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Journal of Mathematical Physics

Conditioning of states

Platon C. Deliyannis

Published May 1, 1976• 7 citations
Publisher

Abstract

A system of axioms for the state space of a quantum system is proposed which, together with the concept of conditioning a state by the occurrence of an event, leads to the construction of the standard orthomodular events system.
DOI
10.1063/1.522958

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A class of ring-like structures of events (RLSEs) is studied that generalizes Boolean rings. Quantum logics represented by orthomodular lattices are characterized within this class and the correspondence between Boolean algebras and Boolean rings is enlarged to orthomodular lattices. The structure of RLSEs and various subclasses is analyzed and classical logics are especially identified. Moreover, sets of numerical events within different contexts of physical problems are described. A numerical event is defined as a function [Formula: see text] from a set [Formula: see text] of states of a physical system to [Formula: see text] such that [Formula: see text] is the probability of the occurrence of an event when the system is in state [Formula: see text]. In particular, the question is answered whether a given (small) set of numerical events will give rise to the assumption that one deals with a classical physical system or a quantum-mechanical one.