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It is proposed that we use the term “approximation” for inexact description of a target system and “idealization” for another system whose properties also provide an inexact description of the target system. Since systems generated by a limiting process can often have quite unexpected, even inconsistent properties, familiar limit systems used in statistical physics can fail to provide idealizations, but are merely approximations. A dominance argument suggests that the limiting idealizations of statistical physics should be demoted to approximations. |
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Recent work by Robert Batterman and Alexander Rueger has brought attention to cases in physics in which governing laws at the base level “break down” and singular limit relations obtain between base- and upper-level theories. As a result, they claim, these are cases with emergent upper-level properties. This paper contends that this inference—from singular limits to explanatory failure, novelty or irreducibility, and then to emergence—is mistaken. The van der Pol nonlinear oscillator is used to show that there can be a (...) |
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Classical mechanics and quantum mechanics are two of the most successful scientific theories ever discovered, and yet how they can describe the same world is far from clear: one theory is deterministic, the other indeterministic; one theory describes a world in which chaos is pervasive, the other a world in which chaos is absent. Focusing on the exciting field of 'quantum chaos', this book reveals that there is a subtle and complex relation between classical and quantum mechanics. It challenges the (...) |
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Robert Batterman examines a form of scientific reasoning called asymptotic reasoning, arguing that it has important consequences for our understanding of the scientific process as a whole. He maintains that asymptotic reasoning is essential for explaining what physicists call universal behavior. With clarity and rigor, he simplifies complex questions about universal behavior, demonstrating a profound understanding of the underlying structures that ground them. This book introduces a valuable new method that is certain to fill explanatory gaps across disciplines. |
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[Time, the fundamental dimension of our existence, has fascinated artists, philosophers, and scientists of every culture and every century. All of us can remember a moment as a child when time became a personal reality, when we realized what a "year" was, or asked ourselves when "now" happened. Common sense says time moves forward, never backward, from cradle to grave. Nevertheless, Einstein said that time is an illusion. Nature's laws, as he and Newton defined them, describe a timeless, deterministic universe (...) |
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The aim of this paper is twofold: First, to present an examination of the principles underlying gauge field theories. I shall argue that there are two principles directly connected to the two well-known theorems of Emmy Noether concerning global and local symmetries of the free matter-field Lagrangian, in the following referred to as "conservation principle" and "gauge principle". Since both these express nothing but certain symmetry features of the free field theory, they are not sufficient to derive a true interaction (...) |
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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. |
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Kim’s model of ‘functional reduction’ of properties is shown to fail in a class of cases from physics involving properties at different spatial levels. The diagnosis of this failure leads to a non-reductive account of the relation of micro and macro properties. |
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In 1894 Pierre Curie announced what has come to be known as Curie's Principle: the asymmetry of effects must be found in their causes. In the same publication Curie discussed a key feature of what later came to be known as spontaneous symmetry breaking: the phenomena generally do not exhibit the symmetries of the laws that govern them. Philosophers have long been interested in the meaning and status of Curie's Principle. Only comparatively recently have they begun to delve into the (...) |
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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 (...) |
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In this article we argue that idealizations and limiting cases in models play an exploratory role in science. Four senses of exploration are presented: exploration of the structure and representational capacities of theory; proof-of-principle demonstrations; potential explanations; and exploring the suitability of target systems. We illustrate our claims through three case studies, including the Aharonov-Bohm effect, the emergence of anyons and fractional quantum statistics, and the Hubbard model of the Mott phase transitions. We end by reflecting on how our case (...) |
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The orthodox characterization of spontaneous symmetry breaking in statistical mechanics appeals to novel properties of systems with infinite degrees of freedom, namely, the existence of multiple equilibrium states. This raises the same puzzles about the status of the thermodynamic limit fueling recent debates about phase transitions. I argue that there are prospects of explaining the success of the standard approach to SSB in terms of the properties of large finite systems. Consequently, despite initial appearances, the need to account for SSB (...) |
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In this paper, I appeal to a distinction made by David Lewis between identifying and determining semantic content in order to defend a complementarity thesis expressed by Anjan Chakravartty. The thesis states that there is no conflict between informational and functional views of scientific modeling and representation. I then apply the complementarity thesis to well-received theories of pictorial representation, thereby stressing the fruitfulness of drawing an analogy between the nature of fictions in art and in science. I end by attending (...) |
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This paper aims to draw attention to an explanatory problem posed by the existence of multiply realized or universal behavior exhibited by certain physical systems. The problem is to explain how it is possible that systems radically distinct at lower-scales can nevertheless exhibit identical or nearly identical behavior at upper-scales. Theoretically this is reflected by the fact that continuum theories such as fluid mechanics are spectacularly successful at predicting, describing, and explaining fluid behaviors despite the fact that they do not (...) |
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This paper addresses issues surrounding the concept of geometric phase or "anholonomy". Certain physical phenomena apparently require for their explanation and understanding, reference to toplogocial/geometric features of some abstract space of parameters. These issues are related to the question of how gauge structures are to be interpreted and whether or not the debate over their "reality" is really going to be fruitful. |
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This paper looks at the nature of idealizations and representational structures appealed to in the context of the fractional quantum Hall effect, specifically, with respect to the emergence of anyons and fractional statistics. Drawing on an analogy with the Aharonov–Bohm effect, it is suggested that the standard approach to the effects— the topological approach to fractional statistics—relies essentially on problematic idealizations that need to be revised in order for the theory to be explanatory. An alternative geometric approach is outlined and (...) |
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This article discusses minimal model explanations, which we argue are distinct from various causal, mechanical, difference-making, and so on, strategies prominent in the philosophical literature. We contend that what accounts for the explanatory power of these models is not that they have certain features in common with real systems. Rather, the models are explanatory because of a story about why a class of systems will all display the same large-scale behavior because the details that distinguish them are irrelevant. This story (...) |
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I present a novel approach to the scholarly debate that has arisen with respect to the philosophical import one should infer from scientific accounts of phase transitions by appealing to a distinction between representation understood as denotation, and faithful representation understood as a type of guide to ontology. It is argued that the entire debate is misguided, for it stems from a pseudo-paradox that does not license the type of claims made by scholars and that what is really interesting about (...) |
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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 (...) |
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This paper explicates two notions of emergencewhich are based on two ways of distinguishinglevels of properties for dynamical systems.Once the levels are defined, the strategies ofcharacterizing the relation of higher level to lower levelproperties as diachronic and synchronic emergenceare the same. In each case, the higher level properties aresaid to be emergent if they are novel or irreducible with respect to the lower level properties. Novelty andirreducibility are given precise meanings in terms of the effectsthat the change of a bifurcation (...) |
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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 (...) |
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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 (...) |
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Two alternative accounts of quantum spontaneous symmetry breaking (SSB) are compared and one of them, the decompositional account in the algebraic approach, is argued to be superior for understanding quantum SSB. Two exactly solvable models are given as applications of our account -- the Weiss-Heisenberg model for ferromagnetism and the BCS model for superconductivity. Finally, the decompositional account is shown to be more conducive to the causal explanation of quantum SSB. |
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Taking scientific practice as its starting point, this book charts the complex territory of models used in science. It examines what scientific models are and what their function is. Reliance on models is pervasive in science, and scientists often need to construct models in order to explain or predict anything of interest at all. The diversity of kinds of models one finds in science – ranging from toy models and scale models to theoretical and mathematical models – has attracted attention (...) |
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This is a prize-winning study of an area of physics not previously explored by philosophy: gauge theory. Gauge theories have provided our most successful representations of the fundamental forces of nature. But how do such representations work? Healey defends an original answer to this question. |
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At first sight the Aharonov- Bohm effect appears nonlocal, though not in the way EPR/Bell correlations are generally acknowledged to be nonlocal. This paper applies an analysis of nonlocality to the Aharonov- Bohm effect to show that its peculiarities may be blamed either on a failure of a principle of local action or on a failure of a principle of separability. Different interpretations of quantum mechanics disagree on how blame should be allocated. The parallel between the Aharonov- Bohm effect and (...) |
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Quantum mechanics predicted the Aharonov-Bohm effect and violations of Bell inequalities before either phenomenon was experimentally verified. It is now commonly taken to explain both phenomena. Maudlin has pointed out significant disanalogies between these phenomena. But he has failed to appreciate the striking analogy that emerges when one examines the structure of their quantum mechanical explanations. The fact that each may be explained quantum mechanically in terms of a locally-acting, but nonseparable process suggests that the lesson of quantum nonlocality may (...) |
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How should we characterise the observable aspects of quantum theory? This paper argues that philosophers and physicists should jettison a standard dogma: that observables must be represented by self-adjoint or Hermitian operators. Four classes of non-standard observables are identified: normal operators, symmetric operators, real-spectrum operators, and none of these. The philosophical and physical implications of each are explored. |
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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 (...) |
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Phase transitions are an important instance of putatively emergent behavior. Unlike many things claimed emergent by philosophers, the alleged emergence of phase transitions stems from both philosophical and scientific arguments. Here we focus on the case for emergence built from physics, in particular, arguments based upon the infinite idealization invoked in the statistical mechanical treatment of phase transitions. After teasing apart several challenges, we defend the idea that phase transitions are best thought of as conceptually novel, but not ontologically or (...) |
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According to standard (quantum) statistical mechanics, the phenomenon of a phase transition, as described in classical thermodynamics, cannot be derived unless one assumes that the system under study is infinite. This is naturally puzzling since real systems are composed of a finite number of particles; consequently, a well‐known reaction to this problem was to urge that the thermodynamic definition of phase transitions (in terms of singularities) should not be “taken seriously.” This article takes singularities seriously and analyzes their role by (...) |
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Thermodynamics and Statistical Mechanics are related to one another through the so-called "thermodynamic limit'' in which, roughly speaking the number of particles becomes infinite. At critical points (places of physical discontinuity) this limit fails to be regular. As a result, the "reduction'' of Thermodynamics to Statistical Mechanics fails to hold at such critical phases. This fact is key to understanding an argument due to Craig Callender to the effect that the thermodynamic limit leads to mistakes in Statistical Mechanics. I discuss (...) |
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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 (...) |
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It is argued that seemingly “merely technical” issues about the existence and uniqueness of self-adjoint extensions of symmetric operators in quantum mechanics have interesting implications for foundations problems in classical and quantum physics. For example, pursuing these technical issues reveals a sense in which quantum mechanics can cure some of the forms of indeterminism that crop up in classical mechanics; and at the same time it reveals the possibility of a form of indeterminism in quantum mechanics that is quite distinct (...) |
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I argue that the metaphysical import of the Aharonov-Bohm effect has been overstated: correctly understood, it does not require either rejection of gauge invariance or any novel form of nonlocality. The conclusion that it does require one or the other follows from a failure to keep track, in the analysis, of the complex scalar field to which the magnetic vector potential is coupled. Once this is recognised, the way is clear to a local account of the ontology of electrodynamics ; (...) |
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A solution to the measurement problem of quantum mechanics is proposed within the framework of an intepretation according to which only quantum systems with an infinite number of degrees of freedom have determinate properties, i.e., determinate values for (some) observables of the theory. The important feature of the infinite case is the existence of many inequivalent irreducible Hilbert space representations of the algebra of observables, which leads, in effect, to a restriction on the superposition principle, and hence the possibility of (...) |
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It is often said that the Aharonov-Bohm effect shows that the vector potential enjoys more ontological significance than we previously realized. But how can a quantum-mechanical effect teach us something about the interpretation of Maxwell's theory—let alone about the ontological structure of the world—when both theories are false? I present a rational reconstruction of the interpretative repercussions of the Aharonov-Bohm effect, and suggest some morals for our conception of the interpretative enterprise. |
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Richard Healey argues that the Aharonov- Bohm effect demands the recognition of either nonlocal or nonseparable physics in much the way that violations of Bell's inequality do. A careful examination of the effect and the arguments, though, shows that Healey's interpretation of the Aharonov- Bohm effect depends critically on his interpretation of gauge theories, and that the analogy with violations of Bell's inequalities fails. |
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Recent experiments undertaken by Caprez, Barwick, and Batelaan should clarify the connections between classical and quantum theories in connection with the Aharonov–Bohm phase shift. It is pointed out that resistive aspects for the solenoid current carriers play a role in the classical but not the quantum analysis for the phase shift. The observed absence of a classical lag effect for a macroscopic solenoid does not yet rule out the possibility of a lag explanation of the observed phase shift for a (...) |
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In this paper I show how certain requirements must be set on any tenable account of scientific representation, such as the requirement allowing for misrepresentation. I then continue to argue that two leading accounts of scientific representation— the inferential account and the interpretational account—are flawed for they do not satisfy such requirements. Through such criticism, and drawing on an analogy from non-scientific representation, I also sketch the outline of a superior account. In particular, I propose to take epistemic representations to (...) |
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