Resolution of the Completeness Problem

Abstract

The theorem proved by Kochen and Specker is the non-imbeddability of the partial Boolean algebra of idempotent magnitudes — propositions — of quantum mechanics into a Boolean algebra, in the case of systems associated with Hilbert spaces of three or more dimensions. This means the impossibility of representing the statistical states of the quantum algorithm as probability measures on a classical probability space, in such a way that the structure of the set of (idempotent) magnitudes is preserved. Now, the structure involved here is the compatibility structure.