Abstract

In a series of recent papers, Randall and Foulis report the development of a generalized theory of probability which is based on the concept of a physical operation. A central concept in this theory is that of a generalized sample space. In this paper, we introduce a generalized sample space, which for historial reasons we shall call the Poincaré sphere sample space. We investigate the relationship between this nonclassical sample space and its classical analogs, and find that the key to this relationship is found in the use of idealized (Gedanken) experiments. The Poincaré sphere sample space is seen to describe a “photon” description of polarization, and the classical analogs represent different classical descriptions. We also discuss superposition and entropy for the Poincaré sphere sample space and its classical analogs, and we comment on the application of this generalized theory of probability to problems in the foundations of quantum theory