Generating M-Indeterminate Probability Densities by Way of Quantum Mechanics

Time, Quantum Mechanics, and Probability

A variety of ideas arisiüg in decoherence theory, and in the ongoing debate over Everett’s relative-state theory, can be linked to issues in relativity theory and the philosophy of time, speci…cally the relational theory of tense and of identity over time. These have been systematically presented in companion papers (Saunders 1995, 1996a); in what follows we shall consider the same circle of id...

Constructing Stieltjes classes for M-indeterminate absolutely continuous probability distributions

If P is a moment-indeterminate probability distribution, then it is desirable to present explicitly other distributions possessing the same moments as P. In this paper, a method to construct an infinite family of probability densities called the Stieltjes class all with the same moments is presented. The method is applicable for densities with support (0,∞) which satisfy the lower bound: f(x) ≥...

Probability in modal interpretations of quantum mechanics

Modal interpretations have the ambition to construe quantum mechanics as an objective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix physical reality but yields probabilities. In working out these ideas an important motif is to stay close to the standard formalism of quantum mechanics and to refrain from intr...

Probability Densities for Some One-Dimensional Problems in Statistical Mechanics

Quantum Mechanics as a Theory of Probability

We develop and defend the thesis that the Hilbert space formalism of quantum mechanics is a new theory of probability. The theory, like its classical counterpart, consists of an algebra of events, and the probability measures defined on it. The construction proceeds in the following steps: (a) Axioms for the algebra of events are introduced following Birkhoff and von Neumann. All axioms, except...