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Henri Poincaré
Henri Poincaré, photograph from the frontispiece of the 1913 edition of "Last Thoughts"
Henri Poincaré, photograph from the frontispiece of the 1913 edition of "Last Thoughts"
Born April 29, 1854(1854-04-29)
Nancy, France
Died July 17, 1912 (aged 58)
Paris, France
Residence France
Nationality French
Fields Mathematician and physicist
Institutions Corps des Mines
Caen University
La Sorbonne
Bureau des Longitudes
Alma mater Lycée Nancy
École Polytechnique
École des Mines
Doctoral advisor Charles Hermite
Doctoral students Louis Bachelier
Known for Poincaré conjecture
Three-body problem
Topology
Special relativity
Notable awards Matteucci Medal (1905)

Jules Henri Poincaré (April 29, 1854 – July 17, 1912) (IPA: [ˈʒyl ɑ̃ˈʁi pwɛ̃kaˈʁe][1]) was a French mathematician and theoretical physicist, and a philosopher of science. Events 1429 - Joan of Arc arrives to relieve the Siege of Orleans. Year 1854 ( MDCCCLIV) was a Common year starting on Sunday (link will display the full calendar of the Gregorian Calendar (or a Common year Nancy (nɑ̃si archaic Nanzig Nanzeg is a city and commune in the Lorraine région of northeastern France This article is about the country For a topic outline on this subject see List of basic France topics. Events 180 - Twelve inhabitants of Scillium in North Africa are executed for being Christians Year 1912 ( MCMXII) was a Leap year starting on Monday (link will display the full calendar of the Gregorian calendar (or a Leap year starting Paris (ˈpærɨs in English; in French) is the Capital of France and the country's largest city This article is about the country For a topic outline on this subject see List of basic France topics. This article is about the country For a topic outline on this subject see List of basic France topics. This article is about the country For a topic outline on this subject see List of basic France topics. A mathematician is a person whose primary area of study and research is the field of Mathematics. A physicist is a Scientist who studies or practices Physics. Physicists study a wide range of physical phenomena in many branches of physics spanning The Corps of Mines (in French Corps des Mines) is the foremost of the great technical corps of the French state. The Université de Caen Basse-Normandie or Caen University is a University in Caen, France. The Bureau des Longitudes is a French scientific institution founded by decree of June 25 1795 and charged with the improvement of nautical Navigation Alma mater is Latin for "nourishing mother" It was used in Ancient Rome as a title for the mother Goddess, and in Medieval For other Écoles Polytechniques see École Polytechnique de Montréal and École Polytechnique Fédérale de Lausanne. The École Nationale Supérieure des Mines de Paris (also known as Mines ParisTech, École des Mines de Paris, ENSMP, Mines Paris or simply A doctorate is an Academic degree that indicates the highest level of academic achievement Charles Hermite (ʃaʁl ɛʁˈmit ( December 24, 1822 &ndash January 14, 1901) was a French Mathematician who did Louis Jean-Baptiste Alphonse Bachelier ( March 11, 1870 - April 28, 1946) was a French Mathematician at the turn of the 20th century In Mathematics, the Poincaré conjecture (French pwɛ̃kaʀe is a Theorem about the characterization of the three-dimensional sphere among The n -body problem is the problem of finding given the initial positions masses and velocities of n bodies their subsequent motions as determined by Topology ( Greek topos, "place" and logos, "study" is the branch of Mathematics that studies the properties of Special relativity (SR (also known as the special theory of relativity or STR) is the Physical theory of Measurement in Inertial The Matteucci Medal was established to award Physicists for their fundamental contributions Events 1429 - Joan of Arc arrives to relieve the Siege of Orleans. Year 1854 ( MDCCCLIV) was a Common year starting on Sunday (link will display the full calendar of the Gregorian Calendar (or a Common year Events 180 - Twelve inhabitants of Scillium in North Africa are executed for being Christians Year 1912 ( MCMXII) was a Leap year starting on Monday (link will display the full calendar of the Gregorian calendar (or a Leap year starting This article is about the country For a topic outline on this subject see List of basic France topics. A mathematician is a person whose primary area of study and research is the field of Mathematics. A physicist is a Scientist who studies or practices Physics. Physicists study a wide range of physical phenomena in many branches of physics spanning Philosophy of science is the study of assumptions foundations and implications of Science. Poincaré is often described as a polymath, and in mathematics as The Last Universalist, since he excelled in all fields of the discipline as it existed during his lifetime. A polymath ( Greek polymathēs, πολυμαθής "having learned much" is a person whose knowledge is not restricted to one subject area

As a mathematician and physicist, he made many original fundamental contributions to pure and applied mathematics, mathematical physics, and celestial mechanics. Broadly speaking pure mathematics is Mathematics motivated entirely for reasons other than application Applied mathematics is a branch of Mathematics that concerns itself with the mathematical techniques typically used in the application of mathematical knowledge to other domains Mathematical physics is the scientific discipline concerned with the interface of Mathematics and Physics. Celestial mechanics is the branch of Astrophysics that deals with the motions of Celestial objects The field applies principles of Physics, historically He was responsible for formulating the Poincaré conjecture, one of the most famous problems in mathematics. In Mathematics, the Poincaré conjecture (French pwɛ̃kaʀe is a Theorem about the characterization of the three-dimensional sphere among In his research on the three-body problem, Poincaré became the first person to discover a chaotic deterministic system which laid the foundations of modern chaos theory. The n -body problem is the problem of finding given the initial positions masses and velocities of n bodies their subsequent motions as determined by In Mathematics, chaos theory describes the behavior of certain dynamical systems – that is systems whose state evolves with time – that may exhibit dynamics that He is considered to be one of the founders of the field of topology. Topology ( Greek topos, "place" and logos, "study" is the branch of Mathematics that studies the properties of

Poincaré introduced the modern principle of relativity and was the first to present the Lorentz transformations in their modern symmetrical form. A principle of relativity is a criterion for judging physical theories, stating that they are inadequate if they do not prescribe the exact same laws of physics in In Physics, the Lorentz transformation converts between two different observers' measurements of space and time where one observer is in constant motion with respect to Poincaré discovered the remaining relativistic velocity transformations and recorded them in a letter to Lorentz in 1905. Thus he obtained perfect invariance of all of Maxwell's equations, an important step in the formulation of the theory of special relativity. In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric Special relativity (SR (also known as the special theory of relativity or STR) is the Physical theory of Measurement in Inertial

The Poincaré group used in physics and mathematics was named after him. In Physics and Mathematics, the Poincaré group, named after Henri Poincaré, is the group of isometries of Minkowski spacetime

Contents

Life

Poincaré was born on April 29, 1854 in Cité Ducale neighborhood, Nancy, France into an influential family (Belliver, 1956). Events 1429 - Joan of Arc arrives to relieve the Siege of Orleans. Year 1854 ( MDCCCLIV) was a Common year starting on Sunday (link will display the full calendar of the Gregorian Calendar (or a Common year Nancy (nɑ̃si archaic Nanzig Nanzeg is a city and commune in the Lorraine région of northeastern France His father Leon Poincaré (1828-1892) was a professor of medicine at the University of Nancy (Sagaret, 1911). Nancy-Université federates the three principal institutes of higher education of Nancy, in Lorraine: Henri Poincaré University His adored younger sister Aline married the spiritual philosopher Emile Boutroux. Étienne Émile Marie Boutroux ( July 28 1845 - November 22 1921) was an eminent 19th century French Philosopher of Another notable member of Jules' family was his cousin, Raymond Poincare, who would become the President of France, 1913 to 1920, and a fellow member of the Académie française. Raymond Poincaré (20 August 1860 – 15 October 1934 was a French conservative Statesman who served as Prime Minister of France on five L'Académie française, or the French Academy, is the pre-eminent French learned body on matters pertaining to the French language. [2]

Education

During his childhood he was seriously ill for a time with diphtheria and received special instruction from his gifted mother, Eugénie Launois (1830-1897). Diphtheria ( Greek διφθερα ( diphthera)—“pair of leather scrolls" is an upper respiratory tract illness characterized by sore

In 1862 Henri entered the Lycée in Nancy (now renamed the Lycée Henri Poincaré in his honour, along with the University of Nancy). He spent eleven years at the Lycée and during this time he proved to be one of the top students in every topic he studied. He excelled in written composition. His mathematics teacher described him as a "monster of mathematics" and he won first prizes in the concours général, a competition between the top pupils from all the Lycées across France. In France, the concours général is a national Competition held every year between students of Première (11th grade and Terminale (12th and (His poorest subjects were music and physical education, where he was described as "average at best" (O'Connor et al. , 2002). However, poor eyesight and a tendency towards absentmindedness may explain these difficulties (Carl, 1968). He graduated from the Lycée in 1871 with a Bachelor's degree in letters and sciences.

During the Franco-Prussian War of 1870 he served alongside his father in the Ambulance Corps. The Franco-Prussian War or Franco-German War, often referred to in France as the 1870 War ( 19 July, 1870 — 10 May, 1871

Poincaré entered the École Polytechnique in 1873. For other Écoles Polytechniques see École Polytechnique de Montréal and École Polytechnique Fédérale de Lausanne. There he studied mathematics as a student of Charles Hermite, continuing to excel and publishing his first paper (Démonstration nouvelle des propriétés de l'indicatrice d'une surface) in 1874. Charles Hermite (ʃaʁl ɛʁˈmit ( December 24, 1822 &ndash January 14, 1901) was a French Mathematician who did He graduated in 1875 or 1876. He went on to study at the École des Mines, continuing to study mathematics in addition to the mining engineering syllabus and received the degree of ordinary engineer in March 1879. The École Nationale Supérieure des Mines de Paris (also known as Mines ParisTech, École des Mines de Paris, ENSMP, Mines Paris or simply

As a graduate of the École des Mines he joined the Corps des Mines as an inspector for the Vesoul region in northeast France. The Corps of Mines (in French Corps des Mines) is the foremost of the great technical corps of the French state. Vesoul is a French town and commune located in the Haute-Saône département. He was on the scene of a mining disaster at Magny in August 1879 in which 18 miners died. Le Magny|Les Magny Magny (pro mah-NJEE is the name or part of the name of the following communes in France Magny Eure-et-Loir, in the Eure-et-Loir department He carried out the official investigation into the accident in a characteristically thorough and humane way.

At the same time, Poincaré was preparing for his doctorate in sciences in mathematics under the supervision of Charles Hermite. Charles Hermite (ʃaʁl ɛʁˈmit ( December 24, 1822 &ndash January 14, 1901) was a French Mathematician who did His doctoral thesis was in the field of differential equations. A differential equation is a mathematical Equation for an unknown function of one or several variables that relates the values of the It was named Sur les propriétés des fonctions définies par les équations différences. Poincaré devised a new way of studying the properties of these equations. He not only faced the question of determining the integral of such equations, but also was the first person to study their general geometric properties. He realised that they could be used to model the behaviour of multiple bodies in free motion within the solar system. The Solar System consists of the Sun and those celestial objects bound to it by Gravity. Poincaré graduated from the University of Paris in 1879.

The young Henri Poincaré
The young Henri Poincaré

Career

Soon after, he was offered a post as junior lecturer in mathematics at Caen University, but he never fully abandoned his mining career to mathematics. The Université de Caen Basse-Normandie or Caen University is a University in Caen, France. He worked at the Ministry of Public Services as an engineer in charge of northern railway development from 1881 to 1885. He eventually became chief engineer of the Corps de Mines in 1893 and inspector general in 1910.

Beginning in 1881 and for the rest of his career, he taught at the University of Paris (the Sorbonne). The historic University of Paris (Université de Paris first appeared in the second half of the 13th century He was initially appointed as the maître de conférences d'analyse (associate professor of analysis) (Sageret, 1911). Eventually, he held the chairs of Physical and Experimental Mechanics, Mathematical Physics and Theory of Probability, and Celestial Mechanics and Astronomy.

Also in that same year, Poincaré married Miss Poulain d'Andecy. Together they had four children: Jeanne (born 1887), Yvonne (born 1889), Henriette (born 1891), and Léon (born 1893).

In 1887, at the young age of 32, Poincaré was elected to the French Academy of Sciences. The French Academy of Sciences ( French: Académie des sciences) is a Learned society, founded in 1666 by Louis XIV at the He became its president in 1906, and was elected to the Académie française in 1909. L'Académie française, or the French Academy, is the pre-eminent French learned body on matters pertaining to the French language.

In 1887 he won Oscar II, King of Sweden's mathematical competition for a resolution of the three-body problem concerning the free motion of multiple orbiting bodies. Early life At his birth in Stockholm Oscar Frederik was created Duke of Östergötland. The n -body problem is the problem of finding given the initial positions masses and velocities of n bodies their subsequent motions as determined by (See #The three-body problem section below)

In 1893 Poincaré joined the French Bureau des Longitudes, which engaged him in the synchronisation of time around the world. The Bureau des Longitudes is a French scientific institution founded by decree of June 25 1795 and charged with the improvement of nautical Navigation In 1897 Poincaré backed an unsuccessful proposal for the decimalisation of circular measure, and hence time and longitude (see Galison 2003). Longitude (ˈlɒndʒɪˌtjuːd or ˈlɒŋgɪˌtjuːd symbolized by the Greek character Lambda (λ is the east-west Geographic coordinate measurement It was this post which led him to consider the question of establishing international time zones and the synchronisation of time between bodies in relative motion. (See #Work on Relativity section below)

In 1899, and again more successfully in 1904, he intervened in the trials of Alfred Dreyfus. Alfred Dreyfus (9 October 1859 &ndash 12 July 1935 was a French artillery officer of Jewish background whose trial and conviction in 1894 on charges of treason He attacked the spurious scientific claims of some of the evidence brought against Dreyfus, who was a Jewish officer in the French army charged with treason by anti-Semitic colleagues.

In 1912 Poincaré underwent surgery for a prostate problem and subsequently died from an embolism on July 17, 1912, in Paris. The prostate (from Greek προστάτης - prostates, literally "one who stands before" "protector" "guardian" is a In Medicine, an embolism occurs when an object (the embolus, plural emboli) migrates from one part of the Body (through circulation Events 180 - Twelve inhabitants of Scillium in North Africa are executed for being Christians Year 1912 ( MCMXII) was a Leap year starting on Monday (link will display the full calendar of the Gregorian calendar (or a Leap year starting He was 58 years of age. He is buried in the Poincaré family vault in the Cemetery of Montparnasse, Paris. Montparnasse Cemetery ( French: Cimetière de Montparnasse) is a famous cemetery in the Montparnasse quarter of Paris, part of the

The French Minister of Education, Claude Allegre, has recently (2004) proposed that Poincaré be reburied in the Panthéon in Paris, which is reserved for French citizens only of the highest honour. Claude (Jean Allègre (born 31 March 1937, Paris) is a French Politician and Scientist. The Panthéon ( Latin Pantheon, from Greek Pantheon meaning "All the gods" is a building in the Latin Quarter [3]

Students

Poincaré had two notable doctoral students at the University of Paris, Louis Bachelier (1900) and Dimitrie Pompeiu (1905) [4]

Work

Summary

Poincaré made many contributions to different fields of pure and applied mathematics such as: celestial mechanics, fluid mechanics, optics, electricity, telegraphy, capillarity, elasticity, thermodynamics, potential theory, quantum theory, theory of relativity and physical cosmology. Louis Jean-Baptiste Alphonse Bachelier ( March 11, 1870 - April 28, 1946) was a French Mathematician at the turn of the 20th century Dimitrie Pompeiu ( Broscǎuţi, Botoşani County, Romania &ndash October 8, 1954, Bucharest) was a well-known Romanian Celestial mechanics is the branch of Astrophysics that deals with the motions of Celestial objects The field applies principles of Physics, historically Fluid mechanics is the study of how Fluids move and the Forces on them Capillary action, capillarity, capillary motion, or wicking is the ability of a substance to draw another substance into it A material is said to be elastic if it deforms under stress (e In Physics, thermodynamics (from the Greek θερμη therme meaning " Heat " and δυναμις dynamis meaning " Potential theory may be defined as the study of Harmonic functions Definition and comments The term "potential theory" arises from the fact that Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons This page is about the scientific concept of relativity for philosophical or sociological theories about relativity see Relativism. Physical cosmology, as a branch of Astronomy, is the study of the large-scale structure of the Universe and is concerned with fundamental questions about its

He was also a populariser of mathematics and physics and wrote several books for the lay public.

Among the specific topics he contributed to are the following:

The three-body problem

The problem of finding the general solution to the motion of more than two orbiting bodies in the solar system had eluded mathematicians since Newton's time. Sir Isaac Newton, FRS (ˈnjuːtən 4 January 1643 31 March 1727) Biography Early years See also Isaac Newton's early life and achievements This was known originally as the three-body problem and later the n-body problem, where n is any number of more than two orbiting bodies. The n -body problem is the problem of finding given the initial positions masses and velocities of n bodies their subsequent motions as determined by The n-body solution was considered very important and challenging at the close of the nineteenth century. Indeed in 1887, in honour of his 60th birthday, Oscar II, King of Sweden, advised by Gösta Mittag-Leffler, established a prize for anyone who could find the solution to the problem. Early life At his birth in Stockholm Oscar Frederik was created Duke of Östergötland. Magnus Gustaf (Gösta Mittag-Leffler ( 16 March 1846 – 7 July 1927) was a Swedish Mathematician. The announcement was quite specific:

“ Given a system of arbitrarily many mass points that attract each according to Newton's law, under the assumption that no two points ever collide, try to find a representation of the coordinates of each point as a series in a variable that is some known function of time and for all of whose values the series converges uniformly. In Physics, an inverse-square law is any Physical law stating that some physical Quantity or strength is inversely proportional In the mathematical field of analysis, uniform convergence is a type of Convergence stronger than Pointwise convergence. ”

In case the problem could not be solved, any other important contribution to classical mechanics would then be considered to be prizeworthy. The prize was finally awarded to Poincaré, even though he did not solve the original problem. One of the judges, the distinguished Karl Weierstrass, said, "This work cannot indeed be considered as furnishing the complete solution of the question proposed, but that it is nevertheless of such importance that its publication will inaugurate a new era in the history of celestial mechanics. Karl Theodor Wilhelm Weierstrass ( Weierstraß) ( October 31, 1815 &ndash February 19, 1897) was a German mathematician " (The first version of his contribution even contained a serious error; for details see the article by Diacu). The version finally printed contained many important ideas which lead to the theory of chaos. In Mathematics, chaos theory describes the behavior of certain dynamical systems – that is systems whose state evolves with time – that may exhibit dynamics that The problem as stated originally was finally solved by Karl F. Sundman for n = 3 in 1912 and was generalised to the case of n > 3 bodies by Qiudong Wang in the 1990s. Karl Frithiof Sundman (1873 &ndash 1949 was a Finnish Mathematician who used analytic methods to prove the existence of a convergent Infinite series solution Qiudong Wang is an Associate Professor at the Department of Mathematics the University of Arizona.

Work on relativity

Marie Curie and Poincaré talk at the 1911 Solvay Conference.
Marie Curie and Poincaré talk at the 1911 Solvay Conference. The International Solvay Institutes for Physics and Chemistry, located in Brussels, were founded by the Belgian industrialist Ernest Solvay
Main articles: Lorentz ether theory and History of special relativity

Local time

Poincaré's work at the Bureau des Longitudes on establishing international time zones led him to consider how clocks at rest on the Earth, which would be moving at different speeds relative to absolute space (or the "luminiferous aether"), could be synchronised. What is now called Lorentz Ether theory ("LET" has its roots in Hendrik Lorentz 's "Theory of electrons" which was the final point in the development of The History of special relativity consists of many theoretical and empirical results of physicists like Hendrik Lorentz and Henri Poincaré, which culminated in the At the same time Dutch theorist Hendrik Lorentz was developing Maxwell's theory into a theory of the motion of charged particles ("electrons" or "ions"), and their interaction with radiation. The Netherlands ( Dutch:, ˈnedərlɑnt is the European part of the Kingdom of the Netherlands, which consists of the Netherlands the Netherlands Hendrik Antoon Lorentz ( July 18, 1853 &ndash February 4, 1928) was a Dutch Physicist who shared the 1902 Nobel He had introduced in 1895 an auxiliary quantity (without physical interpretation) called "local time" t^\prime = t-vx^\prime/c^2,\; \mathrm{where}\; x^\prime = x - vt and introduced the hypothesis of length contraction to explain the failure of optical and electrical experiments to detect motion relative to the aether (see Michelson-Morley experiment). Length contraction, according to Hendrik Lorentz, is the physical phenomenon of a decrease in Length detected by an observer in objects that travel at any non-zero The Michelson–Morley experiment, one of the most important and famous experiments in the History of physics, was performed in 1887 by Albert Michelson and [7] Poincaré was a constant interpreter (and sometimes friendly critic) of Lorentz's theory. Poincaré as a philosopher, was interested in the "deeper meaning". Thus he interpreted Lorentz's theory and in so doing he came up with many insights that are now associated with special relativity. In "The Measure of Time" (1898), Poincaré discussed the difficulty of establishing simultaneity at a distance and concluded it can be established by convention. He also argued, that scientists have to set the constancy of the speed of light as a postulate to give physical theories the simplest form. In traditional Logic, an axiom or postulate is a proposition that is not proved or demonstrated but considered to be either self-evident, or subject [8] Based on these assumptions he discussed in 1900 Lorentz's "wonderful invention" of local time and remarked that it arose when moving clocks are synchronised by exchanging light signals assumed to travel with the same speed in both directions in a moving frame. [9]

Principle of relativity and Lorentz transformations

He discussed the "principle of relative motion" in two papers in 1900[10][9] and named it the principle of relativity in 1904, according to which no mechanical or electromagnetic experiment can discriminate between a state of uniform motion and a state of rest. A principle of relativity is a criterion for judging physical theories, stating that they are inadequate if they do not prescribe the exact same laws of physics in [11] In 1905 Poincaré wrote to Lorentz about Lorentz's paper of 1904, which Poincaré described as a "paper of supreme importance. " In this letter he pointed out an error Lorentz had made when he had applied his transformation to one of Maxwell's equations, that for charge-occupied space, and also questioned the time dilation factor given by Lorentz. [12] In a second letter to Lorentz, Poincaré gave his own reason why Lorentz's time dilation factor was indeed correct after all: it was necessary to make the Lorentz transformation form a group and gave what is now known as the relativistic velocity-addition law. [13] Poincaré later delivered a paper at the meeting of the Academy of Sciences in Paris on 5 June 1905 in which these issues were addressed. Events 70 - Titus and his Roman Legions breach the middle wall of Jerusalem in the Siege of Jerusalem Year 1905 ( MCMV) was a Common year starting on Sunday (link will display full calendar of the Gregorian calendar (or a Common year starting In the published version of that he wrote[14]:

“ The essential point, established by Lorentz, is that the equations of the electromagnetic field are not altered by a certain transformation (which I will call by the name of Lorentz) of the form:
x^\prime = k\ell\left(x + \varepsilon t\right),~t^\prime = k\ell\left(t + \varepsilon x\right),~y^\prime = \ell y,~ z^\prime = \ell z,~k = 1/\sqrt{1-\varepsilon^2}.
 ”

and showed that the arbitrary function \ell\left(\varepsilon\right) must be unity for all \varepsilon (Lorentz had set \ell = 1 by a different argument) to make the transformations form a group. In an enlarged version of the paper that appeared in 1906 Poincaré pointed out that the combination x2 + y2 + z2 − c2t2 is invariant. He noted Lorentz transformation is merely a rotation in four-dimensional space about the origin by introducing ct\sqrt{-1} as a fourth imaginary coordinate, and he used an early form of four-vectors. In relativity, a four-vector is a vector in a four-dimensional real Vector space, called Minkowski space. [15] Poincaré’s attempt of a four-dimensional reformulation of the new mechanics was rejected by himself in 1907, because in his opinion the translation of physics into the language of four-dimensional metry would entail too much effort for limited profit. [16] So it was Hermann Minkowski, who worked out the consequences of this notion in 1907. Hermann Minkowski ( June 22 1864 – January 12 1909) was a Russian born German Mathematician, of Jewish

Mass-energy relation

Like others before, Poincaré (1900) discovered a relation between mass and electromagnetic energy. In Physics, mass–energy equivalence is the concept that for particles slower than light any Mass has an associated Energy and vice versa. While studying the conflict between the action/reaction principle and Lorentz ether theory, he tried to determine whether the center of gravity still moves with a uniform velocity when electromagnetic fields are included. Newton's laws of motion are three Physical laws which provide relationships between the Forces acting on a body and the motion of the What is now called Lorentz Ether theory ("LET" has its roots in Hendrik Lorentz 's "Theory of electrons" which was the final point in the development of [9] He noticed that the action/reaction principle does not hold for matter alone, but that the electromagnetic field has its own momentum. Poincaré concluded that electromagnetic field energy of the ether behaves like a fictitious fluid ("fluide fictif") with a mass density of E/c². FLUID ( F ast L ight '''U'''ser '''I'''nterface D esigner is a graphical editor that is used to produce FLTK Source code If the center of mass frame is defined by both the mass of matter and the mass of the fictitious fluid, and if the fictitious fluid is indestructible — it's neither created or destroyed — then the motion of the center of mass frame remains uniform. A center of momentum frame (or zero-momentum frame or COM frame of a system is any Inertial frame in which the Center of mass is at rest (has zero velocity But electromagnetic energy can be converted into other forms of energy. So Poincaré assumed that there exists a non-electric energy fluid at each point of space, into which electromagnetic energy can be transformed and which also carries a mass proportional to the energy. In this way, the motion of the center of mass remains uniform. Poincaré said that one should not be too surprised by these assumptions, since they are only mathematical fictions.

However, Poincaré's resolution led to a paradox when changing frames: if a Hertzian oscillator radiates in a certain direction, it will suffer a recoil from the inertia of the fictitious fluid. This article is about backward Momentum produced in firearms when fired Poincaré performed a Lorentz boost (to order v/c) to the frame of the moving source. In Physics, the Lorentz transformation converts between two different observers' measurements of space and time where one observer is in constant motion with respect to He noted that energy conservation holds in both frames, but that the law of conservation of momentum is violated. This would allow perpetual motion, a notion which he abhorred. The term perpetual motion, taken literally refers to movement that goes on forever The laws of nature would have to be different in the frames of reference, and the relativity principle would not hold. Therefore he argued that also in this case there has to be another compensating mechanism in the ether.

Poincaré himself came back to this topic in his St. Louis lecture (1904). [11] This time (and later also in 1908) he rejected[17] the possibility that energy carries mass and also the possibility, that motions in the ether can compensate the above mentioned problems:

“ The apparatus will recoil as if it were a cannon and the projected energy a ball, and that contradicts the principle of Newton, since our present projectile has no mass; it is not matter, it is energy. [. . ] Shall we say that the space which separates the oscillator from the receiver and which the disturbance must traverse in passing from one to the other, is not empty, but is filled not only with ether, but with air, or even in inter-planetary space with some subtile, yet ponderable fluid; that this matter receives the shock, as does the receiver, at the moment the energy reaches it, and recoils, when the disturbance leaves it? That would save Newton's principle, but it is not true. If the energy during its propagation remained always attached to some material substratum, this matter would carry the light along with it and Fizeau has shown, at least for the air, that there is nothing of the kind. Michelson and Morley have since confirmed this. We might also suppose that the motions of matter proper were exactly compensated by those of the ether; but that would lead us to the same considerations as those made a moment ago. The principle, if thus interpreted, could explain anything, since whatever the visible motions we could imagine hypothetical motions to compensate them. But if it can explain anything, it will allow us to foretell nothing; it will not allow us to choose between the various possible hypotheses, since it explains everything in advance. It therefore becomes useless. ”

He also discussed two other unexplained effects: (1) non-conservation of mass implied by Lorentz's variable mass γm, Abraham's theory of variable mass and Kaufmann's experiments on the mass of fast moving electrons and (2) the non-conservation of energy in the radium experiments of Madame Curie. Walter Kaufmann ( June 5, 1871, Elberfeld - January 1, 1947, Freiburg im Breisgau) was a German physicist

It was Albert Einstein's concept of mass–energy equivalence (1905) that a body losing energy as radiation or heat was losing mass of amount m = E / c2 that resolved[18] Poincare's paradox, without using any compensating mechanism within the ether. Albert Einstein ( German: ˈalbɐt ˈaɪ̯nʃtaɪ̯n; English: ˈælbɝt ˈaɪnstaɪn (14 March 1879 – 18 April 1955 was a German -born theoretical In Physics, mass–energy equivalence is the concept that for particles slower than light any Mass has an associated Energy and vice versa. [19] The Hertzian oscillator loses mass in the emission process, and momentum is conserved in any frame. However, concerning Poincaré's solution of the Center of Gravity problem, Einstein noted that Poincaré's formulation and his own from 1906 were mathematically equivalent. [20]

Poincaré and Einstein

Einstein's first paper on relativity was published three months after Poincaré's short paper,[14] but before Poincaré's longer version. [15] It relied on the principle of relativity to derive the Lorentz transformations and used a similar clock synchronisation procedure (Einstein synchronisation) that Poincaré (1900) had described, but was remarkable in that it contained no references at all. Einstein synchronisation (or Einstein-Poincaré synchronisation) is a convention in relativity for synchronizing clocks at different places Poincaré never acknowledged Einstein's work on Special Relativity. Special relativity (SR (also known as the special theory of relativity or STR) is the Physical theory of Measurement in Inertial Einstein acknowledged Poincaré in the text of a lecture in 1921 called Geometrie und Erfahrung in connection with Non-Euclidean geometry, but not in connection with special relativity. A lecture is an oral Presentation intended to present information or teach people about a particular subject for example by a University or College In mathematics non-Euclidean geometry describes how this all works--> hyperbolic and Elliptic geometry, which are contrasted with Euclidean geometry A few years before his death Einstein commented on Poincaré as being one of the pioneers of relativity, saying "Lorentz had already recognised that the transformation named after him is essential for the analysis of Maxwell's equations, and Poincaré deepened this insight still further . . . "[21]

Assessments

Poincaré's work in the development of special relativity is well recognised[18], though most historians stress that despite many similarities with Einstein's work, the two had very different research agendas and interpretations of the work. [22] Poincaré developed a similar physical interpretation of local time and noticed the connection to signal velocity, but contrary to Einstein he continued to use the ether-concept in his papers and argued that clocks in the ether show the "true" time, and moving clocks show the "apparent" time. A minority go much further, such as E.T. Whittaker, who held that Poincaré and Lorentz were the true discoverers of Relativity. Edmund Taylor Whittaker ( 24 October[[ 873]] - 24 March[[ 956]] was a mathematician who contributed widely to Applied mathematics, Mathematical physics [23]. See → Relativity priority dispute. Albert Einstein presented the theories of Special Relativity and General Relativity in groundbreaking publications that did not include references to the work of others

Poincaré consistently credited Lorentz's achievements, ranking his own contributions as minor. Thus, he wrote:

“ Lorentz has tried to modify his hypothesis so as to make it in accord with the postulate of complete impossibility of measuring absolute motion. He has succeeded in doing so in his article [Lorentz 1904]. The importance of the problem has made me take up the question again; the results that I have obtained agree on all important points with those of Lorentz; I have been led only to modify or complete them on some points of detail. "[14] [emphasis added]. ”

In an address in 1909 on "The New Mechanics", Poincaré discussed the demolition of Newton's mechanics brought about by Max Abraham and Lorentz, without mentioning Einstein. Max Abraham ( March 26 1875 – November 16 1922) was a German Physicist. In one of his last essays entitled "The Quantum Theory" (1913), when referring to the Solvay Conference, Poincaré again described special relativity as the "mechanics of Lorentz"[24]:

“ . The International Solvay Institutes for Physics and Chemistry, located in Brussels, were founded by the Belgian industrialist Ernest Solvay . . at every moment [the twenty physicists from different countries] could be heard talking of the new mechanics which they contrasted with the old mechanics. Now what was the old mechanics? Was it that of Newton, the one which still reigned uncontested at the close of the nineteenth century? No, it was the mechanics of Lorentz, the one dealing with the principle of relativity; the one which, hardly five years ago, seemed to be the height of boldness . . . the mechanics of Lorentz endures . . . no body in motion will ever be able to exceed the speed of light . . . the mass of a body is not constant . . . no experiment will ever be able [to detect] motion either in relation to absolute space or even in relation to the aether. [emphasis added] ”

On the other hand, in a memoir written as a tribute after Poincaré's death, Lorentz readily admitted the mistake he had made and credited Poincaré's achievements[25]:

“ For certain of the physical magnitudes which enter in the formulae I have not indicated the transformation which suits best. This has been done by Poincaré, and later by Einstein and Minkowski. My formulae were encumbered by certain terms which should have been made to disappear. [. . . ] I have not established the principle of relativity as rigorously and universally true. Poincaré, on the other hand, has obtained a perfect invariance of the electro-magnetic equations, and he has formulated 'the postulate of relativity', terms which he was the first to employ. [. . . ] Poincaré remarks [. . ] that if one considers x,y,z, and t \sqrt{-1} as the coordinates of a space of four dimensions, the transformations of relativity are reduced to rotations in that space. [emphasis added] ”

In summary, Poincaré regarded the mechanics as developed by Lorentz in order to obey the principle of relativity as the essence of the theory, while Lorentz stressed that perfect invariance was first obtained by Poincaré. The modern view is inclined to say that the group property and the invariance are the essential points.

Character

Poincaré's work habits have been compared to a bee flying from flower to flower. Poincaré was interested in the way his mind worked; he studied his habits and gave a talk about his observations in 1908 at the Institute of General Psychology in Paris. He linked his way of thinking to how he made several discoveries.

The mathematician Darboux claimed he was un intuitif (intuitive), arguing that this is demonstrated by the fact that he worked so often by visual representation. He did not care about being rigorous and disliked logic. He believed that logic was not a way to invent but a way to structure ideas and that logic limits ideas.

Toulouse' characterisation

Poincaré's mental organisation was not only interesting to Poincaré himself but also to Toulouse, a psychologist of the Psychology Laboratory of the School of Higher Studies in Paris. Toulouse wrote a book entitled Henri Poincaré (1910). In it, he discussed Poincaré's regular schedule:

These abilities were offset to some extent by his shortcomings:

In addition, Toulouse stated that most mathematicians worked from principles already established while Poincaré started from basic principles each time (O'Connor et al. , 2002).

His method of thinking is well summarised as:

"Habitué à négliger les détails et à ne regarder que les cimes, il passait de l'une à l'autre avec une promptitude surprenante et les faits qu'il découvrait se groupant d'eux-mêmes autour de leur centre étaient instantanément et automatiquement classés dans sa mémoire. "("Accustomed to neglecting details and to looking only at mountain tops, he went from one peak to another with surprising rapidity, and the facts he discovered, clustering around their center, were instantly and automatically pigeonholed in his memory. ") Belliver (1956)

Shortcomings

Although a brilliant researcher, Poincaré was resistant to contributions from mathematicians like Georg Cantor and saw mathematical work in economics and finance as peripheral. Georg Ferdinand Ludwig Philipp Cantor ( – January 6 1918) was a German Mathematician, born in Russia. In 1900 Poincaré commented on Louis Bachelier's thesis "The Theory of Speculation", saying: "M. Louis Jean-Baptiste Alphonse Bachelier ( March 11, 1870 - April 28, 1946) was a French Mathematician at the turn of the 20th century Bachelier has evidenced an original and precise mind [but] the subject is somewhat remote from those our other candidates are in the habit of treating. " (Bernstein, 1996, p. 199-200) However, Bachelier's work explained what was then the French government's pricing options on French Bonds and anticipated many of the pricing theories in financial markets used even today. {title= INVENTING MONEY }

Honours

Awards

Named after him

Philosophy

Poincaré had philosophical views opposite to those of Bertrand Russell and Gottlob Frege, who believed that mathematics was a branch of logic. The American Philosophical Society is a discussion group founded in 1743 by Benjamin Franklin as an offshoot of his earlier club the Junto. The Gold Medal is the highest award of the Royal Astronomical Society. The Matteucci Medal was established to award Physicists for their fundamental contributions The French Academy of Sciences ( French: Académie des sciences) is a Learned society, founded in 1666 by Louis XIV at the L'Académie française, or the French Academy, is the pre-eminent French learned body on matters pertaining to the French language. The Catherine Wolfe Bruce Gold Medal is awarded every year by the Astronomical Society of the Pacific for outstanding lifetime contributions to Astronomy. The Henri Poincaré Prize sponsored by the Daniel Iagolnitzer Foundation was created in 1997 to recognize outstanding contributions in mathematical physics and contributions Annales Henri Poincaré (A Journal of Theoretical and Mathematical Physics is a Scientific journal which collects and publishes original Research papers in the field The Poincaré Seminars, named for the mathematician and theoretical physicist Henri Poincaré, were founded in 2001 Poincaré is a large lunar impact basin that lies in the southern hemisphere on the far side of the Moon. Asteroids, sometimes called Minor planets or planetoids', are bodies—primarily of the inner Solar System —that are smaller than planets but 2021 Poincaré is a main belt Asteroid that was discovered by the French Astronomer Louis Boyer on June 26, 1936 Bertrand Arthur William Russell 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970 was a British Philosopher, Historian Friedrich Ludwig Gottlob Frege ( 8 November 1848, Wismar, Grand Duchy of Mecklenburg-Schwerin  &ndash 26 July 1925 Logic is the study of the principles of valid demonstration and Inference. Poincaré strongly disagreed, claiming that intuition was the life of mathematics. Intuition is apparent ability to acquire knowledge without a clear inference or the use of reason Poincaré gives an interesting point of view in his book Science and Hypothesis:

For a superficial observer, scientific truth is beyond the possibility of doubt; the logic of science is infallible, and if the scientists are sometimes mistaken, this is only from their mistaking its rule.

Poincaré believed that arithmetic is a synthetic science. Arithmetic or arithmetics (from the Greek word αριθμός = number is the oldest and most elementary branch of mathematics used by almost everyone The analytic-synthetic distinction is a conceptual distinction used primarily in Philosophy to distinguish propositions into two types analytic propositions and He argued that Peano's axioms cannot be proven non-circularly with the principle of induction (Murzi, 1998), therefore concluding that arithmetic is a priori synthetic and not analytic. In Mathematical logic, the Peano axioms, also known as the Dedekind-Peano axioms or the Peano postulates, are a set of Axioms for the Natural "A priori" redirects here For other uses see A priori. The analytic-synthetic distinction is a conceptual distinction used primarily in Philosophy to distinguish propositions into two types analytic propositions and Poincaré then went on to say that mathematics cannot be deduced from logic since it is not analytic. His views were the same as those of Immanuel Kant (Kolak, 2001). Immanuel Kant (ɪmanuəl kant 22 April 1724 12 February 1804 was an 18th-century German Philosopher from the Prussian city of Königsberg

However Poincaré did not share Kantian views in all branches of philosophy and mathematics. For example, in geometry, Poincaré believed that the structure of non-Euclidean space can be known analytically. In mathematics non-Euclidean geometry describes how this all works--> hyperbolic and Elliptic geometry, which are contrasted with Euclidean geometry Poincaré held that convention plays an important role in physics. His view (and some later, more extreme versions of it) came to be known as "conventionalism". Conventionalism is the philosophical attitude that fundamental principles of a certain kind are grounded on (explicit or implicit agreements in society rather than on Poincaré believed that Newton's first law was not empirical but is a conventional framework assumption for mechanics. Newton's laws of motion are three Physical laws which provide relationships between the Forces acting on a body and the motion of the He also believed that the geometry of physical space is conventional. He considered examples in which either the geometry of the physical fields or gradients of temperature can be changed, either describing a space as non-Euclidean measured by rigid rulers, or as a Euclidean space where the rulers are expanded or shrunk by a variable heat distribution. However, Poincaré thought that we were so accustomed to Euclidean geometry that we would prefer to change the physical laws to save Euclidean geometry rather than shift to a non-Euclidean physical geometry. Euclidean geometry is a mathematical system attributed to the Greek Mathematician Euclid of Alexandria.

See also

References

This article incorporates material from Jules Henri Poincaré on PlanetMath, which is licensed under the GFDL. In Mathematics, the Poincaré–Bendixson theorem is a statement about the long term behaviour of orbits of Continuous dynamical systems on the plane In the theory of Lie algebras the Poincaré–Birkhoff–Witt theorem (stated by Henri Poincaré (1900 and proved by Garrett Birkhoff (1937 and In Non-Euclidean geometry, the Poincaré half-plane model is the Upper half-plane, together with a metric the Poincaré metric, that makes it a model In Physics and Mathematics, the Poincaré group, named after Henri Poincaré, is the group of isometries of Minkowski spacetime In Mathematics, the Poincaré–Hopf theorem (also known as the Poincaré–Hopf index formula, Poincaré–Hopf index theorem, or Hopf index theorem In Mathematics, the Poincaré metric, named after Henri Poincaré, is the Metric tensor describing a two-dimensional surface of constant negative Curvature In Mathematics, the Poincaré duality theorem named after Henri Poincaré, is a basic result on the structure of the homology and Cohomology In Physics and Mathematics, the Poincaré group, named after Henri Poincaré, is the group of isometries of Minkowski spacetime In Mathematics, particularly in Dynamical systems, a first recurrence map or Poincaré map, named after Henri Poincaré, is the intersection The Institut Henri Poincaré is a mathematical institute in Paris which has established itself over its eighty year history as an important meeting place for French and international The History of special relativity consists of many theoretical and empirical results of physicists like Hendrik Lorentz and Henri Poincaré, which culminated in the Albert Einstein presented the theories of Special Relativity and General Relativity in groundbreaking publications that did not include references to the work of others In Mathematics, the Poincaré conjecture (French pwɛ̃kaʀe is a Theorem about the characterization of the three-dimensional sphere among PlanetMath is a free, collaborative online Mathematics Encyclopedia.

Footnotes and primary sources

  1. ^ [1] Poincaré pronunciation example at Bartleby. com
  2. ^ The Internet Encyclopedia of Philosophy Jules Henri Poincaré article by Mauro Murzi - accessed November 2006.
  3. ^ Lorentz, Poincaré et Einstein - L'Express
  4. ^ Mathematics Genealogy Project North Dakota State University, Accessed April 2008
  5. ^ McCormmach, Russell (Spring, 1967), “Henri Poincaré and the Quantum Theory”, Isis 58 (1): 37-55 
  6. ^ Irons, F. E. (August, 2001), “Poincaré's 1911–12 proof of quantum discontinuity interpreted as applying to atoms”, American Journal of Physics 69 (8): 879-884 
  7. ^ Lorentz, H. A. (1895), Versuch einer theorie der electrischen und optischen erscheinungen in bewegten Kõrpern, Leiden: E. J. Brill 
  8. ^ Poincaré, H. (1898), “La mesure du temps”, Revue de métaphysique et de morale 6: 1-13  Reprinted in "The Value of Science", Ch. 2.
  9. ^ a b c Poincaré, H. (1900), “La théorie de Lorentz et le principe de réaction”, Archives néerlandaises des sciences exactes et naturelles 5: 252-278 . Reprinted in Poincaré, Oeuvres, tome IX, pp. 464-488. See also the English translation
  10. ^ Poincaré, H. (1900), “Les relations entre la physique expérimentale et la physique mathématique”, Revue générale des sciences pures et appliquées 11: 1163-1175 . Reprinted in "Science and Hypothesis", Ch. 9-10.
  11. ^ a b Poincaré, H. (1904), “The present and the future of mathematical physics”, Bull. Amer. Math. Soc. 37: 25-38  Reprinted in "The value of science", Ch. 7-9.
  12. ^ Letter from Poincaré to Lorentz, Mai 1905
  13. ^ Letter from Poincaré to Lorentz, Mai 1905
  14. ^ a b c Poincaré, H. (1905b), “Sur la dynamique de l'électron”, Comptes Rendus 140: 1504-1508  Reprinted in Poincaré, Oeuvres, tome IX, S. 489-493.
  15. ^ a b Poincaré, H. (1906), “Sur la dynamique de l'électron”, Rendiconti del Circolo matematico Rendiconti del Circolo di Palermo 21: 129-176  Reprinted in Poincaré, Oeuvres, tome IX, pages 494-550. Partial English translation in Dynamics of the electron.
  16. ^ Walter (2007), Secondary sources on relativity
  17. ^ Miller 1981, Secondary sources on relativity
  18. ^ a b Darrigol 2005, Secondary sources on relativity
  19. ^ Einstein, A. (1905b), “Ist die Trägheit eines Körpers von dessen Energieinhalt abhängig?”, Annalen der Physik 18: 639–643 . See also English translation.
  20. ^ Einstein, A. (1906), “Das Prinzip von der Erhaltung der Schwerpunktsbewegung und die Trägheit der Energie”, Annalen der Physik 20: 627-633 
  21. ^ Darrigol 2004, Secondary sources on relativity
  22. ^ Galison 2003 and Kragh 1999, Secondary sources on relativity
  23. ^ Whittaker 1953, Secondary sources on relativity
  24. ^ See Poincaré, Last Essays (1913)
  25. ^ Lorentz, H. A. (1921), “Deux Memoirs de Henri Poincaré sur la Physique Mathematique”, Acta Mathematica 38: 293-308  Reprinted in Poincaré, Oeuvres tome XI, S. 247-261.

Poincaré's Writings in English translation

Popular writings on the philosophy of science:

On algebraic topology:

On celestial mechanics:

On the philosophy of mathematics:

General references

Secondary sources to work on relativity

Non-mainstream

External links

Preceded by
Sully Prudhomme		 Seat 24
Académie française
1908-1912		 Succeeded by
Alfred Capus
Persondata
NAME Poincaré, Henri
ALTERNATIVE NAMES Poincaré, Jules
SHORT DESCRIPTION Mathematician and physicist
DATE OF BIRTH April 29, 1854
PLACE OF BIRTH Nancy, Lorraine, France
DATE OF DEATH July 17, 1912
PLACE OF DEATH Paris, France
René-François-Armand (Sully Prudhomme ( Paris, France, March 16, 1839 - Châtenay-Malabry, France, September This is a list of members of the Académie française (French Academy by seat number L'Académie française, or the French Academy, is the pre-eminent French learned body on matters pertaining to the French language. Year 1908 ( MCMVIII) was a Leap year starting on Wednesday (link will display the full calendar of the Gregorian calendar (or a Leap year Year 1912 ( MCMXII) was a Leap year starting on Monday (link will display the full calendar of the Gregorian calendar (or a Leap year starting Alfred Capus (November 25 1858 - November 1 1922 was a French Journalist and Playwright, born in Aix-en-Provence and deceased in Neuilly-sur-Seine A mathematician is a person whose primary area of study and research is the field of Mathematics. A physicist is a Scientist who studies or practices Physics. Physicists study a wide range of physical phenomena in many branches of physics spanning Events 1429 - Joan of Arc arrives to relieve the Siege of Orleans. Year 1854 ( MDCCCLIV) was a Common year starting on Sunday (link will display the full calendar of the Gregorian Calendar (or a Common year Nancy (nɑ̃si archaic Nanzig Nanzeg is a city and commune in the Lorraine région of northeastern France This article is about the country For a topic outline on this subject see List of basic France topics. Events 180 - Twelve inhabitants of Scillium in North Africa are executed for being Christians Year 1912 ( MCMXII) was a Leap year starting on Monday (link will display the full calendar of the Gregorian calendar (or a Leap year starting Paris (ˈpærɨs in English; in French) is the Capital of France and the country's largest city This article is about the country For a topic outline on this subject see List of basic France topics.
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