Quantum probability - quantum logic. (English) Zbl 0668.60096

Pitowsky, Itamar

Lecture Notes in Physics, 321. Berlin etc.: Springer-Verlag. ix, 209 p. DM 42.00 (1989).

This volume, that is intended as a research monograph on the conceptual foundations of quantum mechanics, shows new ways of investigation of quantum mechanical problems.
At its center is the concept of correlation as it appears in probability theory and quantum physics. It is closely related to and characterizes the possible range of values of quantum correlations, Bell-type inequalities in the Einstein-Podolsky-Rosen experiment, and classical and quantum propositional logic, mentioning only some of the notably questions. The subject has applications in studying problems outside of physics, too.
The book includes a detailed construction of local hidden variable theories, based on an extension of classical probability.

Reviewer: I.G.Kalmár

MSC:

81P10	Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
81-02	Research exposition (monographs, survey articles) pertaining to quantum theory
03G12	Quantum logic
46N50	Applications of functional analysis in quantum physics

Keywords:

foundations of quantum mechanics; quantum correlations; quantum propositional logic; local hidden variable theories; extension of classical probability