Causal Probabilities in GRW Quantum Mechanics

Lorenzo Lorenzetti

Abstract Spontaneous collapse theories of quantum mechanics turn the usual Schrödinger equation into a stochastic dynamical law. In particular, in this paper I will focus on the GRW theory. Two philosophical issues that can be raised about GRW concern (a) the ontology of the theory, in particular the nature of the wave function and its role within the theory, and (b) the interpretation of the objective probabilities involved in the dynamics of the theory. During the last years, it has been claimed that we can take advantage of dispositional properties in order to develop an ontology for GRW theory, and also in order to ground the objective probabilities which are postulated by it. However, in this paper I will argue that the dispositional interpretations which have been discussed in the literature so far are either flawed or—at best—incomplete. If we want to endorse a dispositional interpretation of GRW theory we thus need an extended account which specifies the precise nature of those properties and which makes also clear how they can correctly ground all the probabilities postulated by the theory. Thus, after having introduced several different kinds of probabilistic dispositions, I will try to fill the gap in the literature by proposing a novel and complete dispositional account of GRW, based on what I call spontaneous weighted multi-track propensities. I claim that such an account can satisfy both of our desiderata.

Patrick Suppes

Patrick Suppes

Christopher G. Timpson

Abstract This chapter examines probabilities in views that take a realist stance on quantum mechanics, i.e., the Ghirardi-Rimini-Weber (GRW) theory, the Bohm theory and the Everett interpretation. The GRW theory is found to claim a world that is chancy at a fundamental level at which ‘hits’ occur following an objective probability distribution. Although the Bohm theory gives up indeterminism, it is shown to allow for objective probabilities, this time ranging over initial conditions. However, the theory has difficulties in explaining the validity of the Born Rule. The Everett interpretation is found to be more satisfying in this respect. As Wallace and Deutsch have shown, rational agents in a many-world scenario should set their credences following the Born Rule if they choose among quantum games.

C. T. K. Chari

Peter J. Lewis

Abstract What are the consequences of quantum mechanics for the structure of causal explanation? It depends on the interpretation you choose. According to a hidden variable theory like Bohm’s, a measurement on one particle can have instantaneous effects on another, no matter how distant. This nonlocality is in prima facie conflict with special relativity. The prospects for constructing a local hidden variable theory are assessed, in particular by invoking backward-in-time causation. Many-worlds theories do not invoke nonlocal causation. However, they do entail that microcausal explanations are in terms of waves, not particles, and they inject consideration of the observer’s location among the worlds into causal explanations. Spontaneous collapse theories like GRW do invoke nonlocal causation; the prospects for a local spontaneous collapse theory are investigated. All of the major interpretations of quantum mechanics modify the structure of causal explanation from the received classical ideal.