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)

We offer a framework for organizing the literature regarding the debates revolving around infinite idealizations in science, and a short summary of the contributions to this special issue.

One realist response to the pessimistic meta-induction distinguishes idle theoretical wheels from aspects of successful theories we can expect to persist and espouses realism about the latter. Implementing the response requires a strategy for identifying the distinguished aspects. The strategy I will call renormalization group realism has the virtue of directly engaging the gears of our best current physics—perturbative quantum field theories. I argue that the strategy, rather than disarming the skeptical possibilities evinced by the pessimistic meta-induction, forces them to (...) retreat a level. I also suggest that those skeptical possibilities continue to carry force. (shrink)

The availability of unitarily inequivalent representations of the canonical commutation relations constituting a quantization of a classical field theory raises questions about how to formulate and pursue quantum field theory. In a minimally technical way, I explain how these questions arise and how advocates of the Hilbert space and of the algebraic approaches to quantum theory might answer them. Where these answers differ, I sketch considerations for and against each approach, as well as considerations which might temper their apparent rivalry.

Taking Arthur Fine’s The Shaky Game as my inspiration, and the recent 25th anniversary of the publication of that work as the occasion to exercise that inspiration, I sketch an alternative to the “Naturalism” prevalent among philosophers of physics. Naturalism is a methodology eventuating in a metaphysics. The methodology is to seek the deep framework assumptions that make the best sense of science; the metaphysics is furnished by those assumptions and supported by their own support of science. The alternative presented (...) here, which I call “Locavoracity,” shares Naturalism’s commitment to making sense of science, but alters Naturalism’s methodology. The Locavore’s sense-making projects are piecemeal, rather than sweeping. The Locavore’s hypothesis is that the collection of local sense-making projects fails to issue a single overarching unifying framework deserving of the title “the metaphysics that makes the best sense of science.” I muster some examples supporting the Locavore hypothesis from the interpretation of quantum field theories. (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.

Stephen Hawking has argued that universes containing evaporating black holes can evolve from pure initial states to mixed final ones. Such evolution is non-unitary and so contravenes fundamental quantum principles on which Hawking's analysis was based. It disables the retrodiction of the universe's initial state from its final one, and portends the time-asymmetry of quantum gravity. Small wonder that Hawking's paradox has met with considerable resistance. Here we use a simple result for C*-algebras to offer an argument for pure-to-mixed state (...) evolution in black hole evaporation, and review responses to the Hawking paradox with respect to how effectively they rebut this argument. (shrink)

Starting from the standard quantum formalism for a single spin 1/2 system (e.g., an electron), this essay develops a model rich enough not only to afford an explication of symmetry breaking but also to frame questions about how to circumscribe physical possibility on behalf of theories that countenance symmetry breaking.

We discuss the intertwined topics of Fulling non‐uniqueness and the Unruh effect. The Fulling quantization, which is in some sense the natural one for an observer uniformly accelerated through Minkowski spacetime to adopt, is often heralded as a quantization of the Klein‐Gordon field which is both physically relevant and unitarily inequivalent to the standard Minkowski quantization. We argue that the Fulling and Minkowski quantizations do not constitute a satisfactory example of physically relevant, unitarily inequivalent quantizations, and indicate what it would (...) take to settle the open question of whether a satisfactory example exists. A popular gloss on the Unruh effect has it that an observer uniformly accelerated through the Minkowski vacuum experiences a thermal flux of Rindler quanta. Taking the Unruh effect, so glossed, to establish that the notion of particle must be relativized to a reference frame, some would use it to demote the particle concept from fundamental status. We explain why technical results do not support the popular gloss and why the attempted demotion of the particle concept is both unsuccessful and unnecessary. Fulling non‐uniqueness and the Unruh effect merit attention despite these negative verdicts because they provide excellent vehicles for illustrating key concepts of quantum field theory and for probing foundational issues of considerable philosophical interest. (shrink)

The simplest case of quantum field theory on curved spacetime—that of the Klein–Gordon field on a globally hyperbolic spacetime—reveals a dilemma: In generic circumstances, either there is no dynamics for this quantum field, or else there is a dynamics that is not unitarily implementable. We do not try to resolve the dilemma here, but endeavour to spell out the consequences of seizing one or the other horn of the dilemma.

A normal state on a von Neumann algebra defines a countably additive probability measure over its projection lattice. The von Neumann algebras familiar from ordinary QM are algebras of all the bounded operators on a Hilbert space H, aka Type I factor von Neumann algebras. Their normal states are density operator states, and can be pure or mixed. In QFT and the thermodynamic limit of QSM, von Neumann algebras of more exotic types abound. Type III von Neumann algebras, for instance, (...) have no pure normal states; the pure states they do have fail to be countably additive. I will catalog a number of temptations to accord physical significance to non-normal states, and then give some reasons to resist these temptations: pure though they may be, non-normal states on non-Type I factor von Neumann algebras can't do the interpretive work we've come to expect from pure states on Type I factors; our best accounts of state preparation don't work for the preparation of non-normal states; there is a sense in which non-normal states fail to instantiate the laws of quantum mechanics. (shrink)

Philosophical accounts of quantum theory commonly suppose that the observables of a quantum system form a Type-I factor von Neumann algebra. Such algebras always have atoms, which are minimal projection operators in the case of quantum mechanics. However, relativistic quantum field theory and the thermodynamic limit of quantum statistical mechanics make extensive use of von Neumann algebras of more general types. This chapter addresses the question whether interpretations of quantum probability devised in the usual manner continue to apply in the (...) more general setting. Features of non-type I factor von Neumann algebras are cataloged. It is shown that these novel features do not cause the familiar formalism of quantum probability to falter, since Gleason's Theorem and the Lüders Rule can be generalized. However, the features render the problem of the interpretation of quantum probability more intricate. (shrink)

When Sandra Harding called for an epistemology of science whose systematic attention to the gendered Status of epistemic agents renders it ‘less partial and distorted’ than ‘traditional’ epistemologies, some commentators recoiled in horror. Propelled by ‘a mad form of the genetic fallacy’ they said, she descends ‘the slide to an arational account of science.’ On a less melodramatic reading, feminist epistemologies such as Harding's advocate not irrationalism, but senses of rationality more expanded than those which they associate with ‘traditional’ epistemology.

Some feminist epistemologists make the radical claim that there are varieties of epistemically valid warrant that agents access only through having lived particular types of contingent history, varieties of epistemic warrant to which, moreover, the confirmation-theoretic accounts of warrant favored by some traditional epistemologists are inapplicable. I offer Aristotelian virtue as a model for warrant of this sort, and use loosely Aristotelian vocabulary to express, and begin to evaluate, a range of feminist epistemological positions.

A number of arguments have been given to show that the modal interpretation of ordinary nonrelativistic quantum mechanics cannot be consistently extended to the relativistic setting. We find these arguments inconclusive. However, there is a prima facie reason to think that a tension exists between the modal interpretation and relativistic invariance; namely, the best candidate for a modal interpretation adapted to relativistic quantum field theory, a prescription due to Rob Clifton, comes out trivial when applied to a number of systems (...) of physical interest. However, it is far from clear whether this difficulty for the modal interpretation is traceable to relativistic invariance per se or to the infinite number of degrees of freedom involved. In any case, the proponents of the modal interpretation have work to do. (shrink)

An “intrinsically mixed” state is a mixed state of a system that is ‘orthogonal’ to every pure state of that system. Although the presence of such states in the quantum theories of infinite systems is well known to those who work with such theories, intrinsically mixed states are virtually unheralded in the philosophical literature. Rob Clifton was thoroughly familiar with intrinsically mixed states. I aim here to introduce them to a wider audience—and to encourage that audience to cultivate their acquaintance (...) by suggesting that intrinsically mixed states undermine assumptions framing standard discussions of the quantum measurement problem. (shrink)

: Some feminist epistemologists make the radical claim that there are varieties of epistemically valid warrant that agents access only through having lived particular types of contingent history, varieties of epistemic warrant to which, moreover, the confirmation-theoretic accounts of warrant favored by some traditional epistemologists are inapplicable. I offer Aristotelian virtue as a model for warrant of this sort, and use loosely Aristotelian vocabulary to express, and begin to evaluate, a range of feminist epistemological positions.

This chapter contains sections titled: Introduction: Interpretation Bohr and Complementarity The Einstein‐Podolsky‐Rosen (EPR) Argument Bell's Theorem and Other No‐Go Results The Measurement Problem Future Directions: Interpreting QFT.

Van Fraassen's 1991 modal interpretation of Quantum Mechanics offers accounts of measurement and state preparation. I argue that both accounts overlook a class of interactions I call General Unitary Measurements, or GUMs. Ironically, GUMs are significant for van Fraassen's account of measurement because they challenge it, and significant for his account of preparation because they simplify it. Van Fraassen's oversight prompts a question about modal interpretations: developed to account for ideal measurement outcomes, can they consistently account as well for the (...) whole horizon of laboratory practices by which we investigate QM? (shrink)

According to a regnant criterion of physical equivalence for quantum theories, a quantum field theory (QFT) typically admits continuously many physically inequivalent realizations. This, the second of a two-part introduction to topics in the philosophy of QFT, continues the investigation of this alarming circumstance. It begins with a brief catalog of quantum field theoretic examples of this non-uniqueness, then presents the basics of the algebraic approach to quantum theories, which discloses a structure common even to ‘physically inequivalent’ realizations of a (...) QFT. Finally, it introduces and evaluates a handful of strategies for interpreting quantum theories in the face of the non-uniqueness of their Hilbert space representations. (shrink)

This is the first of a two-part introduction to some interpretive questions that arise in connection with quantum field theories (QFTs). Some of these questions are continuous with those familiar from the discussion of ordinary non-relativistic quantum mechanics (QM). For example, questions about locality can be rigorously posed and fruitfully pursued within the framework of QFT. A stark disanalogy between QFTs and ordinary QM – the former, but not the latter, typically admit infinitely many putatively physically inequivalent realizations – prompts (...) relatively novel questions, questions about how to understand and adjudicate different strategies for equipping quantum theories with content. Part I sketches the fate of locality and related notions in QFT, then documents the non-uniqueness unprecedented in ordinary QM but rampant in QFT. Part II presents foundations issues raised by non-uniqueness. (shrink)

In a pair of articles (1996, 1997) and in his recent book (1998), Miklos Redei has taken enormous strides toward characterizing the conditions under which relativistic quantum field theory is a safe setting for the deployment of causal talk. Here, we challenge the adequacy of the accounts of causal dependence and screening off on which rests the relevance of Redei's theorems to the question of causal good behavior in the theory.

Van Fraassen's 1991 modal interpretation of Quantum Mechanics offers accounts of measurement and state preparation. I argue that both accounts overlook a class of interactions I call General Unitary Measurements, or GUMs. Ironically, GUMs are significant for van Fraassen's account of measurement because they challenge it, and significant for his account of preparation because they simplify it. Van Fraassen's oversight prompts a question about modal interpretations: developed to account for ideal measurement outcomes, can they consistently account as well for the (...) whole horizon of laboratory practices by which we investigate QM? (shrink)

Comments and replies from the 2021 Eastern APA book symposium on Jill North's Physics, Structure, and Reality.

It has been suggested that the Modal Interpretation of Quantum Mechanics (QM) is "incomplete" if it lacks a dynamics for possessed values. I argue that this is only one of two possible attitudes one might adopt toward a Modal Interpretation without dynamics. According to the other attitude, such an interpretation is a complete interpretation of QM as standardly formulated, an interpretation whose innovation is to attempt to make sense of the quantum realm without the expedient of novel physics. Then I (...) explain why this attitude, though available, is unattractive. Without dynamics, the Modal Interpretation vanquishes the measurement problem only, it seems, to succumb to the problem of state preparation. On this view, the Modal Interpretation needs dynamics not to be an interpretation at all, but to be an adequate one. I review reasons to suspect that the dynamics which would best suit the Modal Interpretation--a dynamics equivalent to a set of two time transition probabilities of the sort used to solve the preparation problem--is not a dynamics the interpretation can have. I close with a brief discussion of versions of the Modal Interpretation that may not succumb to the considerations presented here. (shrink)

Philosophy and Phenomenological Research, Volume 103, Issue 2, Page 481-487, September 2021.

Why are quantum probabilities encoded in measures corresponding to wave functions, rather than by a more general class of measures? Call this question WHY BORN? I argue that orthodox quantum mechanics has a compelling answer to WHY BORN? but Bohmian mechanics might not. I trace Bohmian difficulties with WHY BORN? to its antistructuralism, its denial of physical significance to the algebraic structure of quantum observables, and I propose other cases where Bohmian antistructuralism might have an explanatory cost.

To most laypersons and scientists, science and progress appear to go hand in hand, yet philosophers and historians of science have long questioned the inevitability of this pairing. As we take leave of a century acclaimed for scientific advances and progress, Science at Century's End, the eighth volume of the Pittsburgh-Konstanz Series in the Philosophy and History of Science, takes the reader to the heart of this important matter. Subtitled Philosophical Questions on the Progress and Limits of Science, this timely (...) volume contains twenty penetrating essays by prominent philosophers and historians who explore and debate the limits of scientific inquiry and their presumed consequences for science in the 21st century. (shrink)

In a pair of articles and in his recent book, Miklos Redei has taken enormous strides toward characterizing the conditions under which relativistic quantum field theory is a safe setting for the deployment of causal talk. Here, we challenge the adequacy of the accounts of causal dependence and screening off on which rests the relevance of Redei's theorems to the question of causal good behavior in the theory.

On Itamar Pitowsky’s subjective interpretation of quantum mechanics, “the Hilbert space formalism of quantum mechanics [QM] is just a new kind of probability theory”, one whose probabilities correspond to odds rational agents would accept on the outcomes of gambles concerning quantum event structures. Our aim here is to ask whether Pitowsky’s approach can be extended from its original context, of quantum theories for systems with an finite number of degrees of freedom, to systems with an infinite number of degrees of (...) freedom, such as quantum field theory and quantum statistical mechanics in the thermodynamic limit. An impediment to generalization is that Pitowsky adopts the framework of event structures encoded by atomic algebras, whereas the algebras typical of QM for infinitely many degrees of freedom are usually non-atomic. We describe challenges to Pitowsky’s approach deriving from this impediment, and sketch and assess strategies Pitowsky might use to meet those challenges. Although we offer no final verdict about the eventual success of those strategies, a testament to the worth of Pitowsky’s approach is that attempting to extend it engages us in provocative foundational issues. (shrink)

The conjunction of Schrodinger dynamics and the usual way of thinking about the conditions under which quantum systems exhibit determinate values implies that measurements don't have outcomes. The orthodox fix to this quantum measurement problem is von Neumann's postulate of measurement collapse, which suspends Schrodinger dynamics in measurement contexts. Contending that the fundamental dynamical law of quantum theory breaks down every time we test the theory empirically, the collapse postulate is unsatisfactory. Recently philosophers and physicists have proposed a less violent (...) solution to the measurement problem. Their modal interpretations of quantum mechanics advocate unusual ways of thinking about the situations under which quantum systems exhibit determinate observable values, semantics which reconcile determinate measurement outcomes with universal Schrodinger dynamics. Thus modal interpretations hold out hope that quantum theory is complete and exceptionless. ;This dissertation tempers that hope. I consider the modal approach to the neglected problem of state preparation. A promising modal account exploits standard quantum transition probabilities. But, I claim, modal interpretations must subject these transition probabilities to a consistency constraint which they can be shown to violate. Non-standard transition probabilities might avoid this inconsistency, but they would also introduce novel dynamics, and so undo the modal triumph of taking Schrodinger dynamics to be complete and universal. Next I consider Albert and Loewer's assault on modal accounts of "error-prone" measurements. I argue that the Albert-Loewer problem is more general than Albert, Loewer, or their critics appreciate, and that the Araki-Yanase theorem implies the existence of a class of observables whose error-free measurements succumb to the Albert-Loewer problem. I review modal responses to Albert and Loewer which appeal to the palliative effects of a decohering environment and find them incomplete. Finally, based on the physicist Anthony Leggett's work with SQUIDs, I present a system concerning which the empirical commitments of modal interpretations contradict those of the quantum statistical algorithm, minimally interpreted. I conclude that these modal difficulties can be resolved only by taking the quantum formalism to be incomplete. (shrink)