The Formative Years of Relativity. Gravitational waves go in one ear and out the other

The purpose of this piece is to review Hanoch Gutfreund’s and Jürgen Renn’s new book The Formative Years of Relativity: The History and Meaning of Einstein’s Princeton Lectures, Princeton University Press and Oxford University Press. I have found two problems in the book the first of which is Poincaré’s influence on Einstein and the second problem is related to gravitational waves. The first part of the review deals with Poincaré’s influence on Einstein. In this part I discuss the problem related to gravitational waves.

Gravitational waves have won the 2017 Nobel Prize in Physics. The prize is awarded to Kip Thorne, Rainer Weiss, Barry Barish for their work on Ligo experiment. Actually, Kip Thorne’s interesting work is on wormholes: the Einstein-Rosen bridges, the Schwarzschild (non-traversable) wormholes and traversable wormeholes converted into time machines. Wormholes spark our imagination because of the possibility of travelling backwards in time and sending signals through the throat in space-time with causality violation.

However, let us concentrate on gravitational waves.

I have ordered the book from Amazon together with The Asshole Survival Guide: How to Deal with People who Treat you Like Dirt written by Robert Sutton, a Stanford University professor:

formative1

It seems that the book, The Formative Years of Relativity has mistakes and also errors in English (the book needs proofreading). I therefore ask the second writer: Are you living in a fool’s paradise?

Right at the beginning Gutfreund argues that gravitational waves is the only major topic debated during the formative years that has no trace in Einstein’s book The Meaning of Relativity. He writes: “Had we restricted our commentaries to the contents of Einstein’s book, there would be no reason to mention gravitational waves; however, it would be inconceivable to talk about the formative years without thoroughly discussing them. What is worth emphasizing in this context is how Einstein’s predominant interest in this phenomenon which developed immediately after the completion of his general theory, had faded away completely by the time he delivered the Princeton lectures” (Gutfreund’s book, page 8):

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And the above conclusion is mentioned in the New York Times book review section:

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Gutfreund and Renn “note, however, a conspicuous absence. There is ‘no trace’ in Einstein’s lectures of what is today considered a key topic in relativity: gravitational waves”.

In fact quite the opposite is true. Einstein’s mathematical derivations in his 1916 and 1918 two gravitational waves papers play a central role in The Meaning of Relativity of 1922. It therefore appears that Einstein’s interest in this topic had not faded away by the time he delivered the Princeton lectures.

Consider Einstein’s gravitational waves paper of 1916:

Picture2

And here is the same equation in his 1921 book, The Meaning of Relativity (Gutfreund’s book, page 240):

Picture1

Equation (92) represents the metric of general relativity Picture1 - Copy, which is the sum of the Minkowski flat metric Picture1 - Copy - Copy of special relativity and Picture1 - Copy (2) a very small disturbance.

And again, Einstein’s gravitational waves paper of 1916:

Picture4

And his book, The Meaning of Relativity (Gutfreund’s book, page 246):

Picture3 - Copy

We write the field equations in terms of Picture1 - Copy (2). Equation (96b) below is the linearized approximation of Einstein’s field equations. Then we can solve the field equations in the same way that we solve Maxwell’s electromagnetic field equations (Gutfreund’s book, page 247):

Picture3

Equations (101) above from the book The Meaning of Relativity, which are exactly like equations (9) from the gravitational waves paper of 1916, are the method of retarded potentials.

In his review paper of 1916, The Foundation of the General Theory of Relativity, Einstein’s field equations were valid for systems in unimodular coordinates, i.e. he chose the coordinates so that Picture1111.

However, in his gravitational waves paper of 1916, Einstein thanked de Sitter for sending him the following metric, the one below: “Herr [Willem] de Sitter sent me these values by letter”:

Picture6

And in the book, The Meaning of Relativity he writes the the same metric (Gutfreund’s book, page 249):

Picture5

Indeed, in the book, The Formative Years of Relativity, Gutfreund writes: “On 22 June 1916, Einstein wrote to Willem de Sitter […] ‘For I found that the gravitation equations in first-order approximation [i.e. equations (96b) the linearized approximation of Einstein’s field equations] can be solved exactly by means of retarded potentials, if the condition of Picture1111is abandoned. Your solution for the mass point is then the result upon specialization to this case'” (Gutfreund’s book, page 97):

Picture7

Daniel Kennefick explains Einstein’s letter to de Sitter in his book, Traveling at the Speed of Thought: Einstein and the Quest for Gravitational Waves (page 51):

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By the way I highly recommend Kennefick’s book.

That being said, Gutfreund begins the chapter on gravitational waves with Max Born. Born asked Einstein how fast does the effect of gravitation propagates according to his theory? Einstein replied to him that it is simple to write down the equation for the case where the disturbances one places into the field are infinitesimal. In that case the metric Picture1 - Copy differs only infinitesimally (Picture1 - Copy (2)) from the values (Picture1 - Copy - Copy) that would be present without that disturbance; and the disturbance propagates with the velocity of light (Gutfreund’s book, page 94):

Picture9a

I wrote in my 2015 book General Relativity Conflict and Rivalries and in other places as well that the first time Einstein mentioned gravitational waves was in the discussion after the Vienna lecture in 1913:

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However, Gutfreund does not cite my 2015 book.

In 2016 Gutfreund wrote a blog post and added Jürgen Renn and Diana Buchwald as co-authors:

Picture10

They told the story of the origin of gravitational waves:

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They briefly summarize the history of gravitational waves: “The first debates about the existence of gravitational waves even preceded the completion of general relativity by Einstein in November, 1915”. They only mention Max Abraham but don’t write that the first time that Einstein had mentioned gravitational waves was after the Vienna lecture in 1913, in the discussion, Max Born asked Einstein how fast does the effect of gravitation propagates according to his Entwurf theory.

Finally, in the same book, General Relativity Conflict and Rivalries, of 2015 I wrote:

Picture14

And I read in Gutfreund’s book of 2017 and discover that he writes exactly the same thing but does not cite my book (Gutfreund’s book, page 35):

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The Formative Years of Relativity and a Prejudice on Poincaré’s Conventionalism

The purpose of this piece is to review Hanoch Gutfreund’s and Jürgen Renn’s new book The Formative Years of Relativity: The History and Meaning of Einstein’s Princeton Lectures, Princeton University Press and Oxford University Press. I find two problems in the book the first of which is Poincaré’s influence on Einstein. This is the first part of the review which deals with Poincaré’s influence on Einstein. Since the book has mistakes and also errors in English and Jürgen Renn is considered a notable scholar, I assume that Gutfreund is probably responsible for the mistakes and for the errors in English.

Let us begin with page 26 of the book The Formative Years of Relativity. Gutfreund is apparently much attracted by “the painstaking analysis by the philosopher of science Yemima Ben-Menachem” in her book Conventionalism: From Poincaré to Quine. Cambridge University Press, Cambridge (2006):

Yemima 1921

Gutfreund writes that “Until 1921, Einstein did not mention Poincaré explicitly”.

Einstein obviously mentioned Poincaré before 1921. For instance, after the first Solvay congress in 1911, Einstein wrote to Heinrich Zangger (see the Collected Papers of Albert Einstein, CPAE):

Zangger1

……

Zangger2

Einstein says that Poincaré was in general simply antagonistic and for all his acuity showed little understanding of the situation.

There was then great excitement among philosophers and historians of science when they discovered, as Gutfreund writes on page 26 above that “We know that he [Einstein] read Science and Hypothesis with his friends in the Akademie Olympia in 1902″.

Poincaré’s publisher Flammarion published La science et l’hypothèse (Science and Hypothesis) in Paris in 1902. How do we know that Einstein read this book in 1902 and not in 1903 or 1904? Take a look at Gutfreund’s words: “We know that he [Einstein] read Science and Hypothesis with his friends in the Akademie Olympia in 1902″. It means that Einstein rushed to the local bookstore in Bern the day the book was out, dodged people in the crowd waiting outside the bookstore and found the first French edition of Poincaré’s book. But maybe Einstein read the 1904 German translation of Poincaré’s 1902 book? This could be quite different from the original 1902 French edition.

Subsequently,  on page 26 Gutfreund writes: “Einstein’s biographer Abraham Pais quotes one of the members, Maurice Solovine, as saying: ‘This book profoundly impressed us and kept us breathless for weeks on end'”:

Pais

Gutfreund simply takes the Pais paragraph from Yemima Ben-Menahem’s book, Conventionalism, see footnote 80 below (page 134):

134

This is a mistake: We cannot cite Einstein’s biographer Abraham Pais quoting one of the members of the Akademie Olympia (Olympia Academy). The biography of Pais is not a primary source. We have to check a primary source and see whether Maurice Solovine himself said: “This book profoundly impressed us and kept us breathless for weeks on end”.

Here is the original primary source:

soloving

Lettres à Maurice Solovine. Paris: Gauthier-Villars, 1956.

Here luck plays an important role because in the above book Solovine writes in French that Poincaré’s book “profoundly impressed us and kept us breathless for many weeks”. One should, however, check the original quote in French.

On page 30 Gutfreund tells the story of Einstein who explored “a famous example that goes back Poincaré”. There are several typos in the book.

Poincare typo

It is interesting, however, to look at the following sentence, several sentences below the above one on page 30:

He typo

“Without the distinction between axiomatic Euclidean geometry and practical rigid-body geometry, we arrive at the view advanced by Poincaré”. And then Gutfreund adds an end-note 15: “For an extensive analysis of Poincaré’s conventionalism, see Yemima Ben-Menachem, […]” Her book Conventionalism.

Yemima 1921-2

You might, of course, be tempted to suppose that Ben-Menahem has said the above words in her book. But this is by no means the case. Einstein says this in his 1921 talk, “Geometry and Experience” (see CPAE):

geometry and experience

After the words: “Without the distinction between axiomatic […]” Gutfreund writes: “He suggested that […]”

He typo

Who is “He”? Einstein or Poincaré?

Let us then examine Yemima Ben-Menahem’s book, Conventionalism.

I am quoting from Yemima Ben-Menahem’s book Conventionalism, page 84:

“… as both GR [general relativity] and the special theory of relativity originated in insights about equivalence, an element of conventionality might seem to be built right into the theory.  It is important to recognize, however, that Einstein’s use of equivalence arguments differs fundamentally from that of the conventionalist”.

And on page 134 Ben-Menahem writes: “The preceding discussion should alert us to the traces of Poincaré’s equivalence argument in Einstein’s work on GR as well. […] The centrality of equivalence arguments and their geometric implications is too obvious in Science and Hypothesis to be missed by a reader such as Einstein, who, we know, was familiar with the book. Beginning with the hypothesis of equivalence in 1907, Einstein makes use not only of the general idea of equivalent descriptions, but also of the types of examples Poincaré used”.

page_134

and on page 135, Yemima Ben Menahem argues that “Einstein was deeply influenced by the idea of equivalence, and to that extent could concede that Poincaré was right”:

page 135

I have found no historical evidence (primary documents, i.e. correspondence of Einstein with others, manuscripts, and also interviews with Einstein) supporting the claim that Einstein makes use of Poincaré’s equivalent descriptions.

In the 1920 unpublished draft of a paper for Nature magazine, “Fundamental Ideas and Methods of the Theory of Relativity, Presented in Their Development”, Einstein explained how he arrived at the principle of equivalence (see CPAE):

happiest happiest2

(Original in German). “When I (in Y. 1907) [in Bern] was busy with a comprehensive summary of my work on the special theory relativity for the ‘Jahrbuch für Radioaktivität und Elektronik’, I also had to try to modify Newton’s theory of gravitation in such a way that its laws fitted into the theory. Attempts in this direction showed the feasibility of this enterprise, but did not satisfy me, because they had to be based upon unfounded physical hypotheses. Then there came to me the happiest thought of my life in the following form:

The gravitational field is considered in the same way and has only a relative existence like the electric field generated by magneto-electric induction. Because for an observer freely falling from the roof of a house there is during the fall – at least in his immediate vicinity – no gravitational field. Namely, 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’.

The extremely strange experimental law that all bodies fall in the same gravitational field with the same acceleration, immediately receives through this idea a deep physical meaning. If there were just one single thing that fell differently in a gravitational field from the others, the observer could recognize with its help that he was in a gravitational field and that he was falling in the latter. But if such a thing does not exist – as experience has shown with great precision – then there is no objective reason for the observer to regard himself as falling in a gravitational field. Rather, he has the right to consider his state at rest with respect to gravitation, and his environment as field-free.

The experimental fact of independence of the material of acceleration, therefore, is a powerful argument for the extension of the relativity postulate to coordinate systems moving nonuniformly relative to each other”.

Isaac Newton had already recognized that Galileo’s law of free fall was connected with the equality of the inertial and gravitational mass. In approximately 1685, Newton realized that there was an (empirical) equality between inertial and gravitational mass (Newton 1726, Book I, 9). For Newton, however, this connection was accidental. Einstein, on the other hand, said that Galileo’s law of free fall could be viewed as Newton’s equality between inertial and gravitational mass, but for him the connection was not accidental.

Hence, Einstein made use of Newton’s equality (accidental equivalence) between inertial and gravitational mass and Galileo’s law of free fall and in his 1907 paper, “On the Relativity Principle and the Conclusions Drawn from It”, he invoked a new principle, the equivalence principle or hypothesis. He assumed the complete physical equivalence of a homogeneous gravitational field and a corresponding (uniform) acceleration of the reference system. Acceleration in a space free of homogeneous gravitational fields is equivalent to being at rest in a homogeneous gravitational field.

Ernst Mach criticized Newton’s bucket experiment. He said that we cannot know which of the two, the water or the sky, are rotating; both cases produce the same centrifugal force. Mach thus expressed a kind of equivalence principle: Both explanations lead to the same observable effect. Einstein could have been influenced by Mach’s idea that we cannot know which of the two, the water or the sky, are rotating. Indeed Charles Nordmann interviewed Einstein and wrote: “Perhaps even more than Poincaré, Einstein admits to have been influenced by the famous Viennese physicist Mach”.

On page 31, Gutfreund writes in his book:

disk

“Had he [Einstein] instead accepted the conventionalist position […]” and then Gutfreund writes: “This in fact is exactly the situation in which Einstein introduced the mental model of a rotating disk, which he used as early as 1912 to show that the new theory of ravitation requires a new framework for space and time”.

Another typo: it should be the new theory of gravitation.

The rotating disk story starts with a problem in special relativity, with Max Born’s notion of rigidity and not with Poincaré! Einstein never mentioned any influence Poincaré had had on him when inventing the disk thought experiment.

At the annual eighty-first meeting of the German Society of Scientists and Physicians in Salzburg on 21-25 September 1909, Born first analyzed the rigid body problem and showed the existence of a class of rigid motions in special relativity.

John Stachel describes this state of affairs in his seminal paper of 1980: “The Rigidly Rotating Disk as a ‘Missing Link’ in the History of General Relativity”. It seems that Gutfreund is unacquainted with Stachel’s paper.

On September 29, 1909 the Physikalische Zeitschrift received a short note from Paul Ehrenfest. In his note Ehrenfest demonstrated that according to Born’s notion of rigidity, one cannot bring a rigid body from a state of rest into uniform rotation about a fixed axis. Ehrenfest had pointed out that a uniformly rotating rigid disk would be a paradoxical object in special relativity; since, on setting it into motion its circumference would undergo a contraction whereas its radius would remain uncontracted.

Born noted: “Mr. Ehrenfest shows that the rigid body at rest can never be brought into uniform rotation; I have discussed the same fact with Mr. Einstein in the meeting of natural scientists in Salzburg”. Born discussed the subject with Einstein and they were puzzled about how the rigid body at rest could never be brought into uniform motion. Born and Einstein discovered in that discussion that setting a rigid disk into rotation would give rise to a paradox: the rim becomes Lorenz-contracted, whereas the radius remains invariant. This problem was discussed almost simultaneously by Ehrenfest in the above short note.

Later in 1919, Einstein explained to Joseph Petzoldt why it was impossible for a rigid disk in a state of rest to gradually set into rotation around its axis:

PetoltzPetoltz2

On page 32 Gutfreund mentions the 10th German edition of Einstein’s popular book Relativity the Special and General Theory. He says that in a copy of this book there is a sheet of paper in the handwriting of Einstein’s stepdaughter containing a remark:

disk2

As you can see this remark is quite similar to Einstein’s letter to Petzoldt. Thus, it is preferable to quote Einstein’s own words, his letter to Petzhold. It seems that Gutfreund is unacquainted with the history of the rotating disk, because according to his book he is unaware of Stachel’s paper and the letter to Petzhold.

At the end of October 1909 Born submitted an extended version of his Salzburg talk to Physikalische Zeitschrift. In December 1909 Gustav Herglotz published a paper in which he noted that according to Born’s notion of rigidity, a “rigid” body with a fixed point can only rotate uniformly about an axis that goes through it, like an ordinary rigid body. Several months later, Einstein mentioned Born’s and Herglotz’s papers in a letter from March 1910 to Jakob Laub, in which he said that he was very much interested in their then recent investigations on the rigid body and the theory of relativity.  A month later, in conversations with Vladimir Varičak Einstein explained that the great difficulty lies in bringing the “rigid” body from a state of rest into rotation. In this case, each material element of the rotating body must Lorentz contract. See my new book Einstein’s Pathway to the Special Theory of Relativity 2Ed for full details.

In his paper from February 1912, Einstein considered a system K with coordinates x, y, z in a state of uniform rotation (disk) in the direction of its x-coordinate and referred to it from a non-accelerated system. Einstein wrote that K‘s uniform rotation is uniform “in Born’s sense”, namely, he considered a rotating disk already in a state of uniform rotation observed from an inertial system and reproduced his conversations with Varičak. Einstein then extended the 1907–1911 equivalence principle to uniformly rotating systems as promised in conversations with Sommerfeld in 1909.

All we know according to primary sources is that the origin of the rotating disk story is in a problem in special relativity, Max Born’s notion of rigidity and Ehrenfest’s paradox, which Einstein mentioned many times before 1912. Einstein never mentioned any influence Poincaré had had on him when inventing the disk thought experiment. Writing that Einstein was influenced by Poincaré’s conventionalism and equivalent arguments is speculating about the influence of the later on the former.

Gutfreund’s mistake about Poincaré’s influence on Einstein and Einstein’s so-called failure to acknowledge Poincaré’s work in connection with the equivalence principle and the rotating disk thought experiment in general relativity comes from Yemima Ben-Menahem’s book, Conventionalism. However, this misconception or prejudice on the part of Ben-Menahem comes from my PhD thesis which was submitted to the Hebrew University of Jerusalem back in 1998. I was a PhD student in the program for the history and philosophy of science and Yemima Ben-Menahem was a professor there. Here for example are several paragraphs from my PhD thesis:

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thesis

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And Poincaré’s disk thought experiment:

thesis4

…..

thesis5

……

thesis6

…..

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I have thus written in my thesis about Poincaré’s disk thought experiment and the equivalence of Euclidean and non-Euclidean geometries. I then mentioned Einstein’s rotating disk thought experiment and said that we eliminate absolute motion of the disk by assuming the equivalence of gravity and inertia. I then spoke about conventionalism and Einstein’s equivalence principle.

After the PhD I corrected and edited my PhD but then I was horrified to discover what looked like a magnification of the prejudice of Poincaré’s conventionalism and equivalence argument and his disk thought experiment influencing Einstein when creating general relativity: In 2006 Yemima Ben-Menahem said exactly the same thing in her book, Conventionalism. You might say that it is even a more unfortunate instance to write about Poincaré’s influence on Einstein in connection with the equivalence principle and the disk thought experiment in general relativity over and over again in a single book… (see now for instance her book, pages 64-65):

diskyemima

…….

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……

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Going on to Hanoch Gutfreund, in his new book of 2017, The Formative Years of Relativity, he has simply brought this incidence to the surface when he told the whole story of this prejudice all over again.

 

 

 

 

 

 

The Einstein Legacy Project

Happy Birthday Albert Einstein!

Einstein once wrote to his close friend: “With fame I became more and more stupid, which of course, is a very common phenomenon”.

Bingo. This exactly describes the spirit of a new project called, “The Einstein Legacy Project”.

Here is “the official Einstein Legacy Project video. It tells the story of how and WHY this project was born”.

However, the people in the official Einstein Legacy Project video use Einstein’s name in order to throw lavish parties. Entire fortunes are spent for celebrations and demonstrations of pomp and power. Einstein was not a Sun king, Louis le Grand.

The Einstein Legacy Project consists of two lavish projects and two (I hope so) less lavish projects (I will present 3 of them):

1) Dinner of the Century: (here)

“To celebrate the centennial of Einstein’s Relativity theory and to launch the publication of Genius: 100 Visions of the Future, the Einstein Legacy Project will be holding the ‘Dinner of the Century’; a star studded event that will bring together our Genius contributors, along with young Einsteins and dignitaries from around the world”.

While we celebrate and launch the grandiose 3D book, in the presence of Hollywood actors and other dignitaries from around the world, and mid all the pomp and ceremony, we receive Einstein’s response to the “Dinner of the Century” as told to his biographer Carl Seelig (see full story in my book Einstein’s Pathway to the Special theory of Relativity, 2015):

“The celebration ended with the most opulent banquet that I have ever attended in my life. So I said to a Genevan patrician who sat next to me, ‘Do you know what Calvin would have done if he were still here?’ When he said no and asked what I thought, I said: ‘He would have erected a large pyre and had us all burned because of sinful gluttony’. The man uttered not another word, and with this ends my recollection of that memorable celebration”.

In September 2017 the Einstein Legacy Project will throw an opulent banquet, a parodic dinner, a celebration of sinful gluttony.

2) 3D printed book: Genius: 100 Visions of the Future: (here)

“To celebrate the 100th anniversary of the publication of Einstein’s General Theory of Relativity, the Einstein Legacy Project is embarking on a publishing milestone: collecting the visions of the 100 greatest innovators, artists, scientists and visionaries of our time in the world’s first 3D-printed book – Genius: 100 Visions of the Future. It’s the creation of world renowned designer Ron Arad, formed in the likeness of Einstein himself in a 3D limited edition book for the ages”.

Here is Einstein’s response to the 3D book formed in the likeness of his head:

“Generally I find it tasteless… I have also prohibited …[this] book from appearing in the German language, but allowed the book to appear in foreign languages, I also hold the latter [author] to be quite tasteless. … [He] need[s] to earn money, which serves as an excuse for and for that […he] cannot wait until I’m dead. Is the mention of such a basic fact an accusation?”

I agree with you Einstein, I also find it tasteless.

Who are contributing to this book? For instance, Barbra Streisand, Deepak Chopra and others.

I would like to ask the contributors a question: A uniformly moving train could as well be seen at rest and the tracks, including the landscape, as uniformly moving. Will the common sense of the locomotive engineer allow this? He will object that he does not go on to heat and grease the landscape but rather the locomotive, and that consequently it must be the latter whose motion shows the effect of his labor. Why? Can you explain why? After all you are “genius contributors”…. If you can explain this, then I can pose questions about general relativity.

3) Einstein’s Archives and Visitor Center: (here)

“The first and only institution to celebrate the life, history and vision of Einstein. Built around the unique collection of The Hebrew University of Jerusalem, where Einstein bequeathed his entire personal archive, the Einstein Archive and Visitor Center will be a global attraction dedicated to science and humanitarian ideals”.

This is the only project that Einstein probably would have approved. However, in light of the above two projects (pomp “Dinner of the Century” and 3D book), I am very doubtful that the people who are organizing the Einstein’s Legacy Project really care about Einstein, his legacy and his writings.

Stay tuned. More to come…. … ….

General Relativity without the Equivalence principle?

I have skimmed through this book Handbook of Spacetime:

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

I read this paper:

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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):

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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:

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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:

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in the chapter:

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Hence Joshi says:

Picture34

in the chapter:

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Lewis Ryder

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writes in the above paper:

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(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:

Picture11

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:

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

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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:

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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:

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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 :

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Einstein’s equivalence principle was criticized by Synge:

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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:

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

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

Graham S. Hall in his paper:

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writes the following:

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“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:

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

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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:

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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):

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

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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:

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Wesson in this paper:

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

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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:

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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):

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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:

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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):

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

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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. Picture20

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)

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the following:

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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.

 

 

 

 

 

 

 

The prediction of gravitational waves emerged as early as 1913

On February 11, 2016, The Max Planck Institute for the History of Science in Berlin published the following announcement: “One Hundred Years of Gravitational Waves: the long road from prediction to observation”:

“Collaborative work on the historiography 20th century physics by the Einstein Papers Project at Caltech, the Hebrew University of Jerusalem, and the Max Planck Institute for the History of Science carried out over many years has recently shown that the prediction of gravitational waves emerged as early as February 1916 from an exchange of letters between Albert Einstein and the astronomer Karl Schwarzschild . In these letters Einstein expressed skepticism about their existence. It is remarkable that their significant physical and mathematical work was carried out in the midst of a devastating war, while Schwarzschild served on the Eastern Front”.

Collaborative work by experts on the physics of Einstein from the Einstein papers Project, from the Max Planck Institute for the History of Science in Berlin: Prof. Jürgen Renn, Roberto Lalli and Alex Blum; and from the Hebrew University of Jerusalem the only representative is Prof. Hanoch Gutfreund, the academic director of the Albert Einstein Archives. Their main finding is therefore:

The prediction of gravitational waves emerged as early as February 1916 from an exchange of letters between Albert Einstein and the astronomer Karl Schwarzschild. However, from a historical point of view this is not quite accurate because Einstein reached the main idea of gravitational waves three years earlier, as I demonstrate below. Any way the group published two summaries of the study.

A summary was published in German:

“Als Einstein dann seine abschließende Arbeit zur allgemeinen Relativitätstheorie am 25. November 1915 der Preussischen Akademie in Berlin vorlegte, war die Frage, ob solche Wellen tatsächlich aus seiner Theorie folgen, noch offen. Einstein erwähnte das Thema zum ersten Mal in einem Brief, den er am 19. Februar 1916 an Karl Schwarzschild schickte. Nach einigen obskuren technischen Bemerkungen, stellte er lakonisch fest: „Es gibt also keine Gravitationswellen, welche Lichtwellen analog wären”.”

“Gravitationswellen – verloren und wiedergefunden” von Diana K. Buchwald, Hanoch Gutfreund und Jürgen Renn.

and also in English:

“When Einstein presented his theory of general relativity on Nov. 25, 1915 in Berlin, the question of whether such waves would constitute a consequence of his theory remained untouched. Einstein mentioned gravitational waves for the first time in a letter of 19 February 1916 to Karl Schwarzschild, a pioneer of astrophysics. After some obscure technical remarks, he laconically stated: “There are hence no gravitational waves that would be analogous to light waves”.”

“Gravitational Waves: Ripples in the Fabric of Spacetime Lost and Found” by Hanoch Gutfreund, Diana K. Buchwald and Jürgen Renn.

And here as well.

Hence, according to the three above authors Einstein mentioned gravitational waves for the first time in a letter of 19 February 1916 to Karl Schwarzschild. However, this is wrong . Einstein reached the main idea of gravitational waves three years earlier, which is not when the above group of scholars had thought the gravitational waves were mentioned for the first time. As early as  1913, Einstein started to think about gravitational waves when he worked on his Entwurf gravitation theory.

In the discussion after Einstein’s 1913 Vienna talk on the Entwurf theory, Max Born asked Einstein about the speed of propagation of gravitation, whether the speed would be that of the velocity of light. Here is Einstein’s reply:

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In 1916, Einstein followed these steps and studied gravitational waves.

See my papers on gravitational waves (one and two) and my book for further information.

A Historical Note on Gravitational Waves

Dr. Roni Gross (press conference) holds Einstein’s general relativity paper from May 1916, “The Foundation of the General Theory of Relativity” (“Die Grundlage der allgemeinen Relativitätstheorie.” Annalen der Physik 49, 769-822). However, in this paper Einstein did not discover gravitational waves. Prof. Hanoch Gutfreund, the academic director of the Albert Einstein Archives, asked Dr. Rony Gross to present this document to the journalists.

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here.

Equations (52) and (53) from the original page on the right above:

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are Einstein’s field equations for systems in unimodular coordinates. There are no gravitational waves here!

In his 1916 general relativity paper, “The Foundation of the General Theory of Relativity”, Einstein imposed a restrictive condition on his field equations. This condition is called unimodular coordinates.

Einstein presented the gravitational waves later in 1916, in a paper published under the title, “Approximate Integration of the Field Equations of Gravitation” (“Näherungsweise Integration der Feldgleichungen der Gravitation.” Königlich Preußische Akademie der Wissenschaften (Berlin). Sitzungsberichte, 688–696).

After the 1916 general relativity paper, Einstein succeeded in relinquishing the restrictive unimodular coordinates condition and in his new gravitational waves paper his equations were not restricted to systems in unimodular coordinates.

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How did Einstein predict the existence of gravitational waves?

Einstein’s Discovery of Gravitational Waves 1916-1918

Einstein and Gravitational Waves 1936-1938

For further details on Einstein predicting gravitational waves read Chapter 3, section 1 in my new book: General Relativity Conflict and Rivalries, Einstein Polemics with physicists.

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I present and read several sections of my books on Einstein

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I present my two books and read several sections of my books out loud:

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Until February 29, 2016, you can all receive a generous discount when purchasing my book, General Relativity Conflict and Rivalries: Einstein’s Polemics with Physicists by Cambridge Scholars.

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Some of the topics discussed in my first book, Einstein’s Pathway to the Special Theory of Relativity

People ask questions about Einstein’s special theory of relativity: How did Einstein come up with the theory of special relativity? What did he invent? What is the theory of special relativity? How did Einstein discover special relativity? Was Einstein the first to arrive at special relativity? Was Einstein the first to invent E = mc2?

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

In my book, Einstein’s Pathway to the Special Theory of Relativity, I try to answer these and many other questions.The topics discussed in my book are the following:

I start with Einstein’s childhood and school days.

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I then discuss Einstein’s student days at the Zurich Polytechnic. Einstein the rebellious cannot take authority, the patent office, Annus Mirabilis, University of Bern and University of Zurich, Minkowski’s space-time formalism of special relativity.

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Young Einstein, Aarau Class 1896

Additional topics treeated in my book are the following: Fizeau’s water tube experiment, Fresnel’s formula (Fresnel’s dragging coefficient), stellar aberration, and the Michelson and Michelson-Morley Experiments.

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Albert Einstein at the Patent office

Mileva Marić and Einstein

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Eduard Tete, Mileva Marić and Hans Albert

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Einstein’s road to the special theory of relativity: Einstein first believes in the ether, he imagines the chasing a light beam thought experiment and the magnet and conductor thought experiment. Did Einstein respond to the Michelson and Morley experiment? Emission theory, Fizeau’s water tube experiment and ether drift experiments and Einstein’s path to special relativity; “The Step”.

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

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Einstein’s methodology and creativity, special principle of relativity and principle of constancy of the velocity of light, no signal moves beyond the speed of light, rigid body and special relativity, the meaning of distant simultaneity, clock synchronization, Lorentz contraction, challenges to Einstein’s connection of synchronisation and Lorentz contraction, Lorentz transformation with no light postulate, superluminal velocities, Laue’s derivation of Fresnel’s formula, the clock paradox and twin paradox, light quanta, mass-energy equivalence, variation of mass with velocity, Kaufmann’s experiments, the principles of relativity as heuristic principles, and Miller ether drift experiments.

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The book also briefly discusses general relativity: Einstein’s 1920 “Geometry and Experience” talk (Einstein’s notion of practical geometry), equivalence principle, equivalence of gravitational and inertial mass, Galileo’s free fall, generalized principle of relativity, gravitational time dilation, the Zurich Notebook, theory of static gravitational fields, the metric tensor, the Einstein-Besso manuscript, Einstein-Grossmann Entwurf theory and Entwurf field equations, the hole argument, the inertio-gravitational field, Einstein’s general relativity: November 1915 field equations, general covariance and generally covariant field equations, the advance of Mercury’s perihelion, Schwarzschild’s solution and singularity, Mach’s principle, Einstein’s 1920 suggestion: Mach’s ether, Einstein’s static universe, the cosmological constant, de Sitter’s universe, and other topics in general relativity and cosmology which lead directly to my second book, General Relativity Conflict and Rivalries.

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My books

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

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The back cover of my book:

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

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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.

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Grossmann and Einstein

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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

 

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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.

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

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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.

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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.

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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.

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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.

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Elwin Bruno Christoffel

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Gregorio Curbastro Ricci

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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:

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(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.

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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.

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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.

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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’s biographer Albrecht Fölsing explained: Einstein presented his field equations on November 25, 1915, but six days earlier, on November 20, Hilbert had derived the identical field equations for which Einstein had been searching such a long time. On November 18 Hilbert had sent Einstein a letter with a certain draft, and Fölsing asked about this possible draft: “Could Einstein, casting his eye over this paper, have discovered the term which was still lacking in his own equations, and thus ‘nostrified’ Hilbert?” Historical evidence support a scenario according to which Einstein discovered his final field equations by “casting his eye over” his own previous works. In November 4, 1915 Einstein wrote the components of the gravitational field and showed that a material point in a gravitational field moves on a geodesic line in space-time, the equation of which is written in terms of the Christoffel symbols. Einstein found it advantageous to use for the components of the gravitational field the Christoffel symbols. Einstein had already basically possessed the field equations in 1912, but had not recognized the formal importance of the Christoffel symbols as the components of the gravitational field. Einstein probably found the final form of the generally covariant field equations by manipulating his own (November 4, 1915) equations. Other historians’ findings seem to support the scenario according to which Einstein did not “nostrify” Hilbert.

Einstein and Hilbert

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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.

Schwarzschild

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”.

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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.

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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.

Lemaitre

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.

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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.

 

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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.

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

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