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arXiv:1206.6491

A problem with the Pusey, Barrett, Rudolph analysis of the reality of the quantum state

Casey Blood

Published Jun 27, 2012• 7 citations
arXivHTMLPDF

Abstract

The analysis of Pusey, Barrett and Rudolph aims to show there can be no objective physical reality which underlies, and is more general than, the state vector. But there appears to be a gap in their reasoning. To show their result, they use entangled states of independent systems. However, no specific experimental arrangement to detect these entangled states has been proposed. Thus their argument as it stands does not fully show there is a detectable conflict between the predictions of quantum mechanics and the existence of an underlying reality. And it is not clear that one can devise the necessary measuring device.

DOI
10.48550/arxiv.1206.6491

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The analysis of Pusey, Barrett and Rudolph aims to show there can be no objective physical reality which underlies, and is more general than, the state vector. But there appears to be a gap in their reasoning. To show their result, they use entangled states of independent systems. However, no specific experimental arrangement to detect these entangled states has been proposed. Thus their argument as it stands does not fully show there is a detectable conflict between the predictions of quantum mechanics and the existence of an underlying reality. And it is not clear that one can devise the necessary measuring device.
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This paper explores the philosophical as well as the physical arguments made by Matthew Pusey, Jonathan Barrett and Terry Rudolph in their recently published article on the reality of the quantum state in order to attain a full understanding of the statements they make in their article. This is essential because not even all respondents to the article agree on how to interpret the article. In their article Pusey, Barrett and Rudolph present a no-go theorem; they show that a particular situation is, according to quantum theory, not physically possible if one were to be psi-epistemic about it. They argue that for this particular situation, or thought-experiment, the psi-epistemic interpretation makes predictions that are inconsistent with those predictions made by quantum theory itself.
I argue for a realist interpretation of the quantum state. I begin by reviewing and critically evaluating two arguments for an antirealist interpretation of the quantum state, the first derived from the so-called ‘measurement problem’, and the second from the concept of local causality. I argue that existing antirealist interpretations do not solve the measurement problem. Furthermore, I argue that it is possible to construct a local, realist interpretation of quantum mechanics, using methods borrowed from quantum field theory and based on John S. Bell’s concept of ‘local beables’.\nIf the quantum state is interpreted subjectively, then the probabilities it associates with experimental outcomes are themselves subjective. I address the prospects for developing a subjective Bayesian interpretation of quantum mechanical probabilities based on the Quantum de Finetti Representation Theorem. Epistemic interpretations of the quantum state can be divided into those that are epistemic with respect to underlying ontic states, and those that are epistemic with respect to measurement outcomes. The Pusey Barrett and Rudolph (PBR) theorem places serious constraints on the former family of interpretations. I identify an important explanatory gap in the latter sort of interpretation. In particular, if the quantum state is a subjective representation of beliefs about future experimental outcomes, then it is not clear why those experimenters who use quantum mechanics should be better able to negotiate the world than those who do not.\nI then turn to the task of articulating a positive argument for the thesis of quantum state realism. I begin by articulating a minimal set of conditions that any realist interpretation must meet. One assumption built into the PBR result is that systems prepared in a given quantum state have a well-defined set of physical properties, which may be completely or incompletely described by the quantum state. Antirealist interpretations that reject this assumption are therefore compatible with the PBR result. A compelling case for quantum state realism must therefore be made on more general grounds. I consider two concrete examples of phenomena described by quantum mechanics that strongly suggest that the quantum state is genuinely representational in character.
Is The Quantum Wave Function Real?The conflict between all we know about the physics of quantum systems and what we say or believe is real about them is brought forward dramatically with the concept of the quantum wave function (QWF). Is the QWF ontic or merely epistemic? Here I review and clarify through original examples the recent work of M. F. Pusey, J. Barrett, and T. Rudolph who have formed a novel theorem to decide on the ontology or epistemology of a QWF based on a hidden variable (HV) theory dating back to the mid-20th century.