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):




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'”:


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


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”.


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:


“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:


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:


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:




And Poincaré’s disk thought experiment:








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):






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.








Centenary of the Death of Poincaré – Einstein and Poincaré 2012 פואנקרה ואיינשטיין

לרגל מאה שנה למותו של פואנקרה, פרסמתי בשלושה חלקים מחקר על הנרי פואנקרה, תרומתו בתחום של תורת האלקטרון והאלקטרודינמיקה של הגופים בתנועה והשאלה האם פואנקרה הגיע לתורת יחסות ולגילויים שאותם אנו מוצאים בתורת היחסות הפרטית לפני או במקביל לאיינשטיין. כמובן שהשאלה היא מעט יותר מורכבת ולא פשטנית כפי שהצגתי אותה כאן. בנושא זה כתבתי את עבודת הדוקטורט שלי והמאמרים הם סיכום ועדכון של הדוקטורט שלי שנכתב לפני 14 שנה.

A Biography of Poincaré  – Researcher in dynamics of the electron and electrodynamics –  2012 Centenary of the Death of Poincaré. Here

On January 4, 2012 (the centenary of Henri Poincaré’s death) a colloquium was held in Nancy, France the subject of which was “Vers une biographie d’Henri Poincaré”. Scholars discussed several approaches for writing a biography of Poincaré


I present a personal and scientific biographical sketch of Poincaré and his contributions to electrodynamics of moving bodies, which does not in any way reflect Poincaré’s rich personality and immense activity in science. When Poincaré traveled to parts of Europe, Africa and America, his companions noticed that he knew well everything from statistics to history and curious customs and habits of peoples. He was almost teaching everything in science. He was so encyclopedic that he dealt with the outstanding questions in the different branches of physics and mathematics; he had altered whole fields of science such as non-Euclidean geometry, Arithmetic, celestial mechanics, thermodynamics and kinetic theory, optics, electrodynamics, Maxwell’s theory, and other topics from the forefront of Fin de Siècle physical science

As opposed to the prosperity of biographies and secondary papers studying the life and scientific contributions of Albert Einstein, one finds much less biographies and secondary sources discussing Poincaré’s life and work. Unlike Einstein, Poincaré was not a cultural icon. Beginning in 1920 Einstein became a myth and a world famous figure. Although Poincaré was so brilliant in mathematics, he mainly remained a famous mathematician within the professional circle of scientists. He published more papers than Einstein, performed research in many more branches of physics and mathematics, received more prizes on his studies, and was a member of more academies in the whole world. Despite this tremendous yield, Poincaré did not win the Nobel Prize

Most famous is Poincaré’s philosophy of conventionalism, which sprang out of his research into geometry during a period (the end of the 1880’s) when non-Euclidean geometries were a matter of a consistent possibility. Poincaré developed two kinds of conventionalism, conventionalism applicable to geometry and conventionalism for the principles of physics. Both sprang from Poincaré’s mathematical group theory

In addition to the geometries of Euclid, Lobachewski, and Riemann, Poincaré proposed another geometry, the truth of which was not incompatible with the other geometries; he called it the “fourth geometry”. The first time that Poincaré’s fourth geometry appeared in print was in 1891

Einstein did not feel at ease with Poincaré’s standpoint. In 1992 Michel Paty commented on Einstein’s presentation of Poincaré’s conventionalism in 1921, “Actually this is not exactly Poincaré’s point of view, but a translation of it made by Einstein in his own perspective, that is according to his conception of physical Geometry”. See

Scott Walter’s papers here

And Peter Galison’s book Einstein’s Clocks, Poincare’s Maps here

Review by John Stachel: here and by Alberto Martínez here

Scientific contributions in electrodynamics: Before 1905, Poincaré stressed the importance of the method of clocks and their synchronization, but unlike Einstein, magnet and conductor (asymmetries in Lorentz’s theory regarding the explanation of Faraday’s induction) or chasing a light beam and overtaking it, were not a matter of great concern for him

In 1905 Poincaré elaborated Lorentz’s electron theory from 1904 in two papers entitled “On the Dynamics of the Electron”. Poincaré’s theory was a space-time mathematical theory of groups at the basis of which stood the postulate of relativity; Einstein’s 1905 theory was a kinematical theory of relativity

Poincaré did not renounce the ether. He wrote a new law of addition of velocities, but he did not abandon the tacit assumptions made about the nature of time, simultaneity, and space measurements implicit in Newtonian kinematics

Although he questioned absolute time and absolute simultaneity, he did not make new kinematical tacit assumptions about space and time. He also did not require reciprocity of the appearances, and therefore did not discover relativity of simultaneity

These are the main hallmarks of Einstein’s special theory of relativity. Nevertheless, Poincaré had arrived at many novel findings that went way beyond Fin de Siècle physics. here


Read other point of views: Olivier Darrigol’s papers here and here

Darrigol, Olivier, “Henri Poincaré’s criticism of fin de siècle electrodynamics”, Studies in History and Philosophy of Modern Physics 26, 1995, pp. 1-44. here

Darrigol, Olivier, Electrodynamics from Ampère to Einstein, 2000, Oxford: Oxford University Press. Here

Mass-energy equivalence: In 1900 Poincaré considered a device creating and emitting electromagnetic waves. The device emits energy in all directions. As a result of the energy being emitted, it recoils. No motion of any other material body compensates for the recoil at that moment. Poincaré found that as a result of the recoil of the oscillator, in the moving system, the oscillator generating the electromagnetic energy suffers an “apparent complementary force”. In addition, in order to demonstrate the non-violation of the theorem of the motion of the centre of gravity, Poincaré needed an arbitrary convention, the “fictitious fluid”

Einstein demonstrated that if the inertial mass E/c2 is associated with the energy E, and on assuming the inseparability of the theorem of the conservation of mass and that of energy, then – at least as a first approximation – the theorem of the conservation of the motion of the centre of gravity is also valid for all systems in which electromagnetic processes take place

Before 1905 (and also afterwards) Poincaré did not explore the inertial mass-energy equivalence

Einstein was the first to explore the inertial mass-energy equivalence. In 1905 Einstein showed that a change in energy is associated with a change in inertial mass equal to the change in energy divided by c2


For a different point of view: Darrigol, Olivier, “Poincaré, Einstein, et l’inertie de l’énergie”, Comptes rendus de l’Académie des sciences IV 1, 2000, pp. 143-153. Here

See also this paper by Stephen Boughn and  Tony Rothman. A report of the paper here


Did Poincaré influence Einstein on his way to the Special theory of relativity? One differentiates two kinds of questions here

  1What was the effect of Poincaré’s studies on the development of the Special Theory of relativity? and

 2What was the effect Poincaré’s research may have had on the development of Einstein’s own pathway towards the Special Theory of Relativity? hence

Poincaré did contribute to the theory of relativity a great deal. His 1905 space-time theory of groups greatly influenced Minkowski on his way to reformulate and recast mathematically the special theory of relativity. In addition, he arrived at many interesting ideas. However, it appears from examining the primary sources that Poincaré did not influence Einstein on his route to the special theory of relativity. See my papers here

אלברט איינשטיין – דרכו ליחסות Albert Einstein – pathway to theory of relativity

My Einstein and Relativity Papers – Gali Weinstein

Einstein’s Pathway to the Special Theory of Relativity

Einstein’s Pathway to the General Theory of Relativity

The papers describe the genesis and history of special relativity and the discovery and history of general relativity – Einstein chases a light beam, the magnet and conductor thought experiment, Michelson-Morley experiment, emission theory, ether superfluous, Fizeau water-tube experiment, the principle of relativity and the principle of the constancy of the velocity of light (light postulate), The Step, Besso-Einstein meeting, Relativity 1905 paper. 1907 equivalence principle, lift experiments, Galileo principle, coordinate-dependant theory of relativity, Zurich Notebook, Einstein-Grossmann theory (Entwurf theory), deflection of light near the sun, Einstein’s struggles with Entwurf theory, hole argument, 1915 General Theory of Relativity: Hilbert – Einstein, precession or advance of Perihelion of Mercury, how Einstein found the generally covariant field equations, and Einstein’s 1916 general theory of relativity – Mach’s principle, rotating disk thought experiment, and point coincidence argument. These papers do not discuss the affine connection. For a discussion of the affine connection please consult Prof. John Stachel’s works

Philosophyof physics andof Special Relativity – papers discussing philosophical questions about space and time and interpretations of Special Relativity. A rigid body does not exist in the special theory of relativity, distant simultaneity defined with respect to a given frame of reference without reference to synchronized clocks, Einstein synchronization, challenges on Einstein’s connection of synchronization and Lorentz contraction, a theory of relativity without light – Ignatowski, Einstein’s composition of relative velocities – addition theorem for relative velocities, and space of relative velocities, Max Born and rigid body problem, Paul Ehrenfest’s paradox, relativity of simultaneity, Einstein’s clocks: Einstein’s 1905 Clock Paradox, Paul Langevin and the Twin Paradox

Poincaré and EinsteinThe inertial mass-energy equivalence, Lorentz’s theory of the electron violated the principle of action and reaction, Henri Poincaré trying to mend this violation, in 1905 Einstein showed that a change in energy is associated with a change in inertial mass equal to the change in energy divided by c2. Einstein and Poincaré– Method of clocks and their synchronization, Sur la dynamique de l’electron, Dynamics of the Electron, Einstein’s 1905 letter to Conrad Habicht, Poincaré’s 1905 letters to Lorentz, Poincaré’s spacetime mathematical theory of groups, As opposed to Einstein, before 1905 Poincaré stressed the importance of the method of clocks and their synchronization by light signals. Poincaré’s Lorentz group, Poincaré’s La Science et l’hypothèse  – Science and Hypothesis 

Innovation never comes from the established institutions… – Eric Schmidt

מאמרי איינשטיין והיחסות שלי – גלי וינשטיין

דרכו של איינשטיין ליחסות הפרטית.

דרכו של איינשטיין ליחסות הכללית.

אני מתכננת לפרסם ספר ולכן המאמרים הם טיוטא ולא גרסא סופית.

“חידוש אף פעם לא מגיע ממוסדות מוכרים” – אריק שמידט.

Einstein Archives – Jerusalem and Einstein Papers Project – Caltech

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פרויקט איינשטיין

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