Abstract:

This dissertation interprets the formalism of quantum field theory (QFT) to help determine which physical properties are fundamental in worlds with natural laws like ours. I begin by arguing briefly that good metaphysical evidence can be drawn from mathematically rigorous forms of QFT. Although these rigorous QFTs are presently limited in their domain of applicability, insofar as our world resembles that domain we should expect these theories to be approximately true.

Chapter Two addresses the most central question about the fundamental ontology of QFT: is it a theory of fields or of particles? Any theory describes reality in terms of some basic constituents. Historically, philosophers have assumed these to be either point particles (following Locke and the atomists) or continuous fields (following Descartes). Recent philosophical arguments suggest that the most basic ontology of QFT cannot consist of particles; it is commonly supposed that it must therefore consist of fields (Halvorson and Clifton, 2001; Malament, 1996). To the contrary, I show that two of the most persuasive arguments against particles are also arguments against the most widely advocated form of field interpretation. First, the configuration of fields, like the number of particles, cannot generally be carried over between different inequivalent representations of QFT. Since the differences between some representations encode only perspectival information about the observer, it follows that QFT states possess no objective field content. Second, arguments which rule out the possibility of particle states in interacting QFT also rule out the standard way of representing states as field configurations.

So what is the most basic ontology of QFT? Chapter Three examines a possible answer, according to which fundamental reality is made up of properties, called quasi-local observables, which can be measured in regions of space and do not depend on our choice of representation. This third way has the potential to avoid the pitfalls of both field and particle interpretations. One objection to this view is that it is too "stingy" about properties--that is, it doesn't include enough properties to explain some of QFT's predictions (see Ruetsche, 2002, forthcoming). I answer this objection by showing that any extra properties appealed to by QFT can be seen as nothing but complicated combinations of quasi-local observables. This manifests in two ways: the extra properties are mathematically constructible from quasi-local observables, and they strongly supervene on the quasi-local observables.

If (as we have compelling reason to believe) particles are not fundamental parts of reality in QFT, what becomes of the notion of antimatter, which is often characterized as matter made up of antiparticles? Chapter Four examines whether this concept is (like the concept of particle) not a fundamental part of reality as the theory describes it. I show that the notion of antimatter is more general than the notion of antiparticle, so that solutions of QFT which cannot be described as systems of particles still have antimatter counterparts. So the matter-antimatter distinction may be fundamental even if the particle concept is not; whether it is fundamental depends on which mathematically definable states represent real physical possibilities. This result contradicts the views of Wallace (in progress) that realistic interacting systems admit of only an approximate matter-antimatter distinction.