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H074 Front Rabbits Colin Bruce Joseph Henry Press Washington, DC Joseph Henry Press • 500 Fifth Street, N.W. • Washington, D.C. 20001 The Joseph Henry Press, an imprint of the National Academies Press, was created with the goal of making books on science, technology, and health more widely available to professionals and the public. Joseph Henry was one of the founders of the National Academy of Sciences and a leader in early American science. Library of Congress Cataloging-in-Publication Data Bruce, Colin. Schrödinger’s rabbits : the many worlds of quantum / Colin Bruce. p. cm. ISBN 0-309-09051-2 (case) 1. Quantum theory—Popular works. I. Title. QC174.12.B78 2004 530.12—dc22 2004021021 Any opinions, findings, conclusions, or recommendations expressed in this volume are those of the author and do not necessarily reflect the views of the National Academy of Sciences or its affiliated institutions. Cover design by Michele de la Menardiere. Copyright 2004 by Colin Bruce. All rights reserved. Hand-drawn illustrations by Laura Dawes from sketches by Colin Bruce. Printed in the United States of America Dedicated to Paul Dirac physicist extraordinary who believed we must seek visualizable processes and Jim Cushing philosopher of science who believed we must find local stories PREFACE oes the weirdness of quantum indicate that there is a deep problem with the theory? Some of the greatest minds in phys- Dics, including Einstein, have felt that it does. Others prefer to believe that any conceptual difficulties can be ignored or finessed away. I would put the choice differently. The flip side of a problem is an opportunity, and the problems with the old interpretations of quan- tum present us with valuable opportunities. First, there is the hope of finding ways to think more clearly about the subject. I have several times seen highly respected scientists— physicists whose ability to work with the math of quantum mechanics is certainly better than my own—make appalling freshman howlers in describing what the result of an experiment would be, because their qualitative thinking about such matters as quantum collapse was as fuzzy as everyone else’s. Better conceptual tools are badly needed— and now they are becoming available. Second, there is the possibility that a clearer view of quantum will cause us to see the universe in a fundamentally different way, with implications both practical and philosophical. Then, as has happened so many times in physics, the resolution of a seemingly arcane prob- lem will open our eyes to great new wonders. To ignore such an op- portunity would be sheer cowardice. The past few years have seen a sudden explosion of light in the vii viii / Preface murkier corners of quantum. The old stories, involving such quaint characters as dead-alive cats and conscious observers with the power to “collapse” the whole universe, or even split it in two, are passé. There are new stories to choose from, one of them particularly promising. It restores us to a classical universe where things behave predictably rather than randomly and where interactions between things are local rather than long range. But it comes at a price. We must accept that the universe we inhabit is much vaster than we thought, in an unex- pected way. Although the many-worlds view was invented in the United States, it is in Europe, and especially in Oxford, that it has developed to matu- rity. That is my good luck, for I have had the privilege of seeing the process at first hand. Here I describe the remarkable new picture that has recently emerged, which I dub the Oxford Interpretation. My warmest thanks go to my editor Jeff Robbins at Joseph Henry Press for his vision and determination in ensuring that this book came to be. Also to many physicists and philosophers at Oxford and else- where for valuable advice and discussion, including in particular Harvey Brown, David Deutsch, Roger Penrose, Simon Saunders, David Wallace and Anton Zeilinger. Special thanks to Lev Vaidman, Jacob Foster, and Heather Bradshaw, who read the manuscript at an ad- vanced stage and made many useful comments. Responsibility for any mistakes that remain, and any controversial opinions expressed herein, is of course entirely my own. Colin Bruce Oxford, 2004 CONTENTS 1 A Magical Universe 1 2 Clinging to the Classical 13 3 Collapse by Inference 27 4 A Horror Story Writ Large 40 5 The Old Testament 57 6Let’s All Move into Hilbert Space 74 7 Pick Your Own Universe 92 8 A Desirable Locality 106 9 Introducing Many-Worlds 126 10 Harnessing Many-Worlds 1: Impossible Measurements 140 11 Harnessing Many-Worlds 2: Impossible Computers 155 12 Many-Worlds Heroes and Dragons 169 13 The Terror of Many-Worlds 185 14 The Classical Warrior: Roger Penrose 198 15 The New Age Warrior: Anton Zeilinger 211 16 Proving and Improving Many-Worlds 228 Appendix 251 Notes 253 Index 261 ix CHAPTER 1 A MAGICAL UNIVERSE s a teenager, I was a great fan of science fiction and fantasy. The stories I most enjoyed were those set in a universe very A like our own, but with an extra twist—some magical feature that made it much more fun to live in than the mundane world I knew. Then I grew up and discovered something wonderful. Our own real universe does in fact contain at least one magical feature, a built-in conjuring trick that seems to violate all the normal rules. Here is a demonstration. Imagine that a conjurer of impressive reputation is in town and one night you go along to his show. “For my next trick,” he says, “I want a couple from the audience.” To your embarrassment he points straight at you and moments later you find yourself on stage with your partner. “I would like to give you a chance to get rich,” he says, pointing to a large pile of scratch-off lottery cards, all seemingly identical, and looking like the one in Figure 1-1. “All you have to do to win a prize,” he goes on, “is select one of these cards, and tear it in half between you. Each take your half of the card and scratch off 1 of the 60 silvered spots on the clock face to 1 2 / Schrödinger’s Rabbits FIGURE 1-1 Lottery card. reveal the color, either black or white. If the spots you scratch turn out to be different colors, you win $500. And it costs only $10 to play! “Of course each of you is allowed to scratch off only one spot on your respective half of the card. And there is one further rule: To win the prize, you and your partner must choose spots exactly one place apart on the clock face. For example, here is a card that won for two lucky, lucky people on yesterday’s show.” He shows you and the rest of the audience the card shown in Figure 1-2. “You must allow me some secrets, so I will not tell you exactly how the cards are colored. But I will tell you this much. Half of all the FIGURE 1-2 Winning lottery card. A Magical Universe / 3 spots are black, and half white. Also if you and your partner were to scratch off the same spot on each clock face, you would always get the same color—both spots would be black, or both white. But if you were to scratch off spots exactly 90 degrees apart from each other, you would always get opposite colors; white and black, or black and white.” It seems like a bargain, but you hesitate. How do you know he is telling the truth? “I’m from this town, and you’ve got to show me,” you reply, to cheers from the rest of the audience. The conjuror nods, unsurprised. “Be my guest,” he says. “You and your partner may choose any card from the pile, and perform either of those two tests—scratch the same spot on each half, or spots 90 degrees apart on each half. Do that as many times as you like. If you prove me a liar, I’ll pack up my magic show and take an honest job!” You and your partner duly pull out and test numerous cards. The results confirm the conjurer’s predictions, as shown in Figure 1-3a and b. Is it worth playing the game? You think carefully. First, the left and right halves of each card must be identically colored—otherwise you would not be sure of getting the same color every time you scratch spots in matching positions. Second, there must be at least one place in each 90-degree arc where the color changes between black and white. If any card had an arc of more than 90 degrees all one color, you could sometimes scratch spots 90 degrees apart and get the same color. The most obvious guess—and no doubt what the conjurer in- tends you to think—is that the cards are colored in four quarters, as shown in Figure 1-4a. There cannot be fewer segments, as shown in Figure 1-4b, because then you could scratch spots 90 degrees apart and get the same color, which never happens. They might be divided into more segments, as shown in Figure 1-4c, but that would actually increase your chances of winning—there are more black-white bound- aries to hit. As you go round the circle, from spot to spot, you take a total of 60 steps. At least 4 of those steps—maybe more, but certainly no fewer— involve a color change, stepping from a black spot to a white one or vice versa.
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