Stephane Collion - Academia.edu (original) (raw)
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Papers by Stephane Collion
arXiv (Cornell University), Oct 2, 2010
arXiv (Cornell University), Oct 5, 2010
Transactions of the American Mathematical Society, Jan 4, 2007
arXiv (Cornell University), Oct 1, 2010
arXiv (Cornell University), Sep 13, 2017
arXiv (Cornell University), Sep 13, 2017
arXiv (Cornell University), Oct 5, 2010
We propose in this paper a mathematicians' view of the Kaluza-Klein idea of a five dimensional sp... more We propose in this paper a mathematicians' view of the Kaluza-Klein idea of a five dimensional space-time unifying gravitation and electromagnetism. By considering the classification of positive Einstein curvature tensors and the classical Cauchy-Choquet-Bruhat theorems in general relativity, we introduce concepts of types and rigidity. Then, abandoning the usual requirement of a Ricci-flat five dimensional space-time, we show that a unified geometrical frame can be set for gravitation and electromagnetism, giving, by projection on the classical 4-dimensional space-time, the known Einstein-Maxwell-Lorentz equations for charged fluids. Thus, although not introducing, at least at this stage, new physics, we get a very aesthetic presentation of classical physics in the spirit of general relativity. The usual physical concepts, such as mass, energy, charge, trajectory, Maxwell-Lorentz law, are shown to be only various aspects of the geometry, for example curvature, of space-time considered as a Lorentzian manifold; that is no physical objects are introduced in space-time, no laws are given, everything is only geometry! This work is therefore in the continuation of the various attempts made since Einstein, Weyl, Nordstrom, Kaluza, Klein, Rainich, Wheeler.
arXiv (Cornell University), Oct 5, 2010
We consider in this paper, the geometrization of classical physics, i.e gravitation and electroma... more We consider in this paper, the geometrization of classical physics, i.e gravitation and electromagnetism. The goal is therefore to show that all the usual physical concepts, such as mass, energy, charge, trajectory, Maxwell-Lorentz law, are only various aspects of the geometry, for exemple curvature, of spacetime considered as a Lorentzian manifold; that is no object is "put" in spacetime, no laws are given, everything is only geometry. We show why this goal is probably inaccessible in dimension 4, and put forward, while studying this case, the concepts leading to a solution in a five-dimensional spacetime. The solution we propose does not use truly new mathematics, but more a different view of the classical axiomatism of the classical theories, and in particular the suppression of an hypothesis usually made about the Ricci curvature, unjustified from our point of view. This work is therefore in the continuation of the various attempts made since Einstein, Weyl, Nordstrom, Kaluza, Klein, Rainich, Wheeler.
arXiv (Cornell University), Oct 2, 2010
Advances in Differential Equations
arXiv (Cornell University), Sep 13, 2017
arXiv (Cornell University), Sep 13, 2017
arXiv (Cornell University), Oct 1, 2010
arXiv (Cornell University), Oct 5, 2010
Ce livre est une invitation a decouvrir le lien profond qui unit la relativite generale (la theor... more Ce livre est une invitation a decouvrir le lien profond qui unit la relativite generale (la theorie de la gravitation d'Einstein) et la geometrie differentielle, branche de la geometrie issue de la decouverte des geometries non-euclidiennes par Gauss et Riemann au XIXe siecle.En abordant la relativite par ses aspects geometriques, ce livre montre que les phenomenes surprenants de la relativite, tels que le paradoxe des jumeaux, les boucles temporelles, les trous noirs, les trous de ver, ne sont que des consequences de la geometrie de l'espace-temps. Le livre explore egalement la fascinante relation entre les mathematiques et la physique a travers une des theories les plus passionnantes de notre siecle, la relativite generale, sujet particulierement d'actualite depuis les recentes observations des ondes gravitationnelles et les observations de plus en plus directes des trous noirs. Il montre ainsi que les mathematiques, loin d'etre simplement un « outil », sont une des sources d'inspiration les plus fecondes des physiciens theoriciens. Ce livre offrira une introduction plaisante aux mathematiques de la relativite, autant a l'etudiant en sciences qu'au lecteur curieux et motive par les decouvertes scientifiques les plus fascinantes de notre epoque.
Comptes Rendus De L Academie Des Sciences Serie 1 Mathematique, 1996
arXiv (Cornell University), Oct 2, 2010
arXiv (Cornell University), Oct 5, 2010
Transactions of the American Mathematical Society, Jan 4, 2007
arXiv (Cornell University), Oct 1, 2010
arXiv (Cornell University), Sep 13, 2017
arXiv (Cornell University), Sep 13, 2017
arXiv (Cornell University), Oct 5, 2010
We propose in this paper a mathematicians' view of the Kaluza-Klein idea of a five dimensional sp... more We propose in this paper a mathematicians' view of the Kaluza-Klein idea of a five dimensional space-time unifying gravitation and electromagnetism. By considering the classification of positive Einstein curvature tensors and the classical Cauchy-Choquet-Bruhat theorems in general relativity, we introduce concepts of types and rigidity. Then, abandoning the usual requirement of a Ricci-flat five dimensional space-time, we show that a unified geometrical frame can be set for gravitation and electromagnetism, giving, by projection on the classical 4-dimensional space-time, the known Einstein-Maxwell-Lorentz equations for charged fluids. Thus, although not introducing, at least at this stage, new physics, we get a very aesthetic presentation of classical physics in the spirit of general relativity. The usual physical concepts, such as mass, energy, charge, trajectory, Maxwell-Lorentz law, are shown to be only various aspects of the geometry, for example curvature, of space-time considered as a Lorentzian manifold; that is no physical objects are introduced in space-time, no laws are given, everything is only geometry! This work is therefore in the continuation of the various attempts made since Einstein, Weyl, Nordstrom, Kaluza, Klein, Rainich, Wheeler.
arXiv (Cornell University), Oct 5, 2010
We consider in this paper, the geometrization of classical physics, i.e gravitation and electroma... more We consider in this paper, the geometrization of classical physics, i.e gravitation and electromagnetism. The goal is therefore to show that all the usual physical concepts, such as mass, energy, charge, trajectory, Maxwell-Lorentz law, are only various aspects of the geometry, for exemple curvature, of spacetime considered as a Lorentzian manifold; that is no object is "put" in spacetime, no laws are given, everything is only geometry. We show why this goal is probably inaccessible in dimension 4, and put forward, while studying this case, the concepts leading to a solution in a five-dimensional spacetime. The solution we propose does not use truly new mathematics, but more a different view of the classical axiomatism of the classical theories, and in particular the suppression of an hypothesis usually made about the Ricci curvature, unjustified from our point of view. This work is therefore in the continuation of the various attempts made since Einstein, Weyl, Nordstrom, Kaluza, Klein, Rainich, Wheeler.
arXiv (Cornell University), Oct 2, 2010
Advances in Differential Equations
arXiv (Cornell University), Sep 13, 2017
arXiv (Cornell University), Sep 13, 2017
arXiv (Cornell University), Oct 1, 2010
arXiv (Cornell University), Oct 5, 2010
Ce livre est une invitation a decouvrir le lien profond qui unit la relativite generale (la theor... more Ce livre est une invitation a decouvrir le lien profond qui unit la relativite generale (la theorie de la gravitation d'Einstein) et la geometrie differentielle, branche de la geometrie issue de la decouverte des geometries non-euclidiennes par Gauss et Riemann au XIXe siecle.En abordant la relativite par ses aspects geometriques, ce livre montre que les phenomenes surprenants de la relativite, tels que le paradoxe des jumeaux, les boucles temporelles, les trous noirs, les trous de ver, ne sont que des consequences de la geometrie de l'espace-temps. Le livre explore egalement la fascinante relation entre les mathematiques et la physique a travers une des theories les plus passionnantes de notre siecle, la relativite generale, sujet particulierement d'actualite depuis les recentes observations des ondes gravitationnelles et les observations de plus en plus directes des trous noirs. Il montre ainsi que les mathematiques, loin d'etre simplement un « outil », sont une des sources d'inspiration les plus fecondes des physiciens theoriciens. Ce livre offrira une introduction plaisante aux mathematiques de la relativite, autant a l'etudiant en sciences qu'au lecteur curieux et motive par les decouvertes scientifiques les plus fascinantes de notre epoque.
Comptes Rendus De L Academie Des Sciences Serie 1 Mathematique, 1996