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/c^{2} 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 *c*^{2}

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