Henri Poincare


Henri Poincare : biography

29 April 1885 – 17 July 1912

The last two years of his life Poincare had been very interested in quantum theory. In his detailed article about the theory of quantum of 1911, he proved that it was impossible to receive the law of radiation by Plank without a hypothesis of quantum. Having explained that, Poincare buried all the hopes to maintain the classic theory.

Scientific terms, associated with Poincare’s research

Poincare’s hypothesis

Poincare’ group

Poincare’s duality

Poincare’s lemma

Poincare’s metrics

Poincare’s variant of Lobachevski’s space

Normal form by Poincare-Dulac

Poincare’s reflection

The last theorem by Poincare

Poincare’s sphere

Poincare-Bendixson’s theorem

Poincare-Volterra’s theorem

Poincare-Bendixson’s theorem

Poincare’s theorem about vectorial field

Poincare’s theorem about speed of growing of function

Poincare’s theorem about classification of homeomorphisms of circumference

Poincare–Birkhoff–Witt theorem

And many others

Poincare’s role in developing the relative theory

Poincare’s works in the sphere of relative dynamics

Poincare’s name was directly connected with the success of the relative theory. He actively took part in developing Lorentz’s theory. That theory accepted that there was immovable ether and the speed of light in that ether was not influenced by the speed of its source. In transition to the moving reference frame, Lorentz’s transformations instead of Galilee‘s came true (Lorentz considered those transformations to be real dimensions of bodies measures). It was just Poincare who gave correct mathematical formulation to those transformations (while Lorentz himself offered only their approximations of first range) and showed the way they made a group of transformation.

Already in 1898, long before Einstein, Poincare, in his work “Dimension of time” formulated the general (not only for mechanics) principal of relativity and later he even brought in four-dimensional space-time, the theory of which was developed later by German Minkovski. However, Poincare continued using the conception of ether, although he had opinion that nobody would ever discover it. Poincare told about that in his report at a congress of physicists in 1900. In that very report, Poincare firstly expressed his idea that the simultaneity of events was not absolute and represented only a conditional agreement or convention. There was also expressed a supposition that the speed of light might be limited.

Under the influence of criticism by Poincare, Lorentz offered a new variant of his theory in 1904. In that theory he supposed that Newton’s mechanics. Being applied to high speeds, needed being corrected. One year later, in 1905 Poincare developed that idea considerably in his article about dynamics of electron. The preliminary variant of that article appeared on 5 June 1905 in “Comptes Rendus”. And the finishing variant was finished in July of 1905 and published in January of 1906. For some reason it was published in small Italian mathematical magazine.

In that article the general principal of relativity applying to all physical phenomena was clearly explained again, particularly electromagnetic, mechanical and even gravitational): with the transformations by Lorentz, as the only possible transformations of coordinates, remaining the same system of counting of physical equations for all systems. Poincare managed to find formulae for four-dimensional interval as an invariant of Lorentz’s transformations and four-dimensional formulation for the principal of minor action. In that article the scientist also offered the first sketch of the relative theory of gravitation. In his model gravitation spread in ether with the speed of light. As for the theory itself, it was unconventional enough to remove limiting, that had been found by Laplace already, at the downside for the speed of spreading the gravitational field. The preliminary short message was released even before Albert Einstein’s work. And the finishing big article was received by publishers even before the Einstein’s one. However, by the time the article was published, Albert Einstein’s work had already been released.