TIME, QUANTUM-MECHANICS, AND PROBABILITY

A variety of ideas arising in decoherence theory, and in the ongoing d ebate over Everett's relative-state theory, can be linked to issues in relativity theory and the philosophy of time, specifically the relati onal theory of tense and of identity over time. These have been system atically presented in companion papers (Saunders 1995; 1996a); in what follows we shall consider the same circle of ideas, but specifically in relation to the interpretation of probability, and its identificati on with relations in the Hilbert Space norm. The familiar objection th at Everett's approach yields probabilities different from quantum mech anics is easily dealt with. The more fundamental question is how to in terpret these probabilities consistent with the relational theory of c hange, and the relational theory of identity over time. I shall show t hat the relational theory needs nothing more than the physical, minima l criterion of identity as defined by Everett's theory, and that this can be transparently interpreted in terms of the ordinary notion of th e chance occurrence of an event, as witnessed in the present. It is in this sense that the theory has empirical content.