Jauch-Piron logics with finiteness conditions
- Technical Univ. of Prague, (Czechoslovakia)
An event structure (so-called quantum logic) of a quantum mechanical system is commonly assumed to be an orthomodular poset L. A state of such a system is then interpreted as a probability measure on L. It turns out that the orthomodular posets which may potentially serve as logics must have reasonably rich spaces of states. Moreover, the following condition on the state space appears among the axioms of a quantum system: if {Phi} is a state on a logic L, and {Phi}(a) = {Phi}(b) = 1 for some a, b {element of} L, then there is a c {element of} L such that c {le} a, c {le} b, and {Phi}(c) = 1. Such a state is said to be a Jauch-Piron state. If all states on L fulfill this condition, then L is called a Jauch-Piron logic. The condition was originally introduced by Jauch (1968) and Piron (1976). The author investigates unital Jauch-Piron logics with finitely many blocks (maximal Boolean subalgebras). He shows that such a logic is always Boolean, i.e., it represents a purely classical system. In other words, and orthomodular poset must have infinitely many blocks in order to describe a (nonclassical) quantum system.
- OSTI ID:
- 5448659
- Journal Information:
- International Journal of Theoretical Physics; (United States), Vol. 30:4; ISSN 0020-7748
- Country of Publication:
- United States
- Language:
- English
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