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Abstract : The problem of the relation between Geometry and Physics has been the object of extensive discussions, through the present century, by mathematicians, physicists and philosophers of science, who have considered the possibility to decide which geometry corresponds to physical space, with respect to the General Theory of Relativity. At first sight, the Special Theory of Relativity seems to be independent from this problem.
In this debate, which made reference to Poincaré's philosophy of Geometry, Einstein has been directly involved. Although he concludes positively about the decidability of Geometry, he is not a rejoinder of empiricism. He himself invokes frequently Poincaré in his arguments against empiricists, in particular Poincaré's alleged "indissociability between Geometry and Physics", which sounds like Poincaré's indissociability between space and dynamics contrary to Einstein's separation of kinematics from dynamics in Special Relativity. It is thus tempting to compare his own position to Poincaré's one before and after his elaboration of the General Theory of Relativity. We would like to know, in particular, whether Einstein's conception of the relations between Geometry and Physics has drastically changed when he has passed from Special to General Theory of Relativity, adopting henceafter the essential of Poincaré's conception which he did not share at the time of Special Relativity.
This inquiry has led us to a reevaluation of Poincaré's conception of the relation between Geometry and Physics, quite at variance with the received view. It also has led us to consider again the problem of why Poincaré did not fully develop Special Relativity as we now understand it, i.e. in Einstein's sense, and to show evidence for a strong influence of his conception of Geometry when dealing with classical and relativistic Mechanics. Finally we show what has been actually - in our view - the evolution of Einstein's thought concerning the relations of Physics and Geometry, which is indeed an adaptation of his previous implicit conception, at work with Special Relativity, to the requirements of the general theory. This adaptation revealed to him the complexity of a problem he had considered previously in a simplified way, and made him conscious of the well-foundedness of important aspects of Poincaré's conceptions, which he translated, then adapted, for the use of his own physical thinking.
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Submitted on : Tuesday, August 14, 2007 - 6:20:56 PM
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Michel Paty. PHYSICAL GEOMETRY AND SPECIAL RELATIVITY : EINSTEIN AND POINCARE. L. Boi, D. Flament et J.M. Salanski. 1830-1930 : un siècle de géométrie, de C.F. Gauss et B. Riemann à H. Poincaré et E. Cartan. Epistémologie, histoire et mathématiques, Springer-Verlag, pp.126-149, 1992. ⟨halshs-00167113⟩



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