One Hundred Years of Quantum Physics
Author(s): Daniel Kleppner and Roman Jackiw
Source: Science, New Series, Vol. 289, No. 5481 (Aug. 11, 2000), pp. 893-898
Published by: American Association for the Advancement of Science
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PATHWAYS
One
OF
DISCOVERY
Hundred Years
of
Quantum Physics
FEBRUARY
Planetary
Sciences
MARCH
Genomics
Daniel Kleppnerand RomanJackiw
of the 20thcenturyis likelyto include
An informedlist of themostprofoundscientificdevelopments
of the geneticcode,evoluquantummechanics,big bangcosmology,theunraveling
generalrelativity,
tionarybiology,andperhapsa few othertopicsof the reader'schoice.Amongthese,quantummechanicsis uniquebecauseof its profoundlyradicalquality.Quantummechanicsforcedphysiciststo
reshapetheirideasof reality,to rethinkthe natureof thingsat the deepestlevel, andto revisetheir
conceptsof positionandspeed,as well as theirnotionsof causeandeffect.
Althoughquantummechanicswas createdto describean abstractatomicworldfarremovedfrom
dailyexperience,its impacton our dailylives couldhardlybe greater.The spectacularadvancesin
chemistry,biology,andmedicine-and in essentiallyeveryotherscience-could
nothaveoccurredwithoutthetoolsthatquantummechanicsmadepossible.
Withoutquantummechanicstherewouldbe no globaleconomyto speak
of, becausetheelectronicsrevolutionthatbroughtus thecomputerage
is a childof quantummechanics.So is thephotonicsrevolutionthat
Age. The creationof quantumphysics
broughtus the Information
ourworld,bringingwith it all the benefits-and
has transformed
therisks-of a scientificrevolution.'
Unlikegeneralrelativity,whichgrewoutof a brilliantinsight
intothe connectionbetweengravityandgeometry,or the decipheringof DNA, whichunveileda new worldof biology,quantummechanicsdid not springfroma singlestep.Rather,it was
of geniusthatoccur
createdin one of thoserareconcentrations
fromtime to time in history.For20 yearsaftertheirintroduction,quantumideaswere so confusedthattherewas littlebasis
for progress;then a small groupof physicistscreatedquantum
mechanics in three tumultuous years.These scientists
were troubled by what they
"Quantum
o
weredoingandin somecasesdis|:
tressedby whattheyhaddone.
theory is the
The uniquesituationof this
crucialyetelusivetheoryis per- Papa Quanta. In 1900, Max
most precisely
t
haps best summarizedby the Planckstarted the quantumsnowball.
|tested and most
following observation:Quan- mechanical
tumtheoryis themostprecisely
successful
testedandmostsuccessfultheoryin thehistoryof science.Nevermechanicsdeeplydisturbing
to its
theless,not onlywas quantum
in the
theory in
founders,today-75 yearsafterthetheorywas essentiallycastin
theory
te
of scienceremaindisits currentform-some of the luminaries
historyof
evenas they
andits interpretation,
satisfiedwith its foundations
its
acknowledge stunningpower.
<riscience."
of Max Planck'screThis yearmarksthe 100thanniversary
his
seminal
In
the
ation
of
paperon thermal
quantum
concept.
|
- radiation,Planckhypothesizedthatthe totalenergyof a vibratingsystemcannotbe changedconE tinuously.Instead,the energymustjump fromone valueto anotherin discretesteps,or quanta,of
x energy.The idea of energyquantawas so radicalthatPlancklet it lay fallow.Then,Einstein,in his
| wonderyearof 1905,recognizedthe implicationsof quantizationfor light.Eventhenthe concept
| was so bizarrethattherewas littlebasis for progress.Twentymoreyearsanda freshgenerationof
_ physicistswererequiredto createmodemquantumtheory.
the revolutionary
To understand
impactof quantumphysicsone need only look at prequantum
? physics.From1890to 1900,physicsjournalswerefilled with paperson atomicspectraandessenwww.sciencemag.org SCIENCE VOL289
JANUARY
"ScienceWars"
11 AUGUST2000
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893
PATHWAYS
=s1~11
;I?r?
OF DISCOVERY
It shouldhavebeen possibleto understand
the shapeof
tially every othermeasurablepropertyof matter,such as
viscosity,elasticity,electricalandthermalconductivity,co- the spectrumby combiningconceptsfromthermodynamics
efficientsof expansion,indicesof refraction,and thermo- andelectromagnetic
theory,butall attemptsfailed.However,
elasticcoefficients.Spurredby the energyof the Victorian by assumingthatthe energiesof the vibratingelectronsthat
work ethic and the developmentof ever more ingenious radiatethe light are quantized,Planckobtainedan expression thatagreedbeautifulexperimental methods,
ly withexperiment.
Butas
knowledgeaccumulatedat
a prodigiousrate.
he recognizedall too well,
the theorywas physically
What is most striking
to the contemporaryeye,
absurd,"anact of desperation," as he later dehowever,is that the comscribedit.
pendious descriptions of
the properties of matter
Planck applied his
were essentiallyempirical.
quantumhypothesisto the
Thousands of pages of
of the vibratorsin
.?~ ,?.~~~~?energy
U
the walls of a radiating
spectraldatalistedprecise _ H
valuesfor the wavelengths
body. Quantumphysics
mighthaveendedthereif
of the elements, but no- _B
in 1905 a novice-Albert
body knew why spectral
_.
:1
Einstein-had not reluclines occurred,much less
tantlyconcludedthatif a
whatinformation
theycon_
vibrator'senergyis quanveyed.Thermalandelectritized, then the energy of
cal conductivitieswere inthe electromagneticfield
terpreted by suggestive
models that fitted roughly Superatom. Thesecolorfuldatal,frrom NISTin 1995, emerged from that it radiates-lightintothe firstdocument- must also be quantized.
half of the facts. There measurements
of rubidium
atomIS C:oalescing
condensate.
Einstein thus imbued
were numerousempirical ed Bose-Einstein
laws,buttheywerenot satlightwith particlelikebelawestablisheda sim- havior,notwithstanding
thatJamesClerkMaxwell'stheory,
isfying.Forinstance,theDulong-Petit
and over a centuryof definitiveexperiments,testified to
ple relationbetweenspecificheatandtheatomicweightof a
material.Muchof the time it worked;sometimesit didn't. light'swavenature.Experiments
on the photoelectric
effect
Themassesof equalvolumesof gas werein theratiosof in- in the followingdecaderevealedthatwhenlightis absorbed
tegers-mostly. The PeriodicTable,whichprovideda key its energyactuallyarrivesin discretebundles,as if carried
organizingprincipleforthe flourishingscienceof chemistry, by a particle.Thedualnatureof light-particlelikeor wavelike dependingon whatone looks for-was the firstexamhadabsolutelyno theoretical
basis.
of therevolution
is this: ple of a vexingthemethatwouldrecurthroughout
Amongthegreatestachievements
quantum
for
Quantummechanicshas provideda quantitative
physics.Thedualityconstituteda theoreticalconundrum
theoryof
matter.Wenow understand
essentiallyeverydetailof atomic thenext20 years.
thePeriodicTablehasa simpleandnaturalexplanaThe first step towardquantumtheoryhadbeen precipistructure;
tion;andthevastarraysof spectraldatafit intoanelegantthe- tatedby a dilemmaaboutradiation.The second step was
oreticalframework.
Quantumtheorypermitsthe quantitative precipitated
by a dilemmaaboutmatter.It was knownthat
of molecules,of solidsandliquids,andof con- atomscontainpositivelyand negativelychargedparticles.
understanding
It explainsbizarrephenomena But oppositelychargedparticlesattract.Accordingto elecductorsand semiconductors.
suchas superconductivity
andsuperfluidity,
andexoticforms
tromagnetictheory,therefore,
they should spiral into each
of mattersuchas the stuffof neutronstarsandBose-Einstein
in whichall theatomsin a gasbehavelikea sincondensates,
Atoms_~~ i;
other,radiatinglightin a broad
Nesor
r
gle superatom.
Quantummechanicsprovidesessentialtools
spectrumuntiltheycollapse.
1913,_
Once again, the door to I
forall of thesciencesandforeveryadvanced
technology.
progress was opened by a o
Quantumphysicsactuallyencompassestwo entities.The
firstis thetheoryof matterat the atomiclevel:quantummeof_n~ ao
anovice:Niels Bohr. In 1913,
chanics.It is quantummechanicsthatallowsus to under_Bohr proposed a radical hypothesis:Electronsin an atom
standandmanipulatethe materialworld.The secondis the
_
quantumtheoryof fields. Quantumfield theoryplaysa to_
exist only in certainstationary
oaoisb
proble
states,includinga groundstate.
tallydifferentrolein science,to whichwe shallreturnlater.
Electronschangetheir energy
by "jumping"
stabetween
the
Quantum Mechanics
dictions,
states,
emitting
light
The clue thattriggeredthe quantumrevolutioncame not
..tionary
the
b
.p..--fromstudiesof matterbutfroma problemin radiation.The Atoms go quantum. In whose wavelengthdependson
the spectrumof light 1913, Niels Bohrushered the energydifference.By com- ,
specific challengewas to understand
emitted by hot bodies: blackbody radiation.The phe- quantumphysicsintoworld biningknownlawswithbizarre~'
assumptions
aboutquantumbe- X
nomenonis familiarto anyonewho has staredat a fire. Hot of atoms.
havior, Bohr swept away the o
matterglows,andthehotterit becomesthebrighterit glows.
The spectrumof the light is broad,with a peakthatshifts problemof atomicstability.Bohr'stheorywas full of contra-g
fromredto yellow andfinallyto blue (althoughwe cannot dictions,but it provideda quantitativedescriptionof the F
spectrumof thehydrogenatom.He recognizedboththe sucsee that)as thetemperature
is raised.
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2000 VOL289 SCIENCEwww.sciencemag.org
11AUGUST
PATHWAYS OF DISCOVERY
* Diraclaid the foundationsof quantumfield theoryby
cess andthe shortcomings
of his model.Withuncannyforeof theelectromagnetic
field.
sight,he ralliedphysiciststo createa newphysics.His vision providinga quantumdescription
* Bohr announcedthe complementarityprinciple, a
was eventuallyfulfilled,althoughit took 12 yearsanda new
of youngphysicists.
generation
philosophicalprinciplethathelpedto resolveapparentparaAt first,attemptsto advanceBohr'squantumideas-the
doxesof quantumtheory,particularly
wave-particle
duality.
so-calledold quantumtheory-sufferedone defeatafteranThe principalplayersin the creationof quantumtheory
other.Then a series of developmentstotally changedthe were young. In 1925, Pauliwas 25 years old, Heisenberg
courseof 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.BornandBohr
thattheparticlebehaviorof lightshould
wereolderstill,andit is significantthattheir
haveits counterpart
in the wavebehavcontributionswere largely interpretative.
ior of particles.He associateda waveThe profoundlyradicalnatureof the intellectualachievementis revealedby Einstein's
lengthwiththemomentumof a particle:
The higherthe momentumthe shorter
reaction.Havinginventedsome of the key
thewavelength.
Theideawas intriguing,
concepts that led to quantumtheory,Einbutno one knewwhata particle'swave
steinrejectedit. His paperon Bose-Einstein
naturemightsignifyor how it relatedto
statisticswas his last contributionto quanatomic structure. Nevertheless, de
tumphysicsandhis lastsignificantcontribuBroglie'shypothesiswas an important
tionto physics.
i~!'
foreventssoonto takeplace.
Thata new generationof physicistswas
~
precursor
^
In the summerof 1924, there was
needed to create quantummechanics is
hardly surprising.Lord Kelvin described
yet anotherprecursor.SatyendraN.
Bose proposeda totallynew wayto exhim
why in a letterto Bohr congratulating
plainthe Planckradiationlaw.He treaton his 1913paperon hydrogen.He saidthat
therewas muchtruthin Bohr'spaper,buthe
ed light as if it were a gas of massless
would neverunderstandit himself. Kelvin
particles(now called photons)that do
not obey the classical laws of Boltz- Getting weirder. Louisde Broglie recognizedthatradicallynew physicswould
minds.
mannstatisticsbutbehaveaccordingto saidthatif wavelike
. lightcanbehave needto comefromunfettered
In 1928, the revolutionwas finishedand
a new type of statisticsbasedon parti- likeparticles,then particlescan benature.Einstein havelikewaves.
the foundationsof quantummechanicswere
cles' indistinguishable
immediatelyappliedBose's reasoning
essentiallycomplete.The freneticpace with
to a realgas of massiveparticlesandobtaineda new lawwhich it occurredis revealedby an anecdoterecountedby
to 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 Samuel
circumstances,
however,the new andold theoriespredicted GoudsmitandGeorgeUhlenbeck.Bohrwas deeplyskeptithe samebehaviorfor atomsin a gas. Einsteintook no fur- cal. In December,he traveledto Leiden,theNetherlands,
to
therinterest,and the resultlay undevelopedfor more
attend the jubilee of
HendrikA. Lorentz's
thana decade.Still,its key idea,the indistinguishability
of particles,was aboutto becomecriticallyimportant.
d oct
orate. Pauli met
Suddenly,a tumultuousseries of events occurred,
the train
atHamburg,
culminatingin a scientificrevolution.In the 3-yearpefind out
Germany,to
riodfromJanuary1925to January1928:
Bohr's
opinion a bout
* WolfgangPauliproposedthe exclusionprinciple,
the possibility
ele of cbasisforthePeriodicTable.
tronspin.Bohrsaidthe
providinga theoretical
* WernerHeisenberg,with Max Born and Pascual
proposal was "very,
Jordan,discoveredmatrixmechanics,the first version
very interesting,"his
of quantummechanics.The historicalgoal of underwell-knownput-down
phrase. Later at Leistandingelectronmotionwithinatomswas abandoned
in favorof a systematicmethodfor organizingobservden, Einsteinand Paul
Ehrenfest met Bohr's
VC
U ablespectrallines.
* ErwinSchrddingerinventedwave mechanics,a
train, also to discuss
?l
t secondformof
spin. There, Bohr exquantummechanicsin whichthe state
|L of a systemis described
plained his objection,
by a wave function,the solu2
<
is tion to Schrodinger's
but Einsteinshowed a
equation.Matrixmechanicsand
were shown
way
aroundit andconapparently
incompatible,
<l wavemechanics,
Z
to be equivalent.
Unlknowablereality.WernerHeisenberg vertedBohrinto a sup* Electronswereshownto obeya new typeof statis- articulatedone of the mostsocietallyab- porter. On his return
a tical law,Fermi-Dirac
statistics.It was recognizedthat sorlbedideasof quantumphysics:
the Un- journey,Bohrmet with
3
all particlesobey eitherFermi-Dirac
statisticsor Bose- ceritaintyPrinciple.
yet more discussants.
2c
andthatthe two classeshavefundaWhen the trainpassed
> Einsteinstatistics,
C
es mentally
differentproperties.
through
Gdttingen,
Germany,
Heisenberg
and Jordanwere
?
*Heisenbergenunciated
theUncertainty
waiting
at
the
station
to
ask
his
opinion.
And
at the Berlin
Principle.
3
* PaulA. M. Diracdevelopeda relativisticwave equa- station,Pauliwas waiting,havingtraveledespeciallyfrom
! tion for the electronthatexplainedelectronspin and pre- Hamburg.Bohrtold themall thatthe discoveryof electron
spinwas a greatadvance.
Edictedantimatter.
2000
www.sciencemag.orgSCIENCEVOL289 11AUGUST
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PATHWAYS
OF DISCOVERY
The 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 to
Schrodinger's
:
r
-~~~~~~~;
equation for the helium atom in 1927, and general tech~~~~~sl~
niques for calculating the structuresof atoms were created
soon after by John Slater, Douglas Rayner Hartree, and
Vladimir Fock. The structureof the hydrogen molecule was
solved by Fritz London and Walter Heitler; Linus Pauling
built on their results to found theoretical chemistry. Arnold
Sommerfeld and Pauli laid the fbundationsof the theory of
:
11;: N111
electrons in metals, and Felix Bloch created band structure
theory. Heisenberg explained the origin of ferromagnetism.
_3111~
The enigma of the random nature of radioactive decay by
alpha particle emission was explained in 1928 by
IllrI
George Gamow, who showed that it occurs by quantum_;3Z_I?
mechanical tunneling. In the following years Hans Bethe
- ~~~~~l
laid the foundations for nuclear physics and explained the
source of stars.With
energy
_GI1111~1~
these
atomic,
developments
1Z1111~
molecular, solid state, and
nuclear physics entered the
&1z&s1tmodern age.
',
-~l~
;
Controversyand Confusion
Alongside these advances,
v
however, fierce debates
_na
P]qv=s
1-11
weretakingplaceon the interpretation and validity of
quantum mechanics. Fore-
most among the protago-
I;
*K"t-t-]-t
1Ls_~
11k;
s1111?1
1
:1I;xU-1'i I
_1111?
896
nists were Bohr and Heisenberg, who embraced the
new theory, and Einstein
and Schrodinger,who were
dissatisfied. To appreciate
the reasons for such turmoil, one needs to
understand some
of the key features
;
/t 0
? y
of quantum theoS7
ry, which we summarize here. (For
simplicity, we describe the Schrodingerversion of quantum
mechanics, sometimes called wave mechanics.)
Fundamentaldescription: the wavefinction. The behavior of a system is described by Schrodinger'sequation. The
solutions to Schrodinger'sequation are known as wave functions. The complete knowledge of a system is described by
its wave function, and from the wave function one can calculate the possible values of every observable quantity.The
probabilityof finding an electron in a given volume of space
is proportionalto the square of the magnitude of the wave
function. 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 is
also "spreadout."'The need to abandona classical picture in
which position and velocity can be determined with arbitraryaccuracyin favor of a blurredpictureof probabilitiesis
at 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 wave
11 AUGUST2000
VOL289
function. Consequently,the concept of an electron having a
particular location and a particular momentum loses its
foundation.The UncertaintyPrinciple quantifies this: To locate a particle precisely, the wave function must be sharply
peaked (that is, not spread out). However, a sharp peak requires a steep slope, and so the spread in momentum will be
great. Conversely, if the momentum has a small spread,the
slope of the wave function must be small, which means that
it must spread out over a large volume, thereby portraying
the particle'slocation less exactly.
Waves can interfere. Their heights add or subtract depending on their relativephase. Where the amplitudes are in
phase, they add; where they are out of phase, they subtract.
If a wave can follow several paths from source to receiver,as
a light wave undergoing two-slit interference,then the illumination will generally display interference fringes. Particles obeying a wave equation will do likewise, as in electron
diffraction.The analogy seems reasonableuntil one inquires
about the nature of the wave. A wave is generally
thought of as a disturbancein a medium. In quantum
mechanics there is no medium, and in a sense there is
no wave, as the wave function is fundamentally a
statementof our knowledge of a system.
Symmetryand identity. A helium atom consists of
a nucleus surrounded by two electrons. The wave
function of helium describes the position of each
electron. However, there is no way of distinguishing
which 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 the
Omniscient math. It'stough probability depends on
j
to solve, but ErwinSchrod- the sqare of the maginger's famous equation nitudeofthewavefunc(shown in one of its many tion, the wave function
forms)describeseveryobserv- for the system with the
ablestate of a physicalsystem. interchanged particles
must be related to the
original wave function
in one oftwo ways:
r(vt)
JI' (V ) w -?'l) Either
it is identical to
the original wave function, or its sign is simply reversed, i.e., it is multiplied by a factor of-1. Which
one is it?
One of the astonishing discoveries in quantummechanics
is that for electrons the wave function always changes sign.
The consequences are dramatic, for if two electrons are in
the same quantumstate, then the wave function has to be its
negative opposite. Consequently, the wave function must
vanish. Thus, the probabilityof finding two electrons in the
same state is zero. This is the Pauli exclusion principle. All
particles with half-integer spin, including electrons, behave _
this way and are called fermions. For particles with integer :
spin, including photons, the wave function does not change
sign. Such particles are called bosons. Electrons in an atom ^
arrangethemselves in shells because they are fermions, but
light 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 U
condensate, in which the system can emit a superintense 2
matterbeam-forming an atom laser.
These ideas apply only to identical particles, because if a
different particles are interchanged the wave function will ?
)
SCIENCE www.sciencemag.org
PATHWAYS OF DISCOVERY
certainlybe different.Consequently,particlesbehavelike TheSecondRevolution
fermionsor likebosonsonlyif theyaretotallyidentical.The Duringthe freneticyearsin the mid-1920swhenquantum
absoluteidentityof likeparticlesis amongthemostmysteri- mechanics was being invented,anotherrevolutionwas
underway.The foundationswere being laid
ous aspectsof quantummechanof
ics. Amongthe achievements
for the secondbranchof quantumphysicsquantumfield theory is that it
quantumfield theory.Unlike quantummecanexplainthismystery.
chanics,which was createdin a shortflurry
Whatdoes it mean? Quesof activity and emerged essentially comtions suchas whata wavefuncplete, quantumfield theory has a tortuous
tion "really is" and what is
history that continuestoday.In spite of the
meant by "makinga measuredifficulties,the predictionsof quantumfield
ment"wereintenselydebatedin
theoryare the most precisein all of physics,
the earlyyears.By 1930, howand quantum field theory constitutes a
ever,a moreor less standardinparadigmfor some of the most crucialareas
of theoreticalinquiry.
terpretation of quantum mechanicshad been developedby
The problem that
motivated quantum field
Bohrandhis colleagues,the socalled Copenhageninterpretatheory was the questionof
tion. The key elementsare the
how an atom radiateslight
as its electrons "jump"
probabilistic
descriptionof matfrom excited states to the
ter and events, and reconcilia^
tion of the wavelikeand partigroundstate. Einsteinpro:
posed such a process,
clelikenaturesof thingsthrough
called spontaneous emisBohr'sprincipleof complemen^
tarity.Einsteinnever accepted
IHI^H sion, in 1916,buthe hadno
quantumtheory.He and Bohr Quantumwebs. BycreatingF)articlesthat way to calculate its rate. B
E
debatedits 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-generated
_
rings,re;searchersare relativisticquantumtheory
unencryption of electromagnetic
fields, a
A central issue in the de- developing new quantur
quantumtheory of light. Quantummechancomrnters.
2 bates on quantummechanics schemesandquantum
ics is the theory of matter.Quantumfield
' was whetherthe wave function
z containsall possibleinformationabouta systemor if there theory,as its name suggests, is the theory of fields, not
fields but otherfields thatwere sub< mightbe underlyingfactors-hiddenvariables-thatdeter- only electromagnetic
In the mid- sequentlydiscovered.
| minethe outcomeof a particularmeasurement.
In 1925 Born,Heisenberg,and Jordanpublishedsome
| 1960sJohnS. Bell showedthatif hiddenvariablesexisted,
_ experimentallyobservedprobabilitieswould have to fall initial ideas for a theory of light, but the seminal steps
Experi- were takenby Dirac-a young and essentiallyunknown
| below certainlimits, dubbed"Bell'sinequalities."
S ments were carried out by a numberof groups, which
physicist working in isolation-who presented his
field theory in 1926. The
~-foundthatthe inequalitieswere violated.Theircollective
theory was full of pitfalls:
t datacame down decisivelyagainstthe possibilityof hidformidable calculational
v den variables.Formost scientists,this resolvedany doubt
complexity, predictionsof
E aboutthe validityof quantummechanics.
infinite quantities,and apNevertheless,the natureof quantumtheorycontinuesto
parentviolationsof the corM attractattentionbecause of the fascinationwith what is
respondenceprinciple.
p sometimesdescribedas "quantumweirdness."The weird
In the late 1940s a new
of quantumsystemsarisefromwhatis knownas
o properties
approach to the quantum
Briefly,a quantumsystem,such as an atom,
5 entanglement.
statesbutalso
theory of fields, QED (for
. canexistin anyone of a numberof stationary
in a superposition-orsum-of suchstates.If one measures
quantumelectrodynamics),
was developedby Richard
M 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,called
v tem in an entangledstate in which the propertiesof both
< atomsaresharedwitheachother.If the atomsareseparated, Fields go quantum. Paul renormalization,which esworklead- sentially subtractsinfinite
Diracspearheaded
information
aboutone is shared,or entangled,in the stateof
z the other.The behavioris unexplainable
exceptin the lan- ing to quantumfieldtheory quantitiesso as to leavefisuchas nite results.Becausethereis
^guageof quantummechanics.The effectsare so surprising as wellas discoveries
no exact solution to the
v thattheyarethe focusof studyby a smallbutactivetheoret- antimatter.
complicatedequationsof the
Theissuesarenot limited
community.
| ical andexperimental
to questionsof principle,as entanglement
canbe useful.En- theory,an approximateansweris presentedas a series of
g tangledstateshavealreadybeenemployedin quantumcom- termsthatbecomemoreandmoredifficultto calculate.Alunderliesall propos- though the terms become successively smaller,at some
- municationsystems,andentanglement
e als forquantumcomputation.
pointtheyshouldstartto grow,indicatingthebreakdownof
I
I
.
www.sciencemag.org SCIENCE VOL289
11 AUGUST2000
897
PATHWAYS
the approximation. In spite of these
perils, QED ranks among the most brilliant successes in the history of physics.
Its prediction of the interactionstrength
between an electron and a magnetic
field has been experimentally con-
OF DISCOVERY
fica.com enhancesthe
Eachmonth,Britann
accessthis month'sIPatl
hwaysessayandall niscent of the frenzied and miraculous
previous ones, go tc) www.britannica.comdays in which quantum mechanics was
andclickonthe Sciei
nce
created, and whose outcome may be
even morefar-reaching.
The effortis in1,000,000,000,000.
extricablyboundto the questfor a quantumdescriptionof
Notwithstandingits fantasticsuccesses, QED harbors gravity.The procedurefor quantizingthe electromagnetic
enigmas.The view of emptyspace-the vacuum-that the field thatworkedso brilliantlyin QEDhas failedto work
theoryprovidesinitiallyseems preposterous.It turnsout for gravity,in spiteof a half-centuryof effort.Theproblem
that empty space is not really empty.Rather,it is filled is critical,for if generalrelativityandquantummechanics
fields.Thesevacu- are bothcorrect,then they mustultimatelyprovidea conwith small,fluctuatingelectromagnetic
um fluctuationsare essential for explainingspontaneous sistentdescriptionfor the sameevents.Thereis no contraemission.Furthermore,
theyproducesmallbutmeasurable dictionin the normalworldaroundus, becausegravityis
so fantasticallyweak comparedto the electricalforces in
shifts in the energies of atoms and certainpropertiesof
particlessuch as the electron.Strangeas they seem, these atoms that quantumeffects are negligibleand a classical
effects have been confirmedby some of the most precise descriptionworksbeautifully.But for a system such as a
firmed to a precision of two parts in
?I
-l~I
-I
:IrI
:II
experiments ever carried out.
At the low energies of the world
around us, quantummechanics is fantastically accurate. But at high energies
where relativistic effects come into play,
a more general approach is needed.
Quantum field theory was invented to
reconcile quantum mechanics with spe-
cial relativity.
)II
51
-lI
-l~
The towering role that quantum field
theoryplaysin physicsarisesfromtheanswers it provides to some of the most profound questions about the nature of matter. Quantum field theory explains why
there are two fundamentalclasses of particles-fermions and bosons-and how
their properties are related to their intrinsic spin. It describes how particles-not
only photons, but electrons and positrons
(antielectrons)-are created and annihiIt explains the mysterious natureof
B |
~~~~~lated.
identity in quantum mechanics-how
_SHH|
identical particles are absolutely identical
_IUjju
because they are created by the same underlying field. QED describes not only
the electron but the class of particles called leptons that includes the muon, the tau meson, and their antiparticles.
Because QED is a theory for leptons, however, it cannot
describe more complex particles called hadrons. These include protons, neutrons, and a wealth of mesons. For
hadrons, a new theory had to be invented, a generalization
of QED called quantumchromodynamics, or QCD. Analogies aboundbetween QED and QCD. Electrons are the constituents of atoms; quarks are the constituents of hadrons.
In QED the force between chargedparticles is mediated by
the photon; in QCD the force between quarks is mediated
by the gluon. In spite of the parallels, there is a crucial difference between QED and QCD. Unlike leptons and photons, quarks and gluons are forever confined within the
hadron.They cannot be liberatedand studied in isolation.
QED and QCD are the cornerstonesfor a grand synthesis
known as the StandardModel. The StandardModel has successfully accountedfor every particle experimentcarriedout
to date. However,for many physicists the StandardModel is
inadequate,because data on the masses, charges, and other
of thefundamental
particlesneedto be foundfrom
properties
An idealtheorywouldpredictall of these.
experiments.
898
Today,the quest to understandthe ul-
Pathwaysof Discove*ryessay with links to timate nature of matter is the focus of
relevantitems withinlanidwithout EncylopediaBritannica's
vaststtore.s of information.
To an intense scientific study that is remi-
11 AUGUST2000
VOL289
black hole where gravity is incredibly strong, we have no
reliable way to predict quantumbehavior.
One century ago our understandingof the physical world
was empirical. Quantumphysics gave us a theory of matter
and fields, and that knowledge transformedour world. Looking to the next century,quantummechanics will continue to
provide fundamentalconcepts and essential tools for all of
the sciences. We can make such a predictionconfidently because for the world aroundus quantumphysics provides an
exact and complete theory. However, physics today has this
in common with physics in 1900: It remains ultimatelyempirical-we cannot fully predictthe propertiesof the elementary constituentsof matter,we must measurethem.
Perhaps string theory-a generalization of quantum
field theory that eliminates all infinities by replacing
pointlike objects such as the electron with extended
objects-or some theory only now being conceived, will
solve the riddle. Whatever the outcome, the dream of ultimate understandingwill continue to be a driving force for
new knowledge, as it has been since the dawn of science.
One century from now, the consequences of pursuing that
dream will belie our imagination.
FurtherReading
B. Bederson, Ed., More Things in Heaven and Earth: A Celebration of Physics at
the Millennium (Springer Verlag, New York, 1999).
J. S. Bell, Speakable and Unspeakable in Quantum Mechanics: Collected Papers
on Quantum Mechanics (reprint edition) (Cambridge University Press,
Cambridge, 1989).
L. M. Brown, A. Pais, B. Pippard, Eds., Twentieth Century Physics (Institute of
Physics, Philadelphia 1995).
D. Cassidy, Uncertainty: The Life and Science of Werner Heisenberg (W. H.
Freeman, New York, 1993).
A. Einstein, Born-Einstein Letters, trans. Irene Born (Macmillan, London, 1971).
H. Kragh, Dirac: A Scientific Biography (Cambridge University Press, Cambridge, 1990).
W. Moore, Schrodinger: Life and Thought (Cambridge University Press, Cambridge, 1989).
A. Pais, Inward Bound: Of Matter and Forces in the Physical World (Oxford
University Press, Oxford, 1986).
A. Pais, Niels Bohr's Times: In Physics, Philosophy, and Polity (Oxford University Press, Oxford, 1991).
DanielKleppneris LesterWolfProfessorof PhysicsandActingDirectorof
of Electronicsat the MassachusettsInstituteof
the ResearchLaboratory
Technology.His researchinterestsincludeatomic physics,quantumopcondensation.
tics, ultraprecise
spectroscopy,and Bose-Einstein
RomanJackiwis JerroldJachariasProfessorof Physicsat MIT.Hisresearchi
interestsincludeapplyingquantumfieldtheoryto physicalproblems,the- z
oreticalparticlephysics,andthe searchfor unexpected,subtleeffectsthat |
physics.
mayapplyto particle,condensedmatter,andgravitational
SCIENCE www.sciencemag.org
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