Yes-No Experiments

The first five sections of this chapter are intended to provide some intuitive physical content to the notions of state and proposition of a quantum system. We deliberately avoid any deductive attitude, and we also avoid formalizations: the ingredients we shall start with (yes-no experiments and preparations) are so primitive and unstructured that the construction of quantum mechanics out of them is certainly not at hand. What we are going to see is simply that there is natural physical motivation for the occurrence at the very basis of every statistical theory—quantum mechanics in particular—of an ordered structure of propositions, of a convex structure of states, and of a relationship between these structures that makes the states behave as probability measures on propositions. From Section 13.6 on, we shall sketch a more formalized model, based on Mackey's approach.

By a yes-no experiment is meant an experiment that makes use of a measuring instrument having just two outcomes, which without loss of generality we can agree to label “yes” and “no”. Of course, when talking of a yes-no experiment we always imagine that we have specified the physical system to which it pertains. We also imagine that the interaction between