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arXiv:1911.10874 · Oxford University Press eBooks

On the Status of Quantum State Realism

Wayne C. Myrvold

Published Feb 27, 2020• 11 citations
arXivHTMLPDF

Abstract

Chapter 12 argues that there is good reason for being realist about quantum states. Though a research programme of attempting to construct a plausible theory that accounts for quantum phenomena without ontic quantum states is well motivated, that research programme is confronted by considerable obstacles. Two theorems are considered that place restrictions on a theory of that sort: a theorem due to Barrett, Cavalcanti, Lal, and Maroney, and an extension, by the author, of the Pusey-BarrettRudolph theorem, that employs an assumption weaker than their Cartesian Product Assumption. These theorems have assumptions, of course. If there were powerful evidence against the conclusion that quantum states correspond to something in physical reality, it might be reasonable to reject these assumptions. But the current situation is the opposite: there is no evidence at all supporting irrealism about quantum states.

DOI
10.1093/oso/9780198814979.003.0012

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Chapter 12 argues that there is good reason for being realist about quantum states. Though a research programme of attempting to construct a plausible theory that accounts for quantum phenomena without ontic quantum states is well motivated, that research programme is confronted by considerable obstacles. Two theorems are considered that place restrictions on a theory of that sort: a theorem due to Barrett, Cavalcanti, Lal, and Maroney, and an extension, by the author, of the Pusey-BarrettRudolph theorem, that employs an assumption weaker than their Cartesian Product Assumption. These theorems have assumptions, of course. If there were powerful evidence against the conclusion that quantum states correspond to something in physical reality, it might be reasonable to reject these assumptions. But the current situation is the opposite: there is no evidence at all supporting irrealism about quantum states.
Towards the end of 2011, Pusey, Barrett and Rudolph derived a theorem that aimed to show that the quantum state must be ontic (a state of reality) in a broad class of realist approaches to quantum theory. This result attracted a lot of attention and controversy. The aim of this review article is to review the background to the Pusey–Barrett–Rudolph Theorem, to provide a clear presentation of the theorem itself, and to review related work that has appeared since the publication of the Pusey–Barrett–Rudolph paper. In particular, this review: Explains what it means for the quantum state to be ontic or epistemic (a state of knowledge); Reviews arguments for and against an ontic interpretation of the quantum state as they existed prior to the Pusey–Barrett–Rudolph Theorem; Explains why proving the reality of the quantum state is a very strong constraint on realist theories in that it would imply many of the known no-go theorems, such as Bell's Theorem and the need for an exponentially large ontic state space; Provides a comprehensive presentation of the Pusey–Barrett–Rudolph Theorem itself, along with subsequent improvements and criticisms of its assumptions; Reviews two other arguments for the reality of the quantum state: the first due to Hardy and the second due to Colbeck and Renner, and explains why their assumptions are less compelling than those of the Pusey–Barrett–Rudolph Theorem; Reviews subsequent work aimed at ruling out stronger notions of what it means for the quantum state to be epistemic and points out open questions in this area. The overall aim is not only to provide the background needed for the novice in this area to understand the current status, but also to discuss often overlooked subtleties that should be of interest to the experts. Quanta 2014; 3: 67–155.
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.
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.
In this paper we consider theories in which reality is described by some underlying variables, λ. Each value these variables can take represents an ontic state (a particular state of reality). The preparation of a quantum state corresponds to a distribution over the ontic states, λ. If we make three basic assumptions, we can show that the distributions over ontic states corresponding to distinct pure states are nonoverlapping. This means that we can deduce the quantum state from a knowledge of the ontic state. Hence, if these assumptions are correct, we can claim that the quantum state is a real thing (it is written into the underlying variables that describe reality). The key assumption we use in this proof is ontic indifference — that quantum transformations that do not affect a given pure quantum state can be implemented in such a way that they do not affect the ontic states in the support of that state. In fact this assumption is violated in the Spekkens toy model (which captures many aspects of quantum theory and in which different pure states of the model have overlapping distributions over ontic states). This paper proves that ontic indifference must be violated in any model reproducing quantum theory in which the quantum state is not a real thing. The argument presented in this paper is different from that given in a recent paper by Pusey, Barrett and Rudolph. It uses a different key assumption and it pertains to a single copy of the system in question.
Scientific realism has traditionally maintained that our best scientific theories can be regarded as more or less true and as representing the world as it is (more or less). However, one of our very best current theories—quantum mechanics—has famously resisted such a realist construal, threatening to undermine the realist stance altogether. The chapters in this volume carefully examine this tension and the reasons behind it, including the underdetermination generated by the multiplicity of formulations and interpretations of quantum physics, each presenting a different way the world could be. Authors in this volume offer a range of alternative ways forward: some suggest new articulations of realism, limiting our commitments in one way or another; others attempt to articulate a ‘third way’ between traditional forms of realism and antirealism, or are critical of such attempts. Still others argue that quantum theory itself should be reconceptualised, or at least alternative formulations should be considered in the hope of evading the problems faced by realism. And some examine the nature of these issues when moving beyond quantum mechanics to quantum field theory. Taken together they offer an exciting new set of perspectives on one of the most fundamental questions in the philosophy of modern physics: how can one be a realist about quantum theory, and what does this realism amount to?
In a recent paper (arXiv:1111.3328), Pusey, Barrett and Rudolph claim to prove that statistical interpretations of quantum mechanics do not work. In fact, their proof assumes that all statistical interpretations must be based on hidden variable realism. Effectively, the authors demand from the start that reality must be decided by mathematics, and not by measurements. If this unjustified assumption is dropped, the quantum formalism has a natural statistical interpretation that fully explains the paradox presented by the authors. It is therefore possible to conclude that the paradox actually supports the statistical interpretation, demonstrating once more that quantum mechanics should not be explained by measurement independent realities that are never observed and therefore lie beyond the reach of empirical tests.