$5.95 U.S. $6.50 CAN. COPYRIGHT 2003 … Edge Of Physics.pdfgravitation by Albert Einstein from 1905 to 1916. And the unraveling of chemistry and atomic physics through the advent

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Letter from the Editor

A Unified Physics by 2050?By Steven WeinbergExperiments at CERN and elsewhere shouldlet us complete the Standard Model of particlephysics, but a unified theory of all forces willprobably require radically new ideas.

The Theory Formerly Known as StringsBy Michael J. DuffThe Theory of Everything is emerging as onein which not only strings but also membranesand black holes play a role.

Black Holes and the Information ParadoxBy Leonard SusskindWhat happens to the information in matterdestroyed by a black hole? Searching for thatanswer, physicists are groping toward aquantum theory of gravity.

Simple Rules for a ComplexQuantum WorldBy Michael A. NielsenAn exciting new fundamental discipline of research combines information scienceand quantum mechanics.

Quantum TeleportationBy Anton ZeilingerThe science-fiction dream of “beaming”objects from place to place is now a reality—at least for particles of light.

Frozen LightBy Lene Vestergaard HauSlowing a beam of light to a halt may pave the way for new optical communicationstechnology, tabletop black holes andquantum computers.

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Cover illustration by Tom Draper Design; Tom Draper Design (left); Chip Simons (right); page 2: William Pelletier/ Photo Services, Inc., courtesy of the University of Michigan (left); Tom Draper Design (inset and right)

contents contentsphysicsphysics

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SCIENTIFIC AMERICAN Volume 13 Number 1


The Large Hadron ColliderBy Chris Llewellyn SmithThe Large Hadron Collider, a global collaborationto uncover an exotic new layer of reality, will be a particle accelerator of unprecedentedenergy and complexity.

The Asymmetry between Matter and AntimatterBy Helen R. Quinn and Michael S. WitherellNew accelerators will search for violations in afundamental symmetry of nature, throwing opena window to physics beyond the known.

Detecting Massive NeutrinosBy Edward Kearns, Takaaki Kajita and Yoji TotsukaA giant detector in the heart of Mount Ikenoyamain Japan has demonstrated that neutrinosmetamorphose in flight, strongly suggesting that these ghostly particles have mass.

Extreme LightBy Gérard A. Mourou and Donald UmstadterFocusing light with the power of 1,000 HooverDams onto a point the size of a cell nucleusaccelerates electrons to the speed of light in a femtosecond.

Negative Energy, Wormholes and Warp DriveBy Lawrence H. Ford and Thomas A. RomanThe construction of wormholes and warpdrive would require a very unusual form ofenergy. But the same laws of physics thatallow this “negative energy” also appear tolimit its behavior.

Nanophysics: Plenty of Room, IndeedBy Michael RoukesThere is plenty of room for practicalinnovation at the nanoscale. But first,scientists have to understand the uniquephysics that governs matter there.

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S c i e n t i f i c A m e r i c a n S p e c i a l ( I S S N 10 4 8 - 0 9 4 3 ) , V o l u m e 1 3 , N u m b e r 1 , 2 0 0 3 ,p u b l i s h e d b y S c i e n t i f i c A m e r i c a n , I n c . , 415 M a d i s o n A v e n u e , N e w Y o r k , N Y10 017- 1 1 1 1 . C o p y r i g h t © 2 0 0 3 b y S c i e n t i f i c A m e r i c a n , I n c . A l l r i g h t sr e s e r v e d . N o p a r t o f t h i s i s s u e m a y b e r e p r o d u c e d b y a n y m e c h a n i c a l ,p h o t o g r a p h i c o r e l e c t r o n i c p r o c e s s , o r i n t h e f o r m o f a p h o n o g r a p h i cr e c o r d i n g , n o r m a y i t b e s t o r e d i n a r e t r i e v a l s y s t e m , t r a n s m i t t e d o ro t h e r w i s e c o p i e d f o r p u b l i c o r p r i v a t e u s e without written per m ission of thepublisher. Canadian BN No. 127387652RT; QST No. Q1015332537. To purchaseaddit ional quantit ies: 1 to 9 copies: U.S. $5.95 each plus $2.00 per copy forpostage and handling (outside U.S. $5.00 P&H). Send payment to ScientificAmerican, D e p t . P H Y , 415 M a d i s o n A v e n u e , New York, NY 10017-1111.Inquir ies: Fax 212-355-0408 or telephone 212-451-8890. Printed in U.S.A.

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struction of even more fantastic phenomena, such as shortcuts through spacecalled wormholes and faster-than-light warp drives.

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John RennieEditor in Chief

Scientific [email protected]


letterfromtheeditor

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he primary goal of physics is to understandthe wonderful variety of nature in a unifiedway. The greatest advances of the past havebeen steps toward this goal: The unificationof terrestrial and celestial mechanics byIsaac Newton in the 17th century. The the-

ories of electricity and magnetism by James Clerk Maxwellin the 19th century. Spacetime geometry and the theory ofgravitation by Albert Einstein from 1905 to 1916. And theunraveling of chemistry and atomic physics through theadvent of quantum mechanics in the 1920s.

Einstein devoted the last 30 years of his life to an un-successful search for a “unified field theory,” which wouldunite general relativity—his own theory of spacetime andgravitation—with Maxwell’s theory of electromagnetism.Progress toward unification has been made more recent-ly, but in a different direction. Our current theory of ele-mentary particles and forces, known as the Standard Mod-

el of particle physics, has achieved a unification of elec-tromagnetism with the weak interactions, the forces re-sponsible for the change of neutrons and protons into eachother in radioactive processes and in the stars. The Stan-dard Model also gives a separate but similar description ofthe strong interactions, the forces that hold quarks togetherinside protons and neutrons and hold protons and neu-trons together inside atomic nuclei.

We have ideas about how the theory of strong interac-tions can be unified with the theory of weak and electro-magnetic interactions (often called Grand Unification), butthis may only work if gravity is included, which presentsgrave difficulties. We suspect that the apparent differencesamong these forces have been brought about by events in

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By Steven Weinberg 2050?

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QUANTUM NATURE of space and time must be dealt with in a unified theory. At the shortest distance scales, space may be replaced

by a continually reconnecting structure of strings and membranes—or by something stranger still.


Experiments at CERN and elsewhere should let us complete the Standard Model of particle

physics, but a unified theory of all forces willprobably require radically new ideas

w w w . s c i a m . c o m T H E E D G E O F P H Y S I C S 5COPYRIGHT 2003 SCIENTIFIC AMERICAN, INC.

the very early history of the big bang, butwe cannot follow the details of cosmichistory at those early times without a bet-ter theory of gravitation and the otherforces. There is a chance the work of uni-fication will be completed by 2050. Butcan we actually do it?

Quantum FieldsTHE STANDARD MODEL of particlephysics is a quantum field theory. Its ba-sic ingredients are fields, among them theelectric and magnetic fields of 19th-cen-tury electrodynamics. Little ripples inthese fields carry energy and momentumfrom place to place, and quantum me-chanics tells us that these ripples come in

bundles, or quanta, that are recognizedin the laboratory as elementary particles.For instance, the quantum of the electro-magnetic field is a particle known as thephoton.

The Standard Model includes a fieldfor each type of elementary particle thathas been observed in high-energy physicslaboratories [see top illustration on page8]. There are the lepton fields: their quan-ta include the familiar electrons, whichmake up the outer parts of ordinaryatoms, similar heavier particles known asmuons and tauons, and related electri-cally neutral particles known as neutri-nos. There are fields for quarks of vari-ous types, some of which are bound to-

gether in the protons and neutrons thatmake up the nuclei of ordinary atoms.Forces between these particles are pro-duced by the exchange of photons andsimilar elementary particles: the W+, W–

and Z0 transmit the weak force, andeight species of gluon produce the strongforces.

These particles exhibit a wide varietyof masses that follow no recognizable pat-tern, with the electron 350,000 times aslight as the heaviest quark, and neutrinoseven lighter. The Standard Model has nomechanism that would account for any ofthese masses, unless we supplement it byadding additional fields, of a type knownas scalar fields. “Scalar” means that these

Electricity

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UNIFICATION of disparatephenomena within onetheory has long been acentral theme of physics.The Standard Model ofparticle physicssuccessfully describesthree (electromagnetism,weak interactions andstrong interactions) of thefour known forces ofnature but remains to beunited definitively withgeneral relativity, whichgoverns the force ofgravity and the nature ofspace and time.


fields do not carry a sense of direction, un-like the electric and magnetic fields andthe other fields of the Standard Model.This opens up the possibility that thesescalar fields can pervade all of space with-out contradicting one of the best estab-lished principles of physics, that spacelooks the same in all directions. (In con-trast, if, for example, there were a signif-icant magnetic field everywhere in space,we could then identify a preferred direc-tion by using an ordinary compass.) Theinteraction of the other fields of the Stan-dard Model with the all-pervasive scalarfields is believed to give the particles of theStandard Model their masses.

Beyond the TopTO COMPLETE the Standard Model,we need to confirm the existence of thesescalar fields and find out how many typesthere are. This is a matter of discoveringnew elementary particles, often calledHiggs particles, that can be recognized asthe quanta of these fields. We have everyreason to expect that this task will be ac-complished before 2020, when the accel-erator called the Large Hadron Colliderat CERN, the European laboratory forparticle physics near Geneva, will havebeen operating for more than a decade.

The very least thing that will be dis-

covered is a single electrically neutral sca-lar particle. It would be a disaster if thiswere all that were found by 2020, though,because that would leave us without aclue to the solution of a formidable puz-zle called the hierarchy problem.

The heaviest known particle of theStandard Model is the top quark, with amass equivalent to an energy of 175 giga-electron-volts (GeV). One GeV is a littlemore than the energy contained in a pro-ton mass. [See “The Discovery of the TopQuark,” by Tony M. Liss and Paul L.Tipton; Scientific American, Septem-ber 1997.] The not yet discovered Higgsparticles are expected to have similarmasses, from 100 to several hundredGeV. But there is evidence of a muchlarger scale of masses that will appear inequations of the not yet formulated uni-fied theory. The gluon, W, Z and photonfields of the Standard Model have inter-actions of rather different strengths withthe other fields of this model; that is why

the forces produced by exchange of glu-ons are about 100 times as strong as theothers under ordinary conditions. Grav-itation is vastly weaker: the gravitationalforce between the electron and proton inthe hydrogen atom is about 10–39 thestrength of the electric force.

But all these interaction strengths de-pend on the energy at which they aremeasured [see top illustration on page 9].It is striking that when the interactions ofthe fields of the Standard Model are ex-trapolated, they all become equal to oneanother at an energy of a little more than1016 GeV, and the force of gravitationhas the same strength at an energy notmuch higher, around 1018 GeV. (Re-finements to the theory of gravitationhave been suggested that would evenbring the strength of gravitation intoequality with the other forces at about1016 GeV.) We are used to some prettybig mass ratios in particle physics, likethe 350,000 to 1 ratio of the top quark tothe electron mass, but this is nothingcompared with the enormous ratio of thefundamental unification energy scale of1016 GeV (or perhaps 1018 GeV) to theenergy scale of about 100 GeV that is


STEVEN WEINBERG is head of the Theory Group at the University of Texas at Austin and amember of its physics and astronomy departments. His work in elementary particlephysics has been honored with numerous prizes and awards, including the Nobel Prize forPhysics in 1979 and the National Medal of Science in 1991. The third volume (Supersym-metry) of his treatise The Quantum Theory of Fields was published in 2000. The secondvolume (Modern Applications) was hailed by Physics Today as being “unmatched by anyother book on quantum field theory for its depth, generality and definitive character.”

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Quantum mechanics: wave-particle duality, superposition, probabilities

Quantum field theory: virtual particles, renormalization

?General relativity: equivalence principle, dynamic spacetime

Special relativity: spacetime geometry, relativity of motion

Newtonian mechanics: universal gravitation, force and acceleration

MOST PROFOUND ADVANCESin fundamental physics tend to occur

when the principles of different types oftheories are reconciled within a single

new framework. We do not yet know what guiding principle underlies

the unification of quantum field theory,as embodied in the Standard Model,

with general relativity.


typical of the Standard Model [see illus-tration below]. The crux of the hierarchyproblem is to understand this huge ratio,this vast jump from one level to the nextin the hierarchy of energy scales, and todo so not just by adjusting the constantsin our theories to make the ratio comeout right but as a natural consequence offundamental principles.

Theorists have proposed several in-teresting ideas for a natural solution tothe hierarchy problem, incorporating anew symmetry principle known as su-persymmetry (which also improves theaccuracy with which the interactionstrengths converge at 1016 GeV), or new

strong forces known as technicolor, orboth [see illustration on page 10]. Allthese theories contain additional forcesthat are unified with the strong, weakand electromagnetic forces at an energyof about 1016 GeV. The new forces be-come strong at some energy far below1016 GeV, but we cannot observe themdirectly, because they do not act on theknown particles of the Standard Model.Instead they act on other particles thatare too massive to be created in our lab-oratories. These “very heavy” particlesare nonetheless much lighter than 1016

GeV because they acquire their massfrom the new forces, which are strongonly far below 1016 GeV. In this picture,the known particles of the StandardModel would interact with the very

heavy particles, and their masses wouldarise as a secondary effect of this rela-tively weak interaction. This mechanismwould solve the hierarchy problem, mak-ing the known particles lighter than thevery heavy particles, which are them-selves much lighter than 1016 GeV.

All these ideas share another com-mon feature: they require the existence ofa zoo of new particles with masses notmuch larger than 1,000 GeV. If there isany truth to these ideas, then these parti-cles should be discovered before 2020 atthe Large Hadron Collider, and some ofthem may even show up before then atFermilab or CERN, although it may takefurther decades and new accelerators toexplore their properties fully. When theseparticles have been discovered and their

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HIERARCHY PROBLEM is a measure of our ignorance. Experiments (yellow band ) haveprobed up to an energy of about 200 GeV and haverevealed an assortment of particle masses (red )and interaction energy scales (green) that areremarkably well described by the Standard Model.The puzzle is the vast gap to two further energyscales, that of strong-electroweak unification near1016 GeV and the Planck scale, characteristic ofquantum gravity, around 1018 GeV.

STANDARD MODEL of particle physics describeseach particle of matter andeach force with a quantumfield. The fundamentalparticles of matter arefermions; they come in threegenerations (a). Eachgeneration of particlesfollows the same pattern ofproperties. The fundamentalforces are caused by bosons(b), which are organizedaccording to three closelyrelated symmetries. In addition, one or more Higgsparticles or fields (c)generate the masses of theother fields.

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properties measured, we will be able totell whether any of them would have sur-vived the early moments of the big bangand could now furnish the “dark matter”in intergalactic space that is thought tomake up most of the present mass of theuniverse. At any rate, it seems likely thatby 2050 we will understand the reasonfor the enormous ratio of energy scalesencountered in nature.

What then? There is virtually nochance that we will be able to do experi-ments involving processes at particle en-ergies like 1016 GeV. With current tech-nology the diameter of an accelerator isproportional to the energy given to the ac-celerated particles. To accelerate particlesto an energy of 1016 GeV would requirean accelerator a few light-years across.Even if someone found another way toconcentrate macroscopic amounts of en-

ergy on a single particle, the rates of in-teresting processes at these energieswould be too slow to yield useful infor-mation. But even though we cannot studyprocesses at energies like 1016 GeV di-rectly, there is a very good chance thatthese processes produce effects at accessi-ble energies that can be recognized ex-perimentally because they go beyond any-thing allowed by the Standard Model.

The Standard Model is a quantumfield theory of a special kind, one that is“renormalizable.” This term goes backto the 1940s, when physicists were learn-ing how to use the first quantum field the-ories to calculate small shifts of atomicenergy levels. They discovered that cal-culations using quantum field theorykept producing infinite quantities, whichusually means that a theory is flawed oris being pushed beyond its limits of va-lidity. In time, they found a way to dealwith the infinite quantities by absorbingthem into a redefinition, or “renormal-ization,” of only a few physical constants,such as the charge and mass of the elec-tron. (The minimum version of the Stan-dard Model, with just one scalar particle,has 18 of these constants.) Theories inwhich this procedure worked were calledrenormalizable and had a simpler struc-ture than nonrenormalizable theories.

Suppressed InteractionsIT IS THIS SIMPLE, renormalizablestructure of the Standard Model that haslet us derive specific quantitative predic-

tions for experimental results, predictionsthe success of which has confirmed the va-lidity of the theory.

In particular, the principle of renorm-alizability, together with various symme-try principles of the Standard Model,rules out unobserved processes such asthe decay of isolated protons and forbidsthe neutrinos from having masses. Physi-cists commonly used to believe that for aquantum field theory to have any validi-ty, it had to be renormalizable. This re-quirement was a powerful guide to theo-rists in formulating the Standard Model.It was terribly disturbing that it seemedimpossible, for fundamental reasons, toformulate a renormalizable quantum fieldtheory of gravitation.

Today our perspective has changed.Particle physics theories look different de-pending on the energy of the processesand reactions being considered. Forcesproduced by exchange of a very massiveparticle will typically be extremely weakat energies that are low compared withthat mass.

Other effects can be similarly sup-pressed, so that at low energies one haswhat is known as an effective field theo-ry, in which these interactions are negli-gible. Theorists have realized that anyfundamental quantum theory that is con-sistent with the special theory of relativi-ty will look like a renormalizable quan-tum field theory at low energies. But al-though the infinities are still canceled,these effective theories do not have the

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a bTHEORETICALEXTRAPOLATIONshows that the threeStandard Model forces(the strong force and theunified weak andelectromagnetic forces)have roughly equalstrength at very highenergy (a), and theequality is improved by allowing forsupersymmetry (b).Curve thickness indicatesapproximate uncertaintyin the coupling strengths.


simple structure of theories that are renor-malizable in the classic sense. Additionalcomplicated interactions are present; in-stead of being completely excluded, theyare merely highly suppressed below somecharacteristic energy scale.

Gravitation itself is just such a sup-pressed nonrenormalizable interaction. Itis from its strength (or rather weakness)at low energies that we infer that its fun-damental energy scale is roughly 1018

GeV. Another suppressed nonrenormal-izable interaction would make the protonunstable, with a half-life in the range of1031 to 1034 years, which might be tooslow to be observed even by 2050 [see myarticle “The Decay of the Proton”; Scien-tific American, June 1981]. Yet anoth-er suppressed nonrenormalizable interac-tion would give the neutrinos tiny mass-es, about 10–11 GeV. There is now strongevidence being collected at giant detectorsfor neutrino masses, very likely of this or-der [see “Detecting Massive Neutrinos,”on page 68].

Observations of this kind will yieldvaluable clues to the unified theory of allforces, but the discovery of this theorywill probably not be possible withoutradically new ideas. Some promisingones are already in circulation. There arefive theories of tiny one-dimensional enti-ties known as strings, which in their dif-ferent modes of vibration appear at lowenergy as various kinds of particles andapparently furnish perfectly finite theoriesof gravitation and other forces in 10

spacetime dimensions. Of course, we donot live in 10 dimensions, but it is plausi-ble that six of these dimensions could berolled up so tightly that they could not beobserved in processes at energies below1016 GeV per particle. Evidence has ap-peared in the past several years that thesefive string theories (and also a quantumfield theory in 11 dimensions) are all ver-sions of a single fundamental theory(sometimes called M-theory) that applyunder different approximations [see “The


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WHAT COMES NEXT? There areseveral possibilities for theunified physics that lies beyondthe Standard Model. Technicolormodels (a) introduce newinteractions analogous to the“color” force that binds quarks.Accompanying the interactionsare new generations ofparticles unlike the threeknown generations.Supersymmetry (b) relatesfermions to bosons and addsthe supersymmetric partners ofeach known particle to themodel. M-theory and stringtheory (c) recast the entiremodel in terms of new entitiessuch as tiny strings, loops andmembranes that behave likeparticles at low energies.

New particles New forcesa


Theory Formerly Known as Strings,” onpage 12]. But no one knows how to writedown the equations of this theory.

Outside of SpacetimeTWO GREAT OBSTACLES stand in theway of this task. One is that we do notknow what physical principles govern thefundamental theory. In developing gener-al relativity, Einstein was guided by aprinciple he had inferred from the knownproperties of gravitation, the principle ofthe equivalence of gravitational forces toinertial effects such as centrifugal force.The development of the Standard Modelwas guided by a principle called gaugesymmetry, a generalization of the well-known property of electricity that it isonly differences of voltages that matter,not voltages themselves.

But we have not discovered any fun-damental principle that governs M-theo-ry. The various approximations to thistheory look like string or field theories inspacetimes of different dimensionalities,but it seems probable that the funda-mental theory is not to be formulated inspacetime at all. Quantum field theory ispowerfully constrained by principlesconcerning the nature of four-dimen-sional spacetime that are incorporated inthe special theory of relativity. How canwe get the ideas we need to formulate atruly fundamental theory, when this the-ory is meant to describe a realm where allintuitions derived from life in spacetimebecome inapplicable?

The other obstacle is that even if wewere able to formulate a fundamental the-ory, we might not know how to use it tomake predictions that could confirm itsvalidity. Most of the successful predic-tions of the Standard Model have beenbased on a method of calculation knownas perturbation theory. In quantum me-

chanics, the rates of physical processes aregiven by sums over all possible sequencesof intermediate steps by which the processmight occur. Using perturbation theory,one first considers just the simplest inter-mediate steps, then the next simplest, andso on. This works only if increasinglycomplicated intermediate steps make de-creasingly large contributions to the rate,which is usually the case if the forces in-volved are sufficiently weak. Sometimes atheory with very strong forces is equiva-lent to another theory with very weakforces, which can be solved by the meth-ods of perturbation theory. This seems tobe true of certain pairs of the five stringtheories in 10 dimensions and the fieldtheory in 11 dimensions mentioned ear-lier. Unfortunately, the forces of the fun-damental theory are probably neithervery strong nor very weak, ruling out anyuse of perturbation theory.

Recognizing the AnswerIT I S IMPOSS IBLE to say when theseproblems will be overcome. They may besolved in a preprint put out tomorrow bysome young theorist. They may not besolved by 2050, or even 2150. But whenthey are solved, even though we cannotdo experiments at 1016 GeV or look intohigher dimensions, we will not have anytrouble recognizing the truth of the fun-damental unified theory. The test will bewhether the theory successfully accounts

for the measured values of the physicalconstants of the Standard Model, alongwith whatever other effects beyond theStandard Model may have been discov-ered by then.

It is possible that when we finally un-derstand how particles and forces behaveat energies up to 1018 GeV, we will justfind new mysteries, with a final unifica-tion as far away as ever. But I doubt it.There are no hints of any fundamentalenergy scale beyond 1018 GeV, andstring theory even suggests that higherenergies have no meaning.

The discovery of a unified theory thatdescribes nature at all energies will put usin a position to answer the deepest ques-tions of cosmology: Did the expandingcloud of galaxies we call the big banghave a beginning at a definite time in thepast? Is our big bang only one episode ina much larger universe in which big andlittle bangs have been going on eternally?If so, do what we call the constants—oreven the laws—of nature vary from onebang to another?

This will not be the end of physics. Itprobably won’t even help with some ofthe outstanding problems of today’sphysics, such as understanding turbu-lence and high-temperature supercon-ductivity. But it will mark the end of acertain kind of physics: the search for aunified theory that entails all other factsof physical science.


Unified Theories of Elementary-Particle Interaction. Steven Weinberg in Scientific American, Vol. 231, No. 1, pages 50–59; July 1974.

Dreams of a Final Theory. Steven Weinberg. Pantheon Books, 1992.

Reflections on the Fate of Spacetime. Edward Witten in Physics Today, Vol. 49, No. 4, pages 24–30;April 1996.

Duality, Spacetime and Quantum Mechanics. Edward Witten in Physics Today, Vol. 50, No. 5, pages28–33; May 1997.

The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory.Brian Greene. W. W. Norton, 1999.

M O R E T O E X P L O R E

Perhaps when we understand how particles and forces behave at energies up to 1018 GeV

we will find new mysteries, but I doubt it.


A t a time when certain punditsclaim that all the importantdiscoveries have already been

made, it is worth emphasizing that thetwo main pillars of 20th-century physics,quantum mechanics and Einstein’s gen-eral theory of relativity, are mutually in-compatible. General relativity fails to com-ply with the quantum rules that governthe behavior of elementary particles, whileblack holes are challenging the very foun-dations of quantum mechanics. Somethingbig has to give.

Until recently, the best hope for a the-ory that would unite gravity with quantummechanics and describe all physical phe-nomena was based on strings: one-dimen-sional objects whose modes of vibrationrepresent the elementary particles. In 1995,however, strings were subsumed by M-theory. In the words of the guru of stringtheory, Edward Witten of the Institute forAdvanced Study in Princeton, N.J., “Mstands for magic, mystery or membrane,according to taste.” New evidence in fa-vor of this theory is appearing daily, rep-resenting the most exciting developmentsince strings first swept onto the scene.

M-theory, like string theory, relies cru-

cially on the idea of supersymmetry.Physicists divide particles into two classes,according to their inherent angular mo-mentum, or “spin.” Supersymmetry re-quires that for each known particle havinginteger spin—0, 1, 2 and so on, measuredin quantum units—there is a particle withthe same mass but half-integer spin (1/2,3/2, 5/2 and so on), and vice versa.

Unfortunately, no such superpartnerhas yet been found. The symmetry, if itexists at all, must be broken, so that thepostulated particles do not have the samemass as known ones but instead are tooheavy to be seen in current accelerators.Even so, theorists believe in supersymme-try because it provides a framework with-in which the weak, electromagnetic andstrong forces may be united with the mostelusive force of all: gravity.

Supersymmetry transforms the coor-dinates of space and time such that thelaws of physics are the same for all ob-servers. Einstein’s general theory of rela-tivity derives from this condition, and so

supersymmetry implies gravity. In fact,supersymmetry predicts “supergravity,”in which a particle with a spin of 2—thegraviton—transmits gravitational inter-actions and has as a partner a gravitino,with a spin of 3/2.

Conventional gravity does not placeany limits on the possible dimensions ofspacetime: its equations can, in principle,be formulated in any dimension. Not sowith supergravity, which places an upperlimit of 11 on the dimensions of space-time. The familiar universe, of course, hasthree dimensions of space: height, lengthand breadth; time is the fourth dimensionof spacetime. But in the early 1920s Pol-ish physicist Theodore Kaluza and Swe-dish physicist Oskar Klein suggested thatspacetime may have a hidden fifth dimen-sion. This extra dimension would not be

12 S C I E N T I F I C A M E R I C A N U p d a t e d f r o m t h e F e b r u a r y 1 9 9 8 i s s u e

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the theory formerly known as

STRINGSThe Theory of Everything is emerging as onein which not onlystrings but also membranesand black holesplay a role

By Michael J. Duff

übertheory


infinite, like the others; instead it wouldclose in on itself, forming a circle. Aroundthat circle could reside quantum waves,fitting neatly into a loop. Only integernumbers of waves could fit around the cir-cle; each of these would correspond to aparticle with a different energy. So the en-ergies would be “quantized,” or discrete.

An observer living in the other four di-mensions, however, would see a set ofparticles with discrete charges, ratherthan energies. The quantum, or unit, ofcharge would depend on the circle’s ra-dius. In the real world as well, electricalcharge is quantized, in units of e, thecharge on the electron. To get the rightvalue for e, the circle would have to betiny, about 10 –33 centimeter in radius.

The unseen dimension’s small size ex-plains why humans, or even atoms, areunaware of it. Even so, it would yield elec-tromagnetism. And gravity, already pres-ent in the four-dimensional world, wouldbe united with that force.

In 1978 Eugene Cremmer, BernardJulia and Joel Scherk of the École Nor-male Supérieure in Paris realized that su-pergravity not only permits up to sevenextra dimensions but is most elegantwhen existing in a spacetime of 11 di-mensions (10 of space and one of time).The kind of real, four-dimensional world

the theory ultimately predicts depends onhow the extra dimensions are rolled up, àla Kaluza and Klein. The several curled di-mensions could conceivably allow physi-cists to derive, in addition to electromag-netism, the strong and weak nuclearforces. For these reasons, many physicistsbegan to look to supergravity in 11 di-mensions for the unified theory.

In 1984, however, 11-dimensional su-pergravity was rudely knocked off itspedestal. An important feature of the realworld is that nature distinguishes betweenright and left. Witten and others empha-sized that such “handedness” cannotreadily be derived by reducing spacetimefrom 11 dimensions down to four.

P-BranesSUPERGRAVITY’S position was usurpedby superstring theory in 10 dimensions.Five competing theories held sway, desig-nated by their mathematical characteris-tics as the E8 × E8 heterotic, the SO(32)heterotic, the SO(32) Type I, and the Type

IIA and Type IIB strings. (TheType I is an “open” string con-sisting of just a segment; the oth-ers are “closed” strings that formloops.) The E8× E8 seemed—at

least in principle—capable of ex-plaining the elementary particles

and forces, including their handed-ness. And strings seemed to provide a

theory of gravity consistent with quan-tum effects. All these virtues enabled stringtheory to sweep physicists off their feetand supergravity into the doghouse.

After the initial euphoria over strings,however, doubts began to creep in. First,important questions—especially how toconfront the theory with experiment—seemed incapable of being answered bytraditional methods of calculation. Sec-ond, why were there five different stringtheories? If one is looking for a uniqueTheory of Everything, surely this is an em-barrassment of riches. Third, if super-symmetry permits 11 dimensions, why dosuperstrings stop at 10? Finally, if we aregoing to conceive of pointlike particles asstrings, why not as membranes or moregenerally as p-dimensional objects, in-evitably dubbed p-branes?

Consequently, while most theoristswere tucking into super-spaghetti, a smallgroup was developing an appetite for su-per-ravioli. A particle, which has zero di-mensions, sweeps out a one-dimensionaltrace, or “worldline,” as it evolves in space-time [see top illustration on next page].Similarly a string—having one dimension:length—sweeps out a two-dimensional“worldsheet,” and a membrane—havingtwo dimensions: length and breadth—

sweeps out a three-dimensional “world-volume.” In general, a p-brane sweepsout a worldvolume of p + 1 dimensions.

As early as 1962, Paul A. M. Dirac


LIFE, THE UNIVERSE AND EVERYTHINGmay arise from the interplay of strings,bubbles and sheets in higherdimensions of spacetime.

MICHAEL J. DUFF conducts research on unified theories of elementary particles, quantumgravity, supergravity, superstrings, supermembranes and M-theory. He earned his Ph.D. intheoretical physics in 1972 at Imperial College, London, and joined the faculty there in1980. He became a Distinguished Professor at Texas A&M University in 1992. Duff is nowOskar Klein Professor of Physics at the University of Michigan and director of the MichiganCenter for Theoretical Physics.TH

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had constructed an imaginative modelbased on a membrane. He postulatedthat the electron, instead of resembling apoint, was in reality a minute bubble, amembrane closed in on itself. Its oscilla-tions, Dirac suggested, might generateparticles such as the muon, a heavier ver-sion of the electron. Although his attemptfailed, the equations that he postulatedfor the membrane are essentially the oneswe use today.

Supersymmetry severely restricts thepossible dimensions of a p-brane. In thespacetime of 11 dimensions floats amembrane, which may take the form of abubble or a two-dimensional sheet. PaulS. Howe of King’s College London, Ta-keo Inami of Kyoto University, KelloggStelle of Imperial College, London, and Iwere able to show that if one of the 11 di-mensions is a circle, we can wrap the sheetaround it once, pasting the edges togeth-er to form a tube. If the radius becomessufficiently small, the rolled-up membraneends up looking like a string in 10 di-mensions; it yields precisely the Type IIAsuperstring.

Notwithstanding such results, themembrane enterprise was largely ignoredby the string community. Fortunately, thesituation was about to change because ofprogress in an apparently unrelated field.

In 1917 German mathematician Ama-lie Emmy Noether had shown that themass, charge and other attributes of ele-mentary particles are conserved because

of symmetries of the laws of physics. Forinstance, conservation of electrical chargefollows from a symmetry under a changeof a particle’s wave function.

Sometimes, however, attributes maybe maintained because of deformationsin fields. Such conservation laws arecalled topological. Thus, it may happenthat a knot in a set of field lines, called asoliton, cannot be smoothed out. As a re-sult, the soliton is prevented from dissi-pating and behaves much like a particle.A classic example is a magnetic mono-pole, which has not been found in naturebut shows up as twisted configurations insome field theories.

In the traditional view, then, particlessuch as electrons and quarks (which car-ry Noether charges) are seen as funda-mental, whereas particles such as magnet-ic monopoles (which carry topologicalcharge) are derivative. In 1977, however,Claus Montonen, now at the Helsinki In-stitute of Physics in Finland, and David I.Olive, now at the University of Wales atSwansea, made a bold conjecture. Mightthere exist an alternative formulation ofphysics in which the roles of Noethercharges (like electrical charge) and topo-logical charges (like magnetic charge) arereversed? In such a “dual” picture, themagnetic monopoles would be the ele-mentary objects, whereas the familiar par-ticles—quarks, electrons and so on—

would arise as solitons. More precisely, a fundamental parti-

cle with charge e would be equivalent toa solitonic particle with charge 1/e. Be-cause its charge is a measure of howstrongly a particle interacts, a monopolewould interact weakly when the originalparticle interacts strongly (that is, whene is large), and vice versa.

The conjecture, if true, would lead toa profound mathematical simplification.In the theory of quarks, for instance,physicists can make hardly any calcula-tions when the quarks interact strongly.But any monopoles in the theory mustthen interact weakly. One could imaginedoing calculations with a dual theorybased on monopoles and automaticallygetting all the answers for quarks, be-cause the dual theory would yield thesame final results.

Unfortunately, the idea presented achicken-and-egg problem. Once proved,the Montonen-Olive conjecture could leapbeyond conventional calculational tech-niques, but it would need to be proved bysome other method in the first place.

As it turns out, p-branes can also beviewed as solitons. In 1990 Andrew Stro-minger of the Institute for TheoreticalPhysics in Santa Barbara, Calif., found thata 10-dimensional string can yield a soli-ton that is a five-brane. Reviving a conjec-ture of mine, Strominger suggested that astrongly interacting string is the dual equiv-alent of weakly interacting five-branes.

There were two major impedimentsto this duality. First, the duality proposedby Montonen and Olive—between elec-tricity and magnetism in four dimen-sions—was still unproved, so duality be-tween strings and five-branes in 10 di-mensions was even more tenuous. Sec-ond, there were issues about how to findthe quantum properties of five-branes and

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TRAJECTORY of a particle in spacetime traces a worldline. Similarly, that of a string or a membrane sweeps out a worldsheet orworldvolume, respectively.

SIMULTANEOUS SHRINKING of a membrane and adimension of spacetime can result in a string. As theunderlying space, shown here as a two-dimensionalsheet, curls into a cylinder, the membrane wrapsaround it. The curled dimension becomes a circle sosmall that the two-dimensional space ends up lookingone-dimensional, like a line. The tightly wrappedmembrane then resembles a string.


hence how to prove the new duality.The first of these impediments was re-

moved, however, when Ashoke Sen of theTata Institute of Fundamental Researchin Bombay, India, established that super-symmetric theories would require the ex-istence of certain solitons with both elec-trical and magnetic charges. These objectshad been predicted by the Montonen-Olive conjecture. This seemingly incon-spicuous result converted many skepticsand unleashed a flood of papers. In par-ticular, it inspired Nathan Seiberg of Rut-gers University and Edward Witten tolook for duality in more realistic (thoughstill supersymmetric) versions of quarktheories. They provided a wealth of in-formation on quantum fields, of a kindunthinkable just a few years before.

Duality of DualitiesIN 1990 SEVERAL theorists general-ized the idea of Montonen-Olive dualityto four-dimensional superstrings, in whoserealm the idea becomes even more natur-al. This duality, which was then specula-tive, goes by the name S-duality.

In fact, string theorists had already be-come used to a totally different kind ofduality called T-duality. T-duality relatestwo kinds of particles that arise when astring loops around a compact dimension.One kind (call them “vibrating” particles)is analogous to those predicted by Kaluzaand Klein and comes from vibrations ofthe loop of string [see box on next page].Such particles are more energetic if the cir-cle is small. In addition, the string canwind many times around the circle, like arubber band on a wrist; its energy be-comes higher the more times it wraps

around and the larger thecircle is. Moreover, each energy

level represents a new particle (call them“winding” particles).

T-duality states that the winding par-ticles for a circle of radius R are the sameas the vibrating particles for a circle of ra-dius 1/R, and vice versa. To a physicist, thetwo sets of particles are indistinguishable:a fat, compact dimension may yield thesame particles as a thin one.

This duality has a profound implica-tion. For decades, physicists have beenstruggling to understand nature at the ex-tremely small scales near the Plancklength of 10 –33 centimeter. We have al-ways supposed that laws of nature breakdown at smaller distances. What T-dual-ity suggests, however, is that at thesescales, the universe looks just the same asit does at large scales. One may even imag-ine that if the universe were to shrink toless than the Planck length, it wouldtransform into a dual universe that growsbigger as the original one collapses.

Duality between strings and five-branes was still conjectural, however, be-cause of the problem of quantizing five-branes. Starting in 1991, a team at TexasA&M University, with Jianxin Lu, Ru-ben Minasian, Ramzi Khuri and myself,dealt with the problem by sidestepping it.If four of the 10 dimensions curl up andthe five-brane wraps around these, thelatter ends up as a one-dimensional ob-ject—a (solitonic) string in six-dimen-sional spacetime. In addition, a funda-mental string in 10 dimensions remainsfundamental even in six dimensions. Sothe concept of duality between strings

and five-branes gave way to another con-jecture, duality between a solitonic and afundamental string.

The advantage is that we do knowhow to quantize a string. Hence, the pre-dictions of string-string duality could betested. One can show, for instance, thatthe strength with which the solitonicstrings interact is given by the inverse ofthe fundamental string’s interactionstrength, in agreement with the conjecture.

In 1994 Christopher M. Hull of QueenMary and Westfield College at the Uni-versity of London, along with Paul K.Townsend of the University of Cam-bridge, suggested that a weakly interact-ing heterotic string can even be the dualof a strongly interacting Type IIA string,if both are in six dimensions. The barriersbetween the different string theories werebeginning to crumble.

It occurred to me that string-string du-ality has another unexpected payoff. If wereduce the six-dimensional spacetime tofour dimensions by curling up two di-mensions, the fundamental string and thesolitonic string each acquire a T-duality.But here is the miracle: the T-duality of thesolitonic string is just the S-duality of thefundamental string, and vice versa. Thisphenomenon—in which the interchangeof charges in one picture is the inversion oflength in the dual picture—is called theDuality of Dualities. It places the previ-ously speculative S-duality on as firm afooting as the well-established T-duality.In addition, it predicts that the strengthwith which objects interact—their charg-es—is related to the size of the invisible di-mensions. What is charge in one universemay be size in another.

In a landmark talk at the University ofSouthern California in 1995, Witten

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“BRANE” SCAN lists the membranes that arise inspacetimes of different dimensions. A p-brane ofdimension 0 is a particle, that of dimension 1 is a

string and that of dimension 2 is a sheet orbubble. Some branes have no spin (red), but

Dirichlet-branes have spin of 1 (blue).

EXTRA DIMENSION curled into a tube offersinsights into the fabric of spacetime.


drew together all the work on T-duality,S-duality and string-string duality underthe umbrella of M-theory in 11 dimen-sions. In the following months, literallyhundreds of papers appeared on the In-ternet confirming that whatever M-theo-ry may be, it certainly involves mem-branes in an important way.

Even the E8× E8 string, whose hand-edness was thought impossible to derivefrom 11 dimensions, acquired an origin inM-theory. Witten, along with Petr Horavaof Princeton University, showed how toshrink the extra dimension of M-theoryinto a segment of a line. The resulting pic-ture has two 10-dimensional universes(each at an end of the line) connected bya spacetime of 11 dimensions. Particles—

and strings—exist only in the parallel uni-verses at the ends, which can communi-cate with each other only via gravity. (Onecan speculate that all visible matter in ouruniverse lies on one wall, whereas the

“dark matter,” believed to account for theinvisible mass in the universe, resides in aparallel universe on the other wall.)

This scenario may have importantconsequences for confronting M-theorywith experiment. For example, physicistsknow that the intrinsic strengths of all theforces change with the energy of the rele-vant particles. In supersymmetric theories,one finds that the strengths of the strong,weak and electromagnetic forces all con-verge at an energy E of 1016 giga-electron-volts. Further, the interaction strengths al-most equal—but not quite—the value ofthe dimensionless number GE2, where Gis Newton’s gravitational constant. Thisnear miss, most likely not a coincidence,

seems to call for an explanation; it has beena source of great frustration for physicists.

But in the bizarre spacetime envisionedby Horava and Witten, one can choose thesize of the 11th dimension so that all fourforces meet at this common scale. It is farless than the Planck energy of 1019 giga-electron-volts, at which gravity was for-merly expected to become strong. (High

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THREE FORCES CONVERGE to the same strengthwhen particles are as energetic as 10 16 giga-

electron-volts. Until now, gravity was believed tomiss this meeting point. But calculationsincluding the 11th dimension of M-theory

suggest that gravity may indeed converge.

T-DUALITY CONNECTS the physics of large spacetimes with that ofsmall ones. Visualize a curled spacetime as a cylinder. A string

looped around it has two kinds of energy states. One set arisesfrom the waves in the string that fit around the cylinder; call

these the “vibration” modes. If the cylinder is fat, thevibrations tend to have long wavelengths and less energy.

So the energies corresponding to different numbers ofwaves around the cylinder are separated by small

amounts—that is, they are “closely spaced.”The string can, however, also loop around the

cylinder like a stretched rubber band. If the cylinderis fat, the string needs to stretch more, requiring

more energy. Thus, the energies of the statescorresponding to different numbers of loops—call

these the “winding” modes—are widely spaced.For a thin cylinder, the waves fitting around

it are small and have high energy; the vibrationstates are widely spaced. But the loops

require less energy, so the winding modesare closely spaced.

To an outside observer, the physicalorigins of the vibration and winding

states are not apparent. Both the thinand the fat tube yield the same energy

levels, which physicists interpret asparticles. As such, the minute scales

of the thin spacetime may yield thesame physics as the large scales

of our universe. —M.J.D.

DUALITY BETWEEN LARGE AND SMALL


energy is connected to small distance viaquantum mechanics. So Planck energy issimply Planck length expressed as energy.)Quantum-gravitational effects may thusbe far closer in energy to everyday eventsthan physicists previously believed, a re-sult that would have all kinds of cosmo-logical consequences. The Horava-Wittenidea has prompted a variation on theKaluza-Klein theme known as “brane-world,” in which our universe is a three-brane in a higher-dimensional universe.The strong, weak and electromagneticforces are confined to the brane, but grav-ity lives in the bulk. The extra dimensionmay be as a large as a millimeter.

In 1995 Joseph Polchinski of the In-stitute for Theoretical Physics realizedthat some p-branes resemble a surface dis-covered by 19th-century German mathe-matician Peter G. L. Dirichlet. On occa-sion these branes can be interpreted asblack holes or, rather, black-branes—ob-jects from which nothing, not even light,can escape. Open strings, for instance,may be regarded as closed strings, part ofwhich are hidden behind the black-branes. Such breakthroughs have led to anew interpretation of black holes as inter-secting black-branes wrapped around sev-en curled dimensions. As a result, there arestrong hints that M-theory may even clearup the paradoxes of black holes raised byStephen W. Hawking of the University ofCambridge.

In 1974 Hawking showed that blackholes are not entirely black but may radi-ate energy. In that case, black holes mustpossess entropy, which measures the dis-order by accounting for the number ofquantum states available. Yet the micro-scopic origin of these states stayed a mys-tery. The technology of Dirichlet-braneshas enabled Strominger and Cumrun Vafaof Harvard University to count the num-ber of quantum states in black-branes.They find an entropy that agrees withHawking’s prediction, placing anotherfeather in the cap of M-theory.

Black-branes also promise to solveone of the biggest problems of string the-ory: there seem to be billions of differentways of crunching 10 dimensions downto four. So there are many competing pre-dictions of how the real world works—in

other words, no prediction at all. It turnsout, however, that the mass of a black-brane can vanish as a hole it wrapsaround shrinks. This feature miraculouslyaffects the spacetime itself, allowing onespacetime with a certain number of inter-nal holes to change to another with a dif-ferent number of holes, violating the lawsof classical topology.

If all the spacetimes are thus related,finding the right one becomes a moretractable problem. The string may ulti-mately choose the spacetime with, say,the lowest energy and inhabit it. Its un-dulations would then give rise to the ele-mentary particles and forces as we knowthem—that is, the real world.

In an interesting offshoot of Dirichlet-branes, Juan Maldacena of the Institutefor Advanced Study has posed a five-dimensional spacetime known as anti deSitter space, a negatively curved, saddle-shaped spacetime. This world, includingall its gravitational interactions, may bedescribed by a nongravitational theorythat resides on its four-dimensional bound-ary. This may shed light on the four-di-mensional quark theories that govern thestrong nuclear interactions. If this so-called holographic picture is correct, thenthe universe is like the wall of Plato’s cave,and we are the shadows projected on it.

In another variation, Lisa Randall ofHarvard and Raman Sundrum of JohnsHopkins University combine the brane-world and holographic ideas to suggestthat our universe is a three-brane sittingon a five-dimensional anti de Sitter space.

It has even been suggested that the bigbang was simply the collision of twothree-branes.

Thus, branes are no longer the uglyducklings of string theory. They have tak-en center stage as the microscopic con-stituents of M-theory, as the higher-di-mensional progenitors of black holes andas entire universes in their own right.

10 to 11: Not Too LateDESPITE ALL THESE successes, physi-cists are glimpsing only small corners ofM-theory; the big picture is still lacking.Physicists have long suspected that unify-ing gravity—the geometry of spacetime—

with quantum physics will lead to space-time’s becoming similarly ill defined, atleast until a new definition is discovered.Over the next few years we hope to dis-cover what M-theory really is.

Witten is fond of imagining howphysics might develop on a planet wherediscoveries such as general relativity,quantum mechanics and supersymmetrywere made in a different order than onEarth. In a similar vein, I would like tosuggest that on planets more logical thanours, 11 dimensions would have been thestarting point from which 10-dimension-al string theory was subsequently derived.Indeed, future terrestrial historians mayjudge the late 20th century as a time whentheorists were like children playing on theseashore, diverting themselves with thesmooth pebbles of superstrings while thegreat ocean of M-theory lay undiscoveredbefore them.


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M-THEORY in 11 dimensions gives rise to the five string theories in 10 dimensions. When the extradimension curls into a circle, M-theory yields the Type IIA superstring, further related by duality to theType IIB string. If the extra dimension shrinks to a line segment, M-theory becomes the physicallyplausible E8× E8 heterotic string, connected to the SO(32) string theories by dualities.

Unity from Duality. Paul Townsend in Physics World, Vol. 8, No. 9, pages 1–6; September 1995.Explaining Everything. Madhusree Mukerjee in Scientific American, Vol. 274, No. 1, pages 88–94;January 1996.Duality, Spacetime and Quantum Mechanics. Edward Witten in Physics Today, Vol. 50, No. 5, pages 28–33; May 1997.The Universe’s Unseen Dimensions. Nima Arkani-Hamed, Savas Dimopoulos and Georgi Dvali inScientific American, pages 62–69; August 2000.



SOMEWHERE in outer space, ProfessorWindbag’s time capsule has been sabo-taged by his rival, Professor Goulash. Thecapsule contains a mathematical formulavital to future generations. But Goulash’sdiabolical scheme to plant a bomb onboard has succeeded. Bang! The formulais vaporized into a cloud of electrons, nu-cleons, photons and an occasional neu-trino. Windbag is distraught. He has norecord of the formula and cannot re-member its derivation.

Later, in court, Windbag charges thatGoulash has sinned irrevocably: “Whatthat fool has done is irreversible. Off withhis tenure!”

“Nonsense,” says an unflustered Gou-lash. “Information can never be destroyed.It’s just your laziness, Windbag. All youhave to do is go and find each particle inthe debris and reverse its motion. Thelaws of nature are time symmetric, so onreversing everything, your stupid formu-la will be reassembled. That proves, be-

yond a shadow of a doubt, that I couldnever have destroyed your precious in-formation.” Goulash wins the case.

Windbag’s revenge is equally diabol-ical. While Goulash is out of town, hiscomputer is burglarized, along with all hisfiles, including his culinary recipes. Wind-bag then launches the computer into out-er space, straight into a nearby black hole.

At Windbag’s trial, Goulash is besidehimself. “There’s no way to get my filesout. They’re inside the black hole, and ifI go in to get them I’m doomed to be

crushed. You’ve truly destroyed infor-mation, and you’ll pay.”

“Objection, Your Honor!” Windbagjumps up. “Everyone knows thatblack holes eventually evaporate.Wait long enough, and the

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BLACKHOLES

INFORMATION PARADOXand the

BLACK HOLE’S SURFACE looks to Windbag (in thespaceship) like a spherical membrane, called thehorizon. Windbag sees Goulash, who is falling intothe black hole, being slowed down and flattened atthe horizon; according to string theory, Goulashalso seems to be spread all over it. Thus, Windbag,who represents the outside observer, sees theinformation contained in everything that falls intothe black hole as stopping at the surface. ButGoulash finds himself falling right through thehorizon to the center of the black hole, where hebecomes crushed.

What happens to the information in matterdestroyed by a black hole? Searching for

that answer, physicists are groping toward a quantum theory of gravity

By Leonard Susskind

übertheory


black hole will radiate away all its massand turn into outgoing photons and oth-er particles. True, it may take 1070 years,but it’s the principle that counts. All Gou-lash has to do is reverse the paths of thedebris, and his computer will come flyingback out of the black hole.”

“Not so!” cries Goulash. “This is dif-ferent. My recipe was lost behind theblack hole’s boundary, its horizon. Oncesomething crosses the horizon, it can nev-er get back out without exceeding thespeed of light, and nothing can do that.There is no way the evaporation products,which come from outside the horizon, cancontain my recipes even in scrambledform. He’s guilty, Your Honor.”

Her Honor is confused. “We needsome expert witnesses. Professor Hawk-ing, what do you say?”

Stephen W. Hawking of the Univer-sity of Cambridge comes to the stand.“Goulash is right. In most situations, in-formation is scrambled and in a practicalsense is lost. For example, if a new deck

of cards is tossed in the air, the original or-der of the cards vanishes. But in principle,if we know the exact details of how thecards are thrown, the original order canbe reconstructed. This is called microre-versibility. But in my 1976 paper I showedthat the principle of microreversibility,which has always held in classical andquantum physics, is violated by blackholes. Because information cannot escapefrom behind the horizon, black holes area fundamental new source of irreversibil-ity in nature. Windbag really did destroyinformation.”

Her Honor turns to Windbag: “Whatdo you have to say to that?” Windbagcalls on Professor Gerard ’t Hooft ofUtrecht University in the Netherlands.

“Hawking is wrong,” begins ’t Hooft.“I believe black holes must not lead to vi-olation of the usual laws of quantum me-chanics. Otherwise the theory would beout of control. You cannot underminemicroscopic reversibility without de-stroying energy conservation. If Hawking

were right, the universe would heat up toa temperature of 1031 degrees in a tinyfraction of a second. Because this has nothappened, there must be some way out.”

Twenty more famous theoretical phys-icists are called to the stand. All that be-comes clear is that they cannot agree.

The Information ParadoxWINDBAG AND GOULASH are, ofcourse, fictitious. Not so Hawking and ’t Hooft, nor the controversy of whathappens to information that falls into ablack hole. Hawking’s claim that a blackhole consumes information has drawn at-tention to a potentially serious conflict be-tween quantum mechanics and the gen-eral theory of relativity. The problem isknown as the information paradox.

When something falls into a blackhole, one cannot expect it ever to comeflying back out. The information coded inthe properties of its constituent atoms is,according to Hawking, impossible to re-trieve. Albert Einstein once rejected quan-


tum mechanics with the protest: “Goddoes not play dice.” But Hawking statesthat “God not only plays dice, He some-times throws the dice where they cannotbe seen”—into a black hole.

The problem, ’t Hooft points out, isthat if the information is truly lost, quan-tum mechanics breaks down. Despite itsfamed indeterminacy, quantum mechan-ics controls the behavior of particles in avery specific way: it is reversible. Whenone particle interacts with another, it maybe absorbed or reflected or may even breakup into other particles. But one can al-ways reconstruct the initial configurationsof the particles from the final products.

If this rule is broken by black holes, en-ergy may be created or destroyed, threat-ening one of the most essential under-pinnings of physics. The conservation ofenergy is ensured by the mathematicalstructure of quantum mechanics, whichalso guarantees reversibility; losing onemeans losing the other. As Thomas Banks,Michael Peskin and I showed in 1980 atStanford University, information loss in ablack hole leads to enormous amounts ofenergy being generated. For such reasons,’t Hooft and I believe the information thatfalls into a black hole must somehow be-come available to the outside world.

Some physicists feel the question ofwhat happens in a black hole is academ-ic or even theological. But at stake are thefuture rules of physics. Processes inside ablack hole are merely extreme examplesof interactions between elementary parti-cles. At the energies that particles can ac-quire in today’s largest accelerators (about1012 electron volts), the gravitational at-traction between them is negligible. But ifthe particles have a “Planck energy” ofabout 1028 electron volts, so much ener-

gy—and therefore mass—becomes con-centrated in a tiny volume that gravitation-al forces outweigh all others. The result-ing collisions involve quantum mechanicsand the general theory of relativity inequal measure.

It is to Planckian accelerators that wewould nominally look for guidance inbuilding future theories of physics. Alas,Shmuel Nussinov of Tel Aviv Universityconcludes that such an accelerator wouldhave to be at least as big as the entireknown universe.

Nevertheless, the physics at Planck en-ergies may be revealed by the knownproperties of matter. Elementary particleshave a variety of attributes that lead phys-icists to suspect that they are not so ele-mentary after all: they must actually havea good deal of undiscovered internal ma-chinery, which is determined by thephysics at Planck energies. We will rec-ognize the right confluence of general rel-ativity and quantum physics—or quan-tum gravity—by its ability to explain themeasurable properties of electrons, pho-tons, quarks and neutrinos.

Very little is known with absolute cer-tainty about collisions at energies beyondthe Planck scale, but there is a good edu-cated guess. Head-on collisions at theseenergies involve so much mass concen-trated in a tiny volume that a black holewill form and subsequently evaporate. Sofiguring out whether black holes violatethe rules of quantum mechanics or not isessential to unraveling the ultimate struc-ture of particles.

A black hole is born when so muchmass or energy gathers in a small volumethat gravitational forces overwhelm allothers and everything collapses under itsown weight. The material squeezes intoan unimaginably small region called a sin-gularity, the density inside of which is es-sentially infinite. Surrounding the singu-larity is an imaginary surface called thehorizon. For a black hole with the mass ofa galaxy, the horizon is 1011 kilometers


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SINGULARITY

Horizon:“point of no return”

Rising pullof gravity

Rising pullof gravity

INVISIBLE HORIZON is represented in this analogy as a point of no return in a river. To the left of it, waterflows faster than a “lightfish” can swim. If a lightfish happens to drift beyond this line, it can never getback upstream; it is doomed to be crushed in the falls. But the fish notices nothing special at the line.Likewise, a light ray or person who is inside the horizon of a black hole can never get out; the objectinevitably falls into the singularity at the center but without noticing anything special about the horizon.


from the center—as far as the outermostreaches of the solar system are from thesun. For a black hole of solar mass, thehorizon is roughly a kilometer away; fora black hole with the mass of a smallmountain, the horizon is 10–13 centime-ter away, roughly the size of a proton.

The horizon separates space into tworegions that we can think of as the interi-or and exterior of the black hole. Supposethat Goulash, who is scouting for hiscomputer near the black hole, shoots aparticle away from the center. If he is nottoo close and the particle has a high ve-locity, then it may overcome the gravita-tional pull of the black hole and fly away.It will be most likely to escape if it is shotwith the maximum velocity—that of light.If, however, Goulash is too close to thesingularity, the gravitational force will beso great that even a light ray will besucked in. The horizon is the place withthe (virtual) warning sign: POINT OF NO

RETURN. No particle or signal of any kindcan cross it from the inside to the outside.

At the HorizonAN ANALOGY inspired by William G.Unruh of the University of British Colum-bia, a pioneer in black hole quantum me-chanics, helps to explain the relevance ofthe horizon. Imagine a river that getsswifter downstream. Among the fish thatlive in it, the fastest swimmers are the“lightfish.” But at some point, the riverflows at the fish’s maximum speed; clear-ly, any lightfish that drifts behind thispoint can never get back up. It is doomedto be crushed on the rocks below Singu-

larity Falls, downstream. To the unsus-pecting lightfish, though, passing the pointof no return is a nonevent. No currents or shock waves warn it of the crossing.

What happens to Goulash, who in acareless moment gets too close to the blackhole’s horizon? Like the freely drifting fish,he senses nothing special: no great forces,no jerks or flashing lights. His pulse andbreathing rate remain normal. To him thehorizon is just like any other place.

But Windbag, watching Goulash froma spaceship safely outside the horizon,sees Goulash acting in a bizarre way.Windbag has lowered to the horizon a ca-ble equipped with a camcorder and oth-er probes. As Goulash falls toward theblack hole, his speed increases until it ap-proaches that of light. Einstein found thatif two persons are moving fast relative toeach other, each sees the other’s clockslow down; in addition, a clock that isnear a massive object will run slowlycompared with one in empty space. Wind-bag sees an oddly lethargic Goulash. Ashe falls, the latter shakes his fist at Wind-bag, but Windbag sees Goulash’s motionsslow to a halt. Although Goulash fallsthrough the horizon, Windbag neverquite sees him get there.

In fact, not only does Goulash seem toslow down, but his body looks as if it is be-ing squashed into a thin layer. Einstein

also showed that if two persons move fastwith respect to each other, each will seethe other as being flattened in the directionof motion. More strangely, Windbagshould also see all the material that everfell into the black hole, including the orig-inal matter that made it up—and Gou-lash’s computer—similarly flattened andfrozen at the horizon. With respect to anoutside observer, all of that matter suffersa relativistic time dilation. To Windbag,the black hole consists of an immensejunkyard of flattened matter at its horizon.But Goulash sees nothing unusual untilmuch later, when he reaches the singular-ity, there to be crushed by ferocious forces.

Black hole theorists have discoveredover the years that from the outside, theproperties of a black hole can be describedin terms of a mathematical membraneabove the horizon. This layer has manyphysical qualities, such as electrical con-ductivity and viscosity. Perhaps the mostsurprising of its properties was postulatedin the early 1970s by Hawking, Unruh andJacob D. Bekenstein of the Hebrew Uni-versity of Jerusalem. They found that as aconsequence of quantum mechanics, ablack hole—in particular, its horizon—be-haves as though it contains heat. The hori-zon is a layer of hot material of some kind.

The temperature of the horizon de-pends on where it is measured. Supposeone of the probes that Windbag has at-tached to his cable is a thermometer. Farfrom the horizon he finds that the temper-ature is inversely proportional to the blackhole’s mass. For a black hole of solarmass, this “Hawking temperature” isabout 10–8 degree—far colder than inter-galactic space. As Windbag’s thermome-ter approaches the horizon, however, itregisters higher. At a distance of a cen-timeter, it measures about a thousandth ofa degree; at a nuclear diameter, it records10 billion degrees. The temperature ulti-mately becomes so high that no imagin-able thermometer could measure it.


LEONARD SUSSKIND is one of the early inventors of string theory. He holds a Ph.D. from Cor-nell University and has been a professor at Stanford University since 1978. He has mademany contributions to elementary particle physics, quantum field theory, cosmology and,most recently, the theory of black holes. His current studies in gravitation have led him tosuggest that information can be compressed into one lower dimension, a concept he callsthe holographic universe.TH

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Hot objects also possess an intrinsicdisorder called entropy, which is related tothe amount of information a system canhold. Think of a crystal lattice with Nsites; each site can house one atom or noneat all. Thus, every site holds one “bit” ofinformation, corresponding to whether anatom is there or not; the total lattice has Nsuch bits and can contain N units of in-formation. Because there are two choicesfor each site and N ways of combiningthese choices, the total system can be inany one of 2N states (each of which cor-responds to a different pattern of atoms).The entropy (or disorder) is defined as thelogarithm of the number of possible states.It is roughly equal to N—the same num-ber that quantifies the capacity of the sys-tem for holding information.

Bekenstein found that the entropy of ablack hole is proportional to the area of itshorizon. The precise formula, derived byHawking, predicts an entropy of 3.2× 1064 per square centimeter of horizonarea. Whatever physical system carries thebits of information at the horizon must beextremely small and densely distributed:their linear dimensions have to be 1⁄1020 thesize of a proton’s. They must also be quitespecial for Goulash to miss them com-pletely as he passes through.

The discovery of the thermodynamicproperties of black holes led Hawking toa very interesting conclusion. Like otherhot bodies, a black hole must radiate en-ergy and particles into the surroundingspace. The radiation comes from the hori-zon and does not violate the rule thatnothing can escape from within. But itcauses the black hole to lose energy andmass. In time an isolated black hole radi-ates away all its mass and vanishes.

All of the above, though peculiar, hasbeen known to relativists for some de-cades. The true controversies arise when,following Hawking, we seek the fate ofthe information that fell into the blackhole during and after its formation. Inparticular, can it be carried away by theevaporation products—albeit in a veryscrambled form—or is it lost forever be-hind the horizon?

Goulash, who followed his computerinto the black hole, would insist that itscontents passed behind the horizon, wherethey were lost to the outside world; this ina nutshell is Hawking’s argument. The op-posing point of view might be describedby Windbag: “I saw the computer fall to-ward the horizon, but I never saw it fallthrough. The temperature and radiationgrew so intense I lost track of it. I believethe computer was vaporized; later its en-ergy and mass came back out in the formof thermal radiation. The consistency ofquantum mechanics requires that thisevaporating energy also carried away allthe information in the computer.” This isthe position that ’t Hooft and I take.

Black Hole ComplementarityIS IT POSSIBLE that Goulash and Wind-bag are in a sense both correct? Can it bethat Windbag’s observations are indeedconsistent with the hypothesis that Gou-lash and his computer are thermalizedand radiated back into space before everreaching the horizon, even though Gou-lash discovers nothing unusual until longafter, when he encounters the singularity?The idea that these are not contradictorybut complementary scenarios was firstput forward as the principle of black holecomplementarity by Lárus Thorlacius,

John Uglum and me at Stanford. Verysimilar ideas are also found in ’t Hooft’swork. Black hole complementarity is anew principle of relativity. In the specialtheory of relativity, we find that althoughdifferent observers disagree about thelengths of time and space intervals, eventstake place at definite spacetime locations.Black hole complementarity does awaywith even that.

Suppose that Windbag, whose cableis also equipped with a powerful micro-scope, watches an atom fall toward thehorizon. At first he sees the atom as a nu-cleus surrounded by a blur of negativecharge. But as the atom gets closer to theblack hole, its internal motions seem toslow down and the electrons become vis-ible. A little later the electrons freeze, andthe protons and neutrons start to showup. Later yet, the quarks making up theseparticles are revealed. (Goulash, who fallswith the atom, sees no changes.)

Quite a few physicists believe elemen-tary particles are made of even smaller con-stituents. Although there is no definitivetheory for this machinery, one candidatestands out: string theory. In this theory,an elementary particle does not resemblea point; rather it is like a tiny rubber bandthat can vibrate in many modes. The fun-damental mode has the lowest frequency;then there are higher harmonics, whichcan be superimposed on top of one an-other. There are an infinite number ofsuch modes, each of which correspondsto a different elementary particle.

Here another analogy helps. One can-not see the wings of a hovering humming-bird, because its wings flutter too fast. Butin a photograph taken with a fast shutterspeed, one can see the wings—so the birdlooks bigger. If a hummer falls into theblack hole, Windbag will see its wings takeform as the bird approaches the horizonand the vibrations appear to slow down;it seems to grow. Now suppose that thewings have feathers that flap even faster.Soon these, too, would come into view,adding further to the apparent size of thebird. Windbag sees the hummer enlargecontinuously. But Goulash, who falls withthe bird, sees no such strange growth.

Like the hummingbird’s wings, thestring’s oscillations are usually too rapid


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LIGHT CONES describe the path of light rays emanating from a point. Outside the horizon the cones pointupward—that is, forward in time. But inside, the cones tip so that light falls into the black hole’s center.


to detect. A string is a minute object, 1⁄1020

the size of a proton. But as it falls into ablack hole, its vibrations slow down andmore of them become visible. Mathemat-ical studies done at Stanford by Thor-lacius, Amanda W. Peet, Arthur Mezhlu-mian and me have demonstrated the be-havior of a string as its higher modesfreeze out. The string spreads and grows,just as if it were being bombarded by par-ticles and radiation in a very hot environ-ment. In a relatively short time the stringand all the information it carries aresmeared over the entire horizon.

This picture applies to all the materi-al that ever fell into the black hole—be-cause according to string theory, every-thing is ultimately made of strings. Eachelementary string spreads and overlaps allthe others until a dense tangle covers thehorizon. Each minute segment of string,measuring 10–33 centimeter across, func-tions as a bit. Thus, strings provide ameans for the black hole’s surface to holdthe immense amount of information thatfell in during its birth and thereafter.

String TheoryIT SEEMS, THEN, that the horizon ismade of all the substance in the black hole,resolved into a giant tangle of strings. Theinformation, as far as an outside observeris concerned, never actually fell into theblack hole; it stopped at the horizon andwas later radiated back out. String theo-ry offers a concrete realization of blackhole complementarity and therefore away out of the information paradox. Tooutside observers—that is, us—informa-tion is never lost. Most important, it ap-pears that the bits at the horizon are mi-nute segments of strings.

Tracing the evolution of a black holefrom beginning to end is far beyond thecurrent techniques available to string the-orists. But some exciting new results aregiving quantitative flesh to these ghostlyideas. Mathematically, the most tractableblack holes are the “extremal” blackholes. Whereas black holes that have noelectrical charge evaporate until all theirmass is radiated away, black holes withelectrical or (in theory) magnetic chargecannot do that; their evaporation ceaseswhen the gravitational attraction equals

the electrostatic or magnetostatic repul-sion of whatever is inside the black hole.The remaining stable object is called anextremal black hole.

Ashoke Sen of the Tata Institute ofFundamental Research (TIFR) in Mum-bai, India, showed in 1995 that for cer-tain extremal black holes with electricalcharge, the number of bits predicted bystring theory exactly accounts for the en-tropy as measured by the area of the hori-zon. This agreement was the first power-ful evidence that black holes are consis-tent with quantum-mechanical strings.

Sen’s black holes were, however, mi-croscopic. More recently, Andrew Stro-minger of the University of California atSanta Barbara, Cumrun Vafa of HarvardUniversity and, slightly later, Curtis G.Callan and Juan Maldacena of PrincetonUniversity extended this analysis to blackholes with both electrical and magneticcharge. These new black holes could belarge enough to allow Goulash to fallthrough unharmed. Again, the theoristsfind complete consistency.

Two groups have done an even moreexciting new calculation of Hawking ra-diation: Sumit R. Das of TIFR, with Sa-mir Mathur of the Massachusetts Insti-tute of Technology; and Avinash Dhar,Gautam Mandal and Spenta R. Wadia,also at TIFR. The researchers studied theprocess by which an extremal black holewith some excess energy or mass radiatesoff this flab. String theory fully accountedfor the Hawking radiation that was pro-

duced. Just as quantum mechanics de-scribes the radiation of an atom by show-ing how an electron jumps from a high-energy “excited” state to a low-energy“ground” state, quantum strings seem toaccount for the spectrum of radiationfrom an excited black hole. The informa-tion paradox is well on its way to being re-solved. Windbag will be right.

The principle of black hole comple-mentarity has received spectacular math-ematical confirmation by Maldacena andothers. Following the introduction by ’t Hooft and myself of a so-called holo-graphic principle, Maldacena discovereda powerful “holographic” equivalencebetween quantum gravity in a dimensioncalled anti de Sitter space and a conven-tional quantum system. He gives a com-pelling argument that information inblack holes in this space is never lost be-hind the horizon. As a result of Maldace-na’s work, physicists have made blackhole complementarity one of the workingassumptions of modern string theory.

Quantum mechanics, I believe, will inall likelihood turn out to be consistentwith the theory of gravitation; these twogreat streams of physics are merging intoa quantum theory of gravity based onstring theory. The information paradoxhas played an extraordinary role in thisongoing revolution in physics. And al-though Goulash would never admit it,Windbag will probably turn out to beright: his recipe for matelote d’anguilles isnot forever lost to the world.


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CASCADE OF VIBRATIONS on a string slows down and becomes visible if the string falls into a black hole.Strings are small enough to encode all the information that ever fell into a black hole, thereby offering away out of the information paradox.

Black Holes and Time Warps: Einstein’s Outrageous Legacy. Kip S. Thorne. W. W. Norton, 1994.

The Illustrated A Brief History of Time. Stephen W. Hawking. Bantam Books, 1996.

Trends in Theoretical Physics: Explaining Everything. Madhusree Mukerjee in Scientific American,Vol. 274, No. 1, pages 88–94; January 1996.



harnessingquanta


An exciting new fundamental discipline

of research combinesinformation science and

quantum mechanics

By Michael A. Nielsen

An exciting new fundamental discipline

of research combinesinformation science and

quantum mechanics

By Michael A. Nielsen

U p d a t e d f r o m t h e N o v e m b e r 2 0 0 2 i s s u e 25

Simple Rules for a Complex Quantum

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Over the past few decades, scientists have learned that simplerules can give rise to very rich behavior. Agood example is chess. Imagine you’re anexperienced chess player introduced tosomeone claiming to know the game. Youplay a few times and realize that althoughthis person knows the rules of chess, hehas no idea how to play well. He makesabsurd moves, sacrificing his queen for apawn and losing a rook for no reason atall. He does not truly understand chess:he is ignorant of the high-level principlesand heuristics familiar to any knowl-edgeable player. These principles are col-lective or emergent properties of chess,features not immediately evident from therules but arising from interactions amongthe pieces on the chessboard.

Scientists’ current understanding ofquantum mechanics is like that of a slow-learning student of chess. We’ve knownthe rules for more than 70 years, and wehave a few clever moves that work insome special situations, but we’re onlygradually learning the high-level princi-ples that are needed to play a skillfuloverall game.

The discovery of these principles is the

goal of quantum information science, afundamental field that is opening up in re-sponse to a new way of comprehendingthe world. Many articles about quantuminformation science focus on technologi-cal applications: research groups “tele-port” quantum states from one locationto another. Other physicists use quantumstates to create cryptographic keys thatare absolutely secure from eavesdrop-ping. Information scientists devise algo-rithms for hypothetical quantum-me-chanical computers, much faster than thebest known algorithms for conventional,or classical, computers.

These technologies are fascinating,but they obscure the fact that they are aby-product of investigations into deep newscientific questions. Applications such asquantum teleportation play a role similarto the steam engines and other machinesthat spurred the development of thermo-dynamics in the 18th and 19th centuries.Thermodynamics was motivated by pro-found, basic questions about how energy,heat and temperature are related, the trans-formations among these quantities in phys-

ical processes, and the key role of entropy. Similarly, quantum information sci-

entists are fathoming the relation betweenclassical and quantum units of informa-tion, the novel ways that quantum infor-mation can be processed, and the pivotalimportance of a quantum feature calledentanglement, which entails peculiar con-nections between different objects.

Popular accounts often present en-tanglement as an all-or-nothing propertyin which quantum particles are either entangled or not. Quantum informationscience has revealed that entanglement is a quantifiable physical resource, likeenergy, that enables information-pro-cessing tasks: some systems have a littleentanglement; others have a lot. Themore entanglement available, the bettersuited a system is to quantum informa-tion processing.

Furthermore, scientists have begun todevelop powerful quantitative laws of en-tanglement (analogous to the laws of ther-modynamics governing energy), whichprovide a set of high-level principles for un-derstanding the behavior of entanglementand describing how we can use it to do in-formation processing.

Quantum information science is newenough that researchers are still comingto grips with its very nature, and they dis-agree about which questions lie at itsheart. From my point of view, the centralgoal of quantum information science isto develop general principles, like thelaws of entanglement, that will enable usto understand complexity in quantumsystems.

Complexity and QuantaNUMEROUS STUDIES in complexityconcentrate on systems, such as the weath-er or piles of sand, that are described byclassical physics rather than quantumphysics. That focus is natural becausecomplex systems are usually macroscop-

■ Information is not purely mathematical. Instead it always has a physicalembodiment. In traditional information science the embodiment followsclassical, or nonquantum, physics. The burgeoning field of quantum informationscience puts information in a quantum context.

■ The basic resource of classical information is the bit, which is always either a 0 or a 1. Quantum information comes in quantum bits, or qubits (pronounced“cue-bits”). Qubits can exist in superpositions, which simultaneously involve 0 and 1, and groups of qubits can be “entangled,” which gives themcounterintuitive correlations.

■ Quantum computers processing qubits, particularly entangled qubits, canoutperform classical computers. Entanglement behaves like a resource, similarto energy, that can be used to do quantum information processing.

■ The goal of quantum information science is to understand the general high-levelprinciples that govern complex quantum systems such as quantum computers.These principles relate to the laws of quantum mechanics in the way thatheuristics for skillful play at chess relate to the game’s basic rules.

Overview/Quantum Information



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ic, containing many constituent parts, andmost systems lose their quantum natureas their size is increased. This quantum-to-classical transition occurs becauselarge quantum systems generally interactstrongly with their environment, causinga process of decoherence, which destroysthe system’s quantum properties [see “100Years of Quantum Mysteries,” by MaxTegmark and John A. Wheeler; Scien-tific American, February 2001].

As an example of decoherence, thinkof Erwin Schrödinger’s famous cat insidea box. In principle, the cat ends up in aweird quantum state, somewhere be-tween dead and alive; it makes no sense todescribe it as either one or the other. In areal experiment, however, the cat inter-acts with the box by exchange of light,heat and sound, and the box similarly in-teracts with the rest of the world. In nano-seconds, these processes destroy the deli-cate quantum states inside the box and re-place them with states describable, to agood approximation, by the laws of clas-sical physics. The cat inside really is either

alive or dead, not in some mysteriousnonclassical state that combines the two.

The key to seeing truly quantum be-havior in a complex system is to isolatethe system extremely well from the rest ofthe world, preventing decoherence andpreserving fragile quantum states. Thisisolation is relatively easy to achieve withsmall systems, such as atoms suspendedin a magnetic trap in a vacuum, but ismuch more difficult with the larger onesin which complex behavior may befound. Accidental laboratory discoveriesof remarkable phenomena such as super-conductivity and the quantum Hall effectare examples in which physicists haveachieved large, well-isolated quantumsystems. These phenomena demonstratethat the simple rules of quantum me-chanics can give rise to emergent princi-ples governing complex behaviors.

Resources and TasksWE ATTEMPT TO understand the high-level principles that govern in those rareinstances when the quantum and the

complex meet by abstracting, adaptingand extending tools from classical infor-mation theory. In 2001 Benjamin W.Schumacher of Kenyon College proposedthat the essential elements of informationscience, both classical and quantum, canbe summarized as a three-step procedure:

1. Identify a physical resource. A fa-miliar classical example is a string of bits.Although bits are often thought of as ab-stract entities—0’s and 1’s—all informa-tion is inevitably encoded in real physicalobjects, and thus a string of bits shouldbe regarded as a physical resource.

2. Identify an information-processingtask that can be performed using thephysical resource of step 1. A classical ex-ample is the two-part task of compressingthe output from an information source(for example, the text in a book) into a bitstring and then decompressing it—that is,recovering the original information fromthe compressed bit string.

3. Identify a criterion for successfulcompletion of the task of step 2. In ourexample, the criterion could be that the

THE FUNDAMENTAL QUESTION

300-digit number

MUCH OF INFORMATION SCIENCE, both classical and quantum,can be summed up by analyzing variants of a basic question:

“What quantity of an information resource is needed to perform a specific information-processing task?”

For example: “How many computational steps are needed to find

the prime factors of a 300-digit number?” The best classicalalgorithm known would take about 5 × 1024 steps, or about 150,000years at terahertz speed. By taking advantage of innumerablequantum states, a quantum factoring algorithm would take only5 × 1010 steps, or less than a second at terahertz speed.

Classical computer

Quantum computer

2:30:00 P.M.Year: 2012

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output from the decompression stageperfectly matches the input to the com-pression stage.

The fundamental question of infor-mation science is then “What is the mini-mal quantity of the physical resource (1)we need to perform the information-pro-cessing task (2) in compliance with thesuccess criterion (3)?” Although this ques-tion does not quite capture all of informa-tion science, it provides a powerful lensthrough which to view much research inthe field [see box on preceding page].

The data-compression example cor-responds to a basic question of classicalinformation science—namely, what is theminimum number of bits needed to storethe information produced by somesource? This problem was solved byClaude E. Shannon in his famous 1948papers founding information theory. Inso doing, Shannon quantified the infor-mation content produced by an informa-tion source, defining it to be the minimumnumber of bits needed to reliably storethe output of the source. His mathemati-cal expression for the information content

is now known as the Shannon entropy.Shannon’s entropy arises as the an-

swer to a simple, fundamental questionabout classical information processing. Itis perhaps not surprising, then, thatstudying the properties of the Shannonentropy has proved fruitful in analyzingprocesses far more complex than datacompression. For example, it plays a cen-tral role in calculating how much infor-mation can be transmitted reliably througha noisy communications channel andeven in understanding phenomena suchas gambling and the behavior of the stockmarket. A general theme in informationscience is that questions about elemen-tary processes lead to unifying conceptsthat stimulate insight into more complexprocesses.

In quantum information science, allthree elements of Schumacher’s list takeon new richness. What novel physical re-sources are available in quantum me-chanics? What information-processingtasks can we hope to perform? What areappropriate criteria for success? The re-sources now include superposition states,

like the idealized alive and dead cat ofSchrödinger. The processes can involvemanipulations of entanglement (mysteri-ous quantum correlations) between wide-ly separated objects. The criteria of suc-cess become more subtle than in the clas-sical case, because to extract the result ofa quantum information-processing taskwe must observe, or measure, the sys-tem—which almost inevitably changes it,destroying the special superposition statesthat are unique to quantum physics.

QubitsQUANTUM INFORMATION science be-gins by generalizing the fundamental re-source of classical information—bits—toquantum bits, or qubits. Just as bits areideal objects abstracted from the princi-ples of classical physics, qubits are idealquantum objects abstracted from theprinciples of quantum mechanics. Bitscan be represented by magnetic regionson disks, voltages in circuitry, or graphitemarks made by a pencil on paper. Thefunctioning of these classical physicalstates as bits does not depend on the de-

QUBITS EXPLAINED

A BIT can have one oftwo states: 0 or 1. A bitcan be represented bya transistor switch setto “off” or “on” orabstractly by an arrowpointing up or down.

A QUBIT, the quantumversion of a bit, hasmany more possiblestates. The states canbe represented by anarrow pointing to alocation on a sphere.The north pole isequivalent to 1, thesouth pole to 0. Theother locations arequantum super-positions of 0 and 1.

A QUBIT MIGHT SEEM TO CONTAIN an infinite amount of informationbecause its coordinates can encode an infinite sequence of digits. Butthe information in a qubit must be extracted by a measurement. Whenthe qubit is measured, quantum mechanics requires that the result isalways an ordinary bit—a 0 or a 1. The probability of each outcomedepends on the qubit’s “latitude.”

N =

S =

N 23º 34′ 41.4422. . .″ E 32º 48′ 10.3476. . .″


tails of how they are realized. Similarly,the properties of a qubit are independentof its specific physical representation asthe spin of an atomic nucleus, say, or thepolarization of a photon of light.

A bit is described by its state, 0 or 1.Likewise, a qubit is described by its quan-tum state. Two possible quantum statesfor a qubit correspond to the 0 and 1 of aclassical bit. In quantum mechanics, how-ever, any object that has two differentstates necessarily has a range of other pos-sible states, called superpositions, whichentail both states to varying degrees. Theallowed states of a qubit are precisely allthose states that must be available, in prin-ciple, to a classical bit that is transplantedinto a quantum world. Qubit states cor-respond to points on the surface of asphere, with the 0 and 1 being the southand north poles [see box on oppositepage]. The continuum of states between 0and 1 fosters many of the extraordinaryproperties of quantum information.

How much classical information canwe store in a qubit? One line of reasoningsuggests the amount is infinite: To speci-fy a quantum state we need to specify thelatitude and longitude of the correspond-ing point on the sphere, and in principleeach may be given to arbitrary precision.These numbers can encode a long stringof bits. For example, 011101101... couldbe encoded as a state with latitude 01 de-grees, 11 minutes and 01.101.. . seconds.

This reasoning, though plausible, isincorrect. One can encode an infiniteamount of classical information in a sin-gle qubit, but one can never retrieve thatinformation from the qubit. The simplestattempt to read the qubit’s state, a stan-dard direct measurement of it, will give aresult of either 0 or 1, south pole or northpole, with the probability of each out-come determined by the latitude of theoriginal state. You could have chosen adifferent measurement, perhaps using the“Melbourne–Azores Islands” axis in-stead of north-south, but again only onebit of information would have been ex-tracted, albeit one governed by probabil-ities with a different dependence on thestate’s latitude and longitude. Whichev-er measurement you choose erases all theinformation in the qubit except for the

single bit that the measurement uncovers. The principles of quantum mechanics

prevent us from ever extracting morethan a single bit of information, no mat-ter how cleverly we encode the qubit orhow ingeniously we measure it afterward.This surprising result was proved in 1973by Alexander S. Holevo of the SteklovMathematical Institute in Moscow, fol-lowing a 1964 conjecture by J. P. Gordonof AT&T Bell Laboratories. It is asthough the qubit contains hidden infor-mation that we can manipulate but notaccess directly. A better viewpoint, how-ever, is to regard this hidden informationas being a unit of quantum informationrather than an infinite number of inacces-sible classical bits.

Notice how this example followsSchumacher’s paradigm for informationscience. Gordon and Holevo asked howmany qubits (the physical resource) arerequired to store a given amount of clas-sical information (the task) in such a way

that the information can be reliably re-covered (the criterion for success). Fur-thermore, to answer this question, theyintroduced a mathematical concept, nowknown as the Holevo chi (represented bythe Greek letter χ), that has since beenused to simplify the analysis of more com-plex phenomena, similar to the simplifi-cations enabled by Shannon’s entropy.For example, Michal Horodecki of theUniversity of Gdansk in Poland hasshown that the Holevo chi can be used toanalyze the problem of compressingquantum states produced by a quantuminformation source, which is analogousto the classical data compression consid-ered by Shannon.

Entangled StatesS INGLE QUBITS are interesting, butmore fascinating behavior arises whenseveral qubits are brought together. A keyfeature of quantum information science isthe understanding that groups of two or


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INCREASING COMPLEXITY

QUANTUM FOURIER TRANSFORM

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THEORY OF ENTANGLEMENT

HERE THERE BE QUANTUM TYGERSQUANTUM INFORMATION SCIENTISTS are still mapping out the broad topography oftheir nascent field. Some simpler processes, such as teleportation and quantumcryptography, are well understood. In contrast, complex phenomena such asquantum error correction and Peter W. Shor’s factorization algorithm are surroundedby large tracts of terra incognita. One effort to bridge the gaps between the simpleand the complex is work on a comprehensive theory of entanglement, analogous tothe theory of energy embodied in thermodynamics.



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The Standard E-BitWHEN TWO QUBITS are entangled, they nolonger have individual quantum states.Instead a relation between the qubits isdefined. For example, in one type ofmaximally entangled pair, the qubits giveopposite results when measured. If onegives 0, the other returns 1, and vice versa.A maximally entangled pair carries one “e-bit” of entanglement.

DISENTANGLING ENTANGLEMENT

AliceBob

IF DICE COULD BE “entangled” in the manner of quantum particles,each entangled pair would give the same outcome, even if rolledlight-years apart or at very different times.

Weighing EntanglementINCOMPLETELY ENTANGLED PAIRS carry less than one e-bit. If Alice and Bob share two partiallyentangled pairs, they can try to “distill” the entanglement onto a single pair. If distillationproduces a maximally entangled pair, then Alice and Bob know their pairs originally carried a total of at least one e-bit of entanglement.

By using distillation (and theinverse process, entanglementdilution), one constructs a virtualset of scales for weighing theentanglement of various statesagainst the standard e-bit.

AliceBob AliceBob

2⁄3 e-bit

Qubit to beteleported

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AliceBob AliceBobBEFORE

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Quantum TeleportationIF ALICE AND BOB share one e-bit,they can teleport one qubit. Theshared e-bit is “used up,” in that theyno longer share it after teleporting.

If Bob teleports a member (b) of anentangled pair to Alice, that particle’sentanglement with its original partner (c) is transferred to Alice’sparticle (a). Alice and Bob cannotuse teleportation, however, toincrease their stock of shared e-bits.

AFTER

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Maximally entangled pair

Incompletely entangled pair

Qubit to beteleported


Entangled quantum systems behave in waysimpossible in any classical world.


more quantum objects can have statesthat are entangled. These entangled stateshave properties fundamentally unlikeanything in classical physics and are com-ing to be thought of as an essentially newtype of physical resource that can be usedto perform interesting tasks.

Schrödinger was so impressed by en-tanglement that in a seminal 1935 paper(the same year that he introduced his catto the world) he called it “not one butrather the characteristic trait of quantummechanics, the one that enforces its entiredeparture from classical lines of thought.”The members of an entangled collectionof objects do not have their own individ-ual quantum states. Only the group as awhole has a well-defined state [see box onopposite page]. This phenomenon ismuch more peculiar than a superpositionstate of a single particle. Such a particledoes have a well-defined quantum stateeven though that state may superpose dif-ferent classical states.

Entangled objects behave as if theywere connected with one another no mat-ter how far apart they are—distance doesnot attenuate entanglement in the slight-est. If something is entangled with otherobjects, a measurement of it simultane-ously provides information about its part-ners. It is easy to be misled into thinkingthat one could use entanglement to sendsignals faster than the speed of light, in vi-olation of Einstein’s special relativity, butthe probabilistic nature of quantum me-chanics stymies such efforts.

Despite its strangeness, for a long timeentanglement was regarded as a curiosityand was mostly ignored by physicists. Thischanged in the 1960s, when John S. Bell ofCERN, the European laboratory for par-ticle physics near Geneva, predicted thatentangled quantum states allow crucialexperimental tests that distinguish be-tween quantum mechanics and classicalphysics. Bell predicted, and experimentershave confirmed, that entangled quantumsystems exhibit behavior that is impossi-

ble in a classical world—impossible evenif one could change the laws of physics totry to emulate the quantum predictionswithin a classical framework of any sort!Entanglement represents such an essen-tially novel feature of our world that evenexperts find it very difficult to think about.Although one can use the mathematics ofquantum theory to reason about entangle-ment, as soon as one falls back on analo-gies, there is a great danger that the clas-sical basis of our analogies will mislead us.

In the early 1990s the idea that en-tanglement falls wholly outside the scopeof classical physics prompted researchersto ask whether entanglement might beuseful as a resource for solving informa-tion-processing problems in new ways.The answer was yes. The flood of exam-ples began in 1991, when Artur K. Ekertof the University of Cambridge showedhow to use entanglement to distributecryptographic keys impervious to eaves-dropping. In 1992 Charles H. Bennett ofIBM and Stephen Wiesner of Tel AvivUniversity showed that entanglement canassist the sending of classical informationfrom one location to another (a processcalled superdense coding, in which twobits are transferred on a particle thatseems to have room to carry only one). In1993 an international team of six collab-orators explained how to teleport aquantum state from one location to an-other using entanglement. An explosionof further applications followed.

Weighing EntanglementAS WITH INDIVIDUAL qubits, whichcan be represented by many differentphysical objects, entanglement also hasproperties independent of its physicalrepresentation. For practical purposes, itmay be more convenient to work withone system or another, but in principle it does not matter. For example, onecould perform quantum cryptographywith an entangled photon pair or an en-tangled pair of atomic nuclei or even a

photon and a nucleus entangled together.Representation independence sug-

gests a thought-provoking analogy be-tween entanglement and energy. Energyobeys the laws of thermodynamics re-gardless of whether it is chemical energy,nuclear energy or any other form. Coulda general theory of entanglement be de-veloped along similar lines to the laws ofthermodynamics?

This hope was greatly bolstered in thelate 1990s, when researchers showed thatdifferent forms of entanglement are qual-itatively equivalent—the entanglement ofone state could be transferred to anoth-er, similar to energy flowing from, say, abattery charger to a battery. Building onthese qualitative relations, investigatorshave begun introducing quantitative mea-sures of entanglement. These develop-ments are ongoing, and researchers havenot yet agreed as to the best way of quan-tifying entanglement. The most successfulscheme thus far is based on the notion ofa standard unit of entanglement, akin toa standard unit of mass or energy [see boxon opposite page].

This approach works analogously tomeasuring masses by using a balance. Themass of an object is defined by how manycopies of the standard mass are needed tobalance it on a set of scales. Quantum in-formation scientists have developed a the-oretical “entanglement balance” to com-pare the entanglement in two differentstates. The amount of entanglement in astate is defined by seeing how many copiesof some fixed standard unit of entangle-ment are needed to balance it. Notice thatthis method of quantifying entanglementis another example of the fundamentalquestion of information science. We haveidentified a physical resource (copies ofour entangled state) and a task with a cri-terion for success. We define our measureof entanglement by asking how much ofour physical resource we need to do ourtask successfully.

The quantitative measures of entan-



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glement developed by following this pro-gram are proving enormously useful asunifying concepts in the description of awide range of phenomena. Entanglementmeasures improve how researchers cananalyze tasks such as quantum teleporta-tion and algorithms on quantum-me-chanical computers. The analogy with en-ergy helps again: to understand processessuch as chemical reactions or the opera-tion of an engine, we study the flow of en-ergy between different parts of the system

and determine how the energy must beconstrained at various locations andtimes. In a similar way, we can analyzethe flow of entanglement from one sub-system to another required to perform aquantum information-processing taskand so obtain constraints on the resourcesneeded to perform the task.

The development of the theory of en-tanglement is an example of a bottom-upapproach—starting from simple ques-tions about balancing entanglement, wegradually gain insight into more complexphenomena. In contrast, in a few cases,people have divined extremely complexphenomena through a great leap of in-sight, allowing quantum information sci-ence to proceed from the top down. Themost celebrated example is an algorithmfor quickly finding the prime factors of acomposite integer on a quantum comput-er, formulated in 1994 by Peter W. Shorof AT&T Bell Labs. On a classical com-puter, the best algorithms known take ex-ponentially more resources to factor larg-

er numbers. A 500-digit number needs100 million times as many computationalsteps as a 250-digit number. The cost ofShor’s algorithm rises only polynomially—

a 500-digit number takes only eight timesas many steps as a 250-digit number.

Shor’s algorithm is a further exampleof the basic paradigm (how much compu-tational time is needed to find the factorsof an n-bit integer?), but the algorithm ap-pears isolated from most other results ofquantum information science [see box onpage 29]. At first glance, it looks like mere-ly a clever programming trick with littlefundamental significance. That appear-ance is deceptive; researchers have shownthat Shor’s algorithm can be interpreted asan instance of a procedure for determin-ing the energy levels of a quantum system,a process that is more obviously funda-mental. As time goes on and we fill inmore of the map, it should become easierto grasp the principles underlying Shor’sand other quantum algorithms and, onehopes, to develop new algorithms.

MICHAEL A. NIELSEN is associate pro-fessor in the department of physics atthe University of Queensland in Brisbane,Australia. Born in Brisbane, he receivedhis Ph.D. in physics as a Fulbright Scholarat the University of New Mexico in 1998.He is the author, with Isaac L. Chuang ofthe Massachusetts Institute of Technol-ogy, of the first comprehensive gradu-ate-level textbook on quantum informa-tion science, Quantum Computation andQuantum Information.

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DEALING WITH ERRORSClassical Repetition CodeTHIS SIMPLE CLASSICAL scheme forreducing errors encodes each bit as atriplet of identical bits. If noise flips onebit, the error can be corrected by fixingthe minority bit of a triplet.

Error Correction for QubitsTHE REPETITION STRATEGY IS IMPOSSIBLE for qubits for two reasons. First, qubits in unknownstates cannot be perfectly cloned (a). Even if duplicates are produced (for example, byrunning multiple copies of the computation), a simple measurement will not reveal errors (b).

ONE QUANTUM ERROR-CORRECTING CODE works by entangling each data qubit with two preset0 qubits. These three qubits are in turn entangled with six others. Joint measurements onpairs of qubits will reveal whether one of these nine qubits suffers an error and, if so, how tocorrect it without disrupting the qubits’ individual states.

Data qubit

a b

Entangled qubits

Preset 0 qubits Preset 0 qubits Entangled qubits

Encoding

Noise

Error correction



One final application, quantum errorcorrection, provides the best evidence todate that quantum information science isa useful framework for studying theworld. Quantum states are delicate, eas-ily destroyed by stray interactions, ornoise, so schemes to counteract these dis-turbances are essential.

Classical computation and communi-cations have a well-developed assortmentof error-correcting codes to protect infor-mation against the depredations of noise.A simple example is the repetition code [seebox on opposite page]. This scheme rep-resents the bit 0 as a string of three bits,000, and the bit 1 as a string of three bits,111. If the noise is relatively weak, it maysometimes flip one of the bits in a triplet,changing, for instance, 000 to 010, but itwill flip two bits in a triplet far less often.Whenever we encounter 010 (or 100 or001), we can be almost certain the correctvalue is 000, or 0. More complex gener-alizations of this idea provide very gooderror-correcting codes to protect classicalinformation.

Quantum Error CorrectionINITIALLY IT APPEARED to be impos-sible to develop codes for quantum errorcorrection because quantum mechanicsforbids us from learning with certainty theunknown state of a quantum object—theobstacle, again, of trying to extract morethan one bit from a qubit. The simple clas-sical triplet code therefore fails becauseone cannot examine each copy of a qubitand see that one copy must be discardedwithout ruining each and every copy in theprocess. Worse still, making the copies inthe first place is nontrivial: quantum me-chanics forbids taking an unknown qubitand reliably making a duplicate, a resultknown as the no-cloning theorem.

The situation looked bleak in the mid-1990s, when prominent physicists such asthe late Rolf Landauer of IBM wrote skep-tical articles pointing out that quantum er-ror correction would be necessary for

quantum computation but that the stan-dard classical techniques could not be usedin the quantum world. The field owes agreat debt to Landauer’s skepticism forpointing out problems of this type thathad to be overcome [see “Riding the Backof Electrons,” by Gary Stix; Profile, Sci-entific American, September 1998].

Happily, clever ideas developed inde-pendently by Shor and Andrew M. Steaneof the University of Oxford in 1995showed how to do quantum error cor-rection without ever learning the states ofthe qubits or needing to clone them. Aswith the triplet code, each value is repre-sented by a set of qubits. These qubits arepassed through a circuit (the quantumanalogue of logic gates) that will success-fully fix an error in any one of the qubitswithout actually “reading” what all theindividual states are. It is as if one ran thetriplet 010 through a circuit that couldspot that the middle bit was different andflip it, all without determining the identi-ty of any of the three bits.

Quantum error-correcting codes are atriumph of science. Something that bril-liant people thought could not be done—

protecting quantum states against the ef-fects of noise—was accomplished using acombination of concepts from informa-tion science and basic quantum mechan-ics. These techniques have now receivedpreliminary confirmation in experimentsconducted at Los Alamos National Lab-oratory, IBM and the Massachusetts In-stitute of Technology, and more extensiveexperiments are planned.

Quantum error correction has alsostimulated many exciting new ideas. Forexample, the world’s best clocks are cur-rently limited by quantum-mechanicalnoise; researchers are asking whether theprecision of those clocks can be improvedby using quantum error correction. An-other idea, proposed by Alexei Kitaev ofthe California Institute of Technology, isthat some physical systems might possessa type of natural noise tolerance. Thosesystems would in effect use quantum er-ror correction without human interven-tion and might show extraordinary in-herent resilience against decoherence.

We have explored how quantum in-formation science progresses from fun-damental questions to build up an un-derstanding of more complex systems.What does the future hold? By followingSchumacher’s program, we will surelyobtain novel insights into the informa-tion-processing capabilities of the uni-verse. Perhaps the methods of quantuminformation science will even yield in-sights into systems not traditionallythought of as information-processingsystems. For instance, condensed matterexhibits complex phenomena such ashigh-temperature superconductivity andthe fractional quantum Hall effect. Quan-tum properties such as entanglement areinvolved, but their role is currently un-clear. By applying what we have learnedfrom quantum information science, wemay greatly enhance our skills in the on-going chess match with the complexquantum universe.

Quantum Theory and Measurement. Edited by John A. Wheeler and Wojciech H. Zurek. Contains reprints of landmark papers, including a translation of Erwin Schrödinger’s 1935 “cat paradox” paper. Princeton University Press, 1983.The Fabric of Reality. David Deutsch. Penguin Books, 1998.The Bit and the Pendulum. Tom Siegfried. John Wiley & Sons, 2000.Quantum Computation and Quantum Information. Michael A. Nielsen and Isaac L. Chuang.Cambridge University Press, 2000.The Center for Quantum Computation’s Web site: www.qubit.orgJohn Preskill’s lecture notes are available at www.theory.caltech.edu/people/preskill/ph229/See www.sciam.com for Scientific American articles related to quantum information science.


Quantum error correction might improve the precision of the world’s best clocks.


The scene is a familiar one from science fiction and TV:an intrepid band of explorers enters a special cham-ber; lights pulse, sound effects warble, and our heroesshimmer out of existence to reappear on the surface

of a faraway planet. This is the dream of teleportation—the abil-ity to travel from place to place without having to pass throughthe tedious intervening miles accompanied by a physical vehicleand airline-food rations. Although the teleportation of large ob-jects or humans still remains a fantasy, quantum teleportationhas become a laboratory reality for photons, the individual par-ticles of light.

Quantum teleportation exploits some of the most basic (andpeculiar) features of quantum mechanics, a branch of physics in-vented in the first quarter of the 20th century to explain processesthat occur at the level of individual atoms. From the beginning,theorists realized that quantum physics led to a plethora of newphenomena, some of which defy common sense. Technologicalprogress in the final quarter of the 20th century enabled re-searchers to conduct many experiments that not only havedemonstrated fundamental, sometimes bizarre aspects of quan-tum mechanics but, as in the case of quantum teleportation, haveapplied them to achieve previously inconceivable feats.

In science-fiction stories, teleportation often permits travelthat is instantaneous, violating the speed limit set down by Al-bert Einstein, who concluded from his theory of relativity thatnothing can travel faster than light. Teleportation is also lesscumbersome than the more ordinary means of space travel. Itis said that Gene Roddenberry, the creator of Star Trek, con-ceived of the “transporter beam” as a way to save the expenseof simulating landings and takeoffs on strange planets.

The procedure for teleportation in science fiction varies fromstory to story but generally goes as follows: A device scans theoriginal object to extract all the information needed to describeit. A transmitter sends the information to a receiving station,where it is used to obtain an exact replica of the original. In some

cases, the material that made up the original is also transportedto the receiving station, perhaps as energy of some kind; in oth-er cases, the replica is made of atoms and molecules that werealready present at the receiving station.

Quantum mechanics seems to make such a teleportationscheme impossible in principle. Heisenberg’s uncertainty princi-ple rules that one cannot know both the precise position of anobject and its momentum at the same time. Thus, one cannot per-form a perfect scan of the object to be teleported; the location orvelocity of every atom and electron would be subject to errors.Heisenberg’s uncertainty principle also applies to other pairs ofquantities, making it impossible to measure the exact, total quan-tum state of any object with certainty. Yet such measurementswould be necessary to obtain all the information needed to de-scribe the original exactly. (In Star Trek the “Heisenberg Com-pensator” somehow miraculously overcomes that difficulty.)

A team of physicists overturned this conventional wisdomin 1993, when they discovered a theoretical way to use quan-tum mechanics itself for teleportation. The team—Charles H.Bennett of IBM; Gilles Brassard, Claude Crépeau and RichardJosza of the University of Montreal; Asher Peres of Tech-nion–Israel Institute of Technology; and William K. Woottersof Williams College—found that a peculiar but fundamental fea-ture of quantum mechanics, entanglement, can be used to cir-cumvent the limitations imposed by Heisenberg’s uncertaintyprinciple without violating it.

EntanglementIT IS THE YEAR 2100. A friend who likes to dabble in physicsand party tricks has brought you a collection of pairs of dice. Helets you roll them once, one pair at a time. You handle the firstpair gingerly, remembering the fiasco with the micro black hole

34 S C I E N T I F I C A M E R I C A N U p d a t e d f r o m t h e A p r i l 2 0 0 0 i s s u e

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TRAVELERS ARRIVE at Grand Central Station’s teleport terminal. Althoughteleporting large objects, let alone living beings, will never be practical,teleportation of elementary quantum states has been demonstrated.

The science-fiction dream of “beaming” objects from place to place is now a reality—at least for particles of light

harnessingquanta

QUANTUM



last Christmas. Finally, you roll the twodice and get double 3. You roll the nextpair. Double 6. The next: double 1. Theyalways match.

The dice in this fable are behaving asif they were quantum-entangled particles.Each die on its own is random and fair,but its entangled partner somehow al-ways gives the correct matching outcome.Such behavior has been demonstratedand intensively studied with real entan-gled particles. In typical experiments,pairs of atoms, ions or photons stand infor the dice, and properties such as polar-ization stand in for their different faces.

Consider the case of two photonswhose polarizations are entangled to berandom but identical. Beams of light andeven individual photons consist of oscil-lations of electromagnetic fields, and po-larization refers to the alignment of theelectric field oscillations [see illustrationabove]. Suppose that Alice has one of the

entangled photons and Bob has its part-ner. When Alice measures her photon tosee if it is horizontally or vertically polar-ized, each outcome has a 50 percentchance. Bob’s photon has the same prob-abilities, but the entanglement ensuresthat he will get exactly the same result asAlice. As soon as Alice gets the result“horizontal,” say, she knows that Bob’sphoton will also be horizontally polar-ized. Before Alice’s measurement the twophotons do not have individual polariza-tions; the entangled state specifies onlythat a measurement will find that the twopolarizations are equal.

An amazing aspect of this process isthat it doesn’t matter if Alice and Bob arefar away from each other; the processworks so long as their photons’ entangle-ment has been preserved. Even if Alice ison Alpha Centauri and Bob on Earth,their results will agree when they comparethem. In every case, it is as if Bob’s pho-

ton is magically influenced by Alice’s dis-tant measurement, and vice versa.

You might wonder if we can explainthe entanglement by imagining that eachparticle carries within it some recorded in-structions. Perhaps when we entangle thetwo particles, we synchronize some hiddenmechanism within them that determineswhat results they will give when they aremeasured. This would explain away themysterious effect of Alice’s measurementon Bob’s particle. In the 1960s, however,Irish physicist John Bell proved a theoremthat in certain situations any such “hiddenvariables” explanation of quantum en-tanglement would have to produce resultsdifferent from those predicted by standardquantum mechanics. Experiments haveconfirmed the predictions of quantum me-chanics to a very high accuracy.

Austrian physicist Erwin Schrödinger,one of the co-inventors of quantum me-chanics, called entanglement “the essen-


QUANTUM TELEPORTATION OF A PERSON (impossible in practicebut a good example to aid the imagination) would begin with theperson inside a measurement chamber (left) alongside an

equal mass of auxiliary material (green). The auxiliary matterhas previously been quantum-entangled with its counterpart,which is at the faraway receiving station (right).

PREPARING FOR QUANTUM TELEPORTATION . . .

Unpolarized light

a b

Verticalpolarizing filter

Light polarizedat an angle

Crystal splitsvertical andhorizontal

polarizations

Calcitecrystal

UNPOLARIZED LIGHT consists of photons polarized in all directions (a). In polarized light the photons’ electric-field oscillations (arrows) are allaligned. A calcite crystal (b) splits a light beam, sending photons that arepolarized parallel with its axis into one beam and those that are perpendicular

into the other. Intermediate angles go into a quantum superposition of bothbeams. Each such photon can be detected in one beam or the other, withprobability depending on the angle. Because probabilities are involved, wecannot measure the polarization of a single photon with certainty.

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tial feature” of quantum physics. Entan-glement is often called the EPR effect andthe particles EPR pairs, after Einstein,Boris Podolsky and Nathan Rosen, whoin 1935 analyzed the effects of entangle-ment acting across large distances. Ein-stein talked of it as “spooky action at adistance.” If one tried to explain the re-sults in terms of signals traveling betweenthe photons, the signals would have totravel faster than the speed of light. Nat-urally, many people have wondered if thiseffect could be used to transmit informa-tion faster than the speed of light.

Unfortunately, the quantum rulesmake that impossible. Each local mea-

surement on a photon, considered in iso-lation, produces a completely random re-sult and so can carry no information fromthe distant location. It tells you nothingmore than what the distant measurementresult probabilities would be, dependingon what was measured there. Neverthe-less, we can put entanglement to work inan ingenious way to achieve quantumteleportation.

Teleporting Photons ALICE AND BOB anticipate that theywill want to teleport a photon in the fu-ture. In preparation, they share an entan-gled auxiliary pair of photons, Alice tak-

ing photon A and Bob photon B. Insteadof measuring them, they each store theirphoton without disturbing the delicateentangled state [see top illustration onnext page].

In due course, Alice has a third pho-ton—call it photon X—that she wants toteleport to Bob. She does not know whatphoton X’s state is, but she wants Bob tohave a photon with that same polariza-tion state. She cannot simply measure thephoton’s polarization and send Bob theresult. In general, her measurement resultwould not be identical to the photon’soriginal state. This is Heisenberg’s un-certainty principle at work.


JOINT MEASUREMENT carried out on the auxiliary matter and theperson (left) changes them to a random quantum state andproduces a vast amount of random (but significant) data—two

bits per elementary state. By “spooky action at a distance,” themeasurement also instantly alters the quantum state of thefaraway counterpart matter (right). MORE >>>

. . . A QUANTUM MEASUREMENT . . .

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ENTANGLED PHOTON PAIRS are created when a laser beam passes through acrystal such as beta barium borate. The crystal occasionally converts a singleultraviolet photon into two photons of lower energy, one polarized vertically(on red cone), one polarized horizontally (on blue cone). If the photons

happen to travel along the cone intersections (green), neither photon has adefinite polarization, but their relative polarizations are complementary;they are then entangled. Colorized image (at right) is a photograph ofdown-converted light. Colors do not represent the color of the light.


Instead, to teleport photon X, Alicemeasures it jointly with photon A, with-out determining their individual polar-izations. She might find, for instance, thattheir polarizations are “perpendicular” toeach other (she still does not know the ab-solute polarization of either one, howev-er). Technically, the joint measuremententangles photon A and photon X and iscalled a Bell-state measurement. Alice’s

measurement produces a subtle effect: itchanges Bob’s photon to correlate with acombination of her measurement resultand the state that photon X originallyhad. In fact, Bob’s photon now carries herphoton X’s state, either exactly or modi-fied in a simple way.

To complete the teleportation, Alicemust send a message to Bob—one thattravels by conventional means, such as atelephone call or a note on a scrap of pa-per. After he receives this message, if nec-essary Bob can transform his photon B,with the end result that it becomes an ex-act replica of the original photon X.Which transformation Bob must applydepends on the outcome of Alice’s mea-surement. There are four possibilities,corresponding to four quantum relationsbetween her photons A and X. A typicaltransformation that Bob must apply tohis photon is to alter its polarization by90 degrees, which he can do by sending itthrough a crystal with the appropriateoptical properties.

Which of the four possible results Al-ice obtains is completely random and in-dependent of photon X’s original state.Bob therefore does not know how to pro-cess his photon until he learns the resultof Alice’s measurement. One can say thatBob’s photon instantaneously contains allthe information from Alice’s original,transported there by quantum mechanics.Yet to know how to read that informa-tion, Bob must wait for the classical in-formation, consisting of two bits that can

travel no faster than the speed of light.Skeptics might complain that the only

thing teleported is the photon’s polariza-tion state or, more generally, its quantumstate, not the photon “itself.” But becausea photon’s quantum state is its definingcharacteristic, teleporting its state is com-pletely equivalent to teleporting the par-ticle [see box on page 41].

Note that quantum teleportation doesnot result in two copies of photon X.Classical information can be copied anynumber of times, but perfect copying ofquantum information is impossible, a re-sult known as the no-cloning theorem,which was proved in 1982 by Woottersand Wojciech H. Zurek of Los AlamosNational Laboratory. (If we could clonea quantum state, we could use the clonesto violate Heisenberg’s principle.) Alice’smeasurement actually entangles her pho-ton A with photon X, and photon X los-es all memory, one might say, of its orig-inal state. As a member of an entangledpair, it has no individual polarizationstate. Thus, the original state of photon Xdisappears from Alice’s domain.

Circumventing HeisenbergFURTHERMORE, photon X’s state hasbeen transferred to Bob with neither Al-ice nor Bob learning anything about whatthe state is. Alice’s measurement result,being random, tells them nothing aboutthe state. This is how the process circum-vents Heisenberg’s principle, which stopsus from determining the complete quan-


MEASUREMENT DATA must be sent to the distant receivingstation by conventional means. This process is limited by the

speed of light, making it impossible to teleport the personfaster than the speed of light.

. . . TRANSMISSION OF RANDOM DATA . . .

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From: [email protected]: [email protected]

Re: PhotonMessage: Use number 3

1 2 3 4

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1 2 3 4

IDEAL QUANTUM TELEPORTATION relies on Alice,the sender, and Bob, the receiver, sharing a pairof entangled particles A and B. Alice has aparticle that is in an unknown quantum state X.Alice performs a Bell-state measurement onparticles A and X, producing one of four possibleoutcomes. She tells Bob about the result byordinary means. Depending on Alice’s result, Bobleaves his particle unaltered (1) or rotates it (2,3, 4). Either way it ends up a replica of particle X.

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tum state of a particle but does not pre-clude teleporting the complete state so longas we do not try to see what the state is!

Also, the teleported quantum infor-mation does not travel materially fromAlice to Bob. All that travels materially isthe message about Alice’s measurementresult, which tells Bob how to process hisphoton but carries no information aboutphoton X’s state itself.

In one out of four cases, Alice is luckywith her measurement, and Bob’s photonimmediately becomes an identical repli-ca of Alice’s original. It might seem as ifinformation has traveled instantly fromAlice to Bob, beating Einstein’s speedlimit. Yet this strange feature cannot beused to send information, because Bobhas no way of knowing that his photonis already an identical replica. Only whenhe learns the result of Alice’s Bell-statemeasurement, transmitted to him viaclassical means, can he exploit the infor-mation in the teleported quantum state.If he tries to guess in which cases tele-portation was instantly successful, he willbe wrong 75 percent of the time, and hewill not know which guesses are correct.If he uses the photons based on suchguesses, the results will be the same asthey would had he taken a beam of pho-tons with random polarizations. Thus,Einstein’s relativity prevails; even thespooky instantaneous action at a dis-tance of quantum mechanics fails to sendusable information faster than the speedof light.

It would seem that the theoretical pro-posal described above laid out a clearblueprint for building a teleporter; on thecontrary, it presented a great experimen-tal challenge. Producing entangled pairsof photons has become routine in physicsexperiments in the past decade, but car-rying out a Bell-state measurement ontwo independent photons had never beendone before.

Building a TeleporterA POWERFUL WAY to produce entan-gled pairs of photons is spontaneous par-

ametric down-conversion: a single pho-ton passing through a special crystalsometimes generates two new photonsthat are entangled so that they will showopposite polarization when measured.

A much more difficult problem is toentangle two independent photons thatalready exist, as must occur during theoperation of a Bell-state analyzer. Thismeans that the two photons (A and X)somehow have to lose their private fea-tures. In 1997 my group (Dik Bouw-meester, Jian-Wei Pan, Klaus Mattle,Manfred Eibl and Harald Weinfurter),


RECEIVER RE-CREATES THE TRAVELER, exact down to thequantum state of every atom and molecule, by adjusting the

counterpart matter’s state according to the randommeasurement data sent from the scanning station.

. . . RECONSTRUCTION OF THE TRAVELERD

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INNSBRUCK EXPERIMENT begins with a short pulse of ultraviolet laser light. Traveling left to rightthrough a crystal, this pulse produces the entangled pair of photons A and B, which travel to Alice andBob. Reflected back through the crystal, the pulse creates two more photons, C and D. A polarizerprepares photon D in a specific state, X. Photon C is detected, confirming that photon X has been sentto Alice. Alice combines photons A and X with a beam splitter. If she detects one photon in eachdetector (as occurs at most 25 percent of the time), she notifies Bob, who uses a polarizing beamsplitter to verify that his photon has acquired X’s polarization, thus demonstrating teleportation.

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then at the University of Innsbruck, ap-plied a solution to this problem in ourteleportation experiment [see top illustra-tion on preceding page].

In our experiment, a brief pulse of ul-traviolet light from a laser passes througha crystal and creates the entangled pho-tons A and B. One travels to Alice, and theother goes to Bob. A mirror reflects the ul-traviolet pulse back through the crystalagain, where it may create another pair ofphotons, C and D. (These will also be en-tangled, but we don’t use their entangle-ment.) Photon C goes to a detector, whichalerts us that its partner, D, is available tobe teleported. Photon D passes througha polarizer, which we can orient in anyconceivable way. The resulting polarizedphoton is our photon X, the one to beteleported, which travels on to Alice.Once it passes through the polarizer, X isan independent photon, no longer entan-gled. And although we know its polariza-tion because of how we set the polarizer,Alice does not. We reuse the same ultra-violet pulse in this way to ensure that Al-ice has photons A and X at the same time.

Now we arrive at the problem of per-forming the Bell-state measurement. Todo this, Alice combines her two photons(A and X) using a semireflecting mirror, adevice that reflects half the incident light.An individual photon has a 50–50 chanceof passing through or being reflected. Inquantum terms, the photon goes into asuperposition of these two possibilities.

Now suppose that two photons strikethe mirror from opposite sides, with theirpaths aligned so that the reflected path ofone photon lies along the transmitted pathof the other, and vice versa. A detectorwaits at the end of each path. Ordinarilythe two photons would be reflected inde-pendently, and there would be a 50 per-cent chance of them arriving in separatedetectors. If the photons are indistin-guishable and arrive at the mirror at thesame instant, however, quantum interfer-ence takes place: some possibilities cancel

out and do not occur, whereas others re-inforce and occur more often. When thephotons interfere, they have only a 25percent likelihood of ending up in sepa-rate detectors. Furthermore, that outcomecorresponds to detecting one of the fourpossible Bell states of the two photons—

the case that we called “lucky” earlier. Theother 75 percent of the time the two pho-tons both end up in one detector, whichcorresponds to the other three Bell statesbut does not discriminate among them.

When Alice simultaneously detectsone photon in each detector, Bob’s pho-ton instantly becomes a replica of Alice’soriginal photon X. We verified that thisteleportation occurred by showing thatBob’s photon had the polarization thatwe imposed on photon X. Our experi-ment was not perfect, but the correct po-larization was detected 80 percent of thetime (random photons would achieve 50percent). We demonstrated the procedurewith a variety of polarizations: vertical,horizontal, linear at 45 degrees and evena nonlinear, circular polarization.

The most difficult aspect of our Bell-state analyzer is making photons A and Xindistinguishable. Even the timing ofwhen the photons arrive could be used toidentify which photon is which, so it isimportant to “erase” the time informa-tion carried by the particles. In our ex-periment, we used a clever trick first sug-gested by Marek Zukowski of the Uni-versity of Gdansk in Poland: we send thephotons through very narrow bandwidthwavelength filters. This process makes thewavelength of the photons extremely pre-cise, and by Heisenberg’s uncertainty re-lation it smears out the photons in time.

A mind-boggling case arises when theteleported photon is itself entangled withanother and thus does not have its ownpolarization. In 1998 my Innsbruck groupdemonstrated this scenario by giving Al-ice photon D without polarizing it, so thatit was still entangled with photon C. Weshowed that when the teleportation suc-

ceeded, Bob’s photon B ended up entan-gled with C. The entanglement with Chad been transmitted from D to B.

My current group at the University ofVienna was able to perform teleportationof entanglement in such high fidelity thatthe nonlocal correlation between photonsB and C violated a Bell inequality. Thequality was high enough to make quan-tum repeaters possible, necessary to con-nect quantum computers over large dis-tances. Shortly thereafter we overcame alimitation of our initial experiment. Ear-lier Bob had to actually detect and so de-stroy his photon X to make sure that tele-portation succeeded. Our experimentprovided a freely propagating beam ofteleported qubits emerging from Bob’sside, thus showing that this step is not es-sential. This is important in a case wherethe qubits will be used again in some way.

Piggyback StatesOUR EXPERIMENT clearly demonstrat-ed teleportation, but it had a low rate ofsuccess. Because we could identify justone Bell state, we could teleport Alice’sphoton only 25 percent of the time—theoccasions when that state occurred. Nocomplete Bell-state analyzer exists for in-dependent photons or for any two inde-pendently created quantum particles, soat present there is no experimentallyproven way to improve our scheme’s effi-ciency to 100 percent.

In 1994 a way to circumvent this


ANTON ZEILINGER ([email protected]) is at the Institute for Exper-imental Physics at the University of Vi-enna, having teleported there in 1999from the University of Innsbruck. He con-siders himself very fortunate to have theprivilege of working on exactly the mys-teries and paradoxes of quantum me-chanics that drew him into physics near-ly 40 years ago. In his little free time,Zeilinger interacts with classical musicand with jazz and loves to ski.

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Teleportation could transfer quantum informationbetween quantum processors in a quantum computer.


problem was proposed by Sandu Popes-cu, then at the University of Cambridge.He suggested that the state to be tele-ported could be a quantum state ridingpiggyback on Alice’s auxiliary photon A.Francesco De Martini’s group at the Uni-versity of Rome I “La Sapienza” success-fully demonstrated this scheme in 1997.The auxiliary pair of photons was entan-gled according to the photons’ locations:photon A was split, as by a beam splitter,and sent to two different parts of Alice’sapparatus, with the two alternativeslinked by entanglement to a similar split-ting of Bob’s photon B. The state to beteleported was also carried by Alice’sphoton A—its polarization state. Withboth roles played by one photon, detect-ing all four possible Bell states becomes astandard single-particle measurement: de-tect Alice’s photon in one of two possiblelocations with one of two possible polar-izations. The drawback of the scheme isthat Alice cannot teleport a separate un-known photon X. Doing that would re-quire her to somehow transfer its stateonto her photon A, which is essentiallya teleportation procedure by itself.

Polarization of a photon, the featureemployed by the Innsbruck and Rome ex-periments, is a discrete quantity, in thatany polarization state can be expressed asa superposition of just two discrete states,such as vertical and horizontal polariza-tion. The electromagnetic field associatedwith light also has continuous featuresthat amount to superpositions of an infi-nite number of basic states. For example,a light beam can be “squeezed,” meaningthat one of its properties is made extreme-ly precise, or noise-free, at the expense ofgreater randomness in another property(à la Heisenberg). In 1998 Jeffrey Kim-ble’s group at the California Institute ofTechnology teleported such a squeezedstate from one beam of light to another,thus demonstrating teleportation of acontinuous feature. In 2002 a group atthe Australian National University inCanberra led by Ping Koy Lam realizedsuch a teleportation with unprecedentedhigh fidelity.

Remarkable as all these experimentsare, they are a far cry from quantum tele-portation of large objects. There are two

essential problems: First, one needs an en-tangled pair of such large objects. Second,the object to be teleported and the entan-gled pairs must be sufficiently isolatedfrom the environment. If enough infor-mation leaks to or from the environmentthrough stray interactions, the objects’quantum states degrade, a process calleddecoherence. It is hard to imagine how wecould achieve such extreme isolation foran object, let alone a living creature thatbreathes air and radiates heat. But whoknows how fast development might go inthe future?

Certainly we could use existing tech-nology to teleport elementary states, likethose of the photons in our experiment,across distances of a few kilometers and

maybe even up to satellites. The technol-ogy to teleport states of individual atomsis at hand today: the group led by SergeHaroche at the École Normale Supérieurein Paris has demonstrated entanglementof atoms. The entanglement and telepor-tation of molecules may reasonably be ex-pected within the next decade.

What happens beyond that is any-body’s guess. In 2002 Eugene Polzik’sgroup at the University of Århus in Den-mark demonstrated entanglement of thespin of two ensembles, each containingabout 1012 atoms. This experiment opensup the possibility of teleporting systemscontaining large numbers of atoms.

An important application of telepor-tation might be in quantum computation,


Isn’t it an exaggeration to call this teleportation? After all, it is only a quantumstate that is teleported, not an actual object. What do we mean by identity? Howdo we know that an object—say, the car we find in our garage in the morning—is thesame one we saw a while ago? When it has all the right features and properties.Quantum physics reinforces this point: particles of the same type in the samequantum state are indistinguishable even in principle. If one could carefully swap allthe iron atoms in the car with those from a lump of ore and reproduce the atoms’states exactly, the end result would be identical, at the deepest level, to the originalcar. Identity cannot mean more than this: being the same in all properties.

Isn’t it more like “quantum faxing”? Faxing produces a copy that is easy todistinguish from the original. Moreover, because of the quantum no-cloning theorem,in quantum teleportation the original must be destroyed.

Can we hope to teleport a complicated object? There are severe obstacles. First,the object has to be in a pure quantum state, and such states are very fragile.Experiments with atoms and larger objects must be done in a vacuum to avoidcollisions with gas molecules. Even a tiny lump of matter would be disturbed merelyby thermal radiation from the walls of the apparatus. This is why we do not routinelysee quantum effects in our everyday world. Another problem is the Bell-statemeasurement. What would it mean to do a Bell-state measurement of a virusconsisting of, say, 107 atoms? How would we extract the 108 or more bits ofinformation that such a measurement would generate? For an object of just a fewgrams the numbers become impossible: more than 1024 bits of data.

Would teleporting a person require quantum accuracy? Being in the samequantum state does not seem necessary for being the same person. We change ourstates all the time and remain the same people—at least as far as we can tell!Conversely, identical twins or biological clones are not “the same people,” becausethey have different memories. Does Heisenberg uncertainty prevent us fromreplicating a person precisely enough for her to think she was the same as theoriginal? Who knows. It is intriguing, however, that the quantum no-cloning theoremprohibits us from making a perfect replica of a person. —A.Z.

SKEPTICS CORNERANSWERS TO COMMON TELEPORTATION QUESTIONS


THE QUANTUM ADVENTURES OF ALICE & BOB

Intrepid explorer Alice discovers stable einsteinium crystals. Her competitor, the evil Zelda, also “discovers” the crystals. But Alice and her partner Bob (on Earth) have one advantage: QUANTUM COMPUTERS AND TELEPORTERS. Alice does some quantum data processing ...

AAtt AAllpphhaa CCeennttaauurrii......

... and teleports the output —”qubits” of data—to Bob. They are very lucky: the teleportation succeeds cleanly!

Alice sends a message to Bob by laser beam, telling himhis qubits have accurate data. Zelda laser beams herpartner, Yuri, about the crystals.

Before the laser beam arrives onEarth, Bob feeds his qubits into aquantum simulation of the economy.

Bob gets Alice’s messagethat his qubits were accu-rate replicas of hers!

Yuri gets Zelda’s messagebut can only now start hiscomputer simulation.

Bob invests his and Alice’s nest egg in einsteiniumfutures ahead of the crowd. Their success depend-ed on luck, one chance in four per qubit ...

… but they only had to get lucky once to strike itrich. Yuri and Zelda change to careers in the non-quantum service industry. THE END

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where the ordinary notion of bits (0’s and1’s) is generalized to quantum bits, orqubits, which can exist as superpositionsand entanglements of 0’s and 1’s. Tele-portation could be used to transfer quan-tum information between quantum pro-cessors. Quantum teleporters can also beused to build a quantum computer [seebox at right]. The cartoon on the oppositepage illustrates an intriguing situation inwhich a combination of teleportation andquantum computation could occasional-ly yield an advantage, as if one had re-ceived the teleported information in-stantly instead of having to wait for it toarrive by normal means.

Quantum mechanics is probably one ofthe most profound theories ever discov-ered. The problems that it poses for oureveryday intuition about the world ledEinstein to criticize it very strongly. He in-sisted that physics should be an attempt tograsp a reality that exists independently ofits observation. Yet he realized that we runinto deep problems when we try to assignsuch an independent physical reality to theindividual members of an entangled pair.His great counterpart, Danish physicistNiels Bohr, insisted that one has to takeinto account the whole system—in the caseof an entangled pair, the arrangement ofboth particles together, no matter how farthey may be separated from each other.Einstein’s desideratum, the independentreal state of each particle, has no meaningfor an entangled quantum system.

Quantum teleportation is a direct de-scendant of the scenarios debated by Ein-stein and Bohr. We run into all kinds ofproblems if we ask ourselves what theproperties of the individual particles real-ly are when they are entangled. We haveto analyze carefully what it means to“have” a polarization. We cannot escapethe conclusion that all we can talk aboutare certain experimental results obtainedby measurements. In our polarizationmeasurement, a click of the detector letsus construct a picture in our mind inwhich the photon actually “had” a cer-tain polarization. Yet we must always re-member that this is just a made-up story.It is valid only if we talk about that spe-cific experiment, and we should be cau-tious when using it in other situations.

Indeed, following Bohr, I would arguethat we can understand quantum me-chanics if we realize that science does notdescribe how nature is but rather articu-lates what we can say about nature. Ex-pressed in modern language, this means

that quantum mechanics is a science ofknowledge, of information. This is wherethe current value of fundamental experi-ments such as teleportation lies: in help-ing us to reach a deeper understanding ofour mysterious quantum world.


QUANTUM COMPUTERSPERHAPS THE MOST IMPORTANT, yet still hypothetical, application of quantumteleportation outside of physics research is in quantum computation. A conventionaldigital computer works with bits, which take definite values of 0 or 1, but a quantumcomputer uses quantum bits, or qubits. Qubits can be in quantum superpositions of0 and 1 just as a photon can be in a superposition of horizontal and verticalpolarization. Indeed, in sending a single photon, the basic quantum teleportertransmits a single qubit of quantum information.

Superpositions of numbers may seem strange, but as the late Rolf Landauer ofIBM put it, “When we were little kids learning to count on our very sticky classicalfingers, we gained the wrong intuition. We thought that information was classical.We thought that we could hold up three fingers, then four. We didn’t realize that therecould be a superposition of both.”

A quantum computer can work on a superposition of many different inputs atonce. It could run an algorithm simultaneously on one million inputs, using only as

many qubits as a conventional computer wouldneed bits to run the algorithm once on a single input.Theorists have proved that the algorithms runningon quantum computers can solve certain problemsfaster (in fewer computational steps) than anyknown algorithm running on a classical computer.The problems include finding items in a databaseand factoring large numbers, which is of greatinterest for breaking secret codes.

So far only the most rudimentary elements ofquantum computers have been built: logic gates that can process one or two qubits.The realization of even a small-scale quantum computer is still far away. A keyproblem is transferring quantum data reliably between different logic gates orprocessors, whether within a single quantum computer or across quantum networks.Quantum teleportation is one solution.

Daniel Gottesman of Microsoft and Isaac L. Chuang of IBM proved that a general-purpose quantum computer can be built out of three basic components: entangledparticles, quantum teleporters and gates that operate on a single qubit at a time.This result provides a systematic way to construct two-qubit gates. In general,building a two-qubit gate for independent qubits provides the same experimentalchallenge as realizing a Bell-state analyzer for independent systems, and eitherone, once realized, can be used to build the other one. —A.Z.

Experimental Quantum Teleportation. D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurterand A. Zeilinger in Nature, Vol. 390, pages 575–579; December 11, 1997.Quantum Information. Special issue of Physics World, Vol. 11, No. 3; March 1998.Quantum Theory: Weird and Wonderful. A. J. Leggett in Physics World, Vol. 12, No. 12, pages 73–77;December 1999.Entanglement: The Greatest Mystery in Physics. Amir D. Aczel. Four Walls Eight Windows, New York, 2002.More about quantum teleportation is available at www.quantum.at


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44 S C I E N T I F I C A M E R I C A N U p d a t e d f r o m t h e J u l y 2 0 0 1 i s s u e

EVERYONE KNOWS OF THE SPEED OF LIGHT ASone of the unshakable properties of the universe.It’s not surprising, then, that experiments to rad-ically alter light’s speed require some seriousequipment and hard work. Running such an ex-periment requires first a careful tune-up and op-timization of the setup and then a long period ofpainstaking data-gathering to get a consistent setof measurements. At the Rowland Institute forScience in Cambridge, Mass., our original ultra-slow-light experiments took place in stints last-ing 27 hours nonstop. Instead of breaking formeals, we learned to balance a slice of pizza inone hand, leaving the other clean to flip mirrorsin and out on the optics table during 38 secondsof total darkness at a crucial stage of each run.

Our goal was to drastically slow down light,which travels through empty space at the uni-verse’s ultimate speed limit of nearly 300,000kilometers a second. We saw the first sign of light

pulses slowing down in March 1998. As hap-pens so often in experimental physics—becauseit can take so many hours to get all the compo-nents working together for the first time—thisoccurred in the wee hours of the morning, at 4 A.M. By July we were down to airplane speed.At that time I had to go to the Niels Bohr Insti-tute in Copenhagen to teach a class. I remembersitting in the plane marveling that I was travel-ing “faster than light”—that I could beat one ofour slow pulses to Denmark by a full hour.

Needless to say, I was restless during the weekin Copenhagen and eager to get back to Cam-bridge to continue the light-slowing experiments.In the next month we reached 60 kilometers an hour and decided that it was time to publish.The real payoff for the hard work, prior to thoseresults, was sitting in the lab in the middle of the night and observing the slow-light pulses,knowing that we were the first in history to

BY LENE VESTERGAARD HAU

Slowing a beam of light to a halt may pave the way for new optical communications technology, tabletop black holes and quantum computers

LIGHTFrozen

harnessingquanta


FREEZING OF LIGHT begins with a process in which a carefully tuned laser beam renders an opaque materialtransparent to a second laser beam.


see light go so slowly that you could outpace it on a bicycle.In the summer of 2000 we brought pulses of light to a com-

plete halt within tiny gas clouds cooled to near absolute zero.We could briefly keep the pulses on ice, so to speak, and thensend them back on their way.

As well as being of great intrinsic interest, slowing and freez-ing light have a number of applications. At sufficiently low tem-peratures the ultracold clouds of atoms used in our slow-lightexperiments form Bose-Einstein condensates, remarkable sys-tems in which all the atoms gather in a single quantum state andact in synchrony. Further uses could involve sending a lightpulse through a condensate as slowly as a sound wave, whichwe expect would cause a wave of atoms to “surf” on the lightpulse, setting off oscillations of the entire condensate.

The slow and frozen light work also opens up new possi-bilities for optical communications and data storage and forquantum-information processing—that is, for quantum com-puters, which would utilize quantum phenomena to outper-form conventional computers. The freezing-light system essen-tially converts between motionless forms of quantum informa-tion and photons flying around at the usual speed of light.

Getting Atoms into a StateMANY ORDINARY MATERIALS slow down light. Water, forinstance, slows light to about 75 percent of its velocity in a vac-uum. But that type of speed reduction, associated with a mate-rial’s refractive index, is limited. Diamond, which has one ofthe highest refractive indices of a transparent material, slowslight by a factor of only 2.4. Reducing light’s speed by factorsof tens of millions requires new effects that depend on quan-tum mechanics. My group produces the conditions for these ef-fects in a cigar-shaped cloud of sodium atoms—typically 0.2

millimeter long and 0.05 millimeter in diameter—trapped in amagnetic field and cooled to within a millionth of a degree ofabsolute zero.

Sodium belongs to the family of alkali atoms, which havea single outermost, or valence, electron. The valence electronproduces almost all the action: Different excited states of a sodi-um atom correspond to that electron’s being promoted to larg-er orbits around the nucleus, with higher energies than its usu-al lowest energy state, or ground state. These states determinehow the atom interacts with light—which frequencies it will ab-sorb strongly and so on. In addition, both the valence electronand the atom’s nucleus are magnets, in effect acting like tinycompass needles. The electron’s magnetism is associated withits intrinsic angular momentum, or spin, a little like the associ-ation of the earth’s rotational axis with magnetic north but withexact alignment. The precise energies of an atom’s excited statesdepend on how the spins of the nucleus and the valence elec-tron are aligned.

Although an atom can assume many states, we use just threeto slow light. When we finish preparing and cooling the atomcloud, every atom is internally in state 1, its ground state: thevalence electron is in its lowest orbit, and its spin is exactly op-posite, or anti-aligned, with the nuclear spin. Also, the totalmagnetism of each atom is anti-aligned with the magnetic fieldthat we use to hold the cloud in place. State 2 is very similar,only with the electron and nuclear spins aligned, which raisesthe atom’s energy a little. State 3 has about 300,000 times moreenergy than state 2 (with state 1 as the reference level) and isproduced by boosting the valence electron up to a larger orbit.Atoms relaxing from state 3 down to state 1 or 2 generate thecharacteristic yellow glow of sodium streetlights.

The pulse of laser light that we wish to slow (the “probe”pulse) is tuned to the energy difference between states 1 and 3.If we sent a pulse of that light into the cloud without doing anyother preparation, the atoms would completely absorb the pulseand jump from state 1 to state 3. After a brief time, the excitedatoms would relax by reemitting light, but at random and in alldirections. The cloud would glow bright yellow, but all infor-mation about the original light pulse would be obliterated.

To prevent this absorption, we use electromagnetically in-duced transparency, a phenomenon first observed in 1990 byStephen E. Harris’s group at Stanford University. In electro-magnetically induced transparency, a laser beam with a care-fully chosen frequency shines on the cloud and changes it frombeing as opaque as a wall to being as clear as glass for light ofanother specific frequency.

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■ Nothing travels faster than light in a vacuum, but even lightis slowed down in many media. Scientists have manipulatedclouds of atoms with lasers so that pulses of light travelthrough the clouds at one 20-millionth of their normalspeed—slower than highway traffic.

■ A similar technique completely halts the pulses, turningthem into a quantum imprint on the atoms. Later, anotherlaser beam converts the frozen pulse back into a movinglight pulse with all the properties of the original.

■ The process of slowing and stopping light has manyresearch and technological applications.

Overview/Stopping Light

Compressing a kilometer-long laser pulseto one millionth of a meter sets off quantum shock waves

in sodium atoms near absolute zero.


is tuned to the energy difference between states 2 and 3. Theatoms, in state 1, cannot absorb this beam. As the light of theprobe laser pulse, tuned to state 3, arrives, the two beams shiftthe atoms to a quantum superposition of states 1 and 2, mean-ing that each atom is in both states at once. State 1 alone wouldabsorb the probe light, and state 2 would absorb the couplingbeam, each by moving atoms to state 3, which would then emitlight at random. Together, however, the two processes cancelout, like evenly matched competitors in a tug of war—an effectcalled quantum interference. The superposition state is called adark state because the atoms in essence cannot see the laserbeams (they remain “in the dark”). The atoms appear trans-parent to the probe beam because they cannot absorb it in thedark state. Which superposition is dark—what ratio of states1 and 2 is needed—varies according to the ratio of light in thecoupling and probe beams at each location. But once the sys-tem starts in a dark state (in this case, 100 percent couplingbeam and 100 percent state 1), it adjusts to remain dark evenwhen the probe beam lights up.

A similar cancellation process makes the refractive index ex-actly one—like empty space—for probe light tuned precisely tostate 3. At very slightly different frequencies, however, the can-cellation is less exact and the refractive index changes. A shortpulse of light “sniffs out” this variation in the index because apulse actually contains a small range of frequencies. Each of thesefrequency components sees a different refractive index and there-fore travels at a different velocity. This velocity, that of a contin-uous beam of one pure frequency, is the phase velocity. The pulseof light is located where all these components are precisely in sync(or, more technically, in phase). In an ordinary medium such asair or water, all the components move at practically the same ve-locity, and the place where they are in sync—the location of thepulse—also travels at that speed. When the components movewith the range of velocities that occurs in the transparent atoms,the place where they are in sync gets shifted progressively fartherback; in other words, the pulse is slowed. The velocity of the pulseis called the group velocity, because the pulse consists of a groupof beams of different frequencies.

This process differs in a number of important respects fromthe usual slowing of light by a medium with a refractive indexgreater than one: the group velocity is slowed, not the phase ve-locity; a steep variation of the refractive index with frequency,not a large value of the index itself, causes the slowing; and thecoupling laser beam has to be on the entire time.

Ultracold Atoms for Freezing LightTHE MORE RAPIDLY the refractive index changes with fre-quency, the slower the pulse travels. How rapidly the index canchange is limited by the Doppler effect: the incessant thermalmotion of the atoms in the gas smears out each atomic stateacross a small range of energies. The Doppler effect is like thechange in tone of a siren moving toward or away from you.Imagine the cacophony you would hear if many police carswere racing toward and away from you at various speeds.

My research group uses extremely cold atoms (which move

slowly) to minimize this Doppler spreading. Consequently, theenergy states are sharply defined, and the variation of refractiveindex can be made very steep. Slow light in hot gases has sincebeen obtained by Marlan O. Scully’s group at Texas A&MUniversity and Dmitry Budker’s group at the University of Cal-ifornia at Berkeley. The use of hot atoms removes the need toproduce ultracold atoms, but it puts severe constraints on, forexample, the geometry of the setup; the probe and couplingbeams must propagate in exactly the same direction.

We chill our sodium atoms with a combination of laserbeams, magnetic fields and radio waves. The atoms first emergefrom a hot source as an intense beam, traveling about 2,600kilometers an hour. A laser beam hits the atoms head-on andin a millisecond slows them to 160 kilometers an hour—a de-celeration of 70,000 times gravity produced by a laser beamthat wouldn’t burn your finger. Further laser cooling in an op-tical molasses—six beams bathing the atoms from all sides—

chills the atoms to 50 millionths of a degree above absolutezero. In a few seconds we accumulate 10 billion atoms in themolasses. Next we turn off the laser beams, plunging the labinto total darkness, and turn on electromagnets, whose com-bined field holds the atom cloud like a trap. For 38 seconds we


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WAYLAYING LIGHT: Before the light pulse (yellow) reaches the cloud ofcold atoms (purple) that will freeze it, all the atoms’ spins (small arrows)are aligned and a coupling laser beam (red) renders the cloud transparentto the pulse (1, 2). The cloud greatly slows and compresses the pulse(3), and the atoms’ states change; an imprint of the pulse is created inthe cloud, and it accompanies the slow light. When the pulse is fullyinside the cloud (4), the coupling beam is turned off (5), halting theimprint and the light; at zero velocity the light vanishes but the imprintstays. Later the coupling beam is turned on (6), regenerating the lightpulse and setting the imprint and the light back in motion.

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cool the atoms through evaporation, kicking out the hotteratoms and leaving the cooler ones behind. Specially tuned ra-dio waves help to speed the hot atoms on their way. This wholeprocess—from hot atom beam to cold, trapped atoms—takesplace inside a vacuum chamber pumped out to 10–14 (10quadrillionths) of atmospheric pressure.

When we cool the cloud to about 500 billionths of a degree,it forms a Bose-Einstein condensate, a very odd state of matterin which the several million atoms left after the evaporativecooling behave in a completely synchronized fashion [see “TheCoolest Gas in the Universe,” by Graham P. Collins; ScientificAmerican, December 2000]. These ultracold atom clouds, freelysuspended in the middle of a vacuum chamber by a magneticfield, are the coldest places in the universe. And yet the rest ofthe experimental setup, within one centimeter of the cloud, isat room temperature. Vacuum-sealed windows on the cham-ber let us see the atoms directly by eye during laser cooling: acold atom cloud in the optical molasses looks like a little brightsun, five millimeters in diameter. Such easy optical access al-lows us to massage the atoms with laser beams and make themdo exactly what we want.

When our cigar of cold atoms is in place, we illuminate itfrom the side with the coupling laser. Then we launch a probepulse along the axis of the cigar. To measure the speed of the lightpulse, we do the most direct measurement imaginable: we sit be-hind the atom cloud with a light detector and wait for the pulseto come out, to see how long it takes. Immediately after the pulse

has gone through, we measure the length of the cloud with yet an-other laser beam, shone from below to project the cloud’s shad-ow onto a camera. That length divided by the delay of the pulsegives us the velocity. The delays are in the range of microsecondsto milliseconds; this might sound short, but it is equivalent tolight taking a detour through kilometers of optical fiber woundin a coil—and our clouds are only 0.1 to 0.2 millimeter long.

When we slow a light pulse down by a factor of 20 million,more happens than just a change of speed. At the start our pulseof light is a kilometer long, racing through the air at nearly300,000 kilometers a second. (Of course, our laboratory’slength is much less than a kilometer, but if we could place ourlaser that far away, its pulses would be that long in the air.) Thepulse’s leading edge crosses the glass window into the vacuumchamber and enters our levitating speck of sodium atoms. In-side this tenuous cloud the light travels at 60 kilometers an hour.A cyclist on a racing bike could overtake such sluggish light.

Through the Gas, DarklyWITH THE FRONT of the light pulse traveling so slowly andits tail still going full tilt through the air, the pulse piles into thegas like a concertina. Its length is compressed by a factor of 20million to a mere twentieth of a millimeter. Even though theatom cloud is small, the pulse compresses so much that it fitscompletely inside—important for stopping light. One might ex-pect the light’s intensity to increase greatly because the sameamount of energy is crammed into a smaller space. This am-plification does not happen, however; instead the electromag-netic wave remains at the same intensity. To put it another way,in free space the pulse contains 50,000 photons, but the slowpulse contains 1⁄400 of a photon (the factor of 20 million again).What has happened to all the other photons and their energy?Some of that energy goes into the sodium atoms, but most ofit is transferred to the coupling laser beam. We have monitoredthe intensity of the coupling laser to observe this energy trans-fer directly.

These transfers of energy also change the states of the sodi-um atoms where the pulse is passing by. At the front of the pulsethe atoms are changed from their original state 1 to a superpo-sition of states 1 and 2, the dark state. This state has the largestproportion of state 2 at the central, most intense part of thepulse. As the rear of the slow pulse leaves a region of atoms, theatoms revert to state 1. The spatial pattern of atomic dark statesin the cloud mimics the shape of the compressed slow-light pulseand accompanies it through the gas as an imprint. When this im-print and the light pulse reach the end of the gas cloud, the lightpulse sucks energy back out of the atoms and the coupling beam


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OPTICAL PROPERTIES induced in a cloud of atoms by a carefully tunedlaser beam are the key to the light-slowing process. A coupling laserbeam passing through the cloud makes it transparent to light of aprecise frequency (top) and causes an associated sharp variation of itsrefractive index (bottom). The transparency allows properly tuned lightto pass through the cloud without being absorbed, and the steeper thechange in the refractive index, the slower the light travels.

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LENE VESTERGAARD HAU is a MacArthur Fellow and Gordon McKayProfessor of Applied Physics and professor of physics at HarvardUniversity. She received her Ph.D. in theoretical solid state physicsfrom the University of Århus in Denmark. The author wishes to thankthe team of Zachary Dutton, Christopher Slowe, Chien Liu, Cyrus H.Behroozi, Brian Busch and Michael Budde, as well as Stephen E. Har-ris of Stanford University, for an extremely fruitful collaboration.

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to dash away through the air at its customary 300,000 kilome-ters a second, restored to its original kilometer of length.

The velocity of the slow light pulse depends on several pa-rameters. Some of these are fixed once we choose our atom spe-cies and which excited states to use, but two of the variables areunder our control: the density of the atom cloud and the in-tensity of the coupling laser beam. Increasing the cloud’s den-sity decreases the light’s speed, but we can push that only so far,in part because very dense clouds leak atoms out of the mag-netic trap too rapidly. The pulse speed is also reduced if the cou-pling laser beam is weaker. Of course, if the coupling laser istoo feeble, the cloud will not be transparent and will absorb thepulse. Nevertheless, we can still achieve the ultimate in slowingwithout losing the pulse to absorption if we turn off the cou-pling laser beam while the compressed slowed pulse is con-tained in the middle of the gas.

In response, the light pulse comes to a grinding halt and

turns off. But the information that was in the light is not lost.Those data were already imprinted on the atoms’ states, andwhen the pulse halts, that imprint is simply frozen in place,somewhat like a sound recorded on a magnetic tape. The stop-ping process does not compress the pattern of states, because theimprinted atoms in unison force the light pulse to turn off, un-like the earlier stage in which the pulse gradually entered the gas.

The frozen pattern imprinted on the atoms contains all theinformation about the original light pulse. We effectively havea hologram of the pulse written in the atoms of the gas. Thishologram is read by turning the coupling laser back on. Likemagic, the pulse reappears and sets off in slow motion again,along with the imprint in the atoms’ states, as if nothing had in-terrupted it.

We can store the light for several milliseconds, long enoughfor a pulse to travel hundreds of kilometers in air. The pulse doesdegrade the longer it is stored, because even though the gas


A BENCHTOP GUIDE TO STOPPING LIGHT

WHAT STOPPED LIGHT LOOKS LIKEThe precise times of detection of light pulsesreveal the slowing and stopping of light. Withno atom cloud present, the input pulse isdetected at time “zero” (top). Slowing of thepulse by a cloud is revealed by the pulse’sdelay (dotted curve). To stop a pulse, thecoupling beam (bottom) is turned off while theslowed pulse is inside the cloud. The time thatthe pulse is stopped—about 40 microseconds—

adds to its delay. The slowed pulse losesintensity because the cloud is not perfectlytransparent, but the pulse is stopped andrevived with 100 percent efficiency.

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EXPERIMENTAL SETUPThree laser beams and an ultracold cloud of sodium atoms (size exaggerated) ina high vacuum lie at the heart of the slow-light experiment. The coupling beaminteracts with the cloud, making it transparent but molasseslike to a pulse of theprobe beam. A photomultiplier tube measures the pulse’s time of arrival to better-than-microsecond precision. The imaging beam then measures the length of thecloud by projecting its shadow onto a camera. Not shown are the system thatdelivers and cools a new ultracold cloud for each pulse, electromagnets whosecombined field holds the atoms in place, and additional details of the optics.

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atoms are very cold they still move a bit, causing the pattern ofdark states to diffuse slowly. In addition, collisions betweenatoms can disrupt the dark superposition states. After some mil-liseconds, the revived output pulse will begin to be weaker thanthe original. Yet these limits show that cold atoms allow for longstorage times of immensely compressed optical information.And storage times are maximized with condensates in whichatom collisions tend not to destroy the dark states.

We can also play some tricks. If the coupling beam is turnedback on at a higher intensity, the output pulse will be brighterbut shorter than the one we sent in. Turning the coupling beamon and off quickly several times regenerates the stored pulse inseveral pieces. Such manipulations demonstrate the degree ofcontrol that we have over stored pulses and may be extremelyuseful in future applications.

Since our initial observation in 2000 of stopped light, it hasbeen obtained in a hot gas by Ronald L. Walsworth and MikhailD. Lukin of the Harvard-Smithsonian Center for Astrophysicsin Cambridge, Mass., and in a cooled, doped solid by Philip R.Hemmer, then at the Air Force Research Laboratory in Hans-com, Mass.

Quantum Shock WavesSLOW AND STOPPED LIGHT open up many interesting ex-periments. In our latest trial we turned everything around: ratherthan using cold atoms and condensates to slow light, we usedslow light pulses to probe the odd properties of Bose-Einsteincondensates.

A condensate is a superfluid—it flows through a tube with-out friction, just as electric current flows through a supercon-ductor without resistance. Helium turns superfluid when it iscooled to very low temperatures. Once a superfluid gets going,it flows forever with no need for further energy input. Super-fluids are described by a characteristic length scale called thehealing length, the minimum distance over which a superfluidcan adjust (heal itself) to an external perturbation. In our con-densates, the healing length is about 0.001 millimeter. So if wecan compress our light pulses to that scale, we should be able

to cause dramatic excitations of the superfluid, helping us tolearn about the superfluid state.

We have succeeded in compressing a light pulse this drasti-cally by creating a “roadblock” that forces the pulse to stop ata particular point in space, where it becomes totally compressedand localized. This is possible because when the probe light pulseis propagating at right angles to the coupling laser, we can spa-tially manipulate the intensity of the coupling laser along thepropagation direction of the incoming light pulse. The speed ofthe pulse is controlled by the coupling laser intensity: the lowerthe intensity, the lower the speed.

To create the roadblock, we illuminate only the front half ofthe condensate with the coupling laser. When the light pulse en-ters the atom cloud, it slows to bicycle speed as before. Then,as the pulse runs into the roadblock region in the middle of thecondensate, the pulse really slows down and compresses. With-in the light pulse region at the roadblock, the atoms are almostentirely in state 2 (the dark state) because the coupling intensi-ty is very low. Outside, the atoms are all in state 1. So we havea way of creating very localized defects in the condensate. Wehave taken direct images of this process in our laboratory.

As described earlier, for an atom in state 2, the spin of thevalence electron is aligned opposite to the electron spin of anatom in state 1. This has severe consequences, because the elec-tromagnet is used to trap atoms and hold them in place; atomsin state 2 will get kicked out of the magnet, as if a magnetic northpole was facing another north pole. So the localized defect ofatoms in state 2 will zip out of the magnet in less than 0.5 mil-lisecond. That process is by itself interesting and gives rise towhat is called a pulsed atom laser.

Let’s concentrate, however, on what is left in the trap. Weend up with a condensate of state 1 atoms, with a hole punchedin the middle. As you might imagine, condensates do not likeholes punched in their middles, and the response we observedis fascinating. Two density “dimples” are created. They startpropagating out toward the condensate boundaries, at thespeed of sound in the condensate, about 1 to 10 millimeters asecond. During this process, the back edge of the dimples steep-

0 milliseconds

IT TAKES A HURRICANEFROZEN LIGHT can be used to examine the nature of superfluids, which flow withoutfriction when close to absolute zero. To probe a Bose-Einstein condensate—a sodiumsuperfluid—a light pulse was stopped at a roadblock within the condensate (at thelarge black hemisphere in micrographs), compressing a kilometer-long pulse to 0.001millimeter. Within the compressed light pulse region, the sodium atoms wereconverted from their ground state to a slightly energized state, which leaves a narrowvoid in the condensate. This action causes density “dimples” that propagate outtoward the boundaries, at the speed of sound in the condensate, which almostimmediately forms quantum shock waves (moving to the right, at time 0 milliseconds).The fronts of the shock waves curve up (at 0.5 millisecond), creating quantizedvortices with zero atom density at their centers (two white voids at 2.5 milliseconds)—the superfluid analogue of the eye of a hurricane. At 5 milliseconds there is a longsausage-shaped region (black) with high atom density, which relaxes over time andrepresents the presence of a large collective excitation of the condensate.

CREATING QUANTUM SHOCK WAVES


ens because there is a dramatic variation of the atom densityand thus the sound speed across the dimple structures. The backpart of each dimple, where the density is high, will catch up tothe central part, where the density is the lowest. Such a steep-ening of the back edge is what in a normal fluid, like water,would lead to shock wave formation. But because a condensateis a superfluid, the steepening forms the superfluid analogue ofthat phenomenon—a quantum shock wave, a quantized rota-tion pattern, a quantized vortex shaped like a smoke ring.

Our lab has photographed this process [see illustrationabove]. The central parts of the quantized vortices appear aswhite dots. In these places there is no atom density and the lightjust goes right through the condensate, as in the eye of a hurricane.

This process shows how the superfluid nature of the con-densate will break down during the formation of these dramat-ic excitations. The vortices even seem to have a life of their own:they move around and sometimes bounce off one another likebilliard balls. At other times they collide and seem to explodeinto a bunch of sound waves. Because a slow light pulse alwayscreates vortices in pairs of opposite circulation, they are verymuch like particle and antiparticle pairs that can annihilate. Weare excited about probing this rich system further.

Black Holes and ComputersCONDENSATES CAN BE PRODUCED in a vortex statewherein the gas rotates, reminiscent of water going down thedrain. Ulf Leonhardt of the University of St. Andrews in Scot-land has suggested that a pulse of slow light traveling througha vortex would find itself dragged along with the gas—very sim-ilar to a phenomenon believed to occur near black holes. Withslow light, we can perhaps study this and some other black holephenomena in the laboratory.

Slow light also enables a new kind of nonlinear optics thatoccurs, in particular, when one laser beam alters the propertiesof another beam. Nonlinear optics is a huge field of research,both of fundamental interest and with applications from imag-ing to telecommunications. Extremely intense beams are usual-ly needed to achieve nonlinear optical effects, but with slow light

the corresponding phenomena can be produced with a verysmall number of photons. Such effects could be useful for cre-ating ultrasensitive optical switches.

Another application for slow and stopped light could bequantum computers, in which the usual 1’s and 0’s are replacedwith quantum superpositions of 1’s and 0’s called qubits. Suchcomputers, if they can be built, could solve certain problems thatwould take an ordinary computer a very long time. Two broadcategories of qubits exist: those that stay in one place and inter-act with one another readily (such as quantum states of atoms)and those that travel rapidly from place to place but are difficultto make interact in the ways needed in a quantum computer(photons). The slow-light system, by transforming flying pho-tons into stationary dark state patterns and back, provides a ro-bust way to convert between these types of qubits, a process thatcould be essential for building large-scale quantum computers.We can imagine imprinting two pulses in the same atom cloud,allowing the atoms to interact and then reading out the result bygenerating new output light pulses.

Even if frozen light doesn’t prove to be the most convenientand versatile component for building a quantum computer, ithas opened up more than enough research applications to keepus—and other groups—busy for many more all-night sessions inthe years to come.


Electromagnetically Induced Transparency. Stephen E. Harris in PhysicsToday, Vol. 50, No. 7, pages 36–42; July 1997.

Light Speed Reduction to 17 Metres per Second in an Ultracold AtomicGas. Lene Vestergaard Hau, S. E. Harris, Zachary Dutton and Cyrus H.Behroozi in Nature, Vol. 397, pages 594–598; February 18, 1999.

Observation of Coherent Optical Information Storage in an AtomicMedium Using Halted Light Pulses. Chien Liu, Zachary Dutton, Cyrus H.Behroozi and Lene Vestergaard Hau in Nature, Vol. 409, pages 490–493;January 25, 2001.

Observation of Quantum Shock Waves Created with Ultra-CompressedSlow Light Pulses in a Bose-Einstein Condensate. Zachary Dutton,Michael Budde, Christopher Slowe and Lene Vestergaard Hau in Science, Vol.293, pages 663–668; July 27, 2001.


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When two protons traveling at 99.999999 percentof the speed of light collide head-on, the ensuingsubatomic explosion provides nature with 14 tril-

lion electron volts (TeV) of energy to play with. This energy,equal to 14,000 times that stored in the mass of a proton at rest,is shared among the smaller particles that make up each proton:quarks and the gluons that bind them together. In most colli-sions the energy is squandered when the individual quarks andgluons strike only glancing blows, setting off a tangential sprayof familiar particles that physicists have long since cataloguedand analyzed. On occasion, however, two of the quarks willthemselves collide head-on with an energy as high as 2 TeV ormore. Physicists are sure that nature has new tricks up her sleevethat must be revealed in those collisions—perhaps an exotic par-ticle known as the Higgs boson, perhaps evidence of a miracu-lous effect called supersymmetry, or perhaps something unex-pected that will turn theoretical particle physics on its head.

The last time that such violent collisions of quarks occurredin large numbers was billions of years ago, during the first pi-cosecond of the big bang. They will start occurring again in2007, in a circular tunnel under the Franco-Swiss countrysidenear Geneva. That’s when thousands of scientists and engineers

from dozens of countries expect to finish building the giant de-tectors for the Large Hadron Collider (LHC) and start experi-ments. This vast and technologically challenging project, coor-dinated by CERN (the European laboratory for particlephysics), which is taking the major responsibility for con-structing the accelerator, is already well under way.

The LHC will have about seven times the energy of the Teva-tron collider based at Fermi National Accelerator Laboratory inBatavia, Ill., which discovered the long-sought “top” quark inexperiments spanning from 1992 to 1995. The LHC willachieve its unprecedented energies despite being built within theconfines of an existing 27-kilometer tunnel. That tunnel housedCERN’s Large Electron-Positron Collider (LEP), which operat-ed from 1989 to 2000 and was used to carry out precision testsof particle physics theory at about 1 percent of the LHC’s ener-gy. By using LEP’s tunnel, the LHC avoids the problems and vastexpense of siting and building a new, larger tunnel and con-structing four smaller “injector” accelerators and supporting fa-cilities. But bending the trajectories of the 7-TeV proton beamsaround the old tunnel’s curves will require magnetic fieldsstronger than those any accelerator has used before. Those fieldswill be produced by 1,232 15-meter-long magnets installedaround 85 percent of the tunnel’s circumference. The magnetswill be powered by superconducting cables carrying currentsof 12,000 amps cooled by superfluid helium to –271 degreesCelsius, two degrees above the absolute zero of temperature.

The Large Hadron Collider willbe a particle accelerator ofunprecedented energy and

complexity, a global collaboration to uncover anexotic new layer of reality

STRADDLING THE FRANCO-SWISS BORDER, the location of the 27-kilometer tun-nel that will house the Large Hadron Collider (LHC) 100 meters below the groundis indicated in gold. Smaller circles mark the positions of caverns that house de-tectors or ancillary equipment.

By Chris Llewellyn Smith


To carry out productive physics ex-periments, one needs more than justhigh-energy protons. What counts is theenergy of collisions between the protons’constituent quarks and gluons, whichshare a proton’s energy in a fluctuatingmanner. The LHC will collide beams ofprotons of unprecedented intensity to in-crease the number of rare collisions be-tween quarks and gluons carrying un-usually large fractions of their parentprotons’ energy. The LHC’s intensity, orluminosity, will be 100 times as great asthat of previous colliders and 10 timesthat of the canceled Superconducting Su-per Collider (SSC). The SSC would havebeen a direct competitor to the LHC, col-liding 20-TeV proton beams in an 87-kilometer-circumference tunnel aroundWaxahachie, Tex. The LHC’s higher in-tensity will mostly compensate for thelower beam energy, but it will make theexperiments much harder. Furthermore,such large intensities can provoke prob-lems, such as chaos in the beam orbits,that must be overcome to keep the beamsstable and well focused.

At four locations around the LHC’sring, a billion collisions will occur eachsecond, each one producing about 100secondary particles. Enormous detect-ors—the largest roughly the height of asix-story building—packed with thou-sands of sophisticated components will

track all this debris. Elaborate computeralgorithms will have to sift through thisavalanche of data in real time to decidewhich cases (perhaps 10 to 100 per sec-ond) appear worthy of being recorded forfull analysis later, off-line.

Unanswered QuestionsAS WE STUDY nature with higher-ener-gy probes, we are delving into the struc-ture of matter at ever smaller scales. Ex-periments at existing accelerators haveexplored down to one billionth of one bil-lionth of a meter (10–18 meter). TheLHC’s projectiles will penetrate evendeeper into the heart of matter, down to10–19 meter. This alone would be enoughto whet scientific appetites, but pulses arereally set racing by compelling argumentsthat the answers to major questions mustlie in this new domain.

In the past 35 years, particle physicistshave established a relatively compact pic-ture—the Standard Model—that success-fully describes the structure of matterdown to 10–18 meter. The Standard Mod-el [see box on page 57] succinctly charac-terizes all the known constituents of mat-ter and three of the four forces that con-trol their behavior. The constituents ofmatter are six particles called leptons andsix called quarks. One of the forces,known as the strong force, acts on quarks,binding them together to form hundredsof particles known as hadrons. The pro-ton and the neutron are hadrons, and aresidual effect of the strong force bindsthem together to form atomic nuclei. Theother two forces are electromagnetismand the weak force, which operates onlyat very short range but is responsible forradioactive beta decay and is essential forthe sun’s fuel cycle. The Standard Modelelegantly accounts for these two forces asa “unified” electroweak force, which re-lates their properties despite their ap-pearing very different.

More than 20 physicists have wonNobel Prizes for work that has con-tributed to the Standard Model, from thetheory of quantum electrodynamics (the1965 prize) to the discovery of the neu-trino and the tau particle (1995) and thetheoretical work of Gerardus ’t Hooftand Martinus J. G. Veltman while at theUniversity of Utrecht (1999). Never-theless, although it is a great scientificachievement, confirmed by a plethora ofdetailed experiments, the Standard Mod-el has a number of serious flaws.

First, it does not consistently includeAlbert Einstein’s theory of the propertiesof spacetime and its interaction with mat-ter. This theory, general relativity, pro-vides a beautiful, experimentally very wellverified description of the fourth force,gravity. The difficulty is that unlike gen-eral relativity, the Standard Model is a ful-ly quantum-mechanical theory, and itspredictions must therefore break down atvery small scales (very far from the do-main in which it has been tested). The ab-sence of a quantum-mechanical descrip-tion of gravity renders the Standard Mod-el logically incomplete.

Second, although it successfully de-scribes a huge range of data with simpleunderlying equations, the Standard Mod-el contains many apparently arbitrary fea-tures. It is too byzantine to be the full sto-ry. For example, it does not indicate whythere are six quarks and six leptons in-stead of, say, four. Nor does it explainwhy there are equal numbers of leptonsand quarks—is this just a coincidence? Onpaper, we can construct theories that ex-plain why there are deep connections be-tween quarks and leptons, but we do notknow if any of these theories is correct.

Third, the Standard Model has an un-finished, untested element. This is notsome minor detail but a central compo-nent: a mechanism to generate the ob-served masses of the particles. Particle


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CHRIS LLEWELLYN SMITH is a senior research fellow in the physics department of the Uni-versity of Oxford. He served as president and provost of University College London from1999 to 2002. He spent periods at the Lebedev Institute in Moscow, at CERN near Genevaand at the Stanford Linear Accelerator Center in California before returning to Oxford for mostof his career as a theoretical physicist. His 1994–98 term as director general of CERN sawthe approval of the Large Hadron Collider project and the negotiation of new relations withnonmember countries, including Japan and the U.S., that will participate in the project.

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SUPERCONDUCTING MAGNET test string is laid outin the assembly hall; 1,232 large magnets willbend the trajectory of the two proton beams tofollow the curve of the accelerator’s tunnel.


masses are profoundly important—alter-ing the mass of the electron, for example,would change all of chemistry, and themasses of neutrinos affect the expansionof the universe. (A neutrino’s mass is atmost a few millionths of an electron’smass, but recent experiments show that itis not zero. The scientists who led two pi-oneering experiments that made this dis-covery were awarded a share of the 2002Nobel Prize for Physics.)

Higgs MechanismPHYSICISTS BELIEVE that particle mass-es are generated by interactions with afield that permeates the entire universe; thestronger a particle interacts with the field,the more massive it is [see illustration onpage 59]. The nature of this field, howev-er, remains unknown. It could be a newelementary field, called the Higgs field af-ter British physicist Peter Higgs. Alterna-tively, it may be a composite object, madeof new particles (“techniquarks”) tightlybound together by a new force (“techni-color”). Even if it is an elementary field,there are many variations on the Higgs

theme: How many Higgs fields are there,and what are their detailed properties?

Nevertheless, we know with virtuallymathematical certainty that whatevermechanism is responsible, it must pro-duce new phenomena in the LHC’s ener-gy range, such as observable Higgs parti-cles (which would be a manifestation ofripples in the underlying field) or techni-particles. The principal design goal of theLHC is therefore to discover these phe-nomena and pin down the nature of themass-generating mechanism.

The LHC experiments will also besensitive to other new phenomena thatcould confirm one or another of the spec-ulative theories that extend or completethe Standard Model. For example, it iswidely thought that the more completetheory must incorporate a “super” sym-metry. Supersymmetry would greatly in-crease the web of relations among the el-ementary particles and forces. Further-more, so-called local supersymmetryautomatically includes gravity; converse-ly, the only known theory (string theory)that could successfully combine general

relativity and quantum mechanics re-quires supersymmetry. If supersymmetryis correct, physicists have very good rea-son to believe that the LHC can find thenew particles that it predicts.

These new phenomena may be dis-covered before the LHC comes into op-eration by experiments at Fermilab’sTevatron, which started colliding beamsof protons and antiprotons again in 2001after a major upgrade. These experi-ments could find new phenomena be-yond the range already explored by LEP.But even if they do “scoop” the LHC,they will reveal only the tip of a new ice-berg, and the LHC will be where physi-cists make comprehensive studies of thenew processes.

If the Tevatron does not observe thesenew phenomena, then the LHC will pickup the chase. The exploratory power ofthe LHC overlaps that of LEP and theTevatron, leaving no gaps in which newphysics could hide. Moreover, high-pre-cision measurements made in the pastdecade at LEP, the Stanford Linear Accelerator Center and Fermilab have

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Superconductingbus bars

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ACCELERATOR MAGNET is shown incross section. The superconductingcoils carry 12,000 amps of current and must be kept cooled to below twokelvins. Each beam pipe carries one ofthe two countermoving proton beams.Other magnets focus the beams andbend them to cross at collision pointswithin the detectors.


essentially eliminated worries that the Higgs boson might be out of reach of theLHC’s energy range. It is now clear thateither the Higgs boson or other newphysics associated with the generation ofmass will be found at the LHC.

Emulating the Big BangTO ADDRESS THIS kind of physics re-quires re-creating conditions that existedjust a trillionth of a second after the bigbang, a task that will push modern tech-

nologies to their limits and beyond. Tohold the 7-TeV proton beams on course,magnets must sustain a magnetic field of8.3 tesla, almost 100,000 times theearth’s magnetic field and the highest everused in an accelerator. They will rely onsuperconductivity: large currents flowingwithout resistance through thin super-conducting wires, resulting in compactmagnets that can generate magnetic-fieldstrengths unobtainable with convention-al magnets made with copper wires [seeillustration on preceding page]. To main-tain the superconductivity under operat-ing conditions—with 12,000 amps of cur-rent—the magnets’ cores must be held at–271 degrees C around 22.4 kilometers ofthe tunnel. Cryogenics on this scale hasnever before been attempted.

In December 1994 a full prototypesection of the LHC was operated for 24

Toroidal magnets

Inner detector

Hadron calorimeters

Shielding

Beam

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Forward calorimeters

Electromagnetic calorimeters

Solenoid

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Innermostlayer

Electromagneticcalorimeter

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Photons

Electrons

Muons

Protons

Neutrons

A TOROIDAL LHC APPARATUS (ATLAS) detector(bottom) uses a novel toroidal magnet system.Protons collide in the center, producing a sprayof particles. The concentric layers of ATLASdetect different species of particles, someprecisely tracking the particle trajectories,others (“calorimeters”) measuring the energycarried. The simplified diagram (below, left)illustrates how such layers work. The toroidalmagnets curve the tracks of charged particles,allowing their momenta to be measured. Theimage (below, right) shows simulated data of acollision in which a Higgs particle decays intofour muons (yellow tracks).

Muon detectors

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hours, demonstrating that the key techni-cal choices for the magnets are correct.Since then, tests on prototypes have sim-ulated about 10 years of running theLHC. Magnets that surpass the designcriteria are now being produced in in-dustry and delivered to CERN for finaltesting and subsequent installation.

With the 1993 demise of the planned40-TeV SSC, the 14-TeV LHC becamethe only accelerator project in the worldthat can support a diverse research pro-gram at the high-energy frontier. TheLHC’s intense beams present those de-signing the experiments with remarkablechallenges of data acquisition. The beamswill consist of proton bunches strung likebeads on a chain, 25 billionths of a secondapart. At each collision point, pairs ofthese bunches will sweep through eachother 40 million times a second, each timeproducing about 20 proton-proton colli-sions. Collisions will happen so often thatparticles from one collision will still be fly-ing through the detectors when the nextone occurs!

Of these 800 million collisions a sec-ond, only about one in a billion will in-volve a head-on quark collision. To keepup with this furious pace, informationfrom the detector will go into electronicpipelines that are long enough to hold thedata from a few thousand collisions. Thiswill give “downstream” electronicsenough time to decide whether a collisionis interesting and should be recorded be-fore the data reach the end of the pipelineand are lost. LHC detectors will have tensof millions of readout channels. Match-ing up all the pipelined signals that origi-nate from the same proton-proton colli-sion will be a mind-boggling task.

When Quarks CollidePARTICLE DETECTORS are the physi-cists’ electronic eyes, diligently watchingeach collision for signs of interestingevents. LHC will have four particle de-tectors. Two will be giants, each built likea Russian matryoshka doll, with modulesfitting snugly inside modules and a beamcollision point at the center. Each module,packed with state-of-the-art technology,is custom-built to perform specific obser-vations before the particles fly out to the

next layer. These general-purpose detec-tors, ATLAS and CMS, standing up to 22meters high, will look for Higgs particlesand supersymmetry and will be on thealert for the unexpected, recording asmuch as possible of the collision debris.Two smaller detectors, ALICE and LHCb,will concentrate on different specific areasof physics.

Both ATLAS and CMS are optimizedto detect energetic muons, electrons andphotons, whose presence could signal theproduction of new particles, includingHiggs bosons. Yet they follow very dif-ferent strategies. Years of computer sim-ulations of their performance have shownthat they are capable of detecting what-ever new phenomena nature may exhib-

it. ATLAS (a toroidal LHC apparatus) isbased on an enormous toroidal magnetequipped with detectors designed to iden-tify muons in air [see illustration on op-posite page]. CMS (compact muon sole-noid) follows the more traditional ap-proach of using chambers inside thereturn yoke of a very powerful solenoidalmagnet to detect muons [see illustrationon next page].

Part of the CMS detector will consistof crystals that glow, or scintillate, whenelectrons and photons enter them. Suchcrystals are extremely difficult to make,and CMS benefits from the experiencegained from a recent CERN experiment,L3, which also used crystals. (The L3 de-tector was one of four that operated from


Higgs

THE STANDARD MODELTHE STANDARD MODEL of particle physics encompassesour knowledge of the fundamental particles. It containsparticles of matter and particles that transmit forces. Forexample, the electromagnetic force between a proton andan electron is generated by photons (particles of light)being passed back and forth between them.

The matter particles come in three families of four,each family differing only by mass. All the matter aroundus is made of particles from the lightest family. These are“up” quarks, “down” quarks, electrons and electron-neutrinos. The other two families of matter particles existonly ephemerally after being created in high-energycollisions (neutrinos, however, are long-lived).

The quarks are stuck together by the strong force,carried by gluons, to form hadrons, which include theprotons and neutrons that make atomic nuclei. Electrons,attracted to these nuclei by the electromagnetic force,orbit nuclei to form atoms and molecules. The weakinteraction, carried by the W and Z particles, helps to fuelthe sun and is responsible when an atomic nucleus decaysand emits an electron and a neutrino.

Gravity, the weakest force, is most familiar to usbecause it acts on mass. Particles called gravitons areassumed to carry gravity, but they have notbeen detected, because the force is so weak.Also, gravitons are not yet properlyincorporated into the Standard Model.

The entire system of matter and forces(except gravity) is encapsulated in a fewsimple equations derived from a function (the system’s“Lagrangian”) that is organized around one core principle, known as local gauge symmetry. Why nature has three families of matter is just one of many questions unanswered by the Standard Model. Considered one of thegreat intellectual triumphs of 20th-century science, the Standard Model canonly be a stepping-stone to a more complete description of nature’s forces.

—Graham P. Collins, staff writer

FERMIONS (MATTER)

Quarks

BOSONS (FORCES)

Gluons

Photon

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1989 to 2000 at the LEP collider, per-forming precision studies of the weakforce that told us that exactly three typesof zero- or low-mass neutrino exist.) Be-fore L3, such crystals had been made onlyin small quantities, but L3 needed 11,000of them. Crystals of the type developedfor L3 have been widely used in medicalimaging devices. CMS needs more thanseven times as many crystals made of a

more robust material. In due course thesuperior CMS crystals are likely to havean even bigger effect on the medical field.

ALICE (a large ion collider experi-ment) is a more specialized experimentthat will come into its own when the LHCcollides nuclei of lead with the colossal en-ergy of 1,150 TeV. That energy is expect-ed to “melt” the more than 400 protonsand neutrons in the colliding nuclei, re-leasing their quarks and gluons to form aglobule of quark-gluon plasma (QGP),which dominated the universe about 10microseconds after the big bang. ALICEis based around the magnet of the L3 ex-periment, with new detectors optimizedfor QGP studies.

There is good evidence that experi-ments at CERN have already created aquark-gluon plasma. Over the comingyears, Brookhaven National Laboratory’sRelativistic Heavy Ion Collider (RHIC)

has a good chance of studying QGP in de-tail by packing 10 times more energy pernucleon into its collisions than CERNdoes. The LHC will extend this by a fur-ther factor of 30. The higher energy at theLHC will complement the more variedrange of experiments at RHIC, guaran-teeing a thorough study of an importantphase in the universe’s early evolution.

B mesons, the subject of LHCb’s in-vestigations, could help tell us why theuniverse is made of matter instead ofequal amounts of matter and antimatter.Such an imbalance can arise only if heavyquarks and antiquarks decay into theirlighter cousins at different rates. The Stan-dard Model can accommodate this phe-nomenon, called CP violation, but prob-ably not enough of it to account com-pletely for the dominance of matter in theuniverse. Physicists observed CP violationin the decay of strange quarks in the 1960s,but data on heavy “bottom” quarks andantiquarks, the constituents of B mesons,are also needed to establish whether theStandard Model description is correct.

In 1999 experiments began at two B

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COMPACT MUON SOLENOID(CMS) detector uses a more traditionalmagnet design than ATLAS does and isoptimized for detecting muons. CMS has muondetectors (yellow) interleaved with iron layers (orange) thatchannel the magnetic field produced by the superconductingsolenoid coil. The electromagnetic calorimeter (blue) contains 80,000lead-tungstate crystals for detecting electrons and photons. Above, a computersimulation shows a collision in which a Higgs particle decays into two muons (the tracks at about “4 o’clock”) and two jets of hadrons (at about “11 o’clock”).


factories in California and Japan that canproduce tens of millions of B mesons ayear. These experiments have observedthe CP violation predicted by the Stan-dard Model in one B meson decay mode.The high luminosity of the LHC beamscan churn out a trillion B mesons a yearfor LHCb. This will allow much higherprecision studies in a wider variety of cir-cumstances and perhaps uncover crucialexotic decay modes too rare for the oth-er factories to see clearly.

A Laboratory for the WorldSCIENTIF IC EXPERIMENTS as ambi-tious as the LHC project are too expen-sive to be palatable for any one country.Of course, international collaborationhas always played a role in particlephysics, scientists being attracted to thefacilities best suited to their research in-terests, wherever situated. As detectorshave become larger and costlier, the sizeand geographic spread of the collabora-tions that built them have grown corre-spondingly. (It was the need to facilitatecommunication between the LEP collab-orations that stimulated the invention ofthe World Wide Web by Tim Berners-Lee at CERN.)

The LHC accelerator originally hadfunding only from CERN’s (then) 19 Eu-ropean member states, with constructionto occur in two phases on a painfully slowtimetable—a poor plan scientifically and

more expensive in toto than a faster, sin-gle-phase development. Fortunately, ad-ditional funds from other countries(which will provide some 40 percent ofthe LHC’s users) will speed up the proj-ect. Contributions of money or labor havebeen agreed to by Canada, India, Israel,Japan, Russia and the U.S. For example,Japan’s KEK laboratory will supply 16special focusing magnets. The U.S., withmore than 550 scientists already in-volved, will furnish the largest nationalgroup; accelerator components will bedesigned and fabricated by Brookhaven,Fermilab and Lawrence Berkeley Na-tional Laboratory.

Furthermore, 5,000 scientists and en-gineers in more than 300 universities andresearch institutes in 50 countries on sixcontinents are building the ATLAS andCMS detectors. When possible, compo-nents will be built in the participating in-stitutions, close to students (who get greattraining by working on such projects) andin collaboration with local industries. Thedata analysis will also be dispersed. It willbe a formidable challenge to managethese projects, with their stringent techni-cal requirements and tight schedules,while maintaining the democracy andfreedom for scientific initiatives that areessential for research to flourish.

Until now, CERN has been primarilya European laboratory. With the LHC, itis set to become a laboratory for the

world. Already its 7,000 scientific usersamount to more than half the world’s ex-perimental particle physicists. In 1994John Peoples, Jr., then director of Fermi-lab, summed it up nicely: “For 40 years,CERN has given the world a living dem-onstration of the power of internationalcooperation for the advancement of hu-man knowledge. May CERN’s next 40years bring not only new understandingof our Universe, but new levels of under-standing among nations.”


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The Particle Century. Edited by Gordon Fraser. Institute of Physics, 1998.

Supersymmetry. Gordon Kane. Perseus Publishing, 2000.

Links to home pages for all four LHC experiments are on the CERN Web site atwww.cern.ch/CERN/Experiments.html

Two other excellent sites are http://pdg.lbl.gov/atlas/atlas.html and www.particleadventure.org


A particle crossing that region of space is likea celebrity arriving . . .

. . . and attracting a cluster of admirers who impede his progress—he acquires “mass.”

. . . creating a similar cluster that is self-sustaining, analogous to a Higgs particle itself.

HOW HIGGS PARTICLESARE CREATED

HOW THE HIGGS FIELD GENERATES MASS

“Empty” space, which is filled with the Higgs field, is like a roomful of people chatting quietly.

Energy from a particle collision can be like arumor crossing the room . . .


BABAR detector

PositronsElectrons

60 S C I E N T I F I C A M E R I C A N

MATTERtheasymmetry between

B FACTORY, constructed at the Stanford LinearAccelerator Center, began taking data in early 1999. It examines violations of charge parity in B particles toset the stage for 21st-century physics.

extremeexperiments


Positron source

Electron gun

and

New accelerators are searching for

violations in aFUNDAMENTAL SYMMETRY OF

NATURE,throwing open a

window to physicsbeyond the known

ANTI-MATTER


By Helen R. Quinn and Michael S. Witherell


s far as humans can see into the universe,an essential imbal-ance strikes the eye.Stars, planets, rocks,asteroids—everything

is made of matter. Essentially no anti-matter is evident.

Is this imbalance the result of an acci-dent, a chance occurrence during the birthof the universe? Or is it an inevitable out-come of some asymmetry in the laws ofnature? Theorists believe that the excessof matter comes from fundamental dis-parities in how matter and antimatter be-have. These differences amount to viola-tions of a symmetry called charge-parityreversal, or CP.

After years of effort, experimental andtheoretical physicists have found a natur-al way for CP symmetry to be brokenwithin the prevailing theory of particlephysics, called the Standard Model. Cu-riously, the amount of CP violation themodel predicts is too small to explain thematter excess in the universe.

This finding is a vital clue that not allis well with the Standard Model: un-known factors are very likely at play.Two new accelerators in California andin Japan have begun to probe violationsof CP, with the aim of understandingwhether the Standard Model needs to berevamped or replaced. These accelerators,which produce enormous numbers ofparticles called B mesons, are known asasymmetric B factories. They are the lat-est tool in the search for physics beyondthe Standard Model.

Everything known about the elemen-tary properties of matter is encapsulatedin the Standard Model. It describes all thehundreds of observed particles and their

interactions in terms of a few types of fun-damental constituents: six quarks and sixleptons. (The leptons are light particles,such as the electron, the neutrino and theirrelatives.) In addition, each quark andeach lepton comes with an antiparticle,which has the same mass but the oppositesign for some quantum numbers, such aselectric charge. These ingredients arearranged in three generations of increas-ing mass [see box on opposite page], thefirst of which provides the primary con-stituents of matter.

The Standard Model describes threekinds of interactions among particles: thefamiliar electromagnetic force as well asthe strong and the weak forces. (For ob-jects of such low mass, gravity is too weakto be of interest.) Strong interactions con-fine quarks, which are never seen alone,within composite objects such as protons.Weak interactions cause instability—inparticular, the slow decays of the moremassive quarks and leptons into objectsof lower mass. All these forces are trans-mitted by specialized particles that alsoappear in the Standard Model: the pho-ton, the gluon, and the W and Z bosons.Last, the theory requires an as yet unob-served Higgs particle, whose interactionsare held responsible for the masses of thequarks and leptons as well as for much oftheir behavior.

Essential to the story of CP violationis a family of composite objects calledmesons. A meson contains one quark andone antiquark, in an equal mixture ofmatter and antimatter. Of great signifi-cance is the set of mesons called kaons, orK mesons, which contain a strange quarkor antiquark along with up or downquarks and antiquarks. Similar in manyrespects are the B mesons, which contain

a bottom quark or antiquark paired withup or down partners.

Beyond the StandardDESPITE ITS MANIFOLD successes indescribing the behavior of matter, deepquestions remain about the StandardModel. Physicists do not understand themechanisms that determine the model’s18 parameters. For the theory to describethe world as we know it, some of thoseparameters must have very finely tunedvalues, and no one knows why those val-ues would apply. More fundamentally,we do not understand why the model de-scribes nature at all—why, for instance,should there be exactly three generationsof leptons and quarks, no more or less?Finally, aspects of the theory that involvethe Higgs particle are all untested. TheLarge Hadron Collider at CERN, the Eu-ropean laboratory for particle physicsnear Geneva, will allow the Higgs to beobserved if its properties are as predictedby the Standard Model. The Higgs is be-lieved to lie behind most of the mysteriesof the Standard Model, including the vio-lation of CP symmetry.

A theory of physics is said to have asymmetry if its laws apply equally welleven after some operation, such as reflec-tion, transforms parts of the physical sys-tem. An important example is the opera-tion called parity reversal, denoted by P.This operation turns an object into itsmirror reflection and rotates it 180 de-grees about the axis perpendicular to themirror [see box on page 64]. In mathe-matical terms, parity reverses the vectorsassociated with the object.

A theory has P symmetry if the laws ofphysics in the parity-reversed world arethe same as they are in the real world. Par-

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ticles such as leptons and quarks can beclassified as right- or left-handed depend-ing on the sense of their internal rotation,or spin, around their direction of motion.If P symmetry holds, right-handed parti-cles behave exactly the same as left-hand-ed ones.

The laws of electrodynamics and thestrong interactions are the same in a par-ity-reflected universe. But in a famous1957 experiment, Chien-Shiung Wu ofColumbia University and her collabora-tors found that the weak interactions arevery different for particles of differenthandedness. Peculiarly, only left-handedparticles can decay by means of the weakinteraction; right-handed ones cannot.Moreover, it had long been held thatthere are no right-handed neutrinos, onlyleft-handed ones. Because neutrinos haveonly weak interactions with the rest of

the universe, this asymmetry is attrib-uted to the weak force. So the weak forceviolates P.

Another basic symmetry of nature ischarge conjugation, or C. This operationchanges the quantum numbers of everyparticle into those of its antiparticle.Charge symmetry is also violated in weakinteractions: antineutrinos were long con-sidered only right-handed, not left-handed.

Theorists combine C and P to get theoperation CP, which turns all particlesinto their antiparticles and also reversesthe direction of all vectors. When sub-jected to CP, the left-handed neutrino be-comes a right-handed antineutrino. Notonly does the right-handed antineutrinoexist, but its interactions with other part-icles are the same as they are for left-hand-ed neutrinos. So although charge and par-ity symmetry are individually broken by

neutrinos, in combination their dictateswould seem to be obeyed.

Much to the surprise of physicists, thestory of CP turned out to be far from sim-ple. A mathematical theorem proved in1917 by German mathematician EmmyNoether states that every symmetry im-plies the existence of a related quantitythat is conserved, or immutable. For in-stance, the fact that spacetime is the samein all directions—that is, has rotationalsymmetry—leads to the conservation ofangular momentum. Noether’s theoremimplies that if charge parity were an exactsymmetry of nature, then a quantitycalled CP number would be conserved.

CP ViolatedA PARTICLE and its antiparticle movingin opposite directions with equal energiesform a pair with charge-parity symmetry.


CONSTITUENTS OF MATTER

Quarks

Quarks

Quarks

Leptons

Leptons

Leptons

Up

Down

Electron

Electron-neutrino

Charm

Strange

Muon

Muon-neutrino

Top

Bottom

Tau

Tau-neutrino

+2/3

–1/3

–1

0

+2/3

–1/3

–1

0

+2/3

–1/3

–1

0

0.03

0.06

0.0005

?

1.3

0.14

0.106

?

174

4.3

1.7

?

PARTICLE SYMBOL CHARGE MASS(GeV/c2)

u

s

c

t

d

e-

νe

νµ

ντ

µ-

τ-b

FIRST GENERATION

SECOND GENERATION

THIRD GENERATION

PARTICLES OF THESTANDARD MODEL THE PRIMARY CONSTITUENTS of matter, quarksand leptons, are divided into generations. Thefirst generation contains up and down quarksand antiquarks, as well as the electron, aneutrino and their antiparticles. Ordinary matteris made almost exclusively of first-generationparticles: an atom’s nucleus contains protonsand neutrons, themselves made of up and downquarks. The other generations occurred in theearly universe, may still exist in hotenvironments such as neutron stars and areroutinely observed in accelerators.

In addition, the Standard Model containsseveral particles that transmit force as well as amysterious and unobserved particle called theHiggs. In the Standard Model the Higgs isresponsible for the masses of all particles andfor violations in charge-parity symmetry.

—H.R.Q. and M.S.W.

H

TRANSMITTERS OF FORCE

WEAKBOSONS PHOTON GLUON HIGGS

w gγ

Deep questions remain about the Standard Model of everything known about matter.


The CP operation does not change thesystem (taken as a whole), except that itsmathematical representation acquires anoverall factor: the CP number.

Either C or P, if acting twice on a sys-tem, returns it to the original state. Thisproperty is expressed as C2 = P2 = 1(where 1, the identity operation, impartsno change at all). As a result, the CP num-ber can be only +1 or –1. If nature hasperfect charge-parity symmetry, then ac-cording to Noether’s theorem no physicalstate with CP number –1 can transforminto a state with CP number +1.

Consider the electrically neutral ka-ons. The K0 consists of a down quark andan antistrange quark, whereas the anti-K0

consists of an antidown quark and astrange quark. Because CP transposesquarks and antiquarks, it would turn eachkaon into the other instead of leaving itunchanged. Therefore, neither of thesekaons has a definite CP number. Theoristscan, however, construct a pair of kaonswith definite CP numbers by superposingthe wave functions for K0 and anti-K0. Ac-cording to the rules of quantum mechan-ics, these mixtures correspond to real par-

ticles and have definite mass and lifetime.The conservation of CP number

would explain an odd detail: the two“combination” kaons, though apparent-ly similar, differ in their life spans by a fac-tor of about 500 [see illustration on page67]. The kaon with CP number +1 canchange to two pions, a state that has thesame CP number. This decay proceedsrapidly because the kaon is massiveenough to yield two pions readily. But thekaon with CP number –1 can decay onlyto another state with CP number –1: threepions. This latter breakdown takes time,because the kaon has barely enough massto generate three pions. So when physi-cists found a long-lived kaon in addition

to a short-lived one, they acquired strongevidence that the combination kaonsobeyed CP symmetry.

This tidy picture was shattered in1964, when in a groundbreaking experi-ment at Brookhaven National Laborato-ry on Long Island, James Christenson,James Cronin, Val Fitch and René Turlayobserved that about one out of every 500of the long-lived kaons (those with CPnumber –1) decays into two pions. If CPwere an exact symmetry of nature, itwould forbid such a decay. Few experi-ments in particle physics have produced aresult as surprising as this one. Theoristsfound it hard to see why CP symmetryshould be broken at all and even harder


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SYMMETRIES ARE VITAL to the study of physics, and fewsymmetries are more intriguing than the combination of chargeand parity. Charge reversal gives the opposite sign to quantumnumbers such as electric charge, changing a particle to itsantiparticle. Parity reversal reflects an object and also rotates it by180 degrees (equivalent to changing the arrow on all vectorsassociated with the object).

The laws of classical mechanics and electromagnetism are

invariant under either of these operations, as are the stronginteractions of the Standard Model. The weak interactions,however, are changed by the reversal of either charge or parity.

For many years, it appeared that parity and charge flipped insuccession (“charge parity”) were invariant even for weakinteractions. Experiments in 1964 shattered this illusion, posingthe puzzle of why nature looks different when reflected in thecharge-parity mirror. —H.R.Q. and M.S.W.

PARITY

CHARGE

CHARGE PARITY

Left-handedneutrinomoving right

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moving left

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REVERSAL OF CHARGE AND PARITY

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PARITY

HELEN R. QUINN and MICHAEL S. WITHERELL bring complementary skills to the study ofcharge-parity violation. Quinn is a theorist whose contributions include a demonstration ofhow the strong, weak and electromagnetic forces can become unified at high energies, as wellas an explanation of why strong interactions conserve CP symmetry. She is currently involvedin designing tests of the Standard Model being carried out at the B factories and has beena staff scientist at the Stanford Linear Accelerator Center since 1976. Witherell is an ex-perimenter who led a Fermilab effort to study the decays of charm mesons, for which he ob-tained an award from the American Physical Society in 1990. He was instrumental in help-ing to build the silicon vertex detector for the BABAR experiment. He has been director ofFermilab since 1999 and was elected to the National Academy of Sciences in 1998.

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to understand why any imperfectionshould be so small.

In 1972 Makoto Kobayashi and To-shihide Maskawa of Nagoya Universityin Japan showed that charge parity couldbe violated within the Standard Model ifthree or more generations of quarks exist.As it happened, only two generations ofquarks—the first, containing the up anddown, and the second, with the strangeand charm—were known at the time. Sothis explanation began to gain currencyonly when Martin L. Perl and others atthe Stanford Linear Accelerator Center(SLAC) spied τ (tau) leptons, the first par-ticles of the third generation, in 1975.Two years later experimenters at FermiNational Accelerator Laboratory inBatavia, Ill., found the bottom quark. Butonly in 1995, when the top quark wasnailed down, also at Fermilab, was thethird generation completed.

Skewing the UniverseIT IS IMAGINABLE that the universewas born skewed—that is, having un-equal numbers of particles and antiparti-cles. Such an initial imbalance, however,would be quickly eliminated if the earlyuniverse contained any processes thatcould change baryon number—the num-ber of matter particles minus the numberof antimatter particles. (In extensions ofthe Standard Model called Grand UnifiedTheories, such processes would have beenvery common soon after the big bang.)Theorists prefer the alternative scenario,in which particles and antiparticles wereequally numerous in the early universe,but the former came to dominate as theuniverse cooled.

Soviet physicist (and dissident) An-drei Sakharov pointed out three condi-tions necessary for this asymmetry to de-velop. First, processes that do not con-serve baryon number must exist. Second,during the expansion there must be somestage when the universe is not in thermalequilibrium. (When in thermal equilibri-um, all states of equal energy containequal populations of particles, and be-

cause particles and antiparticles haveequal mass or energy, they would be gen-erated at the same rate.) Third, CP sym-metry—essentially, the symmetry be-tween matter and antimatter—must beviolated. Otherwise any process thatchanges the amount of matter would bebalanced by a similar effect for antimatter.

The prevailing theory holds that whenthe universe was born, the quantum fieldassociated with the Higgs particle waseverywhere zero. Then, somewhere in theuniverse, a bubble developed, inside whichthe Higgs field assumed its current nonze-ro value. Outside the bubble, particlesand antiparticles had no mass; once in-side, however, they interacted with theHiggs field to acquire mass. But as the

bubble grew, particles and antiparticleswere swept through its surface at unequalrates because of CP violation. Any imbal-ances between matter and antimatter thuscreated outside the bubble were quicklycorrected by processes that changed bary-on number.

Such processes were extremely rareinside the bubble, however, so the imbal-ance was frozen in. By the time the bub-ble had expanded to occupy the entireuniverse, it contained more particles thanantiparticles. Eventually the universecooled to a point at which particles andantiparticles could no longer be generat-ed in collisions but would annihilatewhen they found one another.

Unfortunately, when theorists calcu-

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w w w . s c i a m . c o m COPYRIGHT 2003 SCIENTIFIC AMERICAN, INC.

late how much of an imbalance betweenmatter and antimatter this mechanism cancreate, it comes out too small—by ordersof magnitude. This failure suggests thatthere must be other ways in which CPsymmetry breaks down and hence thatthe Standard Model may be incomplete.

A fruitful place to search for more vi-olations is most likely among the Bmesons. The Standard Model predicts thevarious decays of the B0 and the anti-B0

to be highly asymmetric. A B0 contains adown quark bound to an antibottomquark, whereas the anti-B0 consists of anantidown quark and a bottom quark. TheB mesons behave much like the kaons dis-cussed earlier: the observed B mesonsconsist of mixtures of the B0 and anti-B0.

Consider the evolution of a B0 mesonproduced at a certain instant. Some timelater an observer has a certain probabili-ty of finding the same particle and also offinding its antiparticle. This peculiar me-son state, oscillating between a givenquark-antiquark combination and its an-tiparticle, is a remarkable illustration ofquantum mechanics at work.

The Bottom LineTO STUDY CP violation, experimentersneed to study decays of B0 into those finalstates that have a definite CP number.Such decays should proceed at a differentrate for a particle that is initially B0 com-

pared with one that is initially anti-B0.This difference will indicate the extent ofCP violation in the system. But ratherthan resulting in the one-in-1,000 effectseen in K0 decays, the predicted asymme-try for B0 decays grows so large that onedecay rate can become several times larg-er than the other.

Models other than the Standard oftenhave additional sources of CP violation—

sometimes involving extra Higgs parti-cles—in general offering any value for im-balances in B0 decays. Thus, measuringthe pattern of asymmetries will provide aclear test of the predictions.

When the bottom quark was discov-ered, its mass was measured at aroundfive giga-electron-volts (GeV), or aboutfive times the mass of a proton. Theoristscalculated that it would take a little morethan 10 GeV of energy to produce two Bmesons (because the added down or anti-down quarks are very light). In the early1980s at Cornell University, operators ofan electron-positron collider—which ac-celerates electrons and positrons intohead-on collisions—tuned it so that anelectron-positron pair would release anenergy of 10.58 GeV on annihilating. Ashad been predicted, this burst of energypreferentially converts to B mesons, pro-viding a rich source of the particles.About one in four annihilations results ina B meson and its antiparticle, leaving be-

hind no other particles in the aftermath.At SLAC in 1983 experimenters

found an unexpectedly long lifetime,about 1.5 picoseconds, for the B meson.The extended life improved the chancesthat a B0 would turn into an anti-B0 be-fore decaying, making CP-violating asym-metries easier to observe. Furthermore, in1987 experimenters at the Electron Syn-chrotron Laboratory (DESY) in Ham-burg, Germany, measured this “mixing”probability at 16 percent, making it like-ly that the asymmetries would be far larg-er than those for the K0. Still, these largeasymmetries occur in relatively rare de-cays of the B mesons. For a true study ofCP violation, a great number of B mesonswould be needed.

In 1988 at a workshop in Snowmass,Colo., the major topic of interest was theHiggs particle. A group of participantsalso discussed CP violation, especially inB mesons, and determined that a favor-able way to study the B mesons would bewith an electron-positron collider tunedto 10.58 GeV, in which the electron andpositron beams had different energies.This rather unusual feature would facili-tate the measurement of a B meson’s lifespan. Experimenters identify the point ofbirth and the point of death (that is, de-cay) of a B meson from traces of particlesin the detector. Dividing the distance be-tween these two points by the calculatedvelocity of the meson yields its life span.But an ordinary electron-positron collid-er at 10.58 GeV produces two B mesonsthat are almost at rest; the small distanc-es they move are hard to measure.

Pier Oddone of Lawrence BerkeleyNational Laboratory had pointed outthat if the electrons and positrons havedifferent energies, the B0 mesons that areproduced move faster. For instance, if theelectron beam has an energy of 9.0 GeVand the positron beam an energy of 3.1GeV, the B0 mesons move at half thespeed of light, traveling about 250 mi-crons (about one hundredth of an inch)


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COMPOSITE PARTICLES are either baryons (such as the proton and the neutron), made up of threequarks, or mesons, made up of one quark and one antiquark. The most common meson is a pion,containing up and down quarks and antiquarks. K mesons and B mesons, important to the study ofcharge-parity violation, contain strange and bottom quarks (or antiquarks), respectively.

Experimenters will identify almost every particleemerging from the decays of B mesons.


before they decay. Such a distance canyield a reasonably accurate measure ofthe lifetime.

An accelerator with two separaterings delivering different energies to theelectrons and positrons would fit the task.Each ring would have to deliver intensebeams of particles, obtaining a high rateof collisions. Such a machine came to becalled an asymmetric B factory: asym-metric because of the different beam en-ergies, and B factory because of the largenumbers of B mesons it would produce.

Teams at several laboratories devel-oped designs that could generate about30 million pairs of B mesons a year. In1993 the U.S. Department of Energy andthe Japanese agency Monbusho approvedtwo proposals for construction: one atSLAC in California and the other at KEK,the High Energy Accelerator Research Or-ganization in Tsukuba, Japan. The SLACproject uses the existing linear tunnel toaccelerate the positrons and electrons.These are then circulated in separate ringsconstructed in a 25-year-old tunnel andset to collide at a point of crossing. Theaccelerator construction cost $177 mil-lion. The Japanese project also employsextant tunnels—those that previouslyhoused the Tristan collider.

Physicists and engineers are operatinga large experiment that can identify therare decays of a B meson and measuretheir positions to within the requisite 80microns. This accuracy is obtained by us-ing the silicon microstrip technology thathelped to unearth the top quark [see “TheDiscovery of the Top Quark,” by TonyM. Liss and Paul L. Tipton; ScientificAmerican, September 1997]. Experi-menters aim to identify almost every par-ticle that emerges from the decays of theB mesons in order to isolate the rareevents that shed light on charge-parityquestions.

In the BABAR detector at SLAC, thesilicon microstrip is the innermost layer,forming a cylinder roughly 30 centimetersin diameter and 60 centimeters long. Out-er layers measure energy, velocity and pen-etration power for each particle created,allowing physicists to reconstruct the orig-inal events. More than 500 participants—

including both of us—from 72 institu-

tions in nine nations built the detector andshared its cost of $110 million. (It was, infact, to facilitate international collabora-tions of this kind that the World WideWeb was invented at CERN.) The BELLEcollaboration established to build theJapanese facility is also international inscope, with members from 10 countries.Both B factories were completed in 1999.

Other kinds of violations of chargeparity, less predictable than the quantum-mechanical mixing, should also occur inB decays. The Cornell collider and detec-tor have been upgraded to search for sucheffects. A number of experiments on Bphysics are either in planning stages or al-ready under way at proton acceleratorsaround the world. Both types of colliderswill provide crucial, and complementary,evidence on CP violation.

The B factories could definitively tellresearchers that the Standard Model con-cept works and then help to determine itsremaining parameters. Alternatively, theycould show that the model’s predictionscannot fit the data no matter what thechoice of parameters. Indeed, the resultscould rule out entire classes of models be-yond the Standard Model, thus helpingtheorists to zero in on a successor. And ifall goes well, we may even come to un-

derstand why our world is made exclu-sively of matter.

Authors’ note: Since this article waswritten, the two B factories have begunachieving better than expected data col-lection rates, and their researchers have re-ported many results. So far the StandardModel reigns supreme. One significantCP-violating asymmetry between B de-cays and anti-B decays has been observed;it is consistent with the predictions of thattheory. Many other measurements areunder way, but most results are not yet atthe level of precision needed to probe thetheory further. Like any good factory,these facilities must work hard for yearsto achieve their total expected output.

Exciting recent results in neutrinophysics have invalidated one statementwe made; these data indicate that neutri-nos have mass, which means that right-handed neutrinos must exist, along withthe left-handed ones. Likewise, theremust be left-handed antineutrinos. Themasses are tiny and do not affect any oth-er statements made in this article. Theydo, however, open up another possibleplace where CP violation can occur, inthe neutrino and the quark sectors. Physi-cists are just beginning to explore thesepossibilities.


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Distance or Time of Flight

Decay time of 0.5 × 10–7 second

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NEUTRAL KAONS, or K mesons, are observed to have two very different life spans. One type of kaondecays quickly into two pions, whereas the other decays slowly into three pions. The differentbehavior comes from the two kaons’ having opposite charge-parity symmetry. On rare occasions,however, the second type of kaon also decays to two pions, proving that charge parity can be violated.

The Character of Physical Law. Richard Feynman. MIT Press, 1965.

Fearful Symmetry: The Search for Beauty in Modern Physics. A. Zee. Macmillan Publishing, 1986.

The Physics of Time Reversal. Robert G. Sachs. University of Chicago Press, 1987.

The New Ambidextrous Universe: Symmetry and Asymmetry from Mirror Reflections toSuperstrings. Martin Gardner. W. H. Freeman and Company, 1990.



BY EDWARD KEARNS, TAKAAKI KAJITAAND YOJI TOTSUKA

MASSIVEDetecting

Neutrinos

68 U p d a t e d f r o m t h e A u g u s t 1 9 9 9 i s s u e

extremeexperiments


SUPER-KAMIOKANDE DETECTOR resides in an active zinc mineinside Mount Ikenoyama. Its stainless-steel tank contains

50,000 tons of ultrapure water so transparent that light canpass through 70 meters of it before losing half its intensity

(for a swimming pool that figure is a few meters). The water ismonitored by 11,000 photomultiplier tubes that cover the walls,

floor and ceiling. Each tube is a handblown, evacuated glass bulbhalf a meter in diameter. The tubes register conical flashes of

Cherenkov light, each of which signals a rare collision of a high-energy neutrino and an atomic nucleus in the water. Technicians

in inflatable rafts clean the bulbs while the tank is filled (right).

A giant detector in the heart of Mount Ikenoyama in Japan hasdemonstrated thatneutrinosmetamorphose in flight, stronglysuggesting that theseghostly particles have mass

One man’s trash is another man’s treasure. Fora physicist, the trash is “background”—someunwanted reaction, probably from a mundane

and well-understood process. The treasure is “signal”—a reaction that we hope will reveal new knowledgeabout the way the universe works. Case in point: overthe past two decades, several groups have been hunt-ing for the radioactive decay of the proton, an exceed-ingly rare signal (if it occurs at all) buried in a back-ground of reactions caused by elusive particles calledneutrinos. The proton, one of the main constituents ofthe atom, seems to be immortal. Its decay would be astrong indication of processes described by the GrandUnified Theories that many believe lie beyond the ex-tremely successful Standard Model of particle physics.Huge proton-decay detectors were placed deep under-ground, in mines or tunnels around the world, to es-cape the constant rain of particles called cosmic rays.But no matter how deep they went, these devices werestill exposed to penetrating neutrinos produced by thecosmic rays.

The first generation of proton-decay detectors, op-erating from 1980 to 1995, saw no signal, no signs ofproton decay—but along the waythe researchers found thatthe supposedly mundane

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neutrino background was not so easy tounderstand.

One such experiment, Kamiokande,was located in Kamioka, Japan, a miningtown about 250 kilometers (155 miles)from Tokyo (as the neutrino flies). Scien-tists there and at the IMB experiment, lo-cated in a salt mine near Cleveland, Ohio,used sensitive detectors to peer into ultra-pure water, waiting for the telltale flash ofa proton decaying.

Such an event would have been hid-den, like a needle in a small haystack,among about 1,000 similar flashes causedby neutrinos interacting with the water’satomic nuclei. Although no proton decaywas seen, the analysis of those 1,000 re-actions uncovered a real treasure—tanta-lizing evidence that the neutrinos were un-expectedly fickle, changing from one spe-cies to another in midflight. If true, thatphenomenon was just as exciting and the-ory-bending as proton decay.

Neutrinos are amazing, ghostly parti-cles. Every second, 60 billion of them,mostly from the sun, pass through eachsquare centimeter of your body (and ofeverything else). But because they seldominteract with other particles, generally all60 billion go through you without somuch as nudging a single atom. In fact,you could send a beam of such neutrinosthrough a light-year-thick block of lead,and most of them would emerge unscathedat the end. A detector as large as Kami-okande catches only a tiny fraction of theneutrinos that pass through it every year.

Neutrinos come in three flavors, cor-responding to their three charged partnersin the Standard Model: the electron andits heavier relatives, the muon and the tauparticle. An electron-neutrino interactingwith an atomic nucleus can produce anelectron; a muon-neutrino makes a muon;a tau-neutrino, a tau. For most of the sev-en decades since neutrinos were first

posited, physicists have assumed that theyare massless. But if they can change fromone flavor to another, quantum theory in-dicates that they most likely have mass.And in that case, these ethereal particlescould collectively outweigh all the stars inthe universe.

A Bigger Neutrino TrapAS IS SO OFTEN the case in particlephysics, the way to make progress is tobuild a bigger machine. Super-Kamio-kande, or Super-K for short, took the ba-sic design of Kamiokande and scaled it upby about a factor of 10 [see illustration onpreceding pages]. An array of light-sensi-tive detectors looks in toward the center of50,000 tons of water whose protons maydecay or get struck by a neutrino. In eithercase, the reaction creates particles that arespotted by means of a flash of blue lightknown as Cherenkov light, discovered byPavel A. Cherenkov in 1934. Much as anaircraft flying faster than the speed ofsound produces a shock wave of sound,an electrically charged particle (such as anelectron or a muon) emits Cherenkovlight when it exceeds the speed of light inthe medium in which it is moving. Thismotion does not violate Einstein’s theoryof relativity, for which the crucial veloci-ty is c, the speed of light in a vacuum. Inwater, light propagates 25 percent slow-er than c, but other highly energetic par-ticles can still travel almost as fast as c it-self. Cherenkov light is emitted in a conealong the flight path of such particles.

In Super-K, the charged particle gen-erally travels just a few meters and theCherenkov cone projects a ring of lightonto the wall of photon detectors [see il-


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CONES OF CHERENKOV LIGHT are emitted when high-energy neutrinos hit a nucleus and produce a charged particle. A muon-neutrino (top) creates a muon, which travels perhaps one meter andprojects a sharp ring of light onto the detectors. An electron, produced by an electron-neutrino(bottom), generates a small shower of electrons and positrons, each with its own Cherenkov cone,resulting in a fuzzy ring of light. Green dots indicate light detected in the same narrow time interval.

EDWARD KEARNS, TAKAAKI KAJITA andYOJI TOTSUKA are members of the Super-Kamiokande Collaboration. Kearns, pro-fessor of physics at Boston University,and Kajita, professor of physics at theUniversity of Tokyo, lead the analysisteam that studies proton decay and atmospheric neutrinos in the Super-Kamiokande data. Totsuka recently be-came the director of KEK, Japan’s na-tional particle physics laboratory, afterserving as spokesperson for Super-Ksince its inception.

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lustration on opposite page]. The size,shape and intensity of this ring reveal theproperties of the charged particle, whichin turn tell us about the neutrino that pro-duced it. We can distinguish the Cheren-kov patterns of electrons from those ofmuons: the electrons generate a shower ofparticles, leading to a fuzzy ring quite un-like the crisper circle from a muon. Fromthe Cherenkov light we also measure theenergy and direction of the electron or mu-on, which are decent approximations ofthe energy and direction of the neutrino.

Super-K cannot easily identify thethird type of neutrino, the tau-neutrino.Such a neutrino can interact with a nu-cleus and make a tau particle only if it hasenough energy. A muon is about 200times as heavy as an electron; the tau,about 3,500 times. The muon mass is wellwithin the range of atmospheric neutri-nos, but only a tiny fraction are at tau en-ergies, so most tau-neutrinos in the mixwill pass through Super-K undetected.

One of the most basic questions ex-perimenters ask is “How many?” Wehave built a beautiful detector to studyneutrinos, and the first task is simply tocount how many we see. The relatedquestion is “How many did we expect?”To answer that, we must analyze how theneutrinos are produced.

Super-K monitors atmospheric neu-trinos, which are born in the spray of par-ticles when a cosmic ray strikes the top ofour atmosphere. The incoming projectiles(called primary cosmic rays) are mostlyprotons, with a sprinkling of heavier nu-clei such as helium or iron. Each collisiongenerates a shower of secondary particles,mostly pions and muons, which decayduring their short flight through the air,creating neutrinos [see illustration atright]. We know roughly how many cos-mic rays hit the atmosphere each secondand roughly how many pions and muonsare made in each collision, so we can pre-dict how many neutrinos to expect.

Tricks with RatiosUNFORTUNATELY, this estimate isonly accurate to 25 percent, so we takeadvantage of a common trick: often theratio of two quantities can be better de-termined than either quantity alone. For


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HIGH-ENERGY COSMIC RAY striking a nucleus in theatmosphere (below) generates a shower of particles,mostly pions. The pion’s sequence of decays producestwo muon-neutrinos for every electron-neutrino. Equalneutrino rates should be seen from opposite directions(above) because both result from cosmic rays hittingthe atmosphere at the same zenith angle, θ. Both theseratios are spoiled when muon-neutrinos traveling longdistances have time to change flavor.


Super-K, the key is the sequential decayof a pion to a muon and a muon-neutri-no, followed by the muon’s decay to anelectron, an electron-neutrino and an-other muon-neutrino. No matter howmany cosmic rays are falling on theearth’s atmosphere, or how many pionsthey produce, there should be about twomuon-neutrinos for every electron-neu-trino. The calculation is more complicat-ed than that, but the final predicted ratiois accurate to 5 percent, providing amuch better benchmark.

After counting neutrinos for almosttwo years, the Super-K team has foundthat the ratio of muon-neutrinos to elec-tron-neutrinos is about 1.3 to 1 instead ofthe expected 2 to 1. Even if we stretch our

assumptions about the flux of neutrinos,how they interact with the nuclei and howour detector responds, we cannot explainsuch a low ratio—unless neutrinos arechanging from one type into another.

We can play the ratio trick again totest this surprising conclusion. The clueto our second ratio is to ask how manyneutrinos should arrive from each possi-ble direction. Primary cosmic rays fall onthe earth’s atmosphere almost equallyfrom all directions, with only two effectsspoiling the uniformity. First, the earth’smagnetic field deflects some cosmic rays,especially the low-energy ones, skewingthe pattern of arrival directions. Second,cosmic rays that skim the earth at a tan-gent make neutrino showers that do not

descend deep into the atmosphere, andthese can develop differently from thosethat plunge straight in from above.

But geometry saves us: if we “look”up into the sky at some angle from thevertical and then down into the groundat the same angle, we should “see” thesame number of neutrinos coming fromeach direction. Both sets of neutrinos areproduced by cosmic rays hitting the at-mosphere at the same angle; it is just thatin one case the collisions happen over-head and in the other they are partwayaround the world. To use this fact, we se-lect neutrino events of sufficiently highenergy (so their parent cosmic ray wasnot deflected by the earth’s magneticfield) and then divide the number of neu-


0% tau-neutrino

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100% muon-neutrino

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Muon

Muon-neutrino created inthe upper atmosphere

Two wave packets of differentmass travel at different velocities

Interference pattern of wave packets determines probability of the neutrino flavor

Which flavor isdetected depends

on the interference

Pion(decays)

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Not enough energy

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WHEN A PION DECAYS (top left), it produces a neutrino.Described quantum-mechanically, the neutrino is apparentlya superposition of two wave packets of different mass (purpleand green). The wave packets propagate at different speeds,with the lighter wave packet getting ahead of the heavier one.As this proceeds, the waves interfere, and the interferencepattern controls what flavor neutrino—muon (red) or tau(blue)—is most likely to be detected at any point along theflight path (bottom). Like all quantum effects, this is a game of

chance, with the chances heavily favoring a muon-neutrinoclose to where it was produced. But the probabilities oscillateback and forth, favoring the tau-neutrino at just the rightdistance and returning to favor the muon-neutrino farther on.When the neutrino finally interacts in the detector (top right),the quantum dice are rolled. If the outcome is muon-neutrino, a muon is produced. If chance favors the tau-neutrino, and theneutrino does not have enough energy to create a tau particle,Super-K detects nothing. —E.K., T.K. and Y.T.

1956

Frederick Reines (center) and Clyde Cowen first detect the neutrino using the Savannah River nuclear reactor.

1962At Brookhaven, the first accelerator beam of neutrinos proves the distinction between electron-neutrinos and muon-neutrinos.

1969

Raymond Davis, Jr., first measures neutrinos from the sun, using 600 tons of cleaning fluid in a mine in Homestake, S.D.

1930

Wolfgang Pauli rescues conservation of energy by hypothesizing an unseen particle that takes away energy missingfrom some radioactive decays.

1933Enrico Fermi formulates the theory of beta-decay incorporating Pauli's particle, now called the neutrino (“little neutral one” in Italian).

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HOW QUANTUM WAVES MAKE A NEUTRINO OSCILLATE


trinos going up by the number goingdown. This ratio should be exactly 1 ifnone of the neutrinos are changing flavor.

We saw equal numbers of high-energyelectron-neutrinos going up and goingdown, as expected, but only half as manyupward muon-neutrinos as downwardones. This finding is the second indicationthat neutrinos are changing identity.Moreover, it provides a clue to the meta-morphosis. The upward muon-neutrinoscannot be turning into electron-neutrinos,because there is no excess of upward elec-tron-neutrinos. That leaves the tau-neu-trino. The muon-neutrinos that becometau-neutrinos pass through Super-K with-out interaction, without detection.

Fickle FlavorTHE ABOVE TWO RATIOS are goodevidence that muon-neutrinos are trans-forming into tau-neutrinos, but whyshould neutrinos switch flavor at all?Quantum physics describes a particlemoving through space by a wave: in addi-tion to properties such as mass and charge,the particle has a wavelength, can diffract,and so on. Furthermore, a particle can bethe superposition of two waves. Nowsuppose that the two waves correspond toslightly different masses. Then, as thewaves travel along, the lighter wave getsahead of the heavier one, and the wavesinterfere in a way that fluctuates along theparticle’s trajectory [see box on oppositepage]. This interference has a musicalanalogue: the beats that occur when twonotes are almost but not exactly the same.

In music this effect makes the volumeoscillate; in quantum physics what oscil-lates is the probability of detecting onetype of neutrino or another. At the out-set the neutrino appears as a muon-neu-

trino with a probability of 100 percent.After traveling a certain distance, it lookslike a tau-neutrino with 100 percent prob-ability. At other positions, it could be ei-ther a muon-neutrino or a tau-neutrino.

This oscillation sounds like bizarre be-havior for a particle, but another familiarparticle performs similar contortions: thephoton, the particle of light. Light can oc-cur in a variety of polarizations, includingvertical, horizontal, left circular and rightcircular. These do not have differentmasses (all photons are massless), but incertain optically active materials, lightwith left circular polarization movesfaster than right circular light. A photonwith vertical polarization is actually a su-perposition of these two alternatives, and

when it is traversing an optically activematerial its polarization will rotate (thatis, oscillate) from vertical to horizontaland so on, as its two circular componentsgo in and out of sync.

For neutrino oscillations of the typewe see at Super-K, no “optically active”material is needed; a sufficient mass dif-ference between the two neutrino com-ponents will cause flavor oscillationswhether the neutrino is passing throughair, solid rock or pure vacuum. When aneutrino arrives at Super-K, the amountit has oscillated depends on its energy andthe distance it has traveled. For down-ward muon-neutrinos, which have trav-eled at most a few dozen kilometers, onlya small fraction of an oscillation cycle has


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Arrival Angle and Distance Traveled by Neutrino

Prediction without neutrino oscillationPrediction with neutrino oscillationSuper-Kamiokande measurement

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NUMBER OF HIGH-ENERGY MUON-NEUTRINOS seen arriving on different trajectories at Super-K clearlymatches a prediction incorporating neutrino oscillations ( green) and does not match the no-oscillation prediction (blue). Upward-going neutrinos (plotted toward left of graph) have traveled farenough for half of them to change flavor and escape detection.

Neutrino astronomy: the IMB and Kamiokande proton-decay experiments detect 19 neutrinos from Supernova 1987A in the Large Magellanic Cloud.

1989The Z decay rate is precisely measured at SLAC and CERN, showing there are only three active neutrino generations.

1998

Super-K assembles evidence of neutrino oscillation using atmospheric neutrinos.

1987

0

picture of SNO detector, or the sun or...

2000 2001

Tau-neutrino events are detected at Fermilab, completing the distinction of neutrinos by flavor begun in 1962.

The solar neutrino puzzle is solved, with key evidence from the Sudbury Neutrino Observatory experiment in Ontario.

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taken place, so the neutrinos’ flavor isslightly shifted, and we are nearly certainto detect their original muon-neutrino fla-vor. The upward muon-neutrinos, pro-duced thousands of kilometers away,have gone through so many oscillationsthat on average only half of them can bedetected as muon-neutrinos. The otherhalf pass through Super-K as undetectabletau-neutrinos.

This description is just a rough pic-ture, but the arguments based on the ra-tio of flavors and the up/down event rateare so compelling that neutrino oscilla-tion is now widely accepted as the mostlikely explanation for our data. We havealso done more detailed studies of howthe number of muon-neutrinos varies ac-cording to the neutrino energy and the ar-rival angle. We compare the measurednumber against what is expected for awide array of possible oscillation scenar-ios (including no oscillations). The datalook quite unlike the no-oscillation ex-pectation but match well with neutrinooscillation for certain values of the massdifference and other physical parameters[see illustration on preceding page].

With about 5,000 events from our firsttwo years of experimentation, we wereable to eliminate any speculation that theanomalous numbers of atmospheric neu-trinos could be just a statistical fluke. Butit is still important to confirm the effect bylooking for the same muon-neutrino os-cillation with other experiments or tech-niques. Detectors in Minnesota and Italyhave provided some verification, but be-cause they have measured fewer eventsthey do not offer the same certainty.

Corroborating EvidenceFURTHER SUPPORT comes from stud-ies of a different atmospheric neutrino in-teraction: collisions with nuclei in therock around our detector. Electron-neu-trinos again produce electrons and subse-quent showers of particles, but these areabsorbed in the rock and never reach Su-per-K’s cavern. High-energy muon-neu-

trinos make high-energy muons, whichcan travel through many meters of rockand enter our detector. We count suchmuons from upward-traveling neutri-nos—downward muons are masked bythe background of cosmic-ray muonsthat penetrate Mount Ikenoyama.

We can count upward-traveling mu-ons arriving on trajectories that rangefrom directly up to nearly horizontal.These paths correspond to neutrino trav-el distances (from production in the atmo-sphere to the creation of a muon near Su-per-K) as short as 500 kilometers (the dis-tance to the edge of the atmosphere whenlooking horizontally) and as long as13,000 kilometers (the diameter of theearth, looking straight down). We findthat the numbers of muon-neutrinos oflower energy that travel a long distanceare more depleted than higher-energymuon-neutrinos that travel a short dis-tance. This behavior is exactly what weexpect from oscillations, and carefulanalysis produces neutrino parameterssimilar to those from our first study.

If we consider just the three knownneutrinos, our data tell us that muon-neu-trinos are changing into tau-neutrinos.Quantum theory says that the underlyingcause of the oscillation is almost certain-ly that these neutrinos have mass—al-though it has been assumed for 70 yearsthat they do not. (The box on the oppo-site page mentions some other scenarios.)

Unfortunately, quantum theory alsolimits our experiment to measuring onlythe difference in mass-squared betweenthe two neutrino components, because

that is what determines the oscillationwavelength. It is not sensitive to the massof either one alone. Super-K’s data give amass-squared difference somewhere be-tween 0.001 and 0.01 electron volt (eV)squared. Given the pattern of masses ofother known particles, it is likely that oneneutrino is much lighter than the other,which would mean that the mass of theheavier neutrino is in the range of 0.03 to0.1 eV. What are the implications?

First, giving neutrinos a mass does notwreck the Standard Model. The mis-match between the mass states that makeup each neutrino requires the introduc-tion of a set of so-called mixing parame-ters. A small amount of such mixing haslong been observed among quarks, butour data imply that neutrinos need amuch greater degree of mixing—an im-portant piece of information that any suc-cessful new theory must accommodate.

Second, 0.05 eV is still very close to


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Fermilab accelerator(Batavia, Ill.)

MINOS detector (Soudan, Minn.)

LONG-BASELINE neutrinooscillation experiments areplanned in Japan and the U.S.Beams of neutrinos fromaccelerators will be detectedhundreds of kilometersaway. The experimentsshould confirm theoscillation phenomenon andprecisely measure theconstants of nature thatcontrol it.

Neutrinos could account for a mass nearlyequal to that of all the stars combined.


zero, compared with other particles. (Thelightest of those is the electron, with a massof 511,000 eV.) So the long-held belief thatneutrinos have zero mass is understand-able. But theoreticians who wish to builda Grand Unified Theory, which would el-egantly combine all the forces except grav-ity at enormously high energies, also takenote of this relative lightness of neutrinos.They often employ a mathematical devicecalled the seesaw mechanism, which ac-tually predicts that such a small but nonze-ro neutrino mass is natural. Here the massof some extremely heavy particle, perhapsat the Grand Unified mass scale, providesthe leverage to separate the very light neu-trinos from the quarks and leptons thatare a billion to a trillion times heavier.

Another implication is that the neu-trino should be considered in the book-keeping of the mass of the universe. Forsome time, astronomers have been tryingto tabulate how much mass is found inluminous matter, such as stars, and in or-dinary matter that is difficult to see, suchas brown dwarfs or diffuse gas. The masscan also be measured indirectly from theorbital motion of galaxies and the rate ofexpansion of the universe. The direct ac-counting falls short of these indirect mea-sures by a factor of 20. The neutrino masssuggested by our result is too small to re-solve this mystery by itself. Nevertheless,neutrinos created during the big bang per-meate space and could account for a massnearly equal to the combined mass of allthe stars. They could have affected theformation of large astronomical struc-tures, such as galaxy clusters.

Finally, our data have an immediateimplication for two new experiments.Based on the earlier hints from smaller de-tectors, many physicists have decided tostop relying on the free but uncontrollableneutrinos from cosmic rays and insteadare creating them with high-energy accel-erators. Even so, the neutrinos must trav-el a long distance for the oscillation effectto be observed. So the neutrino beams areaimed at a detector hundreds of kilome-ters away. One detector, MINOS, is be-ing built in a mine in Soudan, Minn., tostudy neutrinos sent from the Fermilabaccelerator near Batavia, Ill., 730 kilome-ters away on the outskirts of Chicago.

Of course, a good atmospheric neu-trino detector is also a good acceleratorneutrino detector, so in Japan we are us-ing Super-K to monitor a beam of neutri-nos created at the KEK accelerator labo-ratory 250 kilometers away. Unlike at-mospheric neutrinos, the beam can beturned on and off and has a well-definedenergy and direction. Most important, wehave placed a detector similar to Super-K near the origin of the beam to charac-

terize the muon-neutrinos before they os-cillate. We are essentially using the ratio(again) of the counts near the source tothose far away to cancel uncertainty andverify the effect. Since 1999, neutrinosfrom the first long-distance artificial neu-trino beam have passed under the moun-tains of Japan, with 50,000 tons of Super-K capturing a small handful. Exactly howmany are being captured will be the nextchapter in this story.


PARTICLE PHYSICISTS have been busy sorting out other indications of neutrino mass.For more than 30 years, scientists have been capturing electron-neutrinos generatedby nuclear fusion processes in the sun. These experiments have always counted fewerneutrinos than the best models predict.

Super-K has also counted solar neutrinos and finds only about 50 percent of thenumber expected. If solar neutrinos are changing flavor, this deficit is understandable,because at solar energies Super-K responds to the electron flavor and mostly ignoresthose transformed into the muon or tau flavors. The Sudbury Neutrino Observatory(SNO) in Ontario, however, which uses 1,000 tons of heavy water, has recentlyachieved a breakthrough in proving this change. The heavy water allows SNO tomeasure the total number of neutrinos (electron, muon and tau) as well as the numberof electron-neutrinos alone, and it shows that the total is much greater. Theaccounting seems to balance.

It appears that the mass splitting associated with solar neutrinos is much smallerthan that for atmospheric neutrinos. This fits a picture in which the three flavors ofneutrinos are spread over three distinct neutrino masses. But the picture doesn’tallow for the hint of neutrino oscillation, suggesting much larger masses, detected atLos Alamos National Laboratory. Some exotic explanations are waiting in the wingswhile Fermilab checks this signature.

Physicists are also checking the theory that transforms solar neutrinos. In a cavernin the same zinc mine as Super-K, a detector has been built that uses 1,000 tons ofmineral oil doped with a chemical that emits light in response to the neutrino reaction.This detector counts electron-neutrinos from more than two dozen Japanese nuclearpower reactors, from 80 to 400 kilometers away. The results are being compared with aprecise model of how many neutrinos are expected from each reactor. This experimentshould pin down the detailed particle physics revealed by solar neutrinos.

Overall, our picture of neutrinos is just coming into focus. More clarity will rely on moreambitious projects. Later in this decade Super-K will be exposed to a beam of neutrinosfrom a much more intense accelerator being built near Japan’s Pacific coast. The goal is toverify that muon-neutrinos change flavor to tau- and electron-neutrinos in a proportionthat fits our newfound expectations. Follow-up measurements may reveal the role ofneutrinos in the matter-antimatter imbalance of the universe. Or we may be presentedwith new puzzles to solve. —E.K., T.K. and Y.T.

OTHER PUZZLES, OTHER POSSIBILITIES

The Search for Proton Decay. J. M. LoSecco, Frederick Reines and Daniel Sinclair in ScientificAmerican, Vol. 252, No. 6, pages 54–62; June 1985.The Elusive Neutrino: A Subatomic Detective Story. Nickolas Solomey. Scientific American Library,W. H. Freeman and Company, 1997.Official Super-Kamiokande Web site: www-sk.icrr.u-tokyo.ac.jp/doc/sk/K2K Long Baseline Neutrino Oscillation Experiment Web site: neutrino.kek.jp/Super-Kamiokande at Boston University Web site: hep.bu.edu/~superk/



TABLETOP LASER fires terawattpulses 10 times a second,striking a thin cloth in theforeground. The photograph is atriple exposure to accommodatethe range of intensities.

extremeexperiments


w w w . s c i a m . c o m U p d a t e d f r o m t h e M a y 2 0 0 2 i s s u e 77

Focusing light with the power of

1,000 HOOVER DAMSonto a point the size of

A CELL NUCLEUS accelerates

electrons to the speed of light in a

femtosecond

By Gérard A. Mourou and Donald Umstadter

EXTREMELIGHT



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Legend has it that Archimedes focused the sun’s rays with a gi-ant mirror to set the Roman fleet afire at Syracuse in 212 B.C.

Although that story is a myth, it is true that around 200 B.C.

another Greek, Diocles, invented the first ideal focusing op-tic, a parabolic mirror. Two millennia later, mirrors and quan-tum mechanics were put together to make the most versatileof high-intensity light sources: the laser.

The epitome of high-power lasers is Nova, which operatedat Lawrence Livermore National Laboratory from 1985 to1999. Named for the brilliance of an exploding star, Nova wasone of the largest lasers ever built. Ten parallel chains of laseramplifiers occupied a 90-meter enclosure; mirrors made from180-kilogram blocks of glass directed the beams to targets fornuclear fusion and other experiments. Nova was fired no morethan a few times each day to avoid overheating. Clearly, it mar-shaled a lot of energy to achieve its ultrahigh power.

Yet power is the rate at which energy is delivered, so an-other approach to ultrahigh power is to release a modestamount of energy in an extremely short time. Nova’s usualpulses were relatively long by the standards of today’s ultrafastlasers—three nanoseconds—and each one required kilojoulesof energy. By using pulses of one ten-thousandth their duration,

a new type of laser that fits on a tabletop can deliver power sim-ilar to Nova’s [see “Ultrashort-Pulse Lasers: Big Payoffs in aFlash,” by John-Mark Hopkins and Wilson Sibbett; Scientif-ic American, September 2000]. For example, an ultrahigh-power laser that delivers a mere joule in a pulse lasting 100 fem-toseconds (10–13 second) achieves 10 trillion watts (1013 W, or10 terawatts), more than the output of all the world’s powerplants combined.

These compact lasers can fire a hundred million shots a dayand can concentrate their power onto a spot the size of a micron,producing the highest light intensities on earth. Associated withthese gargantuan power densities are the largest electric fields everproduced, in the range of a trillion volts per centimeter. Such in-tense laser light interacting with matter re-creates the extremephysical conditions that can be found only in the cores of stars orin the vicinity of a black hole: the highest temperatures, 1010

kelvins; the largest magnetic fields, 109 gauss; and the largest ac-celeration of particles, 1025 times the earth’s gravity.

Costing $1 million instead of several hundred million dol-lars, these lasers are helping to bring “big science” back to stan-dard university laboratories and to countries with limited re-search budgets. Dozens of such systems have been built through-out the world in the past few years, for use in research in severalsubfields of physics, including nuclear physics, astrophysics,high-energy particle physics and general relativity. This newbreed of laser has already spawned applications, such as x-raylasers, ultracompact particle accelerators and precision medicalradiography. It also shows great promise for radiation thera-py and improvements in nuclear fusion power generation.

The TrickIN THE FIVE YEARS after the invention of the laser in 1960,tabletop lasers advanced in a series of technological leaps toreach a power of one gigawatt (109 W). For the next 20 years,progress was stymied and the maximum power of tabletoplaser systems did not grow. The sole way to increase power was

■ A method of laser amplification invented in the mid-1980shas enabled a new generation of tabletop lasers thatproduce very brief pulses of extremely intense light.

■ Light of such high intensity interacts with matter in newways, directly propelling electrons to nearly the speed oflight in femtoseconds. The lasers can accelerate particlesat 10,000 times the rate of standard accelerators.

■ Potential applications include high-resolution medicalimaging, inexpensive precision radiation therapy, nuclearfusion, and research in numerous subfields of physics.

Overview/Extreme Light

The dream of intensifying light is as old as civilization.


to build ever larger lasers. Trying to operate beyond the limit-ing intensity would create unwanted nonlinear effects in com-ponents of the laser, impairing the beam quality and even dam-aging the components. Only in 1985 was this optical damageproblem circumvented, with the introduction of chirped pulseamplification (CPA), a technique developed by the researchgroup led by one of us (Mourou). Tabletop laser powers thenleaped ahead by factors of 103 to 105.

“Chirping” a signal or a wave means stretching it in time. Inchirped pulse amplification, the first step is to produce a shortpulse with an oscillator and stretch it, usually 103 to 105 timesas long [see illustration below]. This operation decreases the in-tensity of the pulse by the same amount. Standard laser ampli-fication techniques can now be applied to this pulse. Finally, asturdy device, such as a pair of diffraction gratings in a vacuum,recompresses the pulse to its original duration—increasing itspower 103 to 105 times beyond the amplifier’s limit. A typicalexample would begin with a seed pulse lasting 100 femtosec-onds and having 0.2 nanojoule of energy. We stretch it by a fac-tor of 104 to a nanosecond (reducing its power from about twokilowatts to 0.2 watt) and amplify it by 10 orders of magnitude

to two joules and two gigawatts. Recompressing the pulse to100 femtoseconds increases the power to 20 terawatts. Withoutthis method, sending the original two-kilowatt pulse through atabletop amplifier would have destroyed the amplifier—unlesswe increased the amplifier’s cross-sectional area 104 times anddispersed the beam across it. The CPA technique makes it pos-sible to use conventional laser amplifiers and to stay below theonset of nonlinear effects.

Perfecting CPA was not as straightforward as it sounds.Typical devices used to stretch or compress pulses generally donot do so in an exactly linear fashion, and the result will bespoiled if the characteristics of the chirper and the compressorare not closely matched.

A further increase in light intensities has occurred in the pastfew years with the development of corrective optics that allowlaser beams to be focused onto much smaller spots. That ad-vance and further improvements in pulse compression have re-sulted in pulses that have the maximum possible intensity fora given energy of light.

These increases in power and intensity in the 1990s openedup a new regime of interactions between light and matter,

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CHIRPED PULSE AMPLIFICATION

THE KEY to tabletop ultrahigh-intensity lasers is a techniquecalled chirped pulseamplification. An initial shortlaser pulse is stretched out(“chirped”) by a factor ofabout 104, for instance, by apair of diffraction gratings. The stretched pulse’s intensityis low, allowing it to beamplified by a small laseramplifier. A second pair ofgratings recompresses thepulse, boosting it to 104 timesthe peak intensity that the amplifier could have withstood.

Short pulse

Amplifier

Stretched pulse

Grating pair: Pulse stretcher

Grating pair: Pulse compressor

Amplified short pulse

Amplifiedstretched pulse


Tabletop ultrahigh-intensity lasers are bringing “big science” back to standard university laboratories.


known as relativistic optics, in which the light accelerates elec-trons close to the speed of light. Prior to CPA, this regime couldbe reached only by very large and expensive laser systems.

Relativistic OpticsOPTICS IS THE STUDY of how electrons respond to light.That definition may not sound like what many people think ofas optics—light reflecting off mirrors or being refracted by thewater of a swimming pool. Yet all the optical properties of amaterial are a consequence of how light interacts with electronsin the material.

Light is a wave composed of coupled electric and magneticfields oscillating in synchrony at very high frequencies. The elec-tric and magnetic fields oscillate perpendicular to each other andperpendicular to the direction the light is traveling [see illustra-tion below]. When an electron encounters a light wave of ordi-nary power, the electric field of the wave exerts a force on the

electron and makes it oscillate. The electron oscillates parallelto the electric field and at the same frequency, but it does notnecessarily oscillate in phase with the light wave. Depending onhow the electron is bound to the atoms of the material, its os-cillations may lag behind or lead those of the light wave. Theamplitude and phase of these electron oscillations in turn de-termine how the light wave propagates through the material andthereby confer on the material its optical properties.

In classical optics the amplitudes are small enough that theelectrons’ oscillation velocities are always very small comparedwith the speed of light. With the advent of laser intensities above1018 watts per square centimeter, however, the electrons’ oscil-lation velocities approach the speed of light, and relativistic ef-fects fundamentally change the electrons’ response to the light.

First, a high velocity increases the mass of an electron, whichaffects the amplitude and phase of its oscillations. More impor-tant, the magnetic field of the light wave starts to play a role. A

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LIGHT INTERACTING WITH MATTER

RELATIVISTIC OPTICSFOR LIGHT of ordinary intensity (a), the light’selectric field (red waves) makes electronsoscillate at relatively low speeds. At extremelyhigh intensities (b), the electrons oscillate atnearly the speed of light, and the light’s magneticfield (blue waves) makes them fly forward withvery high momentum.

WAKE-FIELD ACCELERATIONHIGH-INTENSITY LIGHT striking a plasma (below)pushes the electrons to very high speeds, leavingthe heavier positive ions (green) behind andproducing a powerful electric field (red lines)between these separated charges. This separationof charges and the associated electric field trailsalong in the wake of the light and can accelerateother charged particles to very high energies.


Electricfield

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a

b

ULTRAHIGH-INTENSITY LASER PULSE (added in blue) focused on a helium gas jet by aparabolic mirror accelerates electrons from the gas to 60 million electron volts in onemillimeter. A fluorescent screen (upper left) detects the high-energy electron beam.


magnetic field exerts a force on an electric charge only when thecharge is moving. In the regime of classical optics the magnet-ic force is negligible. But for electron oscillation velocities nearthe speed of light, it curls the paths of the electrons and givesthem tremendous momentum in the direction of the light beam.This effect plays a central role in relativistic optics.

The interaction of light with atomic nuclei can usually beignored because protons are almost 2,000 times as massive aselectrons and therefore oscillate much less. But at high enoughintensities, the light starts moving protons around at relativis-tic velocities as well. That regime may be called nuclear opticsbecause of the great variety of nuclear processes, such as fusion,that can occur.

“0 to 60” (MeV) in a MillimeterTHE MOST OBVIOUS APPLICATION of the relativistic forceof an ultraintense laser beam is to accelerate particles. Charged-particle accelerators have numerous uses, ranging from televi-sion tubes to cancer therapy to the study of the fundamentalforces of the universe. What they all have in common is that theparticles, such as electrons or protons, are accelerated by elec-tric or magnetic fields. Although light waves in the regime ofclassical optics can have electric fields as strong as those nearbolts of lightning, these fields are not effective for acceleratingparticles on their own, because they oscillate transversely. Incontrast, when an ultraintense pulse of light strikes a plasma (agas of electrons and positive ions), it propels the electrons for-ward at close to the speed of light, as we described above.

That is not the end of the story. The plasma’s positive ions,being thousands of times heavier than the electrons, are left be-hind. This separation of positive and negative charges producesa large electric field, which can be used to accelerate other par-ticles. The region of high electric field travels through the plas-ma as a wave, trailing in the wake of the light pulse. Chargedparticles are accelerated to high energy in laser wake fields justas dolphins gain energy by swimming in phase with the waterwave in the wake of a ship. Such a laser wake-field acceleratorwas first proposed in 1979 by Toshiki Tajima and John M. Daw-son, both then at the University of California at Los Angeles.

The process of converting the oscillating electric field of thelight pulse into a wake field that points always in one directionis called rectification, by analogy with rectifiers in electronicsthat convert alternating current (AC) to direct current (DC).Conventional accelerators, such as the three-kilometer-long oneat the Stanford Linear Accelerator Center (SLAC), use metalcavities to rectify radio-frequency waves to repeatedly “kick”

charged particles along the beam line. (Radio waves are elec-tromagnetic waves just like light but having much lower fre-quencies and longer wavelengths.) The Stanford accelerator hasto be three kilometers long to achieve its target particle energiesbecause the accelerating field of each cavity is limited. The fieldcould be increased by using radio waves of shorter wavelengthand greater intensity, but both of these properties are limitedby the cavity: the cavity size limits the wavelength, and high in-tensities cause electronic breakdown (sparking) of the metalcavity walls. Laser wake-field accelerators avoid these limits byeliminating the cavity. With the highest-intensity pulses, parti-cles might be accelerated directly, the same way that relativis-tic electrons are generated by the beam, allowing the plasma tobe dispensed with.

In the past few years, laser-driven electron and proton ac-celerators have produced beams with energies greater than 50million electron volts (MeV), comparable to a single stage (a fewmeters long) of a conventional accelerator. The laser systemachieves the same energy in a millimeter.

Prompt acceleration with high gradients has advantages.For example, one of us (Umstadter) has demonstrated electronbeams of a few million electron volts whose “brightness” (inessence, the concentration of particles in the beam) exceeds thatof beams made by conventional accelerators, mainly becausethe charges bunched in one pulse of the beam have less time toblow it apart by its own electrostatic forces. In addition, re-searchers have shown that low-cost laser accelerators are suit-able for many of the same applications as conventional accel-erators, such as producing short-lived radioisotopes used inmedical diagnostics and generating neutron and positron beamsfor studies of materials.

The laser systems create beams that have a relatively broadspread of particle energies, however, which is undesirable forsome applications. Also, conventional systems routinely chaintogether numerous accelerator stages, as in SLAC’s three-kilo-meter collider and the seven-kilometer-circumference main ringof the Tevatron at Fermilab. Current research on laser accelera-


GÉRARD A. MOUROU and DONALD UMSTADTER were among thefounders of the National Science Foundation–sponsored Centerfor Ultrafast Optical Science at the University of Michigan at AnnArbor. Mourou is director of the center and professor of electricalengineering; Umstadter is associate professor of both nuclear andelectrical engineering. When they are not accelerating particleswith intense lasers, they can be found accelerating down skislopes to “ultrahigh” speeds.

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Small ultrahigh-power lasers might work like spark plugs, igniting thermonuclear fusion at power plants.


tor systems is concentrated on reducing the beam’s energy spreadand achieving multistaging to increase the beam’s energy. Re-searchers are also exploring the use of innovative waveguides toincrease the distance over which the wake field keeps accelerat-ing particles.

We don’t expect laser accelerators to replace conventionalaccelerators at high-energy particle physics facilities such as theTevatron. Rather they complement and augment present-daysystems and have characteristics that make them useful for spe-cific applications and new types of experiments. One such nichecould be the acceleration of unstable particles.

The Tevatron represents the high-energy frontier today: col-liding protons with energies at the TeV level. Its successor,CERN’s Large Hadron Collider, will also use protons. Such col-lisions are very complicated and messy because protons are ag-glomerations of strongly interacting particles called quarks andgluons. Electrons and positrons have a more elementary struc-ture than protons and consequently produce much “cleaner” col-lisions, which allow more detailed, higher-precision studies. Butaccelerating them runs into a problem: the lightweight electronsand positrons lose too much of their energy to so-called syn-chrotron radiation as they travel around the curves of a circu-lar accelerator.

One solution will be to accelerate muons, which are 200times as heavy as electrons and thereby suffer synchrotron loss-es a billionth the amount. Unfortunately, muons are unstable

and decay in just over two microseconds on average. High-in-tensity lasers could be used to accelerate muons very close to thespeed of light in a fraction of that fleeting lifetime. At that point,relativistic time dilation helps out, extending the muons’ lifetimein proportion to the energy achieved and providing more time fora conventional accelerator to take over. The benefit of promptlaser acceleration would be even greater for particles such as pi-ons, which decay in a mere 26 nanoseconds on average.

Another new type of particle physics experiment enabled byultrahigh-power lasers is the gamma-gamma collider. Gammarays are extremely high energy photons or, equivalently, ex-tremely high frequency light—beyond x-rays on the spectrum.A high-power laser beam colliding with a high-energy electronbeam produces a narrow beam of gamma rays. In essence, thelaser’s photons rebound off the electrons in a process calledCompton scattering. The energy of the gamma rays dependsmostly on the energy of the electron beam: a 250-giga-electron-volt (GeV) electron beam knocks the photons from around 1eV (visible light) to about 200 GeV.

When two such gamma-ray beams collide, the interactionsare even cleaner than electron-positron or muon-antimuon col-lisions. The process is the reverse of matter-antimatter annihi-lation, in which particles merge and become a flash of radia-tion: instead pairs of particles and antiparticles burst into lifeout of a clash of photons. Only with ultrahigh-intensity lasers,however, are there enough photons in each pulse to produce asignificant number of gamma-gamma collisions. In 1997 re-searchers from the University of Rochester, Princeton Universi-ty, the University of Tennessee and SLAC demonstrated a vari-ant of this system and produced electron-positron pairs by col-liding gamma rays and laser photons. Today every linear particlecollider has plans to conduct gamma-gamma experiments,which complement the research possible with the usual electron-positron collisions.

Finding and Curing CancerBY GENERATING HIGHLY PENETRATING radiation suchas x-rays or particle beams, laser-driven charged-particle ac-celerators may also be used for cancer diagnosis and therapy.X-rays, of course, have been a diagnostic workhorse for a cen-tury. Conventional x-ray tubes accelerate electrons in an elec-tric field that is set up between a cathode and an anode. Whenthey strike the anode, the electrons are violently decelerated,which produces copious x-ray emissions. The resolution is lim-ited by the size of the x-ray source, in this case the anode, whichis generally about 100 microns across. The smallest tumor de-tectable by such a system is about a millimeter in diameter.

An ultrahigh-intensity laser, however, can produce x-rayssimply by being focused onto an appropriate metal target. Thebeam accelerates electrons near the surface of the metal to highenergies. These electrons are decelerated by their passagethrough the volume of the metal, once again emitting copiousx-rays. Focusing the laser to a spot a few microns across makesan extremely small x-ray source, allowing detection of verysmall clumps of cancerous cells so that treatment can begin at


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RADIOGRAPH OF A RAT shows the very high resolution that can be achieved by using x-rays generated from a tiny spot of plasma at the focus of a tabletop ultrahigh-intensity laser.


a much earlier stage in a tumor’s development. In principle, res-olution of a micron—a little larger than the wavelength of thedriving laser—is possible. Research groups at Stanford Univer-sity, Lund University in Sweden and the National Institute ofScientific Research in Quebec have already demonstrated thesex-ray systems.

Precision delivery of energy is also of great importance forradiation therapy. The goal is to maximize the dose deliveredto the tumor while minimizing harm to surrounding healthy tis-sues. When treating tumors in such sensitive areas as the brainor the spinal cord, the ability to deposit controlled amounts ofenergy in small, distinct areas is critical. Particles such as pro-tons and carbon ions are particularly well suited to this task.Unlike electrons and photons, these heavier particles suffer onlyminimal lateral scattering, so a beam remains narrow. The par-ticles lose energy at a steady, very low rate along their track andthen dump most of their energy at the end of it. For a specificinitial energy, this dissipation occurs at a well-defined rangethrough the tissue. Consequently, such heavier ions have muchbetter accuracy than electrons and photons for delivering a doseto deep-seated tumors.

Clinical trials of particle-based therapy using proton andcarbon beams are under way in several countries. One of thechief obstacles to wide-scale use of the technology, however,is the high cost of conventional particle accelerators. For ex-ample, the Heavy Ion Medical Accelerator in Chiba, Japan, costalmost $300 million to build. It can treat only about 200 pa-tients a year, a small fraction of the cases that could benefit fromthis form of cancer therapy. At the present time, laser-drivenaccelerators are able to achieve ion energies that are about a fac-tor of five too low and have too great a spread of energies. Butif those two problems can be overcome, ion radiotherapy willbe possible at much lower cost and thus available to many morecancer patients.

Power for Fusion?A PULSE FROM AN ULTRAHIGH-INTENSITY laser deliv-ers as much power as all the world’s power generators. In thefuture, that equation may be turned around, with such lasersbecoming an essential component of nuclear fusion powerplants supplying some of the world’s power needs. Controllednuclear fusion for power generation has been pursued fordecades and has remained frustratingly out of reach. A meth-od that has gained favor in recent years is inertial-confinementfusion, in which capsules of fuel—such as mixtures of deuteri-

um and tritium (heavy isotopes of hydrogen)—are hit from allsides simultaneously by dozens or hundreds of intense laserpulses. The lasers compress and heat the capsules to the extremedensities and temperatures at which the deuterium and tritiumnuclei fuse together to form helium and release large amountsof energy. The huge Nova laser at Livermore was one of theleading experimental devices used in research toward that goal.

Tabletop ultrahigh-intensity lasers cannot supply enoughtotal energy to drive thermonuclear fusion, but in conjunctionwith their Nova-size cousins, they may bring the process muchcloser to economic and technical feasibility. Achieving the con-ditions needed to ignite fusion by compressing the capsules re-quires an extraordinarily symmetrical implosion process. Thetiniest imperfections lead to worthless fizzles. In the new tech-nique, proposed by researchers at Livermore, the large laserswill still do the hard work of compressing the fuel to high den-sity but do not have to achieve the full ignition temperature aswell. Instead, near the point of maximum density, an ultrashortpulse of ions accelerated by a compact, ultrahigh-power CPAlaser strikes the imploding capsule, playing a role like a sparkplug in an automobile engine: the pulse creates an intense hotspot, igniting a wave of fusion that burns across the rest of thepellet. This method should reduce the immensely difficult tech-nical requirements of igniting fusion by implosion alone, and itshould significantly increase the ratio of energy produced to en-ergy used.

Some of the fundamentals of the fast-ignition technique wererecently demonstrated by researchers from Rutherford Apple-ton Laboratory in Oxfordshire, England, and Osaka Universityin Japan. But as is always the case in fusion research, much moremust be accomplished to prove the method’s practicality for eco-nomical power generation. Whether or not that particular ap-plication becomes the stuff of legend, ultrahigh-intensity lighthas a future that is spectacular and diverse beyond the wildestdreams of Archimedes and Diocles.


Terawatt Lasers Produce Faster Electron Acceleration. D. Umstadter inLaser Focus World, pages 101–104; February 1996.Ultrahigh-Intensity Lasers: Physics of the Extreme on a Tabletop. G. A. Mourou, C.P.J. Barty and M. D. Perry in Physics Today, Vol. 51, No. 1, pages 22–28; January 1998.Review of Physics and Applications of Relativistic Plasmas Driven byUltra-Intense Lasers. D. Umstadter in Physics of Plasmas, Vol. 8, No. 5,pages 1774–1785; May 2001.High Field Science Research at the University of Michigan Center forUltrafast Optical Science: www.eecs.umich.edu/USL-HFS/


The lasers can produce x-rays that could detect very small clumps of cancerous cells, so treatment could begin earlier.


84 S C I E N T I F I C A M E R I C A N U p d a t e d f r o m t h e J a n u a r y 2 0 0 0 i s s u e

WORMHOLESThe construction of wormholes and warp drive

But the same laws of physics that allow this

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A WORMHOLE WOULD APPEARas a spherical opening to adistant part of the cosmos. In this doctored photograph ofTimes Square, the wormholeallows New Yorkers to walk tothe Sahara with a single step.Although such a wormholedoes not break any known laws of physics, it wouldrequire unrealistic amounts of negative energy.

exoticspaces



By Lawrence H. Ford and Thomas A. Roman

and WARP DRIVEwould require a very unusual form of energy. “negative energy” also appear to limit its behavior

ENERGY,


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Can a region of space contain less than nothing?


Common sense would say no; the most one could do is removeall matter and radiation and be left with a vacuum. But quan-tum physics has a proven ability to confound intuition, and thiscase is no exception. A region of space, it turns out, can containless than nothing. Its energy per unit volume—the energy den-sity—can be less than zero.

Needless to say, the implications are bizarre. According togeneral relativity, Einstein’s theory of gravity, the presence ofmatter and energy warps the geometric fabric of space and time.What we perceive as gravity is the spacetime distortion pro-duced by normal, positive energy or mass. But when negativeenergy or mass—so-called exotic matter—bends spacetime, allsorts of amazing phenomena might become possible: travers-able wormholes, which could act as tunnels to otherwise dis-tant parts of the universe; warp drive, which would allow forfaster-than-light travel; and time machines, which might per-mit journeys into the past. Negative energy could even be usedto make perpetual-motion machines or to destroy black holes.

For physicists, these ramifications set off alarm bells. The

potential paradoxes of backward time travel—such as killingyour grandfather before your father is conceived—have longbeen explored in science fiction, and the other consequencesof exotic matter are also problematic. They raise a question offundamental importance: Do the laws of physics that permitnegative energy place any limits on its behavior? We and oth-ers have discovered that nature imposes stringent constraintson the magnitude and duration of negative energy, which (un-fortunately, some would say) appear to render the constructionof wormholes and warp drives very unlikely.

Double NegativeBEFORE PROCEEDING, we should draw attention to whatnegative energy is not. It should not be confused with antimat-ter, which has positive energy. When an electron and its an-tiparticle, a positron, collide, they annihilate. The end productsare gamma rays, which carry positive energy. If antiparticleswere composed of negative energy, such an interaction wouldresult in a final energy of zero. One should also not confuse neg-ative energy with the energy associated with the cosmologicalconstant, postulated in inflationary models of the universe. Inthe latter case, there is negative pressure but positive energy.(Some authors call this exotic matter; we reserve that term fornegative energy densities.)

The concept of negative energy is not pure fantasy; someof its effects have even been produced in the laboratory. Theyarise from Heisenberg’s uncertainty principle, which requiresthat the energy density of any electric, magnetic or other fieldfluctuate randomly. Even when the energy density is zero on av-erage, as in a vacuum, it fluctuates. Thus, the quantum vacuumcan never remain empty in the classical sense of the term; it isa roiling sea of “virtual” particles spontaneously popping inand out of existence. In quantum theory, the usual notion ofzero energy corresponds to the vacuum with all these fluctua-

LAWRENCE H. FORD and THOMAS A. ROMAN have collaborated onnegative energy issues for more than a decade. Ford received hisPh.D. from Princeton University in 1974 under John Wheeler, oneof the founders of black hole physics. He is now professor ofphysics at Tufts University and works on problems in both gener-al relativity and quantum theory, with a special interest in quan-tum fluctuations. Roman received his Ph.D. in 1981 from SyracuseUniversity under Peter Bergmann, who collaborated with Albert Ein-stein on unified field theory. He is currently professor of physicsat Central Connecticut State University. His interests include theimplications of negative energy for a quantum theory of gravity.

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WAVES OF LIGHT ordinarily have a positive or zero energy density at differentpoints in space (top). But in a so-called squeezed state, the energy densityat a particular instant in time can become negative at some locations(bottom). To compensate, the peak positive density must increase.


tions. So if one can somehow contrive to dampen the undula-tions, the vacuum will have less energy than it normally does—

that is, less than zero energy.As an example, researchers in quantum optics have creat-

ed special states of fields in which destructive quantum inter-ference suppresses the vacuum fluctuations. These so-calledsqueezed vacuum states involve negative energy. More pre-cisely, they are associated with regions of alternating positiveand negative energy. The total energy averaged over all spaceremains positive; squeezing the vacuum creates negative ener-gy in one place at the price of extra positive energy elsewhere.A typical experiment involves laser beams passing through non-linear optical materials. The intense laser light induces the ma-terial to create pairs of light quanta, photons. These photonsalternately enhance and suppress the vacuum fluctuations, lead-ing to regions of positive and negative energy, respectively.

Another method for producing negative energy introducesgeometric boundaries into a space. In 1948 Dutch physicist Hen-drik B. G. Casimir showed that two uncharged parallel metalplates alter the vacuum fluctuations in such a way as to attracteach other. The energy density between the plates was later cal-culated to be negative. In effect, the plates reduce the fluctuationsin the gap between them; this creates negative energy and pres-sure, which pulls the plates together. The narrower the gap, themore negative the energy and pressure, and the stronger the at-tractive force. The Casimir effect has been measured by Steve K.Lamoreaux of Los Alamos National Laboratory and by UmarMohideen of the University of California at Riverside and his col-league Anushree Roy. Other groups have recently confirmedthese experiments and have even begun to explore the role of theeffect in nanotechnology. Similarly, in the 1970s Paul C. W.Davies and Stephen A. Fulling, then at King’s College at the Uni-versity of London, predicted that a moving boundary, such as amoving mirror, could produce a flux of negative energy.

For both the Casimir effect and squeezed states, researchershave measured only the indirect effects of negative energy. Di-rect detection is more difficult but might be possible using atom-ic spins, as Peter G. Grove, then at the British Home Office,Adrian C. Ottewill, then at the University of Oxford, and oneof us (Ford) suggested in 1992.

Gravity and LevityTHE CONCEPT OF NEGATIVE ENERGY arises in several ar-eas of modern physics. It has an intimate link with black holes.In 1974 Stephen W. Hawking of the University of Cambridgemade his famous prediction that black holes evaporate by emit-ting radiation [see “The Quantum Mechanics of Black Holes,”by Stephen W. Hawking; Scientific American, January1977]. A black hole radiates energy at a rate inversely propor-tional to the square of its mass. Although the evaporation rateis large only for subatomic-size black holes, it provides a cru-cial link between the laws of black holes and the laws of ther-modynamics. The Hawking radiation allows black holes tocome into thermal equilibrium with their environment.

At first glance, evaporation leads to a contradiction. The

black hole’s horizon is a one-way street; energy can only flowinward. So how can a black hole radiate energy outward? Be-cause energy must be conserved, the production of positive en-ergy—which distant observers see as the Hawking radiation—

is accompanied by a flow of negative energy into the hole. Herethe negative energy is produced by the extreme spacetime cur-vature near the hole, which disturbs the vacuum fluctuations.In this way, negative energy is required for the consistency ofthe unification of black hole physics with thermodynamics.

The black hole is not the sole curved region of spacetimewhere negative energy seems to play a role. Another is thewormhole—a hypothesized type of tunnel that connects one re-gion of space and time to another. Physicists used to think thatwormholes exist only on the very finest scales, bubbling in andout of existence like virtual particles.

But in the late 1980s various researchers—notably MichaelS. Morris and Kip S. Thorne, both of the California Institute ofTechnology, and Matt Visser of Washington University—foundthat certain wormholes could in fact be made large enough fora person or spaceship. Someone might enter the mouth of awormhole stationed on Earth, walk a short distance inside thewormhole and exit the other mouth in, say, the Andromedagalaxy. The catch is that traversable wormholes require nega-tive energy. Because negative energy is gravitationally repulsive,it would prevent the wormhole from collapsing.

For a wormhole to be traversable, it ought to (at bare mini-mum) allow signals, in the form of light rays, to pass throughit. Light rays entering one mouth of a wormhole are converging,but to emerge from the other mouth, they must defocus—in oth-er words, they must go from converging to diverging somewherein between [see illustration above]. This defocusing requires neg-ative energy. Whereas the curvature of space produced by the


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WORMHOLE ACTS AS A TUNNEL between two different locations in space.Light rays traveling from A to B can enter one mouth of the wormhole, passthrough the throat and exit the other mouth—a journey that would takemuch longer if they had to go the long way around. At the throat must benegative energy (blue), the gravitational field of which allows converginglight rays to begin diverging. (This diagram is a two-dimensionalrepresentation of three-dimensional space. The mouths and throat of thewormhole are actually spheres.) A wormhole could also connect twodifferent points in time (not shown here).

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attractive gravitational field of ordinary matter acts like a con-verging lens, negative energy acts like a diverging lens.

No Dilithium NeededSUCH SPACETIME CONTORTIONS would enable anotherstaple of science fiction as well: faster-than-light travel. In 1994Miguel Alcubierre Moya, then at the University of Wales inCardiff, discovered a solution to Einstein’s equations that hasmany of the desired features of warp drive. It describes a space-time bubble that transports a starship at arbitrarily high speedsrelative to observers outside the bubble. Calculations show thatnegative energy is required.

Warp drive might appear to violate Einstein’s special theo-ry of relativity. But special relativity says that you cannot out-run a light signal in a fair race in which you and the signal fol-low the same route. When spacetime is warped, it might be pos-sible to beat a light signal by taking a different route, a shortcut.The contraction of spacetime in front of the bubble and the ex-pansion behind it create such a shortcut [see illustration below].

One problem, pointed out by Sergei V. Krasnikov of the Cen-tral Astronomical Observatory in Pulkovo, Russia, is that the in-terior of the warp bubble is causally disconnected from its forwardedge. A starship captain on the inside cannot steer the bubble orturn it on or off; some external agency must set it up ahead of time.To get around this problem, Krasnikov proposed a “superlumi-

nal subway,” a tube of modified spacetime (not the same as awormhole) connecting Earth and a star. Within it, superluminaltravel in one direction is possible. During the outbound journeyat sublight speed, a spaceship crew would create such a tube. Onthe return, members could travel through it at warp speed. Likewarp bubbles, the subway involves negative energy. It has sincebeen shown by Ken D. Olum of Tufts University, by Visser, to-gether with Bruce Bassett of Oxford and Stefano Liberati of theInternational School for Advanced Studies in Trieste, Italy, andby Sijie Gao and Robert M. Wald of the University of Chicagothat any faster-than-light travel requires negative energy.

If one can construct wormholes or warp drives, time travelmight become possible. The passage of time is relative; it de-pends on the observer’s velocity. A person who leaves Earth ina spaceship, travels at near light speed and returns will haveaged less than someone who remains on Earth. If the travelermanages to outrun a light ray, perhaps by taking a shortcutthrough a wormhole or a warp bubble, he may return beforehe left. Morris, Thorne and Ulvi Yurtsever, then at Caltech,proposed a wormhole time machine in 1988, and their paperhas stimulated much research on time travel since. In 1992Hawking proved that any construction of a time machine in afinite region of spacetime inherently requires negative energy.

Negative energy is so strange that one might think it must vi-olate some law of physics. Before and after the creation of equal


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SPACETIME BUBBLE is the closest thatmodern physics comes to the “warpdrive” of science fiction. It can conveya starship at arbitrarily high speeds.Spacetime contracts at the front of thebubble, reducing the distance to thedestination, and expands at its rear,increasing the distance from the origin(arrows). The ship itself stands stillrelative to the space immediatelyaround it; crew members do notexperience any acceleration. Negativeenergy (blue) is required on the sidesof the bubble.

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amounts of negative and positive energy in previously emptyspace, the total energy is zero, so the law of conservation of en-ergy is obeyed. But there are many phenomena that conserve en-ergy yet never occur in the real world. A broken glass does notreassemble itself, and heat does not spontaneously flow from acolder to a hotter body. Such effects are forbidden by the secondlaw of thermodynamics. This general principle states that thedegree of disorder of a system—its entropy—cannot decrease onits own without an input of energy. Thus, a refrigerator, whichpumps heat from its cold interior to the warmer outside room,requires an external power source. Similarly, the second law alsoforbids the complete conversion of heat into work.

Negative energy potentially conflicts with the second law.Imagine an exotic laser, which creates a steady outgoing beamof negative energy. Conservation of energy requires that a by-product be a steady stream of positive energy. One could directthe negative energy beam off to some distant corner of the uni-verse while employing the positive energy to perform usefulwork. This seemingly inexhaustible energy supply could beused to make a perpetual-motion machine, thereby violatingthe second law. If the beam were directed at a glass of water, itcould cool the water while using the extracted positive energyto power a small motor—providing refrigeration with no needfor external power. These problems arise from the unrestrict-ed separation of negative and positive energy.

Unfettered negative energy would also have profound con-

sequences for black holes. When a black hole forms, generalrelativity predicts the formation of a singularity, a region wherethe gravitational field becomes infinitely strong. At this point,all known laws of physics are unable to say what happens next.This inability is a profound failure of the current mathematicaldescription of nature. So long as the singularity is hidden with-in an event horizon, however, the damage is limited. The de-scription of nature everywhere outside of the horizon is unaf-fected. For this reason, Roger Penrose of Oxford proposed thecosmic censorship hypothesis: there can be no naked singular-ities, unshielded by event horizons.

For special types of charged or rotating black holes—knownas extreme black holes—even a small increase in charge or spinor a decrease in mass could theoretically destroy the horizon andconvert the hole into a naked singularity. Attempts to charge upor spin up these black holes using ordinary matter seem to fail.One might instead envision producing a decrease in mass byshining a beam of negative energy down the hole, without al-tering its charge or spin, subverting cosmic censorship. Onemight create such a beam, for example, using a moving mirror.


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VIEW FROM THE BRIDGE of a faster-than-light starship as it heads in thedirection of the Little Dipper (above) looks nothing like the star streakstypically depicted in science fiction. As the velocity increases (right), starsahead of the ship (left column) appear ever closer to the direction of motionand turn bluer in color. Behind the ship (right column), stars shift closer toa position directly astern, redden and eventually disappear from view. Thelight from stars directly overhead or underneath remains unaffected.(Illustration based on calculations by Chad Clark, William A. Hiscock andShane L. Larson of Montana State University.)

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In principle, it would require only a tiny amount of negative en-ergy to produce a dramatic change in the state of an extremeblack hole. Therefore, this might be the scenario in which neg-ative energy is the most likely to produce macroscopic effects.

Not Separate and Not EqualFORTUNATELY (or not, depending on your point of view), al-though quantum theory allows the existence of negative ener-gy, it also appears to place strong restrictions—known as quan-tum inequalities—on its magnitude and duration. These in-equalities were first suggested by Ford in 1978. Over the pastdecade they have been proved and refined by us and others, in-cluding Éanna E. Flanagan of Cornell University, Michael J.Pfenning, then at Tufts, Christopher J. Fewster and Simon P.Eveson of the University of York in England, and Edward Teoof the National University of Singapore.

The inequalities bear some resemblance to the uncertainty

principle. They say that a beam of negative energy cannot be ar-bitrarily intense for an arbitrarily long time. The permissiblemagnitude of the negative energy is inversely related to its tem-poral or spatial extent. An intense pulse of negative energy canlast for a short time; a weak pulse can last longer. Furthermore,an initial negative energy pulse must be followed by a largerpulse of positive energy [see illustration below]. The larger themagnitude of the negative energy, the nearer its positive energycounterpart must be. These restrictions are independent of thedetails of how the negative energy is produced. One can thinkof negative energy as an energy loan. Just as a debt is negativemoney that has to be repaid, negative energy is an energy deficit.

In the Casimir effect, the negative energy density betweenthe plates can persist indefinitely, but large negative energy den-sities require a very small plate separation. The magnitude ofthe negative energy density is inversely proportional to thefourth power of the plate separation. Just as a pulse with a verynegative energy density is limited in time, very negative Casimirenergy density must be confined between closely spaced plates.According to the quantum inequalities, the energy density inthe gap can be made more negative than the Casimir value, butonly temporarily. In effect, the more one tries to depress the en-ergy density below the Casimir value, the shorter the time overwhich this situation can be maintained.

When applied to wormholes and warp drives, the quantuminequalities imply that such structures must be limited to sub-microscopic sizes or, if they are macroscopic, the negative ener-gy must be confined to incredibly thin bands. In 1996 weshowed that a submicroscopic wormhole would have a throatradius of no more than 10–32 meter. This is just slightly largerthan the Planck length, 10–35 meter, the smallest distance thathas meaning. We found that it is possible to model wormholesof macroscopic size but only at the price of confining the nega-tive energy to an extremely thin band around the throat. In onemodel, a throat radius of one meter requires the negative ener-gy to be a band no thicker than 10–21 meter, a millionth the sizeof a proton. Visser has estimated that the negative energy re-quired for this wormhole has a magnitude equivalent to the to-tal energy generated by 10 billion stars in one year. The situa-tion does not improve for larger wormholes. For the same mod-el, the maximum thickness of the negative energy band isproportional to the cube root of the throat radius. Even if thethroat radius is increased to one light-year, the negative energymust still be confined to a region smaller than a proton radius,and the total required increases linearly with the throat size.

It seems that wormhole engineers face daunting problems.They must find a mechanism for confining large amounts of neg-ative energy to extremely thin volumes. So-called cosmic strings,hypothesized in some cosmological theories, involve very largeenergy densities in long, narrow lines. But all known physicallyreasonable cosmic-string models have positive energy densities.

Warp drives are even more tightly constrained. In Alcu-bierre’s model, a warp bubble traveling at 10 times the speedof light must have a wall thickness of no more than 10–32 me-ter. A bubble large enough to enclose a starship 200 meters


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PULSES OF NEGATIVE ENERGY are permitted by quantum theory but onlyunder three conditions. First, the longer the pulse lasts, the weaker it mustbe (a, b). Second, a pulse of positive energy must follow. The magnitude ofthe positive pulse must exceed that of the initial negative one. Third, thelonger the time interval between the two pulses, the larger the positive onemust be—an effect known as quantum interest (c).


across would require a total amount of negative energy equalto 10 billion times the mass of the observable universe. Similarconstraints apply to Krasnikov’s superluminal subway. A mod-ification of Alcubierre’s model was constructed in 1999 byChris Van Den Broeck of the Catholic University of Louvain inBelgium. It requires much less negative energy but places thestarship in a curved spacetime bottle whose neck is about 10–32

meter across, a difficult feat. These results would seem to makeit rather unlikely that one could construct wormholes and warpdrives using negative energy generated by quantum effects.

Cosmic Flashing and Quantum InterestTHE QUANTUM INEQUALITIES prevent violations of the sec-ond law. If one tries to use a pulse of negative energy to cool ahot object, it will be quickly followed by a larger pulse of posi-tive energy, which reheats the object. A weak pulse of negativeenergy could remain separated from its positive counterpart fora longer time, but its effects would be indistinguishable from nor-mal thermal fluctuations. Attempts to capture or split off nega-tive energy from positive energy also appear to fail. One mightintercept an energy beam by, say, using a box with a shutter. Byclosing the shutter, one might hope to trap a pulse of negative en-ergy before the offsetting positive energy arrives. But the very actof closing the shutter creates an energy flux that cancels out thenegative energy it was designed to trap [see illustration at right].

We have shown that there are similar restrictions on violationsof cosmic censorship. A pulse of negative energy injected into acharged black hole might momentarily destroy the horizon, ex-posing the singularity within. But the pulse must be followed bya pulse of positive energy, which would convert the naked sin-gularity back into a black hole, a scenario we have dubbed cos-mic flashing. The best chance to observe cosmic flashing wouldbe to maximize the time separation between the negative andpositive energy, allowing the naked singularity to last as long aspossible. But then the magnitude of the negative energy pulsewould have to be very small, according to the quantum inequali-ties. The change in the mass of the black hole caused by the neg-ative energy pulse would get washed out by the normal quantumfluctuations in the hole’s mass, which are a natural consequenceof the uncertainty principle. The view of the naked singularitywould thus be blurred, so a distant observer could not unam-biguously verify that cosmic censorship had been violated.

Recently we, Frans Pretorius (then at the University of Vic-toria in British Columbia), and Fewster and Teo have all shownthat the quantum inequalities lead to even stronger bounds onnegative energy. The positive pulse that follows an initial negativepulse must do more than compensate for the negative pulse; itmust overcompensate. The overcompensation increases with thetime interval between the pulses. Therefore, the negative and pos-itive pulses can never be made to cancel exactly. The positive en-ergy must always dominate—an effect known as quantum in-terest. If negative energy is thought of as an energy loan, the loanmust be repaid with interest. The longer the loan period or thelarger the loan amount, the greater the interest. Furthermore,the larger the loan, the smaller the maximum allowed loan pe-

riod. Nature is a shrewd banker and always calls in its debts.The concept of negative energy touches on gravitation, quan-

tum theory and thermodynamics. The interweaving of all theseparts of physics illustrates the tight logical structure of the lawsof nature. Negative energy seems to be required to reconcileblack holes with thermodynamics. On the other hand, quantumphysics prevents unrestricted production of negative energy, aphenomenon that would violate the second law of thermody-namics. Whether these restrictions are also features of somedeeper underlying theory, such as quantum gravity, remains tobe seen. Nature no doubt has more surprises in store.


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Black Holes and Time Warps: Einstein’s Outrageous Legacy. Kip S. Thorne. W. W. Norton, 1994.

Quantum Field Theory Constrains Traversable Wormhole Geometries.L. H. Ford and T. A. Roman in Physical Review D, Vol. 53, No. 10, pages 5496–5507; May 15, 1996.

The Unphysical Nature of Warp Drive. M. J. Pfenning and L. H. Ford inClassical and Quantum Gravity, Vol. 14, No. 7, pages 1743–1751; July 1997. Available at xxx.lanl.gov/abs/gr-qc/9702026

Time Machines: Time Travel in Physics, Metaphysics, and ScienceFiction. Second edition. Paul J. Nahin. AIP Press, Springer-Verlag, 1999.

The Quantum Interest Conjecture. L. H. Ford and T. A. Roman in PhysicalReview D, Vol. 60, No. 10, Article No. 104018; November 15, 1999.


ATTEMPT TO CIRCUMVENT the quantum laws that govern negative energyinevitably ends in disappointment. The experimenter intends to detach anegative energy pulse from its compensating positive energy pulse. As thepulses approach a box (a), the experimenter tries to isolate the negativeone by closing the lid after it has entered (b). Yet the very act of closing thelid creates a second positive energy pulse inside the box (c).

POSITIVE ENERGY

PULSE

NEGATIVE ENERGY PULSE

b

c POSITIVE ENERGY PULSE

CREATED BY SHUTTER

a


Back in December 1959, futureNobel laureate Richard Feynman gave avisionary and now oft-quoted talk enti-tled “There’s Plenty of Room at the Bot-tom.” The occasion was an AmericanPhysical Society meeting at the Califor-nia Institute of Technology, Feynman’sintellectual home then and mine today.Although he didn’t intend it, Feynman’s7,000 words were a defining moment innanotechnology, long before anything“nano” appeared on the horizon.

“What I want to talk about,” hesaid, “is the problem of manipulatingand controlling things on a smallscale. . . . What I have demonstrated isthat there is room—that you can de-crease the size of things in a practicalway. I now want to show that there is

plenty of room. I will not now discusshow we are going to do it, but only whatis possible in principle.. . .We are not do-ing it simply because we haven’t yet got-ten around to it.”

The breadth of Feynman’s vision isstaggering. In that lecture 44 years agohe anticipated a spectrum of scientificand technical fields that are now well es-tablished, among them electron-beamand ion-beam fabrication, molecular-beam epitaxy, nanoimprint lithography,projection electron microscopy, atom-by-atom manipulation, quantum-effectelectronics, spin electronics (also calledspintronics) and microelectromechanicalsystems (MEMS). The lecture also pro-jected what has been called the “magic”Feynman brought to everything he turned

his singular intellect toward. Indeed, ithas profoundly inspired my two decadesof research on physics at the nanoscale.

Today there is a nanotechnologygold rush. Nearly every major fundingagency for science and engineering hasannounced its own thrust into the field.Scores of researchers and institutions arescrambling for a piece of the action. Butin all honesty, I think we have to admitthat much of what invokes the hallowedprefix “nano” falls a bit short of Feyn-man’s mark.

We’ve only just begun to take thefirst steps toward his grand vision of as-sembling complex machines and circuitsatom by atom. What can be done now isextremely rudimentary. We’re certainlynowhere near being able to commercial-

92 S C I E N T I F I C A M E R I C A N U p d a t e d f r o m t h e S e p t e m b e r 2 0 0 1 i s s u e

RoomPlenty

By Michael Roukes

There is plenty of room forpractical innovation at the nanoscale.

But first, scientists have to understandthe unique physics that governs matter there

of

Indeed,

exoticspaces


ly mass-produce nanosystems—integrat-ed multicomponent nanodevices thathave the complexity and range of func-tions readily provided by modern mi-crochips. But there is a fundamental sci-ence issue here as well. It is becoming in-creasingly clear that we are only begin-ning to acquire the detailed knowledgethat will be at the heart of future nano-technology. This new science concerns theproperties and behavior of aggregates ofatoms and molecules, at a scale not yetlarge enough to be considered macro-scopic but far beyond what can be calledmicroscopic. It is the science of the meso-scale, and until we understand it, practicaldevices will be difficult to realize.

Scientists and engineers readily fash-ion nanostructures on a scale of one to a

few hundred nanometers—small indeed,but much bigger than simple molecules.Matter at this mesoscale is often awk-ward to explore. It contains too manyatoms to be easily understood by thestraightforward application of quantummechanics (although the fundamentallaws still apply). Yet these systems arenot so large as to be completely free ofquantum effects; thus, they do not sim-ply obey the classical physics governingthe macroworld. It is precisely in this in-termediate domain, the mesoworld, thatunforeseen properties of collective sys-tems emerge.

Researchers are approaching this

transitional frontier using complemen-tary top-down and bottom-up fabrica-tion methods. Advances in top-downnanofabrication techniques, such as elec-tron-beam lithography (used extensivelyby my own research group), yield almostatomic-scale precision, but achieving suc-cess, not to mention reproducibility, aswe scale down to the single-digit-nano-meter regime becomes problematic. Al-ternatively, scientists are using bottom-up techniques for self-assembly of atoms.But the advent of preprogrammed self-assembly of arbitrarily large systems—

with complexity comparable to thatbuilt every day in microelectronics, in


NOVEL NANOTECH DEVICES, such as these nanoelectromechanical resonators, are enabling scientists

to discover the laws of physics that regulate the unique properties of matter at the mesoscale.

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MEMS and (of course) by Mother Na-ture—is nowhere on the horizon. It ap-pears that the top-down approach willmost likely remain the method of choicefor building really complex devices for agood while.

Our difficulty in approaching themesoscale from above or below reflectsa basic challenge of physics. Lately, theessence of Feynman’s “Plenty of Room”talk seems to be taken as a license forlaissez-faire in nanotechnology. YetFeynman never asserted that “anythinggoes” at the nanoscale. He warned, forinstance, that the very act of trying to“arrange the atoms one by one the waywe want them” is subject to fundamen-tal principles: “You can’t put them sothat they are chemically unstable, forexample.”

Accordingly, today’s scanning probemicroscopes can move atoms from placeto place on a prepared surface, but thisability does not immediately confer thepower to build complex molecular as-semblies at will. What has been accom-plished so far, though impressive, is stillquite limited. We will ultimately developoperational procedures to help us coaxthe formation of individual atomic bondsunder more general conditions. But as wetry to assemble complex networks ofthese bonds, they certainly will affect one

another in ways we do not yet under-stand and, hence, cannot yet control.

Feynman’s original vision was clear-ly intended to be inspirational. Were heobserving now, he would surely bealarmed when people take his projec-tions as some sort of gospel. He deliv-ered his musings with characteristicplayfulness as well as deep insight. Sad-ly for us, the field that would be callednanotechnology was just one of manythat intrigued him. He never really con-tinued with it, returning to give but oneredux of his original lecture, at the JetPropulsion Laboratory in 1983.

New Laws Prevail IN 1959, AND EVEN in 1983, thecomplete physical picture of the nano-scale was far from clear. The good newsfor researchers is that, by and large, it stillis! Much exotic territory awaits explo-ration. As we delve into it, we will un-cover a panoply of phenomena that wemust understand before practical nano-technology will become possible. Thepast two decades have seen the elucida-tion of entirely new, fundamental physi-cal principles that govern behavior at themesoscale. Let’s consider three impor-tant examples.

In the fall of 1987 graduate studentBart J. van Wees of the Delft University

of Technology and Henk van Houten ofthe Philips Research Laboratories (bothin the Netherlands) and their collabora-tors were studying the flow of electriccurrent through what are now calledquantum-point contacts. These are nar-row conducting paths within a semicon-ductor, along which electrons are forcedto flow [see illustration on page 96]. Lateone evening van Wees’s undergraduateassistant, Leo Kouwenhoven, was mea-suring the conductance through the con-striction as he varied its width systemat-ically. The research team was expectingto see only subtle conductance effectsagainst an otherwise smooth and unre-markable background response. Insteadthere appeared a very pronounced, andnow characteristic, staircase pattern.Further analysis that night revealed thatplateaus were occurring at regular, pre-cise intervals.

David Wharam and Michael Pepperof the University of Cambridge observedsimilar results. The two discoveries rep-resented the first robust demonstrationsof the quantization of electrical conduc-tance. This is a basic property of smallconductors that occurs when the wave-like properties of electrons are coherent-ly maintained from the “source” to the“drain”—the input to the output—of ananoelectronic device.

Feynman anticipated, in part, suchodd behavior: “I have thought aboutsome of the problems of building electriccircuits on a small scale, and the problemof resistance is serious. . . .” But the ex-perimental discoveries pointed out some-thing truly new and fundamental: quan-tum mechanics can completely governthe behavior of small electrical devices.

Direct manifestations of quantummechanics in such devices were envi-sioned back in 1957 by Rolf Landauer,a theoretician at IBM who pioneeredideas in nanoscale electronics and in thephysics of computation. But only in the


■ Smaller than macroscopic objects but larger than molecules, nanotechnologicaldevices exist in a unique realm—the mesoscale—where the properties of matterare governed by a complex and rich combination of classical physics andquantum mechanics.

■ Engineers will not be able to make reliable or optimal nanodevices until theycomprehend the physical principles that prevail at the mesoscale.

■ Scientists are discovering mesoscale laws by fashioning unusual, complexsystems of atoms and measuring their intriguing behavior.

■ Once we understand the science underlying nanotechnology, we can fully realize the prescient vision of Richard Feynman: that nature has left plenty ofroom in the nanoworld to create practical devices that can help humankind.

Overview/Nanophysics

It is becoming increasingly clear that we are only beginning to acquire the detailed knowledge

that will be at the heart of future nanotechnology.


mid-1980s did control over materialsand nanofabrication begin to provideaccess to this regime in the laboratory.The 1987 discoveries heralded the hey-day of “mesoscopia.”

A second significant example of new-ly uncovered mesoscale laws that haveled to nascent nanotechnology was firstpostulated in 1985 by Konstantin Likha-rev, a young physics professor at MoscowState University working with postdoc-toral student Alexander Zorin and un-dergraduate Dmitri Averin. They antic-ipated that scientists would be able tocontrol the movement of single electronson and off a “coulomb island,” a con-ductor weakly coupled to the rest of ananocircuit. This could form the basisfor an entirely new type of device, calleda single-electron transistor. The physicaleffects that arise when putting a singleelectron on a coulomb island becomemore robust as the island is scaled down-ward. In very small devices, these single-electron charging effects can complete-ly dominate the current flow.

Such considerations are becoming

increasingly important technologically.Projections from the International Tech-nology Roadmap for Semiconductors,prepared by long-range thinkers in theindustry, indicate that by 2014 the min-imum feature size for transistors in com-puter chips will decrease to 20 nanome-ters. At this dimension, each switchingevent will involve the equivalent of onlyabout eight electrons. Designs that prop-erly account for single-electron chargingwill become crucial.

By 1987 advances in nanofabrica-tion allowed Theodore A. Fulton andGerald J. Dolan of Bell Laboratories toconstruct the first single-electron tran-sistor [see illustration on page 98]. Thesingle-electron charging they observed,now called the coulomb blockade, hassince been seen in a wide array of struc-

tures. As experimental devices get small-er, the coulomb blockade phenomenonis becoming the rule, rather than the ex-ception, in weakly coupled nanoscaledevices. This is especially true in experi-ments in which electric currents arepassed through individual molecules.These molecules can act like coulomb is-lands by virtue of their weak couplingto electrodes leading back to the macro-world. Using this effect to advantageand obtaining robust, reproducible cou-pling to small molecules (in ways thatcan actually be engineered) are amongthe important challenges in the new fieldof molecular electronics.

In 1990, against this backdrop, I wasat Bell Communications Research study-ing electron transport in mesoscopicsemiconductors. In a side project, mycolleagues Larry M. Schiavone and AxelScherer and I began developing tech-niques that we hoped would elucidatethe quantum nature of heat flow. Thework required much more sophisticatednanostructures than the planar devicesused to investigate mesoscopic electron-ics. We needed freely suspended devices,structures possessing full three-dimen-sional relief. Ignorance was bliss; I hadno idea the experiments would be so in-volved that they would take almost adecade to realize.

The first big strides were made afterI moved to Caltech in 1992, in a collab-oration with John M. Worlock of theUniversity of Utah and two successivepostdocs in my group. Thomas S. Tighedeveloped the methods and devices thatgenerated the first direct measurementsof heat flow in nanostructures. Subse-quently, Keith C. Schwab revised the de-sign of the suspended nanostructuresand put in place ultrasensitive supercon-ducting instrumentation to interrogatethem at ultralow temperatures, at whichthe effects could be seen most clearly.

In the late summer of 1999 Schwab


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NANOBRIDGE DEVICE allowed Caltech physicists to first observe the quantization of thermal

conductance—a fundamental limit to heat flow in minute objects. Four holes (black) etched into a silicon

nitride membrane defined an isolated thermal reservoir (central green square) suspended by four narrow

bridges. One gold transducer (yellow) electrically heated this reservoir; the second measured its

temperature. Thin superconducting films (blue) on top of the bridges electrically connected the

transducers to off-chip instrumentation but carried no heat. The reservoir therefore cooled only through

the silicon nitride bridges, which were so narrow that they passed only the lowest-energy heat waves.

MICHAEL ROUKES, professor of physics at the California Institute of Technology, heads agroup studying nanoscale systems. Among the holy grails his team is chasing are a bil-lionfold improvement in present-day calorimetry, which would allow observation of the in-dividual heat quanta being exchanged as nanodevices cool, and a quadrillionfold increasein the sensitivity of magnetic resonance imaging, which would enable complex biomole-cules to be visualized with three-dimensional atomic resolution. TH

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finally began observing heat flow throughsilicon nitride nanobridges [see illustra-tion on preceding page]. Even in thesefirst data the fundamental limit to heatflow in mesoscopic structures emerged.The manifestation of this limit is nowcalled the thermal conductance quan-tum. It determines the maximum rateat which heat can be carried by an indi-vidual wavelike mechanical vibration,spanning from the input to the output ofa nanodevice. It is analogous to the elec-trical conductance quantum but governsthe transport of heat.

This quantum is a significant param-eter for nanoelectronics; it represents theultimate limit for the power-dissipationproblem. In brief, all “active” devices re-quire a little energy to operate, and forthem to operate stably without over-heating, we must design a way to extractthe heat they dissipate. As engineers try

continually to increase the density oftransistors and the clock rates (frequen-cies) of microprocessors, the problem ofkeeping microchips cool to avoid com-plete system failure is becoming monu-mental. This will only become furtherexacerbated in nanotechnology.

Considering even this complexity,Feynman said, “Let the bearings run dry;they won’t run hot because the heat es-capes away from such a small device very,very rapidly.” But our experiments indi-cate that nature is a little more restrictive.The thermal conductance quantum canplace limits on how effectively a verysmall device can dissipate heat. WhatFeynman envisioned can be correct onlyif the nanoengineer designs a structure soas to take these limits into account.

From the three examples above, wecan arrive at just one conclusion: we areonly starting to unveil the complex and

wonderfully different ways that nano-scale systems behave. The discovery ofthe electrical and thermal conductancequanta and the observation of the cou-lomb blockade are true discontinuities—

abrupt changes in our understanding.Today we are not accustomed to callingour discoveries “laws.” Yet I have nodoubt that electrical and thermal con-ductance quantization and single-elec-tron-charging phenomena are indeedamong the universal rules of nano-design. They are new laws of the nano-world. They do not contravene but aug-ment and clarify some of Feynman’soriginal vision. Indeed, he seemed tohave anticipated their emergence: “Atthe atomic level, we have new kinds offorces and new kinds of possibilities,new kinds of effects. The problems ofmanufacture and reproduction of mate-rials will be quite different.”

We will encounter many more suchdiscontinuities on the path to true nano-technology. These welcome windfallswill occur in direct synchrony with ad-vances in our ability to observe, probeand control nanoscale structures. Itwould seem wise, therefore, to be rathermodest and circumspect about forecast-ing nanotechnology.

The Boon and Bane of NanoTHE NANOWORLD is often portrayedby novelists, futurists and the popularpress as a place of infinite possibilities.But as you’ve been reading, this domainis not some ultraminiature version of theWild West. Not everything goes downthere; there are laws. Two concrete il-lustrations come from the field of nano-electromechanical systems (NEMS), inwhich I am active.

Part of my research is directed to-ward harnessing small mechanical de-vices for sensing applications. Nanoscalestructures appear to offer revolutionarypotential; the smaller a device, the moresusceptible its physical properties to al-teration. One example is resonant de-tectors, which are frequently used forsensing mass. The vibrations of a tinymechanical element, such as a small can-tilever, are intimately linked to the ele-ment’s mass, so the addition of a minute

ONE STEP AT A TIMEQUANTIZATION OF ELECTRICAL CONDUCTANCE

In 1987 Bart J. van Wees and his collabo-rators at the Delft University of Technolo-gy and Philips Research Laboratories(both in the Netherlands) built a novelstructure (micrograph) that revealed abasic law governing nanotech circuits.Gold gate electrodes (bright areas) wereplaced atop a semiconductor substrate(dark background). Within the substrate,a planar sheet of charge carriers, called atwo-dimensional electron gas, was creat-ed about 100 nanometers below the sur-face. The gates and the gas acted like theplates of a capacitor.

When a negative voltage bias wasapplied to the gates, electrons within thegas underneath the gates, and slightlybeyond the gates’ periphery, werepushed away. (The diagram shows thisstate.) When increasing negative voltagewas applied, this “depletion edge” became more pronounced. At a certain threshold,carriers on either side of the constriction (between points A and B) became separat-ed, and the conductance through the device was zero. From this threshold level, con-ductance did not resume smoothly. Instead it increased in stepwise fashion, where thesteps occurred at values determined by twice the charge of the electron squared, divid-ed by Planck’s constant. This ratio is now called the electrical conductance quantum,and it indicates that electric current flows in nanocircuits at rates that are quantized.

REGION DEPLETEDOF ELECTRONS

(BELOW SURFACE)

ELECTRON GAS(BELOW SURFACE)

DEPLETIONEDGE

ELECTRON FLOWTHROUGH CONSTRICTION

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amount of foreign material (the “sam-ple” being weighed) will shift the reso-nant frequency. Work in my lab by thenpostdoc Kamil Ekinci shows that nano-scale devices can be made so sensitivethat “weighing” individual atoms andmolecules becomes feasible.

But there is a dark side. Gaseousatoms and molecules constantly adsorband desorb from a device’s surfaces. Ifthe device is macroscopic, the resultingfractional change in its mass is negligi-ble. But the change can be significant fornanoscale structures. Gases impingingon a resonant detector can change theresonant frequency randomly. Appar-ently, the smaller the device, the less sta-ble it will be. This instability may posea real disadvantage for various types offuturistic electromechanical signal-pro-cessing applications. Scientists might beable to work around the problem by, forexample, using arrays of nanomechani-cal devices to average out fluctuations.But for individual elements, the problemseems inescapable.

A second example of how “not every-thing goes” in the nanoworld relatesmore to economics. It arises from the in-trinsically ultralow power levels at whichnanomechanical devices operate. Physicssets a fundamental threshold for the min-imum operating power: the ubiquitous,random thermal vibrations of a mechan-ical device impose a “noise floor” belowwhich real signals become increasinglyhard to discern. In practical use, nano-mechanical devices are optimally excitedby signal levels 1,000-fold or a million-fold greater than this threshold. But suchlevels are still a millionth to a billionththe amount of power used for conven-tional transistors.

The advantage, in some future nano-mechanical signal-processing system orcomputer, is that even a million nano-mechanical elements would dissipateonly a millionth of a watt, on average.Such ultralow power systems could lead

to wide proliferation and distribution ofcheap, ultraminiature “smart” sensorsthat could continuously monitor all ofthe important functions in hospitals, inmanufacturing plants, on aircraft, andso on. The idea of ultraminiature devicesthat drain their batteries extremely slow-ly, especially ones with sufficient com-putational power to function autono-mously, has great appeal.

But here, too, there is a dark side. Theregime of ultralow power is quite foreignto present-day electronics. Nanoscale de-vices will require entirely new system ar-chitectures that are compatible withamazingly low power thresholds. Thisprospect is not likely to be received hap-pily by the computer industry, with itsoverwhelming investment in current de-vices and methodology. A new semicon-

ductor processing plant today costs morethan $1 billion, and it would probablyhave to be retooled to be useful. But I amcertain that the revolutionary prospectsof nanoscale devices will eventuallycompel such changes.

Monumental ChallengesCERTAINLY A HOST of looming is-sues will have to be addressed before wecan realize the potential of nanoscale de-vices. Although each research area hasits own concerns, some general themesemerge. Two challenges fundamental tomy current work on nanomechanicalsystems, for instance, are relevant tonanotechnology in general.

Challenge I: Communication betweenthe macroworld and the nanoworld.NEMS are incredibly small, yet theirmotion can be far smaller. For example,a nanoscale beam clamped on both endsvibrates with minimal harmonic distor-tion when its vibration amplitude is keptbelow a small fraction of its thickness.For a 10-nanometer-thick beam, thisamplitude is only a few nanometers.Building the requisite, highly efficienttransducers to transfer information fromsuch a device to the macroworld in-volves reading out information with evengreater precision.

Compounding this problem, the nat-ural frequency of the vibration increasesas the size of the beam is decreased. So totrack the device’s vibrations usefully, theideal NEMS transducer must be capableof resolving extremely small displace-ments, in the picometer-to-femtometer(trillionth to quadrillionth of a meter)range, across very large bandwidths, ex-tending into the microwave range. Thesetwin requirements pose a truly monu-mental challenge, one much more signif-icant than those faced so far in MEMSwork. A further complication is thatmost of the methodologies from MEMSare inapplicable; they simply don’t scaledown well to nanometer dimensions.

The difficulties in communication between the nanoworld and the macroworld represent a central issuein the development of nanotechnology.

RICHARD FEYNMAN predicted the rise of nano-

technology in a landmark 1959 talk at Caltech.

“The principles of physics,” he said, “do not

speak against the possibility of maneuvering

things atom by atom.” But he also anticipated

that unique laws would prevail; they are finally

being discovered today.


These difficulties in communicationbetween the nanoworld and the macro-world represent a generic issue in the de-velopment of nanotechnology. Ulti-mately, the technology will depend onrobust, well-engineered informationtransfer pathways from what are, in

essence, individual macromolecules. Al-though the grand vision of futurists mayinvolve self-programmed nanobots thatneed direction from the macroworldonly when they are first wound up andset in motion, it seems more likely thatmost nanotechnological applications re-

alizable in our lifetimes will entail someform of reporting up to the macroworldand feedback and control back down.The communication problem will re-main central.

Orchestrating such communicationimmediately invokes the very real pos-sibility of collateral damage. Quantumtheory tells us that the process of mea-suring a quantum system nearly alwaysperturbs it. This can hold true evenwhen we scale up from atoms and mol-ecules to nanosystems comprising mil-lions or billions of atoms. Coupling ananosystem to probes that report backto the macroworld always changes thenanosystem’s properties to some degree,rendering it less than ideal. Introducingthe transducers required for communi-cation will do more than just increase thenanosystem’s size and complexity. Theywill also necessarily extract some energyto perform their measurements and candegrade the nanosystem’s performance.Measurement always has its price.

Challenge II: Surfaces. As we shrinkMEMS to NEMS, device physics be-comes increasingly dominated by the sur-faces. Much of the foundation of solid-state physics rests on the premise that thesurface-to-volume ratio of objects is in-finitesimal, meaning that physical prop-erties are always dominated by thephysics of the bulk. Nanoscale systemsare so small that this assumption breaksdown completely.

For example, mechanical devices pat-terned from single-crystal, ultrapure ma-terials can contain very few (even zero)crystallographic defects and impurities.My initial hope was that, as a result,there would be only very weak dampingof mechanical vibrations in monocrys-talline NEMS. But as we shrink mechan-ical devices, we repeatedly find thatacoustic energy loss seems to increase inproportion to the increasing surface-to-volume ratio. This result clearly impli-


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In each new regime, some wonderful scientificphenomenon emerges. But then a thorny host of underlying,

equally unanticipated problems appear.

TAKING CHARGE

SINGLE ELECTRONICSAdvances in nanofabrication allowed Theodore A. Fulton and Gerald J. Dolan to build a single-electron transistor at Bell Laboratories in 1987 (micrograph). In thisstructure, the controlled movement of individual electrons through a nanodevicewas first achieved. At its heart was a coulomb island, a metallic electrode isolatedfrom its counter-electrodes by thin insulating oxide barriers (diagram). The counter-electrodes led up to the macroscale laboratory instrumentation used to carry out theexperiments. An additional gate electrode (visible in the diagram but not themicrograph) was offset from the coulomb island by a small gap; it allowed directcontrol of the charge introduced to the island. Electric current flowed through thedevice from one counter-electrode to another, as in a conventional circuit, but here itwas limited by the stepwise hopping of electrons onto and off the coulomb island.

Fulton and Dolan’s experiments demonstrate both the fundamental physics ofsingle-electron charging and the potential of these devices as ultrasensitiveelectrometers: instruments that can easily detect individual electron charges.Circuits that switch one electron at a time could someday form the basis for anentirely new class of nanoelectronics. The advent of such single electronics,however, also presages problems that will have to be faced as conventionalelectronic circuits are shrunk to the nanoscale.

Gate electrode

Coulomb island

Insulating barrier

Counter-electrode

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cates surfaces in the devices’ vibrationalenergy-loss processes. In a state-of-the-artsilicon beam measuring 10 nanometerswide and 100 nanometers long, morethan 10 percent of the atoms are at ornext to the surface. It is evident that theseatoms will play a central role, but under-standing precisely how will require a ma-jor, sustained effort.

In this context, nanotube structures,which have been heralded lately, lookideal. A nanotube is a crystalline, rodlikematerial perfect for building the minia-ture vibrating structures of interest to us.And because it has no chemical groupsprojecting outward along its length, onemight expect that interaction with “for-eign” materials at its surfaces would beminimal. Apparently not. Although nano-tubes exhibit ideal characteristics whenshrouded within pristine, ultrahigh vacu-um environments, samples in more ordi-nary conditions, where they are exposedto air or water vapor, evince electronicproperties that are markedly different.Mechanical properties are likely to showsimilar sensitivity. So surfaces definitelydo matter. It would seem there is nopanacea.

Payoff in the GlitchesFUTURISTIC THINKING is crucial tomaking the big leaps. It gives us somewild and crazy goals—a holy grail tochase. And the hope of glory propels usonward. Yet the 19th-century chemistFriedrich August Kekulé once said, “Letus learn to dream, gentlemen, then per-haps we shall find the truth.. . . But let usbeware of publishing our dreams beforethey have been put to the proof by thewaking understanding.”

This certainly holds for nanoscience.While we keep our futuristic dreamsalive, we also need to keep our expecta-tions realistic. It seems that every time wegain access to a regime that is a factor of10 different—and presumably “better”—

two things happen. First, some wonder-ful, unanticipated scientific phenomenonemerges. But then a thorny host of under-lying, equally unanticipated new prob-

lems appear. This pattern has held trueas we have pushed to decreased size, en-hanced sensitivity, greater spatial resolu-tion, higher magnetic and electric fields,lower pressure and temperature, and soon. It is at the heart of why projectingforward too many orders of magnitudeis usually perilous. And it is what shouldimbue us with a sense of humility andproportion at this, the beginning of ourjourney. Nature has already set the rulesfor us. We are out to understand and em-ploy her secrets.

Once we head out on the quest, na-ture will frequently hand us what initial-ly seems to be nonsensical, disappoint-ing, random gibberish. But the science inthe glitches often turns out to be evenmore significant than the grail motivat-ing the quest. And being proved the foolin this way can truly be the joy of doingscience. If we had the power to extrapo-late everything correctly from the outset,the pursuit of science would be utterlydry and mechanistic. The delightful truthis that, for complex systems, we do not,and ultimately probably cannot, knoweverything that is important.

Complex systems are often exquis-itely sensitive to a myriad of parametersbeyond our ability to sense and record—

much less control—with sufficient regu-larity and precision. Scientists have stud-ied, and in large part already understand,matter down to the fundamental particlesthat make up the neutrons, protons andelectrons that are of crucial importance tochemists, physicists and engineers. But westill cannot deterministically predict howarbitrarily complex assemblages of thesethree elemental components will finallybehave en masse. For this reason, I firm-ly believe that it is on the foundation ofthe experimental science under way, inintimate collaboration with theory, thatwe will build the road to true nanotech-nology. Let’s keep our eyes open for sur-prises along the way!

Nanoelectromechanical Systems Face the Future. Michael Roukes in Physics World, Vol. 14, No. 2;February 2001. Available at physicsweb.org/article/world/14/2/8

The author’s group: www.its.caltech.edu/~nano

Richard Feynman’s original lecture “There’s Plenty of Room at the Bottom” can be found atwww.its.caltech.edu/~feynman


NANOMECHANICAL AMPLIFIER overcomes the vexing problem of communication with the macroworld

by providing up to 1,000-fold amplification of weak forces. Two suspended bridges of monocrystalline

silicon carbide ( left and right) support the central crossbridge, to which the signal force is applied.

Thin-film electrodes (silver) atop these structures provide very sensitive readouts of nanoscale motion.


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$5.95 U.S. $6.50 CAN. COPYRIGHT 2003 … Edge Of Physics.pdfgravitation by Albert Einstein from 1905 to 1916. And the unraveling of chemistry and atomic physics through the advent