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Philosophy of Science

Are GRW Tails as Bad as They Say?

Alberto Cordero

Published Jan 1, 1999• 31 citations
Publisher

Abstract

GRW models of the physical world are criticized in the literature for involving wave function “tails” that allegedly create fatal interpretive problems and even compromise standard arithmetic. I find such objections both unfair and misguided. But not all is well with the GRW approach. One complaint I articulate in this paper does not have to do with tails as such but with the specific way in which past physical structures linger forever in the total GRW wave function. By pushing the total proposal towards either the “Many Worlds” approach or the Bohmian approach, this feature diminishes extant GRW claims to preferability. I suggest, however, that the problem here is just an artifact of the particular and ultimately optional genre of collapse mechanism chosen by GRW.

DOI
10.1086/392715

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GRW models of the physical world are criticized in the literature for involving wave function “tails” that allegedly create fatal interpretive problems and even compromise standard arithmetic. I find such objections both unfair and misguided. But not all is well with the GRW approach. One complaint I articulate in this paper does not have to do with tails as such but with the specific way in which past physical structures linger forever in the total GRW wave function. By pushing the total proposal towards either the “Many Worlds” approach or the Bohmian approach, this feature diminishes extant GRW claims to preferability. I suggest, however, that the problem here is just an artifact of the particular and ultimately optional genre of collapse mechanism chosen by GRW.
It is often assumed that the only effect of the Ghirardi-Rimini-Weber (`GRW') dynamical collapse mechanism on the `tails' of the wavefunction (that is, the components of superpositions on which the collapse is \emph{not} centred) is to reduce their weight. In consequence the tails are often thought to behave exactly as do the various branches in the Everett interpretation except for their much lower weight. These assumptions are demonstrably inaccurate: the collapse mechanism has substantial and detectable effects within the tails. The relevance of this misconception for the dynamical-collapse theories is debatable, though.
It is often assumed that the only effect of the Ghirardi-Rimini-Weber (`GRW') dynamical collapse mechanism on the `tails' of the wavefunction (that is, the components of superpositions on which the collapse is \emph{not} centred) is to reduce their weight. In consequence it seems to be generally accepted that the tails behave exactly as do the various branches in the Everett interpretation except for their much lower weight. These assumptions are demonstrably inaccurate: the collapse mechanism has substantial and detectable effects within the tails. The relevance of this misconception for the dynamical-collapse theories is debatable, though.
GRW theory oers precise laws for the collapse of the wave function. These collapses are characterized by two new constants, and . Recent work has put experimental upper bounds on the collapse rate, . Lower bounds on have been more controversial since GRW begins to take on a many-worlds character for small values of . Here I examine GRW in this odd region of parameter space where collapse events act as natural disasters that destroy branches of the wave function along with their occupants. Our continued survival provides evidence that we don’t live in a universe like that. I oer a quantitative analysis of how such evidence can be used to assess versions of GRW with small collapse rates in an eort to move towards more principled and experimentally-informed lower bounds for .
Peter Lewis ([1997]) has recently argued that the wavefunction collapse theory of GRW (Chirardi, Rimini and Weber [1986]) can only solve the problem of wavefunction tails at the expense of predicting that arithmetic does not apply to ordinary macroscopic objects. More specifically, Lewis argues that the GRW theory must violate the enumeration principle: that 'if marble 1 is in the box and marble 2 is in the box and so on through marble n, then all n marbles are in the box' ([1997], p. 321). Ghirardi and Bassi ([1999]) have replied that it is meaningless to say that the enumeration principle is violated because the wavefunction Lewis uses to exhibit the violation cannot persist, according to the GRW theory, for more than a split second ([1999], p. 709). On the contrary, we argue that Lewis's argument survives Ghirardi and Bassi's criticism unscathed. We then go on to show that, while the enumeration principle can fail in the GRW theory, the theory itself guarantees that the principle can never be empirically falsified, leaving the applicability of arithmetical reasoning to both micro- and macroscopic objects intact.
Abstract This article provides an overview of the philosophical literature on the GRW theory of quantum mechanics, and argues for a particular position regarding that literature. Much of the literature is ontological; it attempts to defend a conception of what the world is like according to the GRW theory against perceived competitors. I argue that there is no real debate here, since these supposedly conflicting positions are better regarded as alternative and compatible ways of describing the world of the GRW theory.
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.