I examine the epistemological debate on scientific realism in the context of quantum physics, focusing on the empirical underdetermin- ation of different formulations and interpretations of QM. I will argue that much of the interpretational, metaphysical work on QM tran- scends the kinds of realist commitments that are well-motivated in the light of the history of science. I sketch a way of demarcating empirically well-confirmed aspects of QM from speculative quantum metaphysics in a way that coheres with anti-realist evidence from (...) the history of science. The minimal realist attitude sketched withholds realist com- mitment to what quantum state |Ψ⟩ represents. I argue that such commitment is not required for fulfilling the ultimate realist motiva- tion: accounting for the empirical success of quantum mechanics in a way that is in tune with a broader understanding of how theoretical science progresses and latches onto reality. (shrink)

Reduction and reductionism have been central philosophical topics in analytic philosophy of science for more than six decades. Together they encompass a diversity of issues from metaphysics and epistemology. This article provides an introduction to the topic that illuminates how contemporary epistemological discussions took their shape historically and limns the contours of concrete cases of reduction in specific natural sciences. The unity of science and the impulse to accomplish compositional reduction in accord with a layer-cake vision of the sciences, the (...) seminal contributions of Ernest Nagel on theory reduction and how they strongly conditioned subsequent philosophical discussions, and the detailed issues pertaining to different accounts of reduction that arise in both physical and biological science (e.g., limit-case and part-whole reduction in physics, the difference-making principle in genetics, and mechanisms in molecular biology) are explored. The conclusion argues that the epistemological heterogeneity and patchwork organization of the natural sciences encourages a pluralist stance about reduction. (shrink)

We introduce a realist, unextravagant interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes but leaves the theory’s basic dynamical content essentially intact. Much as classical systems have specific states that evolve along definite trajectories through configuration spaces, the traditional formulation of quantum theory permits assuming that closed quantum systems have specific states that evolve unitarily along definite trajectories through Hilbert spaces, and our interpretation extends this intuitive picture (...) of states and Hilbert-space trajectories to the more realistic case of open quantum systems despite the generic development of entanglement. We provide independent justification for the partial-trace operation for density matrices, reformulate wave-function collapse in terms of an underlying interpolating dynamics, derive the Born rule from deeper principles, resolve several open questions regarding ontological stability and dynamics, address a number of familiar no-go theorems, and argue that our interpretation is ultimately compatible with Lorentz invariance. Along the way, we also investigate a number of unexplored features of quantum theory, including an interesting geometrical structure—which we call subsystem space—that we believe merits further study. We conclude with a summary, a list of criteria for future work on quantum foundations, and further research directions. We include an appendix that briefly reviews the traditional Copenhagen interpretation and the measurement problem of quantum theory, as well as the instrumentalist approach and a collection of foundational theorems not otherwise discussed in the main text. (shrink)

A short review of some recent developments in the philosophy of physics is presented. I focus on themes which illustrate relations and points of common interest between philosophy of physics and three of its `neighboring' elds: Physics, metaphysics and general philosophy of science. The main examples discussed in these three `border areas' are decoherence and the interpretation of quantum mechanics; time in physics and metaphysics; and methodological issues surrounding the multiverse idea in modern cosmology.

Karim Thébault has argued that for ontic structural realism to be a viable ontology it should accommodate two principles: physico-mathematical structures it deploys must be firstly consistent and secondly substantial. He then contends that in geometric quantization, a transitional machinery from classical to quantum mechanics, the two principles are followed, showing that it is a guide to ontic structure. In this article, I will argue that geometric quantization violates the consistency principle. To compensate for this shortcoming, the deformation quantization procedure (...) will be offered. (shrink)

Quantum electrodynamics presents intrinsic limitations in the description of physical processes that make it impossible to recover from it the type of description we have in classical electrodynamics. Hence one cannot consider classical electrodynamics as reducing to quantum electrodynamics and being recovered from it by some sort of limiting procedure. Quantum electrodynamics has to be seen not as a more fundamental theory, but as an upgrade of classical electrodynamics, which permits an extension of classical theory to the description of phenomena (...) that, while being related to the conceptual framework of the classical theory, cannot be addressed from the classical theory. (shrink)

While it is widely agreed that decoherence will not solve the measurement problem, decoherence has been used to explain the “emergence of classicality” and to eliminate the need for a Copenhagen edict that some systems simply have to be treated as classical via a quantum-classical “cut”. I argue that decoherence still relies on such a cut. Decoherence accounts derive classicality only in virtue of their incompleteness, by omission of part of the entangled system of which the classical-appearing subsystem is a (...) part. I argue that this omission is only justified by implicit classical assumptions that objectify a subsystem and are employed via either a traditional Copenhagen cut or a functionally equivalent imposition of separability on a system in a non-separable state. I argue that decoherence cannot derive classicality without assuming it in some other form, and I provide an analysis of when it is appropriate to make these otherwise implicit classical assumptions by adopting a minimalistic Copenhagen-style approach to measurement. Finally, I argue that, ironically, the conditions for making these assumptions may be better satisfied in standard measurement situations than in cases of environmental monitoring. (shrink)

We argue against claims that the classical ℏ → 0 limit is “singular” in a way that frustrates an eliminative reduction of classical to quantum physics. We show one precise sense in which quantum mechanics and scaling behavior can be used to recover classical mechanics exactly, without making prior reference to the classical theory. To do so, we use the tools of strict deformation quantization, which provides a rigorous way to capture the ℏ → 0 limit. We then use the (...) tools of category theory to demonstrate one way that this reduction is explanatory: it illustrates a sense in which the structure of quantum mechanics determines that of classical mechanics. (shrink)

Most interpretations of Quantum Mechanics alternative to Copenhagen interpretation try to avoid the dualistic flavor of the latter. One of the basic goals of the former is to avoid the ad hoc introduction of observers and observations as an inevitable presupposition of physics. Non-Copenhagen interpretations usually trust in decoherence as a necessary mechanism to obtain a well-defined, observer-free transition from a unitary quantum description of the universe to classicality. Even though decoherence does not solve the problem of the definite outcomes, (...) it helps to explain why we do not observe superpositions and, according to Zurek’s existential interpretation, why a specific preferred basis emerges through system–environment interactions. The aim of this paper is to show why such interpretation ends up begging the question and provides little progress in understanding the quantum-to-classical transition; the ultimate reason being that preferred bases always correlate to human observation. Benefitting from the technical discussion, some remarks will be offered in the last section regarding the role of classical observations as a necessary condition to make workable the formalism of Quantum Mechanics and scientific activity itself. (shrink)

Lifeworld realism and quantum-physical realism are taken as experience-dependent conceptions of the world that become objects of explicit reflection when confronted with context-external discourses. After a brief sketch of the two contexts of experience—lifeworld and quantum physics—and their realist interpretations, I will discuss the quantum world from the perspective of lifeworld realism. From this perspective, the quantum world—roughly speaking—has to be either unreal or else constitute a different reality. Then, I invert the perspective and examine the lifeworld from the standpoint (...) of quantumphysical realism. This conception of the lifeworld has gained momentum from new research results in recent decades. Despite its experiential basis, quantum-physical realism bears an ambiguity akin to that of lifeworld realism. While the perspectival inversion serves to highlight the problem, it also contributes to an improved understanding of lifeworld-realism. (shrink)

I show explicitly how concerns about wave function collapse and ontology can be decoupled from the bulk of technical analysis necessary to recover localized, approximately Newtonian trajectories from quantum theory. In doing so, I demonstrate that the account of classical behavior provided by decoherence theory can be straightforwardly tailored to give accounts of classical behavior on multiple interpretations of quantum theory, including the Everett, de Broglie-Bohm and GRW interpretations. I further show that this interpretation-neutral, decoherence-based account conforms to a general (...) view of inter-theoretic reduction in physics that I have elaborated elsewhere, which differs from the oversimplified and often ambiguous picture that treats reduction simply as a matter of taking limits. This interpretation-neutral account rests on a general three-pronged strategy for reduction between quantum and classical theories that combines decoherence, an appropriate form of Ehrenfest's Theorem, and a decoherence-compatible mechanism for collapse. It also incorporates a novel argument as to why branch-relative trajectories should be approximately Newtonian, which is based on a little-discussed extension of Ehrenfest's Theorem to open systems, rather than on the more commonly cited but less germane closed-systems version. In the Conclusion, I briefly suggest how the strategy for quantum-classical reduction described here might be extended to reduction between other classical and quantum theories, including classical and quantum field theory and classical and quantum gravity. (shrink)

This study attempts to spell out more explicitly than has been done previously the connection between two types of formal correspondence that arise in the study of quantum–classical relations: one the one hand, deformation quantization and the associated continuity between quantum and classical algebras of observables in the limit \, and, on the other, a certain generalization of Ehrenfest’s Theorem and the result that expectation values of position and momentum evolve approximately classically for narrow wave packet states. While deformation quantization (...) establishes a direct continuity between the abstract algebras of quantum and classical observables, the latter result makes in-eliminable reference to the quantum and classical state spaces on which these structures act—specifically, via restriction to narrow wave packet states. Here, we describe a certain geometrical re-formulation and extension of the result that expectation values evolve approximately classically for narrow wave packet states, which relies essentially on the postulates of deformation quantization, but describes a relationship between the actions of quantum and classical algebras and groups over their respective state spaces that is non-trivially distinct from deformation quantization. The goals of the discussion are partly pedagogical in that it aims to provide a clear, explicit synthesis of known results; however, the particular synthesis offered aspires to some novelty in its emphasis on a certain general type of mathematical and physical relationship between the state spaces of different models that represent the same physical system, and in the explicitness with which it details the above-mentioned connection between quantum and classical models. (shrink)

I distinguish two types of reduction within the context of quantum-classical relations, which I designate “formal” and “empirical”. Formal reduction holds or fails to hold solely by virtue of the mathematical relationship between two theories; it is therefore a two-place, a priori relation between theories. Empirical reduction requires one theory to encompass the range of physical behaviors that are well-modeled in another theory; in a certain sense, it is a three-place, a posteriori relation connecting the theories and the domain of (...) physical reality that both serve to describe. Focusing on the relationship between classical and quantum mechanics, I argue that while certain formal results concerning singular \ limits have been taken to preclude the possibility of reduction between these theories, such results at most provide support for the claim that singular limits block reduction in the formal sense; little if any reason has been given for thinking that they block reduction in the empirical sense. I then briefly outline a strategy for empirical reduction that is suggested by work on decoherence theory, arguing that this sort of account remains a fully viable route to the empirical reduction of classical to quantum mechanics and is unaffected by such singular limits. (shrink)

In the phenomenology of the consciousness of internal time, Edmund Husserl has frequent recourse to sound and melody as illustrations of the processes that give rise to immanent temporal objects. In Husserl’s analysis, there is a philosophically pregnant tension between the geometrical diagrams representing multiple dimensions of immanent time and his intuition that time-points might be no more than fictions leading to absurdities. In this paper, I will address this tension in order to motivate a complementarity approach to temporal objects (...) such as sound and melody that might illuminate the phenomenology of sound-consciousness. (shrink)

We propose a technical reformulation of the measurement problem of quantum mechanics, which is based on the postulate that the final state of a measurement is classical; this accords with experimental practice as well as with Bohr’s views. Unlike the usual formulation (in which the post-measurement state is a unit vector in Hilbert space), our version actually opens the possibility of admitting a purely technical solution within the confines of conventional quantum theory (as opposed to solutions that either modify this (...) theory, or introduce unusual and controversial interpretative rules and/or ontologies).To that effect, we recall a remarkable phenomenon in the theory of Schrödinger operators (discovered in 1981 by Jona-Lasinio, Martinelli, and Scoppola), according to which the ground state of a symmetric double-well Hamiltonian (which is paradigmatically of Schrödinger’s Cat type) becomes exponentially sensitive to tiny perturbations of the potential as ħ→0. We show that this instability emerges also from the textbook wkb approximation, extend it to time-dependent perturbations, and study the dynamical transition from the ground state of the double well to the perturbed ground state (in which the cat is typically either dead or alive, depending on the details of the perturbation).Numerical simulations show that adiabatically arising perturbations may (quite literally) cause the collapse of the wave-function in the classical limit. Thus, at least in the context of a simple mathematical model, we combine the technical and conceptual virtues of decoherence (which fails to solve the measurement problem but launches the key idea that perturbations may come from the environment) with those of dynamical collapse models à la grw (which do solve the measurement problem but are ad hoc), without sharing their drawbacks: single measurement outcomes are obtained (instead of merely diagonal reduced density matrices), and no modification of quantum mechanics is needed. (shrink)

Interference of more and more massive objects provides a spectacular confirmation of quantum theory. It is usually regarded as support for “wave–particle duality” and in an extension of this duality even as support for “complementarity”. We first give an outline of the historical development of these notions. Already here it becomes evident that they are hard to define rigorously, i.e. have mainly a heuristic function. Then we discuss recent interference experiments of large and complex molecules which seem to support this (...) heuristic function of “duality”. However, we show that in these experiments the diffraction of a delocalized center-of-mass wave function depends on the interaction of the localized structure of the molecule with the diffraction element. Thus, the molecules display “dual features” at the same time, which contradicts the usual understanding of wave–particle duality. We conclude that the notion of “wave–particle duality” deserves no place in modern quantum physics. (shrink)

Some physicists and philosophers argue that unitarily inequivalent representations in quantum field theory are mathematical surplus structure. Support for that view, sometimes called ‘algebraic imperialism’, relies on Fell’s theorem and its deployment in the algebraic approach to QFT. The algebraic imperialist uses Fell’s theorem to argue that UIRs are ‘physically equivalent’ to each other. The mathematical, conceptual, and dynamical aspects of Fell’s theorem will be examined. Its use as a criterion for physical equivalence is examined in detail and it is (...) proven that Fell’s theorem does not apply to the vast number of representations used in the algebraic approach. UIRs are not another case of theoretical underdetermination, because they make different predictions about ‘classical’ operators. These results are applied to the Unruh effect where there is a continuum of UIRs to which Fell’s theorem does not apply. _1_ Introduction _2_ Weak Equivalence and Physical Equivalence _3_ Mathematical Overview of Algebraic Quantum Field Theory _4_ Fell’s Theorem and Philosophical Responses to Weak Equivalence _5_ Weak Equivalence in C*-Algebras and W*-Algebras _6_ Classical Equivalence and Weak Equivalence _7_ Interlude: Is Weak Equivalence Really Physical Equivalence? _8_ The Unruh Effect _9_ Time Evolution and Symmetries _10_ Conclusions Appendix. (shrink)

Einstein's philosophy of physics (as clarified by Fine, Howard, and Held) was predicated on his Trennungsprinzip, a combination of separability and locality, without which he believed objectification, and thereby "physical thought" and "physical laws", to be impossible. Bohr's philosophy (as elucidated by Hooker, Scheibe, Folse, Howard, Held, and others), on the other hand, was grounded in a seemingly different doctrine about the possibility of objective knowledge, namely the necessity of classical concepts. In fact, it follows from Raggio's Theorem in algebraic (...) quantum theory that - within an appropriate class of physical theories - suitable mathematical translations of the doctrines of Bohr and Einstein are equivalent. Thus - upon our specific formalization - quantum mechanics accommodates Einstein's Trennungsprinzip if and only if it is interpreted a la Bohr through classical physics. Unfortunately, the protagonists themselves failed to discuss their differences in this constructive way, since their debate was dominated by Einstein's ingenious but ultimately flawed attempts to establish the "incompleteness" of quantum mechanics. This aspect of their debate may still be understood and appreciated, however, as reflecting a much deeper and insurmountable disagreement between Bohr and Einstein about the knowability of Nature. Using the theological controversy on the knowability of God as a analogy, we can say that Einstein was a Spinozist, whereas Bohr could be said to be on the side of Maimonides. Thus Einstein's off-the-cuff characterization of Bohr as a 'Talmudic philosopher' was spot-on. (shrink)

Einstein's philosophy of physics was predicated on his Trennungsprinzip, a combination of separability and locality, without which he believed objectification, and thereby "physical thought" and "physical laws", to be impossible. Bohr's philosophy, on the other hand, was grounded in a seemingly different doctrine about the possibility of objective knowledge, namely the necessity of classical concepts. In fact, it follows from Raggio's Theorem in algebraic quantum theory that - within an appropriate class of physical theories - suitable mathematical translations of the (...) doctrines of Bohr and Einstein are equivalent. Thus - upon our specific formalization - quantum mechanics accommodates Einstein's Trennungsprinzip if and only if it is interpreted a la Bohr through classical physics. Unfortunately, the protagonists themselves failed to discuss their differences in this constructive way, since their debate was dominated by Einstein's ingenious but ultimately flawed attempts to establish the "incompleteness" of quantum mechanics. This aspect of their debate may still be understood and appreciated, however, as reflecting a much deeper and insurmountable disagreement between Bohr and Einstein about the knowability of Nature. Using the theological controversy on the knowability of God as a analogy, we can say that Einstein was a Spinozist, whereas Bohr could be said to be on the side of Maimonides. Thus Einstein's off-the-cuff characterization of Bohr as a 'Talmudic philosopher' was spot-on. (shrink)

Beginning with Anderson, spontaneous symmetry breaking in infinite quantum systems is often put forward as an example of emergence in physics, since in theory no finite system should display it. Even the correspondence between theory and reality is at stake here, since numerous real materials show ssb in their ground states, although they are finite. Thus against what is sometimes called ‘Earman's Principle’, a genuine physical effect seems theoretically recovered only in some idealisation, disappearing as soon as the idealisation is (...) removed.We review the well-known arguments that no finite system can exhibit ssb, using the formalism of algebraic quantum theory in order to control the thermodynamic limit and unify the description of finite- and infinite-volume systems. Using the striking mathematical analogy between the thermodynamic limit and the classical limit, we show that a similar situation obtains in quantum mechanics versus classical mechanics.This discrepancy between formalism and reality is quite similar to the measurement problem, and hence we address it in the same way, adapting an argument of the Landsman and Reuvers that was originally intended to explain the collapse of the wave-function within conventional quantum mechanics. Namely, exponential sensitivity to perturbations of the dynamics as the system size increases causes symmetry breaking already in finite but very large quantum systems. This provides continuity between finite- and infinite-volume descriptions of quantum systems featuring ssb and hence restores Earman's Principle. (shrink)

We propose a technical reformulation of the measurement problem of quantum mechanics, which is based on the postulate that the final state of a measurement is classical; this accords with experimental practice as well as with Bohr’s views. Unlike the usual formulation (in which the post-measurement state is a unit vector in Hilbert space), our version actually opens the possibility of admitting a purely technical solution within the confines of conventional quantum theory (as opposed to solutions that either modify this (...) theory, or introduce unusual and controversial interpretative rules and/or ontologies). To that effect, we recall a remarkable phenomenon in the theory of Schrödinger operators (discovered in 1981 by Jona-Lasinio, Martinelli, and Scoppola), according to which the ground state of a symmetric double-well Hamiltonian (which is paradigmatically of Schrödinger’s Cat type) becomes exponentially sensitive to tiny perturbations of the potential as ħ→0. We show that this instability emerges also from the textbook wkb approximation, extend it to time-dependent perturbations, and study the dynamical transition from the ground state of the double well to the perturbed ground state (in which the cat is typically either dead or alive, depending on the details of the perturbation). Numerical simulations show that adiabatically arising perturbations may (quite literally) cause the collapse of the wave-function in the classical limit. Thus, at least in the context of a simple mathematical model, we combine the technical and conceptual virtues of decoherence (which fails to solve the measurement problem but launches the key idea that perturbations may come from the environment) with those of dynamical collapse models à la grw (which do solve the measurement problem but are ad hoc), without sharing their drawbacks: single measurement outcomes are obtained (instead of merely diagonal reduced density matrices), and no modification of quantum mechanics is needed. (shrink)

Advocates of the New Mechanicism in philosophy of science argue that scientific explanation often consists in describing mechanisms responsible for natural phenomena. Despite its successes, one might think that this approach does not square with the ontological strictures of quantum mechanics. New Mechanists suppose that mechanisms are composed of objects with definite properties, which are interconnected via local causal interactions. Quantum mechanics calls these suppositions into question. Since mechanisms are hierarchical it appears that even macroscopic mechanisms must supervene on a (...) set of “objects” that behave non-classically. In this paper we argue, in part by appeal to the theory of quantum decoherence, that the universal validity of quantum mechanics does not undermine neo-mechanistic ontological and explanatory claims as they occur within in classical domains. Additionally, we argue that by relaxation of certain classical assumptions, mechanistic explanatory strategies can sometimes be carried over into the quantum domain. (shrink)

In October 1924, The Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Using Bohr’s correspondence principle and Einstein’s quantum theory of radiation along with advanced techniques from classical mechanics, Van Vleck showed that quantum formulae for emission, absorption, and dispersion of radiation merge with their classical counterparts in the limit of high quantum numbers. For modern readers Van Vleck’s paper is (...) much easier to follow than the famous paper by Kramers and Heisenberg on dispersion theory, which covers similar terrain and is widely credited to have led directly to Heisenberg’s Umdeutung paper. This makes Van Vleck’s paper extremely valuable for the reconstruction of the genesis of matrix mechanics. It also makes it tempting to ask why Van Vleck did not take the next step and develop matrix mechanics himself. (shrink)

Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hubert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by their nondistributivity and by various other problems. We show that a possible resolution of these difficulties, suggested by the ideas of Bohr, emerges if instead of single projections one considers elementary propositions to be families (...) of projections indexed by a partially ordered set C(A) of appropriate commutative subalgebras of A. In fact, to achieve both maximal generality and ease of use within topos theory, we assume that A is a so-called Rickart C*-algebra and that C(A) consists of all unital commutative Rickart C*-subalgebras of A. Such families of projections form a Hey ting algebra in a natural way, so that the associated propositional logic is intuitionistic: distributivity is recovered at the expense of the law of the excluded middle. Subsequently, generalizing an earlier computation for n x n matrices, we prove that the Heyting algebra thus associated to A arises as a basis for the internal Gelfand spectrum (in the sense of Banaschewski-Mulvey) of the "Bohrification" A̱ of A, which is a commutative Rickart C*-algebra in the topos of functors from C(A) to the category of sets. We explain the relationship of this construction to partial Boolean algebras and Bruns-Lakser completions. Finally, we establish a connection between probability measures on the lattice of projections on a Hubert space H and probability valuations on the internal Gelfand spectrum of A̱ for A = B(H). (shrink)

Jeff Bub has developed an information-theoretic interpretation of quantum mechanics on the basis of the programme to reaxiomatise the theory in terms of information-theoretic principles. According to the most recent version of the interpretation, reaxiomatisation can dissolve some of the demands for explanation traditionally associated with the task of providing an interpretation for the theory. The key idea is that the real lesson we should take away from quantum mechanics is that the ‘structure of in- formation’ is not what we (...) thought it was. In particular a feature of the new structure is intrinsic randomness of measurement, which allegedly dissolves a significant part of the measurement problem. I argue that it is difficult to find an appropriate argument to support the claim that measurement is intrinsically random in the relevant sense. (shrink)

The most striking observable feature of our indeterministic quantum universe is the wide range of time, place, and scale on which the deterministic laws of classical physics hold to an excellent approximation. This essay describes how this domain of classical predictability of every day experience emerges from a quantum theory of the universe’s state and dynamics.

In physics, one is often misled in thinking that the mathematical model of a system is part of or is that system itself. Think of expressions commonly used in physics like “point” particle, motion “on the line”, “smooth” observables, wave function, and even “going to infinity”, without forgetting perplexing phrases like “classical world” versus “quantum world”.... On the other hand, when a mathematical model becomes really inoperative in regard with correct predictions, one is forced to replace it with a new (...) one. It is precisely what happened with the emergence of quantum physics. Classical models were superseded by quantum ones through quantization prescriptions. These procedures appear often as ad hoc recipes. In the present paper, well defined quantizations, based on integral calculus and Weyl–Heisenberg symmetry, are described in simple terms through one of the most basic examples of mechanics. Starting from probability distribution on the Euclidean plane viewed as the phase space for the motion of a point particle on the line, i.e., its classical model, we will show how to build corresponding quantum model and associated probabilities or quasi-probabilities distributions. We highlight the regularizing rôle of such procedures with the familiar example of the motion of a particle with a variable mass and submitted to a step potential. (shrink)

The Ollivier–Poulin–Zurek definition of objectivity provides a philosophical basis for the environment as witness formulation of decoherence theory and hence for quantum Darwinism. It is shown that no account of the reference of the key terms in this definition can be given that does not render the definition inapplicable within quantum theory. It is argued that this is not the fault of the language used, but of the assumption that the laws of physics are independent of Hilbert-space decomposition. All evidence (...) suggests that this latter assumption is true. If it is, decoherence cannot explain the emergence of classicality. (shrink)

Decompositional equivalence is the principle that there is no preferred decomposition of the universe into subsystems. It is shown here, by using a simple thought experiment, that quantum theory follows from decompositional equivalence together with Landauer’s principle. This demonstration raises within physics a question previously left to psychology: how do human—or any—observers identify or agree about what constitutes a “system of interest”?

It is standardly assumed in discussions of quantum theory that physical systems can be regarded as having well-defined Hilbert spaces. It is shown here that a Hilbert space can be consistently partitioned only if its components are assumed not to interact. The assumption that physical systems have well-defined Hilbert spaces is, therefore, physically unwarranted.

It is standardly assumed in discussions of quantum theory that physical systems can be regarded as having well-defined Hilbert spaces. It is shown here that a Hilbert space can be consistently partitioned only if its components are assumed not to interact. The assumption that physical systems have well-defined Hilbert spaces is, therefore, physically unwarranted.

The common practice of advancing arguments based on current physics in support of metaphysical conclusions has been criticized on the grounds that current physics may well be wrong. A further criticism is leveled here: current physics itself depends on metaphysical assumptions, so arguing from current physics is in fact arguing from yet more metaphysics. It is shown that the metaphysical assumptions underlying current physics are often deeply embedded in the formalism in which theories are presented, and hence impossible to dismiss (...) as mere motivational or interpretative speculation. It is then shown that such assumptions, when made explicit, can wreck havoc on otherwise-sensible philosophical arguments. It is argued in conclusion that this situation is both unlikely to be reparable just by being more careful, and unlikely to go away as further, presumably more subtle physical theories are developed. (shrink)

Ruetsche argues that a problem of unitarily inequivalent representations arises in quantum theories with infinitely many degrees of freedom. I provide an algebraic formulation of classical field theories and show that unitarily inequivalent representations arise there as well. I argue that the classical case helps us rule out one possible response to the problem of unitarily inequivalent representations called Hilbert Space Conservatism.

I argue that philosophical issues concerning reductive explanations help constrain the construction of quantum theories with appropriate state spaces. I illustrate this general proposal with two examples of restricting attention to physical states in quantum theories: regular states and symmetry-invariant states. 1Introduction2Background2.1 Physical states2.2 Reductive explanations3The Proposed ‘Correspondence Principle’4Example: Regularity5Example: Symmetry-Invariance6Conclusion: Heuristics and Discovery.

In this article, I examine the relationship between physical quantities and physical states in quantum theories. I argue against the claim made by Arageorgis that the approach to interpreting quantum theories known as Algebraic Imperialism allows for “too many states.” I prove a result establishing that the Algebraic Imperialist has very general resources that she can employ to change her abstract algebra of quantities in order to rule out unphysical states.

This paper provides a prospectus for a new way of thinking about the wavefunction of the universe: a Ψ-epistemic quantum cosmology. We present a proposal that, if successfully implemented, would resolve the cosmological measurement problem and simultaneously allow us to think sensibly about probability and evolution in quantum cosmology. Our analysis draws upon recent work on the problem of time in quantum gravity and causally symmet- ric local hidden variable theories. Our conclusion weighs the strengths and weaknesses of the approach (...) and points towards paths for future development. (shrink)

The overaraching goal of this paper is to elucidate the nature of superselection rules in a manner that is accessible to philosophers of science and that brings out the connections between superselection and some of the most fundamental interpretational issues in quantum physics. The formalism of von Neumann algebras is used to characterize three different senses of superselection rules (dubbed, weak, strong, and very strong) and to provide useful necessary and sufficient conditions for each sense. It is then shown how (...) the Haag–Kastler algebraic approach to quantum physics holds the promise of a uniform and comprehensive account of the origin of superselection rules. Some of the challenges that must be met before this promise can be kept are discussed. The focus then turns to the role of superselection rules in solutions to the measurement problem and the emergence of classical properties. It is claimed that the role for “hard” superselection rules is limited, but “soft” (a.k.a. environmental) superselection rules or N. P. Landsman’s situational superselection rules may have a major role to play. Finally, an assessment is given of the recently revived attempts to deconstruct superselection rules. (shrink)

A decade ago, Isham and Butterfield proposed a topos-theoretic approach to quantum mechanics, which meanwhile has been extended by Döring and Isham so as to provide a new mathematical foundation for all of physics. Last year, three of the present authors redeveloped and refined these ideas by combining the C*-algebraic approach to quantum theory with the so-called internal language of topos theory (Heunen et al. in arXiv:0709.4364). The goal of the present paper is to illustrate our abstract setup through the (...) concrete example of the C*-algebra M n (ℂ) of complex n×n matrices. This leads to an explicit expression for the pointfree quantum phase space Σ n and the associated logical structure and Gelfand transform of an n-level system. We also determine the pertinent non-probabilisitic state-proposition pairing (or valuation) and give a very natural topos-theoretic reformulation of the Kochen–Specker Theorem.In our approach, the nondistributive lattice ℘(M n (ℂ)) of projections in M n (ℂ) (which forms the basis of the traditional quantum logic of Birkhoff and von Neumann) is replaced by a specific distributive lattice $\mathcal{O}(\Sigma_{n})$ of functions from the poset $\mathcal{C}(M_{n}(\mathbb{C}))$ of all unital commutative C*-subalgebras C of M n (ℂ) to ℘(M n (ℂ)). The lattice $\mathcal{O}(\Sigma_{n})$ is essentially the (pointfree) topology of the quantum phase space Σ n , and as such defines a Heyting algebra. Each element of $\mathcal{O}(\Sigma_{n})$ corresponds to a “Bohrified” proposition, in the sense that to each classical context $C\in\mathcal{C}(M_{n}(\mathbb{C}))$ it associates a yes-no question (i.e. an element of the Boolean lattice ℘(C) of projections in C), rather than being a single projection as in standard quantum logic. Distributivity is recovered at the expense of the law of the excluded middle (Tertium Non Datur), whose demise is in our opinion to be welcomed, not just in intuitionistic logic in the spirit of Brouwer, but also in quantum logic in the spirit of von Neumann. (shrink)

In previous work, I described several examples combining reduction and emergence: where reduction is understood a la Ernest Nagel, and emergence is understood as behaviour that is novel. Here, my aim is again to reconcile reduction and emergence, for a case which is apparently more problematic than those I treated before: renormalization. My main point is that renormalizability being a generic feature at accessible energies gives us a conceptually unified family of Nagelian reductions. That is worth saying since philosophers tend (...) to think of scientific explanation as only explaining an individual event, or perhaps a single law, or at most deducing one theory as a special case of another. Here we see a framework in which there is a space of theories endowed with enough structure that it provides a family of reductions. (shrink)

This is a companion to another paper. Together they rebut two widespread philosophical doctrines about emergence. The first, and main, doctrine is that emergence is incompatible with reduction. The second is that emergence is supervenience; or more exactly, supervenience without reduction.In the other paper, I develop these rebuttals in general terms, emphasising the second rebuttal. Here I discuss the situation in physics, emphasising the first rebuttal. I focus on limiting relations between theories and illustrate my claims with four examples, each (...) of them a model or a framework for modelling, from well-established mathematics or physics.I take emergence as behaviour that is novel and robust relative to some comparison class. I take reduction as, essentially, deduction. The main idea of my first rebuttal will be to perform the deduction after taking a limit of some parameter. Thus my first main claim will be that in my four examples (and many others), we can deduce a novel and robust behaviour, by taking the limit N→∞ of a parameter N.But on the other hand, this does not show that the N=∞ limit is “physically real”, as some authors have alleged. For my second main claim is that in these same examples, there is a weaker, yet still vivid, novel and robust behaviour that occurs before we get to the limit, i.e. for finite N. And it is this weaker behaviour which is physically real.My examples are: the method of arbitrary functions (in probability theory); fractals (in geometry); superselection for infinite systems (in quantum theory); and phase transitions for infinite systems (in statistical mechanics). (shrink)

The positive operator (valued) measures (POMs) allow one to generalize the notion of observable beyond the traditional one based on projection valued measures (PVMs). Here, we argue that this generalized conception of observable enables a consistent notion of unsharp reality and with it an adequate concept of joint properties. A sharp or unsharp property manifests itself as an element of sharp or unsharp reality by its tendency to become actual or to actualize a specific measurement outcome. This actualization tendency—or potentiality—of (...) a property is quantified by the associated quantum probability. The resulting single-case interpretation of probability as a degree of reality will be explained in detail and its role in addressing the tensions between quantum and classical accounts of the physical world will be elucidated. It will be shown that potentiality can be viewed as a causal agency that evolves in a well-defined way. (shrink)

Intuitively, the more powerful a theory is, the greater the variety and quantity of ideas can be expressed through its formal language. Therefore, when comparing two theories concerning the same subject, it seems only reasonable to compare the expressive powers of their formal languages. On condition that the quantum mechanical description is universal and so can be applied to macroscopic systems, quantum theory is required to be more powerful than classical mechanics. This implies that the formal language of Hilbert space (...) theory must be more expressive than that of Zermelo-Fraenkel set theory. However, as shown in the paper, such a requirement cannot be met. As a result, classical and quantum formalisms cannot be in a hierarchical relation, that is, include one another. This fact puts in doubt the quantum-classical correspondence and undermines the reductionist approach to the physical world. (shrink)

In previous articles we presented a simple set of axioms named “Contexts, Systems and Modalities”, where the structure of quantum mechanics appears as a result of the interplay between the quantized number of modalities accessible to a quantum system, and the continuum of contexts that are required to define these modalities. In the present article we discuss further how to obtain Born’s rule within this framework. Our approach is compared with other former and recent derivations, and its strong links with (...) Gleason’s theorem are particularly emphasized. (shrink)

As the theory of the atom, quantum mechanics is perhaps the most successful theory in the history of science. It enables physicists, chemists, and technicians to calculate and predict the outcome of a vast number of experiments and to create new and advanced technology based on the insight into the behavior of atomic objects. But it is also a theory that challenges our imagination. It seems to violate some fundamental principles of classical physics, principles that eventually have become a part (...) of western common sense since the rise of the modern worldview in the Renaissance. So the aim of any metaphysical interpretation of quantum mechanics is to account for these violations. (shrink)

This chapter is concerned with the representation of time and change in classical (i.e., non-quantum) physical theories. One of the main goals of the chapter is to attempt to clarify the nature and scope of the so-called problem of time: a knot of technical and interpretative problems that appear to stand in the way of attempts to quantize general relativity, and which have their roots in the general covariance of that theory. The most natural approach to these questions is via (...) a consideration of more clear cases. So much of the chapter is given over to a discussion of the representation of time and change in other, better understood theories, starting with the most straightforward cases and proceeding through a consideration of cases that lead up to the features of general relativity that are responsible for the problem of time. (shrink)

Bundles of C*-algebras can be used to represent limits of physical theories whose algebraic structure depends on the value of a parameter. The primary example is the ℏ→0 limit of the C*-algebras of physical quantities in quantum theories, represented in the framework of strict deformation quantization. In this paper, we understand such limiting procedures in terms of the extension of a bundle of C*-algebras to some limiting value of a parameter. We prove existence and uniqueness results for such extensions. Moreover, (...) we show that such extensions are functorial for the C*-product, dynamical automorphisms, and the Lie bracket (in the ℏ→0 case) on the fiber C*-algebras. (shrink)