Reversibility Versus Irreversibility in the Physical Universe

Part of the International Centre for Mechanical Sciences book series (CISM, volume 261)


What do we mean when we say that the laws of physics are time-reversible? There is an immediate answer: if in the mathematical expression of physical laws, we change t into — t, then we get the same system or an equivalent one. This purely formal criterion needs some clarification. Let us suppose that the considered law is expressed as a differential system. In general, this system is not of first order (more frequently of second order). By introducing new variables (in general put equal to first order derivatives), the p-variables,one gets a new differential system of first order: a flow defined in a manifold M (phase space) by a vector field X. We may define the same flow in the product M × ℝ of M by the time axis ℝ. Then time reversibility can be expressed as follows.


Phase Space Modular Space Hamiltonian Formalism Unitary Formalism Physical Universe 
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    Théorème de S. Newhouse, in Abraham R., Narsden J. Foundations of Mechanics Benjamin 1978 (second edition).Google Scholar
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    Thom R., L’espace et la réalité physique, Orbetello Congress of the International Academy of Sciences, April 1979, Agazzi ed.Google Scholar

Copyright information

© Springer-Verlag Wien 1980

Authors and Affiliations

  • R. Thom
    • 1
  1. 1.Institut des Hautes Etudes SciéntifiquesBures sur YvetteFrance

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