Reversibility Versus Irreversibility in the Physical Universe
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.
KeywordsPhase Space Modular Space Hamiltonian Formalism Unitary Formalism Physical Universe
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