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Ontological Aspects of Quantum Field Theory Ontological Aspects of Quantum Field Theory edited by Meinard Kuhlmann H o Iger Lyre Andrew Wayne World Scientific Ontological Aspects of Quantum Field Theory This page is intentionally left blank Ontological Aspects of Quantum Field Theory edited by Meinard Kuhlmann Department of Philosophy, University of Bremen Holger Lyre Philosophy Department, University of Bonn Andrew Wayne Department of Philosophy, Concordia University VkS% World Scientific wb New Jersey • London • SingaporeSine • Hong Kong Published by World Scientific Publishing Co. Pte. Ltd. P O Box 128, Farrer Road, Singapore 912805 USA office: Suite IB, 1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. ONTOLOGICAL ASPECTS OF QUANTUM FIELD THEORY Copyright © 2002 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 981-238-182-1 This book is printed on acid-free paper. Printed in Singapore by Mainland Press Preface Quantum field theory (QFT) supplies the framework for many fundamental theories in modern physics. Over the last few years there has been increas­ ing interest in ontological aspects of these theories, that is, in investigating what the subatomic world might be like if QFTs were true. Is this a world populated by localizable particles? Or is it best understood as composed of interacting processes? How should we interpret certain non-gauge-invariant structures in QFTs such as ghost fields and antifields? Essays in this vol­ ume investigate ontological aspects of QFTs using a variety of physical and philosophical concepts and methods. Although the focus is ontology, these investigations touch on a broad range of topics, from the most general ques­ tions of metaphysics to the most minute conceptual puzzles of particular QFTs. Many of these essays were first presented as papers at the conference "Ontological Aspects of Quantum Field Theory" held at the Zentrum fur interdisziplinare Forschung (Center for Interdisciplinary Research, ZiF), Bielefeld, Germany, in October 1999. This conference brought together physicists, philosophers of physics and philosophers interested in ontology. By all lights the conference was immensely fruitful, in large part because it was successful in promoting a dialogue among participants from diverse disciplinary background. The aim of the present volume is to give contribu­ tors an opportunity to advance the dialogue begun at the conference, while at the same time reaching a wider audience. For this reason papers are, as far as possible, written in a way accessible to physicists, philosophers and a general science readership. We thank the University of Chicago Press for permission to reprint H. vi Halvorson and R. Clifton's contribution to this volume. We thank Craig Smith for his assistance in the preparation of the manuscript. We also express our deepest gratitude to Daniel Cartin of World Scientific for his help (and patience!) with the publication of this volume. Many thanks, in addition, to the main organizers of our conference, Manfred Stockier (Bremen) and Andreas Bartels (Bonn), and also to the people at the ZiF for their kind hospitality. We finally would like to acknowledge the financial support of the ZiF and the Fritz Thyssen Stiftung (Cologne). May 2002 Meinard Kuhlmann Holger Lyre Andrew Wayne Contents Preface v Chapter 1 Introduction 1 by Meinard Kuhlmann, Holger Lyre and Andrew Wayne 1.1 Ontology of QFT: Aims, Methods and Work Ahead 1 1.2 A Layperson's Guide to QFT 7 1.3 Basic Mathematical Formulations of QFT 11 1.4 A Layperson's Guide to Ontology, Semantics and Epistemology 17 1.5 Overview of this Book 22 PART 1: Approaches to Ontology Chapter 2 Candidate General Ontologies for Situating Quan­ tum Field Theory 33 by Peter Simons 2.1 Methodological Preamble 34 2.2 Substance and Attribute 36 2.3 Applied Set Theory 37 2.4 Fact Ontologies 38 2.5 Occurrent Ontologies 39 2.6 Trope Ontologies 41 2.7 Possible Worlds 43 2.8 Factored Ontologies 43 2.9 Tentative Conclusions 49 vii viii Chapter 3 'Quanta,' Tropes, or Processes: Ontologies for QFT Beyond the Myth of Substance 53 by Johanna Seibt 3.1 A Methodological Preface 54 3.2 'Identical Particles' and the Myth of Substance 64 3.3 Non-Individual Particulars or Quanta 71 3.4 Fields of Trope Structures? 78 3.5 Fields as Free Processes? 82 3.6 Conclusion 93 Chapter 4 Analytical Ontologists in Action: A Comment on Seibt and Simons 99 by Meinard Kuhlmann 4.1 Ontology and Physics: Seibt Versus Simons 99 4.2 Processes and Ontological Parsimony 102 4.3 Tropes, Invariant Factors and Quantum Field Theory 104 4.4 Conclusion 108 Chapter 5 How Do Field Theories Refer to Entities in a Field? Ill by Sunny Y. Auyang 5.1 Introduction Ill 5.2 Direct and Descriptive Reference 112 5.3 How Does Linguistic Analysis Apply to Physical Theories? . 117 5.4 Direct Reference to Local Fields 120 5.5 Summary 122 PART 2: Field Ontologies for QFT Chapter 6 A Naive View of the Quantum Field 127 by Andrew Wayne 6.1 Introduction 127 6.2 What Teller's Quantum Field Is Not 128 6.3 The VEV Interpretation 130 6.4 Conclusion 132 ix Chapter 7 Comments on Paul Teller's Book, "An Interpre­ tive Introduction to Quantum Field Theory" 135 by Gordon Fleming 7.1 Introduction 135 7.2 Teller on Quanta 137 7.3 Teller on Fields 140 7.4 Conclusion 143 Chapter 8 So What Is the Quantum Field? 145 by Paul Teller 8.1 Introduction 145 8.2 Giving a Physical Interpretation to the OVQF 147 8.3 The OVQF is Not an "Active Agent" 154 8.4 What Has and Has Not Been Shown 160 PART 3: Relativity, Measurement and Renormalization Chapter 9 On the Nature of Measurement Records in Rela­ tivistic Quantum Field Theory 165 by Jeffrey A. Barrett 9.1 Introduction 165 9.2 The Measurement Problem 167 9.3 Malament's Theorem 169 9.4 Measurement Records 172 9.5 Conclusion 177 Chapter 10 No Place for Particles in Relativistic Quantum Theories? 181 by Hans Halvorson and Rob Clifton 10.1 Introduction 181 10.2 Malament's Theorem 183 10.3 Hegerfeldt's Theorem 190 10.4 Doing without "No Absolute Velocity" 193 10.5 Are there Unsharply Localizable Particles? 196 10.6 Are there Localizable Particles in RQFT? 200 10.7 Particle Talk without Particle Ontology 203 10.8 Conclusion 206 10.9 Appendix 207 X Chapter 11 Events and Covariance in the Interpretation of Quantum Field Theory 215 by Dennis Dieks 11.1 The Problem 215 11.2 What Has to Be Done 218 11.3 Modal Property Attribution Schemes 219 11.4 A Perspectival Version of the Modal Interpretation 221 11.5 Application to ARQFT 223 11.6 Histories of Modal Properties 226 11.7 Joint Probabilities of Events 228 11.8 A Possible Alternative: Perspectivalism 231 11.9 Conclusion 233 Chapter 12 Measurement and Ontology: What Kind of Evi­ dence Can We Have for Quantum Fields? 235 by Brigitte Falkenburg 12.1 QFT and the Appearances of Particle Physics 235 12.2 Intermezzo: A Kantian Account of Ontology 243 12.3 Toward an Empirical Ontology of QFT 246 12.4 Conclusions 253 Chapter 13 Renormalization and the Disunity of Science 255 by Nick Huggett 13.1 The Need for Renormalization 255 13.2 The Method of Renormalization 256 13.3 The Renormalization Group 258 13.4 Cartwright on Fundamentalism 264 13.5 Renormalization as Grounds for Disunity 267 13.6 Renormalized QFT as a Fundamental Theory 270 PART 4: Gauge Symmetries and the Vacuum Chapter 14 The Interpretation of Gauge Symmetry 281 by Michael Redhead 14.1 Introduction 282 14.2 The Ambiguity of Mathematical Representation 283 14.3 Symmetry 285 xi 14.4 Surplus Structure 286 14.5 Constrained Hamiltonian Systems 288 14.6 Yang-Mills Gauge Theories 290 14.7 The Case of General Relativity 292 14.8 The BRST Symmetry 295 14.9 Conclusion 298 Chapter 15 Comment on Redhead: The Interpretation of Gauge Symmetry 303 by Michael Drieschner, Tim Oliver Eynck and Holger Lyre 15.1 The Ubiquitous Ambiguity 304 15.2 "Prepotentials" 305 15.3 Redhead's Trilemma 308 15.4 Conclusion 310 Chapter 16 Is the Zero-Point Energy Real? 313 by Simon Saunders 16.1 Introduction 313 16.2 The Cosmological Constant Problem 314 16.3 The Classical Ether 318 16.4 The Dirac Negative Energy Sea 320 16.5 Zero-Point Energy 329 16.6 Against Zero-Point Fluctuations 336 16.7 Outlook 340 Chapter 17 Two Comments on the Vacuum in Algebraic Quantum Field Theory 345 by Miklos Redei 17.1 AQFT 345 17.2 Comment 1: Ontological Silence of AQFT is Not Ontological Neutrality 347 17.3 Comment 2: It is Not Known Whether Vacuum Correlations Can Have a Common Cause Explanation 350 List of Contributors 357 Index 360 Chapter 1 Introduction Meinard Kuhlmann University of Bremen Holger Lyre University of Bonn Andrew Wayne Concordia University, Montreal This introduction aims to provide the motivation and background for inves­ tigating ontological aspects of QFT, as well as an overview of the contribu­ tions to this volume.
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