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Routledge eBooks

Reflections and Conclusions

John Forge

Published Aug 20, 2018• 0 citations
Publisher

Abstract

This conclusion presents some closing thoughts on the key concepts discussed in the preceding chapters of this book. The book presents with two different accounts of quantity: the class nominalist ‘neo-Ellisonian’ account and the ‘quasi-realist’ BP. It shows what was involved in making such a move and the class nominalist position was contrasted with realism. The book discusses the various positions and proposals have been restricted by qualifiers like “in the classical domain”. The application of mathematics crucially depends on this - hence the emphasis throughout the book on measurement and what this presupposes. The whole idea of ‘new directions’ in the theory of explanation is to allow for different styles and dimensions of explanations. What is then necessary for the instance view to apply to explanation in quantum mechanics is to incorporate the quantum state into the laws that also feature quantities.

DOI
10.4324/9780429459887-12

Related papers

Introduction

Robert B. Griffiths

Scope of this book Quantum mechanics is a difficult subject, and this book is intended to help the reader overcome the main difficulties in the way to understanding it. The first part of the book, Chs. 2–16, contains a systematic presentation of the basic principles of quantum theory, along with a number of examples which illustrate how these principles apply to particular quantum systems. The applications are, for the most part, limited to toy models whose simple structure allows one to see what is going on without using complicated mathematics or lengthy formulas. The principles themselves, however, are formulated in such a way that they can be applied to (almost) any nonrelativistic quantum system. In the second part of the book, Chs. 17–25, these principles are applied to quantum measurements and various quantum paradoxes, subjects which give rise to serious conceptual problems when they are not treated in a fully consistent manner. The final chapters are of a somewhat different character. Chapter 26 on decoherence and the classical limit of quantum theory is a very sketchy introduction to these important topics along with some indication as to how the basic principles presented in the first part of the book can be used for understanding them. Chapter 27 on quantum theory and reality belongs to the interface between physics and philosophy and indicates why quantum theory is compatible with a real world whose existence is not dependent on what scientists think and believe, or the experiments they choose to carry out. The Bibliography contains references for those interested in further reading or in tracing the origin of some of the ideas presented in earlier chapters.

Cambridge University Press eBooks•Nov 29, 2001•0 citations

Conclusions

George C. Shields

The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation.

CRC Press eBooks•Dec 7, 2013•0 citations

THE REALIST-INSTRUMENTALIST CONTROVERSY IN QUANTUM MECHANICS

Vincent A. Lazara

My aim in this dissertation is to defend a realist interpretation of quantum mechanics.Firstly, I present considerations based on certain general features of theories in the natural sciences which indicate that realism affords a better account of those theories than instrumentalism.In particular, I consider certain issues surrounding the cognitive status of theories, including the role of models, the status of scientific explanation, and the referential character of theoretical terms.Secondly, I develop a detailed realist theory of measurement based on the notion of quantity terms as designators of objective properties of, and relations among, existing entities.I contrast this with the leading instrumentalist theories of measurement, and I argue that the realist theory is the better account of both the logic and practice of scientific measurement.Finally, I consider a number of objections to realism that arise because of certain theoretical features peculiar to quantum mechanics.In the course of this discussion, I consider crucial experimental evidence for the "dual" nature of microentities, various criteria of reality proposed by philosophers of science, the peculiar features of quantum mechanical measurement, and the status of causality in quantum mechanics.I argue that while certain realist viii ix interpretations of the quantum theory, namely the wave and wavicle interpretations, are unsatisfactory, an interpreta tion which construes micro-entities as existing particles is a tenable account.CHAPTER I ignored the considerations which arise at those more general levels of inquiry, but one can not adequately assess the status of quantum mechanics with respect to both realism and instrumentalism apart from those considerations.In the second two chapters of the dissertation, I shall argue that realist interpretations of quantitative theories in the natural sciences are preferable to instrumentalist interpretations.Then in the remainder of the dissertation, I shall go on to argue that realism is tenable at the quantum mechanical level despite the features peculiar to that theory.CHAPTER II THE COGNITIVE STATUS OF THEORIES transitions from one set of experiential statements to another.This view is in marked contrast to that of the realist who regards such terms as referential.This divergence in opinion between realists and instrumentalists about the referential character of theoretical terms leads to a related dispute over the role of models in the inter pretation of scientific theories.Before contrasting the various philosophical positions on this issue, it will be necessary to sort out different senses of the term "model."Upon inspecting the literature surrounding this dispute, it seems that much of the controversy about the role of models stems from a failure to make such distinctions.I will begin this task by distinguishing between 13 model-structures and model-objects.A model-structure is a definitely specifiable schema of mathematical-logical relationships which is exhibited by and can be abstracted from a set of objects.Any set of objects which exhibits a model-structure constitutes a set of model-objects.With respect to any particular scientific theory, there may be a variety of model-objects that scientists employ for various purposes.For example, in the kinetic theory of gases, one can distinguish the following.Firstly, there is the set of molecules themselves, the theoretical entities which we shall 13.For further detail in this regard, see Henry C. Byerly, "Model-Structures and Model-Objects," British Journal for the Philosophy of Science.Vol. 20, 1969, pp.135-144.i In fact, if one were to make that claim, I do not see how it could be supported without again falling prey to Maxwell's criticism cited above.And if one is simply troubled by the "ontological risk" involved in asserting the existence of theoretical entities because of the tentativeness of the corresponding theories, it should be noted that the risk of being wrong is a small price to pay for the potentially deeper understanding of nature that scientific theories afford us in the light of realist commitments.

•Jan 1, 1973•0 citations

Conclusion

Vladimir B. Braginsky, Farid Ya Khalili, Kip S. Thorne

The background for this book was a shift of interest among experimental physicists that began approximately 20 years ago. The shift was from quantum measurements on large ensembles of microscopic quantum objects, to experiments of very high precision on single, macroscopic objects. This shift was accompanied by developments in the “culture” of such measurements and the invention and elaboration of new experimental methods. In parallel with these experimental developments, there was a noticeable increase of theoretical interest in the foundations and interpretation of quantum theory, and even in attempts to revise its foundational principles. Although these efforts have not produced any significant changes in the fundamental structure of quantum theory, they have revealed a rather large number of “blank spots” and unsolved problems, to which the founders of quantum physics had paid no attention. A reasonable number of the blank spots have been filled in during the past decade. The reader has probably noticed that this book can be divided into two parts. In the first (chapters I―VII and XI), the authors have tried to present the modern approach to the quantum theory of measurement. This part can be regarded as a tutorial appendix to textbooks for advanced undergraduate or graduate-level courses in quantum mechanics, where little attention is usually paid to measurement theory.

Cambridge University Press eBooks•Sep 24, 1992•0 citations

Introduction

David Wallace

The basic thesis of this book is that there is no quantum measurement problem. I do not mean by this that the apparent paradoxes of quantum mechanics arise because we fail to recognize ‘that quantum theory does not describe physical reality’ (Fuchs and Peres 2000a). Quantum theory describes reality just fine, like any other scientific theory worth taking seriously: describing (and explaining) reality is what the scientific enterprise is about. Nor do I mean that we have found solutions to the problem, ways to modify or supplement quantum mechanics so that the paradoxes are removed. I don’t actually think that we have found any very satisfactory solutions in this sense (at least not in the relativistic domain) but that isn’t my theme: even if we did have these modifications, they would be ways of changing from quantum physics, which supposedly does have a measurement problem, to some other theory, which supposedly doesn’t.

Oxford University Press eBooks•May 24, 2012•3 citations

The Quantum Revolution in Philosophy

Eddy Keming Chen

In this thought-provoking book, Richard Healey proposes a new interpretation of quantum theory inspired by pragmatist philosophy. Healey puts forward the interpretation as an alternative to realist quantum theories on the one hand such as Bohmian mechanics, spontaneous collapse theories, and many-worlds interpretations, which are different proposals for describing what the quantum world is like and what the basic laws of physics are, and nonrealist interpretations on the other hand such as quantum Bayesianism, which proposes to understand quantum theory as describing agents’ subjective epistemic states. The central idea of Healey's proposal is to understand quantum theory as providing not a description of the physical world but a set of authoritative and objectively correct prescriptions about how agents should act. The book provides a detailed development and defense of that idea, and it contains interesting discussions about a wide range of philosophical issues such as representation, probability, explanation, causation, objectivity, meaning, and fundamentality.Healey's project is at the intersection of physics and philosophy. The book is divided into two parts. Part 1 of the book discusses the foundational questions in quantum theory from the perspective of the prescriptive interpretation. In part 2, Healey discusses the philosophical implications of the view. Both parts are written in a way that is largely accessible to nonspecialists. In this brief book review, I will focus on two questions:1. How does Healey's interpretation work?2. What are the costs and benefits of accepting his interpretation?To understand Healey's ideas, we should provide some background for nonspecialists. Quantum theory has been subject to intense scrutiny and philosophical investigations in the last century. There has been enormous progress on several fronts, including the empirical tests about Bell inequalities and the development of several realist interpretations. It has been proposed that what is revolutionary about quantum theory and what sets it apart from classical physics are quantum entanglement and quantum nonlocality. For many realists, it seems that quantum theory describes a different kind of ontology and a different kind of laws of nature. They are introduced briefly below.Quantum entanglement describes the phenomenon that some physical systems have irreducibly holistic properties that are not the logical sums of the properties of the parts. For example, two electrons A and B are entangled when the pair has a quantum state that cannot be reduced to some combination of the state of A and the state of B. Quantum entanglement, a manifestation of quantum nonseparability, is reflected in the way quantum states, which are typically represented by “wave functions,” get assigned to different systems.Quantum nonlocality (also called “spooky action at a distance”) describes the phenomenon that events that are arbitrarily far apart can influence one another and the strength of the influence does not depend on their distance. Quantum nonlocality is a strange feature, and its falsity was assumed in the 1935 argument by Einstein, Podolsky, and Rosen for the incompleteness of quantum theory. Remarkably, Bell (1964) proved that if the quantum predictions are accurate, then nature is nonlocal. Subsequent experimental tests since the 1980s have verified the quantum predictions to a high level of precision, reinforcing the conclusion that nature is nonlocal.1Among the realist theories of quantum mechanics, Bohmian mechanics and spontaneous collapse theories are nonlocal. Moreover, all three realist theories, including the many-worlds interpretation, affirm the reality of quantum entanglement. The reality of quantum entanglement follows from the reality of the quantum state. After all, the quantum state is so successful in application. If one wants to be a realist, it seems that the most natural way is to accept the reality of the quantum state and its consequences. But what is represented by the wave function? What is its nature? How does it relate to things in the physical world? Some recent discussions in philosophy of physics concern exactly those questions.2I think the key to understanding Healey's interpretation is to think of it as a proposal for an alternative foundation of quantum theory—a proposal to use normative facts instead of descriptive facts as the foundation and to replace “what there is” with “what we ought to expect” as what is fundamental to physical theory. Healey's approach would sound alien to many people, since it is not realist in any traditional sense. It is common to think that fundamental physics, and in particular quantum theory, is in the business of saying what the world is like (even though it may be difficult to discern what it says). It is true that we can learn useful advice from a correct physical theory, such as:one should avoid falling into a black holeone should place detectors far away from sources of interferenceone should get away from a nuclear explosionone should be almost certain to see this particle decay in 1 monthA correct physical theory may explain the correctness of useful practical advices such as above. Such advices are objectively correct insofar as they are derived from the conjunction of some accurate descriptions of physical reality and some correct theories of human rationality.3 For Healey, that might be a fine interpretation of classical physics, but that is not the correct interpretation of quantum theory. Quantum theory, for Healey, directly offers authoritative advice about what we should believe and expect, and such advice is not derived in any way from some underlying descriptive facts. Still, such advice can be objectively true (unlike the quantum Bayesian's emphasis on subjective epistemic states). The advice has the form “one should assign quantum state ψ to the physical system s,” and “one should have 0.5 confidence in M,” where M is some kind of magnitude claim about the physical system s. On Healey's interpretation, quantum theory is about such advice, not some descriptions about what nature is like. Although the magnitude claims are descriptions of nature, they are not contained in quantum theory. Instead, they are assumed to be the targets of explanation, and they are somewhat prior to the application of quantum theory. However, they will be suitably constrained by quantum theory, and only a subclass of them will be empirically significant.There are many parts to Healey's proposal. To simplify our discussions below, here is a short summary of the key points (mostly from chapter 5):Advice on state assignments: agents should follow the standard practice in quantum physics and assign an appropriate quantum state (e.g., a wave function ψ) to a system relative to their physical situation.Magnitude claims: a canonical magnitude claim has the form “the value of dynamical variable M on physical system s lies in set Δ.” One example would be “the position of the particle is on the left side of the box.” Magnitude claims are assumed in the theory and they are the targets of explanation. (See chap. 5, sec. 2, and chap. 12, sec. 3, for elaborations.)Empirical significance: a magnitude claim is empirically significant if the relevant quantum state the agent should assign to the system has properly experienced decoherence due to interactions with the environment, where decoherence is a mathematical property of the quantum state. (See chap. 5, sec. 2, and appendix C for more discussions on decoherence.)Advice on credences: agents should adopt credences about empirically significant magnitude claims according to the Born rule (setting one's credence about an empirically significant magnitude claim to be the squared modulo of the appropriate wave function).Descriptions of nature: none of the above, except for the magnitude claims, describes anything in nature. However, magnitude claims are not contained or entailed by quantum theory. They are given prior to the theory.Let us walk through a simple example. Suppose our physicist Alice sets up an experiment for the position measurement of a particle s. Alice wants to explain some magnitude claim about the particle's position (say, that it is on the left side of the box). Quantum theory tells her that she ought to assign a particular wave function ψ to the particle. (The magnitude claim about the particle's position will only become empirically significant when the particle has appropriately interacted with the environment such that different parts of the wave function are almost separated into macroscopically distinct regions as described by decoherence.) Her expectation about the (empirically significant) magnitude claim should match the probability given by the Born rule, which is the squared modulo of the wave function at this moment.Many questions arise at this point. For example: What makes a particular quantum state assignment appropriate? It is standard to assume that a state assignment is appropriate or correct in virtue of representational accuracy, that is, the system indeed has the particular quantum state. But Healey disagrees; it is more or less a basic fact, and if we want to explain it we can appeal to the practice within the scientific community, not some metaphysical facts about what nature is like. It seems to me that on Healey's project the correctness of state assignments is a fundamental normative fact, and any further inquiry about it may be a metanormative project. This is certainly hard to swallow for many realists, but it sheds light on how Healey tries to solve (or dissolve) traditional problems in quantum foundation. In the following, we discuss how Healey applies his interpretation to the quantum measurement problem, quantum entanglement, and Bell nonlocality.The quantum measurement problem is often presented as an inconsistency among three propositions: (1) the quantum state is a complete description of nature; (2) the quantum state always changes according to some unitary equation (e.g., the Schrödinger equation); and (3) experiments have determinate (unique) outcomes. Applying this to the above experimental setup involving Alice, we can derive a contradiction. If the quantum state is complete and it changes unitarily, then quantum theory implies there is no determinate outcome of the position measurement of the particle, since it will always be in a superposition of ψleft and ψright, which is inconsistent with (3)—the particle is measured to be either on the left side or the right side of the box. For Healey, (1) and (2) are simply nonstarters, and (3) is obviously true so that the measurement problem is a nonproblem. (See chap. 6 and especially p. 99.) This is because, in Healey's view, quantum theory is prescriptive, and it is a mistake to think that the quantum state describes the world, much less describes it completely. Moreover, in typical measurement contexts, such as in Alice's case, the appropriate quantum state has decohered after measurement, giving Alice permission to apply the Born rule to make probabilistic predictions. There is a determinate outcome of measurement, but it is not entailed or contained in quantum theory. Instead, determinate outcomes are something confirmed by our direct experiences. Furthermore, if the outcome were not determinate, quantum theory would lose its empirical justification. So in order to apply quantum theory, we have to assume that experimental outcomes are unique and determinate (in typical cases). This, again, is difficult to accept as a realist conception of quantum mechanics. It stands in sharp contrast to other single-world theories such as Bohmian mechanics and spontaneous collapse theories that aim to justify (3) from a physical point of view. They seek to derive (3) as a theorem, by applying the precise mathematical equations to the microscopic ontology.For Healey, quantum entanglement is no longer metaphysically revolutionary. State assignments may be entangled and nonseparable in the sense that the complete state of the system does not supervene on the states of its parts. However, it seems that Healey would say that the failure of supervenience has no metaphysical significance but only normative significance. The advice about which state to assign to the whole system does not supervene, in general, on any advice on what to assign to the parts.Healey thinks that Bell nonlocality becomes more digestible on the prescriptive view (chap. 4). Healey does not dispute Bell's proof as a demonstration of the existence of nonlocal correlations, that is, probabilities of events happening in region A may depend on events happening in region B, which can be arbitrarily far away from A. But Healey does not think nonlocal correlations imply nonlocal influences or causation. What Bell's theorem (and the subsequent empirical tests) really shows is that the quantum probability of an event localized in some region must be “relativized to arbitrarily distant places and times” (71). Here it would seem that Healey's suggestion runs contrary to the kind of normal inferences we routinely make in science. It is standard to infer there are some goings-on in the world that account for the nonlocal correlations—some kind of underlying physical mechanism of nonlocal influence. For example, the mechanism is accounted for, in explicit physical details, by the guidance equation in Bohmian mechanics and the collapse mechanism in spontaneous collapse theories. But that is a mistake from Healey's perspective. Quantum theory postulates such nonlocal correlations as reliable prescriptions for agents who want to use quantum theory successfully, and it is a mistake to try to describe in virtue of what such correlations obtain.What are the reasons for accepting Healey's new interpretation of quantum theory? I think the main reason, for Healey, is that it allows us to avoid the surprising metaphysical consequences such as nonlocality and the reality of the quantum state. But at what cost? If Healey is right, then quantum theory is no longer in the business of describing nature. For most people, I think, that would be too costly.What about alternatives to Healey's theory? How do they compare to it? Healey gives reasons for thinking that they are inadequate (chap. 7). He thinks that spontaneous collapse theories are too speculative, and that they do not qualify as “interpretations.” He suggests that many-worlds theories still face the conceptual problems of probability and emergence of macroscopic branches. He notes that Bohmian mechanics faces problems in relativistic contexts. (Interestingly, Healey's objection to Bohmian mechanics is that it would postulate theoretical structure [e.g., preferred foliation of space-time, particle motion, and the universal wave function] that is empirically inaccessible, even though Healey himself postulates fundamental normative facts to be the foundation of quantum theory when normative facts have controversial epistemological and metaphysical standing in metaethics.) Healey does not discuss whether these are more costly than abandoning the descriptive role of quantum theory, but I think he would think they are. It is important to note that all of them are not only candidate descriptions of nature but are also in principle applicable to the universe as a whole, while Healey's interpretation is neither descriptive of nature nor applicable to the universe as a whole, since on his theory, the application of the Born rule is appropriate only when there is environmental decoherence (and the universe as a whole by definition has no external environment to interact with) (227).4As is the case with Healey's previous books, this one contains many interesting and controversial ideas that will generate much debate in the years to come. Above all, Healey should be applauded for writing a clear, accessible, and engaging introduction to the prescriptive interpretation of quantum theory. There are many issues that Healey discusses at length in the book that I do not have space to comment on. Even though we may not agree on the truth of the matter, we can certainly agree that Healey's book will be useful to anyone interested in the intersection of physics and philosophy.

arXiv:2110.12102•The Philosophical Review•Apr 1, 2020•0 citations
This conclusion presents some closing thoughts on the key concepts discussed in the preceding chapters of this book. The book presents with two different accounts of quantity: the class nominalist ‘neo-Ellisonian’ account and the ‘quasi-realist’ BP. It shows what was involved in making such a move and the class nominalist position was contrasted with realism. The book discusses the various positions and proposals have been restricted by qualifiers like “in the classical domain”. The application of mathematics crucially depends on this - hence the emphasis throughout the book on measurement and what this presupposes. The whole idea of ‘new directions’ in the theory of explanation is to allow for different styles and dimensions of explanations. What is then necessary for the instance view to apply to explanation in quantum mechanics is to incorporate the quantum state into the laws that also feature quantities.
Scope of this book Quantum mechanics is a difficult subject, and this book is intended to help the reader overcome the main difficulties in the way to understanding it. The first part of the book, Chs. 2–16, contains a systematic presentation of the basic principles of quantum theory, along with a number of examples which illustrate how these principles apply to particular quantum systems. The applications are, for the most part, limited to toy models whose simple structure allows one to see what is going on without using complicated mathematics or lengthy formulas. The principles themselves, however, are formulated in such a way that they can be applied to (almost) any nonrelativistic quantum system. In the second part of the book, Chs. 17–25, these principles are applied to quantum measurements and various quantum paradoxes, subjects which give rise to serious conceptual problems when they are not treated in a fully consistent manner. The final chapters are of a somewhat different character. Chapter 26 on decoherence and the classical limit of quantum theory is a very sketchy introduction to these important topics along with some indication as to how the basic principles presented in the first part of the book can be used for understanding them. Chapter 27 on quantum theory and reality belongs to the interface between physics and philosophy and indicates why quantum theory is compatible with a real world whose existence is not dependent on what scientists think and believe, or the experiments they choose to carry out. The Bibliography contains references for those interested in further reading or in tracing the origin of some of the ideas presented in earlier chapters.
My aim in this dissertation is to defend a realist interpretation of quantum mechanics.Firstly, I present considerations based on certain general features of theories in the natural sciences which indicate that realism affords a better account of those theories than instrumentalism.In particular, I consider certain issues surrounding the cognitive status of theories, including the role of models, the status of scientific explanation, and the referential character of theoretical terms.Secondly, I develop a detailed realist theory of measurement based on the notion of quantity terms as designators of objective properties of, and relations among, existing entities.I contrast this with the leading instrumentalist theories of measurement, and I argue that the realist theory is the better account of both the logic and practice of scientific measurement.Finally, I consider a number of objections to realism that arise because of certain theoretical features peculiar to quantum mechanics.In the course of this discussion, I consider crucial experimental evidence for the "dual" nature of microentities, various criteria of reality proposed by philosophers of science, the peculiar features of quantum mechanical measurement, and the status of causality in quantum mechanics.I argue that while certain realist viii ix interpretations of the quantum theory, namely the wave and wavicle interpretations, are unsatisfactory, an interpreta tion which construes micro-entities as existing particles is a tenable account.CHAPTER I ignored the considerations which arise at those more general levels of inquiry, but one can not adequately assess the status of quantum mechanics with respect to both realism and instrumentalism apart from those considerations.In the second two chapters of the dissertation, I shall argue that realist interpretations of quantitative theories in the natural sciences are preferable to instrumentalist interpretations.Then in the remainder of the dissertation, I shall go on to argue that realism is tenable at the quantum mechanical level despite the features peculiar to that theory.CHAPTER II THE COGNITIVE STATUS OF THEORIES transitions from one set of experiential statements to another.This view is in marked contrast to that of the realist who regards such terms as referential.This divergence in opinion between realists and instrumentalists about the referential character of theoretical terms leads to a related dispute over the role of models in the inter pretation of scientific theories.Before contrasting the various philosophical positions on this issue, it will be necessary to sort out different senses of the term "model."Upon inspecting the literature surrounding this dispute, it seems that much of the controversy about the role of models stems from a failure to make such distinctions.I will begin this task by distinguishing between 13 model-structures and model-objects.A model-structure is a definitely specifiable schema of mathematical-logical relationships which is exhibited by and can be abstracted from a set of objects.Any set of objects which exhibits a model-structure constitutes a set of model-objects.With respect to any particular scientific theory, there may be a variety of model-objects that scientists employ for various purposes.For example, in the kinetic theory of gases, one can distinguish the following.Firstly, there is the set of molecules themselves, the theoretical entities which we shall 13.For further detail in this regard, see Henry C. Byerly, "Model-Structures and Model-Objects," British Journal for the Philosophy of Science.Vol. 20, 1969, pp.135-144.i In fact, if one were to make that claim, I do not see how it could be supported without again falling prey to Maxwell's criticism cited above.And if one is simply troubled by the "ontological risk" involved in asserting the existence of theoretical entities because of the tentativeness of the corresponding theories, it should be noted that the risk of being wrong is a small price to pay for the potentially deeper understanding of nature that scientific theories afford us in the light of realist commitments.
The background for this book was a shift of interest among experimental physicists that began approximately 20 years ago. The shift was from quantum measurements on large ensembles of microscopic quantum objects, to experiments of very high precision on single, macroscopic objects. This shift was accompanied by developments in the “culture” of such measurements and the invention and elaboration of new experimental methods. In parallel with these experimental developments, there was a noticeable increase of theoretical interest in the foundations and interpretation of quantum theory, and even in attempts to revise its foundational principles. Although these efforts have not produced any significant changes in the fundamental structure of quantum theory, they have revealed a rather large number of “blank spots” and unsolved problems, to which the founders of quantum physics had paid no attention. A reasonable number of the blank spots have been filled in during the past decade. The reader has probably noticed that this book can be divided into two parts. In the first (chapters I―VII and XI), the authors have tried to present the modern approach to the quantum theory of measurement. This part can be regarded as a tutorial appendix to textbooks for advanced undergraduate or graduate-level courses in quantum mechanics, where little attention is usually paid to measurement theory.
The basic thesis of this book is that there is no quantum measurement problem. I do not mean by this that the apparent paradoxes of quantum mechanics arise because we fail to recognize ‘that quantum theory does not describe physical reality’ (Fuchs and Peres 2000a). Quantum theory describes reality just fine, like any other scientific theory worth taking seriously: describing (and explaining) reality is what the scientific enterprise is about. Nor do I mean that we have found solutions to the problem, ways to modify or supplement quantum mechanics so that the paradoxes are removed. I don’t actually think that we have found any very satisfactory solutions in this sense (at least not in the relativistic domain) but that isn’t my theme: even if we did have these modifications, they would be ways of changing from quantum physics, which supposedly does have a measurement problem, to some other theory, which supposedly doesn’t.
In this thought-provoking book, Richard Healey proposes a new interpretation of quantum theory inspired by pragmatist philosophy. Healey puts forward the interpretation as an alternative to realist quantum theories on the one hand such as Bohmian mechanics, spontaneous collapse theories, and many-worlds interpretations, which are different proposals for describing what the quantum world is like and what the basic laws of physics are, and nonrealist interpretations on the other hand such as quantum Bayesianism, which proposes to understand quantum theory as describing agents’ subjective epistemic states. The central idea of Healey's proposal is to understand quantum theory as providing not a description of the physical world but a set of authoritative and objectively correct prescriptions about how agents should act. The book provides a detailed development and defense of that idea, and it contains interesting discussions about a wide range of philosophical issues such as representation, probability, explanation, causation, objectivity, meaning, and fundamentality.Healey's project is at the intersection of physics and philosophy. The book is divided into two parts. Part 1 of the book discusses the foundational questions in quantum theory from the perspective of the prescriptive interpretation. In part 2, Healey discusses the philosophical implications of the view. Both parts are written in a way that is largely accessible to nonspecialists. In this brief book review, I will focus on two questions:1. How does Healey's interpretation work?2. What are the costs and benefits of accepting his interpretation?To understand Healey's ideas, we should provide some background for nonspecialists. Quantum theory has been subject to intense scrutiny and philosophical investigations in the last century. There has been enormous progress on several fronts, including the empirical tests about Bell inequalities and the development of several realist interpretations. It has been proposed that what is revolutionary about quantum theory and what sets it apart from classical physics are quantum entanglement and quantum nonlocality. For many realists, it seems that quantum theory describes a different kind of ontology and a different kind of laws of nature. They are introduced briefly below.Quantum entanglement describes the phenomenon that some physical systems have irreducibly holistic properties that are not the logical sums of the properties of the parts. For example, two electrons A and B are entangled when the pair has a quantum state that cannot be reduced to some combination of the state of A and the state of B. Quantum entanglement, a manifestation of quantum nonseparability, is reflected in the way quantum states, which are typically represented by “wave functions,” get assigned to different systems.Quantum nonlocality (also called “spooky action at a distance”) describes the phenomenon that events that are arbitrarily far apart can influence one another and the strength of the influence does not depend on their distance. Quantum nonlocality is a strange feature, and its falsity was assumed in the 1935 argument by Einstein, Podolsky, and Rosen for the incompleteness of quantum theory. Remarkably, Bell (1964) proved that if the quantum predictions are accurate, then nature is nonlocal. Subsequent experimental tests since the 1980s have verified the quantum predictions to a high level of precision, reinforcing the conclusion that nature is nonlocal.1Among the realist theories of quantum mechanics, Bohmian mechanics and spontaneous collapse theories are nonlocal. Moreover, all three realist theories, including the many-worlds interpretation, affirm the reality of quantum entanglement. The reality of quantum entanglement follows from the reality of the quantum state. After all, the quantum state is so successful in application. If one wants to be a realist, it seems that the most natural way is to accept the reality of the quantum state and its consequences. But what is represented by the wave function? What is its nature? How does it relate to things in the physical world? Some recent discussions in philosophy of physics concern exactly those questions.2I think the key to understanding Healey's interpretation is to think of it as a proposal for an alternative foundation of quantum theory—a proposal to use normative facts instead of descriptive facts as the foundation and to replace “what there is” with “what we ought to expect” as what is fundamental to physical theory. Healey's approach would sound alien to many people, since it is not realist in any traditional sense. It is common to think that fundamental physics, and in particular quantum theory, is in the business of saying what the world is like (even though it may be difficult to discern what it says). It is true that we can learn useful advice from a correct physical theory, such as:one should avoid falling into a black holeone should place detectors far away from sources of interferenceone should get away from a nuclear explosionone should be almost certain to see this particle decay in 1 monthA correct physical theory may explain the correctness of useful practical advices such as above. Such advices are objectively correct insofar as they are derived from the conjunction of some accurate descriptions of physical reality and some correct theories of human rationality.3 For Healey, that might be a fine interpretation of classical physics, but that is not the correct interpretation of quantum theory. Quantum theory, for Healey, directly offers authoritative advice about what we should believe and expect, and such advice is not derived in any way from some underlying descriptive facts. Still, such advice can be objectively true (unlike the quantum Bayesian's emphasis on subjective epistemic states). The advice has the form “one should assign quantum state ψ to the physical system s,” and “one should have 0.5 confidence in M,” where M is some kind of magnitude claim about the physical system s. On Healey's interpretation, quantum theory is about such advice, not some descriptions about what nature is like. Although the magnitude claims are descriptions of nature, they are not contained in quantum theory. Instead, they are assumed to be the targets of explanation, and they are somewhat prior to the application of quantum theory. However, they will be suitably constrained by quantum theory, and only a subclass of them will be empirically significant.There are many parts to Healey's proposal. To simplify our discussions below, here is a short summary of the key points (mostly from chapter 5):Advice on state assignments: agents should follow the standard practice in quantum physics and assign an appropriate quantum state (e.g., a wave function ψ) to a system relative to their physical situation.Magnitude claims: a canonical magnitude claim has the form “the value of dynamical variable M on physical system s lies in set Δ.” One example would be “the position of the particle is on the left side of the box.” Magnitude claims are assumed in the theory and they are the targets of explanation. (See chap. 5, sec. 2, and chap. 12, sec. 3, for elaborations.)Empirical significance: a magnitude claim is empirically significant if the relevant quantum state the agent should assign to the system has properly experienced decoherence due to interactions with the environment, where decoherence is a mathematical property of the quantum state. (See chap. 5, sec. 2, and appendix C for more discussions on decoherence.)Advice on credences: agents should adopt credences about empirically significant magnitude claims according to the Born rule (setting one's credence about an empirically significant magnitude claim to be the squared modulo of the appropriate wave function).Descriptions of nature: none of the above, except for the magnitude claims, describes anything in nature. However, magnitude claims are not contained or entailed by quantum theory. They are given prior to the theory.Let us walk through a simple example. Suppose our physicist Alice sets up an experiment for the position measurement of a particle s. Alice wants to explain some magnitude claim about the particle's position (say, that it is on the left side of the box). Quantum theory tells her that she ought to assign a particular wave function ψ to the particle. (The magnitude claim about the particle's position will only become empirically significant when the particle has appropriately interacted with the environment such that different parts of the wave function are almost separated into macroscopically distinct regions as described by decoherence.) Her expectation about the (empirically significant) magnitude claim should match the probability given by the Born rule, which is the squared modulo of the wave function at this moment.Many questions arise at this point. For example: What makes a particular quantum state assignment appropriate? It is standard to assume that a state assignment is appropriate or correct in virtue of representational accuracy, that is, the system indeed has the particular quantum state. But Healey disagrees; it is more or less a basic fact, and if we want to explain it we can appeal to the practice within the scientific community, not some metaphysical facts about what nature is like. It seems to me that on Healey's project the correctness of state assignments is a fundamental normative fact, and any further inquiry about it may be a metanormative project. This is certainly hard to swallow for many realists, but it sheds light on how Healey tries to solve (or dissolve) traditional problems in quantum foundation. In the following, we discuss how Healey applies his interpretation to the quantum measurement problem, quantum entanglement, and Bell nonlocality.The quantum measurement problem is often presented as an inconsistency among three propositions: (1) the quantum state is a complete description of nature; (2) the quantum state always changes according to some unitary equation (e.g., the Schrödinger equation); and (3) experiments have determinate (unique) outcomes. Applying this to the above experimental setup involving Alice, we can derive a contradiction. If the quantum state is complete and it changes unitarily, then quantum theory implies there is no determinate outcome of the position measurement of the particle, since it will always be in a superposition of ψleft and ψright, which is inconsistent with (3)—the particle is measured to be either on the left side or the right side of the box. For Healey, (1) and (2) are simply nonstarters, and (3) is obviously true so that the measurement problem is a nonproblem. (See chap. 6 and especially p. 99.) This is because, in Healey's view, quantum theory is prescriptive, and it is a mistake to think that the quantum state describes the world, much less describes it completely. Moreover, in typical measurement contexts, such as in Alice's case, the appropriate quantum state has decohered after measurement, giving Alice permission to apply the Born rule to make probabilistic predictions. There is a determinate outcome of measurement, but it is not entailed or contained in quantum theory. Instead, determinate outcomes are something confirmed by our direct experiences. Furthermore, if the outcome were not determinate, quantum theory would lose its empirical justification. So in order to apply quantum theory, we have to assume that experimental outcomes are unique and determinate (in typical cases). This, again, is difficult to accept as a realist conception of quantum mechanics. It stands in sharp contrast to other single-world theories such as Bohmian mechanics and spontaneous collapse theories that aim to justify (3) from a physical point of view. They seek to derive (3) as a theorem, by applying the precise mathematical equations to the microscopic ontology.For Healey, quantum entanglement is no longer metaphysically revolutionary. State assignments may be entangled and nonseparable in the sense that the complete state of the system does not supervene on the states of its parts. However, it seems that Healey would say that the failure of supervenience has no metaphysical significance but only normative significance. The advice about which state to assign to the whole system does not supervene, in general, on any advice on what to assign to the parts.Healey thinks that Bell nonlocality becomes more digestible on the prescriptive view (chap. 4). Healey does not dispute Bell's proof as a demonstration of the existence of nonlocal correlations, that is, probabilities of events happening in region A may depend on events happening in region B, which can be arbitrarily far away from A. But Healey does not think nonlocal correlations imply nonlocal influences or causation. What Bell's theorem (and the subsequent empirical tests) really shows is that the quantum probability of an event localized in some region must be “relativized to arbitrarily distant places and times” (71). Here it would seem that Healey's suggestion runs contrary to the kind of normal inferences we routinely make in science. It is standard to infer there are some goings-on in the world that account for the nonlocal correlations—some kind of underlying physical mechanism of nonlocal influence. For example, the mechanism is accounted for, in explicit physical details, by the guidance equation in Bohmian mechanics and the collapse mechanism in spontaneous collapse theories. But that is a mistake from Healey's perspective. Quantum theory postulates such nonlocal correlations as reliable prescriptions for agents who want to use quantum theory successfully, and it is a mistake to try to describe in virtue of what such correlations obtain.What are the reasons for accepting Healey's new interpretation of quantum theory? I think the main reason, for Healey, is that it allows us to avoid the surprising metaphysical consequences such as nonlocality and the reality of the quantum state. But at what cost? If Healey is right, then quantum theory is no longer in the business of describing nature. For most people, I think, that would be too costly.What about alternatives to Healey's theory? How do they compare to it? Healey gives reasons for thinking that they are inadequate (chap. 7). He thinks that spontaneous collapse theories are too speculative, and that they do not qualify as “interpretations.” He suggests that many-worlds theories still face the conceptual problems of probability and emergence of macroscopic branches. He notes that Bohmian mechanics faces problems in relativistic contexts. (Interestingly, Healey's objection to Bohmian mechanics is that it would postulate theoretical structure [e.g., preferred foliation of space-time, particle motion, and the universal wave function] that is empirically inaccessible, even though Healey himself postulates fundamental normative facts to be the foundation of quantum theory when normative facts have controversial epistemological and metaphysical standing in metaethics.) Healey does not discuss whether these are more costly than abandoning the descriptive role of quantum theory, but I think he would think they are. It is important to note that all of them are not only candidate descriptions of nature but are also in principle applicable to the universe as a whole, while Healey's interpretation is neither descriptive of nature nor applicable to the universe as a whole, since on his theory, the application of the Born rule is appropriate only when there is environmental decoherence (and the universe as a whole by definition has no external environment to interact with) (227).4As is the case with Healey's previous books, this one contains many interesting and controversial ideas that will generate much debate in the years to come. Above all, Healey should be applauded for writing a clear, accessible, and engaging introduction to the prescriptive interpretation of quantum theory. There are many issues that Healey discusses at length in the book that I do not have space to comment on. Even though we may not agree on the truth of the matter, we can certainly agree that Healey's book will be useful to anyone interested in the intersection of physics and philosophy.