Abstract This is the first of a two‐part introduction to some interpretive questions that arise in connection with quantum field theories (QFTs). Some of these questions are continuous with those familiar from the discussion of ordinary non‐relativistic quantum mechanics (QM). For example, questions about locality can be rigorously posed and fruitfully pursued within the framework of QFT. A stark disanalogy between QFTs and ordinary QM – the former, but not the latter, typically admit infinitely many putatively physically inequivalent realizations – prompts relatively novel questions, questions about how to understand and adjudicate different strategies for equipping quantum theories with content. Part I sketches the fate of locality and related notions in QFT, then documents the non‐uniqueness unprecedented in ordinary QM but rampant in QFT. Part II presents foundations issues raised by non‐uniqueness.
Abstract This is the first of a two‐part introduction to some interpretive questions that arise in connection with quantum field theories (QFTs). Some of these questions are continuous with those familiar from the discussion of ordinary non‐relativistic quantum mechanics (QM). For example, questions about locality can be rigorously posed and fruitfully pursued within the framework of QFT. A stark disanalogy between QFTs and ordinary QM – the former, but not the latter, typically admit infinitely many putatively physically inequivalent realizations – prompts relatively novel questions, questions about how to understand and adjudicate different strategies for equipping quantum theories with content. Part I sketches the fate of locality and related notions in QFT, then documents the non‐uniqueness unprecedented in ordinary QM but rampant in QFT. Part II presents foundations issues raised by non‐uniqueness.
Abstract According to a regnant criterion of physical equivalence for quantum theories, a quantum field theory (QFT) typically admits continuously many physically inequivalent realizations. This, the second of a two‐part introduction to topics in the philosophy of QFT, continues the investigation of this alarming circumstance. It begins with a brief catalog of quantum field theoretic examples of this non‐uniqueness, then presents the basics of the algebraic approach to quantum theories, which discloses a structure common even to ‘physically inequivalent’ realizations of a QFT. Finally, it introduces and evaluates a handful of strategies for interpreting quantum theories in the face of the non‐uniqueness of their Hilbert space representations.
Introduction: Conceptual issues in quantum field theory Part I. Philosophers' Interests in Quantum Field Theory: 1. Why are we philosophers interested in quantum field theory 2. Quantum field theory and the philosopher Part II. Three Approaches to the Foundations of Quantum Field Theory: 3. The usefulness of a general theory of quantized fields 4. Effective field theory in condensed matter physics 5. The triumph and limitations of quantum field theory 6. Comments Discussions Part III. Does Quantum Field Theory Need a Foundation: 7. Does quantum field theory need a foundation? Part IV. Mathematics, Statistical Mechanics and Quantum Field Theory: 8. Renormalization group theory: its basis and formulation in statistical physics 9. Where does quantum field theory fit into the big picture? 10. The unreasonable effectiveness of quantum field theory 11. Comment: the quantum field theory of physics and of mathematics Part V. Quantum Field Theory and Spacetime: Introduction 12. Quantum field theory and spacetime: formalism and reality 13. Quantum field theory of geometry 14. 'Localization' in quantum field theory: how much of QFT is compatible with what we know about spacetime 15. Comments VI. 16. What is quantum field theory and what did we think it was? 17. Comments Discussions Part VII.Renormalization Group: 18. What is fundamental physics? A renormalization group perspective 19. Renormalization group: an interesting yet puzzling idea Part VIII. Non-Abelian Gauge Theory: 20. Gauge fields, gravity and Bohm's theory 21. Is the Aharonov-Bohm effect local? Discussions Part IX. The Ontology of Particles or Fields: 22. The ineliminable classical face of quantum field theory 23. The logic of quanta 24. Do Feynman diagrams endorse a particle ontology? 25. On the ontology of QFT Part X. Panel Discussion.
Abstract One can consider the developments in quantum field theory from the point of view of foundational problems posed about physical reality at both the epistemological and ontological levels, or as a ‘laboratory’ to study the actual methodology of the scientific enterprise. I shall address both of these issues in this paper. My contention is that at the foundational level there is essentially nothing new in quantum field theory that is not already present in non-relativistic quantum mechanics. This is quite different in emphasis from the view expressed by Redhead (1983a). Even in quantum mechanics most of the difficulties which arise are generated by the realist’s inclination to take the formalism too literally as representing physical reality, often in a modified or distorted classical view. More serious consideration of Bohr’s philosophical framework of complementarity may prove fruitful for coping with this problem, which is not new to quantum field theory, being already the central interpretative problem of quantum mechanics. On the other hand, as a source to illustrate how theories arc constructed and established in actual scientific practice, quantum field theory does provide a wide range of useful examples. Here too, although there are many technically fascinating topics (such as renormalization), quantum field theory is pretty much (meth odological) business as usual. Much more interesting, essentially new, methodological departures are seriously proposed (with varying degrees of credibility) by some rival or alternative developments in modern theoretical physics, such as the S-matrix programme, with its bootstrap conjecture, or cosmology, with various forms of the anthropic principle (Gale 1983) and with the inflationary universe scenario (Guth 1981 ).
The availability of unitarily inequivalent representations of the canonical commutation relations constituting a quantization of a classical field theory raises questions about how to formulate and pursue quantum field theory. In a minimally technical way, I explain how these questions arise and how advocates of the Hilbert space and of the algebraic approaches to quantum theory might answer them. Where these answers differ, I sketch considerations for and against each approach, as well as considerations which might temper their apparent rivalry.
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.
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