5829tp(path) 29/8/05 1:48 PM Page 1 100 Years of Gravity and Accelerated Frames The Deepest lnsig hts of Einstein and Yang-Mills ADVANCED SERIES ON THEORETICAL PHYSICAL SCIENCE A Collaboration between World Scientific and Institute of Theoretical Physics Series Editors: Dai Yuan-Ben, Hao Bai-Lin, Su Zhao-Bin (Institute of Theoretical Physics Academia Sinica) Vol. 1 : Yang-Baxter Equation and Quantum Enveloping Algebras (Zhong-Qi Ma) Vol. 2: Geometric Methods in the Elastic Theory of Membrane in Liquid Crystal Phases (Ouyang Zhong-Can, Xie Yu-Zhang & Liu Ji-Xing) Vol. 4: Special Relativity and Its Experimental Foundation (Yuan Zhong Zhang) Vol. 6: Differential Geometry for Physicists (Bo- Yu Hou & Bo- Yuan Hou) Vol. 7: Einstein’s Relativity and Beyond (Jong-Ping Hsu) Vol. 8: Lorentz and PoincarC Invariance: 100 Years of Relativity (J.- P. Hsu & Y.- Z. Zhang) Vol. 9: 100 Years of Gravity and Accelerated Frames: The Deepest Insights of Einstein and Yang-Mills (J.-P. Hsu & D. Fine) 5829tp(path) 29/8/05 1:48 PM Page 2 100 Years of Gravity and Accelerated Frames The Deepest Insights of Einstein and Yang–Mills Editors Jong-Ping Hsu Dana Fine University of Massachusetts Dartmouth, USA World Scientific NEW JERSEY . LONDON . SINGAPORE . BEIJING . SHANGHAI . HONG KONG . TAIPEI . CHENNAI Published by World Scientific Publishing Co.P te. Ltd. 5 Toh Tuck Link, Singapore 596224 USA ofice: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK ofice: 57 Shelton Street, Covent Garden, London WC2H 9HE Library of Congress Cataloging-in-PublicationD ata 100 years of gravity and accelerated frames : the deepest insights of Einstein and Yang-Mills I editor, Jong-Ping Hsu; advisory editor, Dana Fine. p. cm. -- (Advanced series on theoretical physical science; v. 9) Includes bibliographical references. ISBN 981-256-335-0 (alk. paper) 1. Gravitation. 2. Relativity (Physics). 3. Einstein field equations. 4.Y ang-Mills theory. I. Title: One hundred years of gravity and accelerated frames. 11. Hsu, J. P. (Jong-Ping). 111. Fine, Dana. IV. Series. QC178.Al5 2005 530.1 l--dc22 2005050077 British Library Cataloguing-in-PublicationD ata A catalogue record for this book is available from the British Library. Copyright 0 2005 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, orpartsthereoJ may not be reproducedinany formorby any means, electronicormechanical, 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. Printed in Singapore by B & JO Enterprise Deepest Insights The Deepest Insights of Einstein and Yang-Mills The Deepest Insights of Einstein and Yang-Mills The Deepest Insights of Einstein and Yang-Mills The Deepest Insights of Einstein and Yang-Mills To Arthur Fine Hu/Shih and Tsierm/SAue-Sen The Deepest Insights of Einstein and Yang-Mills The Deepest Insights of Einstein and Yang-Mills The Deepest Insights of Einstein and Yang-Mills The Deepest Insights of Einstein and Yang-Mills Deepest Insights This page intentionally left blank "In 1953-19 54, I was visiting Brookhaven and Bob was my office mate. We discussed many things in physics, from the experimental results pouring out of the new Cosmotron, to theoretical topics like renormalization and the Ward identity. It was in that year that we found the very elegant and unique generalization of Maxwell's equation. We were pleased by the beauty of the generalization, but neither of us had anticipated its great impact on physics 20 years later. C. N. Yang, in "Remembering Robert L. Mills" by Samuel L. Marateck, Physics Today, p. 14, October 2003. Robert Mills and Kitty, the oldest of his 5 kids. "The Rubaiyat" Omar Khayyam (transl. by Edward Fitzgerald) This page intentionally left blank ix Preface This book is a collection of papers and writings from the past 100 years on ideas and problems related to gravity, gauge fields and accelerated frames. The grand triumphs of Einstein's theory of gravity and Yang-Mills' theory in physics are well known. It is believed that both theories are based on the principle of 'gauge invariance,' although not on the same kind of action. Einstein's theory is linear in spacetime curvature, while Yang-Mills' theory is quadratic in gauge curvature. Now, at the dawn of the 2 1s t century, invariance principles in physics have transcended the kinematical and dynamical contexts from which they originated to became the foundation of our understanding of the physical world. Using this framework of invariance principles, this book surveys the development of gravitationa1 and Yang- Mills fields, as well as spacetime transformations of accelerated frames. It also attempts to reveal the problems and limitations of various formulations of gravitational and Yang-Mills fields. The intent is to enlarge and broaden the reader's views on the subjects. As TIME magazine's person of the 20th century (cf. TIME magazine), Einstein's contributions to physics are arguably incomparable, aside from Newton's. The gravitational force and accelerated frames were two ingredients in the young Einstein's 'happiest thoughts' in 1907. The simple thought that 'If a person falls freely he will not feel his own weight,' made a deep impression on him and impelled him toward a successful theory of gravitation. Unfortunately, accelerated spacetime transformations for non-inertial frames have still not been well developed. However, they are important because one cannot claim to have a complete understanding of the physical world, especially the basic gravitational and Yang-Mills fields, if one understands physics only from the viewpoint of the special and limited class of inertial frames. Strictly speaking, all real frames of reference in the physical world are non-inertial because of the long range of the gravitational force. In particular, when one taks about an inherent property of nature (e.g., values of fundamental constants such as the fine structure constant and the speed of light), a reasonable criterion is that the property must be present in both incrtial and non-inertial frames. In this sense, the book suggests that the present understanding of gravitational and Yang-Mills fields is far from complete. The formulations of the gravitational and Yang-Mills theories are both an effect and a cause of scientifk development in experiment and theory. Progress in physics is made through the collective effort of many physicists. The community of physicists is like the thousand-hand Guan-Yin: Each hand accomplishes only a partial or small task, yet the overall accomplishment is enormous. As we shall see in this volume, in the pursuit of physical laws, the right track has often been discovered only after many failures by well-known and not-so-well-known pathfinders.