Remarks on mathematical foundations of quantum mechanics

Abstract

We show that the set-theoretic forcing is the essential part of the continuous measurement of a suitably rich Boolean algebra of quantum observables. The Boolean algebra structure of quantum observables enables us to give a classical and geometric meaning to the results of measurements of the observables. The measurement takes place in the semiclassical state of the system which is the generic filter added by a forcing to the ZFC model based on the Borel measure algebra. The analogue of the semiclassical state (the pseudoclassical state) was described by Wesep in 2006 in his studies of the local hidden variables program in quantum mechanics.