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(1975) The logico-algebraic approach to quantum mechanics I, Dordrecht, Springer.
Starting axiomatically with a system of finite degrees of freedom whose logic ℒ c is an atomic Boolean σ-algebra, we prove the existence of phase space Ω c , as a separable metric space, and a natural (weak) topology on the set of states <Emphasis FontCategory="NonProportional">S</Emphasis> (all the probability measures on ℒ c ) such that Ω c , the subspace of pure states <Emphasis FontCategory="NonProportional">P</Emphasis>, the set of atoms of ℒ c and the space <Emphasis FontCategory="NonProportional">P</Emphasis>(Ω c ) of all the atomic measures on Ω c , are all homeomorphic. The only physically accessible states are the points of Ω c . This probabilistic formulation is shown to be reducible to a purely deterministic theory.
Publication details
DOI: 10.1007/978-94-010-1795-4_27
Full citation:
Kronfli, N. S. (1975)., Probabilistic formulation of classical mechanics, in C. A. Hooker (ed.), The logico-algebraic approach to quantum mechanics I, Dordrecht, Springer, pp. 503-507.
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