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Philosophy of Science

Interpretations of Quantum Field Theory

Nick Huggett, Robert Weingard

Published Sep 1, 1994• 18 citations
Publisher

Abstract

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.

DOI
10.1086/289809

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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.
Abstract 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. For our discussion of the foundations of quantum field theory (QFT) it will be useful to have a map showing where QFT stands in relation to other physical theories. Figure 1 locates theories as points of a three-dimensional lattice: describing particles or fields, formulated in different spacetimes and either classical or quantum. Consider the classical plane of Figure
The formalism of quantum mechanics is presented in a way that its interpretation as a classical field theory is emphasized. Two coupled real fields are defined with given equations of motion. Densities and currents associated to the fields are found with their corresponding conserved quantities. The behavior of these quantities under a galilean transformation suggest the association of the fields with a quantum mechanical free particle. An external potential is introduced in the Lagrange formalism. The description is equivalent to the conventional Schrödinger equation treatment of a particle. We discuss the attempts to build an interpretation of quantum mechanics based on this scheme. The fields become the primary onthology of the theory and the particles appear as emergent properties of the fields. These interpretations face serious problems for systems with many degrees of freedom.
An Interpretive Introduction to Quantum Field Theory (Teller 1995; hereafter IIQFT) supersedes most of my prior work on quantum field theory. The gossip mill has described this book as a popularization of the most elementary parts of Bjorken and Drell (1965), which into the 1980s was the most widely used quantum field theory text. As with any good caricature, there is a great deal of truth in this comparison. Like Bjorken and Drell, who published in 1965, IIQFT presents the theory largely as it existed in the 1950s. But in order to see aspects of structure and interpretation more clearly, IIQFT presents the theory stripped of all the details needed for application. IIQFT also does not treat contemporary methods, such as the functional approach, and important recent developments, especially gauge theories and the renormalization group. Nonetheless it is hoped that by laying out the structure of the theory's original form in the 1950s, much of which survives in contemporary versions, and by developing a range of ways of thinking about that theory physically, one does essential ground work for a thorough understanding of what we have today. Why do we use the term ‘quantum field theory’? A good fraction of the work done in IIQFT aims to clarify the appropriateness, accurate development, and limitations of the application of the epithet ‘field’, as well as examination of alternatives. While called a ‘field theory’, quantum field theory (QFT) is also taken to be our most basic theory of ‘elementary particles’.
There exist dozens of interpretations of quantum theory, but they do not seem to contribute much to understanding the theory. This paper attempts to clarify some issues that are discussed in those interpretations. The main keywords are: "Classical ontology", Indeterminism, Probability, Predictions, The necessity of classical concepts, Minimal interpretation, Lattice, Physical objects, Alternatives to quantum theory?, Measurement, Realism. One of the main points of this paper is the role of predictions in understanding any theory of physics.