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How Is Quantum Field Theory Possible? How Is Quantum Field Theory Possible? Sunny Y. Auyang OXFORD UNIVERSITY PRESS How Is Quantum Field Theory Possible? This page intentionally left blank How Is Quantum Field Theory Possible? Sunny Y. Auyang New York Oxford OXFORD UNIVERSITY PRESS 1995 Oxford University Press Oxford New York Athens Auckland Bangkok Bombay Calcutta Cape Town Dar es Salaam Delhi Florence Hong Kong Istanbul Karachi Kuala Lumpar Madras Madrid Melbourne Maxico City Nairobi Paris Singapore Taipei Tokyo Toronto and associated companies in Berlin Ibadan Copyright © 1995 by Oxford University Press, Inc. Published by Oxford University Press, Inc., 200 Madison Avenue, New York, New York 10016 Oxford is a registered trademark of Oxford University Press All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Oxford University Press. Library of Congress Cataloging-in-Publication Data Auyang, Sunny Y. How is quantum field theory possible? / Sunny Y. Auyang. p. cm. Includes bibliographical references and index. ISBN (invalid) 0-19-509344-5 — ISBN 0-19-509345-3 (pbk.) 1. Quantum field theory. 2. Physics—Philosophy. 3. Space and time. I. Title. QC174.45.A88 1995 530.T43- dc20 95-8562 135798642 Printed in the United Slates of America on acid-free paper To my parents This page intentionally left blank CONTENTS 1. Introduction 3 1. A Human View of the World in Quantum Field Theory 3 2. The Categorical Framework of Objective Knowledge 11 2. Nonrelativistic quantum mechanics 16 3. The Structure of Quantum Mechanics 16 4. The Quantum Measurement Problem 22 3. Relativity and symmetries 26 5. Geometry and Space—Time 26 6. Symmetries in Physics 32 7. The Principles of Relativity and Local Symmetry 38 4. Quantum field theory 43 8. Quantum Fields and Elementary Particles 43 9. Fields, Quantum Fields, and Field Quanta 47 10. Interacting Fields and Gauge Field Theory 54 5. Object of experiences: quantum state—observables—statistics 61 11. Properties and Quantum Properties: Amplitudes 61 12. The Form of Observation and the Reality of Quantum States 70 13. The Gap in Understanding: Eigenvalue and Probability 78 14. Coordinatization of the Quantum World: Observables 85 15. The General-Concept of Objects in Physical Theories 89 16. The Illusion of the Observer 104 17. The Mentalism of yes-no Experiments 113 6. The event structure and the spatio-temporal structure: localfieldss 1fields 18. The Whole and the Individual: Field and Event 119 viii Contents 19. This-Something: Events or Local Fields 122 20. The Basic Spatio-Temporal Structure of the Physical World 133 21. The Referential Structure of Field Theory 152 22. The States of the Field as a Whole: Field Quanta 157 23. Identity and Diversity: Quantum Multi-Particle Systems 160 7. Explicit relations and the causal order: interacting fields 166 24. Relation and Constant Predication 166 25. Permanence, Endurance, and the Concepts of Time 169 26. How Are Regular Successions of Events Possible? 175 27. Relational Properties: Phase and Potential 183 28. Causal Relations: Connection and Parallel Transport 187 29. Thoroughgoing Interaction: Renormalization 189 8. Epilogue 194 30. The Intelligibility of the Objective World 194 APPENDIX A. Measure and probability: quantity, quality, modality 197 Al. Measure: the General Concept of Extensive Magnitudes 197 A2. Function and Distribution: Individual and Collective Qualities 203 A3. Individual, Statistical, and Probabilistic Statements 206 APPENDIX B. Fiber bundles and interaction dynamics 214 APPENDIX C. The cosmic and the microscopic: an application 223 NOTES 229 BIBLIOGRAPHY 265 INDEX 273 How Is Quantum Field Theory Possible? 1 This page intentionally left blank 1 Introduction The whole of science is nothing more than a refinement of everyday think- ing. It is for this reason that the critical thinking of the physicist cannot possibly be restricted to the examination of the concept of his own specific field. He cannot proceed without considering critically a much more diffi- cult problem, the problem of analyzing the nature of everyday thinking. ALBERT EINSTEIN "Physics and Reality" § 1. A Human View of the World in Quantum Field Theory Quantum field theory is the union of quantum mechanics and special relativity. It is our most fundamental physical theory and provides the conceptual frame- work for the twentieth century's answers to questions about the basic structure of the physical world. However, its philosophical significance has been largely ignored, although relativity and quantum mechanics have separately stimu- lated much reflection.1 Consequently, the intimate relations among the mean- ings of object, experience, space-time, and interaction, which are revealed only in the unified structure of quantum field theory, remain in obscurity. The present work fills the gap in philosophy. In 1900, Max Planck postulated that the energy spectrum of blackbody radiation is quantized. Five years later, Albert Einstein introduced the notion of light quanta. Physicists realized that quantum ideas are essential to the understanding of atomic structures; classical physics is inadequate. It took two decades of intensive research and the fresh minds of a new generation that included Werner Heisenberg, Erwin Schrodinger, and Paul Dirac to develop nonrelativistic quantum mechanics. Quantum mechanics quickly became the basis of a large part of physics including atomic, molecular, and solid-state phenomena. However, in nuclear and high-energy physics, it is unsatisfactory because it is incompatible with the principle of special relativity advanced by Einstein in 1905. Dirac founded quantum field theory by uniting quantum mechanics and special relativity. Quantum field theory met with many difficulties that were not solved until after the Second World War when a third generation of phy- sicists from around the world established a satisfactory quantum field theory of the electromagnetic interaction. The extension of the theory to cover the 3 4 Introduction nuclear interactions took another 25 years. During this process, gauge fields or fields with local symmetries, the idea of which first appeared in the general theory of relativity, became dominant. That research effort has yielded a boun- tiful harvest. Quantum field theory underlies the current standard model in elementary particle physics, through which our intellectual eyes behold both the microscopic structure of matter and the cosmic events occurring within split seconds of the Big Bang. Despite the success of quantum theories, their philosophical interpretations have always been difficult and controversial. Richard Feynman said: "We always have had a great deal of difficulty in understanding the world view that quantum mechanics represents."2 Physicists do understand the quantum realm to a significant extent. Their understanding is manifested in the success- ful application of quantum theories to real-world problems. However, it is poorly articulated. The actions and writings of physicists tacitly uphold a world view rooted in practice and robust common sense. Physicists use sub- atomic particles as physical tools in laboratory experiments and components in commercial devices; the electronic industry is mainly based on the manipula- tion of the quantum world. In both technical papers and research proposals, physicists unambiguously assert that they are studying the microscopic struc- ture of matter and the origin of the universe. Thus they uphold a commonsen- sically realistic view of the quantum world. The philosophical difficulty lies in articulating this world view and defending it against phenomenalist challenges. Such an articulation and defense are the aim of the present work. The world-view difficulty has several sources. The world described by quan- tum theories is remote to sensory experiences and is totally different from the familiar classical world. There are scientific puzzles, such as what happens during the process of measurement. Quantum theories disallow certain ques- tions that we habitually ask about physical things, for example, the moment when a radioactive atom decays. The logical structures of quantum theories are more complicated and contain more elements than those of classical mechanics. The working interpretation of quantum theories, which physicists use in practice, invokes the concept of observed results as distinct from physical states. The concept with explicit experiential connotation is not found in clas- sical mechanics and causes interpretive problems. Finally, logical positivism, which dismisses the notion of reality as meaningless metaphysics, casts a long shadow. These factors prompt many interpreters to adopt the phenomenalist position asserting that quantum objects have no definite property, the reality of the microscopic world evaporates, the observer creates what he observes, and what the theories say about the quantum realm are not to be believed for they are fictions that help to predict the behaviors of classical experimental equip- ments.3 The phenomenalist doctrines are espoused by the Copenhagen school that dominates quantum interpretation and are academically influential. However, they conflict with the day-to-day operation of physicists. They would make a scandal out of physicists' requests for public funding of fundamental research. If the microscopic world were fictitious, then billion-dollar accelerators would
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