The Logic of Events

Abstract

In the previous two chapters, I have shown that the statistical relations of quantum mechanics cannot be represented by measures on a classical probability space, because the partial algebra of quantum magnitudes is not imbeddable in a commutative algebra. Thus, the quantum statistics cannot be interpreted as an incomplete classical (i.e. Boolean) statistics. Moreover, the set of statistical states of the theory generates all possible probability measures in the generalized sense on the partial Boolean algebra of idempotent magnitudes. The purpose of this chapter, and the next, is to clarify the significance of non-imbeddability here. My thesis is that the transition from classical to quantum mechanics involves the generalization of the Boolean event structures of classical mechanics to non-Boolean event structures of a particular kind.