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WINNER OF THE NOBEL PRIZE IN PHYSICS

$36.95 CAN
Where are the frontiers of science?
In this age of superstring theories and Big Bang cosmology, we're used to thinking of the unknown as impossibly distant from our everyday lives. The edges of physicists’ knowledge,
were told, lie in the first nanofraction of a second after the
Universe came into existence, or in realms so small that they can't be glimpsed by even the most sophisticated experimental techniques, or else in regions of space where the forces of gravity are so strong that no information can
escape. The latest theories of physics, in fact, deal with
phenomena so inaccessible that we don’t know if we will ever be able to run the experiments needed to test them— a circumstance that has led some people to speak of “the end of science.”
But in A Different Universe, Nobel Laureate Robert B.
Laughlin argues that we haven't reached the end of science at all—not even close. We've only reached the end of a certain kind of reductionist thinking. If instead of looking for ultimate theories we consider the world of emergent properties—meaning the properties, such as the hardness and shape of a crystal, that result from the organization of large numbers of atoms—suddenly the deepest mysteries are as close as the nearest ice cube or grain of salt. And Laughlin goes further: the most fundamental laws of physics—such as Newton's laws of motion or quantum mechanics—are in fact emergent. They are properties of large assemblages of matter, and when their exactness is examined too closely, it vanishes into nothing.
Laughlin shows us why everything we think about fundamental physical laws needs to change, and why the greatest mysteries of physics are not at the ends of the, universe but well within our reach. A Different Univesse takes us into a world—surprisingly, our own—where the vacuum of space has to be considered a kind of solid mat ter, where sound has quantized particles just like those of light, where there are many phases of matter, not just three,
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A Different Universe
REINVENTING Rents tease
from the Bottom Down
Robert B. Laughlin
BASIC BOOKS
A Member of the Perseus Books Group New York

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Copyright © 2005 by Robert B. Laughlin Published by Basic Books, A Member of the Perseus Books Group
All rights reserved. Printed in the United States of America. No part of this book may be reproduced in any manner whatsoever without written permission except in the case of brief quotations embodied in critical articles and reviews. For information, address Basic Books, 387 Park Avenue South, New York, NY 10016-8810.
Books published by Basic Books are available at special discounts for bulk purchases in the United States by corporations, institutions, and other organizations. For more information, please contact the Special Markets Department at the Perseus Books Group, 11 Cambridge Center, Cambridge
MA 02142, or call (617) 252-5298 or (800) 255-1514, or e-mail special. markets@perseusbooks.com.
Designed by Brent Wilcox Text set in 11.75 point Minion
Library of Congress Cataloging-in-Publication Data
Laughlin, Robert B.
A different universe : reinventing physics from the bottom down / Robert B. Laughlin.
Pp. Pent Includes bibliographical references and index. ISBN 0—465-03828-X (hardcover : alk. paper) 1. Physics—Popular works. _I. Title. QC24.5.L38 2005
530—dc22
2004028059
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Not only is the universe stranger than we imagine, it is stranger than we can imagine.
Sir Arthur Eddington

CONDE ENTS

Preface

x

Acknowledgments

Xvii

(7O5NFE*)
Frontier ‘Vaw <1
(awe)
Living with Uncertainty 9
(THREE ) Mount Newton 23
(FOUR ) Waters ice and Vapor? 33
( FIWE) Schrédinger’s Cat 47
fhe The Quantum Computer 59
(SEVEN ) Vin Klitzing 71

viii

CONTENTS

(EIGHT ) I Solved It at Dinner 81
(NINE ) The Nuclear Family 99
TERA The Fabric of Space-Time 117

(ELEVEN ) Carnival of the Baubles 127

(TWELVE ) The Dark Side of Protection 143
(THI EEN | Principles. of Life. 157

(FOURTEEN ) Star Warriors 177

(FIFTEEN ) Picnic Table in the Sun 193

(S St H Be NL)
The Emergent Age 205

Notes

292

Index

245

PREFACE
All the rivers run into the sea; yet the sea is not full; unto the place _z from whence the rivers come, thither they return again.
Eccle 27
There are two conflicting primal impulses of the human mind— one to simplify a thing to its essentials, the other to see through the essentials to the greater implications. All of us live with this conflict and find ourselves pondering it from time to time. At the edge of the sea, for example, most of us fall into thoughtfulness about the majesty of the world even though the sea is, essentially, a hole filled with water. The vast literature on this-subject, some of it very ancient, often expresses the conflict as moral, or as tension between the sacred and the profane. Thus viewing the sea as simple and finite, as an engineer might, is animistic and primitive, whereas viewing it as a source of endless possibility is advanced and human.
But the conflict is not just a matter of perception: it is also physical. The natural world is regulated both by the essentials and by powerful principles of organization that flow out of them. These principles are transcendent, in that they would continue to hold even if the essentials were changed slightly. Our conflicted view of nature reflects a conflict in nature itself, which consists simultaneously of

x

PREFACE

ue
The essence of life.
primitive elements and stable, complex organizational structures
that form from them, not unlike the sea itself.
The edge of the sea is also a place to have fun, of course, something it is good to keep in mind when one is down there by the boardwalk being deep. The real essence of life is strolling too close to the merry-goround and getting clobbered by a yo-yo. Fortunately, we physicists are fully aware of our own sententious tendencies and go to great lengths to keep them under control. This attitude was artfully expressed inaletter my colleague Dan Arovas, a faculty member at the University of California at San Diego, wrote to the humor columnist Dave Barry:
Dear Dave, I am a passionate fan of yours and read your column every day. I would give anything to be able to write like you. I have built a tree house in your honor and live in it. Yours, Dan
Dan reports that Dave wrote back:

PREFACE

x

Dear Dan, Thanks for the fan letter. By the way, do they let you any-
where near nuclear weapons? Best, Dave

A few years ago I had occasion to engage my father-in-law, a retired academician, on the subject of the collective nature of physical law. We had just finished playing bridge late one afternoon and were
working on a couple of gin and tonics in order to escape discussing movies of emotional depth with our wives. My argument was that reliable cause-and-effect relationships in the natural world have something to tell us about ourselves, in that they owe this reliability to principles of organization rather than microscopic rules. The laws of nature that we care about, in other words, emerge through collective self-organization and really do not require knowledge of their component parts to be comprehended and exploited. After listening carefully, my father-in-law declared that he did not understand. He had always thought laws cause organization, not the other way around. He was not even sure the reverse made sense. I then asked him whether legislatures and corporate boards made laws or were made by laws, and he immediately saw the problem. He pondered it for a while, and then confessed that he was now deeply confused about why things happen and needed to think more about it. Exactly so.
It is a terrible thing that science has grown so distant from the rest
of our intellectual life, for it did not start out that way.! The writings
of Aristotle, for example, despite their notorious inaccuracies, are
beautifully clear, purposeful, and accessible.? So is Darwin's Origin of Species. The opacity of modern science is an unfortunate side effect of professionalism, and something for which we scientists are often pilloried—and deservedly so. Everyone gets wicked pleasure from snapping on the radio on the drive home from work to hear Doctor Science give ludicrous answers to phone-in questions such as why _ cows stand in the same direction while grazing (they must face Wisconsin several times a day) and then finish up with, “And remember,

xii

PREFACE

I know more than you. I have a master’s degree in science.”4 On another occasion my father-in-law remarked that economics had been terrific until they made it into a science. He had a point.
The conversation about physical law started me thinking about what science had to say about the obviously very unscientific chicken-and-egg problem of laws, organizations of laws, and laws from organization. I began to appreciate that many people had strong views on this subject but could not articulate why they held them. The matter came to a head recently whenIrealized I was having the same conversation over and over again with colleagues about Brian Greene’s The Elegant Universe, a popular book describing some speculative ideas about the quantum mechanics of space.> The conversation focused on the question of whether physics was a logical creation of the mind or a synthesis built on observation. The impe-
tus for the discussion was never an existential problem, of course, but
money, the lack of which is the universal common denominator of world science. But the subject always seemed to drift from there to the pointlessness of making models of the world that were beautiful but predicted no experiments, and from there to the question of what science is. After this happened a number of times in such disparate venues as Seattle, Taipei, and Helsinki, it struck me that the disagreement spawned by Greene’s book was fundamentally the same problem that had occupied us that day after bridge. Moreover, it was an ideological dispute: it had nothing to do with what was true and everything to do with what “true” was.
It is commonly said in physics that good notation advances while bad notation retards. This is certainly true. A phonetic alphabet takes less time to master than a pictorial one and thus makes writing more accessible. Decimal numbers are easier to use than roman numerals. The same idea applies to ideologies. Seeing our understanding of nature as a mathematical construction has fundamentally different implications from seeing it as an empirical synthesis. One view

PReEeAGE

xiii

identifies us as masters of the universe; the other identifies the universe as the master of us. Little wonder that my colleagues down in the trenches of experimental science had become so animated over this question. At its core the matter is not scientific at all but concerns one’s sense of self and place in the world.
The threads of these two world views run very deep. When I was a kid I drove with my parents to Yosemite for a rendezvous with my aunt and uncle, who had driven in from Chicago. My uncle was a brilliant and highly successful patent attorney who seemed to know everything and was not shy about sharing this fact. For example, he once gave me a long sermon on how lasers work after learning that I had just hada lecture on the subject from Charles Townes, the laser’s inventor. Evidently, he knew more about it than Professor Townes.
On this occasion he and my aunt checked in at the Ahwahnee, the
fanciest hotel in the place, held court there with us, consumed a few
buffet breakfasts, and then left to drive over Tuolumne Pass to the desert and home. I don’t think they sawa single waterfall up close. There was no point, since they had seen waterfalls before and understood the concept. After they left, my family and I hiked up the
Merced river, amid the violence and roar, to Nevada Falls and had a
picnic on a massive piece of granite next to a meadow full of wild-
flowers. We understood the concept too but were wise enough not to take our understanding too seriously.
The world view motivating my uncle’s attitude toward Yosemite,
_ and arguably also Brian Greene’s attitude toward physics, is expressed with great clarity in John Horgan’s The End of Science, in which he argues that all-fundamental things are now known and there is nothing left for us to do but fill in details.© This pushes my experimental colleagues beyond their already strained limits of patience, for it is both wrong and completely below the belt. The search for new things always looks like a lost cause until one makes a discovery. If it were ob-
vious what was there, one would not have to look for it!

xiv

PREFAGE

Unfortunately, this view is widely held. I once had a conversation with the late David Schramm, the famous cosmologist at the University of Chicago, about galactic jets. These are thin pencils of plasma
that beam out of some galactic cores to fabulous distances, some-
times several galactic radii, powered somehow by mechanical rotation in the core. How they can remain thin over such stupendous
distances is not understood, and something I find tremendously in-
teresting. But David dismissed the whole effect as “weather.” He was interested only in the early universe and astrophysical observations that could shed light on it, even if only marginally. He categorized the jets as annoying distractions on the grounds that they had nothing in particular to tell him about what was fundamental. I, in contrast, am fascinated by weather and believe that people claiming not to be are fibbing.
I think primitive organizational phenomena such as weather have something of lasting importance to tell us about more complex ones, including ourselves: their primitiveness enables us to demonstrate with certainty that they are ruled by microscopic laws but also, paradoxically, that some of their more sophisticated aspects are insensitive to details of these laws. In other words, we are able to prove in these simple cases that the organization can acquire meaning and life of its own and begin to transcend the parts from which it is made. What physical science thus has to tell us is that the whole being more than the sum of its parts is not merely a concept but a physical phenomenon. Nature is regulated not only by a microscopic rule base but by powerful and general principles of organization. Some of these principles are known, but the vast majority are not. New ones are being discovered all the time. At higher levels of sophistication
the cause-and-effect relationships are harder to document, but there
is no evidence that the hierarchical descent of law found in the primitive world is superseded by anything else. Thus if a simple physical phenomenon can become effectively independent of the more fun-

PREFACE

XV

damental laws from which it descends, so can we. I am carbon, but I need not have been. I have a meaning transcending the atoms from which I am made.
The essential elements of this message are articulated in the extensive writings of Ilya Prigogine” and even more originally in a famous essay by P. W. Anderson entitled “More is Different”’ published over 30 years ago. This essay is just as fresh and inspiring today as it was then, and still required reading for any student wishing to work with me.
_ My views are considerably more radical than those of either of my predecessors, however, because they have been sharpened by recent events. I am increasingly persuaded that all physical law we know about has collective origins, not just some of it. In other words, the distinction between fundamental laws and the laws descending from them is a myth, as is the idea of mastery of the universe through mathematics alone. Physical law cannot generally be anticipated by
pure thought, but must be discovered experimentally, because control of nature is achieved only when nature allows this through a principle of organization. One might subtitle this thesis the end of reductionism (the belief that things will necessarily be clarified
when they are divided into smaller and smaller component parts), but that would not be quite accurate. All physicists are reductionists at heart, myself included. I do not wish to impugn reductionism so
much as establish its proper place in the grand scheme of things. To defend my assertion I must openly discuss some shocking
ideas: the vacuum of space-time as “matter,” the possibility that relativity is not fundamental, the collective nature of computability, epistemological barriers to theoretical knowledge, similar barriers to experimental falsification, and the mythological nature of important parts of modern theoretical physics. The radicality is, of course, partly a stage prop, for science, as an experimental undertaking, cannot be radical or conservative but only faithful to the facts. But these

xvi

PREFACE

larger conceptual issues, which are not science at all but philosophy, are often what most interest us because they are what we call upon to weigh merit, write laws, and make choices in our lives.
The objective, then, is not to make controversy for the sake of itself
but to help us see clearly what science has become. To do this we must forcibly separate science’s function as the facilitator of technology from its function as a means of' understanding things—including ourselves. The world we actually inhabit, as opposed to the happy idealization of modern scientific mythology, is filled with wonderful and important things we have not yet seen because we have not
looked, or have not been able to look at due to technical limitations.
The great power of science is its ability, through brutal objectivity, to reveal to us truth we did not anticipate. In this it continues to be in-
valuable, and one of the greatest of human creations.

ACKNOWLEDGMENTS
This book would not have come into being without the invaluable efforts of Mr. Steve Lew, whose original concept it was and who worked tirelessly to promote the project with publishers and to encourage me to write. The latter was central, for we scientists have responsibilities and contractual obligations that must be sacrificed to accomplish a task of this size. My interaction with Steve has been one of the most memorable of my long academic career, and I gratefully acknowledge both his extraordinary gifts as a facilitator and organizer and the immense help he provided me in seeing the problem of physical emergence from a humanistic perspective. I also acknowledge his ideas. The tone, form, and scope of the project are partly his, as they emerged out of a series of conversations we had in my office over the course of many months. For all of this, and for helping me edit the manuscript, Steve has my most heartfelt thanks.
I am also deeply indebted to Professor David Pines for much patient help in getting the project off the ground and for critical reading of the manuscript. During David’s visit to Stanford in the spring of 1999 we discovered that our views on the physics of collective organization were identical—a great surprise, considering the differences in our backgrounds—as were our perceptions for the need to translate what was so obvious to us into accessible everyday language. This culminated in our coauthoring the essay “The Theory _of Everything,” in which the main themes of what would eventually
xvii

XViii

ACKNOWLEDGMENTS

become this book were first articulated.! The immense popularity of that essay, which caught us both off guard, caused us to realize that a bigger version had to be written. David’s visit also induced me to become actively involved in his Institute for Complex Adaptive Matter, a cross-disciplinary forum dedicated to the worldview that mathematics grows out of experimental observation, not the other way
around. Among its other functions, the institute encourages (forces) scientists to explain their work to each other in pedestrian terms. The
value of this practice is impossible to overstate. I have learned more about science through workshops sponsored by this institute and the personal contacts they generated than I have from all other professional activities combined.
I wish to express special thanks to two institutions that shielded me from academic duties while I was writing. One is the Institute for Materials Research in Sendai, Japan, where I spent part of my sabbatical leave in November 2002. I gratefully acknowledge the warm hospitality of Professor Sadamichi Maekawa, with its many fine evenings of expensive sushi and eel near the banks of the Hirose River. The other is the Korea Institute for Advanced Study in Seoul, where I am currently an adjunct professor. My visit there in September 2003 was especially productive, and I owe my host, Professor C. W. Kim, an immense debt of gratitude for this—not to mention for the dazzling variety of restaurants we sampled.
Finally, of course, I must thank my wife, Anita, for her seemingly endless patience, and the promise that I will indeed now take a break so that we can make that trip to Maine she has been anticipating for so long to revisit family haunts and track down some good lobster.

LSO5NE.)
Een ter Slaw
Nature 1s a collective idea, and though its essence exist in each indi_2 vidual of the species, can never its perfection inhabit a single object.
Henri Fuseli
M ANY YEARS AGO, WHEN | WAS LIVING NEAR NEW YORK,
I attended a retrospective of Ansel Adams, the great nature photographer, at the Museum of Modern Art. Like many people born in the American West, I had always liked Mr. Adams’s work and felt I appreciated it better than New Yorkers ever could, so I jumped at the chance to see it firsthand. It was well worth the effort. Anyone seeing these images close up realizes at once that they are not simply sterile pictures of rocks and trees but thoughtful comments on the meaning of things, the immense age of the earth, and the impermanence of human concerns. This exhibition made a much stronger impression on me than I had expected, and it flashes into my mind even now when I am wrestling with a tough problem or having difficulty separating what is important from what is not.
Public television viewers were reminded recently by Ric Burns’s excellent American Experience documentary that Mr. Adams's work, like any other art, was as much a creation of a specific time and place _as of the artist himself.! In the early part of the twentieth century,

2

A DIFFERENT UNIVERSE

In Europe, the myth of the frontier is often dismissed as quaint provincialism.
when Adams was a boy and the frontier had been declared closed, Americans debated vigorously over what its loss implied for their future.” In the end, they decided that they did not want to be like Europe, that part of their identity, and of meaningful life generally, was in close proximity to wildness. Thus was born the metaphorical frontier—the myth of the cowboy, the vast landscape of the possible, the ideal of the rugged individual—that defines American culture to this day. Adams’s work grew to maturity alongside this

Frontier Law

3

metaphor and derives its power by eliciting the nostalgia for untamed wilderness at its core.
The idea of the frontier is not just quaint provincialism. It is often spoken of as such, especially in Europe, where the mythological nature of the American West has always been easier to discern than it is here and is often viewed with suspicion. Ifirst saw this idea expressed in a lengthy article on America in the magazine Stern when I was a soldier stationed in Germany in the early 1970s. Such articles are appearing with increasing frequency nowadays as the cold war recedes inté history. But the perception is incorrect. While the confluence of cultural forces that generated Adams’s images is uniquely American, the images themselves are not. The longing for a frontier seems to lie deep in the human soul, and people from different parts of the world and with different cultural backgrounds understand it quickly and intuitively. In no country does one have to dig very deep to find an
appreciation of, and identification with, wildness. Adams’s work
travels well for this reason and has universal appeal. The idea of science as a great frontier is similarly timeless.* While
there are clearly many nonscientific sources of adventure left, science is the unique place where genuine wildness may still be found. The
wildness in question is not the lurid technological opportunism to which modern societies seem so hopelessly addicted, but rather the pristine natural world that existed before humans arrived—the vast openness of the lone rider splashing across the stream with three _ pack animals under the gaze of mighty peaks. It is the choreography
of ecologies, the stately evolution of minerals in the earth, the mo-
tion of the heavens, and the birth and death of stars. Rumors of its death, to paraphrase Mark Twain, are greatly exaggerated.
My particular branch of science, theoretical physics, is concerned with the ultimate causes of things. Physicists have no monopoly on ultimate causes, of course, for everyone is concerned with them to some extent. I suspect it is an atavistic trait acquired. long ago in

4

A DIFFERENT UNIVERSE

Africa for surviving in a physical world in which there actually are causes and effects—for example between proximity to lions and being eaten. We are built to look for causal relations between things and to be deeply satisfied when we discover a rule with cascading implications.4 We are also built to be impatient with the opposite— forests of facts from which we cannot extract any meaning. All of us secretly wish for an ultimate theory, a master set of rules from which all truth would flow and that could forever free us from the frustration of dealing with facts. Its concern for ultimate causes gives theoretical physics a special appeal even to nonscientists, even though it is by most standards technical and abstruse.
It is also a mixture of good news and bad news. First you find that your wish for an ultimate theory at the level of human-scale phenomena has been fulfilled. We are the proud owners of a set of
mathematical relationships that, as far as we know, account for
everything in the natural world bigger than an atomic nucleus. They are very simple and beautiful and can be written in two or three lines. But then you find that this simplicity is highly misleading— rather like those inexpensive digital wristwatches with only one or two buttons. The equations are devilishly difficult to manipulate and impossible to solve in all but a small handful of instances. Demonstrating that they are correct requires arguments that are lengthy, subtle, and quantitative. It also requires familiarity with a huge body of work done after the Second World War. While the basic ideas were invented by Schrédinger, Bohr, and Heisenberg in the 1920s, it was not until powerful electronic computers were developed and armies of technically competent people were generated by governments that these ideas could be tested quantitatively against experiment over a wide range of conditions. Key technical developments, such as the purification of silicon and the perfection of atomic beam machines, were also important. Indeed, we might never have known for certain that the whole thing was correct had it

Frontier Law

5

not been for the cold war and the economic importance of electronics, radar, and accurate timekeeping, which made financing easy on various ostensibly practical grounds.
Thus eighty years after the discovery of the ultimate theory we find ourselves in difficulty. The repeated, detailed experimental confirmation of these relationships has now officially closed the frontier of reductionism at the level of everyday things. Like the closing of the American frontier, this is a significant cultural event, causing thoughtful people everywhere to debate what it means for the future of 4enowledge. There is even a best-selling book exploring the premise that science is at an end and that meaningful fundamental discovery is no longer possible. At the same time, the list of even very simple things found “too difficult” to describe with these equations continues to lengthen alarmingly.
Those of us out on the real frontier listening to the coyotes howl at night find ourselves chuckling over all this. There are few things a
real frontiersman finds more entertaining than insights about
wilderness from people back in civilization who can barely find the
supermarket. I find this moment in history charmingly similar to
Lewis and Clark’s wintering on the Columbia estuary. Through grit
and determination their party had pushed its way across a continent,
only to discover that the value had not been in reaching the sea but
in the journey itself. The official frontier at that time was a legal fic-
tion having more to do with property rights and homesteading pol- icy than a confrontation with nature. The same is true today. The real
frontier, inherently wild, may be found right outside the door, if one
only cares to look. Despite beinga wild place, the frontier is regulated by laws. In the
mythical old West the law meant the force of civilization in a land where there was none, and it was often enforced by some heroic fig‘ure holding back the wildness of human nature through strength of
will. A man had a choice of whether to obey this law or not, but he

6

A DIFFERENT UNIVERSE

stood a good chance of getting gunned down if he did not. But there are natural laws as well, relationships among things that are always true regardless of whether people are present to observe them. The sun rises every morning. Heat flows from hot things to cold ones. Herds of deer spotting cougars always dash away. These are the exact opposite of laws of myth, in that they flow out of wildness and constitute its essence rather than being 4 means for its containment. Indeed, describing these things as laws is somewhat misleading, for it implies a kind of statute that otherwise willful natural things choose to obey. This is not correct. It is a codification of the way natural things are.
The important laws we know about are, without exception, serendipitous discoveries rather than deductions. This is fully compatible with one’s everyday experience. The world is filled with sophisticated regularities and causal relationships that can be
quantified, for this is how we are able to make sense of things and ex-
ploit nature to our own ends. But the discovery of these relationships is annoyingly unpredictable and certainly not anticipated by scientific experts. This commonsense view continues to hold when the matter is examined more carefully and quantitatively. It turns out that our mastery of the universe is largely a bluff—all hat and no cattle. The argument that all the important laws of nature are known is simply part of this bluff. The frontier is still with us and still wild.
The logical conflict between an open frontier on the one hand and a set of master rules on the other is resolved by the phenomenon of emergence. The term emergence has unfortunately grown to mean a number of different things, including supernatural phenomena not regulated by physical law. I do not mean this. I mean a physical principle of organization. Human societies obviously have rules of organization that transcend the individual. An automobile company, for example, does not cease to exist if one of its engineers gets run over by a truck. The government of Japan does not change very much

Frontier Law

7

after an election. But the inanimate world also has rules of organization, and they similarly account for many things that matter to us, including most of the higher-level physical laws we use in our daily lives. Such commonplace things as the cohesiveness of water or the rigidity of steel are simple cases in point, but there are countless others. Nature is full of highly reliable things that are primitive versions of impressionist paintings. A field of flowers rendered by Renoir or Monet strikes us as interesting because it is a perfect whole, while the daubs of paint from which it is constructed are randomly shaped and imperfect. The imperfection of the individual brush strokes tells us that the essence of the painting is its organization. Similarly, the ability of certain metals to expel magnetic fields exactly when they are refrigerated to ultralow temperatures strikes us as interesting because the individual atoms out of which the metal is made cannot do this.
Since principles of organization—or, more precisely, their conse-
quences—can be laws, these can themselves organize into new laws,
and these into still newer laws, and so on. The laws of electron mo-
tion beget the laws of thermodynamics and chemistry, which beget
the laws of crystallization, which beget the laws of rigidity and plas-
ticity, which beget the laws of engineering. The natural world is thus
an interdependent hierarchy of descent not unlike Jonathan Swift’s
society of fleas:

So, naturalists observe, the flea Has smaller fleas that on him prey; And these have smaller still to bite ’em And so proceed ad infinitum.

This organizational tendency is so powerful that it can be difficult to distinguish a fundamental law from one of its progeny. The only way we know that the behavior of cats is not fundamental, for example, is because cats fail to work when pushed beyond their proper

8

A DIFFERENT UNIVERSE

operating limits, so to speak. Similarly, the only way we know atoms are not fundamental is that they come apart when caused to collide at great speed. This principle continues down to smaller and smaller scales: the nuclei from which atoms are made come apart when caused to collide at greater speed, the parts liberated from the nucleus come apart at even greater speeds, and so forth. Thus the tendency of nature to form a hierarchical society of physical laws is much more than an academic debating point. It is why the world is knowable. It renders the most fundamental'laws, whatever they are, irrelevant and protects us from being tyrannized by them. It is the reason we can live without understanding the ultimate secrets of the universe.
Thus the end of knowledge and the closing of the frontier it symbolizes is not a looming crisis at all, but merely one of many embarrassing fits of hubris in civilization’s long history. In the end it will pass away and be forgotten. Ours is not the first generation to struggle to understand the organizational laws of the frontier, deceive itself that it has succeeded, and go to its grave having failed. One would be wise to be humble, like the Irish fisherman observing quietly that the sea is so wide and his boat so small. The wildness we all need to live, grow, and define ourselves is alive and well, and its glo-
rious laws are all around.

(TW O-)
ieviliesoew ith Uncertainty
aN
Fast is fine, but accuracy is everything.
Wyatt Earp
My GENETICIST COLLEAGUE DAVID BOTSTEIN OFTEN BEGINS
lectures by explaining that the essence of biology is living with uncertainty. He especially emphasizes this to audiences of physicists, because he knows they have a hard time with the concept and will misinterpret much of what he says unless alerted to the issue ahead of time. He has never revealed to me how he thinks about such audiences, but I happen to know that most biologists consider the physicists’ obsession with certainty and correctness to be exasperatingly childish and evidence of their limited mental capacities. Physi-
cists, in contrast, consider tolerance of uncertainty to be an excuse
for second-rate experimentation and a potential source of false claims. These cultural differences have their roots in the historical development of the two sciences (physics and chemistry evolved together with engineering, while biology came from agriculture and medicine), and they mirror differences in our society generally about what is and is not real and important. But because of them there is

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A DIFFERENT UNIVERSE

relatively little useful communication between physicists and biologists at the moment.
A version of this communication problem comes up now and then in conversations with my wife, typically over money. She usually begins by casually suggesting some horrendously expensive purchase she cannot make on her own. I then ask her questions that I think get to the bottom of things, such as how much interest we will be paying or what the impact will be on our total cash flow. She responds that I am impossible because | always want to see things as black and white, never gray. I explain that I am just trying to solve the problem. She counters that I am oversimplifying. The world is nuanced, she says, not always clear-cut, and my insistence on stuffing things into categories and boxes is simply unreal. I respond that there is nothing unreal about avoiding jail and bankruptcy. The duration of this existential interchange depends on how much money is involved, but it eventually ends with some sort of compromise. Our argument is, of course, not about worldviews and reality at all but control of resources. I am the moralist in the family, so naturally I tend to lose more often than I win.
Physical scientists do not like absolute pronouncements about
what is and is not true. We know that measurements are never per-
fect and thus want to know how true a given measurement is. This is a good practice, for it keeps everyone honest and prevents research reports from degenerating into fish stories. Our lofty attitude, however, belies something considerably easier to understand: the impulse to measure things accurately is the same as the impulse to make doit-yourself repairs. The real allure is not high ideals at all but shiny, complex machines bristling with wires and dials, and staying up all night drinking coffee and manning the computer while the stereo
blasts rock-and-roll in the background. It is monster X-ray tubes,
smoking soldering irons, nuclear reactors with holes in them for neutrons to come out, highly dangerous chemicals, and helpful signs

Living with Uncertainty

11

saying things like, “Do not look into the laser with your remaining good eye.” It is also fundamentally a matter of problem-solving strategy, the notoriously gender-linked personality trait that is the source of all those jokes about wives who cannot read maps and husbands who refuse to ask for directions.! It is why buildings and academic majors at the Massachusetts Institute of Technology have numbers rather than names. Accurate measurement is simply natural behavior for people who see nothing strange in creating building ten, building thirteen, and course eight. I think all of this is mighty fine myself, but it if not for everybody.
One of the things we technological people find gratifying about giving in to this impulse is the world of meaning revealed by increasingly accurate measurement. For example, at an accuracy of one part
in one hundred thousand, one discovers that the length ofa brick is
not the same from one day to the next. A check of environmental fac-
tors reveals this to be due to variations in temperature, which cause
the brick to expand and contract slightly. The brick has become a
thermometer. This observation is not silly, since thermal expansion is
the principle behind all common thermometers.” A weight measure-
ment to similar accuracy shows no such variations—one of many observations leading to the concept of inviolability of mass. But at an accuracy of one part in one hundred million, the weight of the brick
becomes slightly different from one laboratory to the next. The brick
is now a gravity meter, for this is an effect of slight variations in the
force of gravity due to differing densities of rock immediately below
the earth’s surface. Attaching the brick to a string and suspending it from the ceiling turns the brick into a pendulum, whose swing rate is
also a measure of the force of gravity. The extreme stability of the
swing is the principle behind pendulum regulation of mechanical clocks.‘ If the ceiling is high, the mass is large, and the swivel is out-
fitted with alittle electric amplifier to prevent the pendulum from
running down, the plane of the swing may be observed to rotate in

12

A DIFFERENT UNIVERSE

response to the rotation of the earth, the rate of this rotation being a measure of the latitude.5 Nontechnical people put up with this measurement obsession, which they otherwise find annoying, because of the useful new technologies it generates.
Physical scientists, on the other hand, tend to see the matter morally. They orient their lives around the assumption that the
world is precise and orderly, and that its occasional failure to con-
form to this vision is a misperception brought about by their not having measured sufficiently accurately or thought sufficiently carefully about the results. This sometimes has bittersweet consequences. My brother-in-law the divorce attorney says that his most exasperating clients are Silicon Valley engineers, who typically want to just write down the family assets, divide them equally, shake hands, and be done with it. He has to patiently explain that it is not that easy— that people often lie and manipulate in stressful situations, that one
can sometimes deceive oneself, that the value of the assets is not ab-
solute, that there is horse-trading to be done, that there will be messy
contractual obligations left over, and so forth. This does not mean that the simpler view is wrong, merely that it is not always practical.
Over the past three centuries, obsessive attention to detail has slowly revealed that some physical quantities are not only accurately reproducible from one experiment to the next but are completely universal. It is hard to overstate how astonishing and disturbing this is. The extreme reliability and exactness of these quantities elevates their status from mere useful fact to a kind of moral certainty. Many people feel uncomfortable thinking of numbers in moral terms, but they should not. If I hit a dog with my car going forty miles per hour it has different implications than if I hit the dog going one mile per hour. The more carefully these quantities were measured, the more accurately their universal values became known, even as the limits of technical capability were pushed back in breathtaking ways, a process that continues today. The deeper meaning of these discoveries is still

Living with Uncertainty

13

being debated, but everyone agrees that they are important, for such certainty is uncommon in nature and demands explanation.
A familiar example of such a universal quantity is the speed of light. In the late nineteenth century there was increasing interest in measuring the motion of the earth in its orbit around the sun by its effect on the light propagation speed seen by an observer on earth. This was a daunting technical challenge at the time, since it required measuring the speed of light to an accuracy of one part ina billion. How this was accomplished is a wonderful story told over and over again around the campfires of physics, but let us say for the present purposes that it was done with mirrors. By 1891 it had become clear that the effect was at least a factor of two smaller than it should have been based on an analogy with sound and the known speed of earth in its orbit. By 1897 this had improved toa factor of forty, a disparity too great to be dismissed as irrelevant or an experimental artifact. The expected modification of the speed of light due to the earth’s motion did not exist. This finding eventually led Albert Einstein to conclude that the speed of light is fundamental and that moving bodies must gain mass as their speed increases.
The existence of universal quantities that can be measured with
certainty is the anchor of physical science. This essential truth is
sometimes easy to forget, for the fundamentals of physics have been
with us so long that many of them have ossified into clichés. But de-
spite how one may feel about their message, the postmodernist
philosophers have correctly and insightfully understood that scien-
tific theories always have a subjective component that is as much a
creation of the times as a codification of objective reality.” Otto von
Bismarck’s famous quip, “Laws are like sausages—it is best not to
see them being made,” applies even more brilliantly to scientific the-
ories, or so is my experience. As in all other human activities, it is
necessary in science to take stock every now and then and reevaluate
what one deeply understands and what one does not. In physics, this

14

A DIFFERENT UNIVERSE

reevaluation nearly always comes down to precision measurement. Deep inside every physical scientist is the belief that measurement accuracy is the only fail-safe means of distinguishing what is true from what one imagines, and even of defining what true means. There is no need to have postmodernist anxieties about a universal number measured to one part in ten billion.
When physicists get together at parties to talk in uninhibited ways about things that matter to them, one of their favorite subjects is a famous lecture delivered by Irving Langmuir, the inventor of the modem tungsten-filament light bulb, on the subject of pseudoscience.® This lecture contains delicious case histories of scientific fakeries and swindles, but its greater importance lies in its central message: in physics, correct perceptions differ from mistaken ones in that they get clearer when the experimental accuracy is improved. This simple idea captures the essence of the physicist’s mind and explains why they are always so obsessed with mathematics and numbers: through precision, one exposes falsehood.
A subtle but inevitable consequence of this attitude is that truth and measurement technology are inextricably linked. Exactly what
you measure, how the machine works, how one decimates the er-
rors, what uncontrolled factors set the reproducibility ceiling, and so forth matter more in the end than the underlying concept. In public we speak about the inevitability of these universal quantities, but in private we consider it unprofessional to talk about what ought to be universal in the same way we consider it unprofessional to talk about how much money one ought to make on stocks. You have to actually do the experiment. This practice may seem like the worst kind ofpedantry, but it is really just common sense. Time and again things people thought were universal turned out not to be, and other things people thought varied actually didn’t. Accordingly, when we speak of universal quantities we really mean the experiments that measure them.

Living with Uncertainty

15

The handful of experiments that are enormously accurate has, for this reason, a significance in physics greatly exceeding its size. There are between ten and twenty of these special experiments, depending on how one counts, and they are all revered.” Most of these special experiments are unfamiliar to nonexperts. There is the speed of light in vacuum, known now to an accuracy of better than one part in ten trillion. There is also the Rydberg constant, the number characterizing the quantization of light wavelengths emitted from dilute atomic vapors and responsible for the astonishing reliability of atomic
cloéks, known to an accuracy of one part in one hundred trillion. Another example is the Josephson constant, the number relating the
voltage applied to a certain kind of metallic sandwich to the frequency of radio waves it emits, known to an accuracy of one part in one hundred million. Yet another is the von Klitzing resistance, the number relating the electric current forced through aspecially designed semiconductor to the voltage induced at right angles by means of a magnet, known to an accuracy of one part in ten billion.
Paradoxically, the existence of these highly reproducible experi-
ments leads us to think in two mutually incompatible ways about
what is fundamental. One is that exactness reveals something about
the primitive building blocks out of which our complicated, uncer-
tain world is made. Thus we say that the speed of light is constant be-
cause it just is, and because light is not made of anything simpler.
This thought process leads us to render these highly accurate experi-
ments down to a handful of so-called “fundamental” constants. The
other is that exactness is a collective effect that comes into existence
because of a principle of organization. An example of the latter is the
relationship between pressure, volume, and temperature of a gas
such as air. The universal number characterizing the dilute gas law is
known to an accuracy of one part in one million, yet it acquires huge
errors in gas samples that are too small, and ceases to be measurable
at all at the level of a few atoms. The reason for this size sensitivity is

16

A DIFFERENT UNIVERSE

that temperature isastatistical property, like the market demand for houses, which requires a large sample to be defined. There is no way to reconcile these two ideas; they are exact opposites. Yet we use the word fundamental to describe both.
This dilemma is, of course, artificial. Only the collective idea is right. This is not obvious, and would even be denied vehemently by some physicists, but it becomes clear after one thinks critically about the experiments themselves and how they work.
Collective exactness tends to be a tough concept for nonscientists to grasp, but it shouldn’t be. There are many familiar examples of it in daily life—for example, commuting. The sun comes up in the morning, and this is a reliable truth having to do with the primitive
motion of the earth, the huge heat capacity of the sun, and so forth.
But there is another, equally important, truth that the expressways and trains are always jammed with commuters at certain times of day, and moreover that the number of commuters is predictable from one hour to the next. It is certainly imaginable that all these commuters might get the stomach flu on the same day and stay home, but it is so unlikely as to be effectively impossible. The commute condition is a simple, reliable phenomenon that emerges out of complex decisions made by a large number of individuals as they go about their lives. It is not necessary to know what various individuals had for breakfast, where they work, what the numbers and names of their children are, and so forth, in order to appreciate that it’s hell out there at 8:15 in the morning. Commuting traffic, like the behavior of the dilute gas, is a collective certainty. Whether it is as reliable as the sun rising must ultimately be determined by experiment, but my experiences commuting say it is.
A nice example of a collective effect masquerading as a reductionist one is the quantization of atomic spectra. Light is emitted from dilute atomic vapors with special wavelengths so insensitive to outside influences that they can be used to make clocks accurate

Living with Uncertainty

17

to one part in one hundred trillion. But these wavelengths have a detectable shift at one part in ten million—ten million times larger than the timing errors of the clock—which should not have been present in an ideal world containing nothing but the atom.!° Difficult but well-controlled calculations then revealed this shift to be an electrical effect of the vacuum of space not very different from what an electron encounters as it moves about inside a piece of metallic wire or a computer chip. The ostensibly empty vacuum of space, in other words, is not empty at all but full of “stuff” Its sympathetic motion when matter passes by changes the matter’s properties slightly, just the way sympathetic motion of the electrons and atoms in a piece of window glass modifies the properties of light as it passes through, causing it to refract. The extreme reproducibility and reliability of these atomic experiments are thus crucially de-
pendent on the uniformity of this “stuff” the cause of which is un-
known. Identifying a plausible explanation for this uniformity is one of the central problems of modern physics and the chief objec-
tive of inflationary cosmologies—theories of the universe that are inherently emergent.!! So even the constancy of atomic spectra ac-
tually has collective origins, the collective phenomenon in this case being the universe itself.
A much more immediate and troubling case of collectivism is the
determination of the electron charge and Planck’s constant by means
of macroscopic measurements. The electron charge is the indivisible
unit of electricity. Planck’s constant is the universal relation between
momentum and length that characterizes the wave nature of matter.
Both are highly reductionist concepts, and both are traditionally de-
termined using huge machines that measure properties of individual
electrons ripped off of atoms. But their most accurate determination
turns out to come not from these machines at all but simply from
combining the Josephson and von Klitzing constants, the measure-
ment of which requires nothing more sophisticated than a cryogenic

18

A DIFFERENT UNIVERSE

refrigerator and a voltmeter.!? That this was so was a great surprise when it was discovered, because the samples on which the Josephson and von Klitzing measurements are performed are highly imperfect.
Chemical impurities, misplaced atoms, and complex atomic struc-
tures such as grain boundaries and surface morphologies are all plentiful and should have been able to disrupt the measurements at the reported level of accuracy. The fact that they do not proves that powerful principles of organization are at work.
One of the reasons physicists so rarely talk about the collective nature of measurements of fundamental constants is that it has such deeply troubling implications. Insofar as our knowledge of the physical world rests on experimental certainty, it is logical that we should associate the greatest truth with the most certain measurement. But this would seem to imply that a collective effect can be more true than the microscopic rules from which it descends. In the case of temperature, a quantity that never had a reductionist definition in the first place, this conclusion is easy to understand and accept. Every physical scientist understands that the tendency of heat to flow from hot things to cold ones is very general and would not be affected if one were to change the microscopic aspects radically—for example, by doubling the masses of all the atoms in the universe—so long as the system did not get small. But the electron charge is another matter. We are accustomed to thinking of this charge as a building block of nature requiring no collective context to make sense. The experiments in question, of course, refute this idea. They reveal that the electron charge makes sense only in a collective context, which may be provided either by the empty vacuum of space, which modifies this charge the same way it modifies atomic wavelengths, or by some matter that preempts the vacuum’s effects. Moreover, the preemptive ability of matter requires the organizational principles at-work there to be the same as those at work in the vacuum, since otherwise the effects would be miracles.

Living with Uncertainty

19

The electron charge conundrum, as it turns out, is not unique. All
the fundamental constants require an environmental context to make sense. As a practical matter, the distinction between reductionist and emergentist quantities in physics does not exist. It is simply an
artistic invention of humans, rather like the genders we sometimes
assign to inanimate objects. The idea of certainty emerging through organization is deeply em-
bedded in the culture of modern biology, and is one of the reasons
my(Colleagues i in the life sciences are so eager to declare their toleranc of uncertainty. It shows they know the scoop. What they actually mean by such statements is that microscopic uncertainty does not matter, because organization will create certainty later on at a higher level. Another reason, of course, is that they want to loosen up the purse strings, the political strategy employed by my wife in those spending discussions. In neither case should the tolerance be taken at face value. Were it really the case that the essence of biology is uncertainty, then biology would not be science.
In physics, in contrast, the profound ideological disagreement on
where certainty comes from, and what it means, remains unresolved.
Instead, we agree not to talk about it. This compromise calls to mind
Deng Xiaoping’s famous remark that it does not matter whether a cat
is black or white as long as it catches mice.!3 It is not uncommon for
a committed reductionist to dismiss the evidence of the fundamen-
tal nature of collective principles on the grounds that there actually
is a deductive path from the microscopic that explains the repro-
ducibility of these experiments. This is incorrect. The microscopic
explanation of temperature, for example, has a logical step called the
postulate of equal a priori probability—a kind of Murphy’s law of
atoms—that cannot be deduced and is a succinct statement of the
organizing, principle responsible for thermodynamics.'* The ostensi-
bly deductive explanations of the Josephson and von Klitzing ef-
fects always have an “intuitively obvious” step in which the relevant

20

A DIFFERENT UNIVERSE

organizational principles are assumed to be true. They actually are true, of course, so the reasoning is correct, but not necessarily in the sense the reasoner intended. In deference to reductionist culture, theorists often give these effects fancy names, which, on close inspection, are revealed to be nothing more than synonyms for the experiments themselves. In neither case was the great accuracy of the measurement predicted theoretically.
Like other things one does not talk about, unclear thinking about what is fundamental can come back to haunt us later on. Its most insidious effect is to lead us out into the desert by inducing us to search on smaller and smaller scales for meaning that is not there. I have a big problem with this—no doubt for cultural reasons. In the arid part of the world in which I grew up we take the desert seriously.
One of my great-grandfathers came to California by the Santa Fe Trail as a teenager and recorded his experiences along the way in a diary. According to this diary, he and his party had an extremely close shave somewhere in New Mexico. They had pulled into a small town to pick up supplies and water and ask for guidance on how to cross the desert. Upon receiving directions they struck out and, in two days, reached the first water hole and found it dry. Then they pushed on two more days to the second water hole and found it dry, too. Then they pushed on an additional two days and found another dry hole. At this point it became clear that the people back in that town had intended to kill them, so the party held a conclave and resolved on desperate measures. The men unhitched the horses from the wag-
ons, left the women and children in the desert with all the supplies,
rode back into town, shot it up, and brought back water. The story obviously had a happy ending, since I am here.
Despite the evidence that even physicists, ostensibly the most log-
ical of scientists, can draw invalid conclusions from precise measure-
ments, precision and certainty will continue to be scientific values that we cannot live without, because striving for certainty in mea-

Living with Uncertainty

21

surement and interpretation is the only foolproof mechanism we have for revealing the principles of organization regulating the universe. Technical knowledge is just as susceptible to political whim as any other kind of knowledge, and it is only the anchor of certainty that gives science its special status and authority. The striving for certainty is not an anachronism of a bygone era promoted by Luddite physicists but the moral core of science. It is like old-time religion— occasionally annoying and tiresome but never irrelevant. All of us, and perhaps even all living beings, use the especially reliable things thaf nature sees fit to reveal to us as beacons to navigate through an otherwise uncertain world. As with any other aspect of life, one of
the worst things a body can do is to allow this system to weaken by
miscategorizing a falsehood as a truth. The consequence will be that
the system fails at the crucial moment one needs it most, causing one
to lose one’s way.

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Nature's laws are the invisible government of the earth.

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Alfred A. Montapert

| N 1687, ISAAC NEWTON CHANGED HISTORY BY LAYING
down in the Principia the scientific case for universal physical law.! Regularity in the natural world had been well understood since ancient times, and Renaissance figures like Galileo, Kepler, and Tycho Brahe had recently refined and quantified this knowledge through careful experimental observation. But Newton went beyond observation of regularity to identify mathematical relationships that were simple, applied always, and accounted for apparently unrelated behaviors simultaneously. Newton’s laws of motion turned out to be so trustworthy that incompatibility with them soon became areliable indicator of false observations. They found impor-tant applications in engineering, chemistry, and commerce and eventually became the logical basis for our entire technological world. Little wonder that Alexander Pope’s famous eulogy still brings a tear to the eye:
Nature and Nature’s laws lay hid in night. God said, Let Newton be! and all was light.
23

24

A DIFFERENT UNIVERSE

Much creative energy has gone into testing and exploiting Newton’s laws.
The great influence of Newton’s treatise came not from its explanation of planetary orbits and the tides, which was very beautiful, but from its use of these things to demonstrate the legitimacy of the clockwork universe—the idea that things tomorrow, the day after, and the day after that are completely determined from things now throughaset of simple rules and nothing else.2 The stunning quantitative agreement between Newton’s calculations and experimental observations of the planets left no doubt that his rules were correct for astronomical bodies, and that the mystery of the heavens had been
solved. The simplicity of these rules, their reasonableness, and their
compatibility with Galileo’s terrestrial observations also suggested that they applied much more generally—that they were the machinery of the clock. This has been borne out by subsequent observations. In four centuries of careful experimentation the only documented failures of Newton’s laws of motion have been at atomic-length scales, where the laws of quantum mechanics supplant them.
We know Newton’s laws to be highly accurate because so much creative energy has gone into testing and exploiting them. There are

Mount Newton

25

several classes of tests. One is the careful observation of the motion of astronomical bodies. Newton’s laws not only account for shapes and histories of planetary orbits in detail but also correctly predict the sun’s effects on the orbit of the moon, the complex trajectories of asteroids and comets,? and the stability of the asteroid belt. The apparent failure of Uranus to obey Newton’s laws led to the discovery of Neptune and then Pluto.* Another class of test consists in the study
and manufacture of accurate mechanical clocks, ranging from the
original Huygens pendulum clock and its progeny to the balance
whéel chronometer? and to the quartz oscillator used in modern wristwatches.® Yet another class is based on the principle of the gyroscope and the technology of the gyrocompass and gyrostabilizer built upon it.?7 Newtonian ideas are used in designing machinery and the earthquake stability of tall buildings, and are implicit in-laws of elec-
tricity that lead to power transmission, computers, and radio.
Despite the successes of Newton’s laws and the engineering ad-
vances they made possible, many people still find the clockwork
universe difficult to accept. It flies in the face of our commonsense understanding of the complexity of nature and our belief that the future is not completely predestined but depends on how we choose
to behave. It also seems to be inconsistent with everyday experience and to have moral implications that are not right. It can, for example, become an excuse to do anything you wish to other people and create dangerous things as you see fit because nature is, after all, just mechanical. It also can legitimize a bogus faith in logic. I first heard this latter idea articulated by my father long ago during a dinnertable discussion about predestination. At one point he became exasperated with the barrage of ignorant statements about reality from
the kids and explained, barely controlling himself, that logic was the
systematic method of committing error. Now that I am older I understand what he meant. He knew through painful experience in his law practice that human beings reason by analogy. When we say

26

A DIFFERENT UNIVERSE

something is unreasonable, we usually mean it is not suitably analogous to things we already know. Pure logic is a superstructure built on top of this more primitive reasoning facility and is thus inherently fallible. Unfortunately, we need to be most logical precisely when it is most difficult—when confronted with something new that is not analogous to anything we already know. The ability to do this intensely for long periods of time is what distinguishes the Isaac Newtons and Albert Einsteins from the rest of us. So on this matter my father was right, but only partly. Logic sometimes can, and must, be believed. The material evidence for the clockwork universe has grown over the centuries to become overwhelming. One must look somewhere other than a failure of this idea for the answers to the mysteries of life.
The moral conundrum of material determinism was even more troublesome in the seventeenth century, when physics was being invented, than it is today. In 1633 Galileo Galilei was brought to trial before the Italian Inquisition for violating a 1616 edict against promoting the cosmology of Copernicus. He was found “vehemently suspected of heresy,” a judgment slightly less severe than actual heresy, and was forced to publicly recant his belief that the earth moves about the sun.® Like many great scientists, Galileo was a rebellious individual. He had left university without a degree in order to pursue his own intellectual agenda of measuring things rather than just thinking about them. His career was dazzlingly successful. We know Galileo today mostly for his invention of the astronomical telescope and the discoveries he made with it, such as sunspots and the moons of Jupiter,? but his deeper contribution was articulating the fundamental limitations of Aristotle’s discursive approach to science and advocating the need for mathematical precision. The Book of
Nature, he wrote in The Assayer in 1623, “... is written in the lan-
guage of mathematics.”!° Unfortunately, Galileo’s deterministic worldview, forcefully argued in that book, left no room for divine in-

Mount Newton

27

tervention and, perhaps even worse, implicitly promoted the idea that divine things could be understood and mastered by humans. In 1625 he was secretly denounced to the Inquisition for the threat to
Eucharistic theology, in particular the doctrine of transubstantiation,
in The Assayer, which, ironically, he had dedicated to his good friend Cardinal Maffeo Barberini, on the occasion of his election as Pope Urban VIII in 1623.!! The matter came to a head in 1632 when Galileo published his great work, Dialogue Concerning the Two Chief World Systems, a brilliant and devastating scientific attack on the Ptolemaic universe.!? On advice that its arguments were so lucid and persuasive that it was more dangerous than Calvin and Luther combined, the Pope ordered that publication of the book cease and that Galileo be brought to trial. He was found guilty and sentenced to house arrest in Arcetri, a small village outside Florence, where he remained for eight years until his death.
Without Galileo, Newton’s work would have been unthinkable. Nearly all of Newton’s essential physical ideas—and the experiments that backed them up—were originally due to Galileo. It was Galileo
who first realized that objects did not require an external agent to
move them, as Aristotle had thought, but instead moved at constant
speed on straight-line trajectories unless acted upon from without.
Galileo also invented the idea of velocity as a vector, a quantity with
both magnitude and direction. He invented the idea of inertia, the natural resistance of a body to changes in its motion, and was the first to identify the agent for modifying motion as force, a thing that changes the velocity additively from one moment to the next, so that the velocity two seconds from now is the velocity now plus a small increment that depends on the magnitude of the force.
Isaac Newton nonetheless receives the lion’s share of the credit for inventing modern physics because he discovered a way to synthesize all these ideas into a seamless mathematical whole. He was born on
Christmas day 1642, the year Galileo died.1° Like Galileo, Newton

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A DIFFERENT UNIVERSE

was a rebellious individual disinclined to trust authority. In the margin of one of his Cambridge notebooks is scribbled in Latin, “Amicus Plato, amicus Aristoteles; magis amica Veritas.” (Plato is my friend, Aristotle is my friend, but truth is a better friend.) Like many motivated young people of his day, he was fascinated by the new astronomy and had read Galileo and Kepler extensively. We owe Newton's discoveries in no small measure to the Great Plague, from which he hid at his home in Lincolnshire between 1665 and 1667. While there, presumably with time on his hands, he invented the infinitesimal calculus, the key breakthrough required for explaining Kepler’s observations about planetary orbits—their planarity, their perfect elliptical shape with the sun at one focus, their miraculous accelerations and decelerations that caused equal areas of the ellipse to be swept out in equal times, and the exact mathematical relationship between the size of the orbit and its period. With the notation of calculus, Newton was able to write down Galileo’s rules of motion as simple, precise equations, which could then be solved to obtain an exact description of a body’s motion in response to the forces acting upon it. With this mathematical technology and one further assumption— that the force of gravity weakened in a certain way with distance—he was able to prove that Kepler’s observations actually followed from
Galileo’s rules and were not independent phenomena." This, in turn,
enabled him to argue from the extreme accuracy of Kepler’s observations that Galileo's rules were exact. Galileo had missed this point entirely. He had ignored Kepler’s laws, which were discovered in his
lifetime, and had considered the whole idea of universal gravitation
“occult.” Fate had apparently ordained that Galileo should lead his people to the Promised Land but not enter in himself.
One of the greatest disservices we do to our students is to teach them that universal physical law is something that obviously ought to be true and thus may be legitimately learned by rote. This is terrible on many levels, the worst probably being the missed lesson

Mount Newton

29

that meaningful things have to be fought for and often require great suffering to achieve. The attitude of complacency is also opposite to the one that brought these beautiful new ideas into the world in the first place—indeed, what brings things of great importance into the world generally. The existence of physical law is, in fact, astonishing and should be just as troubling to a thinking person today as it was in the seventeenth century when the scientific case for it was first made. We believe in universal physical law not because it ought to be true but because highly accurate experiments have given us no choice.
For some reason I was recently seized with concern about this
problem while on a car trip with my family. I asked my son, who was taking physics in high school, what the evidence was that Newton’s
laws were true. He is a sympathetic person, so he dutifully rose to the bait, bluffed valiantly, realized that what he was saying did not make any sense, twisted in the wind a bit, mumbled something I could not make out, and then fell silent. I clarified the question by asking him what the key experiments were. More silence. This happy moment was an effect of the universal gene parents have for giving their chil-
dren reasons to hate them. I was fully aware that he did not know the answer, and I was trying to provoke a thoughtful discussion about planetary orbits—which I successfully did in the end. I am reasonably sure the outcome was positive, but one will only know for sure
when negotiations begin for dividing up the estate. Universal physical law is the iceberg of which the exact physical
constant is the small part above water. Both are aspects of the same
physical phenomenon, but physical law is the vastly more inclusive concept. In the Far East, where I travel frequently, I like to explain this using an analogy with the Theravada and Mahayana branches of Buddhism.!> In the Theravada, one restricts one’s attention to the conservative teachings of specific historical scholars. In the Mahayana, or “great vehicle,” one considers not only these teachings but

30

A DIFFERENT UNIVERSE

all of their many implications. A universal constant is a measurement that comes out the same every time. A physical law is a relationship between measurements that comes out the same every time. In the
case of laws of motion such as Newton’s, it is a relationship between
measurements at different moments. Thus when we measure certain things now we need not measure them again in the future (assuming they remain undisturbed) because their values are predestined with certainty. In discussing laws we speak of exact equations instead of
exact values, but the core idea is the same. Exactness is what counts.
Like exact universal measurements, we tend to classify laws in our minds as either microscopic or collective in origin and use the word
fundamental to describe both. As with constants, we find that the dif-
ference between these two classifications tends to melt away when the experimental facts are examined closely.
Over the years, as the list of successes of Newton’s laws lengthened, there arose a speculative use of them very different from the original highly conservative one. The new strategy was to assume that Newton’s laws were true in circumstances where one could not verify this directly, compute various physical properties based on this assumption, and then argue from agreement with experiment that the initial
assumptions were correct. Thus, for example, the kinetic theory of
gases assumes the gas to consist of atoms obeying Newton’s laws with short-ranged repulsive forces that cause them to carom off each other like billiard balls. One then finds that the mythical atoms have a strong tendency to be scrambled into randomness by their collisions— as anyone who has played billiards knows well. This tendency is called the principle of chaos and is the origin of the unpredictability of the weather.!° After scrambling, the chaotic swarm of billiard. balls beautifully emulates the behavior of dilute gases, as well as corrections to ideal gas law as the gas density is increased, which come from the interatomic forces. Thus we say that the kinetic theory “explains” the ideal gas law—meaning that it accounts for the origin of the law.

Mount Newton

31

But this reasoning has the obvious logical flaw that the behavior against which one tests the assumptions might be a universal collective phenomenon. In this case the measurement is fundamentally in-
sensitive to microscopic assumptions, such as the existence of atoms,
and therefore does not test them at all. It is a false syllogism: God is love, love is blind, Ray Charles is blind, therefore Ray Charles is God.” Unfortunately, this is precisely what happened in these theo-
ries. Newton’s laws, as it turns out, are wrong at the scale of atoms.
Early in the twentieth century it was discovered that atoms, moleculés, and subatomic particles are described by the laws of quantum
mechanics—rules so different from Newton’s that scientists strug-
gled to find proper words to describe them. Newton’s laws make profoundly false predictions at this scale, such as atoms having zero size and solids having huge heat capacities at zero temperature that they
do not, in fact, have. A beam of helium atoms projected onto an
atomically perfect solid surface does not bounce off in all directions,
as Newton’s laws predict, but diffracts into rainbows as a beam of light would do.!8 Atoms are not billiard balls at all but waves, as are their constituents, which bind together to form atoms the way waves
of water bind to make a surge.!9 Thus Newtons legendary laws have turned out to be emergent.
They are not fundamental at all but a consequence of the aggregation of quantum matter into macroscopic fluids and solids—a collective organizational phenomenon. They were the first laws to be discovered, they brought the technological age into existence, and they are as exact and true as anything we know in physics—yet they vanish into nothingness when examined too closely. Astonishing as it may seem, many physicists remain in denial. To this day, they organize conferences on the subject and routinely speak about Newton’s laws being an “approximation” for quantum mechanics, valid when the system size is large—even though no legitimate approximation scheme has ever been found. The requirement that Newton’s laws emerge in the

BZ

A DIFFERENT UNIVE RSE

macroscopic limit was christened theprinciple ofcorrespondence in the early days of quantum mechanics and was used as a constraint in working out the meaning of quantum measurement. The notoriously illogical (and partly wrong) ideas about quantum indeterminism still with us today are untidy consequences of this process. But the correspondence principle remains mathematically unprovable.
I first learned about thé emergerit nature of Newton’s laws from P. W. Anderson’s famous essay More Is Different. After thinking hard about why metals refrigerated to very low temperatures exhibit the
bizarre exactnesses of superconductivity, Anderson realized that
the central dilemma was precisely that of the correspondence principle. In other words, superconducting behavior reveals to us, through its exactness, that everyday reality is a collective organizational phenomenon.
So it seems that my poor son was intellectually mugged. I apologize, Todd.

be6050. Ro)
Watet,; Ice,
and Vapor
aN
Law is order, and good law is good order.
Aristotle
Every WEEKEND IN JANUARY, ARMIES OF TRUCKS DRIVE
out onto the lakes of Minnesota in search of fish.! The drivers all understand the danger of this but are willing to risk it, for they are being driven bananas by winter and cannot resist the thought of all those waiting crappie, walleye, and jumbo perch. They invent all sorts of justifications for getting away, and even go so far as to claim that their wives love cleaning and preparing fish. It is a lie. Their wives hate fish and are always apprehensive, sometimes terrified, about these trips. They just put up with them because they have no choice. Considering the number of drivers, it is probably surprising that there are not more accidents. According to Tim Smalley, boat and water safety specialist at the Minnesota Department of Natural Re-
sources, there were only 117 ice fatalities between 1976 and 2001,
68% of which involved a vehicle.” Evidently, ice is reliably strong and buoyant—at least in Minnesota’s winters, and provided that the person testing its strength and buoyancy has not been drinking.
33

34

A DIFFERENT UNIVERSE

Not only Minnesotans with cabin fever but all of us entrust our lives to the solid state every day—from standing on ice to ordering peanuts at 40,000 feet—without thinking twice about it. We know empirically that matter sufficiently cold freezes, and that when it does, it universally and exactly acquires shape, form, and springy resistance to deformation. There is no possibility that the solid will suddenly lose its rigidity and betray us, even though a modest temperature rise—sometimes a fraction of a degree—can accomplish just this by causing it to melt.‘In the fiery hell of a furnace the metal may splash and play, but in our world it is sober and responsible.
The phases of matter—among them the familiar liquid, vapor, and solid—are organizational phenomena. Many people are surprised to learn this, since phases seem so basic and familiar, but it is quite true. Trusting the ice is less like buying gold than buying stock in an insurance company. If the organizational structure of the company were to fail for some reason, one’s investment would vanish, for there is no physical asset underneath. Similarly, if the organization of a crystalline solid—the orderly arrangement of the atoms into alattice—were to fail, the rigidity would vanish, since there is no physical asset underneath it either. The property we value in either case is the order. Most of us would prefer not to think we are entrusting our lives to an organization, but we do it every day. Without economies, for example, which are purely organizational phenomena, civilization would collapse and all of us would starve.
Ironically, the immense reliability of phase-related phenomena makes them the reductionists’ worst nightmare—a kind of Godzilla set loose by the chemists to crush, incinerate, and generally terrorize their happy world. A simple, universal phenomenon one encounters frequently cannot depend sensitively on microscopic details. An exact one, such as rigidity, cannot depend on details at all. Moreover, while some aspects of phases are universal and thus easy to anticipate, others, such as which phase one gets under which circumstances, are not—

Water, Ice, and Vapor

35

water being an especially embarrassing case in point. Ordinary water ice displays, at last count (the number keeps rising due to new discoveries) eleven distinct crystalline phases, not one of which was correctly predicted from first principles.3 These phases, known as ice-I, ice-II, and so forth, are not to be confused with ice-9, the fictional weapon of mass destruction satirized in Kurt Vonnegut’s novel Cat’s Cradle.
Phases are a primitive and well-studied case of emergence, one
that conclusively demonstrates that nature has walls of scales: microscopic rules can be perfectly true and yet quite irrelevant to macro-
scopic phenomena, either because what we measure is insensitive to them or because what we measure is overly sensitive to them. Bizarrely, both of these can be true simultaneously. Thus it is presently too difficult to calculate from scratch which crystalline phase of ice will form at a given temperature and pressure, yet there is no need to calculate the macroscopic properties of a given phase, since these are completely generic.
A measure of the seriousness of this problem is provided by the
difficulty of explaining clearly how one knows phases to be organiza-
tional. The evidence always manages to be complicated, indirect, and
annoyingly intermingled with theories—not unlike the evidence of
product superiority in a commercial for soap or cars. The deeper rea-
son in each case is that the logical link from the fundamentals to the conclusion is not very substantial. One thing we know for certain is
that crystalline solids are ordered lattices of atoms—a fact revealed by their tendency to deflect X-rays through specific angles—while liquids and gases are not. We also know that systems with small numbers of atoms are motivated by simple, deterministic laws of motion and nothing else.* We also know that attempts to discover the scale at which these laws cease to work or are supplanted by others have failed. And finally, we know that elementary laws have the ability in principle to generate phases and phase transitions as organizational phenomena.> Thus when one strips away the unhelpful complexities,

36

A DIFFERENT UNIVERSE

one is left with the following simple argument: microscopic laws are true and could plausibly cause phases; therefore we are sure they do cause them, even though we cannot prove this deductively. The argument is believable and, I think, correct, but it does have the strange effect of giving the word “cause” a meaning it does not customarily have. One could say that the laws of chemistry “caused” the destruction of Tokyo, but what really did it'was Godzilla.
The believability of this argument gives phase organization an enormous importance that it would not otherwise have, for it is impossible to disguise the fact that phases are boring. From a practical standpoint there is not much difference between a law that emerges and a miracle that just is, but from a philosophical standpoint the difference is profound. One represents a world ruled by orderly hierarchical development, the other a world ruled by magic. The precedent of phases proves that at least some of the marvels of the world are organizational—and, in so doing, suggests that all of them are. It is one of the main reasons we tend to doubt supernatural causes for things until organizational causes have been ruled out experimentally.
There are lots of other everyday examples of exactness generated by phases. Liquids, for example, will not tolerate pressure differences of any kind between one point and another except those due to gravity. This is a general property of the liquid phase that does not depend on what the liquid is made of. It is not obvious, which is why the renowned Greek mathematician Archimedes screamed “Eureka!” upon discovering it and ran naked through the streets of Syracuse.® It is the principle behind the mercury barometer, the buoyancy of steel ships, and all hydraulic machinery. The liquid phase has an electronic version, the metallic phase, which will not tolerate voltage differences. This exact property of metals is the principle behind conduction of electricity in wires, as well as such practical rules such as not touching commercial radio towers while they are transmitting.

Water, Ice, and Vapor

37

Both the liquid and metallic phases have special low-temperature versions, the superfluid and the superconductor, which have even more impressive exact behaviors.
The simplest prototype of emergent exactness, however, is the regularity of crystal lattices, the effect ultimately responsible for solid rigidity. The atomic order of crystals can be perfect on breathtakingly long scales—in very good samples, as many as one hundred million atomic spacings.” Atomic order was suspected as early as the seventeenth century as the cause of the simplicity and regularity of crystalline shapes,’ but the degree of perfection was not known until X-ray crystallography was invented.? One infers the perfection of the ordering mostly from the exactness of X-ray reflections, although it is also detected indirectly through transport experiments such as conduction of electricity at low temperatures.
To appreciate the miracle of crystallization it is helpful to imagine
a school with ten billion children. The recess bell rings, and the
teachers line up the kids in rows upon rows on the gigantic play-
ground in preparation for ushering them back into class. The kids
have other ideas, however, for they have been wound up by their play
and detest work. They fidget, pester each other, and run around in
circles playing tag while the authorities struggle to achieve control. Without actually doing this experiment it is very hard to tell whether
any long-range ordering pattern would materialize on the playground, for at the range of a few hundred children the pattern is -highly flawed and arguably even nonexistent. But at the scale of one
hundred thousand children the pandemonium ofa single class might become irrelevant, allowing us to say that a one-hundred-kilometer
crystal of children has formed. It is not at all obvious that atoms in a crystal should order so well.
For one thing, it does not always happen. Elemental helium, for example, remains liquid no matter how much its temperature islowered, although it will crystallize when subjected to pressure.!° Amorphous

38

A DIFFERENT UNIVERSE

substances such as glass and plastic can be made to crystallize only with great difficulty and are usually found in a state of semipermanent frozen chaos.!! It is still extremely difficult to predict which proteins will crystallize and which will not, despite its being a matter of immense importance to the modern drug industry.!* Which things crystallize easily can be anticipated to some extent from their microscopic structure, but in the final analysis the perfection of crystal lattices just is. The last time the stock market crashed, the Economist explained that “shift happens.” This is also how we explain the failure of crystals to form.
The most astonishing thing of all about crystalline ordering is that it remains exact when the temperature is raised. Temperature may be thought of as the amount of sugar our ten billion children have in their bloodstreams. Even in good crystals a given atom is always moving and thus always slightly off of its ideal lattice site at any given moment, this being the physical meaning of heat. The proof that this motion is present is that a fraction of the X-rays beamed into a sample are reflected with a small wavelength change, exactly as occurs when radar beams bounce off a moving airplane.!3 But astonishingly, this effect does not fuzz out the specific angles through which the X-rays are deflected; it only steals some of the deflected beam’s intensity and redistributes it as a uniform background reminiscent of fogging in a photograph. This occurs because the location of one atom continues to predict the location of another—with some uncertainty—arbitrarily far away in the structure. The positional errors do not accumulate. This enables the line of children to look chaotic at the hundred-kid level but perfectly ordered at the million-kid level. In the liquid phase, in contrast, the deflected image does fuzz out because the positional errors do accumulate and do cause predictive power to be lost at sufficiently large distances. The lattice positions of a solid evidently have exact meaning even when the atoms are not exactly in them.

Water hee} fand? Vapor

39

The exactness of the lattice registry on long-distance scales explains why melting is abrupt.!4 The ability of an atom to predict the position of another arbitrarily far away cannot be partially present any more than a person can be partially pregnant. When this predictability is present, simple logic tells us that the other properties one normally associates with solids, such as shape and elasticity, must also be present. These properties can therefore be lost only catastrophically. There are, unfortunately, constant misunderstandings about how much this exactness matters to the nature of the solid. state. Most substances are not perfectly regular—even real metals, which owe much of their important engineering properties to structural and chemical imperfections.!5 An acrylic bowling ball dropped on one’s foot may not be solid by a theorist’s definition, but it cer-
tainly seems that way when you are sitting in Urgent Care waiting for
the surgeon. But the abrupt transformation from solid to liquid that
enables us to speak of these things as distinct phases requires order-
ing. In glasses or polymeric materials, such as a bowling ball, no
abrupt phase transition occurs upon cooling; thus there is no mean-
ingful experimental way to determine whether the substance is a solid or a highly viscous liquid.!° The distinction is semantic—hence the intractability and bitterness of the disputes about it. In principle, a similar problem also occurs in impure crystals, but in practice, the
disruption of the phase transition is usually too subtle to matter. Anyone doubting the earnestness of phase transitions should be
_forced to winter in New England, a place notorious for capricious
weather. When I was a graduate student I shared a house in the sub-
urbs of Boston at the end of a cul-de-sac that was always difficult to
deal with in snow emergencies. One day a winter storm blew in. It
dumped snow from early morning until nine o’clock at night, whereupon the temperature suddenly warmed way up and it poured. The rain came down in tropical amounts and mixed with the snow already on the ground to make slush. This clogged the storm drains

40

A DIFFERENT UNIVERSE

and filled the streets up to the curb. Then atabout three in the morning, while everyone was asleep, an arctic front blew in from Canada, plunged the temperature back down below zero, and froze the street into a solid block of ice a foot thick. By morning, plowing was pointless, and cars unfortunate enough to have been parked on the street overnight were entombed. The city waited a week for a thaw that never came, then threw in the towel and dumped sand on top. This remained as a kind of dirty, slippery ice concrete until spring, when it finally melted away.
Once one knows what to look for, the organizational nature of phases other than the solid becomes easy to demonstrate. A collective state of matter is unambiguously identified by one or more behaviors that are exact in a large aggregation of the matter but inexact, or nonexistent, in a small one. Since the behavior is exact, it cannot change continuously as one varies external conditions such as pressure or temperature but can change only abruptly at a phase transition. One unambiguous signature of an organizational phenomenon
is therefore a sharp phase transition. The transition itself, however, is
only a symptom. The important thing is not the transition but the emergent exactness that necessitates it.
The melting and sublimation transitions of ice signal the demise of crystalline order and its replacement by a set of exact behaviors known collectively as hydrodynamics.!” The laws of hydrodynamics amount to a precise mathematical codification of the things we intuitively associate with the fluid state, such as the meaningfulness of hydrostatic pressure, the tendency to flow smoothly in response to differences in pressure, and the rules of viscous drag. No one has ever succeeded in deducing these laws from first principles, although it is possible to make highly plausible arguments in many cases. The
reason we believe them, as with most emergent things, is because we
observe them. Like the laws of rigidity in solids, the laws of hydrodynamics become more and more exact as the length and time scales

Water, Ice, and Vapor

4]

on which they are measured increase, and they fail in the opposite limit. The emergence of hydrodynamic law at long wavelengths is why compressional sound propagates universally in fluids and why the shear strength of a fluid is always exactly zero. The insensitivity of hydrodynamic principles to details allows deep-sea divers to continue speaking to each other, albeit with Donald Duck voices, when nitrogen in their breathing mixtures is replaced with helium.
Isotropic fluids are not just the opposite of solids but rather one of many possible alternatives to them. The most industrially significant of these are the liquid-crystal phases that constitute the active element of flat-panel computer monitors and cheap wristwatches.18 These are characterized by an intolerance to shear stress, as in conventional liquids, but residual anisotropy that enables them to twist
light polarization in response to small electrical signals. Another example is the hexatic phase, a state with fluidlike shear properties but sixfold orientational memory that forms when ordinary rare gas
atoms condense on graphite.!° (The hexatic phase is difficult to de-
tect experimentally, so its existence is more controversial.) Another example is the “incompressible” phase, in which a fluid cannot trans-
mit conventional sound, which occurs in magnetic fields. Yet another
is the supersolid, a theoretical phase with shape rigidity that
nonetheless flows, the experimental observation of which was re-
cently reported.?° These exotic phases are rare, but their existence is nonetheless important because it demonstrates the familiar solid, liquid, and gas to be special cases of something more general.
The exact property distinguishing the liquid phase of water from
vapor is something considerably more subtle: the interface between
them. Water and steam seem so different that it is hard to imagine
that they would be difficult to tell apart, but they sometimes are. As
one raises the steam pressure above a pot of boiling water (a side effect of which is to elevate the boiling temperature), the roiling sur-
face becomes harder and harder to see and, at a critical pressure,

42

A DIFFERENTOUNIVERSE

disappears. Above this pressure the liquid and vapor have lost their separate identities and have merged into a single phase, the fluid, so there is no surface. The pressure at which the liquid and vapor merge is useful to engineers because the special expansion properties of steam they exploit to make engines are maximized there, but is otherwise unimportant. The emergent phenomenon distinguishing the liquid and vapor phases is thus not the development of order but the development of a surface. Like the lattice of a crystalline solid or the laws of hydrodynamics in the fluid, this surface and the rules for its motion become increasingly well defined at large distance and time scales but lose their meaning in the opposite limit. This is the effect that brings us clouds, rain, and the magnificent violence of the sea.?!
By far the most important effect of phase organization is to cause objects to exist. This point is subtle and easily overlooked, since we are accustomed to thinking about solidification in terms of packing
of Newtonian spheres. Atoms are not Newtonian spheres, however,
but ethereal quantum-mechanical entities lacking that most central of all properties of an object—an identifiable position. This is why attempts to describe free atoms in Newtonian terms always result in nonsense statements such as their being neither here nor there but simultaneously everywhere. It is aggregation into large objects that makes a Newtonian description of the atoms meaningful, not the reverse. One might compare this phenomenon with a yet-to-be-filmed Stephen Spielberg movie in which a huge number of little ghosts lock
arms and, in doing so, become corporeal. For this to occur, their
number must be stupendously large. Merely bonding atoms together into a very large molecule will not suffice. Fullerenes, for example— soccer-ball-shaped molecules consisting of 60 or more carbon atoms—diffract very nicely and thus are still measurably quantummechanical.’? But as the sample size grows to infinity, the distinction between the internal motions and the collective motion of the whole body becomes qualitative—and the latter acquires Newtonian reality.

Water, Ice, and Vapor

43

The reason we get away with thinking of atoms as Newtonian is that an emergent phenomenon renders the mistake irrelevant. But it only does so for the motion of the object as a whole. The internal vibrational motions remain quite quantum.
Collective emergence of objects is the principle behind the phenomenon of superness that occurs in ultracold environments.23 Like the comic book character Superman, superfluid helium can leap tall buildings in a single bound—or, more precisely, craw] up the walls of a beaker all on its own and escape. Unlike Superman, it has properties“so strange and implausible that they could never have been accepted for publication at a pulp science fiction magazine. The viscosity of the superfluid is not just small but exactly zero, enabling it to pass through porous plugs as though they were not there and remain exactly stationary when its container is rotated. Superconductors similarly pass electric current with no resistive loss, and generate
magnetism when rotated because the atomic nuclei move while the electrons do not.
Superfluidity and superconductivity are the fluid versions of ideal
crystalline rigidity. This is not at all obvious, particularly since they
appear to be special “quantum” phenomena that have no analogue in
the Newtonian world, just as zero-temperature hydrodynamics does
not, but this is incorrect. The tip-off is the exactness. By good for-
tune, the superfluid order, while exotic, is also simple and thus easy
to understand. You might describe it as a tank of little ghosts drifting
‘through each other but belonging by choice to the same political
party—which one being immaterial, as long as it is the same. If one
then perturbs the tank by forcing the political opinion to be one
thing on the left side and another thing on the right side, the body
politic of ghosts inside becomes stressed and responds with the mass
migration we call superfluid flow.
Superfluid rigidity has enough in common with ordinary crys-
talline rigidity that one can draw useful analogies between the two.

44

A DIFFERENT UNIVERSE

Thus if one cools a rotating container of helium through its super-
fluid transition, the fluid continues to rotate, but only ina lattice of
tiny quantized vortex lines.24 These are the fluid version of line defects in the crystal one could make by removing a thin pie slice with a knife and then squashing it together to reseal the place that was cut.25 In the fluid there is no lattice to be defective, so the memory of the cut is preserved in a special persistent fluid flow about the line.
The crystalline and superfluid phases, and their attendant exact behaviors, are specific examples of an important abstract idea in physics called spontaneous symmetry breaking. It has uses ranging from engineering to the modern theory of the vacuum of space?6 and is even suspected of being relevant to life.” The idea of symmetry breaking is simple: matter collectively and spontaneously acquires a
property or preference not present in the underlying rules themselves. For example, when atoms order into a crystal, they acquire
preferred positions, even though there was nothing preferred about
these positions before the crystal formed. When apiece of iron becomes magnetic, the magnetism spontaneously selects a direction in which to point. These effects are important because they prove that organizational principles can give primitive matter a mind of its own and empower it to make decisions. We say that the matter makes the decision “at random”—meaning on the basis of some otherwise insignificant initial condition or external influence—but that does not
quite capture the essence of the matter. Once the decision is made, it
becomes “real” and there is nothing random about it anymore. Sym-
metry breaking provides a simple, convincing example of how nature can become richly complex all on its own despite having underlying rules that are simple.
The existence of phases and phase transitions provides a sobering
reality check on the practice of thinking of nature solely in terms of
the Newtonian clockwork. Floating on the lakes of Minnesota and
stretching into the sky in large cities are simple, concrete examples of

Water, Ice, and Vapor

45

how organization can cause laws rather than the reverse. The issue is not that the underlying rules are wrong so much as that they are irrelevant—rendered impotent by principles of organization. As with human institutions, emergent laws are not trustworthy, and sometimes hard to discern, when the organization is small, but they become more reliable as it grows in size and eventually become exactly true. This is why you can buy treasury bills with confidence or drive a truck out onto the ice with small risk. The analogy with human in-
stitutions might seem a bit shaky in light of recent revelations of ac-
coufting swindles and financial collapse in large corporations, but
this concern is misplaced. The infirmity does not generalize, for the
laws of nature are enforced by higher authority.

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Schrédinger’s Cat

Reality is nothing but a collective hunch.
&%
Lily Tomlin

Quantum MECHANICS IS THE DETERMINISTIC LAW OF
motion of very small things—atoms, molecules, and the subatomic particles of which they are made.! It was discovered in the

1920s by physicists trying to reconcile numerous strange and

highly embarrassing experimental facts that seemed fundamen-

tally incompatible with Newton’s clockwork: the tendency of

atomic vapors to emit light with distinct wavelengths, the ten-

dency of hot bodies to glow with a color and intensity that in-

creases with their temperature; and the laws of chemical bonding

and radioactivity. The solution to the problem turned out not to

be abandonment of the clockwork but a profound conceptual re-

vision of its machinery. It is a beautiful case history of how science

advances by making theories conform to facts rather than the

other way around.

|

Learning quantum mechanics can resemble an out-of-body expe-

rience.2 Things that cannot be become matter-of-fact truth, words

acquire meanings that are the exact opposite of their customary

ones, and commonsense reality gets turned on its head. Attending

47

48

A DIFFERENT UNIVERSE

classes on the subject is like listening over and over again to Abbott and Costello’s Who’s on First.
By far the craziest aspect of quantum mechanics is its mixture of Newtonian clockwork determinism and rather spooky probabilistic indeterminism, the latter invoked as needed depending on the experimental circumstances.‘ It is part of the lore of quantum mechanics that the act of measurement itself interrupts the deterministic time evolution—a kind of anthropic theory of reality not unlike Bishop Berkeley’s famous proposition that a tree falling in the forest makes no sound.’ This is absurd. A thing cannot be deterministic only when people are not looking at it. The probabilistic rule nonetheless describes certain experiments quite accurately and is in this sense true. How a certain rule could result in an uncertain experimental outcome is an important and interesting question.
The absurdity of the quantum observational paradox was deeply
understood by Erwin Schrédinger, one of its inventors, who cap-
tured it with delicious irony in his famous thought experiment with
a cat.© He imagined a closed box containing a cat, a single radioac-
tive atom, a Geiger counter, and a cyanide capsule rigged to drop into a bucket of acid when the Geiger counter clicks.” The function
of this contraption is to kill the cat with certainty if the atom decays. The deterministic rules of quantum mechanics then say that a mys-
terious quantity called the wave function leaks out of the atom
slowly, the way air escapes from a balloon, so that a finite but con-
stantly diminishing amount of this wave function is still inside.
However, the physical meaning of the amount left inside the atom is
a probability that the atom has not decayed when one measures it,
that is, when one opens the box to see whether the cat is still meowing. Until the measurement is performed, however, the system is inherently a combination of alive and dead cat. The ludicrousness of
this idea is self-evident, especially to anyone who has encountered an actual dead cat. Schrodinger intended it thus.

Schrédinger’s Cat

49

kay. Avtey
[4_H .— Walesh Wheit

The ludicrousness of this idea is self-evident.
Zany illogic of this kind is almost always symptomatic of a missing idea. The Abbott and Costello routine is based firmly on this principle, as is the entire wacky world of Gracie Allen: “I know Babe Ruth has a twin brother because I read that his double won a game for the
Yankees.” “What does he call himself?” “Oh, you're so silly. He doesn’t
have to call himself. He knows who he is.”8 The missing idea in the case of quantum measurement is emer-
gence, specifically the principle of symmetry-breaking required for the apparatus to make sense.
The history of the quantum measurement paradox is fascinating. There is still no general agreement on the matter even after eighty years of heated debate. For some physicists, such as myself, the emergent nature of measurement is obvious and something responsible professionals do not waste time discussing. For others it is unspeakable heresy. The reason for this disagreement is that the arguments are subtle and not transparently resolved by experiments one can presently

50

A DIFFERENT UNIVERSE

do. Scientists have ideological positions fist like everyone else, especially in conflicted situations, and sometimes the consequences are bizarre. The Schrodinger cat has grown over time to become a symbol of transcendence, a meaning exactly opposite to the one Schrédinger himself intended. It has acquired quasi-religious overtones, so that twisting one’s mind around to understand this cat is often viewed by students as a step on the path to enlightenment. Unfortunately, it is not. In science one becomes enlightened not by discovering ways to believe things that make no sense but by identifying things that one does not understand and doing experiments to clarify them.
The thing one does not understand in the case of the cat paradox is the measurement process itself. This quickly becomes apparent when one attempts to describe the measurement apparatus quantummechanically. In every case of ostensible indeterminism, this turns out to be impossibly difficult because the number of atoms is too large. In the case of the cat, for example, measurement might entail removing the top of the box and shining ina flashlight, or even leaving the top on and just sniffing. The impracticality of being tested
against simpler explanations is something quantum indeterminism has in common with fantastic theories of the pyramids or arguments that extraterrestrials must now be running our government. There remain a few logical loose ends. Moreover, close inspection reveals that the number of atoms is necessarily too large, for the apparatus would not work if it were small. Detecting the radioactive decay of an atom using another atom, for example, makes no sense, since it would amount to substituting one tiny unmeasurable thing for another. But measuring with a tube of gas connected to a high voltage supply and an amplifier—a Geiger counter—makes perfect sense. Evidently there is something about the human concept of “measurement” that requires an apparatus to be large.
Once we recognize that largeness is a key factor, the mystery is not
hard to resolve: All quantum detectors are made of solids, and thus

Schrédinger’s Cat

51

all of them exploit the symmetry-breaking characteristic of the solid state, an effect that occurs only in the limit of large size. To qualify as an observation by the conventional human definition, a thing must not be changed by the act of observing it. An example of something not qualifying as an observation is my asking my neighbor his opinion on whether his department chair is having an affair with the previous chair’s wife. I will get a different answer depending on whom he thinks I will talk to, and moreover, the answer may change from one day to the next as the winds of intrigue blow about. The only way I will get a consistent observation is if the various members of his de-
partment communicate with each other, hash the matter out, and de-
cide collectively what the story is. We commonly speak of opinion “crystallizing” on subjects such as this. The physical version of this effect is that the various delicate quantum parts of the experiment cooperate to become aclassical object obeying Newton’s laws. When you read the meter on a Geiger counter, for example, you know with
certainty that the value will be the same when you reread it an instant
later, because the needle is a cumbersome, solid object. If I hear a
click coming out of the speaker, the student across the room will hear
the same click a fraction of a second later with one hundred percent
certainty—unless he was not paying attention, in which case he will be history soon. But at the level of the atomic disintegration itself
this is not true, for the system in question is easily disrupted by the
act of observation. The apparatus works by transforming a quantum
signal to a classical one by means of the emergence of objects.
One reason symmetry-breaking is so difficult to deduce from the
underlying laws of quantum mechanics is that the world is configu-
rationally entangled. Entanglement is a colorful term that brings to
mind knotted electrical cords and unhappy experiences with dis-
count fishing reels, but it is actually more like income tax. Recall
that in an income tax calculation the final outcome is one simple
number—the amount of tax you have to pay—but there are complex,

Ee)

A DIFFERENT UNIVERSE

interdependent rules on the way. Thus to your total wages, tips, etc., please add taxable interest from schedule B, except for tax-exempt interest, but write it here anyway, then add business income from schedule C, capital gain from schedule D, and many other things like this, then subtract moving expenses, after first checking form 3903 that probably prevents you from making this subtraction, then subtract itemized deductions, which include state income tax and mortgage interest, except if you made too much money, in which case adda fraction back that depends on details, and throw in some job expenses unless you have a job, then reckon your tax from the total in one of three ways that are all equivalent, then see page 34 for the alternative minimum tax that we forgot to tell you about, then write a big check. The wave function of a quantum system is like this. It is a rule by which the various inputs—in this case particle positions and orientations rather than income and job information—are converted to a number.
The state of a quantum system, like the state of the tax system, is defined at any moment by this rule. Deterministic motion in quantum
mechanics means logical and systematic evolution of the rule as time advances. Entanglement means interdependency in the rule. The entanglement of quantum mechanics is, however, vastly worse than that
of income tax because everything is correlated with everything else. An
apt tax analogy would be a rule for reckoning the total revenue to the
government in which Joe’s deduction depends on how much Alice
spent on Caesar salad and whether George got a new truck. Expand
this from the number of taxpayers to the number of grains of sand on
all the beaches in the world and you have an idea of the problem of quantum entanglement in a small body such as a sugar cube.®
Quantum entanglement is one of those things that is easy to-under-
stand but almost impossible to believe—like free checking or protestations of innocence from tobacco executives. Nonetheless it is true. The simplest and most direct of the many experiments verifying its validity
is atomic spectroscopy. Atomic vapors emit very specific wavelengths

Schrédinger’s Cat

53

of light, whose exact values depend on the atom but whose sharpness and distinctiveness do not. The wavelengths are accounted for with enormous accuracy by the rules of motion of entangled electron wave functions. Moreover, these rules comply accurately with a property of this light known as the Ritz combination principle, which requires the observed frequencies always to be differences of more fundamental ones. There is much concern lately in demonstrating the entangled nature of quantum mechanics, but in truth it is demonstrated every day with great precision by the light emitted from atoms.!°
Efitanglement is hard to believe, in part, because the very emergent phenomena that enable us to control it also make it hard to see. If the freight train is coming, we need not consider its correlations with nearby insects to know that stepping off the tracks would be a good idea. It is also impractical to measure the mass of the unfortunate insects by carefully observing the train’s jerks as it hits them,
even though this is possible in principle. The insects have become ef-
fectively unobservable. It is similarly difficult to detect the effects of
quantum entanglement in the motion of a voltmeter or the click of a loudspeaker. This is not simply a side effect of building the detector
out of solids, however, but the actual detection strategy itself. The ap-
paratus works like the train. The quantum entanglement in it has not
disappeared but has simply ceased to have experimental conse-
quences that matter.
The probabilistic nature of quantum measurement arises not from
Magic but from the working of amplifiers, the bridges between the
quantum world and the classical one.!! A simple prototype for such
an amplifier is a bowling ball poised in a shallow dimple at the top of
a hill.!2 This ball is a sensitive detector of forces, for once nudged out
of the dimple ina particular direction it will accelerate down the hill
in that direction until it reaches the bottom going at great speed. The
shallower the dimple, the more sensitive the detector. In the limit at
which the dimple disappears altogether, the ball becomes infinitely

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A DIFFERENT UNIVERSE

sensitive and capable of detecting forces that are arbitrarily small, including quantum forces, such as the recoil of an atomic decay. But this highly idealized quantum mechanics problem is sufficiently tractable that it can be solved in its entirety, atom plus detector, without postulating indeterminacy. One finds that the arrival of the ball
at the bottom of the hill, where it is good and classical, is predicted
with certainty by its arrival halfway down, just as Newton’s laws require, and that both are correlated with the decay of the atom, but
that the moment of arrival is uncertain. This occurs because the en-
tire concept of “arrival” is emergent. So is the death of Schrédinger’s cat, to which this example is aptly analogous.
The emergent nature of the principle exploited by quantum am-
plifiers causes them to have certain universal properties, notably the tendency to make false alarms. The ball on the hill is only approximately Newtonian, and will demonstrate this by rolling off of its own accord, no matter how precisely it is positioned at the top, if one waits long enough. This is nicely captured by the famous quantum mechanics problem in which one is asked to calculate the time a pen-
cil can be made to balance on its point. The answer is about five seconds. For a real pencil it is even less because of thermal disturbance and wind, but five seconds is the fundamental limit. It is very generally the case that more sensitive amplifiers generate more quantum
noise (the technical term for such mistakes) and that there is a fundamental relationship between sensitivity and noisiness. This is usually expressed abstractly as a Heisenberg uncertainty paradox, but it amounts to a pencil stood on end.
The generation of uncertainty by amplifiers resembles the generation of vacuousness by news organizations when there is no news. In politics things are often not “real” until they are widely discussed, so news media effectively make small events real by amplifying them. If the reported event is already fairly large, such as a troop movement or a cut in the discount rate, the amplified version is a reasonably

schrodinger’s Cat

55

faithful copy of the original. But if the event is small, e.g., a pork-barrel amendment or an unintentional but inflammatory misstatement, the amplified version can vary significantly from one report to the next and in this sense become uncertain. The limit of this process is reached when there is nothing at all to report, at which point the reporters begin interviewing each other and filling up air time with each other’s opinions. Thus we have Paula Zahn asking Wolf Blitzer what he thinks the President’s position will be on the upcoming tax cut fight, and so forth. In the news business this is called a slow day. In physics it is called quantum noise.
The emergence of conventional physical reality out of quantum mechanics is harder to grasp than the emergence of political structures out of news, however, because the starting point is so otherworldly. Quantum-mechanical matter consists of waves of nothing. This is a tough concept, so one traditionally eases students into it by first explaining something called the wave—particle duality—the idea
that particles are Newtonian objects that sometimes interfere, dif-
fract, and so forth, as though they were waves. This is not true, but teaching it this way prevents the students’ mental circuits from fry-
ing. In fact, there is no such duality. The entire Newtonian idea of a
position and velocity characterizing an object is incorrect and must
be supplanted by something we call a wave function, an abstraction modeled on the slight pressure variations in the air that occur when sound passes. This inevitably raises the question of what is waving— a wonderful instance of the trouble one can create by using an ordinary word to describe an extraordinary thing. In customary usage a wave is a collective motion of something, such as the surface of the sea or a bleacher full of enthusiastic sports fans.!3 It makes no sense for a conventional wave to exist outside the context of something doing the waving. But physics maintains a time-honored tradition of making no distinction between unobservable things and nonexistent ones. Thus even though light behaves as though it were waves of

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some substance—referred to in the earlydays of electromagnetism as
ether—there is no direct evidence for this substance, so we declare it
to be nonexistent. For similar reasons we accept as nonexistent the medium that moves when waves of quantum mechanics propagate. This is a problem considerably more troublesome than that of light, however, because quantum waves are matter and, moreover, have measurable aspects fundamentally incompatible with vibrations of a substance. They are something else, a thing apart. The analogyIlike
best is Christina Rossetti’s:!4 ‘

Who has seen the wind?
Neither you nor I:
But when the trees bow down their heads
The wind ts passing by.

Unhappily, the otherworldliness of quantum mechanics is a convenient justification for indulging in even more otherworldly “interpretations” of it that miss the forest for the trees.!5 The convoluted nature of these arguments infatuates the undergraduates but annoys the rest of us because they boil down in the end to attempts to describe quantum mechanics in terms of behavior that emerges from it, rather than the other way around. They are, in other words, symptoms of a failed worldview. One tries to be nice about this, but the temptations to be mean are sometimes irresistible.
One of the lessons we learn as we age is that misperceptions can appear to cause craziness where there actually is none. This is the source of much good humor, the universal appeal of which comes from the universality of the experience itself. The joke works particularly well if the protagonist is in deep denial of some essential thing. Early in my graduate student days I lived in a seedy apartment that I shared with several other students, who rotated in and out as professional constraints dictated. For a brief period one of these roommates was a

Schrédinger’s Cat

57

warmhearted fellow from Cameroon who was studying engineering. He was an impressive person, particularly for his verbal ability, for English was his second foreign language after French. He had an interesting family too, including a cousin who was a recording star for Decca records. This cousin and a buddy once flew over from Paris to
stay with us for a few weeks, so I got to hear his record. I did not like it
very much. It was French disco, which would go tika tika tika tika for a long time and then pause long enough for him to say “ugh” and then continue with more tika. On this particular occasion they brought lots of presents with them, including food. Now, unfortunately for them, our place was terribly infested with cockroaches. It was not possible to eradicate the little monsters, even though we had complained bitterly to the landlord and tried several times to do it ourselves. They would just scurry next door to wait out the attack and then reoccupy after it
was over. I do not know where they lived or what they ate, but they clearly loved replicating and having gigantic parties in the kitchen after the lights were out. We would find them in daylight in the darnedest
places, such as behind a matchbook, inside the stove top, or under-
neath the forks in the silverware drawer. Like most people in this situation, we took to washing everything assiduously before we ate and keeping all open food containers, such as cereal boxes, in the refrigerator. You can thus imagine my surprise when I came home from work the day these guys blew in from Paris, reached in the cupboard for the peanut butter, and came face to face with the carcass of a dried animal about the size of a rabbit. In horror I called my roommate into the kitchen to ask him about it. “Messi, you can’t keep a rabbit in here,” I said. He looked at me without comprehension for a moment and then smiled broadly as he finally understood. “Ho ho ho,” he said, “There is no problem. That is not a rabbit.”

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The Quantum Computer
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Ours is the age proud of machines that think and suspicious of men who try to.
H. Mumford Jones
D RIVING TO WORK ONE MORNING | HEARD A FASCINATING
allegation on the radio that women understand computers better than men do.! The speaker did this only indirectly and was careful to be politically correct, but the point of her remark was nonetheless clear. After she explained her position I could see that she was probably right. Men always want to tinker with the computer, she said, take it apart, add memory and peripherals, and so forth, while the women concentrate on more important things like sending out ‘hundreds of email invitations to a wedding shower. This is fully consistent with my own experiences with technological things. When our car breaks down I obsess on figuring out what happened while my wife just wants to spend a lot of money to get it fixed and go to the movies. Women just seem to intuitively understand better than men that how a thing works matters much less than what one
uses it for.
59

60

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Computation is based on an enormous tower of functionalities.

Computers are an especially helpful instance of this technological fact of life because they are so transparently hierarchical. At the highest level they are tools that store and process email, manipulate
more formal written communications, and allow one to search for
deals at Internet auctions. (There are less practical uses, such as tasteless video games, secret pornography downloads, and trading copyrighted songs and movies, but these waste time and do not count.) At the next level down one has the processor, motherboard, and expansion slots containing wonderful things with names like voodoo and rage, so powerful that they require extra fans. Below this one finds silicon microchips with their fabulous webs of wires and diffused transistors, and below this the orderly lattice of silicon atoms through which electrons and holes propagate.? It is possible to send out all those shower invitations without thinking about it too carefully because of the reliability of an enormous tower of

The Quantum Computer

61

functionalities, each resting on the one below and supporting the one above. How each level works is immaterial. The invitations could just as easily have been sent out by little gnomes with pads of paper and miniature telephones, although they would probably have demanded more money.
Computers are machines. Like any other machine, such as a lawn
mower or steam engine, a computer works by moving matter from place to place. Because the matter in question is composed of electrons solely, it can be made to move easily and with blazing speed, but it istill conceptually the same as a piston rod or crankshaft in a car.3 In the end, the objective of computer engineering is still to get an assemblage of mechanical linkages to cause some physical thing to occur, such as deposition of ink on a page, motion of a loudspeaker cone, or twisting of the liquid crystal in a display pixel. Computers are often touted as the magical technology of the twenty-first century, but they are actually the crowning achievement of the nineteenth.
A key difference between computers and other kinds of machines is the ease with which their mechanical linkages can be modified.
The modification process is called programming, and it has the gen-
teel appearance of a term paper being typed, except that there is
more coffee consumed and more swearing.‘ But looks can be deceiv-
ing. This activity is not term paper composition at all but auto shop.
It involves construction of complex mechanical relationships between simple parts that then either function or don’t depending on
the workmanship. One has simply traded in lathes and torque
wrenches for pencils and keyboards. There are several qualitative differences between computers and
cars brought about by the ease of modification. For example, the economics of engineering is fundamentally altered by driving the cost of
making the physical microchip way below the labor cost of program-
ming. This is why software costs so much, and why its monopolization is so different from that of steel, railroads, or oil. Programming

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is also sufficiently similar to day-to-day use of the computer that the two become mixed up in people’s minds as a kind of super abstraction of thinking. In the world of computers one begins to confuse play with work, work with play, and business activity with fundamental meaning. Computation, as most people experience it, is separated by complex layers of economic activity from the basics of the machines themselves and is in this sense a classic case of emergence. Modern computer programs are constructed by enormous teams of people, each of whom understands only a small fraction of the task, and these programs often wind up interacting with each other in ways their creators could not have imagined. This sociological phenomenon is a logical implication of the simple fact of cheap programmability made possible by the agency of electricity.
The trick to making modification easy is eradicating the difference between cause and consequence using transistor action. This has a simple analogy in one’s own thought. I will remove my hand quickly
from the stove top if the burner turns on, but I will also remove my
hand if I remember a phone call I have to make. The complex circuitry that moves my hand can be actuated either by an external stimulus, such as fire, or an internal one, such as a surfacing memory. There is no difference between the two other than an abstract categorization. This can go awry in mental illness, in which case a person begins to confuse real events with imaginary ones. The transistor is an equalizer. It senses a motion of electrons in one wire and generates motion of electrons in another that is always the same size, regardless of how small the first motion was. This causes the motions in computers to be all-or-nothing affairs, with each wire being in either an on or off state and never in between. It also causes the measurement of a given wire to contain no information about where the signal originally came from. The decision to be on or off could have
been based on an external stimulus, another transistor, or a huge
nested cascade of transistors. There is no difference.

The Quantum Computer

63

The signals in computers are Newtonian. We sometimes lose sight of this fact, since computers tend to be viewed as mysterious in the Same way that quantum mechanics is, but this is exactly backward. The mysteriousness of computers comes from the emergent nature of their functionalities, not from microscopic considerations. At the level of the transistors themselves computers are grounded firmly in the idea of absolute certainty in measurement, for only this is compatible with the idea of on or off—right or wrong—at any given mo-
ment. Not only are transistors Newtonian concepts, they create
NeWtonianness by outputting large motions of electrons in all circumstances. In the process of doing this they generate heat—lots of it.© This is why modern processor chips are hot to the touch, and why
they will die if their dedicated fan malfunctions. The generation of heat is fundamental to maintaining reliability. To see how this could be so, it is helpful to return to the famous example of a pencil on its tip. In practice, the decision to fall left rather than right is permanent, because the pencil dissipates all its energy into heat when it crashes down on the table. If it didn’t—if the encounter with the table resulted in a perfectly elastic bounce—the pencil would right itself again and make the left-right decision a second time, perhaps with the opposite outcome. So the dissipation of power and the generation of heat are essential to decision-making, particularly in situations involving initial delicate balance, and thus to the functioning of all modern computers. (We might say the same of human institu-
_tions such as companies and government: the decisions that count
are irreversible.) Two small modifications of the transistor design allow one to
build actual computers. One involves giving the transistor two input wires and causing it to be on if either of the two inputs is on. The other involves a negation, so that the transistor is on if the input wire is off and vice versa. These two design elements are called logic, and they form the conceptual basis of all computer circuitry. Modern

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computers are simply an enormous network of logic and a clock—a small bit of circuitry that switches a wire on and off in a regular way, like a heartbeat. The clock hearts of modern home computers beat very fast—effectively about a billion times a second—but sturdily and valiantly. I have had a couple of computers die of heart failure, but such deaths are rare. Computers nearly always become obsolete long before the grim reaper comes to call.
There is a great deal of interest lately in the quantum computer, a fundamentally new kind of computational hardware that would exploit the entanglement of the quantum wave function to perform calculations presently impossible with conventional computers.” The most important of these is the generation of enormous prime numbers and the quick factorization of other enormous numbers. The impossibility of factoring a number that is the product of two large primes in reasonable time with conventional computers is the basis of modern cryptography.’ However, quantum computation has a terrible Achilles heel that becomes clear when one confronts the problem of reading out the answer: the effects that distinguish quan-
tum computers from conventional ones also cause quantum indeter-
minism. Quantum-mechanical wave functions do indeed evolve deterministically, but the process of turning them into signals people can read generates errors. Computers that make mistakes are not
very useful, so the design issue in quantum computation that counts is overcoming mistakes of measurement. A textbook method for doing this is to place a million copies of the same experiment in a small box and measure something they do collectively—generate oscillating magnetic fields, for example, as occurs in a quantum computer built with electron spins. The damage inflicted by the measurement process then affects only a few copies, leaving the rest intact. This trick is so powerful that variations of it enable you to read out the entire wave function of any quantum computer, at least in principle. However, a logical implication of this ability is that you

The Quantum Computer

65

have created not a fabulous new kind of digital computer but a conventional analogue computer—a type of machine we do not use in the modern era because it is so easily disrupted by noise.? Thus the frenzy over quantum computing misses the key point that the physical basis of computational reliability is emergent Newtonianness. One can imagine doing a computation without exploiting these principles, just as one can imagine proving by brute force that broken symmetry occurs, but a much more likely outcome is that eliminating computational mistakes will prove to be fundamentally impossible Because its physical basis is absent. The view that this problem is
trivial is a fantasy spun out of reductionist beliefs. Naturally, I hope I am wrong, and I wish those who invest in quantum computing the best of luck. I also ask that anyone anxious to invest in a bridge in
lower Manhattan contact me right away, for there will be discounts for a limited time only.
The real quantum computer, of course, is good old silicon.!° The
principles of semiconduction on which transistors are based, and
the difference between conventional conducting wires and insula-
tors, are highly quantum-mechanical. This fact was not apparent
when semiconduction was discovered by Ferdinand Braun, who
stumbled upon it in a number of metallic sulfides, notably the lead
ore galena, in 1874.!! Only much later, in conjunction with the de-
velopment of radar and the related invention of the transistor, was
a systematic understanding of the quantum nature of these effects worked out, mostly by the legendary John Bardeen. Crystalline insulators conduct electricity poorly because all of their electrons are tied up in chemical bonds. In the specific case of silicon, for example, each atom has four neighbors and four electrons available for bonding—a number exactly exhausted by the usual rule of two electrons per bond. In contrast to extremely good insulators such as quartz or table salt, however, the chemical bonds of silicon are weak and easily disrupted. Once ripped out of its bond, an electron is

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free to move about in the silicon, as is the hole left behind. The rec-
tifying and amplification actions of semiconductor devices all come from manipulation of these freed electrons and holes by means of chemical modifications and attached wires. The quantum mechanics that matters regulates the bonding rules and the motion of the freed electrons and holes.
Electrons and holes move through cold crystalline silicon as if it were not there.!2 This astonishing fact is central to the working of transistors, and it is why efficient ones can never be made from noncrystalline substances such as rubber or plastic.!3 Indeed, the key technical breakthrough that ushered in the silicon age was not the invention of the transistor but the invention of zone refining, a method of systematically eliminating chemical and structural imperfections of crystals. The ability of electrons and holes to move ballistically
through the lattice is not obvious at all, for a piece of silicon is con-
ceptually no different from a giant molecule and must therefore be characterized by the highly entangled motions of all the electrons, including those in the bonds. The resolution of this problem is that the entanglement is rendered irrelevant by emergence. It turns out to be exactly and universally the case that crystalline insulators have specific collective motions of all the electrons that look and act as though they were motions of isolated electrons. The only effect of all their awful underlying complexity is to make the acceleration mass slightly different from that of a free electron and to effectively reduce the strength of the electric forces. The electric charge of a hole is obviously opposite to that of an electron, since it represents an electron deficit. An engineer speaking of an electron or hole is really speaking about one of these complex collective motions, not an isolated particle. For engineering purposes this complexity does not matter any more than it matters how computers send out shower invitations. The important thing is that the particle-like nature of the collective motion is exact and reliable.

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67

Electrons and holes in silicon are magnificently quantum-mechanical. Despite being not free at all but horrendously entangled, these objects provide some of the most accurate tests of quantum mechanics that have ever been obtained. A beautiful example is the line spectroscopy of phosphorous impurities. Phosphorous atoms added in small amounts to melted silicon substitute for silicon atoms in the lattice when it crystallizes. The substituted phosphorous atom uses up four of its five outer electrons making chemical bonds and gives up the fifth to wander about. When the temperature is reduced to extremely
low“values, however, the errant electron finds its way back to the site
and binds there, just as an electron would bind onto a proton to
make a hydrogen atom.!4 However, rather than emitting visible light at distinct wavelengths, the electron bound to the phosphorous impurity emits infrared light at distinct wavelengths because the electric forces binding it to the phosphorous site are powerfully mitigated. This light can be detected with conventional infrared spectrometers. Not only is the impurity spectrum analogous to that of an atom, it is physically indistinguishable from that of an atom, except for the specific wavelengths of light emitted. The collective nature of the object doing the binding has all but disappeared. There are lots of experiments like this, for inside a piece of silicon is a miniature world in
which the forces of electricity are reduced, the masses of electrons are
changed, and the electron has a sibling of the opposite charge with which it can annihilate to make light.
The quantum nature of electrons and holes almost certainly im-
poses a fundamental limitation on Moore’s law, the celebrated obser-
vation by Intel founder Gordon Moore that the number of transistors on a given area of silicon tends to double every 18 months.'5 Moore's law is one of the main reasons computers have continued to surprise us when the basic principles underneath them are so simple. Back in the beginning of the computer age it was discovered that making transistors and wires smaller so as to pack more of them ontoasilicon

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chip also made them more reliable. Thus began the race to achieve higher and higher densities that continues to this day. Right now, chip manufacturers are fighting terrible problems of heat generation and optical lithography size constraints unlike anything they have faced before, but nearly everyone believes these can be overcome in time to preserve Moore’s law down to the quantum limit. In about a
decade or so, however, the transistors will get so small that they will
become quantum-mechanical—and thus begin making mistakes. When this occurs it will mark the end of a remarkable time in history in which the implications of a small physical discovery exploded into the economy and changed the world.
One of the more interesting trends of the computer age is that physical science students are increasingly unwilling or unable to write computer code. I was very upset whenIfirst observed this and
took stern measures in my department to counteract it, much to the
students’ chagrin, for I myself am very good at coding and consider it something any self-respecting technologist should know how to do. Eventually, however, I realized that the students were right and I
was wrong, and stopped the crusade. Computer programming is one
of those things in life, like fixing one’s own car, that is fascinating, fun, useful—and unacceptably time-consuming. The truth is that it is no longer cost-effective for most well-educated people to program their own computers, or even to learn how to do so. The wise use of time is to spend a few bucks to buy a program that does what one wants or, in extreme cases, search the internet for free software.
When I was a graduate student, in the early 1970s, the economics were exactly reversed. Student labor was cheap and computers were hideously expensive mainframes that occupied entire floors of university computer centers. They were pampered affairs, with legions of attendants working in shifts around the clock and special air conditioning with power backups. We wrote computer programs for these behemoths late at night on grey metal machines about the size of

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bears. One of these machines would hum away with its motor running until one struck a key, at which point it would tremble a bit, go -chunkh, and put a crisp new hole in the card one was punching. After
one was done with a card, one would hit the feed key, and the ma-
chine would rotate the card klicka-ka-chunkha-chunkh to the bottom of the growing stack and feed in a new blank one. The computer programs we wrote were realized as decks of cards punched in this way, held together with rubber bands and stored in cardboard boxes. Running the program involved submitting one’s deck to an attendant, whe would feed it into a card reader, an apparatus that looked like a
gasoline-powered wood plane and sounded rather like a vacuum cleaner with a leaf caught in its fan. The printer would all the time be whining away in the background under its metallic sound hood and frantically throwing off page after enormous page of white computer paper as though it had gone berserk. Every few minutes an attendant
would retrieve this output, which would require opening the sound
hood briefly, thereby filling the room with unbearable screeching. The
attendant would then tear the output at appropriate seams and stuff it into bins for pickup by students. This output consisted mostly of in-
comprehensible operating system mumbo-jumbo with the stuff one had actually calculated on the last page—unless the code had a mistake, in which case one would get either a thin nothing or an inch of
meaningless core dump output, depending on the severity of the mistake. The expense of all this was incomprehensible. I remember talking with one of my fellow students just after he had submitted a deck
in three boxes and seeing his hands shake. Ah, those were the days.
The most famous deck story of all time is the box containing an enormous hydrodynamic simulation code that somebody dropped, causing cards to fly everywhere. The program in question was promptly christened Nixon because it would clearly never run again. But happily it did run again and became the nucleus of the classified program Lasnex, the current workhorse of laser fusion simulation.'®

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The joke about gender bias in computer skills thus has at its core
the more important observation that we owe the existence, reliabil-
ity, and utility of computers to principles of organization—including economic ones. That women have an easier time understanding the supremacy of organizations than men is not news, for this was known to the ancients and recorded in numerous places, notably the I Ching.'7 According to Taoist philosophy, the universe is impelled forward by the conflict of two opposing principles, yin and yang, that constantly produce and supplant each other. Yang represents maleness, the sun, heat, light, dominance, and so forth. Yin repre-
sents femaleness, the moon, material forms, cold, submission, and
so forth. Yang, the sunny southern side of the mountain, creates, while yin, the shady northern side, completes the created thing. One might say that we are presently in an age of yin, and even though computers were brought into existence by yang, they have reached their full potential only under the dominance of yin. A more direct western way of saying this same thing is that computers were originally conceived as dogs but now have become cats. The machine one brings home from the store is clever, self-serving, constantly underfoot, and always scheming how to get you to do what it wants. But when you lobotomize the thing, strip away its sophistication, and reach down past the facade to the wires, transistors, and algorithms underneath you find unquestioning obedience, steadfast loyalty, straightforwardness, and simplicity—i.e., a dog.

(SEVEN)
Vin Klitzing
If scientific reasoning were limited to the logical process of arith@ metic, we should not get very far in our understanding of the phys-
ical world. One might as well attempt to grasp the game of poker entirely by use of the mathematics ofprobability.
Vannevar Bush
Ir IS DIFFICULT TO KEEP PROFESSIONAL CONCERNS IN FOCUS
while floating down a river on a tour boat on a breezy summer afternoon. Scientists are always complaining about the agony of writing all those proposals, delivering all those technical presentations, and accruing all those frequent flyer miles, but such complaints are disingenuous, and they are exposed by such moments as fraud. Most of us are willing to pay the price for the perquisites, and grumble in public only to prevent other people from discovering how pleasant our lives actually are. Right now, the inevitable quid pro quo is far away, for it is warm and there are fields and orchards passing by. Science is a tough job, but somebody has to do it.
I am on the Neckar as guest of a group of alumni of the Max Planck Institute in Stuttgart, who have hired the boat as a sixtieth birthday present for the legendary Klaus von Klitzing.' It is a friendly bunch of people, many of whom I have known since the early 1980s
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when I first began to write theoretical papers about the von Klitzing
effect. Most are locals, but a few, like myself, are from abroad. In the
mix of nationalities, Japan and America are especially well represented, as expected of a community of semiconductor physicists, but so are Israel and Russia, with smaller contingents from England, Brazil, and Mexico. Everyone is here for the common purpose of creating a memory for Klaus, a citizen of the world and an inhabitant of what we must now, apparently, call “Old Europe.”?
Ageless and enthusiastic as always, Klaus is unaware of the real surprise coming downriver—a small vineyard on a bluff rented for him by his friends. He chats away happily as the boat rounds the bend, and then stops abruptly as he spots the big sign with his name on it on the hill. It is manned by a couple of students who drove up in the morning to set it in place. They see that they have been discovered and wave. Klaus instantly figures out what has happened and becomes quite animated, but it is too late. Anticipating this moment, the conspirators have secretly distributed glasses of champagne, with which the birthday is now exuberantly toasted, causing the boat to rock a bit. Klaus is speechless. The boat comes to abrief halt in front of the vineyard for a few photographs and testimonials, including solemn promises to press the wine without cheating by mixing with inferior grapes. It is to be privately bottled and distributed under the label Vin Klitzing.
While the key surprise recedes upstream, others are still in store.
The boat docks at the medieval town of Besigheim, where it is met by
a welcoming committee of curious locals, a terrific high school band, and three gentlemen dressed in eighteenth-century livery. One of these, evidently the leader, sports a three-foot-high stovepipe hat with a wide brim and carries a monstrous glass of wine. He delivers his boatload of guests a ceremonial invitation to enter the town, then leads them through the cobbled streets to a great banquet hall laid out in preparation for a feast. The students are overjoyed to discover

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~ it is an all-you-can-eat affair, no doubt in deference to them. The stuffed guests are then led from the hall on a tour of the medieval wall surrounding the town and reinforcing the protection of the converging rivers below, which bubble and sparkle in the sun as they have for centuries. The party then reboards the boat and climbs back home through mossy locks in the failing light, singing and sampling wine after excellent wine from the stores, for this trip is a tasting tour in addition to everything else. The extremes to which these people have gone to honor Klaus reflecé the esteem in which he is held. Part of this enthusiasm is admittedly a local phenomenon. On the day in 1983 when his Nobel Prize was announced, for example, they interrupted daytime television in Germany, something utterly unthinkable in America, for continuous coverage of the event. He was only the fourth physics Nobel in Germany since the Second World War, a particularly sensitive matter, since modern physics was invented in Germany in the
first years of the twentieth century.’ But he is lavishly féted elsewhere in the world as well, especially in Asia, and is seemingly al-
ways on his way to and from honorary presentations and meetings in the far corners of the earth.
What he did to deserve this celebrity was to discover something
that should not have been—a shocking reminder that human under-
standing of the world is finite, that our prejudices are not laws, and
that quantum physics is magical or often seems to be.4 He made his
discovery in 1980 at the high magnetic field laboratory in Grenoble,
where he was performing interesting but rather routine experiments
on state-of-the-art electronic components. These were built to toler-
ances more exacting than those used in the microcircuit industry
even today and cooled to ultralow temperatures for the purpose of
enhancing any new effects that might be exploited in the next gener-
ation of electronics. He began thinking about an effect in these sam-
ples that had been seen before in which one of the measurements

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became abnormally steady over a range of magnetic field strengths. Motivated by curiosity, academic training, or just plain inspiration he resolved to find out exactly how steady it was by accurately calibrating the experiment. He discovered, to his amazement, that it was the same from one field strength to the next, one day to the next, and one sample to the next to an accuracy of better than one part per million. Improvements in sample quality and refrigeration technology have since improved this reproducibility to one part in ten billion. To put this accuracy in perspective, it is like counting every man, woman, and child on the surface of the earth without missing a single one. The discovery of this unexpected, unpredicted constancy rocketed von Klitzing to international superstardom in science, where he has remained ever since.
The measurement itself is simple—once you know what to look for—and has been reproduced in thousands of laboratories around the world, so we are sure it is right. When a magnet is brought into the vicinity of any wire carrying electric current, a voltage develops at right angles to the current flow. This occurs because electrons moving in the conductor are deflected by the magnet, just as they would be in free space, and so pile up on one side of the wire until the reaction voltage they generate exactly compensates the magnetic deflection. This is called the Hall effect, named after Edwin H. Hall, the physicist who originally discovered it in 1879. It is normally reported as a resistance, computed by dividing the voltage thus generated by the current. At ordinary temperatures the Hall resistance measures the density of electrons in the wire, and is therefore important in semiconductor technology, which works by manipulating this density. At very low temperatures, however, quantum mechanics intervenes. A plot of the Hall resistance versus density is no longer a straight line, as it would be at room temperature, but one that has acquired wiggles. In the case of the special kind of semiconductors von Klitzing was studying—field effect transistors like those in computer

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75

chips—these wiggles evolve intoastaircase with extremely flat steps as the temperature is lowered. The heights of these steps are the universal quantized values of the Hall resistance.
After establishing its universality, von Klitzing quickly realized that the quantum of Hall resistance thus defined was a combination of fundamental constants—the indivisible quantum of electric charge e, Planck’s constant h, and the speed of light c—all of which we think of as building blocks of the universe.> This fact has the obvious implication that you can measure the building blocks with breathtaking accuracy without dealing with the building blocks directly. This is deeply important and deeply upsetting to most physicists. The more thoughtful of them find it impossible to believe until they study the numbers, and even then suspect something to be amiss. But nothing ever is. The experiments are plentiful, consistent, and unassailable. Moreover, the accuracy of the von Klitzing measurement appears to improve without bound as the temperature is lowered and the sample size is increased. For this reason it has be-
come the accepted definition for this particular combination of fundamental constants.
The impact this discovery had on physics would be hard to over-
state. | remember vividly the day my colleague Dan Tsui brought the
von Klitzing paper into the Bell Labs tea room and, barely controlling
his excitement, urged everyone to think about where this astonishing
accuracy could have come from.® No one had an explanation. We all
knew that von Klitzing’s samples were imperfect, and we thus ex-
pected them to vary. In processing semiconductors there are always
variabilities one cannot control, such as structural defects in the crys-
tal lattice, randomly incorporated dopants, amorphous oxides at the
surface, ragged edges left over from optical lithography, bits of metal
strewn about on the surface by clunky soldering irons when wires are
attached, and so forth. These are known to influence other electrical
measurements, for the matter is important for microcircuitry and

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has thus been extensively studied. But this expectation turned out to be wrong. As a result of theoretical work done after the fact, including some of my own, we now understand that imperfection has exactly the opposite effect, namely to cause the perfection of the measurement—a dramatic reversal worthy of the finest Greek drama.’ The quantum Hall effect is, in fact, a magnificent example of perfection emerging out of imperfection. The key clue that this is so is that the quantization accuracy—which is to say, the effect itself— disappears if the sample is too small. Collective phenomena are both common in nature and central to modern physical science, so the effect is in this sense neither unprecedented nor hard to understand. However, the extreme accuracy of the von Klitzing effect makes its collective nature undeniable, and therein lies its special significance.
Over the intervening years, as I have lived inside theoretical physics and become familiar with its ways and historical currents, I have come to understand the von Klitzing discovery to be a watershed event, a defining moment in which physical science stepped
firmly out of the age of reductionism into the age of emergence. This
shift is usually described in the popular press as the transition from
the age of physics to the age of biology, but that is not quite right.
What we are seeing is a transformation of worldview in which the
objective of understanding nature by breaking it down into ever
smaller parts is supplanted by the objective of understanding how
nature organizes itself.
If the quantum Hall effect raised the curtain on the age of emer-
gence, then the fractional quantum Hall discovery was its opening
movement.’ The experimental setup that revealed the fractional ef-
fect was exactly the same as for the original von Klitzing effect, but
the meaning was different. While the extreme reproducibility of the
quantum Hall effect had been unexpected, the broad-brush behavior
had not. Indeed, von Klitzing’s interest in the matter had been
sparked by a theoretical paper by Tsuneya Ando, now a professor of

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physics at the Tokyo Institute of Technology, in which figures very similar to the experimental traces later discovered actually appear.? The fractional effect, in contrast, was unanticipated by any theory and not analogous to anything previously known in nature. Dan Tsui and Horst Stérmer discovered it accidentally one night while looking for evidence of electron crystallization, which is what prevailing theories said should occur. Instead, they found a miniature version of the von Klitzing effect at a magnetic field strength that should have been too high and at a value exactly one-third the ostensibly minimufn allowed value, which should have been impossible. Von Klitzing always says he could kick himself for not finding the fractional effect, but he is being unfair to himself, for it was simply a matter of sample quality. (Imperfections cannot hurt the quantization accuracy, but they can, unfortunately, destroy the effect entirely.) Momentous discoveries often hinge on slight technological advantages. Dan, Horst, and I shared the 1998 Nobel Prize for work on the fractional quantum Hall effect—they for discovering it and I for con-
structing its first mathematical description.!° I did not think of this
discovery as revolutionary at the time, for my discipline is filled with
astonishing quantum-mechanical things that require new mathematics to describe, but I have changed my mind over the years. The
extreme perfection of the effect places it in a different category from
its predecessors in the same way perfection of the original quantum Hall effect did.
The fractional quantum Hall effect reveals that ostensibly indivis-
ible quanta—in this case the electron charge e—can be broken into
pieces through self-organization of phases. The fundamental things,
in other words, are not necessarily fundamental. That such fraction-
alization could occur in principle had been known for decades, and
there was even an experimental literature arguing that particulate
objects carrying fractional charge were responsible for electric con-
duction in organic conductors called polyacetylenes.!! However, all

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of the arguments in place at the time of the discovery had flaws. The theoretical models in which the effect could be demonstrated conclusively were all one-dimensional and thus impossible to realize exactly in the laboratory. The organic conductors in question were always plagued with chemistry problems that prevented their experimental properties from being reproducible. It was always possible to evade fractionalization issues by arguing that the experiments could be explained without them—something that is always true in emergent phenomena but that often misses the forest for the trees. But the fractional quantum Hall discovery stopped this obfuscation in its tracks by virtue of its exactness. It is not possible to account for exact things with approximate theories. The observation of accurately quantized fractional quantum Hall plateaus proved the existence of new phases of matter in which the elementary excitations—the particles—carried an exact fraction of e. The excitations of the state first discovered by Dan and Horst carried charge e/3, an especially intriguing result in light of the charge e/3 carried by quarks, the al-
legedly fundamental constituents of protons and neutrons. Since
then an immense cascading tree of such phases has been discovered,
each characterized bya different small-denominator fraction.”
Once a person reaches a certain plateau of fame it becomes difficult
to think of anything to give him that he does not already have. I had
the unenviable task of delivering a technical lecture at the von Klitz-
ing birthday colloquium that preceded the Neckar boat ride. Since I had not worked in semiconductors for years and had much less to say
about the subject than younger people in the thick of things, I was in
danger of making a fool of myself. I decided in the end to talk about
emergent physical law—the aspect of the von Klitzing discovery that
counts—and to use the occasion to present Klaus a seedling. I
brought two, actually, one for his house and one for the Institute cam-
pus, for one learns over years of technical life to have backups. I ex-
plained in my presentation that these were sequoias, the mightiest of