Bell-type inequalities and orthomodular lattices

Anatolij Dvurečenskij

pp. 209-218

in: Maria L. Dalla Chiara, Roberto Giuntini, Federico Laudisa (eds), Language, quantum, music, Berlin, Springer, 1999

Abstract

Today one of acceptable mathematical models of quantum mechanics is an orthomodular lattice (OML for short) (Beltrametti and Cassinelli [3], Varadarajan [19]), which generalizes models of Kolmogorovian measurable spaces [10] or Boolean algebras which describe classical mechanics The main difference between OMLs and Boolean algebras is the absence of the distributive law in OMLs, in general. However, in particular cases, it can happen that the local character of events in an OML has a classical form.