The possibilities of a realistic interpretation of quantum mechanics are investigated by means of a statistical analysis of experiments performed on the simplest type of quantum systems carrying spin or helicity. To this end, fundamental experiments, some new, for measuring polarization are reviewed and (re)analyzed. Theunsharp reality of spin is essential in the interpretation of some of these experiments and represents a natural motivation for recent generalizations of quantum mechanics to a theory incorporating effect-valued measures as unsharp observables and generalized (...) systems of imprimitivity. (shrink)

Various formalisms for recasting quantum mechanics in the framework of classical mechanics on phase space are reviewed and compared. Recent results in stochastic quantum mechanics are shown to avoid the difficulties encountered by the earlier approach of Wigner, as well as to avoid the well-known incompatibilities of relativity and ordinary quantum theory. Specific mappings among the various formalisms are given.

Working in stochastic spin space and using POV measures as in the Davies and Lewis measurement scheme, we construct a formalism to describe the simultaneous measurement of incompatible spin components. The methods are illustrated with a new analysis of the Stern-Gerlach experiment, and with a discussion of spin dynamics in stochastic spin space. We also present a new short proof of a theorem on representations of spin-1/2 systems, find a joint spectral family for (noncommuting) spin components, and indicate the connection (...) of our result with the Riesz extension theorem. (shrink)

Starting from the phase space representation of quantum mechanics we provide an Euclidean system of covariance for the photon. In particular, we consider systems with the Poincaré group as the symmetry group and use a standard procedure in order to build a phase space and a localization observable on the phase space. Then we focus on the massless representations of the Poincaré group that we use to build a space localization observable for the photon.

It is shown that stochastic observables defined by an instrument need not, and generally do not, commute.