to the Handbook of Spacetime write the following:

Graham S. Hall in his paper:

writes the following:

“The choice of a geodesic path (Einstein’s principle of equivalence) reflects the results of the experiments of Eötvös and others, which suggest that the path of a particle in a pure gravitational field is determined by its initial position and initial velocity”. This is not Einstein’s equivalence principle. This is the Galilean principle of equivalence or the weak equivalence principle.

And according to Vesselin Petkov:

the geodesic line is indeed a manifestation of Galileo’s free fall law:

Ryder presents tests for the equivalence principle. The operation of the global positioning system, the GPS, is a remarkable verification of the time dilation. The GPS system consists of an array of 24 satellites, which describe an orbit round the earth of radius 27,ooo km, and are 7000 km apart, and every 12 hours travel at about 4km/s.  Each satellite carries an atomic clock, and the purpose is to locate any point on the earth’s surface. This is done by sensing radio signals between the satellites and the receiver on the earth, with the times of transmission and reception recorded. The distances are then calculated. Only three satellites are needed to pinpoint the position of the receiver on the earth. Relativistic effects must be taken into account arising both from special relativity (time dilation: moving clocks on the satellites run slower than clocks at rest on the surface of the earth) and from general relativity (gravitational time dilation/gravitational frequency shift: when viewed from the surface of the Earth, clocks on the satellites appear to run faster than identical clocks on the surface of the earth). The combined effect (the special relativistic correction and the general relativistic correction) is that the clocks on the satellites run faster than identical clocks on the surface of the earth by 38.4 microseconds per day. The clocks thus need to be adjusted by about 4 x 10-10s per day. If this factor is not taken into account, the GPS system ceases to function after several hours. This provides a stunning verification of relativity, both special and general.

Neil Ashby dedicates his paper to the GPS:

and gives a critical reason why the equivalence principle is indeed relevant. Consider again the GPS (global positioning system) or generally, Global navigation satellite systems (GNNS). For the GPS or GNNS, the only gravitational potential of significance is that of the earth itself. The earth and the satellites fall freely in the gravitational field of the sun (and external bodies in the solar system). Hence, according to the equivalence principle one can define a reference system which is locally very nearly inertial (with origin at the earth’s center of mass). In this locally inertial coordinate system (ECI) clocks can be synchronized using constancy of the speed of light (remember that special relativity is incorporated into general relativity as a model of space-time experienced locally by an observer in free fall):

One writes an approximate solution to Einstein’s field equation and obtains that clocks at rest on earth

run slow compared to clocks at rest at infinity by about seven parts in 1010.

Unless relativistic effects on clocks [clock synchronization; time dilation, the apparent slowing of moving clocks (STR); frequency shifts due to gravitation, gravitational redshift(GTR)] are taken into account, GPS will not work. GPS is thus a huge and remarkable laboratory for applications of the concepts of special and general relativity. In addition, Shapiro signal propagation delay (an additional general relativistic effect) and spatial curvature effects are significant and must be considered at the level of accuracy of 100 ps of delay. Ashby mentions another effect on earth that is exactly cancelled:

Wesson in this paper:

presents the standard explanation one would find in most recent textbooks on general relativity:

The Christoffel symbols are also used to define the Riemann tensor, which encodes all the relevant information about the gravitational field. However, the Riemann tensor has 20 independent components, and to obtain field equations to solve for the 10 elements of the metric tensor requires an object with the same number of components. This is provided by the contracted Ricci tensor. This is again contracted (taking its product with the metric tensor) to obtain the Ricci curvature scalar.  This gives a kind of measure of the average intensity of the gravitational field at a point in space-time. The combination of the Ricci tensor and the Ricci scalar is the Einstein tensor and it comprises the left hand-side of Einstein’s field equations.

At every space-time point there exist locally inertial reference frames, corresponding to locally flat coordinates carried by freely falling observers, in which the physics of general relativity is locally indistinguishable from that of special relativity. In physics textbooks this is indeed called the strong equivalence principle and it makes general relativity an extension of special relativity to a curved space-time.

Wesson then writes that general relativity is a theory of accelerations rather than forces and refers to the weak equivalence principle:

As said above, Einstein noted that if an observer in free fall lets go of any bodies, they remain relative to him, in a state of rest or uniform motion, regardless of their particular chemical and physical nature. This is the weak principle of equivalence: The worldline of a freely falling test body is independent of its composition or structure. The test body moves along a geodesic line. The geodesic equation is independent of the mass of the particle. No experiment whatsoever is able, locally, to distinguish a gravitational field from an accelerating system – the strong principle of equivalence (see Ryder above). A freely falling body is moving along a geodesic line. However, globally space-time is curved and this causes the body’s path to deviate from a geodesic line and to move along a non-geodesic line. Hence we speak of geodesics, manifolds, curvature of space-time, rather than forces.

José G. Pereira explains the difference between curvature and torsion (and force) (see paper here):

General relativity is based on the equivalence principle and geometry (curvature) replaces the concept of force. Trajectories are determined not by force equations but by geodesics:

How do we know that the equivalence principle is so fundamental?  Gravitational and inertial effects are mixed and cannot be separated in classical general relativity and the energy-momentum density of the gravitational field is a pseudo-tensor (and not a tensor):

General relativity is grounded on the equivalence principle. It includes the energy-momentum of both inertia and gravitation:

In 1928 Einstein proposed a geometrized unified field theory of gravitation and electromagnetism and invented teleparallelism. Einstein’s teleparallelism was a generalization of Elie Cartan’s 1922 idea.

According to Pereira et al: “In the general relativistic description of gravitation, geometry replaces the concept of force. This is possible because of the universal character of free fall, and would break down in its absence. On the other hand, the teleparallel version of general relativity is a gauge theory for the translation group and, as such, describes the gravitational interaction by a force similar to the Lorentz force of electromagnetism, a non-universal interaction. Relying on this analogy it is shown that, although the geometric description of general relativity necessarily requires the existence of the equivalence principle, the teleparallel gauge approach remains a consistent theory for gravitation in its absence”.

See his paper with R. Aldrovandi and K. H. Vu: “Gravitation Without the Equivalence Principle”, General Relativity and Gravitation 36, 2004, 101-110.

Petkov explains in his paper: (see further above)

the following:

The bottom line is that classical general relativity is fundamentally based on the equivalence principle. One cannot reject Einstein’s route to the theory of general relativity.

## My work has been plagiarized at the Century of General Relativity conference

The comparison between the original, my work, and citations from Prof. Gutfreund’s talk will speak for itself.

Professor Hanoch Gutfreund’s lecture presented Einstein’s road to general relativity (the genesis of general relativity) and the formative years of general relativity (a term coined by Prof. Gutfreund and Prof. Jürgen Renn). Six times he lifted ideas, phrases and lines from my work.

1. Einstein does not use the Schwarzschild Solution in his 1916 Review Paper.

Professor Gutfreund speaks about things Einstein could have done: “He could have done it… we know that he could have done it”. In this respect he mentions Einstein and the Schwarzschild solution:

“Another thing which he could have done. So he already knew the Schwarzschild solution, because the Schwarzschild correspondence is in December. He wrote this paper [review paper, 1916] later. He submitted it only in March. So he could have used this Schwarzschild solution who showed a simpler derivation of the motion of the perihelion and of the bending of light and he did not do it”.

It seems Prof. Gutfreund have picked the above passage from my 2012 paper, “From the Berlin ‘Entwurf’ Field equations to the Einstein Tensor III: March 1916”, ArXiv: 1201.5358v1 [physics.hist-ph], 25 January, 2012:

Einstein’s 1916 Equations:

In addition, the above passage from prof. Gutfreund’s speech had been previously explained in great detail in my paper, “Einstein, Schwarzschild, the Perihelion Motion of Mercury and the Rotating Disk Story”, published in 2014. A year before Prof. Gutfreund’s lecture at the Century of General Relativity conference in Berlin, I wrote in the abstract of my paper, “Einstein, Schwarzschild, the Perihelion Motion of Mercury and the Rotating Disk Story”, ArXiv: 1411.7370v [physics.hist-ph], 26 Nov, 2014:

“On November 18, 1915 Einstein reported to the Prussian Academy that the perihelion motion of Mercury is explained by his new General Theory of Relativity: Einstein found approximate solutions to his November 11, 1915 field equations. Einstein’s field equations cannot be solved in the general case, but can be solved in particular situations. The first to offer such an exact solution was Karl Schwarzschild. Schwarzschild found 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. On December 22, 1915 Schwarzschild told Einstein that he reworked the calculation in his November 18 1915 paper of the Mercury perihelion. Subsequently Schwarzschild sent Einstein a manuscript, in which he derived his exact solution of Einstein’s field equations. On January 13, 1916, Einstein delivered Schwarzschild’s paper before the Prussian Academy, and a month later the paper was published. In March 1916 Einstein submitted to the Annalen der Physik a review article on 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. Einstein preferred in his 1916 paper to write his November 18, 1915 approximate solution upon Schwarzschild exact solution (and coordinate singularity therein).”

I demonstrate in my paper that in his 1916 review paper, “The Foundation of the General Theory of Relativity”, Einstein used Huygens principle and the first order approximate solution to his vacuum field equations from the November 18, 1915 perihelion of Mercury paper to derive bending of light, the deflection of a ray of light passing by the sun. I end my paper by saying: “Einstein ended his paper with the final equation from his November 18 paper, the equation for the perihelion advance of Mercury in the sense of motion after a complete orbit. And he only mentioned in a footnote, ‘With respect to the calculation, I refer to the original treatments’: Einstein’s November 18 paper and Schwarzschild’s 1916 paper”. Here are two paragraphs from my own paper:

I wrote above: “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 (8) 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 (6) from his November 18, 1915 paper”.

Einstein preferred in his 1916 review paper to write his November 18, 1915 approximate solution upon the Schwarzschild exact solution because he objected to the “Schwarzschild singularity”. Einstein repeatedly spoke against the Schwarzschild singularity and stated the impossibility of the Schwarzschild singularity.

2. Einstein and the Riemann tensor.

In his talk Professor Gutfreund concentrated on Einstein’s mistakes. In describing Einstein’s mistakes prof. Gutfreund said:

“The Riemann tensor is not a tensor of curvature. There is no affine connection. There is no parallel transport, all that, all the geometrization that is the trademark of the whole theory, that was not a presupposition that led him to the final results. He could have done it, maybe in another step. How could we know that he could have done it?

In 1914 he wrote another review article that was the review article of the Entwurf theory, a long article, he wrote it when he was confident that this was the correct theory; and there where he gets to the point where he has to explain covariant differentiation, he makes a remark: I know that Levi-Civita told us how to do it this way, but I prefer to do it differently, and this differently is abominable. I can tell you. If you look at the text how it is done, and when he did his 1916 review [article] he followed almost word by word except in that chapter where the new Lagrangian has to appear, except there he followed exactly what he did, so he could have done it”.

To begin with, this explanation combines two unrelated elements. The second part of the above passage seems to represent incorrectly a paragraph from my 2012 paper, “From the Berlin ‘Entwurf’ Field equations to the Einstein Tensor II: November 1915 until March 1916”, ArXiv: 1201.5353v1 [physics.hist-ph], 25 January, 2012. In 2012 I sent this paper to prof. Gutfreund.

The opening remarks of my paper, “From the Berlin ‘Entwurf’ Field equations to the Einstein Tensor II: November 1915 until March 1916” (pp. 1-2), deal with Einstein’s 1914 review article and the comment he later made. Einstein had published a comprehensive review article dealing with his Entwurf  theory. On page 1041, he presented the Ricci tensor. On pages 1042 he found a problem with the Ricci tensor. Evidently he did not yet realize that the solution was to restrict himself to unimodular transformations. On page 1053 he presented the Riemann-Christoffel tensor. He did not use this tensor in his 1914 Entwurf field equations. That was the reason why the presentation of this tensor in 1914 was very brief. Of course the reason was also page 1041. In his first talk on the general theory of relativity (November 4, 2015), Einstein postulated that only unimodular transformations were allowed. This solved the problem with the 1914 Ricci tensor (page 1041). He wrote the Riemann-Christoffel tensor, obtained the Ricci tensor G and a gravitational tensor R. The field equations were restricted to unimodular transformations. He then wrote the following remark: the Ricci and Levi-Civita fundamental tensor of page 1041 could be written in a different form, it could be obtained from the Riemann-Christoffel tensor. He explained that he had given this proof in his 1914 paper on page 1053 and had followed this root in 1912 in the Zurich Notebook. Hence, Einstein made the remark (comment) – not in the 1914 Entwurf paper – but rather in the November 4, 1915 paper; and the remark referred to the field equations formulated in a non-Lagrangian form. I explain this in my 2012 paper:

The first part of Prof. Gutfreund’s explanation represents Prof. John Stachel’s memorable phraseology, the importance of “the affine connection”. Prof. Stachel explains that until 1912, Einstein lacked the Riemanian geometry and the tensor calculus as developed by the turn of the century, i.e., based on the concept of the metric tensor; and after 1912 when he was using these, he then lacked more advanced mathematical tools (the affine connection); these could be later responsible for inhibiting him for another few years. Judged from the historical point of view of his time, Einstein did not make a mistake, because he lacked the appropriate mathematical tools. Actually with hindsight the story is more complicated. What was eventually mere coincidence for Einstein would later turn to be a consequence derived by new mathematical tools, the affine connection, which was invented after Einstein had arrived at generally covariant field equations. (See Stachel, John, Einstein from ‘B’ to ‘Z’, 265, 304-306.

The above explanation is from my paper: “Einstein’s 1912-1913 struggles with Gravitation Theory: Importance of Static Gravitational Fields Theory”, ArXiv: 1202.2791v1 [physics.hist-ph], 13 February, 2012, p. 20):

Finally, following the November 4, 1915 field equations, Einstein wrote the 1914 Entwurf Lagrangian and adjusted in 1915 and in 1916 his Entwurf 1914 variational formalism. In section 12 of the 1916 review article, Einstein started from the 1914 equations he had written on page 1053, he contracted the Riemann-Christoffel tensor and obtained the Ricci tensor and the field equations in unimodular coordinates; he also wrote the field equations in Lagrangian form.

In my 2012 paper, “From the Berlin ‘Entwurf’ Field equations to the Einstein Tensor III: March 1916”, ArXiv: 1201.5358v1 [physics.hist-ph], 25 January, 2012, I pinpoint the differences and similarities between Einstein’s first 1914 review paper and second 1916 review paper, “The Foundation of the General Theory of Relativity”. I discuss the differences and similarities among Einstein’s 1914 and 1916 formulations and Einstein’s 1916 manuscript “The Foundation of the General Theory of Relativity” and 1916 review paper, “The Foundation of the General Theory of Relativity”.

3. Friedmann’s model and Einstein’s reaction to it.

Towards the end of his lecture, “100 years of General Relativity – What are we Celebrating?”, prof. Gutfreund lifted phrases from my 2013 paper, “The Mythical Snake which Swallows its Tail: Einstein’s matter world”, ArXiv: 1309.6590v [physics.hist-ph], 26 Sep. 2013.

In 1922, Alexander Friedman published a model of an expanding universe. Einstein was not satisfied with this model and replied by a note; he thought he found a mistake in Friedmann’s results, which when corrected Friedmann’s solution would give Einstein’s good old static model. Friedmann sent Einstein his calculations and asked him to publish a correction to his statement. Einstein was willing to correct the slip in his previous note. Prof. John Stachel discovered that in the draft to the note to the editor Einstein wrote something quite different.

Prof. Gutfreund explained in his lecture:

“But here we have you see the letter, the letter to the editor, the angry letter. You see the last sentence is crossed out. So I will tell you what is it the last sentence. The last sentence says ‘It follows that the field equations, besides the static solution’, there are such static solution and so on. But then what is crossed out is ‘but a physical significance can hardly be attributed to them’.”.

And Professor Gutfreund showed the following slide:

“It follows that the field equations, besides the static solutions, permit dynamic (that is varying with time coordinates) spherically symmetric solutions for the spatial structure. He added the words: ‘but a physical significance can hardly be ascribed to them’, which he crossed out before sending the note to the editor”.

I see phrases here that come from my work and Prof. Stachels’ bookEinstein from B to Z, 2002, for which there is no attribution. I recognize my own words: “but a physical significance can hardly be ascribed to them”.

Prof. Stachel wrote: “to which a physical significance can hardly be ascribed”. Hence, prof. Gutfreund did not even bother to read prof. Stachel’s original paper; he simply lifted phrases from my paper. His above citation and slide contain exact words from my own published paper but he does not give attribution to me. I wrote in my paper, “The Mythical Snake which Swallows its Tail: Einstein’s matter world” the following:

Therefore, in my paper, “The Mythical Snake which Swallows its Tail: Einstein’s matter world”, I wrote the following (pp. 39-40):

“Einstein was willing to correct the slip in his previous note: ‘In my previous note I have criticized the cited work [Friedmann’s 1922 work, ‘On the curvature of Space’], but my objection, as I became convinced by Friedmann’s letter communicated to me by Mr. Krutkov, rested on an error in my calculations. I consider that Mr. Friedmann’s results are correct and shed new light. It follows that the field equations, besides the static solution, permit dynamic (that is, varying with the time coordinate) spherically symmetric solutions for the spatial structure’. 126

Endnote 126 sends the reader to Einstein’s original paper in German and to the following reference: Tropp, Eduard A., Frenkel, Viktor Ya. and Chernin, Artur D., Alexander A Friedmann: The Man who Made the Universe Expand, Cambridge: Cambridge University Press, 1993. In this book one finds a translation of the relevant paragraph of Einstein’s paper into English:

However, in my paper, “The Mythical Snake which Swallows its Tail: Einstein’s matter world”, I have changed this translation. For instance I make a mistake and write: “In my previous note I have criticized”… Prof. Gutfreund reproduces my awkward translation and not the above translation.

In fact, Einstein was little impressed by Friedmann’s mathematical models. In Einstein’s draft of the second note to the Zeitschrift für Physik, in which he withdrew his earlier objection to Friedmann’s dynamical solutions to the field equations, he crossed-out the final last section of the sentence, ‘a physical significance can hardly be ascribed to them’, before sending the note to the editor of the Zeitschrift für Physik, thus Einstein originally wrote in the draft: ‘It follows that the field equations, besides the static solution, permit dynamic (that is, varying with the time coordinate) spherically symmetric solutions for the spatial structure, but a physical significance can hardly be ascribed to them’.127”.

I placed the endnotes at the end of my paper. Footnotes and endnotes are a bother to read and are rarely read. People abstain from reading endnotes. However, endnote 126 refers to Einstein’s (German) paper and to the above said translation and endnote 127 in the above passage refers to the paragraph from Prof. Stachel’s paper, “Eddington and Einstein”, Einstein from ‘B’ to ‘Z’, p. 469:

Prof. Stachel writes:

“Friedmann’s paper came to Einstein’s attention. He thought he had found a mathematical flow in Friedmann’s argument, and said so in print. When he became convinced that the error was his not Friedmann’s, he retracted his mathematical objection, but stuck to his static cosmological model. How little impressed he was by Friedmann’s models can be seen from the final clause of his draft retraction, which (fortunately for him) Einstein deleted before it was printed:

It follows that the field equations, besides the static solution, permit dynamic (that is, varying with the time coordinate) spherically symmetric solutions for the spatial structure, [to which a physical significance can hardly be ascribed.],

The bracketed portion being crossed out in the manuscript”.

Compare prof. Gutfreund’s slide to the passage from my 2013 paper. Professor Gutfreund uses my phrases verbatim in his slide with no citation:

Surely prof. Gutfreund did not read my endnote 127, otherwise he would have mentioned prof. John Stachel’s paper in his lecture, because when there is acknowledgment in prof. Gutfreund’s talk, the impression is of a wholesale attribution to prof. Jürgen Renn and other notable Einstein scholars. This is far from being the only sources for professor Gutfreund’s lecture. Indeed, in his lecture he mentions prof. John Stachel’s paper on Hilbert’s competition with Einstein (priority dispute) written with prof. Jürgen Renn and prof. Leo Corry, while discussing Einstein’s competition with David Hilbert:

“He was concerned that he will be outrun, and was concerned that he will be outrun by David Hilbert; and the question is who gets there first. Now had Einstein read the article by Jürgen Renn, and John Stachel and Leo Corry, he wouldn’t have to worry”.

4. Demarcation between “Mach’s idea” and ‘Mach’s principle”

After presenting the genesis of general relativity, prof. Gutfreund briefly reviewed Mach’s principle. Here I highlight what I see as plagiarized demarcation between “Mach’s idea” and “Mach’s principle”. This demarcation is found in my 2013 paper, “The Mythical Snake which Swallows its Tail: Einstein’s matter world” and in my 2012 paper “Einstein’s 1912-1913 struggles with Gravitation Theory: Importance of Static Gravitational Fields Theory”. I also briefly discuss this matter in my first book, Einstein’s Pathway to the Special Theory of Relativity.

In his lecture Prof. Gutfreund explained:

“So this is a great Challenge, this is what happens, so he talks about the general theory of relativity and that he writes after visiting De Sitter in Leiden. Now at the outset I want to tell you that everything that Einstein did in those years in this context and in other until 1929, and maybe over, it was a little longer, was to defend his strong belief in Mach’s criticism of Newton. Mach’s criticism, I mean there is no absolute space, all inertial effects are due to all the masses in the universe, there is no inertia, except determined by all the masses of the universe. This is Mach’s idea. I am not calling it a principle yet. This is Mach’s idea ….”

When prof. Gutfreund explained the difference between Mach’s idea and Mach’s principle, he raised his hand and pointed his finger to the audience:

Professor Gutfreund then spoke about Einstein’s exchange of letters with de Sitter, Felix Klein and Hermann Weyl and said:

“And then Einstein makes a bold step. He elevates Mach’s idea into a principle. No longer a property of the theory, but a property of an acceptable solution. Only solutions which satisfy Mach are physically acceptable”.

And he showed the following slide:

In my 2013 paper, “The Mythical Snake which Swallows its Tail: Einstein’s matter world”, I demarcated between “Mach’s ideas” and “Mach’s Principle”:

I Therefore write:

“Einstein desired to eliminate what he called the “epistemological weakness” [“erkenntnistheoretischen Schwächen”] of Newtonian mechanics, the absolute space, from physics; he invented a world, finite and spatially closed static universe, bounded in space, 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” (obviously not Ernst Mach’s ideas as has been generally recognized and as Mach himself pronounced them). This would be later called by Einstein “Mach’s principle” (more precisely Mach-Einstein principle)”.

In my 2012 paper “Einstein’s 1912-1913 struggles with Gravitation Theory: Importance of Static Gravitational Fields Theory”, I explain on page 22 the difference between “Mach’s idea” and Mach’s principle”:

I therefore write:

“Einstein ended section §1 with the conclusion that the momentum and kinetic energy are inversely proportional to c. Or, the inertial mass is m/c and independent of the gravitational potential.116 This conforms to Mach’s idea that inertia has its origin in an interaction between the mass point under consideration and all of the other mass points. Einstein explained that if other masses are accumulated in the vicinity of the mass point, the gravitational potential c decreases. And then the quantity m/c increases which is equal to the inertial mass. In the static fields theory Einstein presented the predecessor to Mach’s principle.117“.

In my book, Einstein’s Pathway to the Special Theory of Relativity I again say:

Prof Gutfreund says: “So this is a great Challenge, this is what happens, so he talks about the general theory of relativity and that he writes after visiting De Sitter in Leiden. … And then Einstein makes a bold step. He elevates Mach’s idea into a principle. No longer a property of the theory, but a property of an acceptable solution. Only solutions which satisfy Mach are physically acceptable”. And he presents the above slide.

In my paper, “The Mythical Snake which Swallows its Tail: Einstein’s matter world” I wrote the following:

5. Besso as Einstein’s Sounding Board

Quite at the beginning of his lecture, “100 years of General Relativity – What are we Celebrating?”, prof. Gutfreund borrowed passages from my 2012 paper, “Albert Einstein’s Methodology”. Prof Gutfreund said in his lecture:

“Einstein with his very good friend usually a sounding board, in this case, a collaborator, in this case when they worked together. Usually he was Einstein’s sounding board. They wrote… the Einstein-Besso manuscript… and in that document they calculated the perihelion motion”.

My own words in “Albert Einstein’s Methodology” are:

The Philosophy of Science Portal added a link to my paper, “Albert Einstein’s Methodology”.

Hence, in my 2012 paper, “Albert Einstein’s Methodology”, ArXiv: 1209.5181v1 [physics.hist-ph], 25 September, 2012, I write:

“Later in 1913 Besso came to Zurich and actively participated in solving the Einstein-Grossman (‘Entwurf’) gravitation equations with Einstein. They both tried to find solutions to the problem of the advance of the perihelion of Mercury. The young Einstein may have considered Besso as his sounding board, but was Besso still Einstein’s sounding board in 1913?”

I explain in my paper that in 1913, Besso still functioned as Einstein’s sounding board while they were both working on the Einstein-Besso manuscript:

“Indeed when Einstein wrote Besso a series of letters between 1913 and 1916, and described to him step by step his discoveries of General Relativity, Besso indeed functioned again as the good old sounding board as before 1905”.

I also wrote about Besso in my book, Einstein’s Pathway to the Special Theory of Relativity, April 2015:

Therefore, in my book, Einstein’s Pathway to the Special Theory of Relativity (Newcastle, UK: Cambridge Scholars Publishing), April 2015, I have dedicated a whole chapter to Einstein’s “sounding boards”. In the section explaining Michele Besso’s role as Einstein’s sounding board I write:

“Even in 1913, Besso was still Einstein’s sounding board. In June 1913, Besso visited Einstein in Zurich and actively participated in solving the Einstein-Grossmann Entwurf gravitation equations with Einstein. They both tried to find solutions to the problem of the advance of mercury’s perihelion in the field of a static sun. Their join work is known as the Einstein-Besso manuscript”.

Prof. John Stachel was the first to show that Michele Besso acted as Einstein’s sounding board. The need to put ideas into communicable form led Einstein to search throughout his early life for people to act as sounding boards for his ideas. See his book: Einstein’s Miraculous Year. Five Papers that Changed the Face of Physics (Princeton: Princeton University Press). Following discussions with prof. Stachel I have extended his ideas into the above expression.

I really hoped that some conference would ask me to give a talk about my work, “Albert Einstein’s Methodology”. I thought I had a philosophical paper worth talking about at a conference. Obviously, now that prof. Gutfreund lifted my unique expression of prof. Stachel’s idea of sounding boards from this paper there is no point presenting it at a conference.

6. Cosmological Constant Biggest blunder

A thread that runs through Professor Gutfreund’s entire talk is that Einstein had made many mistakes on his road to general relativity and cosmological model. Towards the end of his talk prof. Gutfreund mentions Einstein’s biggest mistake:

“But you know there is this Myth that Einstein when he abandoned the cosmological constant he said this is the worst error that I made. There is no evidence for that. Probably he never said that”.

In prof. Gutfreund’s book with prof. Jürgen Renn, The Road to Relativity, prof. Gutfreund further explains this:

Compare the above paragraph from prof. Gutfreund’s book The Road to Relativity to the abstract of my 2013 paper, “George Gamow and Albert Einstein: Did Einstein say the cosmological constant was the “biggest blunder” he ever made in his life?”, ArXiv: 1310.1033v [physics.histph], 03 Oct, 2013:

And compare the penultimate paragraph from prof. Gutfreund’s book The Road to Relativity to two paragraphs from my paper, “George Gamow and Albert Einstein: Did Einstein say the cosmological constant was the ‘biggest blunder’ he ever made in his life?”:

In 2016 I received this message from ResearchGate:

My paper gained traffic but no citations, but prof. Gutfreund, who plagiarized the abstract of my paper, received the citations. Allen I. Janis writes in his review: “The Road to Relativity: The History and Meaning of Einstein’s ‘The Foundation of General Relativity’.” American Journal of Physics 84, 2016:

“An interesting sideline in this chapter has to do with the frequently heard story that Einstein called his introduction of the cosmological constant the biggest mistake of his life. It seems there is no evidence that Einstein ever said or wrote this, and that it is in fact an invention of George Gamow”.

The audience of prof. Gutfreund’s lecture, “100 Years of General Relativity – What Are We Celebrating?”, consisted of top experts and known professors in my field. They clapped and cheered when he finished to speak. They seemed to like his lecture. I wish they knew that parts of professor Hanoch Gutfreund’s lecture were based on my papers and I worked so hard to write them.

7. David Hume and Ernst Mach’s influence on Einstein

At the Thursday round table speech Prof. Gutfreund seems to also lifted something from my 2013 paper, “The Mythical Snake which Swallows its Tail: Einstein’s matter world”. At the Berlin MPIWG conference round table discussion about general relativity, professor Gutfreund explained:

“But then in his [Einstein’s] Autobiographical Notes his most, I mean this is for the philosophers of science here, may be his most blant [blatant], most explicit departure from empiricism, you know until almost end he always mentions Mach together with Hume. The two of them who showed him the way to general relativity. I quote”.

“I mean this is for the philosophers of science here”, Prof. Gutfreund said while pointing to where the philosopher of science prof. Yemima Ben Menahem was sitting.

It is fairly obvious that the explanation about Hume and Mach showing Einstein the way to general relativity was either lifted from my 2013 paper, “The Mythical Snake which Swallows its Tail: Einstein’s matter world” or from my book, Einstein’s Pathway to the Special Theory of Relativity.

Hume and Mach showing Einstein the way to general relativity is a mistake in my 2013 paper which prof. Gutfreund seems to have reproduced in his round table discussion. Actually, in 1949 Einstein explicitly expressed in his Autobiographical Notes an intellectual debt to Hume and Mach’s philosophical writings in his discovery of special relativity. However, in my 2013 paper, “The Mythical Snake which Swallows its Tail: Einstein’s matter world”, I wrote about Hume’s influence on the elder Einstein and I said that Hume’s influence on Einstein was greater than Mach’s ideas (general relativity and cosmology):

I thus write:

“The elder Einstein could not remember how far Mach’s writings have influenced his work in the same way as could the young Einstein who was inspired by Mach’s ideas when creating the general theory of relativity. Indeed the elder Einstein often wrote that the influence of David Hume was greater on him. Finally, a year before his death Einstein silently dropped Mach’s principle in itself”.

The philosophy of Hume and Mach had an important influence on Einstein’s development and discovery of special relativity. Mach’s ideas about the relativity of inertia influenced Einstein on his road to general relativity. If Professor Gutfreund “quotes”, then I shall quote as well. Einstein writes in his Autobiographical Notes (1949, p. 53):

“One sees that in this paradox [of Einstein chasing a light beam] the germ of the special relativity theory is already contained. Today everyone knows, of course, that all attempts to clarify this paradox satisfactorily were condemned to failure as long as the axiom of the absolute character of time, or of simultaneity, was rooted unrecognized in the unconscious. To recognize clearly this axiom and its arbitrary character already implies the essentials of the solution of the problem. The type of critical reasoning required for the discovery of this central point was decisively furthered, in my case, especially by the reading of David Hume’s and Ernst Mach’s philosophical writings”.

However, in my first book, Einstein’s Pathway to the Special Theory of Relativity, on page 292, I tried to correct my mistake in my 2013 paper, and I combined the influence of David Hume’s and Ernst Mach’s philosophy on Einstein with Mach’s ideas and Mach’s principle:

I therefore write in my book:

“The older Einstein could not remember how far Mach’s writings influenced his work in the same way as could the young Einstein who was inspired by Mach’s ideas when creating the theory of relativity. Indeed, the older Einstein often wrote that David Hume was a greater influence on him. We should remember that in 1948 Einstein saw Mach’s weakness in his belief more or less that science consists in the mere “ordering” of empirical material. Mach, according to Einstein, misjudged the free constructive element in the formation of concepts. He believed that in some sense theories arise by discovery and not invention (Einstein to Besso, January 6, 1948, Einstein and Besso 1971, Letter 153; see Section 1.1). Finally, a year before his death, Einstein silently dropped Mach’s principle in itself…”.

Prof. Gutfreund seems to have combined in his round table discussion my mistake from 2013 and the above so-called correction.

8. Einstein and Poincare.

Finally, it is not the first time that prof. Gutfreund has endorsed my ideas and presented them as his own. In August 2015, at the World Science Conference – Israel (WSCI), young students from all around the world and 15 Nobel laureates were invited to the WSCI conference. Prof. Gutfreund was part of a panel discussion at the WSCI conference on “Eureka moment!”. He happened to be sitting next to Nobel Laureates prof. Arieh Warshel, prof. Harold Kroto and prof. Sidney Altman. Later the Lectures and panels were uploaded to the website of the homepage of the WSCI conference.

I heard prof. Gutfreund speaking about Einstein’s 1916 interview (“exchange of readers” [letters]) with Max Wertheimer. He told the audience about Einstein describing to Wertheimer how the theory of general relativity occurred to him. Actually Wertheimer discussed with Einstein the development of his special theory of relativity and not the genesis of general relativity and the road to general relativity. Prof. Gutfreund spoke about Einstein’s creativity and Poincaré’s creativity and his Eureka moment, something he had read in my book, Einstein’s Pathway to the Special Theory of Relativity. He told the story of Poincaré who could not find the solution to his problem. Poincaré then took part in an excursion. The events of the trip made him forget his mathematical work. He entered a bus; the moment he put his foot on the step, the idea came to him, without anything in his former thoughts seeming to have prepared him for it.

Prof. Gutfreund told the audience the following, here is the citation from his lecture:

“Einstein had a very close friendly relationship with Max Wertheimer. Max Wertheimer is one of the founding fathers of gestalt psychology, and they exchanged readers [letters]. Max Wertheimer even wrote a book about creativity and they explored this idea of creativity and debation [debated] time, and then this ha-moment according, so I mean the classical example of an ha-moment again according to his, to Einstein’s testimony is this happiest thought in retrospect. There is another ha-moment, because you see, a ha-moment and Eureka does not have always to be something which turns out to be correct. Einstein had an ha-moment in something which turned out completely wrong at the end, that is something I refer to, one day he writes to Lorentz and this I have a theory which is a dark spot there and the next day he writes I am now completely satisfied that this is true. But that was completely wrong. But the person who really discussed it is another physicist, a polyglot of science and that is Poincaré, and Poincaré describes an ha-moment he was troubling with his idea whether it should be Lobachevski’s geometry, this kind of geometry, Euclidean geometry, and suddenly he gets on a bus and he describes the moment when he puts his foot on the step of the bus and suddenly it all comes to him and he runs home and writes it all. So you don’t have to run naked in the streets in an ha-moment. There are all kind of…”.

Compare this to the following several paragraphs from my own book, Einstein’s Pathway to the Special Theory of Relativity, April 2015. Prof. Gutfreund has lifted the Einstein-Wertheimer-creativity-Poincaré bus story discussion from my own book:

Fools had ne’er less wit in a year, For wise men are grown foppish. They know not how their wits to wear, Their manners are so apish. King Lear, Act 1, scene 4.

FIN

## Men Explain Einstein to Me

If you are a woman, a man has probably at some point explained to you something about the area of your expertise. Rebecca Solnit tells about her own experience with a man who tried to explain (mansplain) a book she wrote to her.

Mansplainers usually assume you know less than you do because of your gender. Advices.

Stories.

On March 14 the official Albert Einstein Facebook wall hosted Dr. Debbie Berebiches. This was a Facebook Live Event celebrating Einstein’s birthday. Dr. Berebiches answered questions about Einstein (I haven’t listened to her, I am sorry). Dr. Berebiches is the first Mexican woman to graduate with a Ph.D in physics from Stanford University. Yesterday an Israeli hi-tech veteran explained to her what was “the main contribution of general relativity to GPS”, a topic she clearly knows more about than him. She gave him a like and this was absolutely the right thing to do.

He then explained things to me, about Einstein’s religion. I am terribly sorry. I may not be the number one expert in Einstein’s philosophy of religion and personal views… well not that he is a great expert in this topic. Subsequently he asked me: “Have you read anything Einstein wrote in German? How about the dice quote? How about general relativity? …” and gave me advices:

In fact I read many papers and manuscripts in German and when I wake up in the middle of a dream at night, I think I was speaking German to Albert Einstein in my dream.

I could have stumped him but I preferred not to do this and not to discuss these matters further with him. I don’t believe mansplainers will ever change. Hence, it is better not to stump them and simply ignore them and avoid arguing with them on the area of your expertise. A mansplainer’s advice is unsolicited so you are under no obligation to listen. Advice.

Einstein expressed his religious views in 1922:

and he also expressed his views in 1930:

## 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.

“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.

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:

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.

## 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 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.

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.

Albert Einstein at the Patent office

Mileva Marić and Einstein

Eduard Tete, Mileva Marić and Hans Albert

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”.

Henri Poincaré’s possible influence on Einstein’s road to the special theory of relativity.

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.

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.

My books

## Some of the topics discussed in my new book General Relativity Conflict and Rivalries

General Relativity Conflict and Rivalries: Einstein’s Polemics with Physicists:

This book focuses on Albert Einstein and his interactions with, and responses to, various scientists, both famous and lesser-known. It takes as its starting point that the discussions between Einstein and other scientists all represented a contribution to the edifice of general relativity and relativistic cosmology. These scientists with whom Einstein implicitly or explicitly interacted form a complicated web of collaboration, which this study explores, focusing on their implicit and explicit responses to Einstein’s work.

This analysis uncovers latent undercurrents, indiscernible to other approaches to tracking the intellectual pathway of Einstein to his general theory of relativity. The interconnections and interactions presented here reveal the central figures who influenced Einstein during this intellectual period. Despite current approaches to history presupposing that the efforts of scientists such as Max Abraham and Gunnar Nordström,  which differed from Einstein’s own views, be relegated to the background, this book shows that they all had an impact on the development of Einstein’s theories, stressing the limits of approaches focusing solely on Einstein. As such, General Relativity Conflict and Rivalries proves that the general theory of relativity was not developed as a single, coherent construction by an isolated, brooding individual, but, rather, that it came to fruition through Einstein’s conflicts and interactions with other scientists, and was consolidated by his creative processes during these exchanges.

Grossmann and Einstein

——————————————–

From Zurich to Berlin

1. Einstein and Heinrich Zangger (Einstein and Michele Besso)
2. From Zurich to Prague.
3. Back to Zurich (Einstein and Marcel Grossmann).
4. From Zurich to Berlin (Einstein and Max Planck, Erwin Freundlich and others in Berlin) .

General Relativity between 1912 and 1916

1. The Equivalence Principle.
2. Einstein’s 1912 Polemic with Max Abraham: Static Gravitational Field
3. Einstein’s 1912 Polemic with Gunnar Nordström: Static Gravitational Field
4. Einstein’s 1912-1913 Collaboration with Marcel Grossmann: Zurich Notebook to Entwurf Theory.
5. Einstein’s 1913-1914 Polemic with Nordström: Scalar Theory versus Tensor Theory (Einstein and Adriaan Fokker).
6. Einstein’s Polemic with Gustav Mie: Matter and Gravitation.
7. 1914 Collaboration with Grossmann and Final Entwurf Theory.
8. Einstein’s Polemic with Tullio Levi-Civita on the Entwurf Theory.
9. Einstein’s 1915 Competition with David Hilbert and General Relativity
10. Einstein Answers Paul Ehrenfest‘s Queries: 1916 General Relativity.
11. The Third Prediction of General Relativity: Gravitational RedShift
12. Erich Kretschmann‘s Critiques of Einstein’s Point Coincidence Argument (Einstein and Élie Cartan).
13. Einstein and Mach‘s Ideas.
14. Einstein’s Reaction to Karl Schwarzschild‘s Solution (Einstein and Nathan Rosen and Leopold Infeld and others in Princeton).
15. The Fourth Classic Test of General Relativity: Light Delay.

General Relativity after 1916

1. Einstein’s 1916 Polemic with Willem de Sitter, Levi-Civita and Nordström on Gravitational Waves (Einstein and Nathan Rosen and Leopold Infeld and Howard Percy Robertson).
2. Einstein’s Polemic with de Sitter: Matter World and Empty World.
3. Bending of Light and Gravitational Lens: Einstein and Arthur Stanley Eddington
4. Einstein’s Interaction with Hermann Weyl and the Cosmological Constant
5. Einstein’s 1920 Matter World, Mach’s Ether and the Dark Matter
6. Einstein’s 1920 Polemic with Eddington on de Sitter’s World.
7. Einstein’s Reaction to the Aleksandr Friedmann Solution.
8. Einstein’s Reaction to the Georges Lemaître Solution.
9. Edwin Hubble‘s Experimental Results.
10. The Lemaître-Eddington Model
11. Einstein and the Matter World: the Steady State Solution.
12. Einstein’s Collaboration with de Sitter.
13. Einstein’s Reaction to Lemaître‘s Big Bang Model
14. Einstein’s Interaction with George Gamow: Cosmological Constant is the Biggest Blunder
15. Einstein, Gödel and Backward Time Travel

Einstein 1916

People ask many questions about Einstein’s general theory of relativity. For instance: How did Einstein come up with the theory of general relativity? What did he invent? What is the theory of general relativity? How did Einstein discover general relativity? How did he derive his theory? Why was Einstein the first to arrive at generally covariant field equations even though many lesser-known scientists worked on the gravitational problem?

Did David Hilbert publish the field equations of general relativity before Einstein? Was Einstein’s theory of relativity revolutionary for scientists of his day? How did the scientific community receive Einstein’s theory of general relativity when he published it? What were the initial reaction in the scientific community after Einstein had published his paper on relativity?

Why did Einstein object so fiercely to Schwarzschild’s’ singularity (black holes)? Why did Einstein introduce the cosmological constant? Was it his biggest blunder? Why did Einstein suggest Mach’s principle? Is Mach’s principle wrong? And so forth.

In my book General Relativity Conflict and Rivalries: Einstein’s Polemics with Physicists I try to answer these and many other questions.

Between 1905 and 1907, Einstein first tried to extend the special theory of relativity and explain gravitational phenomena. This was the most natural and simplest path to be taken. These investigations did not fit in with Galileo’s law of free fall. This law, which may also be formulated as the law of the equality of inertial and gravitational mass, was illuminating Einstein, and he suspected that in it must lie the key to a deeper understanding of inertia and gravitation. He found “the happiest thought of my life”. He imagined an observer freely falling from the roof of a house; for the observer there is during the fall – at least in his immediate vicinity – no gravitational field. If the observer lets go of any bodies, they remain relative to him, in a state of rest or uniform motion, regardless of their particular chemical and physical nature. The observer is therefore justified in interpreting his state as being “at rest”. Newton realized that Galileo’s law of free fall is connected with the equality of the inertial and gravitational mass; however, this connection was accidental. Einstein said that Galileo’s law of free fall can be viewed as Newton’s equality between inertial and gravitational mass, but for him the connection was not accidental. Einstein’s 1907 breakthrough was to consider Galileo’s law of free fall as a powerful argument in favor of expanding the principle of relativity to systems moving nonuniformly relative to each other. Einstein realized that he might be able to generalize the principle of relativity when guided by Galileo’s law of free fall; for if one body fell differently from all others in the gravitational field, then with the help of this body an observer in free fall (with all other bodies) could find out that he was falling in a gravitational field.

In June 1911, Einstein published his paper, “On the Influence of Gravitation on the Propagation of Light”. An important conclusion of this paper is that the velocity of light in a gravitational field is a function of the place. In December 1911, Max Abraham published a paper on gravitation at the basis of which was Einstein’s 1911 conclusion about a relationship between the variable velocity of light and the gravitational potential. In February 1912, Einstein published his work on static gravitational fields theory, which was based on his 1911 June theory. In March 1912, Einstein corrected his static gravitational fields paper, but Abraham claimed that Einstein borrowed his equations; however, it was actually Abraham who needed Einstein’s ideas and not the other way round. Einstein thought that Abraham converted to his theory of static fields while Abraham presumed exactly the opposite. Einstein then moved to Zurich and switched to new mathematical tools, the metric tensor as representing the gravitational potential. He examined various candidates for generally covariant field equations, and already considered the field equations of his general theory of relativity about three years before he published them in November 1915. However, he discarded these equations only to return to them more than three years later. Einstein’s 1912 theory of static fields finally led him to reject the generally covariant field equations and to develop limited generally covariant field equations.

Max Abraham

The Finnish physicist Gunnar Nordström developed a competing theory of gravitation to Einstein’s 1912-1913 gravitation theory. The equivalence principle was valid in his theory and it also satisfied red shift of the spectral lines from the sun. However, it was unable to supply the advance of the Perihelion of Mercury, such as Einstein’s theory; it led to a Perihelion like the one predicted by Newton’s law of gravity, and, it could not explain the deflection of light near the sun, because in Nordström’s theory the velocity of light was constant. Einstein’s 1913-1914 Entwurf theory of gravitation, the field equations of which were not generally covariant, remained without empirical support. Thus a decision in favor of one or the other theory – Einstein’s or Nordström’s – was impossible on empirical grounds. Einstein began to study Nordström’s theory from the theoretical point of view and he developed his own Einstein-Nordström theory on the basis of his conception of the natural interval. Eventually, in a joint 1914 paper with Lorentz’s student Adrian Fokker, Einstein showed that a generally covariant formalism is presented from which Nordström’s theory follows if a single assumption is made that it is possible to choose preferred systems of reference in such a way that the velocity of light is constant; and this was done after Einstein had failed to develop a generally covariant formulation for his own Entwurf theory.

Gunnar Nordström

After arriving back to Zurich in summer 1912, Einstein was looking for his old student friend Marcel Grossmann, who had meanwhile become a professor of mathematics in the Swiss Federal Polytechnic institute. He was immediately caught in the fire. So he arrived and he was indeed happy to collaborate on the problem of gravitation. Einstein’s collaboration with Marcel Grossmann led to two joint papers, the first entitled, “Entwurf einer verallgemeinerten Relativitätstheorie und einer Theorie der Gravitation” (“Outline of a Generalized Theory of Relativity and of a Theory of Gravitation”) is called by scholars the Entwurf paper.

Marcel Grossmann

The Entwurf theory was already very close to Einstein’s general theory of relativity that he published in November 1915. The gravitational field is represented by a metric tensor, the mathematical apparatus of the theory is based on the work of Riemann, Christoffel, Ricci and Levi-Civita on differential covariants, and the action of gravity on other physical processes is represented by generally covariant equations (that is, in a form which remained unchanged under all coordinate transformations). However, there was a difference between the two theories, the Entwurf and general relativity. The Entwurf theory contained different field equations that represented the gravitational field, and these were not generally covariant.

Elwin Bruno Christoffel

Gregorio Curbastro Ricci

Bernhard Riemann

Indeed at first though – when Einstein first collaborated with Grossmann – he considered (in what scholars call the “Zurich Notebook) field equations that were very close to the ones he would eventually choose in November 1915:

(See visual explanation of the Zurich Notebook on John Norton’s website).

In 1913, Einstein thought for a while – or persuaded himself – that generally covariant field equations were not permissible; one must restrict the covariance of the equations. He introduced an ingenious argument – the Hole Argument – to demonstrate that generally covariant field equations were not permissible. The Hole Argument seemed to cause Einstein great satisfaction, or else he persuaded himself that he was satisfied. Having found the Hole argument, Einstein spent two years after 1913 looking for a non-generally covariant formulation of gravitational field equations.

Einstein’s collaboration with his close friends included Michele Besso as well. During a visit by Besso to Einstein in Zurich in June 1913 they both tried to solve the Entwurf field equations to find the perihelion advance of Mercury in the field of a static sun in what is known by the name, the Einstein-Besso manuscript. Besso was inducted by Einstein into the necessary calculations. The Entwurf theory predicted a perihelion advance of about 18” per century instead of 43” per century.

Michele Besso

Towards the end of 1915 Einstein abandoned the Entwurf theory, and with his new theory got the correct precession so quickly because he was able to apply the methods he had already worked out two years earlier with Besso. Einstein though did not acknowledge his earlier work with Besso.

Tulio Levi-Civita

Tullio Levi-Civita from Padua, one of the founders of tensor calculus, objected to a major problematic element in the Entwurf theory, which reflected its global problem: its field equations were restricted to an adapted coordinate system. Einstein proved that his gravitational tensor was a covariant tensor for adapted coordinate systems. In an exchange of letters and postcards that began in March 1915 and ended in May 1915, Levi-Civita presented his objections to Einstein’s above proof. Einstein tried to find ways to save his proof, and found it hard to give it up. Finally, Levi-Civita convinced Einstein about a fault in his arguments. Einstein realized that his Entwurf field equations of gravitation were entirely untenable. He discovered that Mercury’s perihelion’s motion was too small. In addition, he found that the equations were not covariant for transformations which corresponded to a uniform rotation of the reference system. Thus he came to the conviction that introducing the adapted coordinate system was a wrong path and that a more far-reaching covariance, preferably a general covariance, must be demanded.

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 (unimodular transformations), and on November 4, 1915, he presented to the Prussian Academy of Sciences these new field equations. Einstein gradually expanded the range of the covariance of the field equations until November 25, 1915. On that day, Einstein presented to the Prussian Academy his final version to the gravitational field equations.

Einstein and Hilbert

David Hilbert

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. In this paper Einstein presented a comprehensive general theory of relativity. In addition, in this paper Einstein presented the disk thought experiment. 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: 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.

Further, Einstein avoided the Hole Argument quite naturally by the Point Coincidence Argument. The point being made in the 1916 Point-Coincidence Argument is, briefly, that unlike general relativity, in special relativity coordinates of space and time have direct physical meaning. Since all our physical experience can be ultimately reduced to such point coincidences, there is no immediate reason for preferring certain systems of coordinates to others, i.e., we arrive at the requirement of general covariance. In 1918 Einstein saw the need to define the principles on which general relativity was based. In his paper, “Principles of the General Theory of Relativity”, he wrote that his theory rests on three principles, which are not independent of each other. He formulated the principle of relativity in terms of the Point Coincidence Argument and added Mach’s principle.

On November 18, 1915 Einstein reported to the Prussian Academy that the perihelion motion of Mercury is explained by his new General Theory of Relativity: Einstein found approximate solutions to his November 11, 1915 field equations. Einstein’s field equations cannot be solved in the general case, but can be solved in particular situations. The first to offer such an exact solution was Karl Schwarzschild. Schwarzschild found 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. On December 22, 1915 Schwarzschild told Einstein that he reworked the calculation in his November 18 1915 paper of the Mercury perihelion. Subsequently Schwarzschild sent Einstein a manuscript, in which he derived his exact solution of Einstein’s field equations. On January 13, 1916, Einstein delivered Schwarzschild’s paper before the Prussian Academy, and a month later the paper was published. Einstein though objected to the Schwarzschild singularity in Schwarzschild’s solution.

Karl Schwarzschild

In 1917 Einstein introduced into his 1915 field equations a cosmological term having the cosmological constant as a coefficient, in order that the theory should yield a static universe. Einstein desired to eliminate absolute space from physics according to “Mach’s ideas”.

Ernst Mach

Willem De Sitter objected to the “world-matter” in Einstein’s world, and proposed a vacuum solution of Einstein’s field equations with the cosmological constant and with no “world-matter”. In 1920 the world-matter of Einstein’s world was equivalent to “Mach’s Ether”, a carrier of the effects of inertia.

Einstein, Paul Ehrenfest and De Sitter; Eddington and Hendrik Lorentz. Location: office of W. de Sitter in Leiden (The Netherlands). Date: 26 Sept. 1923

De Sitter’s 1917 solution predicted a spectral shift effect. In 1923 Arthur Stanley Eddington and Hermann Weyl adopted De Sitter’s model and studied this effect. Einstein objected to this “cosmological problem”. In 1922-1927, Alexander Friedmann and Georges Lemaitre published dynamical universe models.

Friedmann’s model with cosmological constant equal to zero was the simplest general relativity universe. Einstein was willing to accept the mathematics, but not the physics of a dynamical universe.

In 1929 Edwin Hubble announced the discovery that the actual universe is apparently expanding. In 1931 Einstein accepted Friedmann’s model with a cosmological constant equal to zero, which he previously abhorred; he claimed that one did not need the cosmological term anymore. It was very typical to Einstein that he used to do a theoretical work and he cared about experiments and observations.

Einstein in America.

In Princeton in 1949, Kurt Gödel found an exact solution to Einstein’s field equations. Gödel’s solution was a static and not an expanding universe. Gödel’s universe allows the existence of closed timelike curves (CTCs), paths through spacetime that, if followed, allow a time traveler to interact with his/her former self.

The book also discusses other topics: for instance,  gravitational lensing, gravitational waves, Einstein-Rosen bridge, unified field theory and so forth.

## The Einstein Rosen bridge and the Einstein Podolsky Rosen paradox, ER and EPR: Wormhole and entanglement

The Einstein-Rosen Bridge and the Einstein Podolsky Rosen paradox. I demonstrate that the two-body problem in general relativity was a heuristic guide in Einstein’s and collaborators’1935 work on the Einstein-Rosen bridge and EPR paradox.

In 2013 Juan Maldacena and Leonard Susskind demonstrated that the Einstein Rosen bridge between two black holes is created by EPR-like correlations between the microstates of the two black holes. They call this the ER = EPR relation, a geometry–entanglement relationship: entangled particles are connected by a Schwarzschild wormhole. In other words, the ER bridge is a special kind of EPR correlation: Maldacena and Susskind’s conjecture was that these two concepts, ER and EPR, are related by more than a common publication date 1935. If any two particles are connected by entanglement, the physicists suggested, then they are effectively joined by a wormhole. And vice versa: the connection that physicists call a wormhole is equivalent to entanglement. They are different ways of describing the same underlying reality.

This image was published in a Nature article, Ron Cowen, “The quantum source of space-time”,  explaining the geometry–entanglement relationship and Maldacena’s and Susskind’s ER = EPR idea: Quantum entanglement is linked to a wormhole from general relativity. This representation is deterministic and embodies the many worlds interpretation: Collapse of the wave function never takes place. Instead, interactions cause subsystems to become entangled. Each measurement causes the branches of the tree to decohere; the quantum superposition being replaced by classical probabilities. The observer follows a trajectory through a tree. The entire tree, i.e., the entire wave function, must be retained and the universe is the complicated network of entanglements, branches of the tree: the wormhole bifurcating throats and mouths in the universe. See Susskind’s new paper from April 2016. Hence general relativity and quantum mechanics are linked by ER = EPR and Einstein’s soul can rest in peace because god will not play dice.

Maldacena and Susskind explain that one cannot use EPR correlations to send information faster than the speed of light.  Similarly, Einstein Rosen bridges do not allow us to send a signal from one asymptotic region to the other, at least when suitable positive energy conditions are obeyed. This is sometimes stated as saying that (Schwarzschild) Lorentzian wormholes are not traversable.

I uploaded a paper to the ArXiv: “Two-body problem in general relativity: A heuristic guide for the Einstein-Rosen bridge and EPR paradox”

In this paper I discuss the possible historical link between the 1935 Einstein-Rosen bridge paper and the 1935 Einstein-Rosen-Podolsky paper. The paper is a first version and I intend to upload a second version.

Between 1935 and 1936, Einstein was occupied with the Schwarzschild solution and the singularity within it while working in Princeton on the unified field theory and, with his assistant Nathan Rosen, on the theory of the Einstein-Rosen bridges. He was also occupied with quantum theory. He believed that quantum theory was an incomplete representation of real things. Together with Rosen and Boris Podolsky he invented the EPR paradox. In this paper I demonstrate that the two-body problem in general relativity was a heuristic guide in Einstein’s and collaborators’1935 work on the Einstein-Rosen bridge and EPR paradox.

In 1935 Einstein explained that one of the imperfections of the general theory of relativity was that as a field theory it was not complete in the following sense: it represented the motion of particles by the geodesic equation. A mass point moves on a geodesic line under the influence of a gravitational field. However, a complete field theory implements only fields and not the concepts of particle and motion. These must not exist independently of the field but must be treated as part of it. Einstein wanted to demonstrate that the field equations for empty space are sufficient to determine the motion of mass points. In 1935 Einstein attempted to present a satisfactory treatment that accomplishes a unification of gravitation and electromagnetism. For this unification Einstein and Rosen needed a description of a particle without singularity. In 1935, they joined two Schwarzschild solutions at the Schwarzschild limit and omitted part of the space-time beyond the Schwarzschild singularity. They showed that it was possible to do this in a natural way and they proposed the Einstein-Rosen bridge solution.

In the Einstein-Rosen bridges paper of 1935, Einstein negated the possibility that particles were represented as singularities of the gravitational field because of his polemic with Ludwig Silberstein. Silberstein thought he had demonstrated that general relativity was problematic. He constructed, for the vacuum field equations for the two-body problem, an exact static solution with two singularity points that lie on the line connecting these two points. The singularities were located at the positions of the mass centers of the two material bodies. Silberstein concluded that this solution was inadmissible physically and contradicted experience. According to his equations the two bodies in his solution were at rest and were not accelerated towards each other; these were nonallowed results and therefore Silberstein thought that Einstein’s field equations should be modified together with his general theory of relativity. Before submitting his results as a paper to the Physical Review, Silberstein communicated them to Einstein. This prompted Einstein’s remark, in his paper with Rosen in 1935, that matter particles could not be represented as singularities in the field.

Einstein and Rosen were trying to permanently dismiss the Schwarzschild singularity and adhere to the fundamental principle that singularities of the field are to be excluded. Einstein explained that one of the imperfections of the general theory of relativity was that as a field theory it was not complete because it represented the motion of particles by the geodesic equation. Einstein also searched for complete descriptions of physical conditions in quantum mechanics. It seems that the two-body problem in general relativity was a heuristic guide in the search of a solution to the problem that the psi function cannot be interpreted as a complete description of a physical condition of one system. He thus proposed the EPR paradox with Rosen and Podolsky.

Updated 2016

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

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

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

The Publisher uploaded the contents and intro.

I hope you like my drawing on the cover:

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

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

Have a very happy Einstein year!

## Celebrating the centennial of Einstein’s general relativity. (next year)…

“Shaken to its depths by the tragic catastrophe in Palestine, Jewry must now show that it is truly equal to the great task it has undertaken. It goes without saying that our devotion to the cause and our determination to continue the work of peaceful construction will not be weakened in the slightest by any such set-back. But what has to be done to obviate any possibility of a recurrence of such horrors?

The first and most important necessity is the creation of a modus vivendi with the Arab people”.

Albert Einstein, August 1929. (here)

Einstein attends a concert with Helen Dukas at the Great Synagogue in Berlin, 1930.

On December 10, 1915 Einstein told his best friend Michele Besso that his wildest dreams have now come true: general covariance and the perihelion of Mercury. Einstein wished Besso best regards and signed “your satisfied kaput Albert”.

Sometime in October 1915 Einstein dropped his old Einstein-Grossman theory, but he realized that the key to the solution lies in his 1914 review article “The Formal Foundation of the General Theory of Relativity”. He was finally led to general covariance. Starting on November 4 1915, Einstein gradually expanded the range of the covariance of his field equations.

Between November 4 and November 11, 1915, Einstein simplified the field equations, and was able to write them in general covariant form in an addendum to the November 4 paper, published on November 11. But there still remained difficulties.

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. Today, exactly one year from now the world will celebrate one hundred years to this achievement. Mazal Tov.

Between November 18 and November 25 Einstein found that he could write the field equations with an additional term on the right hand side of the field equations involving the trace of the energy-momentum tensor, which now need not vanish. Hence, Einstein resolved the final difficulties of his November 11 1915 theory of gravitation in his final November 25 1915 paper. These were the November 25 1915 field equations.

How did Einstein do this? Read my two papers (one and two) and see how Einstein solved the problem.

In winter 1916 Einstein exchanged letters with his friend from Leiden Paul Ehrenfest and rederived the November 25, 1915 field equations. How did Einstein do this? Read my two papers (one and two) and find out.

Einstein elaborated his 1912 Disk thought experiment, and his 1914 thought experiment, originally suggested by Newton in the Principia, the Two Globes thought experiment. After presenting the 1905 magnet and conductor thought experiment, Einstein wrote, “Examples of this sort … lead to the conjecture that the phenomena of electrodynamics as well as those of mechanics possess no properties corresponding to the idea of absolute rest”. The globes thought experiment was intended to demonstrate that this could be extended to accelerated motions and to the theory of gravitation using Mach’s principle (still not defined as a principle).

## George Gamow and Albert Einstein

Here is my new paper about George Gamow and Albert Einstein (here) x

Mr. Newton once said, momentum conservation
Teach einStein acceleration
If it is in empty space,
Moving straight on a trace,
And flies, never to return,
Then nothing remained of it again. x

Albert Einstein

There was a young fellow from Trinity,
Who took the square root of infinity.
But the number of digits, gave him the fidgets;
He dropped Math and took up Divinity. x

George Gamow, One, Two, Three… Infinity

Mr. Tomkins was in a world where the speed of light was about 30 km/h

George Gamow and Albert Einstein and the “biggest blunder” x