One Hundred Years Of Quantum Physics

PATHWAYS OF DISCOVERY* Diraclaid the foundationsof quantumfield theorybycess andthe shortcomingsof his model.Withuncannyforeof theelectromagneticfield.sight,he ralliedphysiciststo createa newphysics.His vision providinga quantumdescription* Bohr announcedthe complementarityprinciple, awas eventuallyfulfilled,althoughit took 12 yearsanda newof athelpedto resolveapparentparaAt first,attemptsto advanceBohr'squantumideas-thedoxesof calledold quantumtheory-sufferedone defeatafteranThe principalplayersin the creationof quantumtheoryother.Then a series of developmentstotally changedthe were young. In 1925, Pauliwas 25 years old, Heisenbergcourseof thinking.and EnricoFermiwere 24, and Diracand Jordanwere 23.In 1923 Louis de Broglie,in his Ph.D.thesis,proposed Schrodinger,at age 36, was a late bloomer.BornandBohrthattheparticlebehaviorof lightshouldwereolderstill,andit is significantthattheirhaveits counterpartin the wavebehavcontributionswere largely interpretative.ior of particles.He associateda waveThe profoundlyradicalnatureof the intellectualachievementis revealedby Einstein'slengthwiththemomentumof a particle:The higherthe momentumthe shorterreaction.Havinginventedsome of the keythewavelength.Theideawas intriguing,concepts that led to quantumtheory,Einbutno one knewwhata particle'swavesteinrejectedit. His paperon Bose-Einsteinnaturemightsignifyor how it relatedtostatisticswas his last contributionto quanatomic structure. Nevertheless, detumphysicsandhis lastsignificantcontribuBroglie'shypothesiswas an importanttionto physics.i !'foreventssoonto takeplace.Thata new generationof physicistswas precursor In the summerof 1924, there wasneeded to create quantummechanics ishardly surprising.Lord Kelvin describedyet anotherprecursor.SatyendraN.Bose proposeda totallynew wayto exhimwhy in a letterto Bohr congratulatingplainthe Planckradiationlaw.He treaton his 1913paperon hydrogen.He saidthattherewas muchtruthin Bohr'spaper,butheed light as if it were a gas of masslesswould neverunderstandit himself. Kelvinparticles(now called photons)that donot obey the classical laws of Boltz- Getting weirder. Louisde Broglie recognizedthatradicallynew to saidthatif wavelike. lightcanbehave needto comefromunfetteredIn 1928, the revolutionwas finishedanda new type of statisticsbasedon parti- likeparticles,then particlescan benature.Einstein havelikewaves.the foundationsof quantummechanicswerecles' indistinguishableimmediatelyappliedBose's reasoningessentiallycomplete.The freneticpace withto a realgas of massiveparticlesandobtaineda new lawwhich it occurredis revealedby an anecdoterecountedbyto become known as the Bose-Einsteindistribution-for the lateAbrahamPais in InwardBound.In 1925, the conhowenergyis sharedby theparticlesin a gas.Undernormal cept of electron spin had been proposed by Samuelcircumstances,however,the new andold theoriespredicted GoudsmitandGeorgeUhlenbeck.Bohrwas deeplyskeptithe samebehaviorfor atomsin a gas. Einsteintook no fur- cal. In December,he traveledto Leiden,theNetherlands,totherinterest,and the resultlay undevelopedfor moreattend the jubilee ofHendrikA. Lorentz'sthana decade.Still,its key idea,the indistinguishabilityof particles,was aboutto becomecriticallyimportant.d octorate. Pauli metSuddenly,a tumultuousseries of events occurred,the trainatHamburg,culminatingin a scientificrevolution.In the 3-yearpefind outGermany,toriodfromJanuary1925to January1928:Bohr'sopinion a bout* WolfgangPauliproposedthe exclusionprinciple,the possibilityele of idinga theoretical* WernerHeisenberg,with Max Born and Pascualproposal was "very,Jordan,discoveredmatrixmechanics,the first versionvery interesting,"hisof quantummechanics.The historicalgoal of underwell-knownput-downphrase. Later at Leistandingelectronmotionwithinatomswas abandonedin favorof a systematicmethodfor organizingobservden, Einsteinand PaulEhrenfest met Bohr'sVCU ablespectrallines.* ErwinSchrddingerinventedwave mechanics,atrain, also to discuss?lt secondformofspin. There, Bohr exquantummechanicsin whichthe state L of a systemis describedplained his objection,by a wave function,the solu2 is tion to Schrodinger'sbut Einsteinshowed aequation.Matrixmechanicsandwere shownwayaroundit andconapparentlyincompatible, l wavemechanics,Zto be equivalent.Unlknowablereality.WernerHeisenberg vertedBohrinto a sup* Electronswereshownto obeya new typeof statis- articulatedone of the mostsocietallyab- porter. On his returna tical law,Fermi-Diracstatistics.It was recognizedthat sorlbedideasof quantumphysics:the Un- journey,Bohrmet with3all particlesobey eitherFermi-Diracstatisticsor Bose- ceritaintyPrinciple.yet more discussants.2candthatthe two classeshavefundaWhen the trainpassed Einsteinstatistics,Ces ny,Heisenbergand ingatthestationtoaskhisopinion.Andat the BerlinPrinciple.3* PaulA. M. Diracdevelopeda relativisticwave equa- station,Pauliwas waiting,havingtraveledespeciallyfrom! tion for the electronthatexplainedelectronspin and pre- Hamburg.Bohrtold themall thatthe discoveryof electronspinwas a orgSCIENCEVOL289 11AUGUST! -(?I3lIEI[I 111?I-11[-lI;I;LraIIIIE11- IIl)ll - I11U(ll[- 1111 -I4r?r895

PATHWAYSOF DISCOVERYThe creation of quantum mechanics triggered a scientific gold rush. Among the early achievements were these:Heisenberg laid the foundations for atomic structuretheory[E- Iby obtaining an approximate solution toSchrodinger's:r- ;equation for the helium atom in 1927, and general tech sl niques for calculating the structuresof atoms were createdsoon after by John Slater, Douglas Rayner Hartree, andVladimir Fock. The structureof the hydrogen molecule wassolved by Fritz London and Walter Heitler; Linus Paulingbuilt on their results to found theoretical chemistry. ArnoldSommerfeld and Pauli laid the fbundationsof the theory of:11;: N111electrons in metals, and Felix Bloch created band structuretheory. Heisenberg explained the origin of ferromagnetism.3111 The enigma of the random nature of radioactive decay byalpha particle emission was explained in 1928 byIllrIGeorge Gamow, who showed that it occurs by quantum ;3Z I?mechanical tunneling. In the following years Hans Bethe- llaid the foundations for nuclear physics and explained thesource of stars.WithenergyGI1111 1 theseatomic,developments1Z1111 molecular, solid state, andnuclear physics entered the&1z&s1tmodern age.',- l ;Controversyand ConfusionAlongside these advances,vhowever, fierce debatesnaP]qv s1-11weretakingplaceon the interpretation and validity ofquantum mechanics. Fore-most among the protago-I;*K"t-t-]-t1Ls 11k;s1111?11:1I;xU-1'i I1111?896nists were Bohr and Heisenberg, who embraced thenew theory, and Einsteinand Schrodinger,who weredissatisfied. To appreciatethe reasons for such turmoil, one needs tounderstand someof the key features;/t 0? yof quantum theoS7ry, which we summarize here. (Forsimplicity, we describe the Schrodingerversion of quantummechanics, sometimes called wave mechanics.)Fundamentaldescription: the wavefinction. The behavior of a system is described by Schrodinger'sequation. Thesolutions to Schrodinger'sequation are known as wave functions. The complete knowledge of a system is described byits wave function, and from the wave function one can calculate the possible values of every observable quantity.Theprobabilityof finding an electron in a given volume of spaceis proportionalto the square of the magnitude of the wavefunction. Consequently, the location of the particle is"spreadout" over the volume of the wave function. The momentum of a particledepends on the slope of the wave function: The greater the slope, the higher the momentum. Because the slope varies from place to place, momentum isalso "spreadout."'The need to abandona classical picture inwhich position and velocity can be determined with arbitraryaccuracyin favor of a blurredpictureof probabilitiesisat the heartof quantummechanics.Measurementsmade on identical systems that are identically preparedwill not yield identical results. Rather,the resuits will be scattered over a range described by the wave11 AUGUST2000VOL289function. Consequently,the concept of an electron having aparticular location and a particular momentum loses itsfoundation.The UncertaintyPrinciple quantifies this: To locate a particle precisely, the wave function must be sharplypeaked (that is, not spread out). However, a sharp peak requires a steep slope, and so the spread in momentum will begreat. Conversely, if the momentum has a small spread,theslope of the wave function must be small, which means thatit must spread out over a large volume, thereby portrayingthe particle'slocation less exactly.Waves can interfere. Their heights add or subtract depending on their relativephase. Where the amplitudes are inphase, they add; where they are out of phase, they subtract.If a wave can follow several paths from source to receiver,asa light wave undergoing two-slit interference,then the illumination will generally display interference fringes. Particles obeying a wave equation will do likewise, as in electrondiffraction.The analogy seems reasonableuntil one inquiresabout the nature of the wave. A wave is generallythought of as a disturbancein a medium. In quantummechanics there is no medium, and in a sense there isno wave, as the wave function is fundamentally astatementof our knowledge of a system.Symmetryand identity. A helium atom consists ofa nucleus surrounded by two electrons. The wavefunction of helium describes the position of eachelectron. However, there is no way of distinguishingwhich electron is which. Consequently, if the electrons are switched the system must look the same,which is to say the probability of finding the electrons in given positions is unchanged. Because theOmniscient math. It'stough probability depends onjto solve, but ErwinSchrod- the sqare of the maginger's famous equation nitudeofthewavefunc(shown in one of its many tion, the wave functionforms)describeseveryobserv- for the system with theablestate of a physicalsystem. interchanged particlesmust be related to theoriginal wave functionin one oftwo ways:r(vt)JI' (V ) w -?'l) Eitherit is identical tothe original wave function, or its sign is simply reversed, i.e., it is multiplied by a factor of-1. Whichone is it?One of the astonishing discoveries in quantummechanicsis that for electrons the wave function always changes sign.The consequences are dramatic, for if two electrons are inthe same quantumstate, then the wave function has to be itsnegative opposite. Consequently, the wave function mustvanish. Thus, the probabilityof finding two electrons in thesame state is zero. This is the Pauli exclusion principle. Allparticles with half-integer spin, including electrons, behavethis way and are called fermions. For particles with integer :spin, including photons, the wave function does not changesign. Such particles are called bosons. Electrons in an atom arrangethemselves in shells because they are fermions, butlight from a laser emerges in a single superintensebeam- ,essentially a single quantum state--because light is composed of bosons. Recently, atoms in a gas have been cooled to the quantum regime where they form a Bose-Einstein Ucondensate, in which the system can emit a superintense 2matterbeam-forming an atom laser.These ideas apply only to identical particles, because if adifferent particles are interchanged the wave function will ?)SCIENCE www.sciencemag.org

PATHWAYS OF DISCOVERYcertainlybe different.Consequently,particlesbehavelike TheSecondRevolutionfermionsor likebosonsonlyif theyaretotallyidentical.The Duringthe freneticyearsin the mid-1920swhenquantumabsoluteidentityof likeparticlesis amongthemostmysteri- mechanics was being invented,anotherrevolutionwasunderway.The foundationswere being laidous aspectsof quantummechanofics. Amongthe achievementsfor the secondbranchof quantumphysicsquantumfield theory is that itquantumfield theory.Unlike quantummecanexplainthismystery.chanics,which was createdin a shortflurryWhatdoes it mean? Quesof activity and emerged essentially comtions suchas whata wavefuncplete, quantumfield theory has a tortuoustion "really is" and what ishistory that continuestoday.In spite of themeant by "makinga measuredifficulties,the predictionsof quantumfieldment"wereintenselydebatedintheoryare the most precisein all of physics,the earlyyears.By 1930, howand quantum field theory constitutes aever,a moreor less standardinparadigmfor some of the most crucialareasof theoreticalinquiry.terpretation of quantum mechanicshad been developedbyThe problem thatmotivated quantum fieldBohrandhis colleagues,the socalled Copenhageninterpretatheory was the questionoftion. The key elementsare thehow an atom radiateslightas its electrons "jump"probabilisticdescriptionof matfrom excited states to theter and events, and reconcilia tion of the wavelikeand partigroundstate. Einsteinpro:posed such a process,clelikenaturesof thingsthroughcalled spontaneous emisBohr'sprincipleof complemen tarity.Einsteinnever acceptedIHI H sion, in 1916,buthe hadnoquantumtheory.He and Bohr Quantumwebs. BycreatingF)articlesthat way to calculate its rate. BEdebatedits principlesuntilEin- share quantumstates, such ais these "en- Solving the problem restein'sdeathin 1955.tangled"photons at the inte.rsections of quired developing a fully theselaser-generatedrings,re;searchersare relativisticquantumtheoryunencryption of electromagneticfields, aA central issue in the de- developing new quanturquantumtheory of light. Quantummechancomrnters.2 bates on quantummechanics schemesandquantumics is the theory of matter.Quantumfield' was whetherthe wave functionz containsall possibleinformationabouta systemor if there theory,as its name suggests, is the theory of fields, notfields but otherfields thatwere sub mightbe underlyingfactors-hiddenvariables-thatdeter- only electromagneticIn the mid- sequentlydiscovered. minethe outcomeof a particularmeasurement.In 1925 Born,Heisenberg,and Jordanpublishedsome 1960sJohnS. Bell showedthatif bilitieswould have to fall initial ideas for a theory of light, but the seminal stepsExperi- were takenby Dirac-a young and essentiallyunknown below certainlimits, dubbed"Bell'sinequalities."S ments were carried out by a numberof groups, whichphysicist working in isolation-who presented hisfield theory in 1926. The -foundthatthe inequalitieswere violated.Theircollectivetheory was full of pitfalls:t datacame down decisivelyagainstthe possibilityof hidformidable calculationalv den variables.Formost scientists,this resolvedany doubtcomplexity, predictionsofE aboutthe validityof quantummechanics.infinite quantities,and apNevertheless,the natureof quantumtheorycontinuestoparentviolationsof the corM attractattentionbecause of the fascinationwith what isrespondenceprinciple.p sometimesdescribedas "quantumweirdness."The weirdIn the late 1940s a newof quantumsystemsarisefromwhatis knownaso propertiesapproach to the quantumBriefly,a quantumsystem,such as an atom,5 entanglement.statesbutalsotheory of fields, QED (for. canexistin anyone of a numberof stationaryin a superposition-orsum-of suchstates.If one measuresquantumelectrodynamics),was developedby RichardM somepropertysuchas the energyof an atomin a superposition state, in generalthe result is sometimes one value,Feynman,JulianSchwinger,- sometimesanother.So far,nothingis weird.and Sin-Itiro Tomonaga.They sidesteppedthe infiniIt is also possible,however,to constructa two-atomsys ties by a procedure,calledv tem in an entangledstate in which the propertiesof both atomsaresharedwitheachother.If the atomsareseparated, Fields go quantum. Paul renormalization,which esworklead- sentially ne is shared,or entangled,in the stateofz the other.The behavioris unexplainableexceptin the lan- ing to quantumfieldtheory quantitiesso as to leavefisuchas nite results.Becausethereis guageof quantummechanics.The effectsare so surprising as wellas discoveriesno exact solution to thev thattheyarethe focusof studyby a smallbutactivetheoret- antimatter.complicatedequationsof theTheissuesarenot limitedcommunity. ical andexperimentalto questionsof principle,as entanglementcanbe useful.En- theory,an approximateansweris presentedas a series ofg tangledstateshavealreadybeenemployedin quantumcom- termsthatbecomemoreandmoredifficultto calculate.Alunderliesall propos- though the terms become successively smaller,at some- municationsystems,andentanglemente als forquantumcomputation.pointtheyshouldstartto grow,indicatingthebreakdownofII.www.sciencemag.org SCIENCE VOL28911 AUGUST2000897

PATHWAYSthe approximation. In spite of theseperils, QED ranks among the most brilliant successes in the history of physics.Its prediction of the interactionstrengthbetween an electron and a magneticfield has been experimentally con-OF DISCOVERYfica.com enhancestheEachmonth,Britannaccessthis month'sIPatlhwaysessayandall niscent of the frenzied and miraculousprevious ones, go tc) www.britannica.comdays in which quantum mechanics wasandclickonthe Scieincecreated, and whose outcome may beeven morefar-reaching.The effortis in1,000,000,000,000.extricablyboundto the questfor a quantumdescriptionofNotwithstandingits fantasticsuccesses, QED harbors gravity.The procedurefor quantizingthe electromagneticenigmas.The view of emptyspace-the vacuum-that the field thatworkedso brilliantlyin QEDhas failedto worktheoryprovidesinitiallyseems preposterous.It turnsout for gravity,in spiteof a half-centuryof effort.Theproblemthat empty space is not really empty.Rather,it is filled is critical,for if cu- are bothcorrect,then they mustultimatelyprovidea conwith small,fluctuatingelectromagneticum fluctuationsare essential for explainingspontaneous sistentdescriptionfor the sameevents.Thereis no urable dictionin the normalworldaroundus, becausegravityisso fantasticallyweak comparedto the electricalforces inshifts in the energies of atoms and certainpropertiesofparticlessuch as the electron.Strangeas they seem, these atoms that quantumeffects are negligibleand a classicaleffects have been confirmedby some of the most precise descriptionworksbeautifully.But for a system such as afirmed to a precision of two parts in?I-l I-I:IrI:IIexperiments ever carried out.At the low energies of the worldaround us, quantummechanics is fantastically accurate. But at high energieswhere relativistic effects come into play,a more general approach is needed.Quantum field theory was invented toreconcile quantum mechanics with spe-cial relativity.)II51-lI-l The towering role that quantum fieldtheoryplaysin physicsarisesfromtheanswers it provides to some of the most profound questions about the nature of matter. Quantum field theory explains whythere are two fundamentalclasses of particles-fermions and bosons-and howtheir properties are related to their intrinsic spin. It describes how particles-notonly photons, but electrons and positrons(antielectrons)-are created and annihiIt explains the mysterious natureo

gle superatom. Quantum mechanics provides essential tools for all of the sciences and for every advanced technology. Quantum physics actually encompasses two entities. The first is the theory of matter at the atomic level: quantum me- chanics. It is quantum mechanics that allows us to under- stand and manipulate the material world. The second .