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Oxford University Press eBooks

Phenomenological Particle Notions

Laura Ruetsche

Published Jun 2, 2011• 0 citations
Publisher

Abstract

This chapter considers another route to a particle interpretation of quantum field theory, one mediated by the existence of techniques (such as the use of Feynman diagrams to guide calculation) and explanations (such as the appeal to cosmological particle creation to account for decelerating cosmic expansion) best understood in terms of particles. Looking close at these techniques and explanations, the chapter argues that they rely on the presence of unitarily inequivalent representations, the very presence, Chapters 8 and 9 contended, that frustrates fundamental particle interpretation.

DOI
10.1093/acprof:oso/9780199535408.003.0011

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This chapter considers another route to a particle interpretation of quantum field theory, one mediated by the existence of techniques (such as the use of Feynman diagrams to guide calculation) and explanations (such as the appeal to cosmological particle creation to account for decelerating cosmic expansion) best understood in terms of particles. Looking close at these techniques and explanations, the chapter argues that they rely on the presence of unitarily inequivalent representations, the very presence, Chapters 8 and 9 contended, that frustrates fundamental particle interpretation.
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Quantum field theory (QFT) provides us with one and almost only suitable language (or mathematical tool) for describing not only the motion and interaction of particles but also their “annihilation” and “creation” out of a field considered a priori in a sophisticated way, whose view seems to be suited for describing dislocations, as a particle or a string embedded within a crystalline ordered field. This chapter concisely overviews the method of QFT, emphasizing distinction from the quantum mechanics, conventionally used for a single and/or many particle problems, and its equivalence to the statistical mechanics. The alternative formalism based on Feynman path integral and its imaginary time representation are reviewed, as the foundation for our use in Chapter 10.
This chapter begins the project of interpreting quantum gauge field theories. It rejects an interesting recent interpretation and explains why it is so difficult to arrive at a better one. The difficulty stems from the problems of interpreting any quantum field theory. Even the non-relativistic quantum mechanics of particles is a theory whose interpretation remains at best controversial, and at worst simply lacking. Interpretations of quantum field theory face the additional hurdle that it is not clear what the theory is about: neither a field nor a particle ontology is readily squared with the mathematics of the theory. The chapter explores the status of loop representations in several approaches toward the interpretation of quantum field theory.
There are significant problems involved in determining the ontology of quantum field theory (QFT). An ontology involving particles seems to be ruled out due to the problem of defining localized position operators, issues involving interactions in QFT, and, perhaps, the appearance of unitarily inequivalent representations. While this might imply that fields are the most natural ontology for QFT, the wavefunctional interpretation of QFT has significant drawbacks. A modified field ontology is examined where determinables are assigned to open bounded regions of spacetime instead of spacetime points.
QM∞ includes quantum field theory and the thermodynamic limit of quantum statistical mechanics — theories which, unlike the 'ordinary' quantum theories typically discussed by philosophers, concern infinite systems. The mathematical framework appropriate for the presentation of a theory of ordinary quantum mechanics is essentially unique. For theories of QM∞, this is not so. This prompts interpretive questions—for instance, about what makes a quantum theory the quantum theory it is — this work aims to chronicle. Having introduced a formal apparatus (operator algebra theory) suited to pursue these questions, the book articulates a variety of accounts of the content of quantum theories, accounts responsive to QM∞'s characteristic non-uniqueness. To evaluate these accounts, the book examines QM∞ settings (e.g. spontaneous symmetry breaking, cosmological particle creation, superconductivity) in which that characteristic non-uniqueness seems to matter, with a view toward determining which accounts sustain the uses to which the non-uniqueness is put. This approach not only brings work on the foundations of quantum theories in contact with the foundational investigation of other sorts of physical theories (e.g., thermodynamics, statistical mechanics, solid state physics, general relativity, and cosmology), it also brings the philosophy of physics in contact with other sorts of philosophy of science (e.g., accounts of explanation, reduction, and explanationist defenses of scientific realism). The book concludes that received notions of physical content and physical modality must be revised if they are to apply usefully to particular physical theories.
This is an opinionated survey of some interpretive puzzles in quantum field theory. The problem of inequivalent representations is sketched, including its connections with competing accounts of physical equivalence. The controversy between variant formulations of the theory, algebraic versus Lagrangian, is given a conciliatory resolution. Arguments against particles are addressed, demarcating clearly between different forms of particle interpretation. Field interpretations are then considered, including wavefunctional, spacetime state realist and Heisenberg operator realist interpretations. Ruetsche’s coalesced structure interpretation is presented and juxtaposed with an alternative, more traditional view of the theory’s laws and state space. Finally, the CPT theorem is discussed, together with its implications about the nature of spacetime.