Page i The Bit and the Pendulum From Quantum Computing to M Theory—The New Physics of Information Tom Siegfried Page ii This book is printed on acid-free paper Copyright © 2000 by Tom Siegfried All rights reserved Published by John Wiley & Sons, Inc Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, photocopying, recording, scanning, or otherwise, 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 payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4744 Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, (212) 850-6011, fax (212) 8506008, email: PERMREQ@WILEY.COM This publication is designed to provide accurate and authoritative information in regard to the subject matter covered It is sold with the understanding that the publisher is not engaged in rendering professional services If professional advice or other expert assistance is required, the services of a competent professional person should be sought Library of Congress Cataloging-in-Publication Data: Siegfried, Tom The bit and the pendulum : from quantum computing to m theory— the new physics of information / Tom Siegfried p cm Includes index ISBN 0-471-32174-5 (alk paper) Computer science Physics Information technology I Title QA76.S5159 1999 004—dc21 99-22275 Printed in the United States of America 10 Page iii Contents Preface Introduction vii 1 Beam Up the Goulash 13 Machines and Metaphors 37 Information Is Physical 57 The Quantum and the Computer 77 The Computational Cell 95 The Computational Brain 115 Consciousness and Complexity 133 IGUSes 155 Quantum Reality 177 10 From Black Holes to Supermatter 195 11 The Magical Mystery Theory 213 12 The Bit and the Pendulum 235 Notes 249 Glossary 264 Further Reading 268 Index 275 Page v Preface In the course of my job, I talk to some of the smartest people in the universe about how the universe works These days more and more of those people think the universe works like a computer At the foundations of both biological and physical science, specialists today are construing their research in terms of information and information processing As science editor of the Dallas Morning News, I travel to various scientific meetings and research institutions to explore the frontiers of discovery At those frontiers, I have found, information is everywhere Inspired by the computer as both tool and metaphor, today's scientists are exploring a new path toward understanding life, physics, and existence The path leads throughout all of nature, from the interior of cells to inside black holes Always the signs are the same: the world is made of information A few years ago, I was invited to give a talk to a regional meeting of MENSA, the high-IQ society I decided to explore this theme, comparing it to similar themes that had guided the scientific enterprise in the past For it seemed to me that the role of the computer in twentieth-century science was much like that of the steam engine in the nineteenth century and the clock in medieval times All three machines were essential social tools, defining their eras; all three inspired metaphorical conceptions of the universe that proved fruitful in explaining many things about the natural world Out of that talk grew this book It's my effort to put many pieces of current science together in a picture that will make some sense, and impart some appreciation, to anyone who is interested Specialists in the fields I discuss will note that my approach is to cut thin slices through thick bodies of research No doubt any single chapter in this book could easily have been expanded into a book of Page vi its own As they stand, the chapters that follow are meant not to be comprehensive surveys of any research area, but merely to provide a flavor of what scientists at the frontiers are up to, in areas where information has become an important aspect of science Occasional passages in this book first appeared in somewhat different form in articles and columns I've written over the years for the Dallas Morning News But most of the information story would never fit in a newspaper I've tried to bring to life here some of the subtleties and nuances of real-time science that never make it into the news, without bogging down in technicalities To the extent I've succeeded in communicating the ideas that follow, I owe gratitude to numerous people Many of the thoughts in this book have been shaped over the years through conversations with my longtime friend Larry Bouchard of the University of Virginia I've also benefited greatly from the encouragement, advice, and insightful questions over dinner from many friends and colleagues, including Marcia Barinaga, Deborah Blum, K C Cole, Sharon Dunwoody, Susan Gaidos, Janet Raloff, JoAnn Rodgers, Carol Rogers, Nancy Ross-Flanigan, Diana Steele, and Jane Stevens I must also express deep appreciation for my science journalist colleagues at the Dallas Morning News: Laura Beil, Sue Goetinck, Karen Patterson, and Alexandra Witze, as well as former News colleagues Matt Crenson, Ruth Flanagan, Katy Human, and Rosie Mestel Thanks also go to Emily Loose, my editor at Wiley; my agent, Skip Barker; and of course my wife, Chris (my harshest and therefore most valuable critic) There are in addition countless scientists who have been immensely helpful to me over the years, too many to attempt to list here Most of them show up in the pages that follow But I sadly must mention that the most helpful scientist of all, Rolf Landauer of IBM, did not live to see this book He died in April 1999, shortly after the manuscript was completed Landauer was an extraordinary thinker and extraordinary person, and without his influence and inspiration I doubt that this book would have been written TOM SIEGFRIED MAY 1999 Page Introduction I think of my lifetime in physics as divided into three periods In the first period I was in the grip of the idea that Everything is Particles I call my second period Everything is Fields Now I am in the grip of a new vision, that Everything is Information —John Archibald Wheeler, Geons, Black Holes, and Quantum Foam John Wheeler likes to flip coins That's not what he's famous for, of course Wheeler is better known as the man who named black holes, the cosmic bottomless pits that swallow everything they encounter He also helped explain nuclear fission and is a leading expert on both quantum physics and Einstein's theory of relativity Among physicists he is esteemed as one of the greatest teachers of the century, his students including Nobel laureate Richard Feynman and dozens of other prominent contributors to modern science One of Wheeler's teaching techniques is coin tossing I remember the class, more than two decades ago now, in which he told all the students to flip a penny 50 times and record how many times it came up heads He taught about statistics that way, demonstrating how, on average, heads came up half the time, even though any one run of 50 flips was likely to turn up more heads than tails, or fewer.* *Wheeler taught a class for nonscience majors (I was a journalism graduate student at the time) at the University of Texas at Austin In his lecture of January 24, 1978, he remarked that a good rule of thumb for estimating statistical fluctuations is to take the square root of the number of events in question In tossing 50 coins, the expected number of heads would be 25; the square root of 25 (footnote continued on next page) Page Several years later, Wheeler was flipping coins again, this time to help an artist draw a picture of a black hole Never mind that black holes are invisible, entrapping light along with anything else in their vicinity Wheeler wanted a special kind of picture He wanted it to illustrate a new idea about the nature of information As it turns out, flipping a coin offers just about the simplest possible picture of what information is all about A coin can turn up either heads or tails Two possibilities, equally likely When you catch the coin and remove the covering hand, you find out which of the two possibilities it is In the language that computers use to keep track of information, you have acquired a single bit A bit doesn't have to involve coins A bit can be represented by a lightbulb—on or off By an arrow, pointing up or down By a ball, spinning clockwise or counterclockwise Any choice from two equally likely possibilities is a bit Computers don't care where a bit comes from—they translate them all into one of two numbers, or Wheeler's picture of a black hole is covered with boxes, each containing either a zero or a one The artist filled in the boxes with the numerals as a student tossed a coin and called out one for heads or zero for tails The resulting picture, Wheeler says, illustrates the idea that black holes swallow not only matter and energy, but information as well The information doesn't have to be in the form of coins It can be patterns of ink on paper or even magnetic particles on a floppy disk Matter organized or structured in any way contains information about how its parts are put together All that information is scrambled in a black hole's interior, though—incarcerated forever, with no possibility of parole As the cosmologist Rocky Kolb describes the situation, black holes are like the Roach Motel Information checks in, but it doesn't check out If you drop a coin into a black hole, you'll never know whether it lands heads or tails But Wheeler observes that the black hole keeps a record of the information it engulfs The more information swallowed, the bigger (footnote continued from previous page) is 5, so in tossing 50 coins several times you would expect the number of heads to vary between 20 and 30 The 23 of us in the class then flipped our pennies The low number of heads was 21, the high was 30 Average for the 23 runs was 25.4 heads Page the black hole is—and thus the more space on the black hole's surface to accommodate boxes depicting bits To Wheeler, this realization is curious and profound A black hole can consume anything that exists and still be described in terms of how much information it has digested In other words, the black hole converts all sorts of real things into information Somehow, Wheeler concludes, information has some connection to existence, a view he advertises with the slogan "It from Bit." It's not easy to grasp Wheeler's idea of connecting information to existence He seems to be saying that information and reality have some sort of mutual relationship On the one hand, information is real, not merely an abstract idea On the other hand reality—or existence—can somehow be described, or quantified, in terms of information Understanding this connection further requires a journey beyond the black hole (or perhaps deep inside it) to glimpse the strange world of quantum physics In fact, Wheeler's black hole picture grew from his desire to understand not only information, but also the mysteries of the subatomic world that quantum physics describes It's a description encoded in the elaborate mathematical rules known as quantum mechanics Quantum mechanics is like the U.S Constitution Just as the laws of the land must not run afoul of constitutional provisions, the laws of nature must conform to the framework established by quantum mechanics' equations And just as the U.S Constitution installed a radically new form of government into the world, quantum requirements depart radically from the standard rules of classical physics Atoms and their parts not obey the mechanics devised by Newton; rather, the quantum microworld lives by a counterintuitive code, allowing phenomena stranger than anything Alice encountered in Wonderland Take electrons, for example—the tiny, negatively charged particles that swarm around the outer regions of all atoms In the world of large objects that we all know, and think we understand, particles have welldefined positions But in the subatomic world, particles behave strangely Electrons seem to be in many different places at once Or perhaps it would be more accurate to say that an electron isn't anyplace at once It's kind of smeared out in a twilight zone of possi- Page bilities Only a measurement of some sort, an observation, creates a specific, real location for an electron out of its many possible locations Particles like that can strange things Throw a baseball at a wall, and it bounces off If you shoot an electron at a wall, it might bounce off, but it also might just show up on the other side of the wall It seems like magic, but if electrons couldn't that, transistors wouldn't work The entire consumer electronics industry depends on such quantum weirdness Wall-hopping (the technical term is tunneling) is just one of many quantum curiosities Another of the well-known quantum paradoxes is the fact that electrons (and other particles as well) behave sometimes as particles, sometimes as waves (And light, generally thought of as traveling in waves, sometimes seems to be a stream of particles instead.) But light or electrons are emphatically not both particles and waves at the same time Nor are they some mysterious hybrid combining wave and particle features They simply act like waves some of the time and like particles some of the time, depending on the sort of experiment that is set up to look at them It gets even more bizarre Quantum mechanics shows no respect for common notions of time and space For example, a measurement on an electron in Dallas could in theory affect the outcome of an experiment in Denver And an experimenter can determine whether an electron is a wave or particle when it enters a maze of mirrors by changing the arrangement of the mirrors—even if the change is made after the electron has already passed through the maze entrance In other words, the choice of an observer at one location can affect reality at great distances, or even (in a loose sense) in the past And so the argument goes that observers, by acquiring information, are somehow involved in bringing reality into existence and complexity, 167-76 and thermodynamics, 65-66, 70-72 ion channels, 125 J Jacquard loom, 49 Jammer, Max, 180 Joos, Erich, 184 Jozsa, Richard, 25n, 84 K Kaplan, Peter, 111 Kari, Lila, 102 Kauffman, Stuart, 110-11 Kelvin, Lord, 44 Kent, Adrian, 259n.25 Kimble, Jeff, 89-90, 93, 94 Koch, Christof, 119, 135, 145, 146-47 Kolb, Rocky, Kolmogorov, Andrei, 169 Kraus, Per, 260n.14 Kuhn, Thomas, 39 L Landauer, Rolf, 6, 59 on the brain as computer, 131-32 and physics of computation, 66-67, 69-72, 73, 74, 75-76, 241-44 on quantum computers, 78-79, 87-88, 94 Landauer's principle, 66-67, 75, 205-6, 240-44 Landweber, Laura, 101-3 Leggett, Anthony, 259n.25 Leibniz, Gottfried Wilhelm von, 48, 215 Libchaber, Albert, 111 light, 4, 22 Lisberger, Stephen, 125-26 Lloyd, Seth, 35-36, 88 logical depth See depth logic gates, 89-90 cellular, 108-10 See also quantum logic gates Logue, Donald, 78 loop quantum gravity, 220-22, 232-33 Page 279 Lucky, Robert W., 65 Lytton, William, 124 M machines as metaphors, 37-38, 237-40 See also clocks; computers magnetic resonance imaging (MRI), 91-92 manifolds, 225-26 ''many worlds" theory, 180-86, 192-94 matrix mechanics, 21-22 Mauchly, John, 45, 46 Maxwell, James Clerk, 61, 62 Maxwell's demon, 61-64, 70, 73 Mazur, Pawel, 261n.4 meiosis, 98-99 membranes See supermembranes Merkle, Ralph, 74-75 messenger RNA, 99 Minkowski, Hermann, 208 Mitchell, Melanie, 139-43 mitochondria, 101 molecular biology See DNA Morrison, David, 225-26 M-theory, 227-32 N National Institute of Standards and Technology (NIST), 91 National Security Agency, 86 neural networks, 122-24 neuronal group selection, 149-53 neurons, 118, 122-24 See also brain neuroscience See brain; computational neuroscience Newcomen, Thomas, 42 Newman, M.H.A., 53 Newton, Isaac, 7, 39, 41, 140, 179, 206, 215, 237, 257n.3 Nielsen, M A., 250n.15 nuclear magnetic resonance (NMR), 91-92 O observer of information and black holes, 204-5 role of in physics, 60-61, 182, 187-88, 192-94 Ogihara, Mitsunori, 113 Omnès, Roland, 185, 190-91, 262-63n.11 Oresme, Nicole, 40-41, 250n.2 P Pagels, Heinz, 159-60 parallel processing, 82-84 Parent, Antoine, 67-69, 251n.16 Park, Robert, 14 particles, 4, 21-22, 215-17 Pascal, Blaise, 46-47 Pascal, Etienne, 47 Pascal, Gilberte, 48 Pascal, Jacqueline, 47 Pascaline, 47-48 p-branes, 227-29 pendulums, 238, 243-44 Penrose, Roger, 126-27, 145-46, 221, 255n.16 Peres, Asher, 25n phase transition, 226 photons, 19, 25-28 physics, laws of, 241-44 See also quantum mechanics Pierce, John R., 38 Planck, Max, 20, 21 Planck length, 218-19 Planck's constant, 263n.20 Podolsky, Boris, 26 Poe, Edgar Allan, 236 Poincaré, Henri, 136-37 Polchinski, Joseph, 228 Preskill, John, 93-94 Press, William, 159 proteins computational capabilities of, 104-6, 107 Page 280 and DNA, 99 G proteins, 108-11 Q quanta, 21-22 quantum computing, 77-93, 252n.6, 258n.11 and cryptography, 78, 84-87 and magnetic resonance imaging, 91-93 quantum cryptography, 28-33 quantum decoherence, 183-86, 191-92, 258n.15, 259n.25, 262n.11, 263n.12 quantum information, 24-25 quantum logic gates, 88-91 quantum mechanics, 3-5, 19-20, 36, 175, 177-79, 216-17, 260n.14 and black holes, 198-205 origins of, 245-47, 263n.15 probabilistic aspect of, 23-24, 187-90 quantum objects, 18-20 quantum teleportation, 15-18, 25-28 quarks, 160 quasiclassical realms, 188-90 qubits, 34-35 See also quantum computing R Ray, Animesh, 113 receptor proteins, 107 Redford, Robert, 77-78 relativity, theories of, 206, 208, 261n.3 reversible computing, 73-76, 252n.21 ribosomes, 99 Richelieu, Cardinal, 47 Riemann, Georg Friedrich Bernhard, 207-8 Roddenberry Gene, 18 Roosevelt, Franklin, 63 Rosen, Nathan, 26 Ross, Elliott, 109-10 Ross, John, 106 Rovelli, Carlo, 220-21, 232 Russell, Bertrand, 51 S Savery, Thomas, 42 schema, 164, 171 Schrödinger, Erwin, 22, 180 Schrödinger equation, 181-82, 192-93 Schulman, Leonard, 92 Schumacher, Benjamin, 34-35, 36, 78, 92-93, 205 Schwarz, John, 211, 223, 226, 227, 230 science computer's impact on, metaphors for, 37-38, 39-40 Searle, John, 127-29 Seiberg, Nathan, 216-17, 232 Sejnowski, Terry, 122-26, 129-30 Shannon, Claude, 64-66, 67, 70 Shannon's information theory, 167, 168, 169, 175 Shickard, Wilhelm, 250n.7 Shor, Peter, 84, 85-86 Shurkin, Joel, 46 Simon, Daniel, 84 Sinha, Sudeshna, 144 slide rule, 118 Smolin, Lee, 220-21 Sneakers, 32, 77-78, 93 Solomonoff, Ray, 169 space on large scales, 217-18 on small scales, 218-20 theories of, 213-17 special relativity, theory of, 208 spin networks, 221-22 Sporns, Olaf, 152 standard model of particle physics, 216-17 Page 281 steam engine, 42-45 Strasbourg Cathedral clock, 41 Strathairn, David, 78, 85 Strominger, Andy, 215, 225-26, 230 supermembranes, 227-32 superparadigms, 39-40 superposition, 182 superstrings, 222-26 supersymmetry, 210-12 Susskind, Leonard, 198-99, 202, 204, 231 Swanson, John, 70 symmetry, 209-10 Szilard, Leo, 63-64, 251n.6 T Tegmark, Max, 255n.16 teleportation, quantum, 13-15, 25-28 defined, 16-17 of information, 16-18 theory, relationship of to reality, 236-37 theory of everything, 257n.15 thermodynamics, 44 and black holes, 200 and information theory, 65-66, 70-72 laws of, 61-64 Thomson, William, 44 Tipler, Frank, 158 Tononi, Giulio, 152, 153 topology, 225-26 Toulmin, Stephen, 239 transistors, 106 The Truman Show, 235-36 tunneling, Turing, Alan, 37-38, 52-55 Turing machines, 52-55, 81, 126-27, 169, 250n.15 Turing test, 38, 250n.1 typewriters, 38 tyrosine hydroxylase, 121 U uncertainty principle, 18 Updike, John, 158 V Vafa, Cumrun, 230 van Gelder, Tim, 137-38, 139 Vazirani, Umesh, 84, 85-86, 92 vestibulo-ocular reflex, 116, 125 visual awareness, 134-35, 146-48 von Neumann, John, 116-19 W Wagstaff, Samuel, 32 Wald, Robert, 247 waterwheels, 68-69 Watson, James, 96, 98, 134 Watt, James, 42-43 wave mechanics, 22 waves, 4, 21-22 Weaver, Warren, 167 Weinberg, Steven, Weiskrantz, Lawrence, 147 Weyl, Hermann, 209, 247 Wheeler, John Archibald, 1-2, 7, 64-65, 156, 182-83, 219, 233, 240, 251n.7, 257n.3 on black holes, 2-3, 195-97, 199-200 on quantum mechanics, 5-6, 245-46 Whitehead, Alfred North, 174 Wiener, Norbert, 239 Wilczek, Frank, 202-3, 204, 227, 260n 14 WIMPs (weakly interacting massive particles), 211-12 Wineland, Dave, 91, 93 Witten, Edward, 212, 227 Wootters, William, 25n, 34n, 36 wormholes, 219 Z Zeh, H Dieter, 184 Zurek, Wojciech, 36, 60-61, 63, 178, 184-85, 186, 190-91, 251n.15 (chap 2), 258n.16 Page 192 (the consistent histories) Halliwell produced some calculations to indicate that, at least in certain specific cases, the relationship was in fact quantitative ''We thus find verification of our conjecture: the number of bits required to describe a decoherent set of histories is equal to the number of bits of information about the system stored in the environment." 29 This work reiterates a very important point: the idea of reality being related to information is not a mere metaphor Information is real Information is physical And understanding that is opening a whole new avenue for understanding the nature of existence Halliwell notes that his work in this area was inspired by Zurek's observations that ideas from information theory have not been exploited as much as they might be in physics As a further source of inspiration, Halliwell mentions John Wheeler's idea of "It from Bit." It's only fitting, then, that the pursuit of information's importance in science should take us back to Wheeler and in particular to his favorite astrophysical character, the black hole Hugh Everett's Many Worlds Theory Hugh Everett's "many-worlds" interpretation of quantum mechanics has itself been interpreted in many different ways, so it might be worth going into a little more detail about what he actually said Everett did not coin the phrase "many worlds"; rather he called his approach the "relative state" formulation of quantum mechanics His essential idea was to apply the Schrödinger equation to an "isolated system." No system is truly isolated, except the universe as a whole The universe can, however, be broken down into subsystems—in other words, the universe can be considered as a "composite" system The physicist's task is to describe the universe's subsystems without resorting to some "observer" outside the universe to determine what happens A key point is that the universe's subsystems inevitably interact Therefore no subsystem of the universe is independent of all the rest In fact, Everett points out, any observation or measurement is just a special case of an interaction between subsystems So it is impossible to describe a given subsystem completely—in physics lingo, describe its "state"—without regard to the rest of the universe Page 193 Any subsystem can exist in many possible states, then, depending on the state of the rest of the universe's subsystems "It is meaningless to ask the absolute state of a subsystem," Everett asserted "One can only ask the state relative to a given state of the remainder of the subsystems." 30 So far, it's all pretty straightforward But the Schrödinger equation complicates things by allowing more than one pair of relationships between subsystems In fact, the Schrödinger equation allows multiple possible combinations of subsystem states—what physicists call a "superposition" of states If you take the Schrödinger equation seriously, Everett decided, you have to conclude that all the different superpositions of states are equally real "The whole issue of the transition from 'possible' to 'actual' is taken care of in the theory in a very simple way—there is no such transition," Everett commented "From the viewpoint of the theory all elements of a superposition (all 'branches') are 'actual,' none any more 'real' than the rest." In this approach, "observers" are just certain subsystems within the universe, systems that "can be conceived as automatically functioning machines (servomechanisms) possessing recording devices (memory) and which are capable of responding to their environment" (in Gell-Mann's words, IGUSes) As an "observer" interacts with other subsystems (or "object-systems," in Everett's terminology), their states become connected, or ''correlated.'' "From the standpoint of our theory, it is not so much the system which is affected by an observation as the observer, who becomes correlated to the system," Everett wrote "Correlations between systems arise from interaction of the systems, and from our point of view all measurement and observation processes are to be regarded simply as interactions between observer and object-system which produce strong correlations." So any one "observer's" state will change after interaction with an object-system But because there is more than one way to describe the observer-object-system relationship (a superposition of different ways), there is no single state that can uniquely describe the observer after the interaction "It is then an inescapable consequence that after the interaction has taken place there will not, generally, exist a single observer state," Everett commented "There will, however, be a superposition of the composite system states, each element of which contains a definite observer state and a definite relative object-system state [E] ach element of the resulting superposition describes an observer who perceived a definite and generally Page 194 different result." The correlations set up by multiple interactions ensure consistency among multiple communicating observers, Everett points out But any one observer, after an interaction, exists in multiple states "Whereas before the observation we had a single observer state," he explains, "afterwards there were a number of different states for the observer, all occurring in a superposition Each of these separate states is a state for an observer, so that we can speak of the different observers described by the different states On the other hand, the same physical system is involved, and from this viewpoint it is the same observer, which is in different states for different elements of the superposition (i.e., has had different experiences in the separate elements of the superposition)." And the theory does not allow any way of deciding which of the different observer states is the "true" one "It is improper to attribute any less validity or 'reality' to any element of a superposition than any other element," Everett wrote "All elements of a superposition must be regarded as simultaneously existing.''