In this paper I elicit a prediction from structural realism and compare it, not to a historical case, but to a contemporary scientific theory. If structural realism is correct, then we should expect physics to develop theories that fail to provide an ontology of the sort sought by traditional realists. If structure alone is responsible for instrumental success, we should expect surplus ontology to be eliminated. Quantum field theory (QFT) provides the framework for some of the best confirmed theories in (...) science, but debates over its ontology are vexed. Rather than taking a stand on these matters, the structural realist can embrace QFT as an example of just the kind of theory SR should lead us to expect. Yet, it is not clear that QFT meets the structuralist's positive expectation by providing a structure for the world. In particular, the problem of unitarily inequivalent representations threatens to undermine the possibility of QFT providing a unique structure for the world. In response to this problem, I suggest that the structuralist should endorse pluralism about structure. (shrink)

Howard argues that the existence of unitarily inequivalent representations in Quantum Field Theory presents a problem for structural realism in this context. I consider two potential ways round this problem: 1), follow Wallace in adopting the 'naive' Lagrangian form of QFT with cut-offs; 2), adapt Ruetsche's 'Swiss Army Knife' approach. The first takes us into the current debate between Wallace and Fraser on conventional vs. algebraic QFT. The second involves consideration of the role of inequivalent representations in understanding spontaneous symmetry (...) breaking and quantum statistics. In both cases, I suggest, the structural realist has sufficient room to manoeuvre. (shrink)

We pose and resolve a puzzle about spontaneous symmetry breaking in the quantum theory of infinite systems. For a symmetry to be spontaneously broken, it must not be implementable by a unitary operator in a ground state's GNS representation. But Wigner's theorem guarantees that any symmetry's action on states is given by a unitary operator. How can this unitary operator fail to implement the symmetry in the GNS representation? We show how it is possible for a unitary operator of this (...) sort to connect the folia of unitarily inequivalent representations. This result undermines interpretations of quantum theory that hold unitary equivalence to be necessary for physical equivalence. (shrink)

I defend a one category ontology: an ontology that denies that we need more than one fundamental category to support the ontological structure of the world. Categorical fundamentality is understood in terms of the metaphysically prior, as that in which everything else in the world consists. One category ontologies are deeply appealing, because their ontological simplicity gives them an unmatched elegance and spareness. I’m a fan of a one category ontology that collapses the distinction between particular and property, replacing it (...) with a single fundamental category of intrinsic characters or qualities. We may describe the qualities as qualitative charactersor as modes, perhaps on the model of Aristotelian qualitative (nonsubstantial) kinds, and I will use the term “properties” interchangeably with “qualities”. The qualities are repeatable and reasonably sparse, although, as I discuss in section 2.6, there are empirical reasons that may suggest, depending on one’s preferred fundamental physical theory, that they include irreducibly intensive qualities. There are no uninstantiated qualities. I also assume that the fundamental qualitative natures are intrinsic, although physics may ultimately suggest that some of them are extrinsic. On my view, matter, concrete objects, abstract objects, and perhaps even spacetime are constructed from mereological fusions of qualities, so the world is simply a vast mixture of qualities, including polyadic properties (i.e., relations). This means that everything there is, including concrete objects like persons or stars, is a quality, a qualitative fusion, or a portion of the extended qualitative fusion that is the worldwhole. I call my view mereological bundle theory. (shrink)

The paper argues against an intuitive reading of the Stone-von Neumann theorem as a categoricity result, thereby pointing out that this theorem does not entail any model-theoretical difference between the theories that validate it and those that don't.

Classical accounts of intertheoretic reduction involve two pieces: first, the new terms of the higher-level theory must be definable from the terms of the lower-level theory, and second, the claims of the higher-level theory must be deducible from the lower-level theory along with these definitions. The status of each of these pieces becomes controversial when the alleged reduction involves an infinite limit, as in statistical mechanics. Can one define features of or deduce the behavior of an infinite idealized system from (...) a theory describing only finite systems? In this paper, I change the subject in order to consider the motivations behind the definability and deducibility requirements. The classical accounts of intertheoretic reduction are appealing because when the definability and deducibility requirements are satisfied there is a sense in which the reduced theory is forced upon us by the reducing theory and the reduced theory contains no more information or structure than the reducing theory. I will show that, likewise, there is a precise sense in which in statistical mechanics the properties of infinite limiting systems are forced upon us by the properties of finite systems, and the properties of infinite systems contain no information beyond the properties of finite systems. (shrink)

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

Supersymmetry in quantum physics is a mathematically simple phenomenon that raises deep foundational questions. To motivate these questions, I present a toy model, the supersymmetric harmonic oscillator, and its superspace representation, which adds extra anticommuting dimensions to spacetime. I then explain and comment on three foundational questions about this superspace formalism: whether superspace is a substance, whether it should count as spatiotemporal, and whether it is a necessary postulate if one wants to use the theory to unify bosons and fermions.

This paper discusses an outstanding issue in philosophy of physics concerning the relation between quantum symmetries and the notion of physical equivalence. Specifically, it deals with a dilemma arising for quantum symmetry breaking that was posed by Baker, who claimed that if two ground states are connected by a symmetry, even when it is broken, they must be physically equivalent. However, I argue that the dilemma is just apparent. In fact, I object to Baker’s conclusion by showing that the two (...) thermodynamical phases of a ferromagnet, which are connected by the so-called flip-flop symmetry, are physically inequivalent, thereby providing a counter-example to his claim. (shrink)

If we divide our physical theories into theories of matter and theories of spacetime, quantum field theory is our most fundamental empirically successful theory of matter. As such, it has attracted increasing attention from philosophers over the past two decades, beginning to eclipse its predecessor theory of quantum mechanics in the philosophical literature. Here I survey some central philosophical puzzles about the theory's foundations.

Recent work on the hole argument in general relativity by Weatherall has drawn attention to the neglected concept of models’ representational capacities. I argue for several theses about the structure of these capacities, including that they should be understood not as many-to-one relations from models to the world, but in general as many-to-many relations constrained by the models’ isomorphisms. I then compare these ideas with a recent argument by Belot for the claim that some isometries “generate new possibilities” in general (...) relativity. Philosophical orthodoxy, by contrast, denies this. Properly understanding the role of representational capacities, I argue, reveals how Belot’s rejection of orthodoxy does not go far enough, and makes better sense of our practices in theorizing about spacetime. (shrink)

The paper proposes a combined account of identity for physical states and direct empirical significance for symmetries according to which symmetry-related state variables designate distinct physical states if and only if the symmetry that relates them has direct empirical significance. Strengthening an earlier result, I show that, given this combined account, the local gauge symmetries in our leading contemporary theories of particle physics do not have any direct empirical significance.

The article proposes a novel approach to the much discussed question of which symmetries have ‘direct empirical significance’ and which do not. The approach is based on a development of a recently proposed framework by Hilary Greaves and David Wallace, who claim that, contrary to the standard folklore among philosophers of physics, ‘local’ symmetries may have direct empirical significance no less than ‘global’ ones. Partly vindicating the standard folklore, a result is derived here from a number of plausible assumptions, that (...) states that local symmetries can indeed have no direct empirical significance. Ways to interpret the result are considered and possible morals are outlined. 1 Introduction2 Greaves and Wallace on Interior versus Non-interior Symmetries3 Elaborating on the Greaves/Wallace Framework4 The Result5 Problems with ’t Hooft’s Beam Splitter6 Summary and Conclusion. (shrink)