Logic, states, and quantum probabilities
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A careful analysis of mechanical descriptions provides a new logical foundation for the states and probabilities of mechanics which leads to a new understanding of quantum probabilities and their representation in Hilbert space. It is argued that all mechanical theories use a logic which is distributive but only relatively orthocomplemented, and that this, too, is the structure of its states. Probabilities are derived from this analysis using standard Kolmogorov definitions in a way that accounts for the nonstandard peculiarities of the quantum transitional probabilities as well as classicial probability assignments. At the end of the paper this analysis is used to refute arguments that quantum mechanics is nondistributive and that the failure of Bell's inequality in quantum theory threatens our conceptual scheme. Instead we reach a much less drastic interpretation of quantum mechanics.
KeywordsHilbert Space Field Theory Elementary Particle Quantum Field Theory Quantum Mechanic
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