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ADVANCED ELECTROMAGNETISM Foundations, Theory and Applications Nous ne savons le tout de rien. — Blaise Pascal (1623-1662) ADVANCED ELECTROMAGNETISM Foundations, Theory and Applications Editors Terence W, Barrett BSB, USA Dale M. Grimes Pennsylvania State University, USA V fe World Scientific 1M SSininagaappoorere •*N Neeww J Jeerrsseeyy L •L ondon •Hong Kong Published by World Scientific Publishing Co. Pte. Ltd. P O Box 128, Farrer Road, Singapore 9128 USA office: Suite IB, 1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE ADVANCED ELECTROMAGNETISM: FOUNDATIONS, THEORY AND APPLICATIONS Copyright © 1995 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 permissionfrom the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, Massachusetts 01923, USA. ISBN 981-02-2095-2 Printed in Singapore. V FOREWORD There can be little doubt that Maxwell's equations constitute one of the great landmarks in physical theory. Their basic accuracy has been confirmed innumerable times, in many different types of experiment. Their invariance properties led Einstein to his special theory of relativity. Moreover, their gauge-theoretic interpretation led to non-Abelian generalizations, fundamental to modern particle physics. Their elegant mathematical form has provided several important influences on the development of mathematics itself. These facts should not, however, deter theoretical or experimental physicists from seeking alternative descriptions, unconventional formulations, surprising electromagnetic effects, or radical generalizations. The various articles in this book provide the reader with a great variety of different kinds of approach to developments of this nature. We have historically motivated accounts, suggestions for new experiments, unconventional viewpoints and attempts at generalizations. We also see novel and ingenious formulations of electromagnetic theory of various different kinds. I am sure that this book will make it clear that electromagnetism is a subject that is in no way closed to stimulating new developments. It is very much alive as a source of fruitful new ideas. Roger Penrose This page is intentionally left blank vii PREFACE The papers in this book are separated into three categories: Foundations, Theory, and Applications. The unifying theme of all chapters in all categories is a broader view of electromagnetism than usually taken. We have deliberately invited some papers that we know challenge the conventional view of electromagnetism. Our justification for this might be described as follows. Before the development of anything begins — whether theorem, thermometer, or theodolite — the design should be frozen; otherwise continuing developments produce continuous design changes, and ultimate frustration. Therefore during the development of a theory, device or system, careful designers must act with incomplete knowledge. A timely example is the design of computers. The field evolves so rapidly that next year's tools, both software and hardware, will be better and less expensive than this year's, yet the product of today must be based upon last year's frozen design. Just as a system design is frozen for progress may be made in system development, theories are frozen so progress may be made in applications. In the 1920s and '30s the founders of quantum theory knew that their understanding was incomplete. Although serious questions regarding interpretations were raised by de Broglie, Schrodinger, Einstein, et ai, the descriptive equations formed the basis of contemporary quantum theory, and, in turn, solid state physics and, later, the electronic-based evolution of society. But forging ahead in this way carries an inherent risk: With each success of a working model come additional adherents to the view that the interpretation adopted as correct as a pragmatic measure at the time is correct for all time, rather than a photographic still taken during its evolution. For example a Time magazine quote by Hynek (August 1967) states: 'There is a tendency in the twentieth century to forget that there will be a twenty-first century science, and, indeed, a thirtieth century science from which vantage points our knowledge of the universe may appear quite different." The major point with respect to the present endeavor is that great predictive power without physical insight may be an impediment to future progress. In the case of the theory of electromagnetism, the theory was first simplified before being frozen. Maxwell expressed electromagnetism in the algebra of quaternions and made the electromagnetic potential the centerpiece of his theory. In 1881 Heaviside replaced the electromagnetic potential field by force fields as the centerpiece of electromagnetic theory. According to him, the electromagnetic potential field was arbitrary and needed to be "assassinated" (sic). A few years later there was a great debate between Heaviside and Tate about the relative merits of vector analysis and quaternions. The result was the realization that there was no need for the greater physical insights provided by quaternions if the theory was purely local, and vector analysis became commonplace. VIII The vast applications of electromagnetic theory since then were made using vector analysis. Although generations of very effective students were trained using vector analysis, more might be learned physically by returning, if not to quaternions, to other mathematical formulations in certain well-defined circumstances. As examples, since the time when the theoretical design for electromagnetism was frozen, gauge theory has been invented and brought to maturity and topology and geometry have been introduced to field theory. Although most persons view their subject matter through the filter of the mathematical tools in which they are trained, the best mathematical techniques for a specific analysis depend upon the best match between the algebraic logic and the underpinning physical dynamics of a theoretical system. Several chapters in this book challenge the view that the algebraic logic of electromagnetism is constant under all conditions, local and global. Hence the quotation on the frontispiece by the mathematician, physicist, religious philosopher and prose stylist Blaise Pascal (1623-1662): Nous ne savons le tout de rien. We only know everything about nothing.1 Since several chapters present experimental and theoretical evidence that we do not know all that might be known about electromagnetism, to think we do is hubris. We hope that the material presented in this book will inspire others to view electromagnetism as a dynamic field worthy of additional research. Each chapter of this book was invited. The chapters are directed towards a new understanding of previously neglected or misunderstood results and experiments, towards a treatment of new experiments, new physical understanding, new mathematical techniques and an extension of electromagnetism when the appropriate boundary conditions require alteration of the foundation algebraic logic. Several chapters in this book use modern analytical tools to examine empirical evidence that was either unknown, too difficult to interpret, or considered unimportant when the old paradigm was frozen. For example, a common viewpoint is that electromagnetic fields are separate from space-time. Chapters of this book that address the issue consider electromagnetic fields to be an integrated part of space- time. They also stress the importance of the underlying algebraic logic to electromagnetic field theories. This is congruent with the view, beginning with Riemann, that the concept of force is secondary to geometry. Using a group theory description, conventional electromagnetism is a local theory of U(l) symmetry form with electric charge and an absence of magnetic charge. For many, even most, conditions, this description works well. However, electromagnetic solitons are well- known to be of SU(2) symmetry, indicating a need to extend electromagnetic theory We are indebted to O. Costa de Beauregard for this quotation. ix to higher symmetry forms under well-defined topological and boundary conditions. The extension of conventional electromagnetism to higher symmetry forms permits easier and more physically informative descriptions of such entities as solitons, etc. The foundational algebraic logic must reflect the topological and boundary conditions. Armed only with differential calculus there is no awareness that field dynamics is held hostage by the topological restrictions determining the algebraic logic. This view raises a question of importance to those seeking a unification of all forces. Perhaps unification of other forces with electromagnetism needs to be with a higher- order symmetry form of electromagnetism than the U(l) form. Such new approaches have impact not only on the foundations and theory, but also in the applied area. For example, early in this century a dichotomy became apparent between an atomic level application of classical electromagnetism and experimental results. After a score more years, the differences were called irreconcilable; electromagnetic theory was applied to atomic phenomena where results agree and ignored otherwise. One chapter asks if today's technology leads to the same conclusions. Part of the analysis contrasts radiation from antennas and electrons. Although both exchange energy with the fields, descriptive and analysis techniques are disparate: Electron analysis ignores field patterns and emphasizes initial and final states and kinematic radiation properties. Antenna analysis ignores states and kinematics and emphasizes field patterns. Antennas have a lower limit to the diameter-to-wavelength ratio. Electrons do not. The chapter concludes that the imaginary part of the complex Poynting theorem applied to multiple sources has been misinterpreted, and that the working model of an electron needs modification. With these changes, atomic properties are consistent with and derivable from the classical field equations. Two chapters emphasize the importance of exact solutions to electromagnetic field problems. One chapter examines numerical and analytical methods for evaluating field integrals about current-carrying wires and obtains an exact formulation for the vector potential about a current-carrying wire. This chapter is an expansion and compilation of other papers that have received several awards. According to one of the award citations, "This work will significantly impact method of moments wire modeling by eliminating the need to perform numerical integration and extending the range of wire diameters that can be successfully modeled." The other chapter obtains an exact solution to a receiving antenna. Unless users of iterative solution methods are sufficiently imaginative in their choice of starting conditions, solutions will not converge to the complete answer, and the user will not know this lack of convergence. This chapter obtains the electromagnetically complete set of receiving antenna current modes. Among other matters, it is learned that receiving modes are essential for electromagnetic momentum to be conserved during reception. Science and engineering do not march steadily onward, and some of the authors feel that we must return to the literature of the time when the foundations of electromagnetism were being frozen to continue progress in foundations, theory and X applications. The feeling is that re-working some of the old problems reveals that the theoretical choices which have worked so well for us in later years are true only conditionally, and, if the conditions are changed, the choices made then are not wrong, but inappropriate under the changed conditions. The intention of these contributors is to place contemporary electromagnetic theory within a larger context of contemporary developments in all of field theory. In the light of the circumstances described above, we can define the field and endeavor: advanced electromagnetism is the study of the wider development of electromagnetism as a field theory, taking the contemporary formulation as an extremely important special case. Terence W. Barrett, Vienna, Virginia, U.S.A. Dale M. Grimes, University Park, Pennsylvania, U.S.A.