Quantum Logic and Quantum Probability

Abstract

By events, or yes-no experiments, pertaining to some physical system we understand the physical quantities, or observables, that admit only two outcomes. Since the 1936 seminal work of G. Birkhoff and J. Neumann [4] it is recognized that, in the framework of physical systems exhibiting a quantum behaviour, the algebraic structure associated to the events is not an algebraic model of classical logic, it is the algebraic model of a new logic, to be called quantum logic. This fact outlines a deep departure from the realm of classical physics where the events pertaining to a physical system carry the structure of a Boolean algebra, hence an algebraic model of classical logic. In Sect. 2 we shall review the structure of the events of classical and of quantum events and we will recall the main branching point.