Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

State Hopping Mechanics

Altaie, Mohammed Basil

Published Dec 9, 2025• 0 citations
Publisher

Abstract

We propose a framework to deal with the quantum world postulating that the allowed states of a quantum system are under continued hopping following a natural stochastic distribution. We postulate that the rate of hopping is proportional to the total energy of the system. A probabilistic scheme in a stochastic context is proposed. Accordingly, we reconstruct the main equation for the time development of quantum systems. Quantum measurement theory is discussed from this perspective where it is shown that nonlocality is a basic feature of quantum systems, quantum entanglement is a natural result of the phase conservation under renewal of the states and that entangled states, even for isolated systems, cannot be maintained indefinitely. This feature of nonlocality suggests that the probability follows Levy's distribution in most cases and not the Gaussian distribution. The proposed framework violates Bell's inqualities and therefore is expected to produce the same or similar results to those found in standard quantum mechanics. Short demonstrations through several examples shows that the new scheme suggests possible resolutions for some outstanding fundamental problems and paradoxes, in the standard formulation of quantm mechanics. The scheme offers an explanation for the decoherence of quantum states without the collapse postulate while eleminating the observer role in measurements. Several fundamental quantum features, including the quantum uncertainty, emerge naturally. Testing most predictions of the proposed approach is possible, both through simulations and by performing real experiments. These features, with experimentally verifiable predictions, make the proposed framework a distinct alternative for the standard formulation of quantum mechanics.

DOI
10.5281/zenodo.17871997

Related papers

Nelson's Stochastic Mechanics: Measurement, Nonlocality, and the Classical Limit

Partha Ghose

Nelson's stochastic mechanics may be understood as a stochastic underpinning, or reconstruction, of nonrelativistic quantum mechanics, once the diffusion scale is fixed by $\hbar$ and the admissible states are restricted by the usual single-valuedness condition on the wavefunction. In this note I briefly indicate what this route achieves and why it remains conceptually attractive. Four advantages are emphasized. First, it supplies a clear configuration-space stochastic picture of the underlying processes. Second, the Born rule is built in from the outset, with $|ψ|^2$ arising as the probability density $ρ$ of the underlying diffusion process rather than as an independent postulate. Third, it offers a markedly different perspective on measurement and nonlocality: in particular, collapse need not be treated as an extra axiom, and the nonlocality associated with entangled states is softened relative to the deterministic Bohmian guidance picture. Fourth, by tying quantumness to a diffusion scale, it naturally suggests a continuum of physical descriptions ranging from the strictly classical to the strictly quantum-mechanical regime. I conclude by proposing a natural distance scale in stochastic mechanics and examining its implications for testing possible limits of Bell correlations.

quant-pharXiv:2604.03214•Apr 6, 2026•0 citations

The Quantum Revolution in Philosophy

Eddy Keming Chen

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

arXiv:2110.12102•The Philosophical Review•Apr 1, 2020•0 citations

General framework for the behaviour of continuously observed open quantum systems

Ole Eiler Barndorff-Nielsen, Elena R. Loubenets

We develop the general quantum stochastic approach for the description of quantum measurements continuous in time. The framework that we introduce encompasses the various particular models for continuous-time measurements considered previously in the physical and the mathematical literature.

arXiv:quant-ph/0202094•Journal of Physics A Mathematical and General•Jan 14, 2002•13 citations

Quantum Probability Theory and the Foundations of Quantum Mechanics

Jürg Martin Fröhlich, Baptiste Schubnel

We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic framework for the formulation of mathematical models of physical systems that is general enough to encompass classical and quantum mechanical models. After a short discussion on the properties of classical systems (realism and determinism), we move on to the study of a general class of quantum-mechanical models of physical systems and explain what some of the key problems in a quantum theory of observations and measurements are. In the last part of our essay, we attempt to elucidate the roles played by entanglement between a system and its environment and of information loss in understanding "decoherence" and "dephasing", which are key mechanisms in a quantum theory of measurements and experiments. We also discuss the problem of "time in quantum mechanics" and sketch an answer to the question when an experiment can be considered to have been completed successfully.

arXiv:1310.1484•Oct 5, 2013•6 citations

Law without law: from observer states to physics via algorithmic information theory

Markus P. Müller

According to our current conception of physics, any valid physical theory is supposed to describe the objective evolution of a unique external world. However, this condition is challenged by quantum theory, which suggests that physical systems should not always be understood as having objective properties which are simply revealed by measurement. Furthermore, as argued below, several other conceptual puzzles in the foundations of physics and related fields point to limitations of our current perspective and motivate the exploration of an alternative: to start with the first-person (the observer) rather than the third-person perspective (the world).In this work, I propose a rigorous approach of this kind on the basis of algorithmic information theory. It is based on a single postulate: that universal induction determines the chances of what any observer sees next. That is, instead of a world or physical laws, it is the local state of the observer alone that determines those probabilities. Surprisingly, despite its solipsistic foundation, I show that the resulting theory recovers many features of our established physical worldview: it predicts that it appears to observers as if there was an external world that evolves according to simple, computable, probabilistic laws. In contrast to the standard view, objective reality is not assumed on this approach but rather provably emerges as an asymptotic statistical phenomenon. The resulting theory dissolves puzzles like cosmology's Boltzmann brain problem, makes concrete predictions for thought experiments like the computer simulation of agents, and suggests novel phenomena such as ``probabilistic zombies'' governed by observer-dependent probabilistic chances. It also suggests that some basic phenomena of quantum theory (Bell inequality violation and no-signalling) might be understood as consequences of this framework.

arXiv:1712.01826•Quantum•Jul 20, 2020•51 citations

The measurement problem in the stochastic formulation of quantum mechanics.

Blanchard Ph, Cini M, Maurizio Serva

The description of physical systems obtained in the classical limit of quantum mechanics is not consistent with the one given by classical statistical mechanics. In qantum mechanics the complete description of a physical system is given by specifying the wave function, which evolves completely deterministically. Probability comes into play only when a measurement is made. Classical statistical mechanics, on the contrary, concerns systems whose description is not complete and where probability enters as a consequence of a lack of knowledge. We show that Nelson's stochastic mechanics, whose predictions are identical with those of quantum mechanics, provides nevertheless a unified description of the deterministic and random aspects of quantum mechanics which eliminates the inconsistency outlined above and gives a simple and satisfactory solution to the measurement problem.

•Jan 1, 1992•0 citations
We propose a framework to deal with the quantum world postulating that the allowed states of a quantum system are under continued hopping following a natural stochastic distribution. We postulate that the rate of hopping is proportional to the total energy of the system. A probabilistic scheme in a stochastic context is proposed. Accordingly, we reconstruct the main equation for the time development of quantum systems. Quantum measurement theory is discussed from this perspective where it is shown that nonlocality is a basic feature of quantum systems, quantum entanglement is a natural result of the phase conservation under renewal of the states and that entangled states, even for isolated systems, cannot be maintained indefinitely. This feature of nonlocality suggests that the probability follows Levy's distribution in most cases and not the Gaussian distribution. The proposed framework violates Bell's inqualities and therefore is expected to produce the same or similar results to those found in standard quantum mechanics. Short demonstrations through several examples shows that the new scheme suggests possible resolutions for some outstanding fundamental problems and paradoxes, in the standard formulation of quantm mechanics. The scheme offers an explanation for the decoherence of quantum states without the collapse postulate while eleminating the observer role in measurements. Several fundamental quantum features, including the quantum uncertainty, emerge naturally. Testing most predictions of the proposed approach is possible, both through simulations and by performing real experiments. These features, with experimentally verifiable predictions, make the proposed framework a distinct alternative for the standard formulation of quantum mechanics.
Nelson's stochastic mechanics may be understood as a stochastic underpinning, or reconstruction, of nonrelativistic quantum mechanics, once the diffusion scale is fixed by ℏ\hbarℏ and the admissible states are restricted by the usual single-valuedness condition on the wavefunction. In this note I briefly indicate what this route achieves and why it remains conceptually attractive. Four advantages are emphasized. First, it supplies a clear configuration-space stochastic picture of the underlying processes. Second, the Born rule is built in from the outset, with ∣ψ∣2|ψ|^2∣ψ∣2 arising as the probability density ρρρ of the underlying diffusion process rather than as an independent postulate. Third, it offers a markedly different perspective on measurement and nonlocality: in particular, collapse need not be treated as an extra axiom, and the nonlocality associated with entangled states is softened relative to the deterministic Bohmian guidance picture. Fourth, by tying quantumness to a diffusion scale, it naturally suggests a continuum of physical descriptions ranging from the strictly classical to the strictly quantum-mechanical regime. I conclude by proposing a natural distance scale in stochastic mechanics and examining its implications for testing possible limits of Bell correlations.
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.
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic framework for the formulation of mathematical models of physical systems that is general enough to encompass classical and quantum mechanical models. After a short discussion on the properties of classical systems (realism and determinism), we move on to the study of a general class of quantum-mechanical models of physical systems and explain what some of the key problems in a quantum theory of observations and measurements are. In the last part of our essay, we attempt to elucidate the roles played by entanglement between a system and its environment and of information loss in understanding "decoherence" and "dephasing", which are key mechanisms in a quantum theory of measurements and experiments. We also discuss the problem of "time in quantum mechanics" and sketch an answer to the question when an experiment can be considered to have been completed successfully.
According to our current conception of physics, any valid physical theory is supposed to describe the objective evolution of a unique external world. However, this condition is challenged by quantum theory, which suggests that physical systems should not always be understood as having objective properties which are simply revealed by measurement. Furthermore, as argued below, several other conceptual puzzles in the foundations of physics and related fields point to limitations of our current perspective and motivate the exploration of an alternative: to start with the first-person (the observer) rather than the third-person perspective (the world).In this work, I propose a rigorous approach of this kind on the basis of algorithmic information theory. It is based on a single postulate: that universal induction determines the chances of what any observer sees next. That is, instead of a world or physical laws, it is the local state of the observer alone that determines those probabilities. Surprisingly, despite its solipsistic foundation, I show that the resulting theory recovers many features of our established physical worldview: it predicts that it appears to observers as if there was an external world that evolves according to simple, computable, probabilistic laws. In contrast to the standard view, objective reality is not assumed on this approach but rather provably emerges as an asymptotic statistical phenomenon. The resulting theory dissolves puzzles like cosmology's Boltzmann brain problem, makes concrete predictions for thought experiments like the computer simulation of agents, and suggests novel phenomena such as ``probabilistic zombies'' governed by observer-dependent probabilistic chances. It also suggests that some basic phenomena of quantum theory (Bell inequality violation and no-signalling) might be understood as consequences of this framework.
The description of physical systems obtained in the classical limit of quantum mechanics is not consistent with the one given by classical statistical mechanics. In qantum mechanics the complete description of a physical system is given by specifying the wave function, which evolves completely deterministically. Probability comes into play only when a measurement is made. Classical statistical mechanics, on the contrary, concerns systems whose description is not complete and where probability enters as a consequence of a lack of knowledge. We show that Nelson's stochastic mechanics, whose predictions are identical with those of quantum mechanics, provides nevertheless a unified description of the deterministic and random aspects of quantum mechanics which eliminates the inconsistency outlined above and gives a simple and satisfactory solution to the measurement problem.