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A classical extension of quantum mechanics. (English) Zbl 0859.46049

Summary: A physically natural generalization of the notion of observable that encompasses both the classical and the quantum ones is derived. Based on it, the idea of the classical extension of a theory is developed; the states of the extended theory being the probability measures on the pure states of the original one. It is shown that quantum theory admits such a classical extension, and that the qualifying features of quantum observables are preserved in the extended model.

MSC:

46N50 Applications of functional analysis in quantum physics
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
47N50 Applications of operator theory in the physical sciences
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