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Oxford University Press eBooks

Measurement

Richard Healey

Published Jul 20, 2017• 0 citations
Publisher

Abstract

If a quantum state completely specified the properties of a system to which it was assigned then application of quantum theory to an interaction intended to correlate properties of a measured system to those of a measuring device would leave that device recording no determinate outcome, contrary to what we observe. This is the quantum measurement problem. But the problem does not arise if the function of a quantum state assignment is not descriptive but prescriptive, so that all quantum state assignments are relational. Models of decoherence can certify the empirical significance of rival claims about which measurement outcome a device records, but their application does not explain but presupposes that exactly one such claim is true. The reality criterion which Einstein and colleagues applied to show the incompleteness of quantum description of reality is inapplicable to their chosen system while a slightly modified criterion is false.

DOI
10.1093/oso/9780198714057.003.0006

Related papers

Assigning Values and States

Richard Healey

If a quantum state is prescriptive then what state should an agent assign, what expectations does this justify, and what are the grounds for those expectations? I address these questions and introduce a third important idea—decoherence. A subsystem of a system assigned an entangled state may be assigned a mixed state represented by a density operator. Quantum state assignment is an objective matter, but the correct assignment must be relativized to the physical situation of an actual or hypothetical agent for whom its prescription offers good advice, since differently situated agents have access to different information. However this situation is described, it is true, empirically significant magnitude claims that make the description correct, while others provide the objective grounds for the agent’s expectations. Quantum models of environmental decoherence certify the empirical significance of these magnitude claims while also licensing application of the Born rule to others without mentioning measurement.

Oxford University Press eBooks•Jul 20, 2017•0 citations

Persistence of Information in the Quantum Measurement Problem.

Shantena Augusto Sabbadini

The quantum measurement problem has to do with the compatibility of two different prescriptions for the end state of a quantum measurement process: (1) a superposition representing an entangled state of object system and apparatus; (2) a mixture of correlated states of object system and apparatus. The first prescription is a consequence of the linearity of time evolution in quantum mechanics; the second one (corresponding to what is usually called the 'collapse of the wave function') is a basic feature of the axiomatic structure of the theory. This paper proves that the two prescriptions are exactly equivalent whenever information about the results of the measurement persists, i.e. whenever there is some kind of record or trace of the results (all the measurements we are ordinarily concerned with fulfill this requirement). Experimental evidence is cited suggesting that indeed we should expect the equivalence of prescriptions (1) and (2) to hold when and only when information about measurement results persists. Finally the notion of 'element of reality' introduced by Einstein, Podolsky and Rosen is discussed in the context of this description of the measurement process, and a brief remark is offered about the 'classical' nature of the world we experience.

Physics Essays•Mar 1, 2006•2 citations

Effective theory approach to the measurement problem

William Icefield

One understanding of the Niels Bohr's interpretation of quantum mechanics suggests that the measurement problem arises because an observer description of reality is incomplete due to lack of complete access to an entire system of observed and observer. In general, an additional and external measuring observer is required to access the entire system. Inevitable entanglement between observers, measurement apparatus and measured objects is key to such an understanding of the measurement problem. Quantum mechanics only provides a complete `incomplete' description of reality. Nevertheless, some issues, especially providing an account of why a preferred measurement basis arises, remain. Replacing relations between observed and observer in relational quantum mechanics with those between effective (approximate) theories, one arrives at a more clear understanding of why the measurement problem arises and how a preferred measurement basis is determined. The measurement problem exists because of measurement apparatus limitations, which only allow us to formulate and verify effective theories that inevitably neglect some details of nature.

•May 13, 2020•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

Quantum Measurements

Nelson Enrique Bolivar, Gabriel Abellán

A transition would lead the system from its original superposition state to another state, in which the system and the measuring apparatus acquire definite properties. The problem of measurement is approached from the theory of environment-induced decoherence. This theoretical program, based on the study of the effects of the interaction between a quantum system, is considered as an open system and its environment. In turn, even the measurement problem has been reformulated, expanding its scope. As Schlosshauer points out, the conceptual difficulties of quantum measurement can now be concentrated around two cases: The definite outcome, which consists of the traditional question about quantum measurement. The problem of the preferred basis: since there is a theoretical ambiguity in the definition of the observable measured due to the mathematical possibility of a base change in the expression of the system state.

Apple Academic Press eBooks•May 23, 2018•0 citations

Quantum Measurement

Bob Coecke, Aleks Kissinger

A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it. – Max Planck, 1936 The only way quantum theory allows us to interact with quantum systems is via quantum processes. Thus, the only way we can extract information about the state of a quantum system is to apply some non-deterministic process and observe which of the branches happened. For that reason, many people refer to the act of applying certain quantum processes as measurement and sometimes even as observation . A consequence of this unfortunate terminology is that one of the most touted ‘strange’ features of quantum theory is often misleadingly described as follows: ‘The mere act of observing a quantum state changes it.’ ‘Misleading’, since the concept of measurement described in the previous paragraph is far from the passive concept of observation familiar from our macroscopic world, but is rather a non-trivial process that will almost always drastically affect the quantum state. So, the mysterious aspect of quantum theory is not that ‘observation’ alters the quantum state but, rather, that it is impossible, even in principle, to ‘observe’ a quantum system in the classical sense. Given this fundamental restriction on how we can extract information from a quantum system, what can we learn about that system by means of a quantum process? The answer is, in fact, very little! First, performing a particular measurement could, for the vast majority of quantum states, yield any outcome i with a non-zero probability. In that case, obtaining an outcome i doesn't tell us much about what the state of the system was. Second, we say ‘was’, because the measurement will moreover irreversibly change the state according to the outcome. So rather than revealing the state of a system, a quantum measurement typically erases that state from history! Nonetheless, these quantum measurements are crucial to quantum theory since they constitute the only interface between us, in our classical world, and the quantum world. The great insight of the quantum computing community is that the non-deterministic changes induced by these quantum measurements are not a nuisance, but rather an extremely useful resource.

Cambridge University Press eBooks•Mar 16, 2017•0 citations
If a quantum state completely specified the properties of a system to which it was assigned then application of quantum theory to an interaction intended to correlate properties of a measured system to those of a measuring device would leave that device recording no determinate outcome, contrary to what we observe. This is the quantum measurement problem. But the problem does not arise if the function of a quantum state assignment is not descriptive but prescriptive, so that all quantum state assignments are relational. Models of decoherence can certify the empirical significance of rival claims about which measurement outcome a device records, but their application does not explain but presupposes that exactly one such claim is true. The reality criterion which Einstein and colleagues applied to show the incompleteness of quantum description of reality is inapplicable to their chosen system while a slightly modified criterion is false.
If a quantum state is prescriptive then what state should an agent assign, what expectations does this justify, and what are the grounds for those expectations? I address these questions and introduce a third important idea—decoherence. A subsystem of a system assigned an entangled state may be assigned a mixed state represented by a density operator. Quantum state assignment is an objective matter, but the correct assignment must be relativized to the physical situation of an actual or hypothetical agent for whom its prescription offers good advice, since differently situated agents have access to different information. However this situation is described, it is true, empirically significant magnitude claims that make the description correct, while others provide the objective grounds for the agent’s expectations. Quantum models of environmental decoherence certify the empirical significance of these magnitude claims while also licensing application of the Born rule to others without mentioning measurement.
The quantum measurement problem has to do with the compatibility of two different prescriptions for the end state of a quantum measurement process: (1) a superposition representing an entangled state of object system and apparatus; (2) a mixture of correlated states of object system and apparatus. The first prescription is a consequence of the linearity of time evolution in quantum mechanics; the second one (corresponding to what is usually called the 'collapse of the wave function') is a basic feature of the axiomatic structure of the theory. This paper proves that the two prescriptions are exactly equivalent whenever information about the results of the measurement persists, i.e. whenever there is some kind of record or trace of the results (all the measurements we are ordinarily concerned with fulfill this requirement). Experimental evidence is cited suggesting that indeed we should expect the equivalence of prescriptions (1) and (2) to hold when and only when information about measurement results persists. Finally the notion of 'element of reality' introduced by Einstein, Podolsky and Rosen is discussed in the context of this description of the measurement process, and a brief remark is offered about the 'classical' nature of the world we experience.
One understanding of the Niels Bohr's interpretation of quantum mechanics suggests that the measurement problem arises because an observer description of reality is incomplete due to lack of complete access to an entire system of observed and observer. In general, an additional and external measuring observer is required to access the entire system. Inevitable entanglement between observers, measurement apparatus and measured objects is key to such an understanding of the measurement problem. Quantum mechanics only provides a complete `incomplete' description of reality. Nevertheless, some issues, especially providing an account of why a preferred measurement basis arises, remain. Replacing relations between observed and observer in relational quantum mechanics with those between effective (approximate) theories, one arrives at a more clear understanding of why the measurement problem arises and how a preferred measurement basis is determined. The measurement problem exists because of measurement apparatus limitations, which only allow us to formulate and verify effective theories that inevitably neglect some details of nature.
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.
A transition would lead the system from its original superposition state to another state, in which the system and the measuring apparatus acquire definite properties. The problem of measurement is approached from the theory of environment-induced decoherence. This theoretical program, based on the study of the effects of the interaction between a quantum system, is considered as an open system and its environment. In turn, even the measurement problem has been reformulated, expanding its scope. As Schlosshauer points out, the conceptual difficulties of quantum measurement can now be concentrated around two cases: The definite outcome, which consists of the traditional question about quantum measurement. The problem of the preferred basis: since there is a theoretical ambiguity in the definition of the observable measured due to the mathematical possibility of a base change in the expression of the system state.
A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it. – Max Planck, 1936 The only way quantum theory allows us to interact with quantum systems is via quantum processes. Thus, the only way we can extract information about the state of a quantum system is to apply some non-deterministic process and observe which of the branches happened. For that reason, many people refer to the act of applying certain quantum processes as measurement and sometimes even as observation . A consequence of this unfortunate terminology is that one of the most touted ‘strange’ features of quantum theory is often misleadingly described as follows: ‘The mere act of observing a quantum state changes it.’ ‘Misleading’, since the concept of measurement described in the previous paragraph is far from the passive concept of observation familiar from our macroscopic world, but is rather a non-trivial process that will almost always drastically affect the quantum state. So, the mysterious aspect of quantum theory is not that ‘observation’ alters the quantum state but, rather, that it is impossible, even in principle, to ‘observe’ a quantum system in the classical sense. Given this fundamental restriction on how we can extract information from a quantum system, what can we learn about that system by means of a quantum process? The answer is, in fact, very little! First, performing a particular measurement could, for the vast majority of quantum states, yield any outcome i with a non-zero probability. In that case, obtaining an outcome i doesn't tell us much about what the state of the system was. Second, we say ‘was’, because the measurement will moreover irreversibly change the state according to the outcome. So rather than revealing the state of a system, a quantum measurement typically erases that state from history! Nonetheless, these quantum measurements are crucial to quantum theory since they constitute the only interface between us, in our classical world, and the quantum world. The great insight of the quantum computing community is that the non-deterministic changes induced by these quantum measurements are not a nuisance, but rather an extremely useful resource.