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arXiv:2110.12102 · The Philosophical Review

The Quantum Revolution in Philosophy

Eddy Keming Chen

Published Apr 1, 2020• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1215/00318108-8012864

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The Quantum Revolution in Philosophy

Richard Healey

Quantum theory launched a revolution in twentieth-century physics. But we have yet to appreciate the revolution’s significance for philosophy. Most studies of the conceptual foundations of quantum theory first try to interpret the theory—to say how the world could possibly be the way the theory says it is. But, though fundamental, quantum theory is enormously successful without describing the world in its own terms. When properly applied, models of quantum theory offer good advice on the significance and credibility of claims about the world expressed in other terms. This first of several philosophical lessons of the quantum revolution dissolves the quantum measurement problem. Pragmatist treatments of probability and causation show how quantum theory may be used to explain the non-localized correlations that have been thought to involve ‘spooky’ instantaneous action at a distance. Given environmental decoherence, a pragmatist inferentialist approach to content shows when talk of quantum probabilities is licensed, resolves any residual worries about whether a quantum measurement has a determinate outcome, and solves a dilemma about the ontology of a quantum field theory. This approach to meaning and reference also reveals the nature and limits of objective description in the light of quantum theory. While these pragmatist approaches to probability, causation, explanation, and content may be independently motivated by philosophical argument, their successful application here illustrates their practical importance in helping philosophers come to terms with the quantum revolution.

Oxford University Press eBooks•Jul 20, 2017•147 citations

Interpreting Quantum Theories

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Most philosophical work on quantum physics has concerned simple systems. And for good reason. Even one or two particle systems can exhibit the striking features we have come to associate with quantum physics—features such as entanglement, interference, and nonlocality. But as far as physics goes, such systems barely scrape the surface. In particular, they have only a finite number of degrees of freedom, which means their states are characterized by a finite number of independent parameters. The systems studied in fields such as high-energy particle physics and many-body physics, meanwhile, have uncountably many degrees of freedom. They are far more complicated than the usual philosophical fare.This is not troubling as long as the conceptual heart of quantum physics can be effectively condensed down. But what if philosophers' toy systems are fundamentally different from realistic ones? That would be a problem. And indeed, as Laura Ruetsche convincingly argues in Interpreting Quantum Theories, systems with uncountable degrees of freedom—what Ruetsche collectively calls QM∞—are fundamentally different from the systems that have become the stock and trade of philosophy of physics, in ways that change the interpretational project.Ruetsche's book does two things exceedingly well. The first is to provide a (comparatively) accessible and philosophically oriented introduction to the algebraic approach to quantum physics, which is essential for understanding QM∞. This is a valuable contribution. The algebraic approach is the setting for much recent philosophical work. And yet learning it is notoriously difficult, as even pedagogical texts are aimed at research-level mathematicians. Ruetsche's book is technically demanding, but it works to bring nonmathematicians along. It is, without a doubt, the best place to enter this literature.Second, the book sets the agenda for future work on QM∞, by effectively and judiciously drawing important foundational questions out of a sprawling and difficult physics literature. In this regard, it is a close cousin to John Earman's (1995) excellent Bangs, Crunches, Whimpers, and Shrieks, which has had a significant influence on subsequent philosophy of spacetime physics. Philosophers of physics will be addressing the questions Ruetsche has raised, in many cases for the first time, for years to come.Interpreting Quantum Theories centers on what might be called the problem of inequivalent representations. The quantum theories that philosophers are accustomed to are set in a mathematical structure known as a (separable) Hilbert space, which is an at-most countably infinite dimensional complex vector space. Rays in a Hilbert space represent possible states of a physical system, and self-adjoint operators on that Hilbert space correspond to properties of the system.To treat QM∞, meanwhile, physicists pass to a generalization of this formalism. Now one begins with an abstract algebra of operators corresponding to the various properties associated with the system. States in this more general framework are linear functionals on the algebra whose value at each operator is interpreted as the expectation value of a measurement of that property in that state.The trouble with this more general framework is that the interpretational tools of Hilbert space quantum theories do not directly apply. Some solace comes from recognizing that any (appropriate) algebra of operators admits a representation in terms of the operators on a Hilbert space. This suggests that one can always move back to the more familiar Hilbert space formalism. But this is a pyrrhic victory. In general these Hilbert space representations are neither unique nor empirically equivalent. In particular, these inequivalent representations, interpreted in the familiar way, yield disagreements about which algebraic states are physically realizable.Faced with this situation, Ruetsche presents several principled options—what she calls “pristine” interpretations of QM∞. The two most significant are what she calls “Hilbert Space Conservatism” and “Algebraic Imperialism.” The Conservative claims that, for a given system, there is one true Hilbert space representation, which should be interpreted in the familiar ways. The Imperialist, meanwhile, insists that only the abstract algebra matters: the physical states are the algebraic states, properties correspond to the operators in the algebra, and if our old methods do not apply, so much the worse for our methods.At this level of description, Imperialists may appear to have the advantage, since they need not fret over which representation to choose. But there's a catch. As we have seen, there is a sense in which Imperialists generally recognize a broader range of possible physical states. But Conservatives allow for more properties. This is because when one represents the abstract algebra as operators on a Hilbert space, the operators in the representation naturally approximate additional operators on that Hilbert space, in a way that is unavailable in the abstract setting. Thus each interpretation suffers from limitations that the other does not.To adjudicate between the interpretations, Ruetsche takes them to the trenches, to see which provides the resources to support the actual explanatory and representational practices of physics. After a masterful survey, she concludes that neither interpretation has all of the requisite resources. In particular, she argues, physicists regularly make essential use of operators that are only available to Conservatives, while making equally essential use of multiple inequivalent representations—which only Imperialists can support. More, the particular mix of Conservatism and Imperialism varies between applications, apparently ruling out a stable interpretation of the formalism that can be articulated independently of the messy details. We are left with what Ruetsche calls “adulterated” interpretations.Philosophers' practice notwithstanding, it might seem unsurprising that we cannot separate our interpretation of physical theories from the pragmatics of their application to the world. After all, we are interested in these theories only insofar as they are successfully applied. But Ruetsche believes the problem is more acute. It is not merely that pragmatic considerations enter the debate between Conservatives and Imperialists. Ruetsche argues that there may not be any consistent, general interpretation of QM∞ compatible with practice. And this, she claims, makes realism about QM∞ untenable.The idea that the applications of a broad class of our best physical theories undermine their consistent interpretation in a way that renders realism incoherent is striking. Insofar as Ruetsche's case is convincing, it should have serious repercussions for general philosophy of science—both because it bears on important debates and because it shows how generalist questions depend on the details of particular scientific theories and their applications. Indeed, Ruetsche's skepticism about the terms of the realism debate and her radical particularism should influence general philosophy of science. But that said, her argument ultimately leaves room for disagreement.Ruetsche's basic claim is that Conservatism and Imperialism each support practices that the other cannot and that both kinds of practice are essential. But there is an important asymmetry here. Conservatives suffer because they fail to represent putative physical possibilities appealed to in practice. Imperialists, meanwhile, need to justify that in certain applications, they may limit attention to a subset of the physical possibilities their interpretation admits, and then use resources that only make sense in those limited regimes.The trouble is that the Imperialists' opportunism is neither unusual in physics nor difficult to motivate. In spacetime physics, for instance, properties such as the total mass of the universe or global time can be defined only in very special cases. And yet such properties are used in practice, because often the salient spacetimes are precisely the ones in which these quantities make (approximate) sense. To make her case that adulteration in QM∞ undermines realism, Ruetsche would need to establish that the representation-dependent quantities used in applications of QM∞ are different in kind from analogous quantities that appear throughout physics. And here it is not clear that she succeeds.None of this undercuts the importance of the book, however. Indeed, Ruetsche acknowledges that her argument may depend on how one understands idealization in physics. And even if one takes the view just described, there is a great deal of work to do on how Imperialism can support the practices Ruetsche identifies—work that will surely proceed within the framework Ruetsche has laid out, by addressing questions Ruetsche has raised. And so, wherever our study of QM∞ takes us, Ruetsche's book is sure to play a central role.

The Philosophical Review•Apr 1, 2015•0 citations

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Applications of quantum mechanics have led to many successful predictions and explanations of puzzling phenomena, and we now apply quantum mechanics to gain, process, and communicate information in novel ways. We can understand quantum mechanics by understanding how we have applied it. We should not seek agreement on the nature of the world it represents, because this theory does not itself represent the physical world (though its applications do help us to represent it better). When applied to a quantum state, quantum mechanics yields probabilities for physical events: both state and probability are objective—not because they represent elements of physical reality, but because each exerts normative authority over the beliefs of anyone who accepts quantum mechanics and applies it relative to a physical situation they may (but need not) occupy. These events may be described by statements (about values of magnitudes) that are meaningful in an appropriate environmental context, and quantum mechanics can help one to say when that is. Measurement creates an appropriate context, so here the Born rule indirectly yields probabilities of measurement outcomes. The quantum state of a system does not “collapse” on measurement: a new state must be assigned relative to a physical situation in which information about the outcome is accessible. Understood this way, there is no measurement problem, and violation of Bell inequalities does not demonstrate “spooky” non-local action. Quantum field theories have no physical ontology of their own: a quantum field is a mathematical object in a model whose application helps to improve and extend our descriptions of the world in other terms. We cannot realise the scenario of Wigner’s friend and its recent extensions: but the data that provide overwhelming evidence for quantum mechanics are objective in the same sense as the relative measurement outcomes described in those scenarios.

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Applications of quantum mechanics have led to many successful predictions and explanations of puzzling phenomena, and we now apply quantum mechanics to gain, process, and communicate information in novel ways. We can understand quantum mechanics by understanding how we have applied it. We should not seek agreement on the nature of the world it represents, because this theory does not itself represent the physical world (though its applications do help us to represent it better). When applied to a quantum state, quantum mechanics yields probabiities for physical events: both state and probability are objective--not because they represent elements of phyiscal reality, but because each exerts norrmative authority over the beliefs of anyone who accepts quantum mechanics and applies it relative to a physical situation they may (but need not) occupy. These events may be described by statements that are meaningful in an appropriate environmental context, and quantum mechanics can help one to say when that is. Measurement creates an appropriate context, so here the Born rule indirectly yields probabilities of measurement outcomes. The quantum state of a system does not "collapse" on measurement: a new state must be assigned relative to a physical situation in which information about the outcome is accessible. Understood this way, there is no measurement problem, and violations of Bell inequalities does not demonstrate "spooky" non-local action. Quantum field theories have no physical ontology of their own: a quantum field is a mathematical object in a model whose application helps us to improve and extend our descriptions of the world in other terms. We cannot realise the scenario of Wigner's friend and its recent extensions: but the data that provide overwhelming evidence for quantum mechanics are objective in the same sense as the relative measurement outcomes described in those scenarios.

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The Quantum Revolution in Philosophy

David Wallace

Richard Healey’s The Quantum Revolution in Philosophy is a terrific book, and yet I disagree with nearly all its main substantive conclusions.1 The purpose of this review is to say why the book is well worth your time if you have any interest in the interpretation of quantum theory or in the general philosophy of science, and yet why in the end I think Healey’s ambitious project fails to achieve its full goals. The quantum measurement problem is the central problem in philosophy of quantum mechanics, and arguably the most important issue in philosophy of physics more generally; not coincidentally, it has seen some of the field’s best work, and some of its most effective engagement with physics. Yet the debate in the field largely now appears deadlocked: the last few years have seen developments in our understanding of many of the proposed solutions, but not much movement in the overall dialectic. This is perhaps clearest with a little distance: metaphysicians who need to refer to quantum mechanics increasingly tend to talk of ‘the three main interpretations’ (they mean: de Broglie and Bohm’s hidden variable theory; Ghirardi, Rimini and Weber’s (‘GRW’) dynamical-collapse theory; Everett’s many-universes theory) and couch their discussions so as to be, as much as possible, equally valid for any of those three. It is not infrequent for philosophers of physics to use the familiar framework of underdetermination of theory by evidence to discuss the measurement problem.

Analysis•Mar 11, 2020•3 citations

Overview: A New Kind of Science

Richard Healey

This overview introduces the book’s aim of showing how quantum theory marks a radical break from previous scientific theorizing: We are warranted in accepting the fundamental status within contemporary physics of a theory that posits no new physical entities or magnitudes of its own. By contrast with existing interpretations that attempt to say how the world could possibly be the way quantum theory says it is, a pragmatist takes understanding quantum theory to be a matter of knowing how it is applied, and how the theory’s various elements function in these applications. So Part I of the book offers a simple, self-contained presentation of quantum theory, emphasizing applications; while Part II says why the quantum revolution matters for philosophy. Coming to terms with the quantum revolution involves adopting views of scientific theorizing, probability, causation, explanation, objectivity, meaning, and fundamentality that philosophers should have arrived at without its prompting.

Oxford University Press eBooks•Jul 20, 2017•0 citations
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.
Quantum theory launched a revolution in twentieth-century physics. But we have yet to appreciate the revolution’s significance for philosophy. Most studies of the conceptual foundations of quantum theory first try to interpret the theory—to say how the world could possibly be the way the theory says it is. But, though fundamental, quantum theory is enormously successful without describing the world in its own terms. When properly applied, models of quantum theory offer good advice on the significance and credibility of claims about the world expressed in other terms. This first of several philosophical lessons of the quantum revolution dissolves the quantum measurement problem. Pragmatist treatments of probability and causation show how quantum theory may be used to explain the non-localized correlations that have been thought to involve ‘spooky’ instantaneous action at a distance. Given environmental decoherence, a pragmatist inferentialist approach to content shows when talk of quantum probabilities is licensed, resolves any residual worries about whether a quantum measurement has a determinate outcome, and solves a dilemma about the ontology of a quantum field theory. This approach to meaning and reference also reveals the nature and limits of objective description in the light of quantum theory. While these pragmatist approaches to probability, causation, explanation, and content may be independently motivated by philosophical argument, their successful application here illustrates their practical importance in helping philosophers come to terms with the quantum revolution.
Most philosophical work on quantum physics has concerned simple systems. And for good reason. Even one or two particle systems can exhibit the striking features we have come to associate with quantum physics—features such as entanglement, interference, and nonlocality. But as far as physics goes, such systems barely scrape the surface. In particular, they have only a finite number of degrees of freedom, which means their states are characterized by a finite number of independent parameters. The systems studied in fields such as high-energy particle physics and many-body physics, meanwhile, have uncountably many degrees of freedom. They are far more complicated than the usual philosophical fare.This is not troubling as long as the conceptual heart of quantum physics can be effectively condensed down. But what if philosophers' toy systems are fundamentally different from realistic ones? That would be a problem. And indeed, as Laura Ruetsche convincingly argues in Interpreting Quantum Theories, systems with uncountable degrees of freedom—what Ruetsche collectively calls QM∞—are fundamentally different from the systems that have become the stock and trade of philosophy of physics, in ways that change the interpretational project.Ruetsche's book does two things exceedingly well. The first is to provide a (comparatively) accessible and philosophically oriented introduction to the algebraic approach to quantum physics, which is essential for understanding QM∞. This is a valuable contribution. The algebraic approach is the setting for much recent philosophical work. And yet learning it is notoriously difficult, as even pedagogical texts are aimed at research-level mathematicians. Ruetsche's book is technically demanding, but it works to bring nonmathematicians along. It is, without a doubt, the best place to enter this literature.Second, the book sets the agenda for future work on QM∞, by effectively and judiciously drawing important foundational questions out of a sprawling and difficult physics literature. In this regard, it is a close cousin to John Earman's (1995) excellent Bangs, Crunches, Whimpers, and Shrieks, which has had a significant influence on subsequent philosophy of spacetime physics. Philosophers of physics will be addressing the questions Ruetsche has raised, in many cases for the first time, for years to come.Interpreting Quantum Theories centers on what might be called the problem of inequivalent representations. The quantum theories that philosophers are accustomed to are set in a mathematical structure known as a (separable) Hilbert space, which is an at-most countably infinite dimensional complex vector space. Rays in a Hilbert space represent possible states of a physical system, and self-adjoint operators on that Hilbert space correspond to properties of the system.To treat QM∞, meanwhile, physicists pass to a generalization of this formalism. Now one begins with an abstract algebra of operators corresponding to the various properties associated with the system. States in this more general framework are linear functionals on the algebra whose value at each operator is interpreted as the expectation value of a measurement of that property in that state.The trouble with this more general framework is that the interpretational tools of Hilbert space quantum theories do not directly apply. Some solace comes from recognizing that any (appropriate) algebra of operators admits a representation in terms of the operators on a Hilbert space. This suggests that one can always move back to the more familiar Hilbert space formalism. But this is a pyrrhic victory. In general these Hilbert space representations are neither unique nor empirically equivalent. In particular, these inequivalent representations, interpreted in the familiar way, yield disagreements about which algebraic states are physically realizable.Faced with this situation, Ruetsche presents several principled options—what she calls “pristine” interpretations of QM∞. The two most significant are what she calls “Hilbert Space Conservatism” and “Algebraic Imperialism.” The Conservative claims that, for a given system, there is one true Hilbert space representation, which should be interpreted in the familiar ways. The Imperialist, meanwhile, insists that only the abstract algebra matters: the physical states are the algebraic states, properties correspond to the operators in the algebra, and if our old methods do not apply, so much the worse for our methods.At this level of description, Imperialists may appear to have the advantage, since they need not fret over which representation to choose. But there's a catch. As we have seen, there is a sense in which Imperialists generally recognize a broader range of possible physical states. But Conservatives allow for more properties. This is because when one represents the abstract algebra as operators on a Hilbert space, the operators in the representation naturally approximate additional operators on that Hilbert space, in a way that is unavailable in the abstract setting. Thus each interpretation suffers from limitations that the other does not.To adjudicate between the interpretations, Ruetsche takes them to the trenches, to see which provides the resources to support the actual explanatory and representational practices of physics. After a masterful survey, she concludes that neither interpretation has all of the requisite resources. In particular, she argues, physicists regularly make essential use of operators that are only available to Conservatives, while making equally essential use of multiple inequivalent representations—which only Imperialists can support. More, the particular mix of Conservatism and Imperialism varies between applications, apparently ruling out a stable interpretation of the formalism that can be articulated independently of the messy details. We are left with what Ruetsche calls “adulterated” interpretations.Philosophers' practice notwithstanding, it might seem unsurprising that we cannot separate our interpretation of physical theories from the pragmatics of their application to the world. After all, we are interested in these theories only insofar as they are successfully applied. But Ruetsche believes the problem is more acute. It is not merely that pragmatic considerations enter the debate between Conservatives and Imperialists. Ruetsche argues that there may not be any consistent, general interpretation of QM∞ compatible with practice. And this, she claims, makes realism about QM∞ untenable.The idea that the applications of a broad class of our best physical theories undermine their consistent interpretation in a way that renders realism incoherent is striking. Insofar as Ruetsche's case is convincing, it should have serious repercussions for general philosophy of science—both because it bears on important debates and because it shows how generalist questions depend on the details of particular scientific theories and their applications. Indeed, Ruetsche's skepticism about the terms of the realism debate and her radical particularism should influence general philosophy of science. But that said, her argument ultimately leaves room for disagreement.Ruetsche's basic claim is that Conservatism and Imperialism each support practices that the other cannot and that both kinds of practice are essential. But there is an important asymmetry here. Conservatives suffer because they fail to represent putative physical possibilities appealed to in practice. Imperialists, meanwhile, need to justify that in certain applications, they may limit attention to a subset of the physical possibilities their interpretation admits, and then use resources that only make sense in those limited regimes.The trouble is that the Imperialists' opportunism is neither unusual in physics nor difficult to motivate. In spacetime physics, for instance, properties such as the total mass of the universe or global time can be defined only in very special cases. And yet such properties are used in practice, because often the salient spacetimes are precisely the ones in which these quantities make (approximate) sense. To make her case that adulteration in QM∞ undermines realism, Ruetsche would need to establish that the representation-dependent quantities used in applications of QM∞ are different in kind from analogous quantities that appear throughout physics. And here it is not clear that she succeeds.None of this undercuts the importance of the book, however. Indeed, Ruetsche acknowledges that her argument may depend on how one understands idealization in physics. And even if one takes the view just described, there is a great deal of work to do on how Imperialism can support the practices Ruetsche identifies—work that will surely proceed within the framework Ruetsche has laid out, by addressing questions Ruetsche has raised. And so, wherever our study of QM∞ takes us, Ruetsche's book is sure to play a central role.
Applications of quantum mechanics have led to many successful predictions and explanations of puzzling phenomena, and we now apply quantum mechanics to gain, process, and communicate information in novel ways. We can understand quantum mechanics by understanding how we have applied it. We should not seek agreement on the nature of the world it represents, because this theory does not itself represent the physical world (though its applications do help us to represent it better). When applied to a quantum state, quantum mechanics yields probabilities for physical events: both state and probability are objective—not because they represent elements of physical reality, but because each exerts normative authority over the beliefs of anyone who accepts quantum mechanics and applies it relative to a physical situation they may (but need not) occupy. These events may be described by statements (about values of magnitudes) that are meaningful in an appropriate environmental context, and quantum mechanics can help one to say when that is. Measurement creates an appropriate context, so here the Born rule indirectly yields probabilities of measurement outcomes. The quantum state of a system does not “collapse” on measurement: a new state must be assigned relative to a physical situation in which information about the outcome is accessible. Understood this way, there is no measurement problem, and violation of Bell inequalities does not demonstrate “spooky” non-local action. Quantum field theories have no physical ontology of their own: a quantum field is a mathematical object in a model whose application helps to improve and extend our descriptions of the world in other terms. We cannot realise the scenario of Wigner’s friend and its recent extensions: but the data that provide overwhelming evidence for quantum mechanics are objective in the same sense as the relative measurement outcomes described in those scenarios.
Applications of quantum mechanics have led to many successful predictions and explanations of puzzling phenomena, and we now apply quantum mechanics to gain, process, and communicate information in novel ways. We can understand quantum mechanics by understanding how we have applied it. We should not seek agreement on the nature of the world it represents, because this theory does not itself represent the physical world (though its applications do help us to represent it better). When applied to a quantum state, quantum mechanics yields probabiities for physical events: both state and probability are objective--not because they represent elements of phyiscal reality, but because each exerts norrmative authority over the beliefs of anyone who accepts quantum mechanics and applies it relative to a physical situation they may (but need not) occupy. These events may be described by statements that are meaningful in an appropriate environmental context, and quantum mechanics can help one to say when that is. Measurement creates an appropriate context, so here the Born rule indirectly yields probabilities of measurement outcomes. The quantum state of a system does not "collapse" on measurement: a new state must be assigned relative to a physical situation in which information about the outcome is accessible. Understood this way, there is no measurement problem, and violations of Bell inequalities does not demonstrate "spooky" non-local action. Quantum field theories have no physical ontology of their own: a quantum field is a mathematical object in a model whose application helps us to improve and extend our descriptions of the world in other terms. We cannot realise the scenario of Wigner's friend and its recent extensions: but the data that provide overwhelming evidence for quantum mechanics are objective in the same sense as the relative measurement outcomes described in those scenarios.
Richard Healey’s The Quantum Revolution in Philosophy is a terrific book, and yet I disagree with nearly all its main substantive conclusions.1 The purpose of this review is to say why the book is well worth your time if you have any interest in the interpretation of quantum theory or in the general philosophy of science, and yet why in the end I think Healey’s ambitious project fails to achieve its full goals. The quantum measurement problem is the central problem in philosophy of quantum mechanics, and arguably the most important issue in philosophy of physics more generally; not coincidentally, it has seen some of the field’s best work, and some of its most effective engagement with physics. Yet the debate in the field largely now appears deadlocked: the last few years have seen developments in our understanding of many of the proposed solutions, but not much movement in the overall dialectic. This is perhaps clearest with a little distance: metaphysicians who need to refer to quantum mechanics increasingly tend to talk of ‘the three main interpretations’ (they mean: de Broglie and Bohm’s hidden variable theory; Ghirardi, Rimini and Weber’s (‘GRW’) dynamical-collapse theory; Everett’s many-universes theory) and couch their discussions so as to be, as much as possible, equally valid for any of those three. It is not infrequent for philosophers of physics to use the familiar framework of underdetermination of theory by evidence to discuss the measurement problem.
This overview introduces the book’s aim of showing how quantum theory marks a radical break from previous scientific theorizing: We are warranted in accepting the fundamental status within contemporary physics of a theory that posits no new physical entities or magnitudes of its own. By contrast with existing interpretations that attempt to say how the world could possibly be the way quantum theory says it is, a pragmatist takes understanding quantum theory to be a matter of knowing how it is applied, and how the theory’s various elements function in these applications. So Part I of the book offers a simple, self-contained presentation of quantum theory, emphasizing applications; while Part II says why the quantum revolution matters for philosophy. Coming to terms with the quantum revolution involves adopting views of scientific theorizing, probability, causation, explanation, objectivity, meaning, and fundamentality that philosophers should have arrived at without its prompting.