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The Power of Geometry 10 ffirs.qxd 4/28/04 11:00 AM Page i T HE G REAT BEYOND Higher Dimensions, Parallel Universes, and the Extraordinary Search for a Theory of Everything PAUL HALPERN John Wiley & Sons, Inc. ffirs.qxd 4/28/04 11:00 AM Page ii This book is printed on acid-free paper.ࠗ∞ Copyright © 2004 by Paul Halpern. All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada Cartoon p. 8, courtesy of the Library of Congress. Figures pp. 19, 22, 24, 37, 48, 52, 75, 127, 253, 265, 273 concept by Paul Halpern. Rendered by Jerry Antner, RichArt Graphics; p. 56, concept by Paul Halpern, based on an illustration by Edwin Abbott, rendered by Jerry Antner, RichArt Graphics. Photos pp. 27, 93, 134, 168, 187, 194, 242 © Paul Halpern; pp. 29, 42, 143 courtesy of the Archives, California Institute of Technology; p. 154, by John Hagemeyer, cour- tesy of the Archives, California Institute of Technology; p. 106, courtesy of the University of Göttingen; pp. 117, 122, 197, courtesy of the Niels Bohr Archive; p. 163, courtesy of Syracuse University; p. 233, courtesy of Claud Lovelace and Rutgers University; pp. 237, 254 courtesy of the American Institute of Physics, Emilio Ségre Visual Archives, Physics Today Collection 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, scanning, or oth- erwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through pay- ment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748- 6008. Limit of Liability/Disclaimer of Warranty: While the publisher and the author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies con- tained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor the author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequen- tial, or other damages. For general information about our other products and services, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. For more information about Wiley products, visit our web site at www.wiley.com. Library of Congress Cataloging-in-Publication Data: Halpern, Paul, date. The great beyond : higher dimensions, parallel universes, and the extraordinary search for a theory of everything / by Paul Halpern. p. cm. Includes bibliographical regerences. ISBN 0-471-46595-X (cloth : alk. paper) 1. Physics—Philosophy. 2. Relativity (Physics) 3. Particles (Nuclear physics) 4. Cosmology. I. Title. QC6.H273 2004 530'.01—dc22 2004004687 Printed in the United States of America 10987654321 ffirs.qxd 4/28/04 11:00 AM Page iii Dedicated to Michael Erlich and Frederick Schuepfer, for their great friendship and inspiration over the years. ffirs.qxd 4/28/04 11:00 AM Page iv Non-Euclidean calculus and quantum physics are enough to stretch any brain; and when one mixes them with folklore, and tries to trace a strange background of multi-dimensional reality behind the ghoulish hints of the Gothic tales and the wild-whispers of the chim- ney corner, one can hardly expect to be wholly free from mental tension. —H. P. LOVECRAFT, “The Dreams in the Witch-House” (1933) ftoc.qxd 4/28/04 11:00 AM Page v Contents Acknowledgments vii Introduction: The Kaluza-Klein Miracle 1 1 The Power of Geometry 10 2 Visions of Hyperspace 26 3 The Physicist’s Stone: Uniting Electricity, Magnetism, and Light 61 4 Getting Gravity in Shape 84 5 Striking the Fifth Chord: Kaluza’s Remarkable Discovery 101 6 Klein’s Quantum Odyssey 114 7 Einstein’s Dilemma 139 v ftoc.qxd 4/28/04 11:00 AM Page vi vi Contents 8 Truth under Exile: Theorizing at Princeton 158 9 Brave New World: Seeking Unity in an Age of Conflict 179 10 Gauging the Weak and the Strong 206 11 Hyperspace Packages Tied Up in Strings 231 12 Brane Worlds and Parallel Universes 267 Conclusion: Extra-dimensional Perception 290 Notes 299 Further Reading 314 Index 319 flast.qxd 4/28/04 11:00 AM Page vii Acknowledgments I wish to acknowledge the generous support of the John Simon Guggenheim Memorial Foundation, which has provided me with the time and resources for this research. The fine examples set by past and current Guggenheim fellows have offered a constant source of inspiration for my work. Several notable historians of science offered me valuable advice for this project. I thank them sincerely for their help. These include Gerald Holton, John Stachel, Martin J. Klein, and Daniela Wünsch. Thanks also to Jürgen Renn and Anne J. Kox, who offered their friendly support. The Philadelphia Area Seminar on the History of Mathematics has been a great source of guidance. I thank the mem- bers of the group for their comments, and acknowledge the critical assistance of David Zitarelli, Robert Jantzen, Paul Pasles, Jim Beich- ler, and Thomas Bartlow. I would also like to honor the memory of my advisor, Max Dresden, who brought the history of science to life in his colorful lectures. Getting to meet and interview the legendary physicist John Wheeler was a special thrill. I thank him for his insights and hospital- ity, and thank Kenneth Ford for arranging the interview, as well for as his own comments. I was also fortunate to have valuable discussions vii flast.qxd 4/28/04 11:00 AM Page viii viii Acknowledgments with many other leading physicists, whom I thank sincerely for their time, including Bryce DeWitt, Gary Gibbons, Paul Steinhardt, Raman Sundrum, Savas Dimopoulos, Alan Chodos, Lisa Randall, Claud Lovelace, and Paul Wesson. Thanks to Peter van Nieuwenhuizen for useful references. Jeff Harvey kindly gave me permission to quote from his song parody. For the use of Einstein’s quotations, I recog- nize the permission granted by the Einstein Papers Project, Califor- nia Institute of Technology, and the Albert Einstein Archives at the Hebrew University of Jerusalem in Israel. Many thanks to Stanley Deser, who shared his insights and took the time to offer me a window into the world of Oskar Klein. A spe- cial word of appreciation to Bernard Julia and Eugene Cremmer of the École Normale Supérieure in Paris for their hospitality and advice during my visit. I would also like to thank astronomers Harry Shipman and Steven Dick, as well as physicists Dieter Forster and Justin Vasquez-Poritz for their suggestions and support. Mathemati- cians Samuel J. Patterson and Martin Kneser of the University of Göt- tingen were extraordinarily kind in describing the history of their department, especially during the time of Kaluza. Psychiatrist John Smythies was of great help for his comments and references about dimensionality and the mind. For elucidating the background of his multimedia pieces and their connections to higher dimensions, I am grateful to filmmaker Peter Rose. The Bergmann family has been of enormous help to my research. It was a distinct pleasure having the opportunity to speak to Peter Bergmann in summer 2002. With his passing, the physics community has lost an exceptional scholar, organizer, and educator. I very much appreciate the kindness of Ernest Bergmann in answer- ing many questions about his father. I also thank John Bergmann, Joshua Goldberg, and Linda Jean Owens (Peter Bergmann’s care- taker when he was ill) for their help. Engelbert Schucking, one of Peter Bergmann’s closest friends and a great scholar of relativity, was kind enough to offer his valuable insights. I would like to thank Robert S. Cox, Valerie-Anne Lutz, and the staff of the Manuscripts Library at the American Philosophical Soci- ety for their friendly assistance. The staff of the Department of Rare Books and Special Collections at Princeton University, including Margaret Rich and AnnaLee Pauls, have been of tremendous help in flast.qxd 4/28/04 11:00 AM Page ix Acknowledgments ix making it possible for me to examine the Albert Einstein Duplicate Archives. The libraries of the University of Pennsylvania, Temple University, the University of Göttingen, Cambridge University, and the London Metropolitan Archives have also been of great use in my research. Thanks also to David Rose, the librarian at the City of Lon- don school, for his generous assistance, for showing me the Edwin Abbott collection and for taking me on a tour of the school. David Martin, head of mathematics for the school, was also very helpful. I would like to express my appreciation to Felicity Pors, Finn Aaserud, and the staff of the Niels Bohr Archive for permitting me to examine the Oskar Klein papers, and for their great hospitality during my visit to Copenhagen.
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