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

Beltrametti, E. G.; Bugajski, S.

J. Phys. A, Math. Gen. 28, No. 12, 3329-3343 (1995).

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

Keywords:

observable; classical extension; states; probability measures on the pure states