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The measurement problem, quantisation and collapse

Lars‐Göran Johansson

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

The present paper contains a new attack on the measurement problem. The point of departure is a realist view according to which i) state functions in quantum theory describe physical states of affairs and not information states attributed to observers, and ii) in theses states, some observables are indeterminate and not merely unknown, i.e., value determinism is rejected. Furthermore, quantisation of interaction is accepted as an empirically established fact, independently of any interpretations of quantum theory. From these assumptions it follows that Hermitian operators replacing classical variables may be viewed as representing actions from the environment done on physical systems represented by the state functions upon which the operators operate. Sometimes this influence is followed by a discontinuous, indeterministic and irreversible state change; in other words, the system undergoes a collapse, which is represented by a projection operator. Thus, assuming a realistic view on quantum states and their changes, we have an explanation for the collapse of the wave function. Since the collapse is a discontinuous, random and irreversible state change, the classical form of physical explanation in terms of a mechanism which describes how a system continuously changes its state is impossible. Hence, if we accept quantisation of interaction, we must give up our demand for a ordinary mechanical explanation for the collapse. Neither can we state, in advance, sufficient conditions for the collapse, since it is an indeterministic theory.

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Interpreting Quantum Mechanics

Lars‐Göran Johansson

Presenting a realistic interpretation of quantum mechanics and, in particular, a realistic view of quantum waves, this book defends, with one exception, Schrodinger's views on quantum mechanics. Johansson goes on to defend the view that the collapse of a wave function during a measurement is a real physical collapse of a wave and argues that the collapse is a consequence of quantisation of interaction. Lastly Johansson argues for a revised principle of individuation in the quantum domain and that this principle enables a sort of explanation of non-local phenomena.

Routledge eBooks•Dec 5, 2016•9 citations

Why Quantum Collapse May Not Be Fundamental

Atsushi Okamoto

Wave function collapse has long been regarded as a fundamental element of the quantum measurement process, providing a mechanism by which a superposed quantum state yields a single observed outcome. Despite its widespread use, the physical meaning of collapse remains conceptually controversial. In particular, it is often assumed that the quantities associated with a quantum state before measurement and the values obtained after measurement belong to the same conceptual category. This assumption leads naturally to the image of a discontinuous transition in which one value is selected from a superposition of possibilities. In the present work, we reexamine the concept of quantum collapse from the perspective of observability. We argue that pre-measurement quantities do not constitute observable values in the ordinary operational sense. Rather, they represent a structure of potential observability associated with possible measurement outcomes. By contrast, post-measurement outcomes correspond to operationally realized observability, in which a specific result becomes accessible through measurement. From this viewpoint, the apparent collapse does not represent a physical jump of an already existing value, but a transition from potential observability to operationally realized observability. Based on this distinction, we propose that many conceptual difficulties traditionally associated with wave function collapse arise from treating these two fundamentally different forms of observability as if they were physically equivalent. The apparent discontinuity of collapse may therefore originate not from a discontinuous change in reality itself, but from a conceptual conflation of potential observability and operationally realized observability. Within the Intrinsic Observability Framework (IOF), this interpretation naturally leads to the concept of accessibility transition, in which the emergence of a definite outcome is understood as a change in accessible structure rather than as a fundamental non-unitary state reduction. The present analysis suggests that wave function collapse may not be a fundamental physical phenomenon, but instead a consequence of the transition from potential observability to operationally realized observability. This perspective provides a conceptual reorganization of the measurement problem and clarifies the role of observability in the emergence of definite quantum outcomes.

•Jul 11, 2026•0 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

The Nonexisting ‘Measurement Problem’

F. J. Duarte

The indeterminacy and stochasticity of quantum mechanics have nurtured an illustrious gathering of critics including Einstein, Schrödinger, Bell, and Penrose. This has been good for quantum mechanics since it has become the most ruggedized and most battle hardened branch of physics. The one criticism that is often alluded to, now days, is ‘the measurement problem.’ First of all, from a pragmatic perspective it can be categorically stated that there is no measurement problem. Quantum mechanics exquisitely agrees with experimental measurements. Secondly, the so called ‘measurement problem’ is often related, by supporters of this concept, to the alleged ‘collapse of the wave function’ which is an unobserved phenomenon. In this chapter, several aspects of this experimentally nonexisting problem are discussed in order to inform the reader on the measurement reality of quantum mechanics.

CRC Press eBooks•Apr 10, 2026•0 citations

Collapse Theories

Peter J. Lewis

The collapse postulate in quantum mechanics is problematic due to the measurement problem. The problem lies not with collapse per se, but with the appeal to measurement; a theory that could underwrite the collapse process without ineliminable reference to measurement would constitute a solution to the measurement problem. This is the strategy pursued by dynamical (or spontaneous) collapse theories. But dynamical collapse theories face a number of challenges. First, they make different empirical predictions from standard quantum mechanics, and hence are potentially empirically refutable. Second, there are difficulties reconciling the dynamical collapse mechanism with special relativity. Third, the post-collapse state is not the same as the post-measurement state of standard quantum mechanics, raising the possibility that dynamical collapse theories do not solve the measurement problem after all. Assuming that these challenges can be met, dynamical collapse theories can lay claim to being serious contenders for the correct description of the quantum world. And the description they provide has a number of interesting consequences. First, it makes indeterminism an irreducible fact about the physical world. It has been argued that this has important consequences for the foundations of statistical mechanics, for free will, and for consciousness. Second, many dynamical collapse theories can be taken to imply that the quantum wave function is fundamental, giving rise to a new kind of vagueness, since a wave can be fuzzy around the edges in a way that a particle cannot. Furthermore, the quantum wave function is defined over a high-dimensional space, not the three-dimensional space of experience, suggesting to some that three-dimensionality is an illusion.

•Nov 6, 2017•0 citations

Statistical contextual explanation of quantum paradoxes

Marian Kupczyński

This year we celebrate 100 years of quantum mechanics (QM). Incorrect interpretations of QM and incorrect mental models of the invisible details of quantum phenomena lead to paradoxes. To explain these, we advocate the statistical contextual interpretation (SCI) of quantum mechanics. State vectors (wave functions) and various operators are purely mathematical entities that permit quantitative probabilistic predictions. “State vector” describes an ensemble of identically prepared physical systems, and a specific “operator” represents a class of equivalent measurements of a physical observable. A collapse of wavefunction is not a mysterious and instantaneous physical process; a collapsed quantum state describes a new ensemble of physical systems prepared in a particular way. A value of a physical observable, such as a spin projection, associated with a pure quantum ensemble is a characteristic of this ensemble created by its interaction with measuring instruments. Probabilities are objective properties of random experiments in which empirical frequencies stabilize. Following Einstein, SCI rejects the claim that QM provides a complete description of individual physical systems, but it remains agnostic about whether a more detailed subquantum description can be found or is necessary. In conformity with Bohr contextuality, SCI rejects Bell-local and Bell-causal hidden variable models. Nevertheless, by incorporating into a probabilistic model contextual hidden variable measuring instruments, long distance quantum correlations studied in Bell tests can be explained without evoking quantum nonlocality or retro-causality. SCI allows the explanation of several quantum phenomena without evoking quantum magic. SCI does not claim to provide a complete description of quantum phenomena; in fact, it is unknown whether quantum probabilities even provide a complete description of existing experimental data. Time series of experimental data may contain much more information than is obtained using empirical frequencies and histograms. Therefore, predictable completeness of QM must be tested and not taken for granted.

arXiv:2502.16048•Frontiers in Quantum Science and Technology•May 1, 2025•1 citation
The present paper contains a new attack on the measurement problem. The point of departure is a realist view according to which i) state functions in quantum theory describe physical states of affairs and not information states attributed to observers, and ii) in theses states, some observables are indeterminate and not merely unknown, i.e., value determinism is rejected. Furthermore, quantisation of interaction is accepted as an empirically established fact, independently of any interpretations of quantum theory. From these assumptions it follows that Hermitian operators replacing classical variables may be viewed as representing actions from the environment done on physical systems represented by the state functions upon which the operators operate. Sometimes this influence is followed by a discontinuous, indeterministic and irreversible state change; in other words, the system undergoes a collapse, which is represented by a projection operator. Thus, assuming a realistic view on quantum states and their changes, we have an explanation for the collapse of the wave function. Since the collapse is a discontinuous, random and irreversible state change, the classical form of physical explanation in terms of a mechanism which describes how a system continuously changes its state is impossible. Hence, if we accept quantisation of interaction, we must give up our demand for a ordinary mechanical explanation for the collapse. Neither can we state, in advance, sufficient conditions for the collapse, since it is an indeterministic theory.
Presenting a realistic interpretation of quantum mechanics and, in particular, a realistic view of quantum waves, this book defends, with one exception, Schrodinger's views on quantum mechanics. Johansson goes on to defend the view that the collapse of a wave function during a measurement is a real physical collapse of a wave and argues that the collapse is a consequence of quantisation of interaction. Lastly Johansson argues for a revised principle of individuation in the quantum domain and that this principle enables a sort of explanation of non-local phenomena.
Wave function collapse has long been regarded as a fundamental element of the quantum measurement process, providing a mechanism by which a superposed quantum state yields a single observed outcome. Despite its widespread use, the physical meaning of collapse remains conceptually controversial. In particular, it is often assumed that the quantities associated with a quantum state before measurement and the values obtained after measurement belong to the same conceptual category. This assumption leads naturally to the image of a discontinuous transition in which one value is selected from a superposition of possibilities. In the present work, we reexamine the concept of quantum collapse from the perspective of observability. We argue that pre-measurement quantities do not constitute observable values in the ordinary operational sense. Rather, they represent a structure of potential observability associated with possible measurement outcomes. By contrast, post-measurement outcomes correspond to operationally realized observability, in which a specific result becomes accessible through measurement. From this viewpoint, the apparent collapse does not represent a physical jump of an already existing value, but a transition from potential observability to operationally realized observability. Based on this distinction, we propose that many conceptual difficulties traditionally associated with wave function collapse arise from treating these two fundamentally different forms of observability as if they were physically equivalent. The apparent discontinuity of collapse may therefore originate not from a discontinuous change in reality itself, but from a conceptual conflation of potential observability and operationally realized observability. Within the Intrinsic Observability Framework (IOF), this interpretation naturally leads to the concept of accessibility transition, in which the emergence of a definite outcome is understood as a change in accessible structure rather than as a fundamental non-unitary state reduction. The present analysis suggests that wave function collapse may not be a fundamental physical phenomenon, but instead a consequence of the transition from potential observability to operationally realized observability. This perspective provides a conceptual reorganization of the measurement problem and clarifies the role of observability in the emergence of definite quantum outcomes.
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.
The indeterminacy and stochasticity of quantum mechanics have nurtured an illustrious gathering of critics including Einstein, Schrödinger, Bell, and Penrose. This has been good for quantum mechanics since it has become the most ruggedized and most battle hardened branch of physics. The one criticism that is often alluded to, now days, is ‘the measurement problem.’ First of all, from a pragmatic perspective it can be categorically stated that there is no measurement problem. Quantum mechanics exquisitely agrees with experimental measurements. Secondly, the so called ‘measurement problem’ is often related, by supporters of this concept, to the alleged ‘collapse of the wave function’ which is an unobserved phenomenon. In this chapter, several aspects of this experimentally nonexisting problem are discussed in order to inform the reader on the measurement reality of quantum mechanics.
The collapse postulate in quantum mechanics is problematic due to the measurement problem. The problem lies not with collapse per se, but with the appeal to measurement; a theory that could underwrite the collapse process without ineliminable reference to measurement would constitute a solution to the measurement problem. This is the strategy pursued by dynamical (or spontaneous) collapse theories. But dynamical collapse theories face a number of challenges. First, they make different empirical predictions from standard quantum mechanics, and hence are potentially empirically refutable. Second, there are difficulties reconciling the dynamical collapse mechanism with special relativity. Third, the post-collapse state is not the same as the post-measurement state of standard quantum mechanics, raising the possibility that dynamical collapse theories do not solve the measurement problem after all. Assuming that these challenges can be met, dynamical collapse theories can lay claim to being serious contenders for the correct description of the quantum world. And the description they provide has a number of interesting consequences. First, it makes indeterminism an irreducible fact about the physical world. It has been argued that this has important consequences for the foundations of statistical mechanics, for free will, and for consciousness. Second, many dynamical collapse theories can be taken to imply that the quantum wave function is fundamental, giving rise to a new kind of vagueness, since a wave can be fuzzy around the edges in a way that a particle cannot. Furthermore, the quantum wave function is defined over a high-dimensional space, not the three-dimensional space of experience, suggesting to some that three-dimensionality is an illusion.
This year we celebrate 100 years of quantum mechanics (QM). Incorrect interpretations of QM and incorrect mental models of the invisible details of quantum phenomena lead to paradoxes. To explain these, we advocate the statistical contextual interpretation (SCI) of quantum mechanics. State vectors (wave functions) and various operators are purely mathematical entities that permit quantitative probabilistic predictions. “State vector” describes an ensemble of identically prepared physical systems, and a specific “operator” represents a class of equivalent measurements of a physical observable. A collapse of wavefunction is not a mysterious and instantaneous physical process; a collapsed quantum state describes a new ensemble of physical systems prepared in a particular way. A value of a physical observable, such as a spin projection, associated with a pure quantum ensemble is a characteristic of this ensemble created by its interaction with measuring instruments. Probabilities are objective properties of random experiments in which empirical frequencies stabilize. Following Einstein, SCI rejects the claim that QM provides a complete description of individual physical systems, but it remains agnostic about whether a more detailed subquantum description can be found or is necessary. In conformity with Bohr contextuality, SCI rejects Bell-local and Bell-causal hidden variable models. Nevertheless, by incorporating into a probabilistic model contextual hidden variable measuring instruments, long distance quantum correlations studied in Bell tests can be explained without evoking quantum nonlocality or retro-causality. SCI allows the explanation of several quantum phenomena without evoking quantum magic. SCI does not claim to provide a complete description of quantum phenomena; in fact, it is unknown whether quantum probabilities even provide a complete description of existing experimental data. Time series of experimental data may contain much more information than is obtained using empirical frequencies and histograms. Therefore, predictable completeness of QM must be tested and not taken for granted.