Quantum decoherence and the approach to equilibrium (II)

In a previous paper [Hemmo, M & Shenker, O (2003). Quantum decoherence and the approach to equilibrium I. Philosophy of Science, 70, 330–358] we discussed a recent proposal by Albert [(2000). Time and chance. Cambridge, MA: Harvard University Press. Chapter 7] to recover thermodynamics on a purely dynamical basis, using the quantum theory of the collapse of the quantum state of [Ghirardi, G, Rimini, A and Weber, T., (1986). Unified dynamics for microscopic and macroscopic systems. Physical Review, D 34, 470–479]. We proposed an alternative way to explain thermodynamics within no collapse interpretations of quantum mechanics. In this paper some difficulties faced by both approaches are discussed and solved: the spin echo experiments, and the problem of extremely light gases. In these contexts, we point out several ways in which the above quantum mechanical approaches as well as some other classical approaches to the foundations of statistical mechanics may be distinguished experimentally.     

The primitive ontology of quantum physics: Guidelines for an assessment of the proposals

The paper seeks to make progress from stating primitive ontology theories of quantum physics—notably Bohmian mechanics, the GRW matter density theory and the GRW flash theory—to assessing these theories. Four criteria are set out: (a) internal coherence; (b) empirical adequacy; (c) relationship to other theories; and (d) explanatory value. The paper argues that the stock objections against these theories do not withstand scrutiny. Its focus then is on their explanatory value: they pursue different strategies to ground the textbook formalism of quantum mechanics, and they develop different explanations of quantum non-locality. In conclusion, it is argued that Bohmian mechanics offers a better prospect for making quantum non-locality intelligible than the GRW matter density theory and the GRW flash theory.     

Interpretation neutrality in the classical domain of quantum theory

I show explicitly how concerns about wave function collapse and ontology can be decoupled from the bulk of technical analysis necessary to recover localized, approximately Newtonian trajectories from quantum theory. In doing so, I demonstrate that the account of classical behavior provided by decoherence theory can be straightforwardly tailored to give accounts of classical behavior on multiple interpretations of quantum theory, including the Everett, de Broglie–Bohm and GRW interpretations. I further show that this interpretation-neutral, decoherence-based account conforms to a general view of inter-theoretic reduction in physics that I have elaborated elsewhere, which differs from the oversimplified picture that treats reduction as a matter of simply taking limits. This interpretation-neutral account rests on a general three-pronged strategy for reduction between quantum and classical theories that combines decoherence, an appropriate form of Ehrenfest׳s Theorem, and a decoherence-compatible mechanism for collapse. It also incorporates a novel argument as to why branch-relative trajectories should be approximately Newtonian, which is based on a little-discussed extension of Ehrenfest׳s Theorem to open systems, rather than on the more commonly cited but less germane closed-systems version. In the Conclusion, I briefly suggest how the strategy for quantum-classical reduction described here might be extended to reduction between other classical and quantum theories, including classical and quantum field theory and classical and quantum gravity.     

Four tails problems for dynamical collapse theories

The primary quantum mechanical equation of motion entails that measurements typically do not have determinate outcomes, but result in superpositions of all possible outcomes. Dynamical collapse theories (e.g. GRW) supplement this equation with a stochastic Gaussian collapse function, intended to collapse the superposition of outcomes into one outcome. But the Gaussian collapses are imperfect in a way that leaves the superpositions intact. This is the tails problem. There are several ways of making this problem more precise. But many authors dismiss the problem without considering the more severe formulations. Here I distinguish four distinct tails problems. The first (bare tails problem) and second (structured tails problem) exist in the literature. I argue that while the first is a pseudo-problem, the second has not been adequately addressed. The third (multiverse tails problem) reformulates the second to account for recently discovered dynamical consequences of collapse. Finally the fourth (tails problem dilemma) shows that solving the third by replacing the Gaussian with a non-Gaussian collapse function introduces new conflict with relativity theory.     

Finding your marbles in wavefunction collapse theories

Lewis (Br. J. Philos. Sci. 48 (1997) 313) has recently presented an argument claiming that, under the Ghirardi–Rimini–Weber (GRW) theory of quantum mechanics, arithmetic does not apply to ordinary macroscopic objects such as marbles (known as the Counting Anomaly). In this paper, I disentangle two different lines of Lewis's argument, one devoted to what I call the standard GRW interpretation and the other to the mass density interpretation (MDI). I present both strains of Lewis's argument, and move on to criticise Lewis's position, focusing on his argument with respect to MDI. I analyse the structure of his argument, and follow this with a novel refutation of Lewis's argument, drawing on the original presentation of MDI as developed by Ghirardi et al. (Found. Phys. 25 (1995) 5). I briefly consider the debate that ensued between Bassi and Ghirardi and Clifton and Monton and interpret it within the context of my analysis. I conclude that Lewis's Counting Anomaly fails to generate a genuine problem.