Laura Ruetsche

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.

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.

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.

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.

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.

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.

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.

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.

: 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

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.

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.

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.

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.

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