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Why protective measurement establishes the reality of the wave function

Shan Gao

Published Aug 26, 2018• 1 citation
OpenAlex

Abstract

It has been debated whether protective measurement implies the reality of the wave function. In this paper, I present a new analysis of the relationship between protective measurement and the reality of the wave function. First, I briefly introduce protective measurements and the ontological models framework for them. Second, I give a simple proof of Hardy's theorem in terms of protective measurements. It shows that when assuming the ontic state of the protected system keeps unchanged during a protective measurement, the wave function must be real. Third, I analyze two suggested psi-epistemic models of a protective measurement, in which the ontic state of the system is affected by the measurement. It is shown that although these models can explain the appearance of expectation values of observables in a single measurement, their predictions about the variance of the result of a non-ideal protective measurement are different from those of quantum mechanics. Finally, I argue that no psi-epistemic models exist for an ideal protective measurement in the ontological models framework, and in order to account for the definite result of an ideal protective measurement, the wave function must be a property of the protected system, defined either at a precise instant or during an infinitesimal time interval around an instant. Moreover, this result can also be extended to the wave function of an unprotected system. This new proof of the reality of the wave function does not rely on auxiliary assumptions, and it may help settle the issue about the nature of the wave function.

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Protective Measurements and the Reality of the Wave Function

Shan Gao

It has been debated whether protective measurement implies the reality of the wave function. In this article, I present a new analysis of the relationship between protective measurements and the reality of the wave function. First, I briefly introduce protective measurements and the ontological models framework for them. Second, I give a simple proof of Hardy’s theorem in terms of protective measurements. Third, I analyse two suggested ψ-epistemic models of a protective measurement. It is shown that although these models can explain the appearance of expectation values of observables in a single measurement, their predictions about the variance of the result of a non-ideal protective measurement are different from those of quantum mechanics. Finally, I argue that under an auxiliary finiteness assumption about the dynamics of the ontic state, protective measurement implies the reality of the wave function in the ontological models framework.

arXiv:2001.09262•The British Journal for the Philosophy of Science•Jan 18, 2020•5 citations

WHY PROTECTIVE MEASUREMENT IMPLIES THE REALITY OF THE WAVE FUNCTION: FURTHER CONSOLIDATION

Shan Gao

The existing psi-ontology theorems are based on a simplified assumption of the ontological models framework, according to which when a measurement is performed the behaviour of the measuring device is determined by the ontic state of the measured system immediately before the measurement. In this paper, I give an argument for the reality of the wave function in terms of protective measurements under a more reasonable assumption, according to which the behaviour of the measuring device during a measurement is determined by the total evolution of the ontic state of the measured system during the measurement. In addition, I present a new analysis of how a protective measurement obtains the expectation value of the measured observable in the measured wave function. The analysis strengthens my argument by further clarifying the role the protection procedure plays in a protective measurement.

•Nov 20, 2018•0 citations

Does protective measurement imply the reality of the wave function

Shan Gao

Recently the first protective measurement has been realized in experiment [Nature Phys. 13, 1191 (2017)], which can measure the expectation value of an observable from a single quantum system. This raises an important and pressing issue of whether protective measurement implies the reality of the wave function. If the answer is yes, this will improve the influential PBR theorem [Nature Phys. 8, 475 (2012)] by removing auxiliary assumptions, and help settle the issue about the nature of the wave function. In this paper, we demonstrate that this is indeed the case. It is shown that a psi-epistemic model and quantum mechanics have different predictions about the variance of the result of a Zeno-type protective measurement with finite N.

•Apr 14, 2018•0 citations

Reality of the quantum state: A new proof in terms of protective measurements

Shan Gao

The ontological model framework provides a rigorous approach to address the question of whether the quantum state is ontic or epistemic. When considering only conventional projective measurements, auxiliary assumptions are always needed to prove the reality of the quantum state in the framework. For example, the Pusey-Barrett-Rudolph theorem is based on an additional preparation independence assumption. In this paper, we give a new proof of psi-ontology in terms of protective measurements in the ontological model framework. It is argued that the proof needs not rely on auxiliary assumptions, and also applies to deterministic theories such as the de Broglie-Bohm theory. In addition, we give a simpler argument for psi-ontology beyond the framework, which is only based on protective measurements and a weaker criterion of reality. The argument may be also appealing for those people who favor an anti-realist view of quantum mechanics.

•Dec 18, 2015•0 citations

Protective measurement and the nature of the wave function within the primitive ontology approach

Vincent Lam

Introduction One of the crucial issues about protective measurements is the extent to which they provide (additional) grounds for some realist understanding of the wave function. This issue is notoriously subject to debate, which is not the aim of this chapter. Rather, this chapter aims at clarifying the further issue of the ontological picture corresponding to the realist understanding of the wave function possibly suggested by protective measurements. Oddly enough, proponents of a realist reading of protective measurements remain in general rather vague about ontology (see for instance Aharonov et al. (1993, 4624), who assimilate the wave function to an “extended object” without further details, or the brief and somewhat unprecise discussion in Dickson (1995, 135–136) of the interpretation of the wave function within Bohmian mechanics (BM) and within the theoretical framework elaborated by Ghirardi, Rimini and Weber (GRW); in this volume, Gao does propose a more elaborated ontological model for quantum mechanics (QM) based on protective measurements). Despite this vagueness (or maybe because of it), it seems that the most obvious ontological intuition resulting from protective measurements points towards some form of straightforward realism about the wave function understood in the sense of a real, physical field: indeed, protective measurements are claimed to allow measuring expectation values of observables on a single quantum system, thereby providing the possibility of reconstructing (i.e. “measuring” in some sense) the wave function of a single quantum system. Aharonov et al. (1996, 125) clearly express this intuition: “We can observe the expectations values of operators, and we can observe the density and the current of the Schrödinger wave. We can “see” in some sense the Schrödinger wave. This leads us to believe that it has physical reality.” Therefore, this kind of intuition seems in line with a realist conception of the wave function, according to which the wave function is considered as a real substantial, material in some sense) entity on its own (this view is often called “wave function realism”).

Cambridge University Press eBooks•Nov 30, 2014•0 citations

The Meaning of the Wave Function: In Search of the Ontology of Quantum Mechanics

Shan Gao

The meaning of the wave function has been a hot topic of debate since the early days of quantum mechanics. Recent years have witnessed a growing interest in this long-standing question. Is the wave function ontic, directly representing a state of reality, or epistemic, merely representing a state of (incomplete) knowledge, or something else? If the wave function is not ontic, then what, if any, is the underlying state of reality? If the wave function is indeed ontic, then exactly what physical state does it represent? In this book, I aim to make sense of the wave function in quantum mechanics and find the ontological content of the theory. The book can be divided into three parts. The first part addresses the question of the nature of the wave function (Chapters 1-5). After giving a comprehensive and critical review of the competing views of the wave function, I present a new argument for the ontic view in terms of protective measurements. In addition, I also analyze the origin of the wave function by deriving the free Schroedinger equation. The second part analyzes the ontological meaning of the wave function (Chapters 6, 7). I propose a new ontological interpretation of the wave function in terms of random discontinuous motion of particles, and give two main arguments supporting this interpretation. The third part investigates whether the suggested quantum ontology is complete in accounting for our definite experience and whether it needs to be revised in the relativistic domain (Chapters 8, 9).

arXiv:1611.02738•Nov 7, 2016•31 citations
It has been debated whether protective measurement implies the reality of the wave function. In this paper, I present a new analysis of the relationship between protective measurement and the reality of the wave function. First, I briefly introduce protective measurements and the ontological models framework for them. Second, I give a simple proof of Hardy's theorem in terms of protective measurements. It shows that when assuming the ontic state of the protected system keeps unchanged during a protective measurement, the wave function must be real. Third, I analyze two suggested psi-epistemic models of a protective measurement, in which the ontic state of the system is affected by the measurement. It is shown that although these models can explain the appearance of expectation values of observables in a single measurement, their predictions about the variance of the result of a non-ideal protective measurement are different from those of quantum mechanics. Finally, I argue that no psi-epistemic models exist for an ideal protective measurement in the ontological models framework, and in order to account for the definite result of an ideal protective measurement, the wave function must be a property of the protected system, defined either at a precise instant or during an infinitesimal time interval around an instant. Moreover, this result can also be extended to the wave function of an unprotected system. This new proof of the reality of the wave function does not rely on auxiliary assumptions, and it may help settle the issue about the nature of the wave function.
It has been debated whether protective measurement implies the reality of the wave function. In this article, I present a new analysis of the relationship between protective measurements and the reality of the wave function. First, I briefly introduce protective measurements and the ontological models framework for them. Second, I give a simple proof of Hardy’s theorem in terms of protective measurements. Third, I analyse two suggested ψ-epistemic models of a protective measurement. It is shown that although these models can explain the appearance of expectation values of observables in a single measurement, their predictions about the variance of the result of a non-ideal protective measurement are different from those of quantum mechanics. Finally, I argue that under an auxiliary finiteness assumption about the dynamics of the ontic state, protective measurement implies the reality of the wave function in the ontological models framework.
The existing psi-ontology theorems are based on a simplified assumption of the ontological models framework, according to which when a measurement is performed the behaviour of the measuring device is determined by the ontic state of the measured system immediately before the measurement. In this paper, I give an argument for the reality of the wave function in terms of protective measurements under a more reasonable assumption, according to which the behaviour of the measuring device during a measurement is determined by the total evolution of the ontic state of the measured system during the measurement. In addition, I present a new analysis of how a protective measurement obtains the expectation value of the measured observable in the measured wave function. The analysis strengthens my argument by further clarifying the role the protection procedure plays in a protective measurement.
Recently the first protective measurement has been realized in experiment [Nature Phys. 13, 1191 (2017)], which can measure the expectation value of an observable from a single quantum system. This raises an important and pressing issue of whether protective measurement implies the reality of the wave function. If the answer is yes, this will improve the influential PBR theorem [Nature Phys. 8, 475 (2012)] by removing auxiliary assumptions, and help settle the issue about the nature of the wave function. In this paper, we demonstrate that this is indeed the case. It is shown that a psi-epistemic model and quantum mechanics have different predictions about the variance of the result of a Zeno-type protective measurement with finite N.
The ontological model framework provides a rigorous approach to address the question of whether the quantum state is ontic or epistemic. When considering only conventional projective measurements, auxiliary assumptions are always needed to prove the reality of the quantum state in the framework. For example, the Pusey-Barrett-Rudolph theorem is based on an additional preparation independence assumption. In this paper, we give a new proof of psi-ontology in terms of protective measurements in the ontological model framework. It is argued that the proof needs not rely on auxiliary assumptions, and also applies to deterministic theories such as the de Broglie-Bohm theory. In addition, we give a simpler argument for psi-ontology beyond the framework, which is only based on protective measurements and a weaker criterion of reality. The argument may be also appealing for those people who favor an anti-realist view of quantum mechanics.
Introduction One of the crucial issues about protective measurements is the extent to which they provide (additional) grounds for some realist understanding of the wave function. This issue is notoriously subject to debate, which is not the aim of this chapter. Rather, this chapter aims at clarifying the further issue of the ontological picture corresponding to the realist understanding of the wave function possibly suggested by protective measurements. Oddly enough, proponents of a realist reading of protective measurements remain in general rather vague about ontology (see for instance Aharonov et al. (1993, 4624), who assimilate the wave function to an “extended object” without further details, or the brief and somewhat unprecise discussion in Dickson (1995, 135–136) of the interpretation of the wave function within Bohmian mechanics (BM) and within the theoretical framework elaborated by Ghirardi, Rimini and Weber (GRW); in this volume, Gao does propose a more elaborated ontological model for quantum mechanics (QM) based on protective measurements). Despite this vagueness (or maybe because of it), it seems that the most obvious ontological intuition resulting from protective measurements points towards some form of straightforward realism about the wave function understood in the sense of a real, physical field: indeed, protective measurements are claimed to allow measuring expectation values of observables on a single quantum system, thereby providing the possibility of reconstructing (i.e. “measuring” in some sense) the wave function of a single quantum system. Aharonov et al. (1996, 125) clearly express this intuition: “We can observe the expectations values of operators, and we can observe the density and the current of the Schrödinger wave. We can “see” in some sense the Schrödinger wave. This leads us to believe that it has physical reality.” Therefore, this kind of intuition seems in line with a realist conception of the wave function, according to which the wave function is considered as a real substantial, material in some sense) entity on its own (this view is often called “wave function realism”).
The meaning of the wave function has been a hot topic of debate since the early days of quantum mechanics. Recent years have witnessed a growing interest in this long-standing question. Is the wave function ontic, directly representing a state of reality, or epistemic, merely representing a state of (incomplete) knowledge, or something else? If the wave function is not ontic, then what, if any, is the underlying state of reality? If the wave function is indeed ontic, then exactly what physical state does it represent? In this book, I aim to make sense of the wave function in quantum mechanics and find the ontological content of the theory. The book can be divided into three parts. The first part addresses the question of the nature of the wave function (Chapters 1-5). After giving a comprehensive and critical review of the competing views of the wave function, I present a new argument for the ontic view in terms of protective measurements. In addition, I also analyze the origin of the wave function by deriving the free Schroedinger equation. The second part analyzes the ontological meaning of the wave function (Chapters 6, 7). I propose a new ontological interpretation of the wave function in terms of random discontinuous motion of particles, and give two main arguments supporting this interpretation. The third part investigates whether the suggested quantum ontology is complete in accounting for our definite experience and whether it needs to be revised in the relativistic domain (Chapters 8, 9).