Il ruolo del teorema di Kochen-Specker nelle formulazioni con variabili nascoste della meccanica quantistica. On the role of Kochen-Specker theorem in hidden variable formulations of quantum mechanics

In this work we begin with a critical review of the concept of observable in a generical physical theory; relying on C*-algebras formalism and on Gelfand-Naimark theorem we justify the link between observables and operators in an Hilbert space. We discuss particularly observables of quantum mechanics, introducing some mathematical results that characterizes them. We introduce the problem of hidden variables and the hypothesis of non-contextuality, than we give a proof of the Kochen-Specker theorem in dimension greater or equal to 3 using partial algebras formalism; we also show a constructive example of an hidden variable theory in dimension 2. Finally we discuss Meyer’s and Kent’s objections relying on finite precision of physical measurements and we present colorations of S² ∩ Q³ and of dense subsets of the projectors of C^n and l²(C) that respect Kochen-Specker rules.