We generalize the modal interpretation of quantum mechanics so that it may be applied to composite systems represented by arbitrary density operators. We discuss the interpretation these density operators receive and relate this to the discussion about the interpretation of proper and improper mixtures in the standard interpretation.

A variety of ideas arising 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, specifically 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 ideas, but specifically in relation to the interpretation of probability, and its identification with relations in the Hilbert Space (...) norm. The familiar objection that Everett's approach yields probabilities different from quantum mechanics is easily dealt with. The more fundamental question is how to interpret these probabilities consistent with the relational theory of change, and the relational theory of identity over time. I shall show that the relational theory needs nothing more than the physical, minimal criterion of identity as defined by Everett's theory, and that this can be transparently interpreted in terms of the ordinary notion of the chance occurrence of an event, as witnessed in the present. It is in this sense that the theory has empirical content. (shrink)

A proof is given, at a greater level of generality than previous 'no-go' theorems, of the impossibility of formulating a modal interpretation that exhibits 'serious' Lorentz invariance at the fundamental level. Particular attention is given to modal interpretations of the type proposed by Bub.

Through the explicit introduction of hyperplane dependence as a form of relativistic dynamical evolution, we construct a manifestly covariant description of a single positive energy particle interacting with any one of a large class of “moving” external potentials. In1+1 dimensions, the simplified mathematics allows us to display a number of general properties of solutions to the equations of motion for evolution on hyperplanes.

I show that the quantum state ω can be interpreted as defining a probability measure on a subalgebra of the algebra of projection operators that is not fixed (as in classical statistical mechanics) but changes with ω and appropriate boundary conditions, hence with the dynamics of the theory. This subalgebra, while not embeddable into a Boolean algebra, will always admit two-valued homomorphisms, which correspond to the different possible ways in which a set of “determinate” quantities (selected by ω and the (...) boundary conditions) can have values. The probabilities defined by ω (via the Born rule) are probabilities over these two-valued homomorphisms or value assignments. So any universe of interacting systems, including those functioning as measuring instruments, can be modelled quantum mechanically without the projection postulate. (shrink)

An outstanding problem in so-called modal interpretations of quantum mechanics has been the specification of a dynamics for the properties introduced in such interpretations. We develop a general framework (in the context of the theory of stochastic processes) for specifying a dynamics for interpretations in this class, focusing on the modal interpretation by Vermaas and Dieks. This framework admits many empirically equivalent dynamics. We give some examples, and discuss some of the properties of one of them. This approach is applicable (...) to a wider class of theories, in particular, those using (discrete) strict effective—as in decoherence theory—superselection rules. (shrink)

I investigate the character of the definite properties defined by the Basic Rule in the Vermaas and Dieks' (1995) version of the modal interpretation of quantum mechanics, specifically for the case of the continuous model of decoherence by Joos and Zeh (1985). While this model suggests that the characteristic length that might be associated with the localisation of an individual system is the coherence length of the state (which converges rapidly to the thermal de Broglie wavelength), I show in an (...) exactly soluble case that the definite properties that are possessed with overwhelming probability in this modal interpretation are delocalized over the entire spread of the state. (shrink)

According to the modal interpretation, the standard mathematical framework of quantum mechanics specifies the physical magnitudes of a system, which have definite values. Probabilities are assigned to the possible values that these magnitudes may adopt. The interpretation is thus concerned with physical properties rather than with measurement results: it is a realistic interpretation. One of the notable achievements of this interpretation is that it dissolves the notorious measurement problem. The papers collected here, together with the introduction and concluding critical appraisal, (...) explain the various forms of the modal interpretation, survey its achievements, and discuss those problems that have yet to be solved. Audience: Philosophers of science, theoretical physicists, and graduate students in these disciplines. (shrink)

This is one of the most important books on quantum mechanics to have appeared in recent years. It offers a dramatically new interpretation that resolves puzzles and paradoxes associated with the measurement problem and the behavior of coupled systems. A crucial feature of this interpretation is that a quantum mechanical measurement can be certain to have a particular outcome even when the observed system fails to have the property corresponding to that outcome just prior to the measurement interaction.

Relational quantum mechanics is an interpretation of quantum theory which discards the notions of absolute state of a system, absolute value of its physical quantities, or absolute event. The theory describes only the way systems affect each other in the course of physical interactions. State and physical quantities refer always to the interaction, or the relation, between two systems. Nevertheless, the theory is assumed to be complete. The physical content of quantum theory is understood as expressing the net of relations (...) connecting all different physical systems. (shrink)

In this paper I will present conceptions of state reduction and particle and/or system localization which render these subjects fully compatible with the general requirements of a relativistic, i.e. Lorentz invariant, quantum theory. The approach consists of a systematic generalization of the concepts of initial data assignment at definite times, initiation and completion of measurements at definite times, and dynamical evolution as time dependence, to the concepts of initial data assignment on arbitrary space-like hyperplanes, initiation and completion of measurements on (...) arbitrary space-like hyperplanes, and dynamical evolution as space-like hyperplane dependence, respectively. I also briefly discuss the superluminal propagation which emerges from the localization study and the manner in which causal anomalies are nevertheless avoided. (shrink)