Abstract
Quantum mechanics incorporates an algorithm for assigning probabilities to ranges of values of the physical magnitudes of a mechanical system: \( Pw(a \in S) = Tr(WPa(S)) \) where W represents a statistical state, and P A (S) is the projection operator onto the subspace in the Hilbert space of the system associated with the range S of the magnitude A. (I denote values of A by a.) The statistical states (represented by the statistical operators in Hilbert space) generate all possible (generalized) probability measures on the partial Boolean algebra of subspaces of the Hilbert space.1 Joint probabilities \( Pw(a_1 \in S_1 \& a_2 \in S_2 \& \ldots \& a_n \in S_n ) = \) \( {\text{ = Tr(WP}}_{A_1 } {\text{(S}}_1 {\text{)P}}_{A_2 } {\text{(S}}_2 {\text{)}} \ldots {\text{P}}_{A_n } {\text{(S}}_n {\text{))}} \) are defined only for compatible2 magnitudes A1, A2,… A n , and there are no dispersion-free statistical states.
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© 1976 D. Reidel Publishing Company Dordrecht-Holland
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Bub, J. (1976). The Statistics of Non-Boolean Event Structures. In: Harper, W.L., Hooker, C.A. (eds) Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science. The University of Western Ontario Series in Philosophy of Science, vol 6c. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1438-0_1
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DOI: https://doi.org/10.1007/978-94-010-1438-0_1
Publisher Name: Springer, Dordrecht
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