Probabilistic formulation of classical mechanics
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Starting axiomatically with a system of finite degrees of freedom whose logicℒc is an atomic Boolean σ-algebra, we prove the existence of phase spaceΩc, as a separable metric space, and a natural (weak) topology on the set of statesI (all the probability measures onℒc) such thatΩc, the subspace of pure statesP, the set of atoms ofℒc and the spaceP(Ωc) of all the atomic measures on Ωc, are all homeomorphic. The only physically accessible states are the points ofΩc. This probabilistic formulation is shown to be reducible to a purely deterministic theory.
KeywordsField Theory Elementary Particle Quantum Field Theory Classical Mechanic Probabilistic Formulation
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