Understanding is a central aim of science and highly important in present-day society. But what precisely is scientific understanding and how can it be achieved? This book answers these questions, through philosophical analysis and historical case studies, and presents a philosophical theory of scientific understanding that highlights its contextual nature.

Philosophers of quantum mechanics have generally addressed exceedingly simple systems. Laura Ruetsche offers a much-needed study of the interpretation of more complicated systems, and an underexplored family of physical theories, such as quantum field theory and quantum statistical mechanics, showing why they repay philosophical attention. She guides those familiar with the philosophy of ordinary QM into the philosophy of 'QM infinity', by presenting accessible introductions to relevant technical notions and the foundational questions they frame--and then develops and defends answers to (...) some of those questions. Finally, Ruetsche highlights ties between the foundational investigation of QM infinity and philosophy more broadly construed, in particular by using the interpretive problems discussed to motivate new ways to think about the nature of physical possibility and the problem of scientific realism. (shrink)

Mark Wilson presents a highly original and broad-ranging investigation of the way we get to grips with the world conceptually, and the way that philosophical problems commonly arise from this. He combines traditional philosophical concerns about human conceptual thinking with illuminating data derived from a large variety of fields including physics and applied mathematics, cognitive psychology, and linguistics. Wandering Significance offers abundant new insights and perspectives for philosophers of language, mind, and science, and will also reward the interest of psychologists, (...) linguists, and anyone curious about the mysterious ways in which useful language obtains its practical applicability. (shrink)

Four current accounts of theory reduction are presented, first informally and then formally: (1) an account of direct theory reduction that is based on the contributions of Nagel, Woodger, and Quine, (2) an indirect reduction paradigm due to Kemeny and Oppenheim, (3) an "isomorphic model" schema traceable to Suppes, and (4) a theory of reduction that is based on the work of Popper, Feyerabend, and Kuhn. Reference is made, in an attempt to choose between these schemas, to the explanation of (...) physical optics by Maxwell's electromagnetic theory, and to the revisions of genetics necessitated by partial biochemical reductions of genetics. A more general reduction schema is proposed which: (1) yields as special cases the four reduction paradigms considered above, (2) seems to be in better accord with both the canons of logic and actual scientific practice, and (3) clarifies the problems of meaning variance and ontological reduction. (shrink)

I argue that a common philosophical approach to the interpretation of physical theories—particularly quantum field theories—has led philosophers astray. It has driven many to declare the quantum field theories employed by practicing physicists, so-called ‘effective field theories’, to be unfit for philosophical interpretation. In particular, such theories have been deemed unable to support a realist interpretation. I argue that these claims are mistaken: attending to the manner in which these theories are employed in physical practice, I show that interpreting effective (...) field theories yields a robust foundation for a more refined approach to scientific realism in the context of quantum field theory. The paper concludes by briefly sketching some general morals for interpretive practice in the philosophy of physics. (shrink)

Relationships between current theories, and relationships between current theories and the sought theory of quantum gravity (QG), play an essential role in motivating the need for QG, aiding the search for QG, and defining what would count as QG. Correspondence is the broad class of inter-theory relationships intended to demonstrate the necessary compatibility of two theories whose domains of validity overlap, in the overlap regions. The variety of roles that correspondence plays in the search for QG are illustrated, using examples (...) from specific QG approaches. Reduction is argued to be a special case of correspondence, and to form part of the definition of QG. Finally, the appropriate account of emergence in the context of QG is presented, and compared to conceptions of emergence in the broader philosophy literature. It is argued that, while emergence is likely to hold between QG and general relativity, emergence is not part of the definition of QG, and nor can it serve usefully in the development and justification of the new theory. (shrink)

The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and conceptual, but mostly technical and mathematically rigorous, including over 500 references. For example, we sketch how certain intuitive ideas of the founders of quantum theory have fared in the light of current mathematical knowledge. One such idea that has certainly stood the test of time is (...) Heisenberg's `quantum-theoretical Umdeutung (reinterpretation) of classical observables', which lies at the basis of quantization theory. Similarly, Bohr's correspondence principle (in somewhat revised form) and Schroedinger's wave packets (or coherent states) continue to be of great importance in understanding classical behaviour from quantum mechanics. On the other hand, no consensus has been reached on the Copenhagen Interpretation, but in view of the parodies of it one typically finds in the literature we describe it in detail. On the assumption that quantum mechanics is universal and complete, we discuss three ways in which classical physics has so far been believed to emerge from quantum physics, namely in the limit h -> 0 of small Planck's constant (in a finite system), in the limit N goes to infinity of a large system with $N$ degrees of freedom (at fixed h), and through decoherence and consistent histories. The first limit is closely related to modern quantization theory and microlocal analysis, whereas the second involves methods of C*-algebras and the concepts of superselection sectors and macroscopic observables. In these limits, the classical world does not emerge as a sharply defined objective reality, but rather as an approximate appearance relative to certain ``classical" states and observables. Decoherence subsequently clarifies the role of such states, in that they are ``einselected", i.e. robust against coupling to the environment. Furthermore, the nature of classical observables is elucidated by the fact that they typically define (approximately) consistent sets of histories. This combination of ideas and techniques does not quite resolve the measurement problem, but it does make the point that classicality results from the elimination of certain states and observables from quantum theory. Thus the classical world is not created by observation (as Heisenberg once claimed), but rather by the lack of it. (shrink)

Stephen Hawking, among others, has proposed that the topological stability of a property of space-time is a necessary condition for it to be physically significant. What counts as stable, however, depends crucially on the choice of topology. Some physicists have thus suggested that one should find a canonical topology, a single ‘right’ topology for every inquiry. While certain such choices might be initially motivated, some little-discussed examples of Robert Geroch and some propositions of my own show that the main candidates—and (...) each possible choice, to some extent—faces the horns of a no-go result. I suggest that instead of trying to decide what the ‘right’ topology is for all problems, one should let the details of particular types of problems guide the choice of an appropriate topology. (shrink)

Philosophical reflection on quantum field theory has tended to focus on how it revises our conception of what a particle is. However, there has been relatively little discussion of the threat to the "reality" of particles posed by the possibility of inequivalent quantizations of a classical field theory, i.e., inequivalent representations of the algebra of observables of the field in terms of operators on a Hilbert space. The threat is that each representation embodies its own distinctive conception of what a (...) particle is, and how a "particle" will respond to a suitably operated detector. Our main goal is to clarify the subtle relationship between inequivalent representations of a field theory and their associated particle concepts. We also have a particular interest in the Minkowski versus Rindler quantizations of a free Boson field, because they respectively entail two radically different descriptions of the particle content of the field in the *very same* region of spacetime. We shall defend the idea that these representations provide *complementary descriptions* of the same state of the field against the claim that they embody completely *incommensurable theories* of the field. (shrink)

This exploration of the global structure of spacetime within the context of general relativity examines the causal and singular structures of spacetime, revealing some of the curious possibilities that are compatible with the theory, such as `time travel' and `holes' of various types. Investigations into the epistemic and modal structures of spacetime highlight the difficulties in ruling out such possibilities, unlikely as they may seem at first. The upshot seems to be that what counts as a `physically reasonable' spacetime structure (...) in modern physics is far from clear. (shrink)

Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of operator algebras, category theory, etc.. Given the rigor and generality of AQFT, it is a particularly apt tool for studying the foundations of QFT. This paper is a survey of AQFT, with an orientation towards foundational topics. In addition to covering the basics of the theory, (...) we discuss issues related to nonlocality, the particle concept, the field concept, and inequivalent representations. We also provide a detailed account of the analysis of superselection rules by Doplicher, Haag, and Roberts (DHR); and we give an alternative proof of Doplicher and Robert's reconstruction of fields and gauge group from the category of physical representations of the observable algebra. The latter is based on unpublished ideas due to J. E. Roberts and the abstract duality theorem for symmetric tensor *-categories, a self-contained proof of which is given in the appendix. (shrink)

Principles are central to physical reasoning, particularly in the search for a theory of quantum gravity, where novel empirical data are lacking. One principle widely adopted in the search for QG is ultraviolet completion: the idea that a theory should hold up to all possible high energies. We argue— contra standard scientific practice—that UV-completion is poorly motivated as a guiding principle in theory-construction, and cannot be used as a criterion of theory-justification in the search for QG. For this, we explore (...) the reasons for expecting, or desiring, a UV-complete theory, as well as analyse how UV-completion is used, and how it should be used, in various specific approaches to QG. 1Introduction 1.1Principles in theory development and evaluation 2Primer on UV-Completion, Renormalizability, and All That 2.1Renormalizability and UV-completion 2.2Other forms of UV-completion 3Why Should QG Be UV-Complete? 3.1UV-completion and fundamentality 3.2UV-completion and minimal length 4UV-Completion in Different Approaches to QG 4.1String theory 4.2Asymptotic safety 4.3Causal dynamical triangulation 4.4Higher derivative approaches 4.5Supergravity 4.6Causal set theory 4.7Canonical QG 4.8Loop quantum gravity 4.9Approaches based on alternative gravitational theories 4.10Emergent gravity approaches 5UV-Completion as a Guiding Principle in QG 6Conclusion. (shrink)

In times of crisis, when current theories are revealed as inadequate to task, and new physics is thought to be required—physics turns to re-evaluate its principles, and to seek new ones. This paper explores the various types, and roles of principles that feature in the problem of quantum gravity as a current crisis in physics. I illustrate the diversity of the principles being appealed to, and show that principles serve in a variety of roles in all stages of the crisis, (...) including in motivating the need for a new theory, and defining what this theory should be like. In particular, I consider: the generalised correspondence principle, UV-completion, background independence, and the holographic principle. I also explore how the current crisis fits with Friedman’s view on the roles of principles in revolutionary theory-change, finding that while many key aspects of this view are not represented in quantum gravity, the view could potentially offer a useful diagnostic, and prescriptive strategy. This paper is intended to be relatively non-technical, and to bring some of the philosophical issues from the search for quantum gravity to a more general philosophical audience interested in the roles of principles in scientific theory-change. (shrink)

Intertheoretic reduction in physics aspires to be both to be explanatory and perfectly general: it endeavors to explain why an older, simpler theory continues to be as successful as it is in terms of a newer, more sophisticated theory, and it aims to relate or otherwise account for as many features of the two theories as possible. Despite often being introduced as straightforward cases of intertheoretic reduction, candidate accounts of the reduction of general relativity to Newtonian gravitation have either been (...) insufficiently general or rigorous, or have not clearly been able to explain the empirical success of Newtonian gravitation. Building on work by Ehlers and others, I propose a different account of the reduction relation that is perfectly general and meets the explanatory demand one would make of it. In doing so, I highlight the role that a topology on the collection of all spacetimes plays in defining the relation, and how the selection of the topology corresponds with broader or narrower classes of observables that one demands be well-approximated in the limit. (shrink)

Analogue experiments have attracted interest for their potential to shed light on inaccessible domains. For instance, ‘dumb holes’ in fluids and Bose–Einstein condensates, as analogues of black holes, have been promoted as means of confirming the existence of Hawking radiation in real black holes. We compare analogue experiments with other cases of experiment and simulation in physics. We argue—contra recent claims in the philosophical literature—that analogue experiments are not capable of confirming the existence of particular phenomena in inaccessible target systems. (...) As they must assume the physical adequacy of the modelling framework used to describe the inaccessible target system, arguments to the conclusion that analogue experiments can yield confirmation for phenomena in those target systems, such as Hawking radiation in black holes, beg the question. (shrink)

Cosmologists often use certain global properties to exclude "physically unreasonable" cosmological models from serious consideration. But, on what grounds should these properties be regarded as "physically unreasonable" if we cannot rule out, even with a robust type of inductive reasoning, the possibility of the properties obtaining in our own universe?

On standard accounts of scientific theorizing, the role of idealizations is to facilitate the analysis of some real world system by employing a simplified representation of the target system, raising the obvious worry about how reliable knowledge can be obtained from inaccurate descriptions. The idealizations involved in the Aharonov–Bohm effect do not, it is claimed, fit this paradigm; rather the target system is a fictional system characterized by features that, though physically possible, are not realized in the actual world. The (...) point of studying such a fictional system is to understand the foundations of quantum mechanics and how its predictions depart from those of classical mechanics. The original worry about the use of idealizations is replaced by a new one; namely, how can actual world experiments serve to confirm the AB effect if it concerns the behavior of a fictional system? Struggle with this issue helps to account for the fact that almost three decades elapsed before a consensus emerged that the predicted AB effect had received solid experimental support. Standard accounts of idealizations tout the role they play in making tractable the analysis of the target system; by contrast, the idealizations involved in the AB effect make its analysis both conceptually and mathematically challenging. The idealizations required for the AB effect are also responsible for the existence of unitarily inequivalent representations of the canonical commutation relations and of the current algebra, representations which an observer confined to the electron’s configuration space could invoke to ‘explain’ AB-type effect without the need to posit a hidden magnetic field. The goal of this paper is to bring to the attention of the philosophers of science these and other aspects of the AB effect which are neglected or inadequately treated in literature. (shrink)

Does the viability of the discovery program depend on showing either (1) that methods of generating new problem solutions, per se, have special probative weight (the per se thesis); or, (2) that the original conception of an idea is logically continuous with its justification (anti-divorce thesis)? Many writers have identified these as the key issues of the discovery debate. McLaughlin, Pera, and others recently have defended the discovery program by attacking the divorce thesis, while Laudan has attacked the discovery program (...) by rejecting the per se thesis. This disagreement over the central issue has led to communication breakdown. I contend that both friends and foes of discovery mistake the central issues. Recognizing a form of divorce helps rather than hurts the discovery program. However, the per se thesis is not essential to the program (nor is the related debate over novel prediction); hence, the status of the per se thesis is a side issue. With these clarifications in hand, we can proceed to the next stage of the discovery debate--the development (or revival) of a generative conception of justification which goes beyond consequentialism to forge a strong linkage of generation (or rather, generatability) with justification. (shrink)

This paper argues that the much discussed issue between "scientific realism" and "instrumentalism" has not been clearly drawn. Particular attention is paid to the claim that only realism can "explain" the success of scientific theories and---more especially---the progressively increasing success of such theories in a coherent line of inquiry. This claim is used to attempt to reach a clearer conception of the content of the realist thesis that underlies it; but, it is here contended, that attempt fails, and the claim (...) itself hangs in the air. A series of increasingly sophisticated versions of the "instrumentalist" thesis is considered, and both these and the contentions of realism are placed in relation both to particular examples of scientific development and positions historically maintained by philosophers and by scientists. The author’s conclusion is that, when the positions are assessed against the background of the actual history of science, each of the contrary doctrines, interpreted with excessive simplicity, is inadequate as a theory of the dialectic of scientific development; each, so interpreted, has contributed in important instances to actual damage to investigations by great scientists ; whereas in both the theoretical statements and the actual practice of the most sophisticated philosophers/scientists, important aspects of realism and instrumentalism are present together in such a way that the alleged contradiction between them vanishes. (shrink)

This history of physics focuses on the question, "How do bodies act on one another across space?" The variety of answers illustrates the function of fundamental analogies or models in physics as well as the role of so-called unobservable entities. Forces and Fields presents an in-depth look at the science of ancient Greece, and it examines the influence of antique philosophy on seventeenth-century thought. Additional topics embrace many elements of modern physics--the empirical basis of quantum mechanics, wave-particle duality and the (...) uncertainty principle, and the action-at-a-distance theory of Wheeler and Feynman. 1961 ed. (shrink)

The classical field theories that underlie the quantum treatments of the electromagnetic, weak, and strong forces share a peculiar feature: specifying the initial state of the field determines the evolution of some degrees of freedom of the theory while leaving the evolution of some others wholly arbitrary. This strongly suggests that some of the variables of the standard state space lack physical content-intuitively, the space of states of such a theory is of higher dimension than the corresponding space of genuine (...) physical possibilities. The structure of such theories can helpfully be characterized in terms of the action of symmetry groups on their space of states; and the conceptual problems surrounding their strange behavior can be sharpened in light of the observation that it is usually possible to eliminate the redundant variables associated with these symmetries-which turn out to be precisely those variables whose evolution is unconstrained by the dynamical laws of the theory. This paper discusses this approach, uses it to frame questions about the interpretation of classical gauge theories, and to reflect (pessimistically) on our prospects of reaching satisfactory answers to these questions. (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)

A conventional wisdom about the progress of physics holds that successive theories wholly encompass the domains of their predecessors through a process that is often called reduction. While certain influential accounts of inter-theory reduction in physics take reduction to require a single "global" derivation of one theory's laws from those of another, I show that global reductions are not available in all cases where the conventional wisdom requires reduction to hold. However, I argue that a weaker "local" form of reduction, (...) which defines reduction between theories in terms of a more fundamental notion of reduction between models of a single fixed system, is available in such cases and moreover suffices to uphold the conventional wisdom. To illustrate the sort of fixed-system, inter-model reduction that grounds inter-theoretic reduction on this picture, I specialize to a particular class of cases in which both models are dynamical systems. I show that reduction in these cases is underwritten by a mathematical relationship that follows the broad prescriptions of Nagel/Schaffner reduction, and support this claim with several examples. Moreover, I show that this broadly Nagelian analysis of inter-model reduction encompasses several cases that are sometimes cited as instances of the "physicist's" limit-based notion of reduction. (shrink)

Several philosophers of science have claimed that the correspondence principle can be generalized from quantum physics to all of (particularly physical) science and that in fact it constitutes one of the major heuristical rules for the construction of new theories. In order to evaluate these claims, first the use of the correspondence principle in (the genesis of) quantum mechanics will be examined in detail. It is concluded from this and from other examples in the history of science that the principle (...) should be qualified with respect to its nature and relativized with respect to its scope of application. At the same time this conclusion implies a qualification and a relativization of the heuristic power of the principle. Generally speaking, intertheoretical correspondence is primarily of a formal-mathematical and empirical but not of a conceptual nature. Moreover, it only applies to certain parts of the theories involved. Finally, a number of philosophical justifications of the principle are discussed and some conclusions are drawn concerning the debates on theory reduction and on the discovery-justification distinction. (shrink)

On standard accounts of scientific theorizing, the role of idealizations is to facilitate the analysis of some real world system by employing a simplified representation of the target system, raising the obvious worry about how reliable knowledge can be obtained from inaccurate descriptions. The idealizations involved in the Aharonov–Bohm effect do not, it is claimed, fit this paradigm; rather the target system is a fictional system characterized by features that, though physically possible, are not realized in the actual world. The (...) point of studying such a fictional system is to understand the foundations of quantum mechanics and how its predictions depart from those of classical mechanics. The original worry about the use of idealizations is replaced by a new one; namely, how can actual world experiments serve to confirm the AB effect if it concerns the behavior of a fictional system? Struggle with this issue helps to account for the fact that almost three decades elapsed before a consensus emerged that the predicted AB effect had received solid experimental support. Standard accounts of idealizations tout the role they play in making tractable the analysis of the target system; by contrast, the idealizations involved in the AB effect make its analysis both conceptually and mathematically challenging. The idealizations required for the AB effect are also responsible for the existence of unitarily inequivalent representations of the canonical commutation relations and of the current algebra, representations which an observer confined to the electron’s configuration space could invoke to ‘explain’ AB-type effect without the need to posit a hidden magnetic field. The goal of this paper is to bring to the attention of the philosophers of science these and other aspects of the AB effect which are neglected or inadequately treated in literature. (shrink)

If a classical system has infinitely many degrees of freedom, its Hamiltonian quantization need not be unique up to unitary equivalence. I sketch different approaches (Hilbert space and algebraic) to understanding the content of quantum theories in light of this non‐uniqueness, and suggest that neither approach suffices to support explanatory aspirations encountered in the thermodynamic limit of quantum statistical mechanics.

An in-depth look at the science of ancient Greece, this volume examines the influence of antique philosophy on 17th-century thought. Additional topics embrace many elements of modern physics: the empirical basis of quantum mechanics, wave-particle duality and the uncertainty principle, and the action-at-a-distance theory of Wheeler and Feynman. 1961 edition.

Cancer research is experiencing ‘paradigm instability’, since there are two rival theories of carcinogenesis which confront themselves, namely the somatic mutation theory and the tissue organization field theory. Despite this theoretical uncertainty, a huge quantity of data is available thanks to the improvement of genome sequencing techniques. Some authors think that the development of new statistical tools will be able to overcome the lack of a shared theoretical perspective on cancer by amalgamating as many data as possible. We think instead (...) that a deeper understanding of cancer can be achieved by means of more theoretical work, rather than by merely accumulating more data. To support our thesis, we introduce the analytic view of theory development, which rests on the concept of plausibility, and make clear in what sense plausibility and probability are distinct concepts. Then, the concept of plausibility is used to point out the ineliminable role played by the epistemic subject in the development of statistical tools and in the process of theory assessment. We then move to address a central issue in cancer research, namely the relevance of computational tools developed by bioinformaticists to detect driver mutations in the debate between the two main rival theories of carcinogenesis. Finally, we briefly extend our considerations on the role that plausibility plays in evidence amalgamation from cancer research to the more general issue of the divergences between frequentists and Bayesians in the philosophy of medicine and statistics. We argue that taking into account plausibility-based considerations can lead to clarify some epistemological shortcomings that afflict both these perspectives. (shrink)

The physical, mathematical, and philosophical foundations of the quantum theory of free Bose fields in fixed general relativistic spacetimes are examined. It is argued that the theory is logically and mathematically consistent whereas semiclassical prescriptions for incorporating the back-reaction of the quantum field on the geometry lead to inconsistencies. Still, the relations and heuristic value of the semiclassical approach to canonical and covariant schemes of quantum gravity-plus-matter are assessed. Both conventional and rigorous formulations of the theory and of its principal (...) predictions, cosmological particle creation and horizon radiation, are expounded and compared. Special attention is devoted to spacetime properties needed for the existence or uniqueness of the relevant theoretical elements , renormalization of the stress tensor). The emergence of unitarily inequivalent representations in a single dynamical context is used as motivation for the introduction of the abstract $\rm C\sp{\*}$-algebraic axiomatic formalism. The operationalist and conventionalist claims of the original abstract algebraic program are criticized in favor of its tempered outgrowth, local quantum physics. The interpretation of the theory as a wave mechanics of classical field configurations, deriving from the Schrodinger representations of the abstract algebra, is discussed and is found superior, at least on the level of analogy, to particle or harmonic oscillator interpretations. Further, it is argued that the various detector results and the Fulling nonuniqueness problem do not undermine the particle concept in the ways commonly claimed. In particular, arguments are offered against the attribution of particle status to the Rindler quanta, against the physical realizability of the Rindler vacuum, and against the more general notion of observer-dependence as to the definition of 'particle' or 'vacuum'. However, the question of the ontological status of particles is raised in terms of the consistency of quantum field theory with non-reductive realism about particles, the latter being conceived as entities exhibiting attributes of discreteness and localizability. Two arguments against non-reductive realism about particles, one from axiomatic algebraic local quantum theory in Minkowski spacetime and one from quantum field theory in curved spacetime, are developed. (shrink)

Within the traditional Hilbert space formalism of quantum mechanics, it is not possible to describe a particle as possessing, simultaneously, a sharp position value and a sharp momentum value. Is it possible, though, to describe a particle as possessing just a sharp position value (or just a sharp momentum value)? Some, such as Teller, have thought that the answer to this question is No - that the status of individual continuous quantities is very different in quantum mechanics than in classical (...) mechanics. On the contrary, I shall show that the same subtle issues arise with respect to continuous quantities in classical and quantum mechanics; and that it is, after all, possible to describe a particle as possessing a sharp position value without altering the standard formalism of quantum mechanics. (shrink)

Here, we clarify the relationship among three space-time conditions of interest: geodesic completeness, hole-freeness, and inextendibility. In addition, we introduce a related fourth condition: effective completeness.

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)

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.

We show that Bohr's principle of complementarity between position and momentum descriptions can be formulated rigorously as a claim about the existence of representations of the canonical commutation relations. In particular, in any representation where the position operator has eigenstates, there is no momentum operator, and vice versa. Equivalently, if there are nonzero projections corresponding to sharp position values, all spectral projections of the momentum operator map onto the zero element.

In this note, we cast doubt on the requirement of spacetime inextendibility; it is not at all clear that our universe is “as large as it can be.”.

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)