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:


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):


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


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:


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


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:


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):


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”:


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


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):


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):


By the way I highly recommend Kennefick’s book.

That being said, in his book The Formative Years of Relativity, Gutfreund once again fails to mention my work. He 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):


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:


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:


They told the story of the origin of gravitational waves:


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 they write: “Einstein mentioned gravitational waves for the first time in a letter of 19 February 1916 to Karl Schwarzschild..”. Hence, according to Gutfreund (and Jürgen Renn) in 2016, Einstein did not mention gravitational waves for the first time in the 1913 discussion following the Vienna lecture, he rather did it in 1916. At this stage Gutfreund (and Jürgen Renn) seemed to have been unaware that in 1913 Einstein had discussed gravitational waves with Max Born.

Finally, in the same book, General Relativity Conflict and Rivalries, published in 2015, I write:


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):



My new paper on Einstein and general relativity

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


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:



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

I read this paper:




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. 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)


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.








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:



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.




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


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.


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.


I present and read several sections of my books on Einstein


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


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.