Online research in philosophy

In this paper we critically review the various attempts that have been made to understand quantum field theory. We focus on Teller's (1990) harmonic oscillator interpretation, and Bohm et al.'s (1987) causal interpretation. The former unabashedly aims to be a purely heuristic account, but we show that it is only interestingly applicable to the free bosonic field. Along the way we suggest alternative models. Bohm's interpretation provides an ontology for the theory--a classical field, with a quantum equation of motion. This too has problems; it is not Lorentz invariant.

This paper digests technical commonplaces of quantum field theory to present an informal interpretation of the theory by emphasizing its connections with the harmonic oscillator. The resulting "harmonic oscillator interpretation" enables newcomers to the subject to get some intuitive feel for the theory. The interpretation clarifies how the theory relates to observation and to quantum mechanical problems connected with observation. Finally the interpretation moves some way towards helping us see what the theory comes to physically. The paper also argues that, in important respects, interpretive problems of quantum field theory are problems we know well from conventional quantum mechanics. An important exception concerns extending the puzzles surrounding the superposition of properties in conventional quantum mechanics to an exactly parallel notion of superposition of particles. Conventional quantum mechanics seems incompatible with a classical notion of property on which all quantities always have definite values. Quantum field theory presents an exactly analogous problem with saying that the number of "particles" is always definite.

In response to Cushing it is urged that the vicissitudes of quantum field theory do not press towards a nonrealist attitude towards the theory as strongly as he suggests. A variety of issues which Redhead raises are taken up, including photon localizability, the wave-particle distinction in the classical limit, and the interpretation of quantum statistics, vacuum fluctuations, virtual particles, and creation and annihilation operators. It is urged that quantum field theory harbors an unacknowledged inconsistency connected with the fact that the zero point energy has observable consequences, while to avoid infinities it must be "thrown away". Finally, Redhead's conception of ephemerals is pressed and the paper concludes with the suggestion that the particle concept largely drops out of quantum field theory.

I present two relatively independent sets of remarks on common causes and the violation of Bell inequalities in algebraic quantum field theory. The first set of remarks concerns the possibility of reconciling Reichenbachian ideas on common causes with quantum field theory in the face of an already known difficulty: the event shown to satisfy statistical relations for being the common cause of two correlated events has been associated with the union, rather than the intersection, of the backward light cones of the correlated events. I explore a way of overcoming this difficulty by considering the common cause to be a conjunction of suitably located events. But I show that this line of thought too is beset with interpretational problems. My second set of remarks concerns the type of inequality one may derive from the common-common cause hypothesis: I argue, on grounds of interpretation, that the Clauser-Horne type, and not the Bell type, of inequalities emerge more naturally in this context.

A new version of quantum theory is proposed, according to which probabilistic events occur whenever new statioinary or bound states are created as a result of inelastic collisions. The new theory recovers the experimental success of orthodox quantum theory, but differs form the orthodox theory for as yet unperformed experiments.

I analyse the conceptual and mathematical foundations of Lagrangian quantum field theory (QFT) (that is, the ‘naive’ (QFT) used in mainstream physics, as opposed to algebraic quantum field theory). The objective is to see whether Lagrangian (QFT) has a sufficiently firm conceptual and mathematical basis to be a legitimate object of foundational study, or whether it is too ill-defined. The analysis covers renormalisation and infinities, inequivalent representations, and the concept of localised states; the conclusion is that Lagrangian QFT (at least as described here) is a perfectly respectable physical theory, albeit somewhat different in certain respects from most of those studied in foundational work.

Most philosophical discussion of the particle concept that is afforded by quantum field theory has focused on free systems. This paper is devoted to a systematic investigation of whether the particle concept for free systems can be extended to interacting systems. The possible methods of accomplishing this are considered and all are found unsatisfactory. Therefore, an interacting system cannot be interpreted in terms of particles. As a consequence, quantum field theory does not support the inclusion of particles in our ontology. In contrast to much of the recent discussion on the particle concept derived from quantum field theory, this argument does not rely on the assumption that a particulate entity be localizable.

The apparent underdetermination of the formalism of quantum field theory (QFT) as between a particle and a field interpretation is studied in this paper through a detour over the problem of unifying QFT with general relativity. All we have at present is a partial or approximate unification, QFT in non-Minkowskian spaces. The nature of this hybrid and the problem of its internal consistency are discussed. One of its most striking implications is that particles do not have an observer-independent existence. We trace the ways in which physicists reacted to this at first highly implausible ontological consequence. We conclude that quantum fields rather than particles are after all the basic entities in QFT.

In relativistic quantum field theory the notion of a local operation is regarded as basic: each open space-time region is associated with an algebra of observables representing possible measurements performed within this region. It is much more difficult to accommodate the notions of events taking place in such regions or of localized objects. But how can the notion of a local operation be basic in the theory if this same theory would not be able to represent localized measuring devices and localized events? After briefly reviewing these difficulties we discuss a strategy for eliminating the tension, namely by interpreting quantum theory in a realist way. To implement this strategy we use the ideas of the modal interpretation of quantum mechanics. We then consider the question of whether the resulting scheme can be made Lorentz invariant.

Much attention has been directed to the philosophical implications of quantum field theory (QFT) in recent years; this paper attempts a survey in low-technical terms. First the relations of QFT to other kinds of theory, classical and quantum, particle and field, are discussed. Then various formulations of QFT are introduced, along with related interpretations. Finally a review is made of some of the most interesting foundational problems.