TableofContents

TitlePageDedicationAbouttheTitleReader’sGuidePARTI-TheOriginofMass

Chapter1-GettingtoItSensesandWorld-ModelsPower,Meaning,andMethodTheCentralityofMass

Chapter2-Newton’sZerothLawGodandtheZerothLawGettingRealDownfallDoesMassHaveanOrigin?

Chapter3-Einstein’sSecondLawFindingNewLaws,MadeSimpleEinstein’sSecondLawFAQ

Chapter4-WhatMattersforMatterBuildingBlocks

Chapter5-TheHydraWithinFermi’sDragonsWrestlingwithDragonsHydra

Chapter6-TheBitsWithintheItsQuarks:BetaReleaseQuarks1.0:ThroughanUltrastroboscopicNanomicroscopePartons,Put-Ons,andPutdownsTooSimple

AsymptoticFreedom(ChargeWithoutCharge)QuarksandGluons2.0:BelievingIsSeeing

Chapter7-SymmetryIncarnateNutsandBolts,HubsandSticksQuarksandGluons3.0:SymmetryIncarnate

Chapter8-TheGrid(PersistenceofEther)ABriefHistoryofEtherSpecialRelativityandtheGridGluonsandtheGridMaterialGridTheMotherofAllGrids:MetricFieldGridWeighsRecapitulation

Chapter9-ComputingMatterAToyModelinThirty-TwoDimensionsLaplace’sDemonversusGridPandemoniumTheBig(Number)Crunch

Chapter10-TheOriginofMassFirstIdea:BlossomingStormsSecondIdea:CostlyCancellationsThirdIdea:Einstein’sSecondLawScholium

Chapter11-MusicoftheGrid:APoeminTwoEquationsChapter12-ProfoundSimplicity

PerfectionSupportingComplexity:Salieri,JosephII,andMozartProfoundSimplicity:SherlockHolmes,NewtonAgain,andYoung

MaxwellCompression,Decompression,and(In)Tractability

PARTII-TheFeeblenessofGravity

Chapter13-IsGravityFeeble?Yes,inPracticeChapter14-IsGravityFeeble?No,inTheory

UniversalityandUnificationChapter15-TheRightQuestionChapter16-ABeautifulAnswer

Pythagoras’Vision,Planck’sUnitsUnificationScorecardNextSteps

PARTIII-IsBeautyTruth?

Chapter17-Unification:TheSiren’sSongTheCore:ChoiceBitsCritiqueTheChargeAccountTheSiren’sSong

Chapter18-Unification:ThroughaGlass,DarklySymmetryNotCorrectingOurVisionANearMiss

Chapter19-TruthificationUppingtheAnte:MoreUnification

Chapter20-Unification♥SUSYCorrectingtheCorrectionGravityToo

Chapter21-AnticipatingaNewGoldenAgeTheLHCProjectDarkMatterintheBalanceOneShoeHeardFrom;ListeningforOthers

EpilogueAcknowledgementsAppendixA-ParticlesHaveMass,theWorldHasEnergyAppendixB-TheMultilayered,MulticoloredCosmicSuperconductorAppendixC-From“NotWrong”to(Maybe)RightGlossaryNotesIllustrationCreditsIndexCopyrightPage

DedicatedtothememoryofSamTreimanandSidneyColeman—guidesinscience,friendsinlife.

AbouttheTitle

THEUNBEARABLELIGHTNESSOFBEING is thetitleofafamousnovelbyMilanKundera—oneofmyfavoritebooks.Itisaboutmanythings,butperhapsabove all the struggle to find pattern and meaning in the seemingly random,strange,andsometimescruelworldwelivein.OfcourseKundera’sapproachtothese problems, through story and art, looks very different from the one I’vetaken in this book, through science and (light) philosophy. For me at least,coming to understand the deep structure of reality has helped to make Beingseem not merely bearable, but enchanted—and enchanting. Hence, The

LightnessofBeing.

There’salsoajokeinvolved.Acentralthemeofthisbookisthattheancientcontrast between celestial light and earthy matter has been transcended. Inmodernphysics,there’sonlyonething,andit’smorelikethetraditionalideaoflightthanthetraditionalideaofmatter.Hence,TheLightnessofBeing.

Reader’sGuide

THECOREPLANOFTHISBOOKcouldn’tbesimpler:itismeanttobereadchapterbychapter,frombeginningtoend.ButI’vealsosupplied:

• An extensive glossary, so that you don’t get tripped up by unfamiliarwordsorhave tosearchfor theplacefiftypagesbackwhere theywereintroduced.Itcanalsobeminedforcocktailpartynuggets.It’sevengotafewjokes.

•Endnotesthatelaborateonfinepoints,followsomeimportanttangents,orprovidereferences.

• Three appendices. The first two take discussions in Chapters 3 and 8,respectively,intodeeperwaters;thethirdisafirst-personaccountofhowakeydiscoveryreportedinChapter20occurred.

•Awebpage,itsfrombits.com,whereyou’llfindadditionalpictures,links,andnewsrelatedtothebook.

Youcandetourtotheappendicesastheirchapterscomeup,butifyouprefertoget on with the story instead, you should still find it comprehensible. IconsideredoffloadingmoreofthematerialinChapter8,butintheendIcouldn’tbringmyselftodoit.Sointhatchapteryou’llfindmuchadoaboutNothing.

PARTI

TheOriginofMass

MATTER ISNOTWHAT ITAPPEARSTOBE. Itsmostobviousproperty—variouslycalledresistancetomotion,inertia,ormass—canbeunderstoodmoredeeply in completely different terms. The mass of ordinary matter is theembodiedenergyofmorebasicbuildingblocks,themselveslackingmass.Norisspacewhatitappearstobe.Whatappearstooureyesasemptyspaceisrevealedtoourmindsasacomplexmediumfullofspontaneousactivity.

1

GettingtoIt

Theuniverseisnotwhatitusedtobe,norwhatitappearstobe.

WHAT’SITALLABOUT?Peoplereflectinguponthewideworldaroundthem,thevariedandoftenbewilderingexperienceoflife,andtheprospectofdeatharedriventoask thatquestion.Weseekanswersfrommanysources:ancient textsand continuing traditions, the love and wisdom of other people, the creativeproductsofmusicandart.Eachofthesesourceshassomethingtooffer.

Logically, however, the first step in the search for answers should be tounderstandwhat“it”is.Ourworldhassomeimportantandsurprisingthingstosayforitself.That’swhatthisbookisabout.Iwanttoenrichyourunderstandingofjustwhat“it”isthatyouandIfindourselveswithin.

SensesandWorld-Models

To begin, we build our world-models from strange raw materials: signal-processing tools “designed” by evolution to filter a universe swarming withinformationintoaveryfewstreamsofincomingdata.

Data streams?Theirmore familiar names are vision, hearing, smell, and soforth.Fromamodernpointofview,visioniswhatsamplestheelectromagneticradiation that passes through tinyholes in our eyes, pickinguponly a narrowrainbow of colors inside a much broader spectrum. Our hearing monitors airpressureatoureardrums,andsmellprovidesaquirkychemicalanalysisof theairimpingingonournasalmembranes.Othersensorysystemsgivesomeroughinformation about the overall acceleration of our body (kinesthetic sense),temperaturesandpressuresoveritssurface(touch),ahandfulofcrudemeasures

of the chemical composition ofmatter on our tongue (taste), and a few otheroddsandends.

Those sensory systems allowed our ancestors—just as they allow us—toconstruct a rich, dynamic model of the world, enabling them to respondeffectively. Themost important components of thatworld-model aremore-or-less stable objects (such as other people, animals, plants, rocks, . . . the Sun,stars,clouds,...)someofthemmovingaround,somedangerous,somegoodtoeat,andothers—aselectandespeciallyinterestingfew—desirablemates.

Devices to enhance our senses reveal a richer world. When Antonie vanLeeuwenhoek lookedat the livingworld through thefirstgoodmicroscopes inthe1670s,hesawtotallyunsuspected,hiddenordersofbeing.Inshortorderhediscovered bacteria, spermatozoa, and the banded structure of muscle fibers.Todaywetracetheoriginofmanydiseases(andofmanybenefits) tobacteria.Thebasisofheredity(well,halfofit)isfoundwithinthetinyspermatozoa.Andourabilitytomoveisanchoredinthosebands.Likewise,whenGalileoGalileifirst turneda telescope to thesky in the1610s,newrichesappeared:hefoundspotsontheSun,mountainsontheMoon,moonsaroundJupiter,andmultitudesofstarsintheMilkyWay.

But theultimatesense-enhancingdevice isa thinkingmind.Thinkingmindsallowus to realize that theworldcontainsmuchmore,and is inmanywaysadifferentthing,thanmeetstheeye.Manykeyfactsabouttheworlddon’tjumpout toour senses.Theparadeof seasons, in lock-stepwith theyearlycycleofsunriseandsunset,thenightlyrotationofstarsacrossthesky,themoreintricatebutstillpredictablemotionsoftheMoonandplanets,andtheirconnectionwitheclipses—thesepatternsdonotleaptotheeye,ear,ornose.Butthinkingmindscan discern them.And having noticed those regularities, thinkingminds soondiscover that they are more regular than the rules of thumb that guide oureveryday plans and expectations. Themore profound, hidden regularities lendthemselvestocountingandtogeometry:inshort,tomathematicalprecision.

Other hidden regularities emerged from the practice of technology—and,remarkably,ofart.Thedesignofstringedmusicalinstrumentsisabeautifulandhistoricallyimportantexample.Around600BCE,Pythagorasobservedthatthetonesofalyresoundmostharmoniouswhentheratioofstringlengthsformsasimple whole-number fraction. Inspired by such hints, Pythagoras and hisfollowersmade a remarkable intuitive leap. They foresaw the possibility of a

differentkindofworld-model,lessdependentontheaccidentofoursensesbutmore in tunewithNature’s hidden harmonies, and ultimatelymore faithful toreality.ThatisthemeaningofthePythagoreanBrotherhood’scredo:“Allthingsarenumber.”

The scientific revolution of the seventeenth century began to validate thosedreamsofancientGreece.That revolution led to IsaacNewton’smathematicallawsofmotion andof gravity.Newton’s lawspermitted precise calculationofthemotionofplanetsandcomets,andprovidedpowerfultoolsfordescribingthemotionofmatteringeneral.

YettheNewtonianlawsoperateinaworld-modelthat isverydifferentfromeverydayintuition.BecauseNewtonianspaceisinfiniteandhomogeneous,Earthand its surface are not special places. The directions “up,” “down,” and“sideways” are fundamentally similar. Nor is rest privileged over uniformmotion. None of these concepts matches everyday experience. They troubledNewton’scontemporaries,andevenNewtonhimself.(Hewasunhappywiththerelativityofmotion,eventhoughitisalogicalconsequenceofhisequations,andto escape it he postulated the existence of “absolute” space, with respect towhichtruerestandmotionaredefined.)

Another big advance came in the nineteenth century, with James ClerkMaxwell’sequationsforelectricityandmagnetism.Thenewequationscaptureda wider range of phenomena, including both previously known and newlypredictedkindsoflight(whatwenowcallultravioletradiationandradiowaves,for example), in aprecisemathematicalworld-model.Again,however, thebigadvancerequiredareadjustmentandvastexpansionofourperceptionofreality.Where Newton described the motion of particles influenced by gravity,Maxwell’sequationsfilledspacewiththeplayof“fields”or“ethers.”AccordingtoMaxwell,what our senses perceive as empty space is actually the home ofinvisible electric and magnetic fields, which exert forces on the matter weobserve.Althoughtheybeginasmathematicaldevices,thefieldsleapoutoftheequations to take on a life of their own. Changing electric fields producemagneticfields,andchangingmagneticfieldsproduceelectricfields.Thusthesefields can animate one another in turn, giving birth to self-reproducingdisturbancesthattravelatthespeedoflight.EversinceMaxwell,weunderstandthatthesedisturbancesarewhatlightis.

These discoveries of Newton, Maxwell, and many other brilliant people

greatlyexpandedhumanimagination.Butit’sonlyintwentiethandtwenty-firstcentury physics that the dreams of Pythagoras truly approach fruition.As ourdescriptionoffundamentalprocessesbecomesmorecompleteweseemore,andwe see differently. The deep structure of the world is quite different from itssurface structure. The senses we are born with are not attuned to our mostcompleteandaccurateworld-models.Iinviteyoutoexpandyourviewofreality.

Power,Meaning,andMethod

WhenIwasgrowingup,Ilovedtheideathatgreatpowersandsecretmeaningslurk behind the appearance of things.1 I was entranced by magic shows andwanted to become a magician. But my first magic kit was a profounddisappointment.Thesecretofthemagic,Ilearned,wasnotgenuinepower,justtrickery.

Later, Iwas fascinatedby religion: specifically, theRomanCatholic faith inwhichIgrewup.HereIwasinformedthattherearesecretmeaningsbehindtheappearanceofthings,greatpowersthatcanbeswayedbyprayerandritual.Butas I learnedmoreabout science, someof theconcepts andexplanations in theancient sacred texts came to seemclearlywrong; and as I learnedmore abouthistoryandhistoriography(therecordingofhistory),someofthestoriesinthosetextscametoseemverydoubtful.

What I found most disillusioning, however, was not that the sacred textscontainederrors,butthattheysufferedbycomparison.ComparedtowhatIwaslearning in science, they offered few truly surprising and powerful insights.Wherewasthereavisiontocompetewiththeconceptsofinfinitespace,ofvastexpanses of time, of distant stars that rival and surpass our Sun? Of hiddenforces and new, invisible forms of “light”? Or of tremendous energies thathumanscould,byunderstandingnaturalprocesses,learntoliberateandcontrol?IcametothinkthatifGodexists,He(orShe,orThey,orIt)didamuchmoreimpressive job revealingHimself in theworld than in theoldbooks—and thatthepoweroffaithandprayeriselusiveandunreliablecomparedtotheeverydaymiraclesofmedicineandtechnology.

“Ah,”Ihearthetraditionalbelieverobject,“butscientificstudyofthenaturalworlddoesnotrevealitsmeaning.”TowhichIreply:Giveitachance.Science

revealssomeverysurprisingthingsaboutwhattheworldis.Shouldyouexpecttounderstandwhatitmeans,beforeyouknowwhatitis?

InGalileo’s time,professorsofphilosophyand theology—the subjectswereinseparable—producedgranddiscoursesonthenatureofreality,thestructureofthe universe, and the way the world works, all based on sophisticatedmetaphysicalarguments.Meanwhile,Galileomeasuredhowfastballsrolldowninclined planes.Howmundane!But the learned discourses,while grand,werevague. Galileo’s investigations were clear and precise. The old metaphysicsneverprogressed,whileGalileo’sworkboreabundant,andatlengthspectacular,fruit. Galileo too cared about the big questions, but he realized that gettinggenuineanswersrequirespatienceandhumilitybeforethefacts.

Thatlessonremainsvalidandrelevanttoday.Thebestwaytoaddressthebigultimatequestions is likely tobe throughdialoguewithNature.Wemustposepointed sub-questions that give Nature a chance to respond with meaningfulanswers,inparticularwithanswersthatmightsurpriseus.

Thisapproachdoesnotcomenaturally.Inthelifeweevolvedfor, importantdecisionshadtobemadequicklyusingtheinformationathand.Peoplehadtospeartheirpreybeforetheybecametheprey.Theycouldnotpausetostudythelawsofmotion, the aerodynamics of spears, and how to compute a trajectory.And big surprises were definitely not welcome. We evolved to be good atlearning and using rules of thumb, not at searching for ultimate causes andmakingfinedistinctions.Still lessdidweevolvetospinoutthelongchainsofcalculation that connect fundamental laws to observable consequences.Computersaremuchbetteratit!

To benefit fully from our dialogue with Nature, wemust agree to use Herlanguage.ThemodesofthoughtthathelpedustosurviveandreproduceontheAfricansavannahof200000BCEwillnotsuffice.Iinviteyoutoexpandthewayyouthink.

TheCentralityofMass

Inthisbookwe’llexploresomeofthegrandestquestionsimaginable:questionsabouttheultimatestructureofphysicalreality,thenatureofspace,thecontentsoftheUniverse,andthefutureofhumaninquiry.InspiredbyGalileo,however,I

willaddressthesequestionsastheyariseinthecourseofanaturaldialoguewithNature,aboutaspecifictopic.

The topic thatwill be our doorway intomuch bigger questions ismass. Tounderstand mass deeply, we’ll move past Newton, Maxwell, and Einstein,callingonmanyofthenewestandstrangestideasofphysics.Andwe’llfindthatunderstanding mass allows us to address very fundamental issues aboutunificationandgravitythatareattheforefrontofcurrentresearch.

Whyismasssocentral?Letmetellyouastory.

Once upon a time there was something called matter that was substantial,weighty,andpermanent.Andsomethingelse,quitedifferent,calledlight.Peoplesensedtheminseparatedatastreams;touchingone,seeingtheother.Matterandlight served—and still do serve—as powerfulmetaphors for other contrastingaspectsofreality:fleshandspirit,beingandbecoming,earthyandcelestial.

Whenmatterappearedfromnowhere,itwasasuresignofthemiraculous,aswhenJesusservedthemultitudefromsixloavesofbread.

Thescientificsoulofmatter,itsirreducibleessence,wasmass.Massdefinedmatter’sresistancetomotion, its inertia.Masswasunchangeable,“conserved.”It couldbe transferred fromonebody toanotherbutcouldneverbegainedorlost. ForNewton,massdefined quantity ofmatter. InNewton’s physics,massprovided the link between force and motion, and it provided the source ofgravity. For Lavoisier, the persistence of mass, its accurate conservation,providedthefoundationofchemistry,andofferedafruitfulguidetodiscovery.Ifmassseemstodisappear,lookforitinnewforms—voilà,oxygen!

Light had no mass. Light moved from source to receptor incredibly fast,withoutbeingpushed.Lightcouldbecreated(emitted)ordestroyed(absorbed)very easily. Light exerted no gravitational pull. And it found no place in theperiodictable,whichcodifiedthebuildingblocksofmatter.

Formany centuries beforemodern science, and for the first two and a halfcenturiesofmodernscience,thedivisionofrealityintomatterandlightseemedself-evident.Matterhadmass, lighthadnomass;andmasswasconserved.Aslongastheseparationbetweenthemassiveandthemasslesspersisted,aunifieddescriptionofthephysicalworldcouldnotbeachieved.

In the first part of the twentieth century, the upheavals of relativity and(especially)quantumtheoryshatteredthefoundationsbeneathclassicalphysics.

Existing theories ofmatter and light were reduced to rubble. That process ofcreative destructionmade it possible to construct, over the second part of thetwentieth century, a new and deeper theory of matter/light that removed theancientseparation.Thenewtheoryseesaworldbasedonamultiplicityofspace-filling ethers, a totality I call the Grid. The new world-model is extremelystrange,butalsoextremelysuccessfulandaccurate.

The new world-model gives us a fundamentally new understanding of theorigin of themass of ordinarymatter.Hownew?Ourmass emerges, aswe’lldiscuss, from a recipe involving relativity, quantum field theory, andchromodynamics—the specific laws governing the behavior of quarks andgluons.Youcannot understand theoriginofmasswithout profounduseof allthese concepts. But they all emerged only in the twentieth century, and only(special) relativity is really a mature subject. Quantum field theory andchromodynamicsremainactiveareasofresearch,withmanyopenquestions.

Highon theirsuccess,andhaving learnedmuchfromit,physicistsenter thetwenty-first century with ideas for further syntheses. Today, ideas that go fartoward achieving a unified description of the superficially different forces ofnature, and toward achieving a unified account of the superficially differentethersweusetoday,arereadyfortesting.Wehavesomesubtle,tantalizinghintsthat thoseideasareontherighttrack.Thenextfewyearswillbetheir timeoftrial,asthegreatacceleratorLHC(LargeHadronCollider)beginstooperate.

listen:there’sahellofagooduniversenextdoor;let’sgo.—eecummings

2

Newton’sZerothLaw

Whatismatter?Newtonianphysicssuppliedaprofoundanswertothatquestion:matteristhatwhichhasmass.Whilewenolongerseemassastheultimatepropertyofmatter,itisanimportantaspectofreality,towhichwemustdojustice.

INMATHEMATICALPRINCIPLESOFNATURALPHILOSOPHY (1686), themonumental work that perfected classical mechanics and sparked theEnlightenment, Isaac Newton formulated three laws of motion. To this day,courses on classical mechanics usually begin with some version of Newton’sthreelaws.Buttheselawsarenotcomplete.Thereisanotherprinciple,withoutwhichNewton’sthreelawslosemostoftheirpower.ThathiddenprinciplewassobasictoNewton’sviewofthephysicalworldthathetookitnotasalawthatgovernsthemotionofmatter,butasthedefinitionofwhatmatteris.

When I teach classical mechanics, I start by bringing out the hiddenassumptionIcallNewton’szerothlaw.AndIemphasizethatit iswrong!Howcanadefinitionbewrong?Andhowcanawrongdefinitionbe the foundationforgreatscientificwork?

ThelegendaryDanishphysicistNielsBohrdistinguishedtwokindsoftruths.Anordinarytruthisastatementwhoseoppositeisafalsehood.Aprofoundtruthisastatementwhoseoppositeisalsoaprofoundtruth.

Inthatspirit,wemightsaythatanordinarymistakeisonethatleadstoadeadend,whileaprofoundmistakeisonethatleadstoprogress.Anyonecanmakeanordinarymistake,butittakesageniustomakeaprofoundmistake.

Newton’szerothlawwasaprofoundmistake.ItwasthecentraldogmaofanOldRegimethatgovernedphysics,chemistry,andastronomyformorethantwocenturies.OnlyatthebeginningofthetwentiethcenturydidtheworkofPlanck,

Einstein,andothersbegintochallengetheOldRegime.Bymid-century,underbombardment from new experimental discoveries, the Old Regime hadcrumbled.

Thatdestructionopenedthewaytoanewcreation.OurNewRegimeframesanentirelynewunderstandingofwhatmatter is.TheNewRegimeisbasedonlaws that differ from the old ones, notmerely in detail but also in kind. Thisrevolution in basic understanding, and its consequences, are what we’ll beexploring.

ButtojustifytherevolutionwemustfirstbringtheshortcomingsoftheOldRegimeintoclearfocus.Foritsmistakesare,inBohr’ssense,profound.TheOldRegime ofNewtonian physics gave us relatively simple and easy-to-use ruleswithwhichwecouldgovernthephysicalworldprettyeffectively.Inpractice,westill use those rules to administer the more peaceful, well-settled districts ofreality.

So,tobegin,let’stakeacloselookatNewton’shiddenassumption,hiszerothlaw—both its tremendous strength and its fatalweakness.That law states thatmass is neither created nor destroyed. Whatever happens—collisions,explosions,amillionyearsofwindandrain—ifyouaddupthetotalmassofallthematerialinvolvedatthebeginning,orattheend,oratanyintermediatetime,youwillalwaysgetthesamesum.Thescientificjargonforthisis thatmassisconserved. The standard, dignified name for Newton’s zeroth law isconservationofmass.

GodandtheZerothLaw

Of course, to translate the zeroth law into a meaningful, scientific statementabout the physical world, we have to specify how masses are measured andcompared.We’lldothatmomentarily.Butletmefirsthighlightwhythezerothlawisnotjustanotherscientificlaw,butastrategyforunderstandingtheworld—astrategythatlookedverygoodforaverylongtime.

It’srevealingthatNewtonhimselfusuallyusedthephrasequantityofmatterfor what we now call mass. His wording implies that you can’t have matterwithoutmass.Mass is the ultimatemeasure ofmatter; it tells you howmuchmatteryou’vegot.Nomass,nomatter.Thustheconservationofmassexpresses

—indeed,isequivalentto—thepersistenceofmatter.ForNewton,thezerothlawwas not so much an empirical observation or experimental discovery as anecessarytruth;itwasnotaproperlawatall,butadefinition.Orrather,aswe’llsee in amoment, it expresseda religious truth—a fact aboutGod’smethodofcreation. (To avoid misunderstanding, let me emphasize that Newton was ameticulousempiricalscientist,andhecarefullycheckedthattheconsequencesofhis definitions and assumptions described Nature as accurately as themeasurementsofthedaycouldtestthem.I’mnotsayingthathelethisreligiousideas trump reality. It’smore subtle: those ideas gave him his intuition abouthow realityworks.WhatmotivatedNewton to suspect that something like thezerothlawhadtobetruewasnotpainstakingexperimentsbut,rather,powerfulintuition,derivedfromhisreligion,abouthowtheworldisbuilt.NewtonhadnodoubtaboutGod’sexistence,andhesawhistaskinscienceasrevealingGod’smethodofgoverningthephysicalworld.)

InhislaterOpticks(1704),Newtonwasmorespecificinexpressinghisvisionoftheultimatenatureofmatter:

Itseemsprobabletome,thatGodinthebeginningformedmatterinsolid,massy,hard,impenetrable,moveableparticles,ofsuchsizesandfigures,andwithsuchotherproperties,andinsuchproportionstospace,asmostconducedtotheendsforwhichHeformedthem;andthattheseprimitiveparticlesbeingsolids,areincomparablyharderthananyporousbodiescompoundedofthem,evensoveryhard,asnevertowearorbreakinpieces;noordinarypowerbeingabletodividewhatGodHimselfmadeoneinthefirstcreation.

Thisremarkablepassagecontainsafewpointsweshouldnotice.First:Newtontakesthepropertyofhavingafixedmassasoneofthemostbasicpropertiesofthe ultimate building blocks of matter. He calls it being “massy.” Mass, forNewton, is not something you should try to explain in terms of somethingsimpler. It is part of the ultimate description of matter; it reaches bottom.Second: Newton ascribes the changes we observe in the world entirely torearrangements of elementary building blocks, elementary particles. Thebuilding blocks themselves are neither created nor destroyed—they justmovearound.OnceGodhasmadethem,theirproperties, includingtheirmass,neverchange.Newton’szerothlawofmotion,theconservationofmass,followsfromthosetwopoints.

GettingReal

Nowwemustreturnfromtheseheadyphilosophico-theologicalideasaboutwhyconservationofmassmightbetrue,ormustbetrue,totheordinarybusinessofmeasuringtoseewhetheritistrue.

Howdowemeasuremass?Themostfamiliarwayistouseascale.Onesortof scale, thekinddietershave in theirbathrooms, compareshowmuchbodies(thatis,dieters’bodies)cancompressaspring.Closelyrelatedarethescalesthatanglersuse,whichcomparehowmuchdanglingbodies (that is, fish) stretchaspring. The amount the spring stretches (or, for the dieter, compresses) isproportional to thedownwardforce thebodyexerts,which iswhatwecall thebody’sweight,whichisproportionaltoitsmass.

In this very concrete and practical framework, conservation ofmass simplysaysthataclosedsystemwillcontinuetostretchaspringbythesameamount,whatever is going on inside. This is precisely what Antoine Lavoisier (1743-1784) verified—using, to be sure,more sophisticated and accurate scales thanyou’llfindinyourbathroom—inthemanypainstakingexperimentsthatearnedhimthetitle“fatherofmodernchemistry.”Lavoisierchecked,inawidevarietyofchemicalreactions,thatthetotalweightofallthestuffyoustartedwithwasequaltothetotalweightofwhatyouhadafterthereactiontookplace,withintheaccuracyhecouldmeasure(typicallyonepartinathousandorso).Throughthedisciplineofaccountingforallthematterinareaction—capturingthegasesthatmight escape, collecting the ashes of explosions, and so forth—he discoverednew compounds and elements. Lavoisier was guillotined during the FrenchRevolution. The mathematician Joseph Lagrange said, “It took them only amoment to cut off that head, but Francemay not produce another like it in acentury.”

Usingscalestocomparemassesispracticalandeffective,butitwon’tdoasageneral,principleddefinitionofmass.Forexample, ifyou takeyourbodyoutintospace,itsweightasmeasuredbyascalewillgetsmaller,butitsmasswillstaythesame.(Scaleswilllie,butwaistlineswon’tshrink.)Masshadbetterstaythe same, if the law of conservation of mass is going to be true! And thatsuperficiallycircularassertionhasrealcontent,becauseyoucancomparemassesinotherways.Forexample,youcancomparehowfasttwocannonballsstarttoflyafteryoulaunchthemoutofthesamecannon.AccordingtoNewton’sother

laws of motion, a given impulse will give rise to a velocity inverselyproportional to themass. So if one cannonball comes out twice as fast as theother, it has half the mass—whether you do the experiment at the surface ofEarthorinspace.

Iwon’tgofurtherintothetechnicalitiesofmeasuringmass,excepttosaythatthere are many ways to do it besides using scales and shooting things fromcannons,andmanychecksoftheirmutualconsistency.

Downfall

Newton’szerothlawwasacceptedbyscientistsformorethantwocenturies,andnotjustbecauseitfitinwithsomephilosophicalortheologicalintuitions.Itwasacceptedbecause itworked.TogetherwithNewton’sother lawsofmotionandhislawofgravitation,thezerothlawservestodefinethemathematicaldiscipline—classicalmechanics—thataccountswithwonderfulprecisionforthemotionoftheplanetsandtheirmoons,thebewilderingbehaviorofgyroscopes,andmanyotherphenomena.Anditworksbrilliantlyinchemistry,too.

But it doesn’t alwayswork. In fact, the conservation ofmass can fail quitespectacularly.AttheLargeElectron-PositronCollider(LEP),whichoperatedattheCERN laboratory nearGeneva through the 1990s, electrons and positrons(antielectrons)wereacceleratedtovelocitieswithinaboutonepartinahundredbillionth(10-11)of the speedof light.Speedingaround inoppositedirections,the particles smashed into each other, producing a lot of debris. A typicalcollisionmight produce tenπ mesons, a proton, and an antiproton. Now let’scomparethetotalmasses,beforeandafter:

electron+positron:2×10-28gram10pions+proton+antiproton:6×10-24gram

Whatcomesoutweighsabout thirty thousand times asmuchaswhatwent in.Oops.

Fewlawshaveeverappearedmorefundamental,moresuccessful,andmorecarefullyverified than theconservationofmass.Yethere it’sgonecompletelyawry. It’sas ifamagiciandropped twopeas intoherhatandpulledouta fewdozen rabbits. But Mother Nature is no cheap trickster; her “magic” is deep

truth.We’vegotsomeexplainingtodo.

DoesMassHaveanOrigin?

Aslongasmasswasthoughttobeconserved,therewasnosenseinaskingwhatitsoriginis.It’salwaysthesame.Youmightaswellaskwhattheoriginof42is.(Actually there is an answer of sorts. If mass is conserved except when Godmanufactures elementary particles, then God is the origin of mass. That wasNewton’sanswer.But it’snot thekindofexplanationwe’llbepursuingin thisbook.)

Intheframeworkofclassicalmechanics,noanswertothequestion“Whatistheoriginofmass?”couldpossiblymakesense.Tryingtobuildmassiveobjectsfrommasslessonesleadstocontradictions.Therearemanywaystoseethis.Forexample:

• The soul of classicalmechanics is the equationF =ma. This equationrelates the dynamical concept of force (F), which summarizes the pullandtugfeltbyabody,tothekinematicconceptofacceleration(a),whichsummarizes how the bodymoves in response. Themass (m) mediatesbetweenthosetwoconcepts.Inresponsetoagivenforce,abodywithasmallmasswill pickup speed faster than abodywith a largemass.Abodyofzeromasswouldgocrazy!Inordertofigureouthowitshouldmove,itwouldhavetodividebyzero,whichisano-no.Sobodieshadbetterhavemasstobeginwith.

•AccordingtoNewton’slawofgravitation,eachbodyexertsgravitationalinfluencethatisproportionaltoitsmass.Intryingtoimaginethatabodywithnonzeromasscanbeassembledfrombuildingblockswithoutmass,you runsmack intoacontradiction.Thegravitational influenceofeachbuilding block is zero, and no matter how many times you add zeroinfluencetozeroinfluenceyoustillgetzeroinfluence.

But if mass is not conserved—and it’s not!—we can seek its origin. It’s notbedrock.Wecandigdeeper.

3

Einstein’sSecondLaw

Einstein’s“secondlaw,”m=E/c2,raisesthequestionwhethermasscanbeunderstoodmoredeeplyasenergy.Canwebuild,asWheelerputit,“MassWithoutMass”?

WHEN IWASABOUTTOBEGINTEACHING at Princeton,my friend andmentorSamTreimancalledme intohisoffice.Hehadsomewisdomtoshare.Sampulledawell-wornpaperbackmanualfromhisdeskandtoldme,“DuringWorld War II the Navy had to train recruits to set up and operate radiocommunications in ahurry.Manyof those recruitswere rightoff the farm, sobringingthemuptospeedwasabigchallenge.Withthehelpofthisgreatbook,theNavysucceeded.It’samasterpieceofpedagogy.Especiallythefirstchapter.Takealook.”

Hehandedme thebook,opened to the first chapter.Thatchapterwas titled“Ohm’sThreeLaws.”IwasfamiliarwithoneOhm’slaw,thefamousrelationV= IR that connects voltage (V), current (I ), and resistance (R ) in an electriccircuit.ThatturnedouttobeOhm’sfirstlaw.

IwasverycurioustofindoutwhatOhm’sothertwolawswere.Turningthefragile,yellowedpages, Isoondiscovered thatOhm’ssecondlawisI=V/R. Iconjectured that Ohm’s third law might be R = V/I, which turned out to becorrect.

FindingNewLaws,MadeSimple

Now for anyone who’s had experience with elementary algebra, it’s so

immediatelyobvious that those three lawsareall equivalent toeachother thatthisstorybecomesajoke.Butthere’sadeeppointtoit.(There’salsoashallowpoint, which I think is the one Sam wanted me to absorb. When teachingbeginners,youshouldtrytosaythesamethingseveraltimesinslightlydifferentways.Connectionsthatareobvioustoapromightnotcomeautomaticallytothebeginner.And thosestudentswhoseeyoubelaboring theobviouswon’tmind.Veryfewpeoplegetoffendedwhenyoumakethemfeelclever.)

The deep point connects with a statement made by the great theoreticalphysicistPaulDirac.Whenaskedhowhediscoverednewlawsofnature,Diracresponded, “I play with equations.” The deep point is that different ways ofwriting the same equation can suggest very different things, even if they arelogicallyequivalent.

Einstein’sSecondLaw

Einstein’ssecondlawis

Einstein’s first law isofcourseE=mc2.Famously, that first lawsuggests thepossibility of getting large amounts of energy from small amounts ofmass. Itcallstomindnuclearreactorsandnuclearbombs.

Einstein’s second law suggests something quite different. It suggests thepossibility of explaining how mass arises from energy. “Second law” is amisnomer, actually. In Einstein’s original 1905 paper, you do not find theequationE=mc2.Whatyou find ism=E/c2. (Somaybewe should call thatEinstein’s zeroth law.) In fact, the title of that paper is a question: “Does theInertiaofaBodyDependonItsEnergyContent?”Inotherwords:cansomeofabody’smassarisefromtheenergyof thestuff itcontains?RightfromthestartEinsteinwasthinkingabouttheconceptualfoundationsofphysics,notaboutthepossibilityofmakingbombsorreactors.

The concept of energy is much more central to modern physics than the

concept ofmass. This shows up inmanyways. It is energy, notmass, that istrulyconserved.Itisenergythatappearsinourfundamentalequations,suchasBoltzmann’s equation for statistical mechanics, Schrödinger’s equation forquantummechanics,andEinstein’sequationforgravity.Massappearsinamoretechnicalway,asalabelforirreduciblerepresentationsofthePoincarégroup.(Iwon’t even try to explain that statement—fortunately, just the act of stating itconveysthepoint.)

Einstein’squestion,therefore,laysdownachallenge.Ifwecanexplainmassintermsofenergy,we’llbeimprovingourdescriptionoftheworld.We’llneedfeweringredientsinourworld-recipe.

WithEinstein’ssecondlaw,itbecomespossibletothinkofagoodanswertothequestionweearlierdebunked.Whatistheoriginofmass?Itcouldbeenergy.Infact,aswe’llsee,itmostlyis.

FAQ

Here are two excellent questions that people frequently ask me when I givepubliclecturesabouttheoriginofmass.Iftheyoccurredtoyou,congratulations!These questions raise basic issues about the possibility of explainingmass intermsofenergy.

Question1: IfE=mc2, thenmass isproportional toenergy.So ifenergy isconserved,doesn’tthatmeanthatmasswillbeconserved,too?

Answer 1:The short answer is thatE =mc2 really applies only to isolatedbodiesat rest. It’sapity that thisequation, theequationofphysics that isbestknowntothegeneralpublic,isactuallyalittlecheesy.Ingeneral,whenyouhavemovingbodies,or interactingbodies,energyandmassaren’tproportional.E=mc2simplydoesn’tapply.

Foramoredetailedanswer,takealookatAppendixA:“ParticleshaveMass,theWorldhasEnergy.”

Question 2: How can something made from massless building blocks feelgravitational forces?Didn’tNewton tell us that the gravitational force a bodyfeelsisproportionaltoitsmass?

Answer 2: In his law of gravitation, Newton indeed told us that thegravitationalforcefeltbyabodyisproportionaltoitsmass.ButEinstein,inhismoreaccurate theoryofgravity,general relativity, tellsussomethingdifferent.Thecompletestoryisquitecomplicatedtodescribe,andIwon’ttrytodoithere.Veryroughlyspeaking,whathappensisthatwhereNewtonwouldsaytheforceis proportional tom, Einstein’s more accurate theory says it’s proportional toE/c2.Aswediscussedinthepreviousquestionandanswer,thosearen’tthesamething.Theyarealmostequalforisolated,slowlymovingbodies,buttheycanbeverydifferentforinteractingsystemsofbodies,orforbodiesmovingatclosetothespeedoflight.

In fact, light itself is the most dramatic example. The particles of light,photons, have zero mass. Nevertheless light is deflected by gravity, becausephotonshavenonzeroenergy,andgravitypullsenergy.Indeed,oneofthemostfamoustestsofgeneralrelativityinvolvesthebendingoflightbytheSun.Inthatsituation,thegravityoftheSunisdeflectingmasslessphotons.

Carryingthatthoughtastepfurther,oneofthemostdramaticconsequencesofgeneralrelativityisthatyoucanimagineanobjectwhosegravityissopowerfulthat itbendsphotons sodrasticallyas to turn themcompletelyaround,even ifthey’removingstraightoutat thestart.Suchanobject trapsphotons.No lightcanescapeit.Itisablackhole.

4

WhatMattersforMatter

Whatistheworldmadeof?We’llbeexplainingtheoriginofmatter’smassfrompureenergy,with95%accuracy.Toattainthatsortofprecision,we’llhavetobeveryclearaboutwhatitiswe’retalkingabout.Herewe’llbespecificaboutwhatnormalmatteris,andwhatitisn’t.

“NORMAL”MATTERISTHESTUFFWESTUDYinchemistry,biology,andgeology. It is the stuff we use to build things, and it’s what we’re made of.Normalmatterisalsothestuffthatastronomersseeintheirtelescopes.Planets,stars,andnebulaearemadefromthesamekindofstuffthatwefindandstudyhereonEarth.That’sthegreatestdiscoveryinastronomy.

Recently,however,astronomershavemadeanothergreatdiscovery.Ironically,thenewgreatdiscoveryisthatnormalmatterisnotallthereisintheUniverse.Notbyalongshot.Infact,mostofthemassintheUniverseasawholeisinatleasttwootherforms:so-calleddarkmatteranddarkenergy.The“dark”stuffisactually perfectly transparent, which is why it managed to escape notice forhundreds of years. So far it’s been detected only indirectly, through itsgravitationalinfluenceonnormalmatter(thatis,starsandgalaxies).We’llhavemuchmoretosayaboutthedarksideinlaterchapters.

Ifyoujustcountupmass,thennormalmatterisaminorimpurity,contributingonly4-5%ofthetotal.Butit’swherethevastbulkofthestructure,information,andloveintheworldreside.SoIhopeyou’llagreeit’sanespeciallyinterestingpart.Andit’sthepartweunderstandbest,byfar.

In thenext fewchapterswe’ll account for theoriginof95%of themassofnormalmatter, starting frommassless building blocks. Tomake good on thatpromise,we’llhavetobequitespecificaboutwhatitiswe’reexplaining.(Afterall,we’requotingnumbers.)

BuildingBlocks

Speculationthatmatter2couldbeanalyzeddowntoa fewtypesofelementarybuilding blocks goes back at least to the ancient Greeks, but solid scientificunderstandingcameonlyinthetwentiethcentury.Matter,peopleordinarilysay,ismadeofatoms.ThegreatphysicistRichardFeynman,near thebeginningofhisfamousFeynmanLecturesonPhysics,madeabigpointofit:

If,insomecataclysm,allofscientificknowledgeweretobedestroyed,andonlyonesentencepassedontothenextgenerationsofcreatures,whatstatementwouldcontainthemostinformationinthefewestwords?Ibelieveitistheatomichypothesis(oratomicfact,orwhateveryouwishtocallit)thatallthingsaremadeofatoms...(italicsinoriginal).

Thegreatandmostuseful“fact”thatallthingsaremadeofatomsis,however,incomplete in three importantways. (LikeNewton’szeroth law,or thegreatestdiscovery inastronomy, it’saprofound truth inBohr’s sense—that is, it’salsoprofoundlyfalse.)

One aspect of its incompleteness is the existence of dark matter and darkenergy, as we’ve already mentioned. Their existence was barely suspected in1963, when Feynman’s lectures were published. A few astronomers, startingwithFritzZwicky,wereontowhattheycalledamissingmassproblemasearlyas 1933. But the anomalies they noticedwere just a few amongmany in theembryonic science of observational cosmology, and few people took themseriously untilmuch later. In any case, the existence of darkmatter and darkenergy doesn’t really affect Feynman’s point. In the initial steps ofreconstructing science after a cataclysm, awareness of dark matter and darkenergywouldbeaburdensomeluxury.

Two other, much more down-to-earth refinements really are central. Theyreally ought to be included even in our one-sentence message to the nextgenerationsofcreatures,eventhoughitmightleadtotheonesentencebecominga longish run-onsentenceof thekind thatmy teachers taughtme toavoidandthat would cost you points in an SAT essay even though Henry James andMarcel Proust got very famous despite using just those kind of sentencesbecause it’s okay if you’re writing literature but not okay if you’re justconveyinginformation.

First, there’s the matter of light. Light is a most important element of “allthings,”andofcourseitisquitedistinctfromatoms.Thereisanaturalinstincttoregard light as something quite different from matter, as immaterial or evenspiritual.Lightcertainlyappearstobequitedifferentfromtangiblematter—thekindthathurtsyourtoewhenyoukickit,orwhosestreamsandwindscanpushyou around. It would be appropriate to tell Feynman’s hypothetical post-cataclysmians that light is another form ofmatter they could understand.Youmight even tell them that light too is made of particles—particles known asphotons.

Second, atoms are not the end of the story. They are made of morefundamentalbuildingblocks.Afewhintsalongthoselineswouldjump-startthepost-cataclysmiansontheirwaytowardscientificchemistryandelectronics.

Therelevantfactscanbesummarizedinafewsentences.(Iwon’ttrytodoitinone.)All thingsaremadefromatomsandphotons.Atoms in turnaremadefrom electrons and atomic nuclei. The nuclei are verymuch smaller than theatoms as a whole (they have roughly one-hundred-thousandth, or 10-5, theradius),buttheycontainallthepositiveelectricchargeandnearlyallthemassofthe atom—more than 99.9%. Atoms are held together by electrical attractionbetween the electrons and the nuclei. Finally, nuclei in turn are made fromprotonsandneutrons.Thenucleiareheldtogetherbyanotherforce,aforcethatismuchmorepowerfulthantheelectricforcebutactsonlyovershortdistances.

Thataccountofmatterreflectsthestateofknowledgeasof1935orso.It iswhatyoustillfindinmostintroductoryphysicstextbooks.Todojusticetoourbest modern understanding, we’ll need to qualify, modify, and refine almostevery word of it. For example, we’ve come to understand that protons andneutrons themselves are complicated objects, made from more elementaryquarksandgluons.We’llget to therefinements in laterchapters.But the1935pictureisusefulasaconvenientsketch,aroughoutlinethat’sgoodenoughtoletus see clearly justwhat it iswe need to do, ifwe’re going to understand theoriginofmass.

Most mass is in atomic nuclei, and nuclei are made from protons andneutrons.Electronscontributemuchlessthan1%,andphotonsevenless.Sotheproblemoftheoriginofmass,fornormalmatter, takesverydefiniteshape.Tofindtheoriginofmostofthemassofmatter—morethan99%—wemustfindtheoriginofmassofprotonsandneutrons,andmustunderstandhowthoseparticles

combinetomakeatomicnuclei.Nomore,noless.

5

TheHydraWithin

Theprogramtounderstandatomicnuclei“theold-fashionedway,”assystemsofprotonsandneutronsstucktogetherororbitingoneanother,self-destructed.Physicistssearchingforforcesbetweenpersistentparticlesinsteaduncoveredabewilderingnewworldoftransformationandinstability.

IN1930,thedirectionforthenextstepalongthepathtowardacompletetheoryof matter was clear. The inward journey of analysis had reached the core ofatoms,theirnuclei.

Most of themass ofmatter, by far, is locked up in atomic nuclei. And theelectricchargeconcentrated inatomicnucleisetsupelectric fields thatcontrolthe motion of the surrounding electrons. The nuclei, because they are muchheavier,ordinarilymovemuchmoreslowlythantheelectrons.Electronsaretheactorsinchemicalandbiologicalprocesses(nottomentionelectronics),butthenucleilurkbehindthescenes,writingthescript.

Although in biology, chemistry, and electronics atomic nuclei mostly staybackstage, they star in the storyof stars. It is fromnuclear rearrangement andtransformationthatstars, includingofcourseourownSun,derivetheirenergy.Sotheimportanceofunderstandingatomicnucleiwas,andis,obvious.

Butin1930thatunderstandingwasprimitive,andthechallengetoimproveitrosetothetopofthephysicsagenda.InhislecturesEnricoFermiwoulddrawahazy cloud at the center of his diagram of an atom, with the label “Here beDragons,”asinancientmapsofunexploredregions.Herewasthewildfrontierthathadtobeexplored.

Fermi’sDragons

Itwasclearfromthestartthatessentiallynewforcesrulethenuclearworld.Theclassicforcesofpre-nuclearphysicsaregravityandelectromagnetism.But theelectric forces acting in nuclei are repulsive: the nuclei have overall positivecharge,andlikechargesrepel.Gravitationalforces,actingonthetinyamountofmass inanyonenucleus,are far too feeble toovercome theelectric repulsion.(We’llhavealotmoretosayaboutthefeeblenessofgravityinthesecondpartofthisbook.)Anewforcewasrequired.Itwasdubbedthestrongforce.Inorderto keep nuclei so tightly bound together, the strong force had to be morepowerfulthananypreviouslyknownforce.

Ittookdecadesofexperimentaleffortandtheoreticalingenuitytodiscoverthefundamental equations that govern what goes on in atomic nuclei. What’samazingisthatpeoplewereabletofindthematall.

Theobviousdifficulty is simply that it ishard toobserve thoseequationsatwork, because atomic nuclei are very small. They are roughly a hundredthousand times smaller even thanatoms.This takesusamillion timesbeyondnanotechnology.Nucleiareinthedomainofmicro-nanotechnology.Intryingtomanipulate nuclei with macroscopic tools—say, to set the scale, an ordinarytweezer—we’reworseoffthansomegianttryingtopickupagrainofsandusinga pair ofEiffel towers for chopsticks. It’s a tough job.To explore the nucleardomain, wholly new experimental techniques had to be invented, and exotickinds of instruments constructed. We’ll visit an ultrastroboscopicnanomicroscope (known as the Stanford Linear Accelerator, SLAC) and acreativedestructionpowerhouse(knownastheLargeElectron-PositronCollider,LEP),wherediscoveriescentraltoourstorytookplace,inthenextchapter.

Another difficulty is that themicronanocosm turns out to follow new rulesunlike anything that came before. Before they could do justice to the stronginteraction, physicists had to discard ways of thinking that come naturally tohumans,andreplace themwithstrangenewideas.We’lldiscuss those ideas indepthoverthenextfewchapters.Theyaresostrange,thatifIjustassertedthemas facts they might not—they should not—seem credible.3 Some of the newideas are completely unlike anything that came before. Theymight appear tocontradict—andmight actually contradict!—things you learned in school. (Itdependsonwhatschoolyouwentto,andwhen.)Thisshortchapterismeantto

indicatewhyweweredriven to revolution. It serves to connect the traditionalaccountofnuclearphysics(theaccountyoustillfindinmostofthehighschooland introductory college physics textbooks I’ve looked at) with the newunderstanding.

WrestlingwithDragons

James Chadwick’s discovery of the neutron in 1932 was a landmark. AfterChadwick’s discovery, the path to understanding seemed straightforward. Itseemedthatthebuildingblocksofnucleihadbeendiscovered.Theyareprotonsandneutrons, twokindsofparticles thatweighabout the same (theneutron isabout 0.2% heavier) and have similar strong interactions. The most obviousdifferencesbetweenprotonsandneutronsarethattheprotonhaspositiveelectriccharge,whereastheneutroniselectricallyneutral;andthataneutroninisolationisunstable,decaying,withalifetimeofaboutfifteenminutesintoaproton(plusan electron and an antineutrino). Simply by adding together protons andneutrons,youcouldmakemodelnucleiwithdifferentchargesandmasses thatroughlymatchedthoseofknownnuclei.

To understand and sharpen that modeling, it seemed, was just a matter ofmeasuringtheforces thatactamongprotonsandneutrons.Thoseforceswouldhold the nuclei together. The equations describing those forces would be thetheory of the strong interaction. By solving that theory’s equations, we couldboth check the theory andmakepredictions.Thuswewouldwrite aneatnewchapterofphysicscalled“NuclearPhysics”whosecenterpiecewouldbeanice“nuclearforce”describedbyasimple,elegantequation.

Inspiredby thatprogram,experimenters studiedcloseencountersofprotonswithotherprotons(orneutrons,orothernuclei).Wecallthiskindofexperiment,where you shoot one kind of particle at another and studywhat comes out, ascatteringexperiment.Theideaisthatbystudyinghowtheprotonsandneutronsswerve,or(aswesay)scatter,youcanreconstructtheforcethat’sresponsible.

This straightforward strategy failed miserably. First, the force got verycomplicated.Itwasfoundtodependnotonlyonthedistancebetweenparticlesbutalsoontheirvelocitiesandonthedirectionsoftheirspins4inacomplicated,mixed-upway.Itquicklybecameclearthatnosimpleandbeautifullawforthe

force,worthyofstandingbesideNewton’s lawofgravityorCoulomb’s lawofelectricity,wasgoingtoemerge.

Second,andevenworse:the“force”wasn’taforce.Whatyoufindwhenyoushoot two energetic protons together is not simply that they swerve. Instead,oftenmore than two particles come out, and they are not necessarily protons.Indeed,manynewkindsofparticleswerediscoveredin thisway,asphysicistsdidscatteringexperimentsathighenergy.Thenewparticles—eventuallydozenswere discovered—are unstable, so we do not ordinarily encounter them innature.Butwhentheywerestudiedindetailitseemedthattheirotherproperties—inparticular, their strong interactions and their size—are similar to thoseofprotonsandneutrons.

Afterthesediscoveries,itbecameunnaturaltoconsiderprotonsandneutronsbythemselves,ortothinkthatthefundamentalissuewastodeterminetheforcesbetweenthem.Instead“nuclearphysics,”astraditionallyconceived,becamepartof a bigger subject, involving all the new particles and the apparentlycomplicated processes whereby they are created and decay. A new namewasinvented to describe the new zoo of elementary particles, this new genus ofdragons.Theyarecalledhadrons.5

Hydra

Experienceinchemistrysuggestedapossibleexplanationforallthiscomplexity.Maybeprotonsandneutronsandtheotherhadronsarenotelementaryparticles.Maybetheyaremadefrommorebasicobjectswithsimplerproperties.

Indeed,ifyoudothesamesortsofexperimentsforatomsandmoleculesthatwere donewith protons and neutrons, studyingwhat comes out of their closeencounters,you’llalsofindcomplicatedresults.Youcouldhaverearrangementsand break-ups to form new kinds of molecules (or excited atoms, ions, orradicals)—inotherwords,chemicalreactions.Itisonlytheunderlyingelectronsandnuclei thatobeya simple force law.Theatomsandmoleculesmade frommany electrons and nuclei do not. Could there be a similar story for protons,neutrons,andtheirnewlydiscoveredrelatives?Couldtheirapparentcomplexityariseoutoftheirintricateconstructionfrommorebasicbuildingblocksthatobeyradicallysimplerlaws?

Breaking something to bits might be crude, but you might think it’s afoolproofwaytofindoutwhatthatsomethingismadeoutof.Ifyoubangatomstogetherhardenough, theybreakupintotheirconstituentelectronsandnuclei.Thusaretheirunderlyingbuildingblocksrevealed.

Butthesearchforsimplerbuildingblocksinsideprotonsandneutronsranintoa bizarre difficulty. If you bang protons together really hard, what you findcoming out is . . . more protons, sometimes accompanied by their hadronicrelatives.A typicaloutcomewouldbe,youcollide twoprotonsathighenergy,andoutcomethreeprotons,anantineutron,andseveralπmesons.Thetotalmassof the particles that come out is more than what went in. We discussed thatpossibilityearlier,andit’sbackagaintohauntus.Insteadofdiscoveringsmaller,lighterbuildingblocksbygoingtohigherandhigherenergies,andmakingmoreviolent collisions, you just findmore of the same. Things don’t appear to getsimpler.It’sasifyousmashedtogethertwoGrannySmithapples,andgotthreeGrannySmiths, aRedDelicious, a cantaloupe, adozencherries, andapairofzucchini!

Fermi’sdragonhadbecomethenightmarishHydraofmyth.ChopHydraup,andmoreHydrasspringtolifefromthepieces.

There are simpler building blocks. But their fundamental “simplicity”includes some weird and paradoxical behavior that makes them boththeoretically revolutionary and experimentally elusive. To understand them—eventoperceivethem—weneedtomakeafreshstart.

6

TheBitsWithintheIts

Introducedinatheoreticalimprovisationandneverobservedinisolation,quarksatfirstseemedaconvenientfiction.Butwhentheyshowedupinultrastroboscopicnanomicroscopicsnapshotsofprotons,quarksbecameaninconvenientreality.Theirstrangebehaviorcalledbasicprinciplesofquantummechanicsandrelativityintoquestion.Anewtheoryreinventedquarksasidealobjectsofmathematicalperfection.Theequationsofthenewtheoryalsodemandednewparticles,thecolorgluons.Withinafewyears,peopleweretakingpicturesofbothquarksandgluons,atpowerhousesofcreativedestructionbuiltforthepurpose.

THETITLEOFTHISCHAPTER has twomeanings. The first is simply thatthere are littler bits within what not so long ago were thought to be basicbuilding blocks of ordinarymatter, protons and neutrons.These littler bits arecalled quarks and gluons.Of course, knowing something’s name does not tellyouwhatitis,asShakespearehadRomeoexplain:

What’sinaname?ThatwhichwecallaroseByanyothernamewouldsmellassweet.

Which brings us to the second,more profoundmeaning. If quarks and gluonswere just another layer in a never-ending onion of complex structure withinstructure,theirnameswouldprovideimpressive-soundingbuzzwordsyoucouldshow off at a cocktail party, but they themselveswould be of interest only tospecialists. Quarks and gluons, are, however, not “just another layer.” Whenproperly understood, they change our understanding of the nature of physicalrealityinafundamentalway.Forquarksandgluonsarebitsinanotherandmuchdeeper sense, the sense we use when we speak of bits of information. To anextentthatisqualitativelynewinscience,theyareembodiedideas.

For example, the equations that describe gluonswere discovered before thegluonsthemselves.TheybelongtoaclassofequationsinventedbyChenNingYang and Robert Mills in 1954 as a natural mathematical generalization ofMaxwell’sequationsofelectrodynamics.TheMaxwellequationshavelongbeenrenownedfor theirsymmetryandpower.HeinrichHertz, theGermanphysicistwho proved experimentally the existence of the new electromagnetic wavesMaxwell had predicted (what we now call radio waves), said of Maxwell’sequations:

Onecannotescapethefeelingthatthesemathematicalformulaehaveanindependentexistenceandanintelligenceoftheirown,thattheyarewiserthanweare,wisereventhantheirdiscoverers,thatwegetmoreoutofthemthanwasoriginallyputintothem.

The Yang-Mills equations are like Maxwell’s equations on steroids. Theysupportmanykindsofcharges,insteadofjusttheonekind(electriccharge)thatappears in Maxwell’s equations, and they support symmetry among thosecharges.Thespecificversionthatappliestothereal-worldgluonsofthestronginteraction,whichusesthreecharges,wasproposedbyDavidGrossandmein1973. The three kinds of charges that appear in the theory of the stronginteractionareusuallycalledcolorcharges,orsimplycolor,althoughofcoursetheyhavenothingtodowithcolorintheusualsense.

We’lldiscussthenutsandboltsofquarksandgluonsmuchmorebelow.ThepointIwanttoemphasizehere,fromthebeginning,startingwiththetitle,isthatquarksandgluons,ormoreprecisely their fields, aremathematicallycompleteandperfectobjects.Youcandescribetheirpropertiescompletelyusingconceptsalone,withouthaving to supply samplesormakeanymeasurements.Andyoucan’t change those properties. You can’t fiddle with the equations withoutmakingthemworse(indeed,inconsistent).Gluonsaretheobjectsthatobeytheequationsofgluons.Theitsarethebits.

But enough of this all-too-free rhapsody! Puremathematics is chockablockwith beautiful ideas. The special music of physics lies in harmony betweenbeautifulideasandreality.It’stimetobringinsomereality.

Quarks:BetaRelease

By the early 1960s, experimenters had discovered dozens of hadrons, withdifferentmasses, lifetimes, and intrinsic rotation (spin).Theorgyof discoverysoon led to a hangover, as themere accumulationof curious facts, absent anydeeper meaning, became mind-numbing. In his 1955 Nobel Prize acceptancespeech,WillisLambjoked

WhentheNobelPrizeswerefirstawardedin1901,physicistsknewsomethingofjusttwoobjectswhicharenowcalled“elementaryparticles”:theelectronandtheproton.Adelugeofother“elementary”particlesappearedafter1930;neutron,neutrino,μmeson,πmeson,heaviermesons,andvarioushyperons.Ihavehearditsaidthat“thefinderofanewelementaryparticleusedtoberewardedbyaNobelPrize,butsuchadiscoverynowoughttobepunishedbya$10,000fine.”

Inthissituation,MurrayGell-MannandGeorgeZweigmadeagreatadvanceinthetheoryofthestronginteractionbyproposingthequarkmodel.Theyshowedthatpatternsamongthemasses,lifetimes,andspinsofhadronsclickintoplaceifyouimaginethathadronsareassembledfromafewmorebasickindsofobjects,which Gell-Mann named quarks. Dozens of hadrons could be understood, atleastroughly,asdifferentwaysofputtingtogetherjustthreevarieties,orflavors,ofquarks:upu,downd,andstranges.6

Howdoyoubuilddozensofhadronsfromafewflavorsofquarks?Whatarethesimplerulesbehindthecomplicatedpatterns?

Theoriginal ruleswere improvised to fit theobservations, and they’re abitpeculiar.Theydefinedwhat iscalled thequarkmodel.According to thequarkmodel,therearejusttwobasicbodyplansforhadrons.Mesonsareconstructedfrom a quark and an antiquark. Baryons are constructed from three quarks.(Therearealsoantibaryons,constructed fromthreeantiquarks.)Thus therearejustahandfulofpossibilities forcombiningquarksandantiquarksofdifferentflavortomakemesons:youcancombineuwithanti-d(ƌ),ordwiths ,andsoforth.Similarlyforbaryons,thereareonlyafewpossiblecombinations.

According to the quarkmodel, the great diversity of hadrons comes not somuch from which pieces you put together as from how you assemble them.Specifically,agivensetofquarkscanbearrangedindifferentspatialorbits,withtheirspinsalignedindifferentways,inroughlythesamewaythatpairsortriplesofstarscanbeboundtogetherbygravity.

There’s a crucial difference between the submicroscopic “star systems” ofquarks and their macroscopic brethren. Whereas macroscopic solar systems,governedbythelawsofclassicalmechanics,cancomeinallsizesandshapes,themicroscopicversioncannot.Formicroscopicsystems,whichobeythelawsof quantum mechanics, there are restrictions on the allowed orbits and spinalignments.7We say that the system can be in different quantum states. Eachallowedconfigurationoforbitsandspins—eachstate—willhavesomedefinitetotalenergy.

(Confessionandpreview:I’mbeinga littlesloppyhere,soasnot topileontoomanycomplicationsatonce.Accordingtomodernquantummechanics,thecorrectway todescribe the stateof aparticle is in termsof itswave function,which describes the probability of finding it at different places, rather than intermsofanorbit it follows.We’ll talkabout thismore inChapter9.Theorbitpictureisarelicoftheso-calledoldquantummechanics.Itiseasytovisualize,butitcan’tbeusedforprecisionwork.)

Thissetupforusingquarkstounderstandhadronsrunsstrictlyparalleltothewayweuseelectrons tounderstandatoms.Theelectrons inanatomcanhaveorbitsofdifferentshapesandcanalign theirspins indifferentdirections.Thustheatomcanbeinmanydifferentstates,withdifferentenergies.Thestudyofthepossible states is avast subjectknownas atomic spectroscopy.Weuseatomicspectroscopy to revealwhatdistantstarsaremadeof, todesign lasers,and formany other things. Because atomic spectroscopy is so relevant to the quarkmodel,andisextremelyimportantinitself,let’stakeamomenttodiscussit.

Ahotgas,suchasyoufindinaflameorastellaratmosphere,containsatomsindifferentstates.Evenatomswiththesamekindofnucleiandthesamenumberofelectronscanhavetheirelectronsindifferentorbitsorwiththeirspinsalignedindifferentways.Thesestateshavedifferentenergies.Statesofhighenergycandecayintostateswithlowerenergy,emittinglight.Becauseenergyisconservedoverall, the energy of the emitted photon, betrayed by its color, encodes thedifference in energy between the initial and final states. Every kind of atomemitslightfromacharacteristicpaletteofcolors.Hydrogenatomsemitonesetof colors, helium atoms an entirely different set, and so forth. Physicists andchemists call that palette the spectrum of the atom. The spectrum of an atomfunctions as its signature and can be used to identify it.When you put lightthrough a prism the different colors get separated, and the spectrum literally

resemblesabarcode.

It’sbecausethespectraweobserveinstarlightmatchthespectraweobservein terrestrial flames thatwecanbeconfident thatdistant starsaremadeof thesamebasickindofmaterial aswe findonEarth.Also,because the light fromdistant starsmay takebillionsof years to reachus,we can checkwhether thelawsofphysicsthatoperatetodayarethesameasthosethatoperatedlongago.Sofar,theevidenceisthattheyare.(Buttherearegoodreasonstothinkthatthevery earlyuniverse,whichwecan’t seedirectly,at least inordinary light,wasgovernedbyessentiallydifferentlaws.We’lldiscussthatlater.)

Atomicspectragiveusalotofdetailedguidanceforcontructingmodelsoftheinternal structure of atoms. To be valid, a model must predict states whoseenergy differences match the pattern of colors that spectra reveal. Much ofmodern chemistry takes the form of a dialogue. Nature speaks in spectra;chemistsreplyinmodels.

Withthatbackgroundinmind,let’sreturntothequarkmodelofhadrons.Thesameideascomeintoplay,withonemajorrefinement.Inatoms,thedifferenceinenergybetweenanytwostatesoftheelectronsisrelativelysmall,sotheeffectof that energy difference on the overall mass of the atom is insignificant. Acentralideaofthequarkmodelisthatforquark“atoms”(thatis,hadrons),theenergydifferencesbetweendifferentstatesaresolargethattheycontributetothemassinabigway.Turningitaround,exploitingEinstein’ssecondlawm=E/c2,wecaninterprethadronswithdifferentmassesassystemsofquarksindifferentorbitalpatterns—differentquantumstates—thathavedifferentenergies.Inotherwords,weseeatomicspectra,butweweighhadronspectra.Thuswhatappearedto be unrelated particles now appear as merely different patterns of motionwithinagiven“atom”ofquarks.Usingthatidea,Gell-MannandZweigshowedthatonecouldinterpretmanydifferentobservedhadronsasdifferentstatesofafewunderlyingquark“atoms.”

Sofar,soeasy.ExceptfortherefinementintroducedbyEinstein’ssecondlaw,thequarkmodelofhadronslookslikeareplayofchemistry.Butthedevilisinthe details, and to see reality in the quarkmodel, one had to turn a blind eyetowardsometrulyfiendishdeviltry.

The most wicked assumption is the one we already mentioned, that onlymeson(quark-antiquark)andbaryon(three-quark)bodyplansareallowed.Thatassumptionincludes,inparticular,theideathatquarksdon’texistasindividual

particles! For some reason, you had to suppose, the simplest body plan isimpossible.Not just inefficientorunstable, but impossible.Nobodywanted tobelieve that,ofcourse,sopeopleworkedhard tosmashprotons, trying tofindparticles they could identify as single quarks. They scrutinized the debrisminutely. Nobel Prizes and everlasting glory surely would shower down likesweet rainupon theheadsof thediscoverers.Butalas, thatHolyGrailprovedelusive. No particle that has the properties of a single quark has ever beenobserved. Eventually this failure to find individual quarks, like the failure ofinventors to produce a perpetualmotionmachine,was elevated to a principle:thePrincipleofConfinement.Butcallingitaprincipledidn’tmakeitlesscrazy.

Moredeviltrycameinwhenphysiciststriedtomakefleshed-outmodelsoftheinternal structure of mesons and baryons using quarks, to account for theirmassesindetail.Inthemostsuccessfulmodels,itappearedthatwhenquarks(orantiquarks) are close together, they hardly notice one another. That feebleinteraction between quarks was hard to reconcile with the finding that if youtried to isolate one quark—or two—you found you could not. If quarks don’tcare about one another when they’re close, why do they object to beingseparatedwhenthey’refaraway?

Afundamentalforcethatgrowswithdistancewouldbeunprecedented.Anditwouldposeanembarrassingquestion. If forcesbetweenquarkscangrowwithdistance, why is astrology wrong? After all, the other planets contain lots ofquarks. Maybe they could exert a big influence. . . . Well, maybe, but forcenturies scientists and engineers have been very successful at predicting theresultsofdelicateexperimentsandbuildingbridgesanddesigningmicrochipsbyignoringanypossibleinfluenceofdistantobjects.Astrologyshouldbemadeofsternerstuff.

Becauseagoodscientific theoryhas toexplainwhyastrology is so lame, ithad better not contain forces that growwith distance. The old saw “Absencemakestheheartgrowfonder”mayormaynotapplytoromance,butit’ssurelyabizarrewayforparticlestobehave.

Insoftwaredevelopment,oftenabetatestversionissuppliedforusebybraveearly adopters. The beta test version works, more or less, but comes with noguarantees.Therewill bebugs andmissing features.Even theparts thatworkwon’tbesmoothlypolished.

The original quark model was a beta test physical theory. It used peculiar

rules. It left basic questions, like why (or whether) quarks could ever beproducedinisolation,unanswered.Worstofall, thequarkmodelwasvague.Itdid not come with precise equations for the forces between quarks. In thatrespect it resembled pre-Newtonian models of the solar system, or pre-Schrödinger (for experts: even pre-Bohr) models of atoms. Many physicists,includingGell-Mannhimself, thoughtthatquarksmightturnouttobeausefulfiction, like the epicycles of the old astronomyor the orbitals of old quantumtheory. Quarks, it seemed, might turn out to be useful stopgaps in themathematicaldescriptionofnature,not tobe taken too literallyaselementsofreality.

Quarks1.0:ThroughanUltrastroboscopicNanomicroscope

Thetheoreticalpeculiaritiesofquarksripenedintojuicyparadoxesintheearly1970s, when Jerome Friedman, Henry Kendall, Richard Taylor, and theircollaborators at the Stanford Linear Accelerator (SLAC) studied protons in anewway.

Instead of bashing protons together and scrutinizing the debris, theyphotographedprotoninteriors.Idon’twanttomakethatsoundeasy,becauseitisn’t. To look inside protons, you must use “light” of very short wavelength.Otherwiseyou’dbetrying,ineffect,tolocatefishbylookingfortheireffectonlongoceanwaves.Thephotons for this job arenot particlesof ordinary light.They lie beyond ultraviolet or even x-rays.Ananomicroscope fit for studyingstructures a billion times beyond the ken of ordinary optical microscopesrequiresextremeγ-rays.

Also,thingsmovequicklyinsideprotons,sotoavoidblurringthepicturewemust have good time-resolution. Our photons, in other words, must also beextremely short-lived.We need flashes, or sparks, not long exposures.We’retalkingabout“flashes”thatlast10-24second,orless.Thephotonsweneedaresoshort-livedthattheythemselvescan’tbeobserved.That’swhythey’recalledvirtualphotons.Anultrastroboscopetolookatfeaturesthatlastforatrillionthofatrillionthoftheblinkofaneye(actually,evenless)requiresextremelyvirtualphotons.Sothe“picture”can’tbemadeusingthetransient“light”thatprovidestheillumination!Wehavetobecleverer,andworkindirectly.

At SLAC people actually shot electrons at protons, and observed electronsemerging after they collided. The emerging electrons have less energy andmomentum than when they started. Because energy and momentum areconservedoverall,whatwaslostbytheelectronhadtobecarriedawaybythevirtual photon, and transmitted to the proton. This often causes the proton tobreakapartincomplicatedways,aswe’vediscussed.Thestrokeofgenius—thenewapproachthatwonFriedman,Kendall,andTaylortheirNobelPrize—wastoignoreallthosecomplicationsandjustkeeptrackoftheelectron.Inotherwords,wejustgowiththeflow(ofenergyandmomentum).

In this way, by accounting for the flow of energy andmomentum, we canfigureoutwhatkindofvirtualphotonwasinvolved,eventbyevent,eventhoughwedon’t “see” that photon directly.The energy andmomentumof the virtualphoton are precisely the energy and momentum lost by the electron. Bymeasuring theprobability thatdifferentkindsofvirtualphotons,withdifferentenergies andmomenta (corresponding to different lifetimes andwavelengths),“encounteredsomething”andgotabsorbed,wecanpiecetogetherasnapshotoftheproton’sinterior.Theprocedureissimilarinspirittothewaywereconstructa picture of a human body’s interior by measuring how x-rays get absorbed,although the details are considerablymore complicated. Suffice it to say thatsomeveryfancyimageprocessingisinvolved.

Nowofcoursetheinteriorsofprotonsdon’treallylooklikeanythingyou’veeverseen,orcouldsee.Oureyeswerenotdesigned(ahem,didnotevolve) toresolve such small distances and times, so any visual representation of theultrastrobonanomi-croworld must be a mixture of caricature, metaphor, andcheat.Withthatwarning,pleaselooknowatthepanelsofFigure6.1.We’llbediscussingvariousaspectsofthemfurtherbelow.

Inpresentingthesepictures,I’veusedatrickIowetoRichardFeynman.Aswe’venoted,thingsmovefastinsideaproton.Toslowthingsdown,weimaginethattheprotonismovingpastusatverynearlythespeedoflight.(InChapter9,we’ll discuss how protons look if we don’t use Feynman’s trick.) From theexterior,theprotonthencomestolooklikeapancake,flattenedinthedirectionofmotion.ThisisthefamousFitzgerald-Lorentzcontractionofspecialrelativity.More important for our purposes is another famous relativistic effect, timedilation. Time dilationmeans that time appears to flowmore slowlywithin afast-moving object. Thus the stuff inside the protons appears nearly frozen inplace. (It shares the overall motion of the proton as a whole, of course.)

Fitzgerald-Lorentz contraction and time dilation have been explained inhundredsofpopularbooksonrelativity,soratherthanbelaboringthemhere,I’lljustusethem.

It’simportanttoemphasizethatquantummechanicsisabsolutelyessentialfordescribing even the most elementary observations about proton interiors. Inparticular, the indeterminism for which quantum mechanics is famous, andwhich caused Einstein such anguish, hits you in the face. If you take severalsnapshotsofaprotonunderstrictlyidenticalconditions,youseedifferentresults.Like it or not, the facts are straightforward and unavoidable.The bestwe canhopeforistopredicttherelativeprobabilitiesofthedifferentresults.

Figure6.1Picturesoftheinteriorofaproton.a.Aprotonmovingatnearlythespeed of light appears flattened in the direction of motion, according to thetheoryofrelativity.b.Agoodguess,beforeactualsnapshotswereavailable,forwhat the interiormight look like. The reasoning behind this (wrong) guess isexplained in the text. c-d.Twoactual snapshots.Becausequantum-mechanicaluncertainty is a dominant effect in this domain, each snapshot looksdifferent!Inside are quarks and gluons, also moving at nearly the speed of light. Theyshare the total energy of the proton, and the sizes of the arrows indicate theirrelative shares. e-f. If you lookwith finer resolution,more details appear. Forexample,youmayfind thatwhatappeared tobeaquark resolves intoaquarkandagluon,orthatagluonresolvesintoaquarkandanantiquark.

This abundance of coexisting possibilities in the phenomena, and in thequantum theory that describes them, defies traditional logic. The success ofquantumtheoryindescribingrealitytranscendsandinasenseunseatsclassicallogic,whichdependsonone thingbeing“true,”and itscontraries“false.”Butthis is a creative destruction that allows new imaginative constructions. Forexample,itenablesustoreconciletwoseeminglycontradictoryideasaboutwhatprotonsare.Ontheonehand, the interiorofaproton isadynamicplace,with

thingschangingandmovingaround.Ontheotherhand,allprotonseverywhereandeverywhenbehaveinexactlythesameway.(Thatis,eachprotongivesthesameprobabilities!)Ifaprotonatonetimeisnotthesameasitselfatadifferenttime,howcanallprotonsbeidentical??

Here’show.EveryindividualpossibilityAfortheproton’sinteriorevolvesintime into a new and different possibility, say B. But meanwhile, some otherpossibilityCevolves intoA.SoA isstill there; thenewcopyreplaces theold.And more generally, even though each individual possibility evolves, thecomplete distribution of possibilities remains the same. It is like a smoothlyflowing river,whichalways looks the sameeven thougheverydropof it is influx.WadedeeperintothisriverinChapter9.

Partons,Put-Ons,andPutdowns

ThepicturestakenbyFriedmanandcompanypresentedbotharevelationandapuzzle. Within the pictures, you could discern some little entities, little sub-particles, insideprotons.Feynman,whowas responsible fora lotof the imageprocessing,calledtheseinternalentities“partons”(forparticlesthatarepartsofprotons).

That infuriatedMurrayGell-Mann.As I learned firsthand,when I firstmetGell-Mann.HeaskedmewhatIwasworkingon.Imadethemistakeofsaying,“I’mtryingtoimprovethepartonmodel.”I’veheardthatconfessionisgoodforthesoul,sohereIconfessthatitwasn’tentirelyininnocenceandignorancethatImentioned partons. I was curious to see howGell-Mannwould react to hisrival’sidiom.AsIshmaelwroteofhisfirstencounterwithCaptainAhab,realityoutrananticipation.

Gell-Mann gave me a quizzical look. “Partons?” Stage pause, facialexpression of deep concentration. “Partons?? What are partons?” Then hepaused again and looked very thoughtful, until suddenly his face brightened.“Oh,youmustmeanthoseput-onsthatDickFeynmantalksabout!Theparticlesthatdon’tobeyquantumfieldtheory.There’snosuchthing.They’rejustquarks.You shouldn’t let Feynman pollute the language of science with his jokes.”Finally,with a quizzical expression, but a toneof authority: “Don’t youmeanquarks?”

Some of the entities Friedman and company found really did appear to bequarks. They had both the funny fractional electric charges and the preciseamountofspinthatquarksweresupposedtohave.Butprotonsalsocontainbitsthatdon’tlooklikequarks.Theywerelaterinterpretedascolorgluons.SobothGell-MannandFeynmanhadvalidpoints:therearequarksinside,butalsootherthings.

TooSimple

Atmyalmamater,theUniversityofChicago,theysellsweatshirtsthatread

Thatworksinpractice,butwhataboutintheory?

BothGell-Mann’squarksandFeynman’spartonshadtheannoyingfeaturethattheyworkedwellinpracticebutnotintheory.

We’vealreadydiscussedhowthequarkmodelhelpedtoorganizethehadronzoo,butonlybyusingcrazyrules.Thepartonmodeluseddifferentcrazyrules,this time to interpret those pictures of the proton’s interior. The rules of theparton model are very simple: you’re supposed to assume, for purposes ofcalculation,thatthebitsinsidetheproton—quarks,partons,whateveryouwanttocallthem—havenointernalstructureandnointeractionswitheachother.Ofcoursetheydointeract;otherwise,protonswouldjustflyapart.Buttheideaofthepartonmodelisthatyougetagoodapproximatedescriptionofwhathappensinaveryshorttime,oververyshortdistances,byignoringtheinteractions.Andit is that short-time, short-distance behavior you access with the SLACultrascroboscopicnanomicroscope.Sothepartonmodelsaysyouwillgetacleanviewoftheinteriorusingthatinstrument—asinfactyoudo.Andyoushouldseemorebasicbuildingblocks,ifsuchtherebe—asinfactyoudo.

It all soundsvery reasonable, almost intuitivelyobvious.Nothingmuchcanhappeninaveryshorttime,inaverysmallvolume.What’scrazyaboutthat?

The trouble is that when you get down to really short distances and reallyshort times, quantum mechanics comes into play. When you take quantum

mechanicsintoaccount,the“reasonable,almostintuitivelyobvious”expectationthatnothingmuchcanhappeninashorttimeinasmallvolumecomestoseemverynaïve.

Onewaytoappreciatewhy,withoutgoingtoodeepintotechnicalities, isbyconsidering Heisenberg’s uncertainty principles. According to the originaluncertaintyprinciple,topindownapositionaccuratelywemustlivewithalargeuncertainty in momentum. An addendum to Heisenberg’s original uncertaintyprincipleisrequiredbythetheoryofrelativity,whichrelatesspacetotimeandmomentum to energy. This additional principle says that to pin down a timeaccuratelywemust livewitha largeuncertainty inenergy.Combining the twoprinciples, we discover that to take high-resolution, short-time snapshots, wemustletmomentumandenergyfloat.

Ironically,thecentraltechniqueoftheFriedman-Kendall-Taylorexperiments,as we mentioned, was precisely to concentrate on measuring the energy andmomentum.But there’s no contradiction.On the contrary, their technique is awonderful exampleofHeisenberg’suncertaintyprinciple cleverlyharnessed togivecertainty.Thepointisthattogetasharplyresolvedspace-timeimageyoucan—andmust—combineresultsfrommanycollisionswithdifferentamountsofenergyandmomentumgoingintotheproton.Then,ineffect,imageprocessingruns the uncertainty principle backwards.Youorchestrate a carefully designedsampling of results at different energies and momenta to extract accuratepositionsandtimes.(Forexperts:youdoFouriertransforms.)

Becausetogetasharpimageyouneedtoallowforabigspreadinenergyandmomentum,youmustinparticularallowforthepossibilityoflargevalues.Withlarge values of energy and momentum you can access a lot of “stuff”—forinstance, lots of particles and antiparticles. These virtual particles come to beandpassawayveryquickly,withoutgoingveryfar.Remember,we’veonlyruninto them in theprocessofmakinga short-time,high-resolution snapshot!Wedon’t see them, in any ordinary sense, unless we supply the energy andmomentum needed to create them. And even then what we see is not theoriginal, undisturbed virtual particles (the kind that appear and disappearspontaneously) but real particles we can use to recreate the original virtualparticlesbyimageprocessing.

Viruses can come to life only with the help of more complex organisms.Virtualparticlesarestillmoreinsubstantial,fortheyneedexternalhelptocome

intoexistence.Nevertheless, theyappearinourquantum-mechanicalequations,andaccording to thoseequations thevirtualparticlesaffect thebehaviorof theparticleswesee.

And so it seemed reasonable to expect that thevirtualparticles shouldhavebigeffectswhenwe’redealingwithparticles that interactstrongly,suchas thethingsthatmakeprotons.Sophisticatedquantum-mechaniciansexpectedthatthecloser and faster you looked inside protons, the more virtual particles andcomplexities you’d see.And so the Friedman-Kendall-Taylor approachwasn’tconsidered very promising. The ultrastroboscopic nanomicroscopic snapshotwouldjustbeablur.8

Butitwasn’tablur.Itwasthoseinfuriatingpartons.Afamouspieceofwiseadvice from Einstein is to “Make everything as simple as possible, but notsimpler.”Partonsweretoosimple.

AsymptoticFreedom(ChargeWithoutCharge)

Let’simaginewe’revirtualparticles.Wepopintoexistenceandhavetodecidewhattodoinourall-too-brieflifetime.(That’snotsohardtoimagine.)Wesniffaround. Suppose there’s a positively charged particle in the region. If we’renegativelycharged,wefindthatparticleattractiveandtrytosnuggleuptoit.Ifwe’re positively charged, we find that other particle repulsive, or at leastcompetitiveandpossiblyintimidating,andwemoveaway.(Neitheristhat.)

Individualvirtualparticlescomeandgo,buttogethertheymaketheentitywecallemptyspaceintoadynamicmedium.Duetothebehaviorofvirtualparticlesa(real)positivechargeispartiallyscreened.Thatis,thepositivechargetendstobe surrounded by a cloud of compensating negative charges that find itattractive.Fromfarawaywedonotfeelthefullstrengthofthepositivecharge,because that strength is partially canceled by the negative cloud.9 Putting itanotherway, the effective charge grows as you get closer, and shrinks as youmovefartheraway.Forapictureofthissituation,seeFigure6.2.

Figure6.2The screeningof chargebyvirtual particles.The centralworld-lineshowsapositivelycharged realparticle fixed in space—it tracesoutaverticalline as time advances. That real particle is surrounded by virtual particle-antiparticlepairs,whichatrandomtimespopup,brieflyseparate,andwinkout.Thepositivechargeoftherealparticleattractsthenegativelychargedmemberofeachvirtualpairandrepelsthepositivemember.Thustherealparticlebecomessurrounded,anditspositivechargeispartiallyscreened,byanegativelychargedcloud of virtual particles. From far away we see a smaller effective charge,becausethenegativevirtualcloudpartiallycancelsthecentralpositivecharge.

Nowthisisjusttheoppositeofthebehaviorwewantfromquarksinthequarkmodel, or partons in the parton model. The quarks of the quark model aresupposed to interactweaklywhen they’re close together.But if their effectivecharge is largest in their immediatevicinity,we’ll find just theopposite.Theywillinteractmoststronglywhenthey’reclosetogether,andmoreweaklywhentheyarefarapartandtheirchargesarescreened.Thepartonsofthepartonmodelaresupposedtolooklikesimpleindividualparticleswhenyoulookclosely.Butifathickcloudofvirtualparticlesenvelopseachparton,we’llseethosecloudsinstead.

Clearly,we’dbemuchclosertodescribingquarksifwecouldarrangetogettheoppositeofscreening—clouds that reinforce, rather thancancel, thecentralcharge.With suchantiscreening we could have forces that are feeble at shortdistances but growpowerful far away, thanks to the clouds.Electric charge isscreened,notantiscreened,sowehavetolookelsewhereforamodel.We’llfind

it,ofcourse;otherwiseIwouldn’tbeleadingyoudownthisgardenpath.Justsowe can talk about it, let’s temporarily call the hypothetical thing that getsantiscreened “churge.” (What we’ll find is that a generalized kind of charge,colorcharge,behaveslikechurge.)

Ifvirtualparticlecloudsantiscreenchurge,thenthepowerofthereal,centralchurge increases as you go farther away. You can get strong forces at largedistancesfromasmallcentralchurge,becauseitsentourageofvirtualparticlesbuildsupitsinfluence.Thusifquarkshavechurgeinsteadof(orinadditionto)electriccharge,youcanhavequarksthatinteractfeeblywhenclosetogether,asthe quarkmodel wants, but powerfully when far apart. You can even do thiswhileavoidingastrology,asI’llexplaininamoment.Andyoucanhavepartonsthat aren’t hidden in thick clouds, because their cloud-inducing power—theireffectivecharge—wanesintheirimmediateproximity.

Whataboutthatunlimitedgrowthofstrengthwithdistance,whichthreatenedtobringbackastrology?Thatgrowthistheresultwegetforanisolatedchurgedparticle. But the big cloud comes at a price. (You might say that expansivecloudsareexpensive.)Itcostsenergytocreatesuchadisturbance,anditwouldtake an infinite amount of energy to keep it going out to infinite distances.Because the available energy is finite, Nature won’t let us create an isolatedchurgedparticle.Ontheotherhand,wecangetawaywithasystemofchurgedparticles whose churges cancel—for example, and most simply, a churgedparticleanditsantiparticle.Virtualparticlesthatarefarfromboththechurgeanditscancelingantichurgewillfeelnonetattraction,andthereforethecloudswon’tkeepbuilding.All thisbegins to sound less like justifyingastrology,andmorelikejustifyingthedevilishrulesof thequarkmodel!Wecanbotheliminateallthe long-range influencesandconfinewholeclassesofparticleswith thesamecleveridea.

Antiscreeningisahorribleword.Thestandardjargoninphysicsisasymptoticfreedom,whichmaynotbemuchbetter.10Theideaisthatasthedistancetoaquark gets closer and closer to zero, the effective color charge deep inside itscloud approaches closser and closser to zero, but never quite gets there. Zerocolor charge means complete freedom—no influence exerted, and none felt.Such complete freedom is approached, as the mathematicians say,asymptotically.

Whateveryoucall it, asymptotic freedom isapromising idea fordescribing

quarksandmakingpartonsrespectable.We’dliketohaveatheorythatincludesasymptotic freedomand isalsoconsistentwith thebasicprinciplesofphysics.Butistheresuchatheory?

The rules of quantum mechanics and special relativity are so strict andpowerfulthatit’sveryhardtobuildtheoriesthatobeyboth.Thosefewthatdoarecalledrelativisticquantumfieldtheories.Becauseweknowonlyafewbasicwaystoconstructrelativisticquantumfieldtheories, it’spossible toexploreallthepossibilities,toseewhetheranyofthemleadstoasymptoticfreedom.

The necessary calculations are not easy to do, but not impossible either.11Fromthisworkemergedsomethingthateveryscientisthopesforinascientificinvestigation, but rarely finds: a clear, unique answer. Almost all relativisticquantum field theories screen.That intuitive, “reasonable”behavior is, indeed,almost inevitable. But not quite. There is a small class of asymptotically free(antiscreening) theories.Theyall feature, at theircore, thegeneralizedchargesintroduced by Yang andMills.Within this small class of asymptotically freetheories, there is exactly one that looks even remotely as if it might describereal-world quarks (and gluons). It’s the theory we call quantumchromodynamics,orQCD.

AsI’vealreadyhinted,QCDislikethequantumversionofelectrodynamics—quantum electrodynamics, or QED—on steroids. It embodies an enormousamountofsymmetry.TodoQCDevenroughjustice,weneedtolaysomedeepfoundationsusingtheconceptofsymmetry.Thenwe’llbuildupourdescriptionofthetheoryusingdrawingsandanalogies.

The biggest challenge may be to imagine how all those abstractions andmetaphors connect with anything real and concrete. To warm up ourimaginations,let’sstartbycontemplatingaphotographofthingsthatdon’texist.Behold,inColorPlate1,aquark,anantiquark,andagluon.

QuarksandGluons2.0:BelievingIsSeeing

Of course, a legitimate picture doesn’t emerge from the camera with labels“quark,antiquark,gluon”attached.Itneedssomeinterpretation.

First, let’s take stock of the objects in the picture using everyday language.

The complicated-looking bits outline magnets and other components of theacceleratoranddetector.Youcanmakeoutanarrow tube running through themiddle. That’s the beam pipe, through which the electrons and positronscirculate.What’sinthepictureisonlyaverysmallpart,afewmetersonaside,of the LEP machine, built inside a circular tunnel 27 kilometers incircumference.(Bytheway,thesametunnelhousestheLargeHadronCollider(LHC), which uses protons instead of electrons and positrons, and whichoperatesathigherenergies.We’llhavemuchmoretosayabouttheLHCinlaterchapters.)Beamsof electrons andpositrons, circulating in opposite directions,wereaccelerateduptoenormousenergies,untiltheirspeedreachedwithinapartintenbillionofthespeedoflight.Thetwobeamscrossedatafewpoints,wherecollisions occurred. Those special points were surrounded by big detectors,whichcouldtracksparksandcaptureheatfromtheparticlesthatemergedfromthecollisions.Theemergingexplosionof linesyou seeare the tracks, and thedotsontheoutsiderepresenttheheat.

Thenextstepistotranslateourdescriptionofwhatweseefromthelanguageofsurfaceappearanceintothelanguageofdeepstructure.Thistranslationentailssuch a big conceptual step that you might say it involves a leap of faith.12Beforetakingtheleap,let’sfortifyourfaith.

FatherJamesMalley,S.J.,taughtmeamostprofoundandvaluableprincipleofscientifictechnique.(Ithasmanyotherapplicationsaswell.)Heclaimedthathelearnedthisprincipleatseminary,whereitwastaughtastheJesuitCredo.Itstates

Itismoreblessedtoaskforgivenessthanpermission.

I’d been following this credo intuitively for years without realizing itsecclesiastical sanction. Now I use it more systematically, and with a clearerconscience.

Intheoreticalphysics,thereisawonderfulsynergybetweentheJesuitCredoandEinstein’s“make thingssimple,butnot toosimple.”Together, they telluswe should make the most optimistic assumptions we dare about how simplethingsare.13 If it turnsoutbadly,wecanalwayscounton forgivenessand try

again—withoutpausingforpermission.

In that spirit, let’s make the simplest guess for how to account for whatemergesfromthecollisions,startingfromourideasaboutthedeepstructureofthephysicalworld.AccordingtoQEDanelectronanditsantiparticle,apositron,can annihilate one another, producing a virtual photon. The virtual photon, inturn,canturnintoaquarkandanantiquark.SosaysQED.ThiscoreprocessisshowninFigure6.3.

Figure6.3Aspace-timediagramof thecoreprocess, inwhichanelectronandpositron annihilate into a virtual photon, which then materializes as a quark-antiquarkpair.

At that point things get dicey because, as we’ve discussed, the quark (andantiquark)cannotexistinisolation.Theymustbeconfinedinsidehadrons.Theprocessofacquiringvirtualparticlecloudsandcancelingcolorcharges,whichleadsfromquarks tohadrons,mightbeverycomplicated.Thesecomplicationscouldmakeitdifficulttoidentifysignsoftheoriginalquarkandantiquark,justasitwouldbeverydifficult,lookingatthefinalmess,tofigureoutwhichrockstarted a rockslide.But let’s try to think it through, in the spirit of theCredo,hopingforthebest.

Theinitialquarkandantiquarkthatemergefromthecollisionhaveenormousenergyandaremovinginoppositedirections.14Nowsupposethattheprocessofacquiringcloudsandcancelingcolorchargeisusuallyaccomplishedgently,byproducing and rearranging color charges, without much disrupting the overall

flow of energy and momentum.We call this kind of production of particles,withoutmuch change in the overall flow, “soft” radiation.Thenwe’d see twoswarms of particles moving in opposite directions, each inheriting the totalenergy andmomentum of the quark or antiquark that initiated it. And in factthat’swhatwedosee,mostofthetime.AtypicalpictureisColorPlate2.

Occasionallythereisalso“hard”radiation,whichdoesaffecttheoverallflow.Thequark,ortheantiquark,canradiateagluon.Thenwe’llseethreejetsinsteadoftwo.AtLEP,thishappensinabout10%ofthecollisions.Inroughly10%of10%oftheevents(thatis,in1%)therewillbefourjets,andsoon.

The theoretical interpretation of our photographs is sketched in Figure 6.4.Withthisinterpretation,wecaneatourquarksandhavethemtoo.Eventhoughisolated quarks are never observed, we can see them through the flows theyinduce. In particular, we can check whether the probabilities for producingdifferent numbers of jets, coming out at different angles and sharing the totalenergy in different ways, match the probabilities we calculate for quarks,antiquarks, andgluonsdoing these things inQCD.LEPproducedhundredsofmillions of collisions, so the comparison between theoretical predictions andexperimentalresultscanbedonepreciselyandingreatdetail.

It works. And that’s why I can say with total confidence that the objectsyou’re seeing inColor Plate 1 are a quark, an antiquark, and a gluon. To seetheseparticles,however,we’vehad toexpandournotionsofwhat itmeans toseesomething—andofwhataparticleis.

Let’s bring our appreciation of the quark/gluon photographs to a climax byconnectingittotwobigideas:asymptoticfreedomandquantummechanics.

There’sadirectconnectionbetweenquarksandgluonsappearingasjetsandasymptoticfreedom.It’seasytoexplaintheconnectionusingFouriertransforms,butunfortunatelyFouriertransformsthemselvesaren’tsoeasytoexplain,sowewon’tgothere.Here’sawordexplanationthatislessprecisebutcallsformoreimagination(andlesspreparation):

Figure6.4a.Howsoftradiationmakeshadronjetsoutofaquarkandantiquark.b.Howhardradiationofagluon,followedbylotsofsoftradiation,makesthreejets.

Toexplainwhyquarksandgluonsappear (only)as jets,wehave toexplainwhysoftradiationiscommonbuthardradiationisrare.Thetwocentralideasofasymptoticfreedomare:first,thattheintrinsiccolorchargeofthefundamentalparticle—whether quark, antiquark, or gluon—is small andnot very powerful;second,thatthecloudofvirtualparticlesthatsurroundsthefundamentalparticleis thin nearby, but grows thicker far away. It’s the surrounding cloud thatenhancesthefundamentalpoweroftheparticle.It’s thesurroundingcloud,nottheparticle’scorecharge,thatmakesthestronginteractionstrong.

Radiationoccurswhenaparticlegetsoutofequilibriumwithitscloud.Thenrearrangements that restore the equilibrium in color fields cause radiation ofgluonsorquark-antiquarkpairs,muchasrearrangementsinatmosphericelectricfields cause lightning, or rearrangements in tectonic plates cause earthquakes

andvolcanos.Howcanaquark(orantiquark,orgluon)getoutofequilibriumwith its cloud? One way is if it suddenly pops out from a virtual photon, ashappened in the experiments at LEP we’ve been discussing. To reachequilibrium,thenewbornquarkhastobuildupitscloud,startingfromthecenter—where its smallcolorcharge initiates theprocess—andworking itswayout.Thechangesinvolvedaresmallandgraded,sotheyrequireonlysmallflowsofenergyandmomentum—that is, soft radiation.Theotherwayaquark cangetoutofequilibriumwithitscloudisifit’sjostledbyquantumfluctuationsofthegluonfields.Ifthejostlingisviolent,itcancausehardradiation.Butbecausethequark’s intrinsic core color charge is small, the quark’s response to quantumfluctuations in the gluon fields tends to be limited, and thus hard radiation israre.That’swhythreejetsarelesslikelythantwo.

Theconnectionofourphotographstotheprofunditiesofquantummechanicsisevenmoredirect, andneedsno suchelaborateexplanation. It is simply thatoncemore,wefindthatdoingthesamethingoverandoveragaingivesdifferentresultseachtime.Wesawthatbeforewiththeultrastroboscopicnanomicroscopethattakespicturesofprotons;we’reseeingitnowwiththecreativedestructionmachinethattakespicturesofemptyspace.Iftheworldbehavedclassicallyandpredictably, the billion euros invested inLEPwould have underwritten a veryboringmachine:everycollisionwouldjustreproducetheresultofthefirstone,andthere’dbeonlyonephotographtolookat.Instead,ourquantum-mechanicaltheoriespredictthatmanyresultscanemergefromthesamecause.Andthatiswhat we find. We can predict the relative probabilities of different results.Throughmanyrepetitions,wecancheckthosepredictionsindetail.Inthatway,short-termunpredictability canbe tamed.Short-termunpredictability is, in theend,perfectlycompatiblewithlong-termprecision.

7

SymmetryIncarnate

Colorgluonsareembodiedideas:symmetryincarnate.

THE CENTRAL IDEAOF QCD IS SYMMETRY. Now symmetry is a wordthat’s in common use, and likemany such words its meaning is fuzzy at theedges. Symmetry can mean balance, pleasing proportions, regularity. Inmathematics and physics, its meaning is consistent with all those ideas, butsharper.

ThedefinitionIlikeisthatsymmetrymeansyouhaveadistinctionwithoutadifference.

Thelegalprofessionusesthatphrase,distinctionwithoutadifference,aswell.Inthatcontext,ittypicallymeanssayingthesamethingindifferentways,or—toput it less politely—quibbling. Here’s an example, from the comedian AlanKing:

MylawyerwarnedmethatifIdiedwithoutawillI’ddieintestate.

Tounderstandthemathematicalconceptofsymmetry,it’sbesttothinkaboutanexample.Wecanbuildanicelittletowerofexamples,onethatcontainsthemostimportant ideas ineasilydigestibleform, in theworldof triangles.(SeeFigure7.1.) You can’t move most triangles around without changing them (Figure7.1a).Equilateral triangles, however, are special.You can rotate an equilateralthrough120ºor240º(twiceasmuch)andstillgetthesameshape(Figure7.1b).Theequilateraltrianglehasnontrivialsymmetry,becauseitpermitsdistinctions(between a triangle and its rotated versions) that don’t, after all, make anydifference (the rotated versions give the same shape). Conversely, if someonetellsyou that a triangle looks the sameafter rotationby120º,youcandeducethatit’sanequilateraltriangle(orthattheperson’saliar).

Figure7.1Asimpleexampleofsymmetry.a.Youcan’tmovealopsidedtrianglewithoutchangingit.b.Ifyourotateanequilateraltrianglethrough120ºarounditscenter,itdoesnotchange.

Thenextlevelofcomplexitycomeswhenweconsiderasetoftriangleswithdifferentkindsofsides.(SeeFigure7.2.)Now,ofcourse,ifwerotateoneofthetriangles through120º,wedon’tget thesame thing—thesidesdon’tmatch. InFigure7.2, the first triangle (RBG) rotates into the second triangle (BGR), thesecondtrianglerotates into the third(GRB),and the thirdrotates into thefirst.Butthecompleteset,containingallthreetriangles,isnotchanged.15

Conversely, ifsomeone tellsyou thata trianglewith threedifferentkindsofsides,togetherwithsomeotherstuff,looksthesameafterrotationthrough120º,youcandeduceboththatthetriangleisequilateraland thattherearetwomoreequilateraltriangleswithdifferentarrangementsofthesides(orthattheperson’saliar).

Figure7.2Amorecomplicatedexampleofsymmetry.Equilateraltriangleswithdifferent “colored” sides (here the colors are suggested as R(ed), B(lue),G(reen)) change under rotations through 120º; but the entire set of three goesoverintoitself.

Let’saddonelastlayerofofcomplexity.Insteadoftriangleswithdifferentlycolored sides, let’s consider laws involving those triangles. For example, asimplelawcouldbethatifyousqueezethetriangleitcollapsesinaneatway,sothat itssidesbecomebowed.NowsupposethatwehadinvestigatedonlyRBGtriangles,sothatwereallyestablishedthesqueezinglawonlyforthosetriangles.Ifweknewthatrotatingby120ºwasadistinctionwithoutadifference—thatis,that rotatingby120ºdefineda symmetry, in themathematical sense—we’dbeabletodeducenotonlythattherehadtobetheotherkindsoftriangles,butalsothattheytoocollapseneatlywhenyousqueezethem.

Thisseriesofexamplesexhibits,insimpleforms,thepowersofsymmetry.Ifweknowanobjecthassymmetry,wecandeducesomeof itsproperties. Ifweknowa setofobjectshas symmetry,wecan infer fromourknowledgeofoneobjecttheexistenceandpropertiesofothers.Andifweknowthatthelawsoftheworld have symmetry,we can infer from one object the existence, properties,andbehaviorofnewobjects.

Inmodern physics, symmetry has proved a fruitful guide to predicting new

formsofmatterand formulatingnew,morecomprehensive laws.Forexample,thetheoryofspecialrelativitycanbeconsideredapostulateofsymmetry.Itsaysthattheequationsofphysicsshouldlookthesameifwetransformalltheentitiesin those equations by adding a common, constant “boost” to their velocities.Thatboosttakesoneworldintoanother,distinctworldmovingwithaconstantvelocityrelativetothefirst.Specialrelativitysaysthatthatdistinctionmakesnodifference—thesameequationsdescribebehaviorinbothworlds.

Althoughthedetailsaremorecomplicated,theproceduresforusingsymmetrytounderstandourworldarebasicallythesameastheonesweusedinoursimpleexamples from triangle world. We consider that our equations can betransformedinwaysthatcould,inprinciple,changethem—andthenwedemandthattheydon’tinfactchange.Thepossibledistinctionmakesnodifference.Justasinthetriangleworldexamples,soingeneral,forasymmetrytoholdseveralthingshavetobetrue.Theentitiesthatappearintheequationswillneedtohavespecialproperties,tocomeinrelatedsets,andtoobeytightlyrelatedlaws.

Thussymmetrycanbeapowerfulidea,richinconsequences.It’salsoanideathatNatureisveryfondof.Prepareforapublicdisplayofaffection.

NutsandBolts,HubsandSticks

The theoryofquarksandgluons iscalledquantumchromodynamics,orQCD.TheequationsofQCDaredisplayedinFigure7.3.16

Figure 7.3 The QCD Lagrangian L written out here provides, in principle, acompletedescriptionof thestrong interaction.Heremjandqj are themassandquantumfieldofthequarkofjthflavor,andAisthegluonfield,withspace-timeindicesμ,νandcolorindicesa,b,c.Thevaluesofthenumericalcoefficients fand t are completely determined by color symmetry. Aside from the quarkmasses, the couplingconstant g is the single free parameter of the theory. Inpractice,ittakesingenuityandhardworktocalculateanythingusingL.

Pretty compact, no? Nuclear physics, new particles, weird behaviors, theoriginofmass—it’sallthere!

Actually,youshouldn’tbetooquicktobeimpressedbythefactthatwecanwriteequationsincompactform.OurcleverfriendFeynmandemonstratedhowtowritedowntheEquationoftheUniverseinasingleline.Hereitis:

(1)

U is a definitemathematical function, the total unworldliness. It’s the sum ofcontributions fromall thepiddlingpartial lawsof physics.Tobeprecise,U =UNewton + UEinstein + ···. Here, for instance, the Newtonian mechanical

UnworldinessUNewtonisdefinedbyUNewton=(F-ma)2;theEinsteinmass-

energyUnworldliness is defined byUEinstein= (E -mc 2) 2 ; and so forth.Because every contribution is positive or zero, the only way the totalU canvanishisforeverycontributiontovanish,soU=0impliesF=ma,E=mc2,andanyotherpastorfuturelawyoucaretoinclude!

Thuswecancaptureall the lawsofphysicsweknow,andaccommodateallthe laws yet to be discovered, in one unified equation. The Theory ofEverything!!!Butit’sacompletecheat,ofcourse,becausethereisnowaytouse(orevendefine)U,otherthantodeconstructitintoitsseparatepiecesandthenusethose.

The equations displayed in Figure 7.3 are quite unlike Feynman’s satirical

unification.LikeU=0, themasterequationsofQCDencodea lotof separatesmallerequations.(Forexperts:themasterequationsinvolvematricesoftensorsand spinors; the smaller equations, for their components, involve ordinarynumbers.)There’s abigdifference, though.WhenweunpackU=0,wegetabunchofunrelatedstuff.WhenweunpackthemasterequationsofQCD,wegetequationsthatarerelatedbysymmetry—symmetryamongthecolors,symmetryamong different directions in space, and the symmetry of special relativitybetween systems moving at constant velocity. Their complete content is outfront, and the algorithms that unpack them flow from the unambiguousmathematics of symmetry. So let me assure you that you really should beimpressed.It’sagenuinelyeleganttheory.

OnereflectionofthateleganceisthattheessenceofQCDcanbeportrayed,withoutseveredistortion,inafewsimplepictures.They’redisplayedinFigure7.5.We’lldiscussthempresently.

Butfirst,forcomparisonandasawarm-up,I’dliketodisplaytheessenceofquantum electrodynamics (QED) in a similar format. QED is, as its namesuggests,thequantum-mechanicalaccountofelectrodynamics.QEDisaslightlyoldertheorythanQCD.ThebasicequationsofQEDwereinplaceby1931,butfor quite a while people made mistakes in trying to solve them, and gotnonsensical (infinite) answers, so the equations got a bad reputation. Around1950 several brilliant theorists (Hans Bethe, Sin-Itiro Tomonaga, JulianSchwinger,RichardFeynman,andFreemanDyson)straightenedthingsout.

TheessenceofQEDcanbeportrayedinthesinglepictureofFigure7.4a.Itshows that a photon responds to the presence or motion of electric charge.Thoughitlookscartoonish,thatlittlepictureismuchmorethanametaphor.Itisthecoreprocessinarigorousrepresentationofasystematicmethodofsolvingthe equations of QED, which we owe to Feynman. (Yes, him again. SorryMurray.) Feynman diagrams depict processes in space and time wherebyparticlestravelfromgivenplacesatonetimetootherplacesatsomelatertime.Inbetween,theycaninfluenceeachother.Thepossibleprocessesandinfluencesinquantumelectrodynamicsarebuiltupbyconnectingworldlines(thatis,pathsthrough space and time) of electrons and photons in arbitraryways using thecore process. It’s easier done than said, and you’ll get the general idea afterponderingFigures7.4b-f.

Perfectlydefinitemathematicalrulesspecify,foreachFeynmandiagram,how

likely it is for the process it depicts to occur. The rules for complicatedprocesses,perhaps involvingmanyrealandvirtualchargedparticlesandmanyreal and virtual photons, are built up from the core process. It is likemakingconstructionswithTinkerToys.Theparticlesaredifferentkindsofsticksyoucanuse,andthecoreprocessprovidesthehubsthatjointhem.Giventheseelements,therulesforconstructionarecompletelydetermined.Forexample,Figure7.4bshowsawayinwhichthepresenceofoneelectronaffectsanother.TherulesofFeynmandiagramstellyouhowlikelyitisthatexchangeofonevirtualphoton,asdepictedthere,makestheelectronsswervebyanyspecifiedamount.Inotherwords, they tell you the force! This diagram encodes the classic theory ofelectric and magnetic forces that we teach to undergraduates. There arecorrectionstothattheorywhenyoutakeintoaccountrarerprocesses,involvingtheexchangeoftwovirtualphotons,asshowninFigure7.4c.Oraphotoncanbreakfree,asinFigure7.4d;that’swhatwecallelectromagneticradiation,oneformofwhich is light.Youcanalsohaveprocesseswhereall theparticlesarevirtual,asinFigure7.4e.Noneoftheparticlesinvolvedcanbeobserved,sothat“vacuum” process might seem academic or metaphysical, but we’ll see thatprocessesofthiskindaretremendouslyimportant.17

Figure7.4a.TheessenceofQED:photonsrespondtoelectriccharge.b.Agoodapproximation to the force between electrons, due to exchange of virtual

photons.c.Abetterapproximationincludescontributionslikethis.d.Lettherebelight!Anacceleratedelectroncanemitaphoton.e.Atotallyvirtualprocess.f. Radiation of an electron-positron pair. The antielectron, or positron, isrepresentedasanelectronwiththearrowsreversed.

Maxwell’s equations for radio waves and light, Schrödinger’s equation foratomsandchemistry,andDirac’smorerefinedversion,whichincludesspinandantimatter—allthatandmoreisfaithfullyencodedinthesesquiggles.

Inthesamepictoriallanguage,QCDappearsasanexpandedversionofQED.ItsmoreelaboratesetofingredientsandcoreprocessesaredisplayedinFigure7.5,whichhasacorrespondinglymoreelaboratecaption.

AtthispictoriallevelQCDisalotlikeQED,butbigger.Thediagramslooksimilar,andtherulesforevaluatingthemaresimilar,buttherearemorekindsofsticksandhubs.Moreprecisely,whilethereisjustonekindofchargeinQED—namely,electriccharge—QCDhasthree.

ThethreekindsofchargethatappearinQCDarecalled,fornogoodreason,colors.These“colors”ofcoursehavenothing todowithcolor in theordinarysense;rather,theyaredeeplysimilartoelectriccharge.Inanycase,we’lllabelthemred,white,andblue.Everyquarkhasoneunitofoneofthecolorcharges.In addition, quarks come in different species, or flavors.Theonly two flavorsthatplayaroleinnormalmatterarecalleduandd, forupanddown.18Quark“flavors”havenomoretodowithhowanythingtastesthanquarkcolorshavetodowithhowtheylook.Also,thesemixed-metaphoricalnamesforuandd (Zenkoan:What is the taste of up?) donot imply that there is any real connectionbetweenflavorsanddirectionsinspace.Don’tblameme;whenIgetthechance,Igiveparticlesdignifiedscientific-soundingnameslikeaxionandanyon.

Continuing the analogy between QED and QCD, there are photon-likeparticles,calledcolorgluons,thatrespondinappropriatewaystothepresenceormotionofcolorcharge,muchasphotonsrespondtoelectriccharge.

Sothereareuquarkswithaunitofredcharge,dquarkswithaunitofbluecharge—six different possibilities altogether. And instead of one photon thatrespondstoelectriccharge,QCDhaseightcolorgluonsthatcaneitherrespondtodifferentcolorchargesorchangeonecolorchargeintoanother.Sotherearequite a large variety of sticks, andmany different kinds of hubs that connect

them.With all these possibilities, it seems as though things could get terriblycomplicated andmessy.And so theywould,were it not for theoverwhelmingsymmetry of the theory. For example, if you interchange red with blueeverywhere,youmuststillgetthesamerules.ThesymmetryofQCDallowsyoutomixthecolorscontinuously,formingblends,andtherulesmustcomeoutthesame for blends as for pure colors. This extended symmetry is extremelypowerful.Itfixestherelativestrengthofallthehubs.

Figure 7.5 a. Quarks (antiquarks) carry one positive (negative) unit of colorcharge. They play a role in QCD similar to that of electrons in QED. Acomplication is that there are several distinct kinds, or flavors, of quarks.Thetwothatareimportantfornormalmatterarethelightestones,calleduandd.(Tobe honest, there are also different flavors of electrons, called muons and τleptons, but I’ve been suppressingirrelevant complications.) b. There are 8different color gluons. Each carriesaway a unit of color charge and brings inanothercolor (possibly thesame).The totalofeachcolorcharge isconserved.

Therewould seem to be 3 × 3 = 9 possibilitiesfor gluons. But one particularcombination,theso-calledcolorsinglet,whichrespondsequallytoallcharges,isdifferent from the others. We must remove it if we are to have a perfectlysymmetrictheory.Thuswepredictthatexactly8gluonsexist.Fortunately,thatconclusion is vindicatedby experiment.Gluonsplay a role inQCDsimilar tothat of photons in QED. c. Two representative core processes, wheregluonssimplyrespondto,orbothrespondtoandtransform,thecolorchargeofquarks.d.AqualitativelynewfeatureofQCD,comparedtoQED,isthatthereareprocesseswherebycolorgluonsrespondtooneanother.Photonsdonot.

Foralltheirsimilarities,however,thereareafewcrucialdifferencesbetweenQCDandQED.Firstofall,theresponseofgluonstocolorcharge,asmeasuredby the QCD coupling constant, is much more vigorous than the response ofphotonstoelectriccharge.

Second, as shown inFigure7.5c, in addition to responding to color charge,gluons can change one color charge into another.All possible changes of thiskind are allowed. Yet each color charge is conserved, because the gluonsthemselvescancarryunbalancedcolorcharges.Forexample,ifabsorptionofagluonchangesablue-chargedquarkintoared-chargedquark,thenthegluonthatgotabsorbedmusthavecarriedoneunitofredchargeandminusoneunitofbluecharge.Conversely,ablue-chargedquarkcanemitagluonwithoneunitofbluechargeandminusoneunitofredcharge;itbecomesared-chargedquark.

A third difference between QCD and QED, the most profound, is aconsequenceofthesecond.Becausegluonsrespondtothepresenceandmotionofcolorcharge,andgluonscarryunbalancedcolorcharge,itfollowsthatgluons,quiteunlikephotons,responddirectlytooneanother.

Photons, by contrast, are electrically neutral. They don’t respond to oneanother very much at all. We’re all familiar with this, even if we’ve neverthoughtmuchaboutit.Whenwelookaroundonasunnyday,thereisreflectedlight bouncing everywhichway, butwe see right through it. The laser swordfightsyou’veseeninStarWarsfilmswouldn’twork.(Possibleexplanation:it’samovieaboutatechnologicallyadvancedcivilizationinagalaxyfar,faraway,somaybethey’reusingcolorgluonlasers.)

Eachof thesedifferencesmakescalculating theconsequencesofQCDmoredifficultthancalculatingtheconsequencesofQED.Becausethebasiccoupling

isstrongerinQCDthaninQED,morecomplicatedFeynmandiagrams,withlotsofhubson the inside,makerelatively largercontributions toanyprocess.Andbecause therearevariouspossibilities for routing the flowsofcolor,andmorekindsofhubs,therearemanymorediagramsateachlevelofcomplexity.

Asymptotic freedomallows us to calculate some things, such as the overallflowsofenergyandmomentuminjets.That’sbecausethemany“soft”radiationevents don’t much affect the overall flow, and we can ignore them in ourcalculations. Only the small number of hubs where “hard” radiation occursdemand attention. Without too much work, then, using pencil and paper, ahuman being canwork out predictions for the relative probability of differentnumbersofjetscomingoutatdifferentangleswithdifferentsharesofenergy.(Ithelpsifyougivethehumanbeingalaptopandsendherthroughafewyearsofgraduateschool.)Inothercasestheequationshavebeensolved—approximately—only after heroic efforts. We’ll discuss the heroic efforts that enable us tocalculatethemassoftheproton,startingfrommasslessquarksandgluons—andthustoidentifytheoriginofmass—inChapter9.

QuarksandGluons3.0:SymmetryIncarnate

In tryingtodojustice to thewayinwhichpostulatinganenormousamountofsymmetry—whatwecall localsymmetry—forcesus to includecolorgluonsinour equations, and thus to predict their existence and all their properties, I’mremindedofoneofmyfavoritePietHeinGrooks:

loversmeanderinproseandrhyme,tryingtosay—forthethousandthtime—what’seasierdonethansaid.

Anyway,ontotheproseandrhyme.

Backwhenwediscussedthecoloredtrianglesandtheirsymmetry,therewasafussyfootnoteabouthowyouweresupposedtoignorethefactthatthedifferenttriangles were in different places. It makes perfectly good logical andmathematicalsensetodothat.Inmathematicsweoftenignoreirrelevantdetailsinordertoconcentrateonthemostinteresting,essentialfeatures.Forexample,in geometry it’s standard operating procedure to deal, conceptually,with lines

that have zero thickness and continue forever in bothdirections.But from thepointofviewofphysics,it’salittlepeculiartosupposethatsymmetryrequiresyouto takenoaccountofwhere thingsare.Specifically, forexample, itseemspeculiartosupposethatthesymmetrybetweenredcolorchargeandbluecolorcharge requires that you change red charged quarks into blue charged quarks,and vice versa, everywhere in the universe. It might seem more natural tosupposethatyoucouldmakethechangesonlylocally,withouthavingtoworryaboutdistantpartsoftheuniverse.

Thatphysicallynaturalversionofsymmetry iscalled local symmetry.Localsymmetry is amuch bigger assumption than the alternative, global symmetry.Forlocalsymmetryisanenormouscollectionofseparatesymmetries—roughlyspeaking,aseparatesymmetryforeachpointofspaceandtime.Inourexample,we canmake the red-blue charge switch anywhere and at anymoment. Eachplaceandmomentdefines,therefore,itsownsymmetry.Withaglobalsymmetryyouhave tomake the same switcheverywhereandeverywhen, and insteadofinfinitelymanyindependentsymmetriesyouhavejustonelockstepversion.

Becauselocalsymmetryisamuchbiggerassumptionthanglobalsymmetry,itimposesmore restrictions on the equations or, in otherwords, on the form ofphysicallaws.Therestrictionsfromlocalsymmetryaresosevere,infact,thatatfirst sight they appear impossible to reconcile with the ideas of quantummechanics.

Before explaining the problem, a quick summary of the relevant quantummechanics: In quantummechanics,we have to allow for the possibility that aparticle might be observed at different places, with different probabilities.There’sawavefunctionthatdescribesallthesepossibilities.Thewavefunctionhas large values where the probability is large, and small values where theprobability issmall (quantitatively, theprobability isequal to thesquareof thewave function). Furthermore, wave functions that are nice and smooth—thatvarygently in spaceand time—have lowerenergy than those thathaveabruptchanges.

Nowtotheheartoftheproblem:Let’ssupposewehaveanicesmoothwavefunctionforaquarkcarryingredcolorcharge.Thenapplyourexampleoflocalsymmetry in a small region, changing redcolor charge intobluecolor charge.Afterthatchange,ourwavefunctionhasabruptchanges.Insidethesmallregion,ithasonlyabluecolorcomponent;outside,ithasonlyaredcolorcomponent.

Sowe’vechangeda low-energywavefunction,withoutabruptchanges, intoawave function that has abrupt changes and therefore describes a state of highenergy.Thatchangeofstateisgoingtochangethebehaviorofthequarkwe’redescribing, unmistakably, because there aremany detectable effects of energy.Forexample,accordingtoEinstein’ssecondlaw,youcoulddeterminetheenergyof the quark byweighing it. But thewhole point of symmetry is that it’s notsupposedtochangethebehaviorofthethingsittransforms.19Wewanttohaveadistinctionwithoutadifference.

Sotogetequationsthathavelocalsymmetry,wemustaltertheruleaccordingtowhichabruptchangesinthewavefunctionnecessarilyhavelargeenergy.Wehave to suppose that the energy is not governed simply by the steepness ofchangeinthewavefunction;itmustcontainadditionalcorrectionterms.That’swherethegluonfieldscomein.Thecorrectiontermcontainsproductsofvariousgluonfields(eightofthem,forQCD)withthedifferentcolorcomponentsofthequarkwave functions. Ifyoudo things just right, thenwhenyoumakea localsymmetrytransformation,thequarkwavefunctionchanges,andthegluonfieldchanges,buttheenergyofthewavefunction—includingthecorrectionterms—stays the same. There’s no ambiguity about the procedure: local symmetrydictateswhatyoumustdo,everystepoftheway.

Thedetailsoftheconstructionareveryhardtoconveyinwords.Itreallyis,astheGrooksays,“easierdonethansaid,”andifyouwanttoseeitdoneforreal,with equations, you’ll have to look at technical articles or textbooks. I’vementioneda fewof themoreaccessibleones in theendnotes.Fortunately,youdon’t need to work through the detailed construction to understand the grandphilosophicalpoint,whichisthis:

Inordertohavelocalsymmetry,wemustintroducethegluonfields.Andwemust arrange the way those gluons fields interact with quarks, and with oneanother,justso.Anidea—localsymmetry—issopowerfulandrestrictivethatitproducesadefinitesetofequations.Inotherwords,implementinganidealeadstoacandidatereality.

Thecandidaterealitycontainingcolorgluonssucceedsinembodyingtheideaoflocalsymmetry.Newingredients—colorgluonfields—arepartoftherecipeforitscandidateworld.Aretheypresentinourworld?Aswe’vediscussed,andevenseen inphotographs, theyare indeed.Thecandidatereality,hatchedfromideas,isrealityitself.

8

TheGrid(PersistenceofEther)

Whatisspace?Anemptystage,wherethephysicalworldofmatteractsoutitsdrama?Anequalparticipant,thatbothprovidesbackgroundandhasalifeofitsown?Ortheprimaryreality,ofwhichmatterisasecondarymanifestation?Viewsonthisquestionhaveevolved,andseveraltimeschangedradically,overthehistoryofscience.Today,thethirdviewistriumphant.Whereoureyesseenothing,ourbrains,ponderingtherevelationsofsharplytunedexperiments,discovertheGridthatpowersphysicalreality.

PHILOSOPHICALANDSCIENTIFICIDEASaboutwhattheworldismadeofcontinuetochange.Manylooseendsremainintoday’sbestworld-models,andsomebigmysteries.Clearlythelastwordhasnotbeenspoken.Butweknowalot,too—enoughtodrawsomesurprisingconclusionsthatgobeyondpiecemealfacts.Theyaddress,andoffersomeanswersto,questionsthathavetraditionallybeenregardedasbelongingtophilosophyoreventheology.

Fornaturalphilosophy,themostimportantlessonwelearnfromQCDisthatwhatweperceiveasemptyspaceisinrealityapowerfulmediumwhoseactivitymolds theworld.Other developments inmodern physics reinforce and enrichthatlesson.Later,asweexplorethecurrentfrontiers,we’llseehowtheconceptof“empty”spaceasarich,dynamicmediumempowersourbestthinkingabouthowtoachievetheunificationofforces.

So:What is theworldmadeof?Subject,asever, toadditionandcorrection,hereisthemultifacetedanswerthatmodernphysicsprovides:

•Theprimaryingredientofphysicalreality,fromwhichallelseisformed,fillsspaceandtime.

•Everyfragment,eachspace-timeelement,hasthesamebasicpropertiesas

everyotherfragment.•Theprimaryingredientofrealityisalivewithquantumactivity.Quantumactivity has special characteristics. It is spontaneous and unpredictable.Andtoobservequantumactivity,youmustdisturbit.

• The primary ingredient of reality also contains enduring materialcomponents. These make the cosmos a multilayered, multicoloredsuperconductor.

•Theprimaryingredientofrealitycontainsametricfieldthatgivesspace-timerigidityandcausesgravity.

•Theprimaryingredientofrealityweighs,withauniversaldensity.

There arewords that capture different aspects of this answer.Ether is the oldconcept that comes closest, but it bears the stigma of dead ideas and lacksseveral of the new ones. Space-time is logically appropriate to describesomething that is unavoidably there, everywhere and always, with uniformproperties throughout. But space-time carries evenmore baggage, including aheavy suggestion of emptiness. Quantum field is a technical term thatsummarizes the first three aspects, but it doesn’t include the last three and itsounds,well,tootechnicalandforbiddingforuseinnaturalphilosophy.

Iwilluse thewordGrid for theprimaryworld-stuff.Thatwordhas severaladvantages:

• We’re accustomed to using mathematical grids to position layers ofstructure,asinFigure8.1.

Figure 8.1Grid, old and new. a.A grid is often used to describe howvariousthingsaredistributedinspace.b.TheGrid,whichunderliesourmost successful world-model,has several aspects. TheGrid, with theseaspects,ispresentalwaysandeverywhere.OrdinarymatterisasecondarymanifestationoftheGrid,tracingitslevelofexcitation.

•We draw power for appliances, lights, and computers from the electricgrid.Thephysicalworldofappearancedrawsitspower,ingeneral,fromtheGrid.

•Agreatdevelopingproject,driven inpartby theneedsofphysics,20 isthe technology to integrate many dispersed computers into functionalunits,whosetotalpowercanbeaccessedasneededfromanypoint.ThattechnologyisknownasGridtechnology.It’shot,andit’scool.

•Gridisshort.•GridisnotMatrix.I’msorry,butthesequelstarnishedthatcandidate.AndGridisnotBorg.

ABriefHistoryofEther

Debate about the emptiness of space goes back to the prehistory of modernscience, at least to the ancient Greek philosophers. Aristotle wrote, “Natureabhorsavacuum,”whereashisopponentstheatomistsheld,inthewordsoftheirpoetLucretius,that

Allnature,then,asself-sustained,consistsOftwainofthings:ofbodiesandofvoidInwhichthey’reset,andwherethey’removedaround.

That old speculative debate echoed at the dawn of modern science, in theScientific Revolution of the seventeenth century. René Descartes proposed togroundthescientificdescriptionofthenaturalworldonwhathecalledprimaryqualities:extension(essentially,shape)andmotion.Matterwassupposedtohavenopropertiesotherthanthose.Animportantconsequenceisthattheinfluenceofone bit of matter on another can occur only through contact; having noproperties other than extension and motion, a bit of matter has no way ofknowingaboutotherbitsthanbytouchingthem.Thus,todescribe(forinstance)the motion of planets, Descartes had to introduce an invisible space-filling“plenum” of invisiblematter.He envisioned a complex sea ofwhirlpools andeddies,uponwhichtheplanetssurf.

Isaac Newton cut through all those potential complexities by formulatingprecise, successfulmathematicalequations for themotionofplanets,usinghislaws of motion and of gravity. Newton’s law of gravity does not fit intoDescartes’sframework.Itpostulatesactionatadistance,ratherthaninfluencebycontact.Forexample,theSunexertsagravitationalforceonEarth,accordingtoNewton’slaw,eventhoughitisnotincontactwithEarth.Despitethesuccessof

his equations in providing an excellent, detailed account of planetarymotion,Newtonwasnothappywithactionatadistance.

Thatonebodymayactuponanotheratadistancethroughavacuumwithoutthemediationofanythingelse,byandthroughwhichtheiractionandforcemaybeconveyedfromoneanother,istomesogreatanabsurditythat,Ibelieve,nomanwhohasinphilosophicmattersacompetentfacultyofthinkingcouldeverfallintoit.

Neverthelesshelefthisequationstospeakforthemselves:

Ihavenotbeenabletodiscoverthecauseofthosepropertiesofgravityfromphenomena,andIframenohypotheses;forwhateverisnotdeducedfromthephenomenaistobecalledahypothesis,andhypotheses,whethermetaphysicalorphysical,whetherofoccultqualitiesormechanical,havenoplaceinexperimentalphilosophy.

Newton’sfollowers,ofcourse,didnotfailtonoticethathissystemhademptiedout space.Having fewer scruples, theybecamemoreNewtonian thanNewton.HereisVoltaire:

AFrenchmanwhoarrivesinLondon,willfindphilosophy,likeeverythingelse,verymuchchangedthere.Hehadlefttheworldaplenum,andhenowfindsitavacuum.

Mathematicians and physicists, through familiarity and spectacular success,grewcomfortablewithactionatadistance.Sothingsstood,inessence,formorethan150years.Then JamesClerkMaxwell, consolidatingeverything thatwasknownaboutelectricityandmagnetism,foundthattheresultingequationswereinconsistent. In1861,Maxwell found thathecouldrepair the inconsistencybyintroducinganextratermintotheequations—inotherwords,bypostulatingtheexistence of a new physical effect. Some years earlier, Michael Faraday haddiscovered that when magnetic fields change in time, they produce electricfields.To fixhis equations,Maxwellhad topostulate theconverseeffect: thatchanging electric fields producemagnetic fields.With this addition, the fieldscan take on a life of their own. Changing electric fields produce (changing)magneticfields,whichproducechangingelectricfields,andsoforth, inaself-renewingcycle.

Maxwellfoundthathisnewequations—knowntodayasMaxwell’sequations—havepure-fieldsolutionsofthiskind,solutionsthatmovethroughspaceatthe

speed of light. Climaxing a grand synthesis, he concluded that these self-renewingdisturbancesinelectricandmagneticfieldsarelight,aconclusionthathasstoodthetestoftime.ForMaxwell,thesefieldsthatfillallspaceandtakeonalifeoftheirownwereatangiblesymbolofGod’sglory:

Thevastinterplanetaryandinterstellarregionswillnolongerberegardedaswasteplacesintheuniverse,whichtheCreatorhasnotseenfittofillwiththesymbolsofthemanifoldorderofHiskingdom.Weshallfindthemtobealreadyfullofthiswonderfulmedium;sofull,thatnohumanpowercanremoveitfromthesmallestportionofSpace,orproducetheslightestflawinitsinfinitecontinuity.

Einstein’srelationshipwiththeetherwascomplex,andchangedovertime.Itisalso, I think, poorly understood, even by his biographers and historians ofscience(orquitepossiblybyme).Inhisfirst1905paperonspecialrelativity,21“OntheElectrodynamicsofMovingBodies,”hewrote,

Theintroductionofa“luminiferousether”willprovetobesuperfluousinasmuchastheviewheretobedevelopedwillnotrequirean“absolutelystationaryspace”providedwithspecialproperties,norassignavelocity-vectortoapointoftheemptyspaceinwhichelectromagneticprocessestakeplace.

That forceful declaration from Einstein puzzled me for a long time, for thefollowingreason.In1905,theproblemfacingphysicswasnotthattherewasnotheoryofrelativity.Theproblemwasthattherewere twomutually inconsistenttheories of relativity. On one hand was the relativity theory of mechanics,obeyed by Newton’s equations. On the other was the relativity theory ofelectromagnetism,obeyedbyMaxwell’sequations.

Bothoftheserelativitytheoriesshowedthattheirrespectiveequationsdisplayboost symmetry—that is, the equations take the same form when you add acommon, overall velocity to everything. In more physical terms, the laws ofphysics(asstatedbytheequations)lookthesametoanytwoobserversmovingataconstantvelocityrelativetooneanother.Togetfromoneobserver’saccountoftheworldtotheother,however,youhavetorelabelpositionsandtimes.AnobserveronaplanefromNewYorktoChicago,forinstance,wouldinacoupleofhourslabelChicagoas“distance0,”whereasChicagowouldstillbe“distance500mileswest”(roughly)fortheobserverontheground.Theproblemwasthattherelabelingrequiredformechanicalrelativitywasdifferentfromthatrequired

for electromagnetic relativity. According to mechanical relativity you mustrelabel spatial positions but not times; whereas according to electromagneticrelativityyouhadtorelabelboth,inarathermorecomplicatedwaythatmixesspace and time together. (The equations of electromagnetic relativity had, by1905,alreadybeenderivedbyHendrikLorentzandperfectedbyHenriPoincaré;today they are known as Lorentz transformations.) Einstein’s great innovationwas to assert the primacy of electromagnetic relativity, and work out theconsequencesfortherestofphysics.

SoitwasthevenerabletheoryofNewtonianmechanics,nottheupstarttheoryof electromagnetism, that requiredmodification.The theorybasedonparticlesmoving through empty space gave way, not the theory based on continuous,space-fillingfields.Maxwell’sfieldequationswerenotmodifiedbythespecialtheoryof relativity;on thecontrary, theysupplied its foundation.Onestillhadthe space-filling, potentially self-regenerating electric andmagnetic fields thatsentMaxwellintoraptures.Indeed,theideasofspecialrelativityalmostrequirespace-filling fields and, in that sense, explainwhy they exist, aswe’ll discussmomentarily.

Why,then,didEinsteinexpresshimselfsostronglytothecontrary?True,hehadunderminedoldideasaboutamechanicalether,madeofparticlesfollowingNewton’s laws—infacthehadunderminedthoselawsaltogether.Butfarfromeliminating space-filling fields, his new theory elevated their status.Hemighthavesaidwithmorejustice(I’vealwaysthought) that the ideaofanether thatlooksdifferenttomovingobserversiswrongbutareformedether,thatlooksthesame toobserversmovingat a constantvelocity relative tooneanother, is thenaturalsettingforspecialrelativity.

At the time he was hatching special relativity, in 1905, Einstein was alsobroodingover theproblemofwhat laterbecameknownas lightquanta.Afewyears earlier, in 1899, Max Planck had put forward the first idea of whateventually became quantum mechanics. Planck suggested that atoms couldexchange energy with electromagnetic fields—that is, emit and absorbelectromagneticradiation,suchaslight—onlyindiscreteunits,orquanta.Usingthat idea, he was able to explain some experimental facts about blackbodyradiation. (Very roughlyspeaking, theproblemishowthecolorofahotbody,such as a red-hot poker or a glowing star, depends on its temperature. Lessrough,butstill far fromsmoothlypolished:ahotbodyemitsawholerangeofcolors, with different intensities. The challenge was to describe the whole

spectrum of intensities and how it changes with temperature.) Planck’s ideaworked, empirically, but it wasn’t very satisfactory intellectually. It was justtackedontotheotherlawsofphysics,notderivedfromthem.Infact,asEinstein(butnotPlanck)clearly realized,Planck’s ideawas inconsistentwith theotherlaws.

Inotherwords,Planck’s ideawas anotherof those things—like theoriginalquarkmodel, or partons—thatworks in practice but not in theory. Itwouldn’tpassmusterattheUniversityofChicago,anditdidn’tpassmusterwithEinstein.But Einstein was very impressed with the power of Planck’s idea to explainexperimental results.Heextended it inanewdirection,hypothesizing thatnotonlydidatomsemitandabsorblight(andelectromagneticradiationgenerally)indiscreteunitsofenergy,but lightalwayscame indiscreteunitsofenergy,andalso travelled carrying discrete units of momentum. With these extensions,Einstein was able to explain more facts, and even to predict new ones—includingthephotoelectriceffect,whichwastheprimaryworkcitedinhis1921Nobel Prize. In hismind, Einstein had cut theGordian knot: Planck’s idea isinconsistentwithexistingphysicallaws,butitworks—thereforethoselawsmustbewrong!

Andif light travels in lumpsofenergyandmomentum,whatcouldbemorenatural than to consider these lumps—and light itself—to be particles ofelectromagnetism?Fieldsmightbemoreconvenient,aswe’ll see,butEinsteinwasneveronetovalueconvenienceoverprinciple.Withthisissueoccupyinghismind, I suspect that Einstein took an unusual perspective on what lessons todrawfromspecialrelativity.Forhim,theideaofaspace-fillingentitythatlooksthesamewhenyoumovepastitatfinitevelocity(asspecialrelativityshowsthe“luminiferous ether” must) was counterintuitive and therefore suspect. Thisperspective,whichcastashadowoverMaxwell’selectromagneticfieldtheoryoflight, reinforced his intuitions from Planck’s work, and from his own, onblackbody radiation and the photoelectric effect. Einstein thought that thesedevelopments—the ether had become counterintuitive, and it seemed to takeform, physically, only in lumps—togethermade a strong case for abandoningfieldsandgoingbacktoparticles.

Ina1909lectureEinsteinspeculatedpubliclyalongtheselines:

Anyway,thisconceptionseemstomethemostnatural:thatthemanifestationoflight’selectromagneticwavesisconstrainedat

singularitypoints,likethemanifestationofelectrostaticfieldsinthetheoryoftheelectron.Itcan’tberuledoutthat,insuchatheory,theentireenergyoftheelectromagneticfieldcouldbeviewedaslocalizedatthesesingularities,justliketheoldtheoryofaction-at-a-distance.Iimaginetomyself,eachsuchsingularpointsurroundedbyafieldthathasessentiallythesamecharacterofaplanewave,andwhoseamplitudedecreaseswiththedistancebetweenthesingularpoints.Ifmanysuchsingularitiesareseparatedbyadistancesmallwithrespecttothedimensionsofthefieldofonesingularpoint,theirfieldswillbesuperimposed,andwillformintheirtotalityanoscillatingfieldthatisonlyslightlydifferentfromtheoscillatingfieldinourpresentelectromagnetictheoryoflight.

Inotherwords,by1909—andeven, Isuspect, in1905—Einsteindidnot thinkthatMaxwell’sequationsexpressedthedeepestrealityoflight.Hedidnotthinkthe fields truly had a life of their own; instead, they arose from “singularitypoints.”He did not think that they truly filled space: they are concentrated inpacketsnearthesingularitypoints.TheseideasofEinsteinwere,ofcourse,tiedupwithhisconceptthatlightcomesindiscreteunits:today’sphotons.

JustasNewtonhadmisgivingsaboutthenaturalimplicationofhistheory,thatit emptied space, Einstein hadmisgivings about the natural implication of histheory, that it filled space. Like Columbus, who found the NewWorld whileseekingawaytotheOld,explorerswhomakelandfallonunexpectedcontinentsofideasareoftenunpreparedtoacceptwhattheyhavefound.Theycontinuetoseekwhattheywerelookingfor.

By1920,afterhedevelopedthetheoryofgeneralrelativity,Einstein’sattitudehad changed: “More careful reflection teaches us, however, that the specialtheoryofrelativitydoesnotcompelustodenyether.”Indeed,thegeneraltheoryof relativity is very much an “ethereal” (that is, ether-based) theory ofgravitation.(I’msavingEinstein’sowndeclarationonthatscoreforuselaterinthis chapter.) Nevertheless, Einstein never gave up on eliminating theelectromagneticether:

Ifweconsiderthegravitationalfieldandtheelectromagneticfieldfromthestandpointoftheetherhypothesis,wefindaremarkabledifferencebetweenthetwo.Therecanbenospacenoranypartofspacewithoutgravitationalpotentials;fortheseconferuponspaceitsmetricalqualities,

withoutwhichitcannotbeimaginedatall.Theexistenceofthegravitationalfieldisinseparablyboundupwiththeexistenceofspace.Ontheotherhandapartofspacemayverywellbeimaginedwithoutanelectromagneticfield....22

Around1982,IhadamemorableconversationwithFeynmanatSantaBarbara.Usually, at least with people he didn’t know well, Feynman was “on”—inperformancemode.Butafteradayofbravuraperformanceshewasalittletired,andeasedup.Aloneforacoupleofhours,beforedinner,wehadawide-rangingdiscussion about physics. Our conversation inevitably drifted to the mostmysterious aspect of our model of the world—both in 1982 and today—thesubjectofthecosmologicalconstant.(Thecosmologicalconstantis,essentially,thedensityofemptyspace.Anticipatinga little, letme justmention thatabigpuzzle in modern physics is why empty space weighs so little even thoughthere’ssomuchtoit.)

IaskedFeynman,“Doesn’t itbotheryouthatgravityseemsto ignoreallwehavelearnedaboutthecomplicationsofthevacuum?”Towhichheimmediatelyresponded,“IoncethoughtI’dsolvedthatone.”

ThenFeynmanbecamewistful.Ordinarilyhewouldlookyourightintheeye,andspeakslowlybutbeautifully,inasmoothflowoffullyformedsentencesorevenparagraphs.Now,however,hegazedoffintospace;heseemedtransportedforamoment,andsaidnothing.

Gathering himself again, Feynman explained that he had been disappointedwith the outcome of hiswork on quantum electrodynamics. It was a startlingthing for him to say, because that brilliant work was what brought Feynmangraphstotheworld,aswellasmanyofthemethodswestillusetododifficultcalculationsinquantumfieldtheory.ItwasalsotheworkforwhichhewontheNobelPrize.

Feynman told me that when he realized that his theory of photons andelectronsismathematicallyequivalenttotheusualtheory,itcrushedhisdeepesthopes.Hehadhopedthatbyformulatinghistheorydirectlyintermsofpathsofparticlesinspace-time—Feynmangraphs—hewouldavoidthefieldconceptandconstructsomethingessentiallynew.Forawhile,hethoughthehad.

Whydidhewanttogetridoffields?“Ihadaslogan,”hesaid.RachetingupthevolumeandhisBrooklyn23accent,heintonedit:

Thevacuumdoesn’tweighanything[dramaticpause]becausethere’snothingthere!

Then he smiled, seemingly content, but subdued. His revolution didn’t quitecomeoffasplanned,butitwasadamnedgoodtry.

SpecialRelativityandtheGrid

Thetheoryofspecialrelativity,historically,cameoutofthestudyofelectricityand magnetism, which culminated in Maxwell’s field theory. Thus specialrelativityarosefromadescriptionoftheworldbasedontheconceptofentities—the electric andmagnetic fields—that fill all space. That sort of descriptionwas a sharp break from the world-model inspired by Newton’s classicalmechanics and gravity theory, which dominated earlier thinking. Newton’sworld-model was based on particles that exert forces on one another throughemptyspace.

The claimsof special relativity, however, go beyond electromagnetism.Theessence of special relativity is a postulate of symmetry: the laws of physicsshouldtakethesameformafteryouboosteverythingappearinginthembythesame, constant velocity. This postulate is a universal claim, grown beyond itselectromagneticroots.Thatis,theboostsymmetryofspecialrelativityappliestoall the laws of physics.Aswe noted above,Einstein had to changeNewton’slaws of mechanics so that they obeyed the same boost symmetry aselectromagnetism.

While the inkwasdryingonspecial relativity,Einsteinstarted lookingforawaytoincludegravityinthenewframework.Itwasthebeginningofaten-yearsearch,ofwhichEinsteinlatersaid,

...theyearsofsearchinginthedarkforatruththatonefeels,butcannotexpress;theintensedesireandthealternationsofconfidenceandmisgiving,untilonebreaksthroughtoclarityandunderstanding,areonlyknowntohimwhohashimselfexperiencedthem.

Intheendheproduceda field-based theoryofgravity,general relativity.We’llhave much more to say about that theory later in this chapter. Several otherclever people, including notably Poincaré, the great German mathematicianHermannMinkowski,andtheFinnishphysicistGunnarNordström,werealsoin

thehunt, trying toconstruct theoriesofgravityconsistentwith theconceptsofspecialrelativity.Allwereledtofieldtheories.

There’sagoodgeneralreasontoexpectthatphysicaltheoriesconsistentwithspecialrelativitywillhavetobefieldtheories.Hereitcomes:

A major result of the special theory of relativity is that there is a limitingvelocity:thespeedoflight,usuallydenotedc.Theinfluenceofoneparticleonanothercannotbetransmittedfasterthanthat.Newton’slawforthegravitationalforce,accordingtowhichtheforceduetoadistantbodyisproportional to theinverse square of its distance right now, does not obey that rule, so it is notconsistent with special relativity. Indeed the concept “right now” itself isproblematic.Events that appear simultaneous to a stationary observerwill notappear simultaneous toanobservermovingat constantvelocity.Overthrowingtheconceptofauniversal“now”was,accordingtoEinsteinhimself,byfarthemostdifficultstepinarrivingatspecialrelativity:

[A]llattemptstoclarifythisparadoxsatisfactorilywerecondemnedtofailureaslongastheaxiomoftheabsolutecharacteroftimes,viz.,ofsimultaneity,unrecognizedlywasanchoredintheunconscious.Clearlytorecognizethisaxiomanditsarbitrarycharacterreallyimpliesalreadythesolutionoftheproblem.

This is fascinating stuff, but it iswell covered in dozens of popular books onrelativity, so I won’t go further into it here. For present purposes, what’simportantissimplythatthere’salimitingvelocity,c.

NowconsiderFigure8.2. InFigure8.2a,wehave theworld-linesofseveralparticles.Theirpositions in spaceare indicatedon thehorizontal axis, and thevalueoftimeisindicatedontheverticalaxis.Astimeprogresses,theparticles’positions change. The positions for any one particle, followed through time,make that particle’sworld-line. Of coursewe should really have three spatialdimensions,buteventwoaretoomanytofitonaflatpage,andfortunatelyoneisenoughtomakeourpoint.InFigure8.2b,youseethatifinfluencepropagatesatafinitespeed,thentheinfluenceofparticleA(say)onparticleBdependsonwhereparticleAwasinthepast.Sotogetthetotalforceonaparticle,wehaveto sum up the influences from all the other particles, coming from differentearlier times.This leads toacomplicateddescription,asemphasized inFigure8.2b.Analternative,alsoshowninFigure8.2c,istoforgetaboutkeepingtrackof the individual past positions, and instead focus on the total influences. In

otherwords,wekeeptrackofafieldrepresentingthetotalinfluence.

Thatmovefromaparticledescriptiontoafielddescriptionwillbeespeciallyfruitful if the fieldsobey simple equations, so thatwecancalculate the futurevalues of fields from the values they have now, without having to take pastvalues into account.Maxwell’s theory of electromagnetism, general relativity,andQCDallhavethisproperty.Evidently,Naturehastakentheopportunitytokeepthingsrelatively24simplebyusingfields.

Figure8.2Howspecialrelativityleadstofields.a.Herewehavetheworld-linesofseveralparticles,indicatinghowtheirpositions(horizontalaxis)changewithtime (verticalaxis).b. If there’sa limitingvelocity, then the total force feltbyanygivenparticlewilldependonwheretheotherparticleswereinthepast.The“lines of influence” corresponding to propagation of influence at the limitingspeed c are sketched in. c. To get the total force,we can either keep track ofwhereeverybody’sbeeninthepast,orjustfocusonthesummedinfluences.Thefirst procedure corresponds to a particle theory, the second—potentiallymuchsimpler—toafieldtheory.

GluonsandtheGrid

Einstein and Feynman were not unaware of the logic that suggests theinevitabilityof a fielddescription for fundamentalphysics.Yet aswe’ve seen,eachofthemwasready—eveneager—togobacktoaparticledescription.

That these two great physicists, at different times and for different reasons,couldquestion theexistenceof fields that fillall space (acrucialaspectof theGrid)showsthatthecasefortheirexistencedidnotappearoverwhelmingevenwell into the twentieth century. There was room for doubt, because hardevidencethatfieldshavealifeoftheirownwasscanty.InmyargumentsaroundFigure8.2,Imadethecasethatfieldsareconvenient.That’sverydifferentfromtheirbeingnecessaryingredientsofultimatereality.

I’mnotsurethatEinsteinwaseverconvincedabouttheelectromagneticether.Oneofhisgreateststrengthsasatheoreticalphysicistcouldalsobeaweakness:his stubbornness.Stubbornness servedhimwellwhenhe insistedon resolvingthe contradictions between the two relativities, mechanical versuselectromagnetic,infavorofthelatter;againwhenheinsistedontakingPlanck’sideas seriously andextending them,despite their conflictwith existing theory;and again when he struggled with the difficult and unfamiliar mathematics

needed for general relativity. On the other hand, stubbornness kept him fromparticipatinginthetremendoussuccessesofmodernquantumtheoryafter1924,whenuncertaintyand indeterminism tookroot,and itkepthimfromacceptingoneof themostdramaticconsequencesofhisowntheoryofgeneral relativity,theexistenceofblackholes.

Einstein’sdifficultiesinreconcilingthequantumdiscretenessofphotonswithcontinuousspace-fillingfields,whichsinceMaxwellhavebeenusedwithgreatsuccesstodescribelight,areovercomeinthemodernconceptofquantumfields.Quantumfieldsfillallspace,andthequantumelectricandmagneticfieldsobeyMaxwell’sequations.25Nevertheless,whenyouobservethequantumfields,youfindtheirenergypackagedindiscreteunits:photons.I’llhavemuchmoretosayabout the strange but very successful concepts at the root of quantum fieldtheoryinthenextchapter.

AsforFeynman,hegaveupwhen,asheworkedoutthemathematicsofhisversion of quantum electrodynamics, he found the fields, introduced forconvenience,takingonalifeoftheirown.Hetoldmehelostconfidenceinhisprogram of emptying space when he found that both his mathematics andexperimental facts required the kind of vacuum polarization modification ofelectromagneticprocessesdepicted—ashefoundit,usingFeynmangraphs—inFigure8.3.Figure8.3acorresponds toasophisticatedwayofsummarizing thesamephysicswesawinFigure8.2.Heretheinfluenceofoneparticleonanotheris conveyed by the photon. Figure 8.3b adds something new. Here theelectromagnetic field gets modified by its interaction with a spontaneousfluctuation in theelectron—or, inotherwords,by its interactionwithavirtualelectron-positron pair. In describing this process, it becomes very difficult toavoidreferencetospace-fillingfields.

Thevirtualpairisaconsequenceofspontaneousactivityintheelectronfield.It can occur anywhere. Andwherever it occurs, the electromagnetic field cansenseit.Thosetwoactivities—fluctuationsbothoccurringeverywhereandbeingsensedeverywhere—appearquitedirectly in themathematical expressions thatgo with Figure 8.3b. They lead to complicated, small but very specificmodificationsoftheforceyouwouldcalculatefromMaxwell’sequations.Thosemodificationshavebeenobserved,precisely,inaccurateexperiments.

In QED vacuum polarization is a small effect, both qualitatively andquantitatively.InQCD,bycontrast,itisall-important.InChapter6,wesawhow

itleadstoasymptoticfreedomandtherebypermitsasuccessfuldescriptionofjetphenomena.Inthenextchapter,we’llseehowQCDisusedtocalculatethemassof protons and other hadrons. Our eyes were not evolved to resolve the tinytimes(10-24second)anddistances(10-14centimeter)where theaction is.Butwe can “look” inside the computers’ calculations, to seewhat the quarks andgluon fields are up to. To nimbler eyes, space would look like theultrastroboscopicmicronanolava lampyousee inColorPlate4.Creatureswithsucheyeswouldn’tsharethehumanillusionthatspaceisempty.

Figure8.3Theforcebetweenelectricallychargedparticles.Partasummarizes,inthelanguageofFeynmangraphs,thephysicsofFigure8.2.Atthislevel,theelectric andmagnetic fields are given byMaxwell’s equations, but they couldalso be traced back to the influence of charged particles. The fields areconvenient,butperhapswecoulddowithoutthem.Partbgivessomethingnew.In this contribution to the force, the electromagnetic fields are affected byspontaneousactivity(virtualparticle-antiparticlepairs)intheelectronfield.

MaterialGrid

Besides the fluctuating activity of quantum fields, space is filledwith severallayersofmorepermanent,substantialstuff.Theseareethersinsomethingcloserto the original spirit of Aristotle and Descartes—they are materials that fillspace. In some cases, we can even identify what they’re made of and evenproduce little samples of it. Physicists usually call these material ethers

condensates .Onecouldsay that they(theethers,not thephysicists)condensespontaneouslyoutofemptyspaceasthemorningdeworanall-envelopingmistmightcondenseoutofmoist,invisibleair.

The best understood of these condensates consists of quark-antiquark pairs.Here,wearetalkingaboutrealparticles,beyondtheephemeral,virtualparticlesthat spontaneouslycomeandgo.Theusualname for this space-fillingmistofquarksandantiquarksischiralsymmetry-breakingcondensate,butlet’sjustcall

itafterwhatitis: (pronounced“Q-Qbar”),forquark-antiquark.

For ,asfortheothercondensates,thetwomainquestionsare

•Whydowethinkitexists?•Howcanweverifythatit’sthere?

Onlyinthecaseof dowehavegoodanswerstobothquestions.

formsbecauseperfectlyemptyspace isunstable.Supposewecleanoutspacebyremovingthecondensateofquark-antiquarkpairs—somethingwecandomoreeasilyinourminds,withthehelpofequationsandcomputers,thaninlaboratoryexperiments.Then,wecompute,quark-antiquarkpairshavenegativetotalenergy.Themc2energycostofmakingthoseparticlesismorethanmadeup by the energy you can liberate by unleashing the attractive forces betweenthem, as they bind into little molecules. (The proper name for these quark-antiquark molecules is σ mesons.) So perfectly empty space is an explosiveenvironment,readytoburstforthwithrealquark-antiquarkmolecules.

ChemicalreactionsusuallystartwithsomeingredientsA,BandproducesomeproductsC,D;thenwewrite

and,ifenergyisliberated,

(Thisistheequationforanexplosion.)

Inthatnotation,ourreactionis

—no starting ingredients (other than empty space) required! Fortunately, theexplosionisself-limiting.Thepairsrepeleachother,soastheirdensityincreasesitgetshardertofitnewonesin.Thetotalcostforproducinganewpairincludesanextrafee,forinteractingwiththepairsthatarealreadythere.Whenthere’snolonger a net profit, production stops. We wind up with the space-filling

condensate, ,asthestableendpoint.

Aninterestingstory,Ihopeyou’llagree.Howdoweknowit’sright?

One answer is that it’s a mathematical consequence of equations—theequations ofQCD—thatwe havemany otherways of checking.But althoughthatmaybeaperfectlylogicalanswer(thechecks,aswe’vediscussed,areverydetailed and convincing), it’s not exactly science at its best. We’d like theequationstohaveconsequenceswecanseereflectedinthephysicalworld.

Asecondansweris thatwecancalculatetheconsequencesof itself,andcheck whether they match things we see in the phys ical world. To be more

specific,we can calculatewhether , considered as amaterial, can vibrate,and what the vibrations should look like. This is very close to what“luminiferous ether” fans oncewanted to have for light: a goodold-fashioned

material,moresubstantial thanelectromagnetic fields.Vibrationsof aren’tvisible light, but they do describe something quite definite and observable,namelyπmesons.Amongthehadrons,πmesonshaveuniqueproperties.Theyarebyfarthelightest,forexample,26andtheyneverfitcomfortablywithinthequarkmodel.Soit’sverysatisfying—andafteryoustudythedetailsindepth,it’s

veryconvincing—thattheyariseinquiteadifferentway,asvibrationsof .

Athirdansweristhemostdirectanddramaticofall,atleastinprinciple.Westartedbyconsideringthethoughtexperimentofcleaningoutspace.Howaboutdoing it for real? Scientists at the relativistic heavy ion collider (RHIC) atBrookhavenNationalLaboratory,onLongIsland,havebeenworkingonit,andmoresuchworkwillbegoingonattheLHC.Whattheydoisacceleratetwobigcollectionsofquarksandgluonsmovinginoppositedirections—intheformofheavyatomicnuclei,suchasgoldorleadnuclei—toveryhighenergy,andmakethemcollide.Thisisnotagoodwaytostudythebasic,elementaryinteractionsofquarksandgluonsor tolookforsubtlesignsofnewphysics,becausemanymanysuchcollisionswillhappenatonce.Whatyouget, infact, isasmallbutextremely hot fireball. Temperatures over 1012 degrees (Kelvin, Celsius, orFahrenheit—atthislevel,youcantakeyourpick)havebeenmeasured.Thisisabillion times hotter than the surface of the Sun; temperatures this high lastoccurredonlywellwithinthefirstsecondofthebigbang.Atsuchtemperatures,

the condensate vaporizes: the quark-antiquark molecules from which it’smadebreakapart.Soalittlevolumeofspace,forashorttime,getscleanedout.Then, as the fireball expands and cools, our pair-forming, energy-liberating

reactionkicksin,and isrestored.

All thisalmostcertainlyhappens.“Almost”comes in, though,becausewhatweactuallyget toobserve is the flotsamand jetsam thrownoff as the fireballcools. Color Plate 5 is a photograph of what it looks like. Obviously, thephotograph doesn’t come labeled with circles and arrows telling you what’sresponsibleforeachaspectofthisspectacularlycomplicatedmess.Youhavetointerpretit.Inthiscase,evenmore(actually,muchmore)thanwiththepicturesofprotoninteriorsandjetsthatwediscussedinChapter6,theinterpretationisacomplicated business. Today, the most accurate and complete interpretations

buildintheprocessof meltingandreformationwe’vebeendiscussing,butthey’renotyetasclearandconvincingaswemighthopefor.Peoplecontinuetoworkatit—boththeexperimentsandtheinterpretation.

For the next-best-understood condensate, we have good circumstantialevidencethatitexists,butonlyguessesaboutwhatit’smadeupof.Theevidencecomes from a part of fundamental physics we haven’t mentioned so far, thetheoryoftheso-calledweakinteraction.27Wehaveagoodtheoryoftheweakinteractionthat’sgonefromtriumphtotriumphsincetheearly1970s.Notably,

thistheorywasusedtopredicttheexistence,mass,anddetailedpropertiesoftheWandZbosonsbeforetheywereobservedexperimentally.Thetheoryisusuallycalled the standard model, or the Glashow-Weinberg-Salam model, afterSheldon Glashow, Steven Weinberg, and Abdus Salam, three theorists whoplayed key roles in formulating it (for which they shared the Nobel Prize in1979).

In the standardmodel, theW andZ bosons play leading roles.They satisfyequations very similar to the equations for gluons in the quantumchromodynamics. Both are symmetry-based expansions of the equations forphotonsinquantumelectrodynamics(namely,Maxwell’sequations).ActivityintheWandZ boson fields creates theweak interactions, in the same sense thatactivity in thephoton field is responsible forelectromagnetism,andactivity inthecolorgluonfieldsisresponsibleforthestronginteraction.

Thestrikingsimilaritiesamongourfundamentaltheoriesofsuperficiallyverydifferentforceshintatthepossibilityofasynthesis,inwhichallofthemwillbeseen as different aspects of a more encompassing structure. Their differentsymmetries might be sub-symmetries of a larger master symmetry. Extrasymmetryallowstheequationstoberotatedintothemselvesinevenmoreways;thatis,therearemorewaysofmaking“distinctionswithoutdifferences.”Thusitopensnewpossibilities formakingconnectionsamongpatterns thatpreviouslyseemedunrelated.Ifourfundamentalequationsdescribepartialpatternsthatwecan make more symmetric, by making additions, we’re tempted to think thatmaybetheyreallyarejustfacetsofthelarger,unifiedstructure.AntonChekhovfamouslyadvised,

IfinActOnethereisariflehangingoverthemantelpiece,itmusthavebeenfiredbythefifthact.

NowI’vehungtherifleofunification.

Returning to the standard model: TheW and Z bosons are attractive leadplayers, but they need help to fit the parts they’re meant to play. Left tothemselves,accordingtotheequationsthatdefinethem,they’dbemassless,likethephotonandthecolorgluons.Reality’sscript,however,callsfor themtobeheavy.It’sasifTinkerbellehadbeencastasSantaClaus.Toenablethespritetoimpersonatetheplumpkin,we’vegottopadheroutinapillowycostume.

Physicists knowhow to do this trick—that is, tomake theW andZ bosonsacquire mass. We think. In fact Nature showed us how, by giving us a

demonstration.Mywife,who’sanaccomplishedwriteranda fountainofgoodadvice,gavemealistofclichéwordstoavoid,includingamazing,astonishing,beautiful, breathtaking, extraordinary , and others you can probably guess. Imostlyfollowheradvice.ButIhavetosaythatIfindwhatI’mabouttotellyouamazing,astonishing,beautiful,breathtaking,and,yes,extraordinary.

The model Nature gives us for making force-carrying particles heavy issuperconductivity. For inside superconductors, photons become heavy! I’veoffloaded a more detailed discussion of this to Appendix B, but here’s theessentialidea.Photons,aswe’vediscussed,aremovingdisturbancesinelectricandmagneticfields.Inasuperconductor,electronsrespondvigorouslytoelectricandmagneticfields.Theelectrons’attempttorestoreequilibriumissovigorousthat they exert a kind of drag on the fields’motion. Instead ofmoving at theusual speed of light, therefore, inside a superconductor photons move moreslowly. It’s as if they’ve acquired inertia.When you study the equations, youfind that the slowed-down photons inside a superconductor obey the sameequationsofmotionaswouldparticleswithrealmass.

Ifyouhappenedtobealife-formwhosenaturalhabitatwastheinteriorofasuperconductor,you’dsimplyperceivethephotonasamassiveparticle.

Nowlet’s turnthelogicaround.Humansarea life-formthatobserves, in itsnaturalhabitat,photon-likeparticles, theWandZbosons, thataremassive.Soperhapswehumansshouldsuspectthatweliveinsideasuperconductor.Not,ofcourse, a superconductor in theordinary sense, that’s supergood at conductingthe(electric)chargethatphotonscareabout,butratherasuperconductorforthecharges thatW andZ bosons care about.The standardmodel is based on thatidea; and, as we’ve said, the standard model is very successful at describingreality—therealitywefindourselvesinhabiting.Thuswecometosuspect thattheentitywecallemptyspaceisanexotickindofsuperconductor.

Whereyouhavesuperconductivity, there’sgot tobeamaterial thatdoes theconducting.Ourexoticsuperconductivityworkseverywhere,sothejobrequiresaspace-fillingmaterialether.

BigQuestion:Whatisthatmaterial,concretely?Whatisitthat,forthecosmicsuperconductor,playstherolethatelectronsplayinordinarysuperconductors?

Unfortunately,itcan’tbethematerialetherweunderstandwell, .Actually

isanexoticsuperconductoroftherightkind,anditdoescontributetotheWand Z boson masses. But it falls short quantitatively by a factor of about athousand.

Nopresentlyknownformofmatterhastherightproperties.Sowedon’treallyknowwhatthisnewmaterialetheris.Weknowitsname:theHiggscondensate,after Peter Higgs, a Scots physicist who pioneered some of these ideas. Thesimplest possibility, at least if you equate simplicity with adding as little aspossible, is that it’smade fromone new particle, the so-calledHiggs particle.Butthecosmicsuperconductorcouldbeamixtureofseveralmaterials.Infact,

as we’ve mentioned, we already know that is part of the story, though asmallpart.Aswe’llseelater,therearegoodreasonstosuspectthatawholenewworldofparticlesisripefordiscovery,andthatseveralamongthemchipintothecosmicsuperconductor,a.k.a.theHiggscondensate.

Takenatfacevalue,themostpromisingunifiedtheories28seemtopredicttheexistence of all kinds of particles we haven’t yet observed. Additionalcondensates might save the day. New condensates can make the unwantedparticlesveryheavy—justastheHiggscondensatedoesfortheWandZbosons,onlymoreso.Particleswithverylargemassarehardtoobserve.It takesmoreenergy, and hence bigger accelerators, to produce them as real particles.Eventheirindirectinfluence,asvirtualparticles,isdiminished.

Ofcourse,itwouldbecheapspeculationtoaddnewstuffintoyourequationsjustbecauseyouknowhowtomakeexcuseswhenitisn’tobserved.Whatmakestheunifiedfieldtheoriesinterestingisthattheyexplainfeaturesoftheworldthatweobserve,and—betteryet—predictnewones.NowI’vetoldyouthattherifleisloaded.

The entity we perceive as empty space is a multilayered, multicoloredsuperconductor.Whatanamazing,astonishing,beautiful,breathtakingconcept.Extraordinary,too.

TheMotherofAllGrids:MetricField

Here’stheEinsteinquotationIsavedup.In1920hewrote,

Accordingtothegeneraltheoryofrelativityspacewithoutetherisunthinkable;forinsuchspacetherenotonlywouldbenopropagationoflight,butalsonopossibilityofexistenceforstandardsofspaceandtime(measuring-rodsandclocks),northereforeanyspace-timeintervalsinthephysicalsense.

ItservesasasuitableintroductiontothemotherofallGrids:themetricfield.

Let’sbeginwithsomethingsimpleandfamiliar:mapsoftheworld.Becausemapsareflat,whereasthethingthey’remeanttodepict—thesurfaceofEarth—is (approximately) spherical, obviously the maps require interpretation. Therearemanywaysofmakingamap that represents thegeometryof thesurface itdepicts.Allusethesamebasicstrategy.Thecrucialthingistolaydownagridofinstructions for how to do geometry locally. More specifically, in each littleregionofthemap,youlaydownwhichdirectioncorrespondstonorthandwhichdirectioncorrespondstoeast(southandwestwillbetheoppositedirections,ofcourse). You also specify, in each direction, what interval on the mapcorrespondstoamile—orkilometer,orlightmillisecond,orwhatever—onEarth.

Forexample,mapsbasedonthestandardMercatorprojectionmaintainnorthverticalandeasthorizontal.ThenthesurfaceofEarthcanbefittoarectangle.Going“aroundtheworld”fromwesttoeasttakesyouhorizontallyfromonesideofthemaptotheother,whetheryoufollowtheequatororthearcticcircle.Backon Earth the equator covers a much longer distance than the arctic circle, sotaking the map at face value gives a distorted impression: the polar regionsappear,relatively,muchlargerthantheyareonEarth.Butthegridinstructsyouhowtogetthedistancesright.Inthepolarregionsyoushouldusebiggerrulers!(Things get a little crazy right at the poles. The whole top line on the mapcorresponds to a single point onEarth, namely theNorthPole, and thewholebottomlinecorrespondstotheSouthPole.)

All the informationyouneed to reconstruct thegeometryofEarth’s surfacefromthemapiscontainedinthegridofinstructions.29Forexample,here’showyoucantellthemapdescribesasphere.Firstpickapointonthemap.Then,foreachdirection,measureoffafixeddistancerfromthereferencepoint(followingthe grid instructions), and make a dot. The dotted places on the map nowcorrespond to all places onEarth that are distance r from the reference point.Connect the dots. Generally (for instance, if your map is constructed à laMercator),thefigureyougetonthemapwon’tlooklikeacircle,eventhoughit

representsacircleonEarth.Nevertheless,youcanusethemaptomeasure thedistancearoundthecircleonEarththatthefigurerepresents.Andyou’llfindit’sless than 2πr. (For experts: It will beR sin(2πr/R), whereR is the radius ofEarth.)Ifthemapdepictedaflatsurface—whichmightnotbeobvious,ifyou’reusing a distorted grid—you’d get exactly 2πr. You could also find acircumference greater than 2πr. Then you’d have discovered that yourmap isdescribing a saddle-shaped surface. Spheres, naturally, are defined to havepositive curvature; flat surfaces have zero curvature; saddles have negativecurvature.

Althoughvisualizationbecomesmuchmoredifficult,thesameideasapplytothree-dimensionalspace.Insteadofagridofinstructionsfordoinggeometryonasheet,wecanconsideragridofinstructionsthatfillsoutathree-dimensionalregion.Suchbulked-up“maps” contain (as slices) the sort of two-dimensionalmaps we have just discussed, as well as specs for putting the slices together.Theydefinecurvedthree-dimensionalspaces.

Soinsteadofworkingdirectlywithcomplicatedthree-dimensionalshapesthatare (at best) extremely difficult to visualize, we can work in ordinary space,using grids of instructions. We can work with these maps without having tosacrificeanyinformation.

Thegridofinstructionsfordoinggeometrylocallyiscalled,inthescientificliterature,themetricfield.Thelessonofmapsisthatthegeometryofsurfaces,or curved spaces of higher dimensions, is equivalent to a grid, or field, ofinstructions for how to set directions and measure distance locally. Theunderlying “space” of themap can be amatrix of points, or even an array ofregisters in a computer. With the proper grid of instructions, or metric field,either of those abstract frameworks can represent complicated geometryfaithfully.Mapmakersandcomputergraphicswizardsareexpert at exploitingthosepossibilities.

Wecanalsoaddtimetothestory.Specialrelativitytellsusthatoneguy’stimeisanotherguy’smixtureofspaceandtime,soit’snaturaltotreatspaceandtimeon the same footing. To do that we need a four-dimensional array. Theinstructiongrid,ormetricfield,ateachpointspecifieswhichthreedirectionsareto be considered spatial directions—you can call them north, east, and up,although if you’re mapping deep space those names are quaint30—and thestandards of length in those directions. It also specifies that another direction

representstimeandgivesarulefortranslatingmaplengthsinthatdirectionintointervalsoftime.

Inthegeneraltheoryofrelativity,Einsteinusedtheconceptofcurvedspace-time to construct a theory of gravity. According to Newton’s second law ofmotion, bodiesmove in a straight line at constant velocity unless a force actsupon them.Thegeneral theoryof relativitymodifies this law topostulate thatbodies follow the straightest possible paths through space-time (so-calledgeodesics). When space-time is curved, even the straightest possible pathsacquire bumps and wiggles, because they must adapt to changes in the localgeometry.Puttingtheseideastogether,wesaythatbodiesrespondtothemetricfield. These bumps and wiggles in a body’s space-time trajectory—in morepedestrian language,changes in itsdirectionandspeed—provide,according togeneral relativity, an alternative and more accurate description of the effectsformerlyknownasgravity.

We can describe general relativity using either of two mathematicallyequivalent ideas: curved space-time or metric field. Mathematicians, mystics,andspecialistsingeneralrelativitytendtolikethegeometricviewbecauseofitselegance. Physicists trained in the more empirical tradition of high-energyphysics and quantum field theory tend to prefer the field view, because itcorrespondsbettertohowwe(orourcomputers)doconcretecalculations.Moreimportant,aswe’llsee inamoment, the fieldviewmakesEinstein’s theoryofgravitylookmoreliketheothersuccessfultheoriesoffundamentalphysics,andsomakesiteasiertoworktowardafullyintegrated,unifieddescriptionofallthelaws.Asyoucanprobablytell,I’mafieldman.

Once it’sexpressed in termsof themetric field,general relativity resemblesthefieldtheoryofelectromagnetism.Inelectromagnetism,electricandmagneticfieldsbend the trajectoriesof electrically chargedbodies, orbodies containingelectric currents. Ingeneral relativity, themetric fieldbends the trajectoriesofbodiesthathaveenergyandmomentum.Theotherfundamentalinteractionsalsoresemble electromagnetism. In QCD, the trajectories of bodies carrying colorchargearebentbycolorgluonfields;intheweakinteraction,stillothertypesofchargeandfieldsareinvolved;butinallcasesthedeepstructureoftheequationsisverysimilar.

These similarities extend further. Electric charges and currents affect thestrength of the electric and magnetic fields nearby—that is, their average

strength, ignoring quantum fluctuations. This is the “reaction” of fieldscorrespondingtotheir“action”onchargedbodies.Similarly,thestrengthofthemetric field is affected by all bodies that have energy andmomentum (as allknown forms ofmatter do).Thus the presence of a bodyA affects themetricfield,whichinturnaffectsthetrajectoryofanotherbodyB.Thisishowgeneralrelativity accounts for the phenomenon formerly known as the gravitationalforce one body exerts on another. It vindicatesNewton’s intuitive rejection ofactionatadistance,evenasitdethroneshistheory.

Consistencyrequiresthemetricfieldtobeaquantumfield,likealltheothers.Thatis,themetricfieldfluctuatesspontaneously.Wedonothaveasatisfactorytheoryofthesefluctuations.Weknowthattheeffectsofquantumfluctuationsinthemetricfieldareusually—inourexperiencesofar,always—smallinpractice,simplybecausewegetverysuccessfultheoriesbyignoringthem!Fromdelicatebiochemistrytoexoticgoings-onatacceleratorstotheevolutionofstarsandtheearlymomentsofthebigbang,we’vebeenabletomakeprecisepredictions,andhaveseenthemaccuratelyverified,whileignoringpossiblequantumfluctuationsinthemetricfield.Moreover,themodernGPSsystemmapsoutspaceandtimedirectly. It doesn’t allow for quantum gravity, yet it works very well.Experimenters have worked very hard to discover any effect that could beascribed to quantum fluctuations in the metric field, or, in other words, toquantum gravity. Nobel Prizes and everlasting glory would attend such adiscovery.Sofar,ithasn’thappened.31

Nevertheless,theChicagoobjection—“Thatworksinpractice,butwhataboutin theory?”—stillholds.Theproblemthatarises ismuch like theproblemswesaw with the quark model, and especially the parton model, in Chapter 6.Worrying about those theoretical problems eventually led to the concept ofasymptotic freedom and to a complete, extremely successful theory of quarksand the (newly predicted!) color gluons. The analogous problem for quantumgravityhasn’tbeensolved.Superstringtheoryisavaliantattemptbutverymuchaworkinprogress.Atpresentit’smoreacollectionofhintsaboutwhatatheorymight look like than a concrete world-model with definite algorithms andpredictions.Andithasn’tdeeplyincorporatedthebasicGridideas.(Forexperts:stringfieldtheoryisclumsyatbest.)

Inthequotationthatopenedthissection,Einsteinsaidthatspace-timewithoutthemetricfieldis“unthinkable.”Takenliterally,that’sobviouslyfalse—it’seasy

tothinkaboutit!Let’sgobacktoourmap.Ifthegridinstructionsareerasedorgetlost,themapstilltellsusthings.Ittellsuswhichcountriesarenexttowhich,forexample. It justwouldn’t tellus, reliably,howbig theyare,orwhatshape.Even without information about size and shape, we still have what’s calledtopologicalinformation.Thatstillleavesplentytothinkabout.

WhatEinsteinmeantisthatit’shardtoimaginehowthephysicalworldwouldfunctionwithout themetric field.Lightwouldn’tknowwhichway tomoveorhow fast; rulers and clockswouldn’t knowwhat they’re supposed tomeasure.The equations Einstein had for light, and for the materials out of which youmightmakerulersandclocks,can’tbeformulatedwithoutthemetricfield.

Trueenough,buta lotof things inmodernphysicsarehard to imagine.Wehavetoletourconceptsandequationstakeuswheretheywill.WhatHertzsaidaboutthisissoimportant(andsowellexpressed)thatitbearsrepeating:

Onecannotescapethefeelingthatthesemathematicalformulaehaveanindependentexistenceandanintelligenceoftheirown,thattheyarewiserthanweare,wisereventhantheirdiscoverers,thatwegetmoreoutofthemthanwasoriginallyputintothem.

Inotherwords,ourequations—andmoregenerally,ourconcepts—arenot justourproductsbutalsoourteachers.

In that spirit, the discovery that theGrid is filledwith severalmaterials, orcondensates,raisesanobviousquestion:Isthemetricfieldacondensate?Mightitbemadefromsomethingmorefundamental?Andthatquestionraisesanother:

Couldthemetricfield,like ,havevaporizedattheoriginoftheuniverse,intheearliestmomentsofthebigbang?

A positive answerwould open up a newway of addressing a question thatvexed Saint Augustine: “What wasGod doing before He created the world?”(Subtext: What was He waiting for? Wouldn’t it have been better to startsooner?)SaintAugustinegavetwoanswers.

Firstanswer:BeforeGodcreated theworld,HewaspreparingHell forpeoplewhoaskfoolishquestions.

Second answer: Until God creates the world, no “past” exists. So thequestiondoesn’tmakesense.

Hisfirstanswerisfunnier,butthesecond,spelledoutatlengthinChapter10ofAugustine’sConfessions,ismoreinteresting.Augustine’sbasicargumentisthatthe past no longer exists and the future does not yet exist; properly speaking,there isonly thepresent.But thepasthas a sortof existencewithinminds, aspresentmemory(asdoesofcoursethefuture,aspresentexpectations).Thustheexistence of a past depends on the existence of minds, and there can be no“before” in the absence of minds. Before minds were created, there was nobefore!

Amodern,secularversionofAugustine’squestionis“Whathappenedbeforethe big bang?” And a version of his second answer based on physics mightapply. Not that minds are necessary for time—I don’t think many physicistswouldacceptthat(andtheequationsofphysicscertainlydon’t).Butifthemetricfieldvaporizes,withitgoesthestandardoftime.Oncenoclocksexist(andthismeansanendnot just toelaborate time-keepingdevices,but toeveryphysicalprocessthatcouldservetomarktime),timeitself,alongwiththewholenotionof “before,” loses any meaning. The flow of time commences with thecondensationofthemetricfield.

Couldthemetricfieldchangeinsomeotherway(crystallize?)underpressure,for example near the center of black holes? (We know that quarks will formweird condensates under pressure, with funny names like color-flavor locked

superconductor,thataredifferentfrom .)

Couldthemorefundamentalmaterialfromwhichthemetricfieldismadebethesamematerialweneedtounifytheotherforces?

Great questions, I hope you’ll agree! Unfortunately, we don’t have worthyanswersyet.(I’mworkingonit....)Butit’sasignofourprogress,andofthegrowth of our ambition, that we can formulate questions and think seriouslyabout possibilities that Einstein considered “unthinkable.” We have betterequationsnow,andricherconcepts,andweletthembeourguides.

GridWeighs

Mass traditionally has been regarded as the defining property of matter, theunique feature that gives substance to substance. So the recent astronomical

discovery thatGridweighs—that the entityweperceive as empty space has auniversal, nonzero density—crowns the case for its physical reality. Althoughit’ssomewhatperipheraltothemainthrustofthisbook,I’lltakeafewpagestodiscuss thenatureof thatdiscoveryand itscosmological implications,becauseit’sbothfundamentallyimportantandextremelyinteresting.32

TheconceptofGriddensityisessentiallythesameasEinstein’scosmologicalterm,whichisessentiallythesameas“darkenergy.”Thereareslightdifferencesininterpretationandemphasis,whichI’llexplainastheycomeup,butallthreetermsrefertothesamephysicalphenomenon.

In 1917 Einstein introduced a modification of the equations he originallyproposedforgeneralrelativitytwoyearsearlier.Hismotivationwascosmology.Einstein thought that the universe had constant density, both in time and (onaverage) in space, so he wanted to find a solution with those properties. Butwhenheappliedhisoriginalequationstotheuniverseasawhole,hecouldnotfindsuchasolution.Theunderlyingproblemiseasytograsp.ItwasanticipatedbyNewtonin1692,inafamouslettertoRichardBentley:

...[I]tseemstomethatifthematterofoursunandplanetsandallthematteroftheuniversewereevenlyscatteredthroughoutalltheheavens,andeveryparticlehadaninnategravitytowardalltherest,andthewholespacethroughoutwhichthismatterwasscatteredwasbutfinite,thematterontheoutsideofthisspacewould,byitsgravity,tendtowardallthematterontheinsideand,byconsequence,falldownintothemiddleofthewholespaceandtherecomposeonegreatsphericalmass.Butifthematterwasevenlydisposedthroughoutaninfinitespace,itcouldneverconvergeintoonemass;butsomeofitwouldconvergeintoonemassandsomeintoanother...

Simplyput:gravityisauniversalattraction,soit isnotcontent toleavethingsseparate. Because gravity is always trying to bring things together, it’s notterriblysurprisingthatyoucan’tfindasolutionwheretheuniversemaintainsaconstantdensity.

Togetthekindofsolutionhewanted,Einsteinchangedtheequations.Buthechanged them in a very particular way that doesn’t spoil their best feature,namely that they describe gravity in a way consistent with special relativity.Thereisbasicallyonlyonewaytomakesuchachange.Einsteincalledthenewterm that he added to the equations for gravity the “cosmological term.” He

didn’treallyofferaphysical interpretationofit,butmodernphysicssuppliesacompellingone,whichI’lldescribemomentarily.

Einstein’smotivation for adding the cosmological term, to describe a staticuniverse, soonbecameobsolete, as evidence for the expansionof theuniversefirmed up in the 1920s, mainly through the work of Edwin Hubble. Einsteincalledtheideasthatcausedhimtomisspredictingtheexpansionoftheuniversehis“greatestblunder.”(Anditreallywasablunder,becausethemodeluniverseheproduced,evenwithhisnewequations,isunstable.Strictlyuniformdensityisa solution, but any small deviation from uniformity increases with time.)Nevertheless,thepossibilityheidentified,ofaddinganewtermtotheequationsofgeneralrelativitywithoutspoilingthetheory,wasprophetic.

Thecosmological termcanbeviewed in twoways.LikeE =mc2 andm=E/c2, they are equivalent mathematically but suggest different interpretations.Oneway(thewayEinsteinviewedit)isasamodificationofthelawofgravity.Alternatively,thetermcanbeviewedastheresultofhavingaconstantdensityof mass and also a constant pressure everywhere in space and for all time.Becausebothmass-densityandpressurehavethesamevalueeverywhere, theycanberegardedasintrinsicpropertiesofspaceitself.That’stheGridviewpoint.Ifwe take itasgiven thatspacehas theseproperties,andfocusexclusivelyonthegravitationalconsequences,wearrivebackatEinstein’sviewpoint.

Akeyrelationshipgoverningthephysicsofthecosmologicaltermrelatesitsdensity ρ to the pressure p it exerts, using the speed of light c. There’s nostandardnameforthisequation,butitwillbehandytohaveone.I’llcallitthewell-temperedequation,becauseitprescribestheproperwaytotuneaGrid.Thewell-temperedequationreads

(1)

Wheredoesitcomefrom?Whatdoesitmean?

Thewell-temperedequation looks likeamutatedcloneofEinstein’s secondlaw,m=E/c2.Themhasturnedintoaρ,andtheEintoap—andthere’sthat-sign—but you can’t help noticing a resemblance.And in fact they are deeply

related.

Einstein’ssecondlawrelatestheenergyofanisolatedbodyatresttoitsmass.(SeeChapter3andAppendixA.)Itisaconsequenceofspecialrelativitytheory,thoughnot an immediatelyobviousone. In fact it didnot appear inEinstein’sfirstrelativitypaper;hewroteaseparatenoteaboutitafterwards.

Thewell-temperedequationislikewiseaconsequenceofspecialrelativity,butnow applied to a homogeneous, space-filling entity rather than to an isolatedbody.It’snotimmediatelyobvioushowanonzeroGriddensitycanbeconsistentwith special relativity. To appreciate the problem, think about the famousFitzgerald-Lorentz contraction, which we encountered in Chapter 6. To anobserver moving at constant velocity, objects appear foreshortened in thedirectionofmotion. Itwould seem, therefore, that themovingobserverwouldseeahigherGriddensity.That’scontrarytorelativity’sboostsymmetry,whichsaysshemustseethesamephysicallaws.

Thepressurethatgoeswithdensity,accordingtothewell-temperedequation,providesaloophole.Theweighingscalesofthemovingobserver,accordingtotheequationsofspecialrelativity,registeranewdensitythatisamixtureoftheold density and the old pressure—just as, perhapsmore familiarly, her clocksregister time intervals that are mixtures of the old time intervals and the oldspaceintervals.If—andonlyif—theolddensityandtheoldpressurearerelatedinjustthewayprescribedbythewell-temperedequation,thenvaluesofthenewdensity(andthenewpressure)willbethesameastheoldvalues.

Another,closelyrelatedconsequenceofthewell-temperedequationiscentraltothecosmologyofGriddensity.Inanexpandinguniverse, thedensityofanynormalkindofmatterwillgodown.But thedensityof thewell-temperedgridstaysconstant!Ifyou’reupforalittleexerciseinfirst-yearphysicsandalgebra,here comes a pretty connection tying that constancy of density directly toEinstein’ssecondlaw.(Ifnot,justskipthenextparagraph.)

Consider a volume V of space, filled with grid density ρ. Let the volumeexpandbyδV.Ordinarily,asabodyexpandsunderpressureitdoeswork,andsoloses energy.But the - sign in the equation for awell-temperedGridgives usnegative pressure p = -ρc2. So by expanding, our well-tempered Grid gainsenergy δV × ρc2. According to Einstein’s second law, therefore, its massincreases byδV ×ρ.And that’s just enough to fill the added volume δVwith

densityρ,allowingthedensityoftheGridtoremainconstant.

EachoftheGridcomponentswe’vediscussed—fluctuatingquantumfieldsof

many sorts, , Higgs condensate, unification-salvaging condensate, space-timemetricfield(orcondensate?)—iswell-tempered.Eachofthesespace-fillingentities obeys thewell-tempered equation, because each is consistentwith theboostsymmetryofspecialrelativity.

It’spossibletomeasurethecosmicdensityandthepressureseparately,usingquite different techniques. The density affects the curvature of space, whichastronomers can measure by studying the distortion such curvature causes inimages of distant galaxies, or—a powerful new technique—in the cosmicmicrowave background radiation. Using the new technique, by 2001 severalgroupswereabletoprovethattherewasmuchmoremassintheuniversethancould be accounted for by normalmatter alone.About 70% of the totalmassappearstobeveryuniformlydistributed,bothinspaceandtime.

Thepressureaffectstherateatwhichtheuniverseisexpanding.Thatratecanbemeasuredbystudyingdistantsupernovae.Theirbrightnesstellsyouhowfarawaytheyare,whiletheredshiftoftheirspectrallinestellsyouhowfastthey’removingaway.Becausethespeedoflightisfinite,whenweobservethefarther-awayoneswe’relookingattheirpast.Sowecanusesupernovaetoreconstructthehistoryofexpansion. In1998 twopowerhouse teamsofobservers reportedthattherateofexpansionoftheuniverseisincreasing.Thiswasabigsurprise,becauseordinarygravitationalattractiontendstobraketheexpansion.Someneweffectwasshowingup.Thesimplestpossibilityisauniversalnegativepressure,whichencouragesexpansion.

The termdarkenergybecamea shorthand forbothof thesediscoveries: theadditional mass and the accelerating expansion. It was meant to be agnosticabout the relative values of density and pressure. Ifwe simply called both ofthemthecosmological term,we’dbeprejudgingtheir relativemagnitudes.Butapparentlywe’dberight.Thetwoverydifferentquantities,cosmicmassdensityandcosmicpressure,observedinverydifferentways,doseemtoberelatedbyρ=-p/c2.

Istheastronomicaldiscoverythatspaceweighs,andseemstoobeythewell-temperedequation,abrilliantconfirmationofthedeepstructuresuponwhichweerectourbestmodelsoftheworld?Yesandno.Tobehonest,probablyIshould

writeyesandNO.

Theproblemisthatthetotaldensitythatastronomersweighisfar,farsmallerthansimpleestimatesofwhatanyofourcondensatesprovides.Herearesimpleestimatesofthedensitiesinvolved,asmultiplesofwhattheastronomersactuallyfind:

•Quark-antiquarkcondensate:1044

•Weaksuperconductingcondensate:1056

•Unifiedsuperconductingcondensate:10112•Quantumfluctuations,withoutsupersymmetry:∞•Quantumfluctuations,withsupersymmetry:3310• Space-timemetric: ? (The physics here is toomurky to allow a simpleestimate.)

If any of these simple estimates were correct, the evolution of the universewouldbemuchmorerapidthanwhat’sobserved.

Why is the real density of space much smaller? Maybe there’s a vastconspiracy among these and possibly other contributions, some necessarilynegative, to give a total that’s very much smaller than each individualcontribution. Maybe there’s an important gap in our understanding of howgravityrespondstoGriddensity.Maybeboth.Wedon’tknow.

Beforedarkenergywasdiscovered,mosttheoreticalphysicists,lookingattheenormous discrepancy between simple estimates of the density of space andreality, hoped that some brilliant insightwould supply a good reasonwhy thetrueansweriszero.Feynman’s“becauseit’sempty”wasthebest,oratleastthemostentertaining,ideaIheardalongthoselines.Iftheanswerreallyisn’tzero,weneeddifferent ideas. (It’s still logicallypossible that theultimatedensity iszero,andthattheuniverseisveryslowlysettlingtowardthatvalue.)

A popular speculation today is that many different possible condensatescontribute to the density, some positive, some negative. It’s only when thecontributions cancel almost completely that you get a nice slowly evolvinguniversethatissufficientlyuser-friendlytobeobserved.Anobservableuniversehas to allow enough quality time for potential observers to evolve. Thus(according to this speculation) we observe an improbably small total Grid

density because if the total were much larger, nobody would be around toobserve it. Maybe that’s right, but it’s a difficult idea to make precise, or tocheck.Sometimeswecanleverageuncertaintyintoprecisionbygatheringmanysamples. We do that when making insurance tables or applying quantummechanics.Butfortheuniverse,we’restuckwithasamplesizeofone.

Anyway,intheoneuniversewe’vehadalookat,Gridweighs.Fortunately,toclinchthatconclusion,oneuniverseisenough.

Recapitulation

Atthebeginningofthischapter,IadvertisedkeypropertiesoftheGrid,thatur-stuffthatunderliesphysicalreality:

•TheGridfillsspaceandtime.• Every fragment ofGrid—each space-time element—has the same basicpropertiesaseveryotherfragment.

• The Grid is alive with quantum activity.Quantum activity has specialcharacteristics. It is spontaneous and unpredictable. And to observequantumactivity,youmustdisturbit.

•TheGridalsocontainsenduring,material components.Thecosmos is amultilayered,multicoloredsuperconductor.

•TheGridcontainsametricfieldthatgivesspace-timerigidityandcausesgravity.

•TheGridweighs,withauniversaldensity.

Now,afterthesalespitch,Ihopeyoubuyit!

9

ComputingMatter

AplayofBitsoutputsourIts.

JOHNWHEELERHADAGIFTforcapturingprofoundideasincatchyphrases.“Blackhole”isprobablyhisbest-knowncreation,butmyfavorite is“ItsFromBits.”These threewords capture an inspiring ideal for theoretical science.Wetry to find mathematical structures that mirror reality so completely that nomeaningfulaspectescapesthem.Solvingtheequationstellsusbothwhatexistsand how it behaves. By achieving such a correspondence,we put reality in aformwecanmanipulatewithourminds.

Philosophical realists claim thatmatter is primary, brains (minds) aremadefrommatter,andconceptsemergefrombrains.Idealistsclaimthatconceptsareprimary,mindsareconceptualmachines,andconceptualmachinescreatematter.“ItsFromBits”sayswedonothavetochoosebetweenthesealternatives.Bothcan be right at the same time. They describe the same thing using differentlanguages.

Theultimate challenge to “ItsFromBits” is to findmathematical structuresthatmirrorconsciousexperienceandflexible intelligence—inaword, thinkingcomputers.Thathasnotbeenachieved,andpeoplestillargueaboutwhetherit’spossible.34

Themostimpressiveexampleof“ItsFromBits”thathasbeenachievedistheoneI’lldescribeinthischapter.ThealgorithmsofQCDempowerustoprogramcomputerstochurnoutprotons,neutrons,andthewholemotleycrewofstronglyinteractingparticles.Itsfrombits,indeed!

As a bonus, we achieve another Wheelerism: “Mass Without Mass.” Thebuildingblocksofprotonsandneutrons,asrevealedbythekindsofexperiments

wediscussedinChapter6,arestictlymasslessgluonsandverynearlymasslessquarks.(Therelevantquarks,uandd,weighabout1%asmuchas theprotonstheymake.)

At Brookhaven National Laboratory, on Long Island, and at several othercenters around the world, there are special rooms where people rarely tread.Nothingmuchseemstobehappeningintheserooms,there’snovisiblemotion,and theonly sound is thegentlewhirof fans thatkeep the temperature steadyandthehumiditylow.Intheserooms,roughly1030protonsandneutronsareatwork.Theyhavebeenorganizedintohundredsofcomputers,harnessedtoworkin parallel. The team races at teraflop rates, which means 1012—a millionmillion—FLoatingpointOPerationspersecond.Weletthemlaborformonths—107 seconds.At the end, they’ve donewhat a single proton does every 10-24second,whichisfigureouthowtoorchestratequarkandgluonfieldsinthebestpossiblewaysothattheykeeptheGridsatisfiedandmakeastableequilibrium.

Whyisitsohard?

TheGridisaharshmistress.

To be more accurate, she’s complicated. She has many moods, and she’sstormy.

Quantummechanicsworkswithwavefunctionsthatrepresentmanypossibleconfigurationsofthefieldsatonce,butourclassicalcomputerscanhandleonlyoneconfigurationata time.Tomimic interactionsamongmanyconfigurationsthat,inthequantumdescription,arepresentsimultaneously,aclassicalcomputermust:

1.churnforalongtime,toproducetheconfigurations2.storethem3.cross-correlateitsancientmemorieswithitscurrentcontent

Altogether, there’s a poormatchbetween the end and themeans. If andwhenquantum computers become available, we might be in better shape. What’smore,thethingswe’retryingtocalculate—theparticlesweobserve—constitutesmall ripples in a turbulent sea of fluctuating Grid. To find the particles,numerically, we have to model the whole sea, and then hunt out the tinydisturbances.

AToyModelinThirty-TwoDimensions

WhenIwasbutaweeladIlikedtoputtogether,andtakeapart,plasticmodelrockets. Thesemodels couldn’t put up satellites, let alone ferry anyone to theMoon.But theywere thingsIcouldhold inmyhandsandplaywith,and theywere aids to imagination.Theywere built to scale, and therewas also a littleplastic man on the same scale, so I got a sense of the sizes involved, thedifferencebetweenaninterceptorandalaunchvehicle,andsomekeyconceptslikepayloadsanddetachablestages.Toymodelscanbefunanduseful.

Similarly,intryingtounderstandcomplicatedconceptsorequations,it’sgoodtohavetoymodels.Agoodtoymodelcapturessomesenseoftherealthingbutissmallenoughthatwecanwrapourmindsaroundit.

InthenextfewparagraphsI’llshowyouatoymodelofquantumreality.It’savastly simplified model, but I think it’s just intricate enough to suggest thevastnessofquantumreality.ThemainpointisthatquantumrealityisREALLY,REALLYBIG.35We’llbuildupatoymodelthatdescribessociallifeamongthespinsofjust fiveparticles,andwe’lldiscover that it fillsoutaspaceof thirty-twodimensions.

Startwithonequantumparticle thathasaminimalunitofspin.Weabstractaway—that is, ignore—all its other properties. The resulting object iswhat iscalledaquantumbit,orqubit. (For sophisticates:Acoldelectron trapped inadefinite spatial state, say by appropriate electric fields, is effectively a qubit.)Thespinofaqubitcanpointindifferentdirections.We’llwrite

forthestateinwhichthespinofthequbitisdefinitelyup,and

forthestateinwhichthespinisdefinitelydown.

The qubit can also be in states where the spin points sideways, and that’swherethefunbegins.It’sexactlyhere,atthisjuncture,thatthecentralweirdnessofquantummechanicscomesintoplay.

Thesideways-pointingstatesarenotnew,independentstates.Thesesideways-pointers,andallotherstatesofthequbit,arecombinationsofthestates|↑ and|↓ thatwealreadyhave.

Specifically,forinstance,theeast-spinningstateis

Thestatewherethespindefinitelypointseastisanequalmixtureofnorthandsouth.Ifyoumeasurethespininthehorizontaldirection,you’llalwaysfindthatitpointseast.Butifyoumeasurethespinintheverticaldirection,you’reequallylikely to find that it points north or south. That’s themeaning of this strangeequation. In more detail, the rule for computing the probability of finding agivenresult(upordown)whenyoumeasurethespinintheverticaldirectionisthatyoutakethesquareofthenumberthatmultipliesthestatewiththatresult.Here, for example, the - number 1/√2 multiplies the spin up state, so theprobabilityoffindingspinupis(1/√2)2=½.

Thisexampleillustrates,inminiatureform,theingredientsthatenterintothedescriptionofaphysical systemaccording toquantumtheory.Thestateof thesystemisspecifiedbyitswavefunction.You’vejustseenthewavefunctionsforthreespecificstates.Thewavefunctionconsistsofasetofnumbersmultiplyingeachpossibleconfigurationof theobjectbeingdescribed. (Thatnumbermightbezero,soifwewerebeingfussywe’dwrite|↑ =1|↑ +0|↓ .)Thenumbermultiplying a configuration is called the probability amplitude for thatconfiguration. The square of the probability amplitude is the probability ofobservingthatconfiguration.

What about the west-spinning state? By symmetry, it should also have theequalprobabilitiesforspinandforspindown.Butithastobedifferentfromtheeast-spinner.Hereitcomes:

The extraminus sign doesn’t affect the probability, becausewe square it. Foreastversuswest, theprobabilities are the same,but theprobability amplitudesare different. (In a moment we’ll see how the minus sign does haveconsequences,whenweconsiderseveralspinsatonce.)

Nowlet’sconsidertwoqubits.Toget thestatewherebothareeast-spinners,wemultiplytwocopiesoftheeast-spinningstate,andfind

Theprobabilityforfindingbothspinsupis(½)2=¼,asistheprobabilityforfinding the first up, the second down, and so forth. Similarly, when both arewest-spinners,weget

Again,alltheup-and-downprobabilitiesareequal.

Already,withjustthesetwoqubits,wefindsomebehaviorthat’strulygnarly.(The technical termisentangled.)Let’sconsider twostates thatwecangetbycombiningthedoubleeast-pointerwiththedoublewest-pointer.

(1)

(2)

In each of these states, themessage of the left-hand expressions is that ifwemeasure the spins in the horizontal direction, we’ll find either that both arepointing east or that both are pointingwest.Eachof thosepossibilities occurswithprobability½.We’llneverfindthatoneispointingeastandtheotherwest.Soas farasmeasurements in thehorizontaldirectionareconcerned, these twostates look just the same. It’s likeknowingyouhaveamatchedpairof socks,either blackorwhite, but not knowingwhich color.That’s themessageof theleft-handsidesoftheseequations.

The right-hand sides tell you what happens if you measure, in these samestates,bothspinsintheverticaldirection.Nowtheresultsareverydifferent.Inthe first state, both spins will be pointing up, or both down; each possibilityoccurswithprobability½.Thesecondstatepreviously (in the lastparagraph!)lookedthesameasthefirst.Now,viewedfromanotherperspective,itcouldn’tbemoredifferent. In the second stateyounever find the spins pointing in thesameverticaldirection;ifoneisup,theotherisdown.

Either of these states would annoy Einstein, Podolsky, and Rosen, becausetheyexhibittheessenceofthefamousEPRparadox.Measuringthespinofthefirstqubittellsyouabouttheresultyou’llgetbymeasuringthesecondbit,eventhoughtheymightbephysicallyseparatedbyalargedistance.Onthefaceofit,this “spooky action-at-a-distance,” to use Einstein’s phrase, seems capable oftransmittinginformation(tellingthesecondspinwhichwayitmustpoint)fasterthan the speedof light.But that’s an illusion,because toget twoqubits intoadefinitestatewehadtostartwiththemclosetogether.Laterwecantakethemfarapart,butifthequbitscan’ttravelfasterthanthespeedoflight,neithercananymessagetheycarrywiththem.

Moregenerally,toconstructallpossiblestatesoftwoqubits,weaddthefourpossibilities |↑↑ , |↑↓ , |↓↑ , |↓↓ , each multiplied by a separate number. Thatdefines a four-dimensional space—you can step off distances in four differentdirections.36

Todescribethepossiblestatesoffivequbits,wehaveup-or-downchoicesfor

eachofthem(forexample,|↑↓↑↑↓ or|↑↑↓↓↑ ).Thereare2×2×2×2×2=32possibilities,andageneralstatecancontaincontributionsfromallofthem,eachmultiplied by a number. That’s how we find ourselves with a thirty-two-dimensionaltoymodelonourhands.Sometoy!

Laplace’sDemonversusGridPandemonium

Pierre-Simon Laplace’s masterpiece, the five-volume Mécanique Céleste,appeared in installments from 1799 to 1825. It tookmathematical astronomy,based on Newtonian principles, to a new level of elegance and precision.Laplacewassoimpressedwithhowaccuratelyhewasabletocalculatecelestialmotions that he fantasized about what a perfectly knowledgeable calculatingdemoncoulddo.Hedecidedthathisdemonwouldbeabletopredictthefuture,orreconstructthepast,bycalculation:

Anintelligencewhich,foragiveninstant,couldknowalltheforcesbywhichnatureisanimated,andtherespectivesituationofthebeingswhocomposeit,if,moreover,itwassufficientlyvasttosubmitthesedatatoanalysis,ifitcouldembraceinthesameformulathemovementsofthegreatestbodiesintheuniverseaswellasthoseofthelightestatom—nothingwouldbeuncertainforit,andthefuture,likethepast,wouldbepresenttoitseyes.

Laplace,ofcourse,hadinmindauniversebasedonNewtonianmechanics.Howrealisticdoeshisdemonappeartoday?Couldcompleteknowledgeofthepresentandlimitlessmathematicalskillreducethepastandthefuturetocalculation?

GridpandemoniumoverwhelmsLaplace’sdemon.

Let’sfirstconsidertheproblemthedemonisupagainst.Laplacethoughtthatif you specified the position and velocity of every atom in the world, youspecifiedtheworld.Therewouldbenothingelsetoknow.Andhethoughtthatphysicssuppliedequationsrelatingthecompletesetofpositionsandvelocitiesatone time to those at later (or earlier) times.Thus if youknew the state of theworldat some time t0, you could calculate the state of theworld at anyothertimet1.

Withmodernquantumtheory,theworldhasbecomeamuchbiggerplacethan

Laplacecouldhaveimagined.Ourtoymodelfeaturedjustahandfulofqubits37but encompassed a thirty-two-dimensional world. The quantum Grid, whichembodies our deepest understanding of reality, requiresmany qubits at eachpoint in spaceand time.Thequbits at a point describe thevarious things thatmight be happening at that point. For example, one of them describes theprobabilitythat(ifyoulook)youwillobserveanelectronwithspinupordown,another theprobability that (ifyou look)youwillobserveanantielectronwithspinupordown,anothertheprobabilitythat(ifyoulook)youwillobserveareduquarkwithspinupordown,....Othersdescribepossibleresultsifyoulookfor photons, gluons, or other particles. On top of that, if space and time arecontinuous—astheexistinglawsofphysics,sofarverysuccessfully,assume—thenthenumberofspace-timepointsishighlyinfinite.

Theworldisnolongerfoundedonatomsinthevoid,sothestateoftheworldnolongerconsistsofthepositionsandvelocitiesofalotofatoms.Instead,theworld is the tremendous multiple infinity of qubits just described. And todescribe itsstatewemustassignanumber—aprobabilityamplitude—toeverypossibleconfigurationof thequbits. Inour five-qubit toymodelwefound thatthe possible states filled out a space of thirty-two dimensions. The space wemustusetodescribethestateoftheGrid,whichisourworld,bringsininfinitiesofinfinities.

Agoogolis10100—thatis,1followedbyonehundredzeros.Itwasmeanttobe a crazily large number. A googol is, for example, much larger than thenumberofatomsinthevisibleuniverse.Butevenifwereplaceallofspacebyalatticewithjusttenpointsineachdirection,andputjustonequbitateachpoint,thedimensionofthequantum-mechanicalversionofthatschematicmodelworldismuchmorethanagoogol.Infact,it’saspacewhosedimensionismorethanagoogolofgoogols.

Thus the firstpartof thedemon’s task,knowing“the respectivesituationofthe beingswho compose” theworld, is a toughone.Toknow the state of theworld,he’sgottolocateaspecificpointsomewherewithinaREALLYREALLYBIGspace.Compared to thischallenge, findinganeedle inahaystack isdeadeasy.

Itgetsworse.We’vetalkedbeforeaboutthespontaneousactivityoftheGrid.It’sfullofquantumfluctuations,orvirtualparticles.Thosearerough, informaldescriptionsofarealitywenowhavethelanguagetoexpressmoreprecisely.To

say that theGrid contains spontaneous activity is to say that its state is not asimpleone.Ifwelookwithhighresolutioninspaceandtimetoseewhat’sgoingonintheentitywecallemptyspace(asexperimentersdidatLEP,forexample),we findmanypossible results.Each timewe lookwesee somethingdifferent.Eachobservationuncoversapieceofthewavefunctionthatdescribesatypical,verysmallregionofspace.Eachobservationembodiesapossibilitythatoccurs,multipliedbysomeprobabilityamplitude,withinthatwavefunction.

Sowe’relookingforaneedlethatisn’tnearthebottomofthehaystackorinanyparticularlysimpleplace.It’sofftotheside,orratherofftothissideandthatsideandtheothersideandsooninvariousamountsforgoogolsofgoogolsofsides.

Laplace’simaginarydemonisblessedwithperfectknowledgeofthestateoftheworld.Heknowswherethatneedleis.Buthe’simaginary.Thoseofuswhoaren’tblessedwithperfectknowledgeof thestateof theworld,butwouldstillliketopredictsomethingaboutthefuture,facesomeissues.Howcanweacquiresomeoftherelevantknowledge?Howmuchimpactwillgapsinourknowledgehave?

As Yogi Berra apparently learned from Niels Bohr, “prediction is verydifficult, especially about the future.” There are (at least) two fundamentalreasonswhyitcanbeverydifficulttopredictthefuture,evenifwehavealltherightequations.One ischaos theory.Roughlyspeaking,chaos theorysays thatsmall uncertainties in your knowledge of the state of the world at time t0introduceverylargeuncertaintiesinwhatyoucandeduceaboutthestateoftheworldatasignificantlylatertimet1.

Theother isquantumtheory.Aswe’vediscussed,quantumtheorygenerallypredicts probabilities, not certainties. Actually, quantum theory gives youperfectlydefiniteequationsforhowthewavefunctionofasystemchangeswithtime.Butwhenyouusethewavefunctiontopredictwhatyou’llobserve,whatitgivesyouisasetofprobabilitiesfordifferentoutcomes.

In view of all this, we’ve becomemore humble since Laplace’s day aboutwhat we can compute, in principle. In practice, however, we’re answeringquestions thatLaplace could not begin to imagine, throughmeans he couldn’tdreamof.Forexample...

TheBig(Number)Crunch

Well-informed, modern calculating demons know that they can’t simplycalculate everything,à la Laplace’s demon.Their art is to discover aspects ofreality thatwillyield to theircraft.Fortunately,chance,uncertainty,andchaosdonot infesteveryaspectof thenaturalworld.Manyof the thingswe’remostinterestedincalculating,suchastheshapeofamoleculewemightuseasadrug,the strength of a material we might use to make aircraft, and the mass of aproton,arestablefeaturesofreality.Moreover,thesesystemscanbeconsideredin isolation; their properties don’tmuchdependon the state of theworld as awhole.38Intheartofdemoncalculators,stable,isolatedsystemsarethenaturalsubjectsfordetailedportraits.

So:fullyawareofthedifficultiesbutundaunted,heroesofphysicsgirdtheirloins,applyforgrants,buyclustersofcomputers,solder,program,debug,eventhink—whateverittakestowrestanswersfromGridpandemonium.

Howdowecomputetheportraitofaproton?

First, we must replace continuous space and time by a finite structure—alattice of points—that a computer can handle. That is an approximation, ofcourse, but if the distance between points is small enough, the errors will besmall. Second,wemust squeeze theREALLYREALLYBIG quantum realityintoaclassicalcomputingmachine.Thequantum-mechanicalstateofGridlivesin a huge space, where its wave function encompassesmultitudes of possiblepatterns of activity.But the computer canmanipulate only a fewpatterns at atime. Because the equations for the evolution in time of any one pattern ofactivitybringinalltheotherpatterns,theclassicalcomputerhastostoreavastlibrary of patterns, with their probability amplitudes, inmemory. To evolve acurrent pattern forward in time, it fetches the relevant information about oldpatterns step byhalting step.For each storedpattern, it computes the changeswrought. Finally it stores the evolved probability amplitude for the currentpattern,commencestoevolvethenextpattern,andcyclesrepeatedly.TheGridisaharshmistress.

Oureyeswerenotevolvedtoresolvedistancesoforder10-14centimeter,norourbrainstoperceivetimesoforder10-24second.Thosecapabilitieswouldnothelpus toavoidpredatorsor finddesirablemates.Butasourcomputerscycle

throughGridconfigurations, theyareconstructing thepatternsoureyeswouldsee,weretheyadaptedtothosetinydistancesandtimes.Usingournoodles,wecanimproveourvision.That’swhatgaveusColorPlate4.

Oncewe’ve got “empty” space humming,we can pluck it. That is,we candisturbGridbyinjectingsomeextraactivityandlettingthingssettledown.Ifwefindstable,localizedconcentrationsofenergy,we’vefound—thatis,computed—stable particles. We can match them (if the theory’s right!) to protons p,neutronsn,andtherest.Ifwefindlocalizedconcentrationsofenergythatpersistforagoodwhilebeforedissipating,we’vefoundunstableparticles.Theyshouldmatchtheρmeson,theΔbaryon,andtheirkin.

To seewhat it looks like, examineColorPlate6 and its caption.That’s ourdeepestunderstandingofwhatp,n,ρ,Δ,...are.

Figure9.1showstheveryconcretechallengewe’reupagainst.It’spartofthespectrum of hadrons, strongly interacting particles that have been observed.Theyhavekeyidentifyingproperties:theirmassandspin.Thecaptionprovidesa technicaldescriptionofexactlywhat’sbeenplotted.Thesedetails (and thereare lotsmore!) are intricate and full ofmeaning to experts, but the take-homemessageissimplythatthereareplentyofjuicyfactsforthetheorytoexplain.

Figure 9.2 shows how three of the measured masses are used to fix theparametersof the theory.That is, beforedoing thecalculation,wedon’tknowwhatmasseswe should assign to the quarks, or the overall coupling constant.Themostaccuratewaytodeterminethosevaluesisthecalculationitself.Sowetry different values and settle on the ones that give the best fit to theobservations.

Figure9.1AcensusofstronglyinteractingparticlesthatQCDmustaccountfor.Eachpoint encodes anobservedparticle.Theheightof thepoint indicates themassof theparticle.The first twocolumns aremesonswith spin0:π,K, andspin1:ρ,K*,φ.The thirdand fourthcolumnsarebaryonswithspin½:N,Ξ,andspin3/2:Δ,Ω,respectively.Thefifthandsixthcolumnsare“charmonium”and“bottomonium”mesonswithvariousspins.Thesemesonsareinterpretedasboundstatesofaheavyc (charm)quarkanditsantiquark,or, respectively,ab(bottom)quarkanditsantiquark.Inthesecolumnstheheightsrepresentthemassdifferences between the particle in question and the lightest possiblecharmoniumorbottomoniumstate.

Ifatheoryhasalotofparameters,youadjusttheirvaluestofitalotofdata,andyourtheoryisnotreallypredictingthosethings,justaccommodatingthem.Scientistsusewordslikecurvefittingandfudge factors todescribe thatsortofactivity. Those phrases aren’t meant to be flattering. On the other hand, if atheoryhas justa fewparametersbutapplies toa lotofdata, ithas realpower.Youcanuseasmallsubsetof themeasurementstofixtheparameters; thenallothermeasurementsareuniquelypredicted.

In that objective sense, QCD is a very powerful theory indeed. Not onlydoesn’titrequiremanyparameters,itdoesn’tallowmany:justamassforeachkind of quark, and one universal coupling strength. Furthermore, most of the

quarkmassesareirrelevantforcalculatingtheparticlemassesinthefigurewiththeprecisionwecanattain;othereffectsintroducelargeruncertainties.Weneedonlytheaveragemassmlightofthelightestuanddquarksandthemassmsofthestrangequark,togetherwiththecouplingstrength.Havingfixedthosethreethings, we have no more room to maneuver. No fudge factors, no excuses,nowheretohide.If the theoryisright, thecalculationwillmatchreality.If thecalculationdoesn’tmatchreality,thetheoryisirreparablywrong.

Figure9.2ThreemassesareusedtofixthefreeparametersofQCD.Thusthosethreemassesareaccommodated,notpredicted.Butoncethat’sdone,there’snomoreroomtomaneuver.

Figure 9.3 shows how the calculated values of mass and spin—theunambiguouspredictionsofQCD—comparewithobservedvalues.Becausespincomes in discrete units, either the agreement is exact or it’s disagreement. Sowe’dbetterfindobservedparticleswiththeexactlythespinsandapproximatelythemassesofthepredictedparticles,andnoothers.Withasighofrelief,wenotethatnear each“realworld” square there’s either a “calculated”circleor a “fixparameter”diamond.You see that the calculatedmasses agree quitewellwiththeobservedvalues.You’llnoticethevertical“errorbars”aroundthecalculatedvalues. These reflect the residual uncertainties in the calculation. Variousapproximations and compromises had to be made because the available

computerpower,thoughfantasticallylarge,wasfinite.

Figure9.3The successful comparisonofobservedandpredictedparticle spinsandmasses.

AhighlightinthisfigureisthepointlabeledN.Nstandsfornucleon—thatis,proton or neutron. (On the scale of this figure, their masses areindistinguishable). QCD succeeds in accounting for the mass of protons andneutrons from first principles. The mass in protons and neutrons, in turn,accountsforoverwhelminglymostofthemassofnormalmatter.Ipromisedtoaccountfortheoriginof95%ofthatmass.Thereitis.

Alsoremarkableiswhatyoudon’tseecomingoutofthecomputer.Thereareno extra circles floating around, indicating predicted particles that aren’tobserved.Especiallynoteworthy:althoughthebasicinputstothecalculationarequarks and gluons, they don’t appear among the outputs! The Principle ofConfinement,whichseemedsoweirdanddesperate,hereappearsasafootnotetocompleteandcomprehensivereality-matching.

Of course computing something—or having a gigantic ultra-fast computercomputesomethingforyou—isnotthesameasunderstandingit.Understandingisthemissionofthenextchapter.

Before ending this one, however, I’d like to pause for a brief tribute to the

austere Figure 9.3 and the community that produced it. Through difficultcalculations of merciless precision that call upon the full power of moderncomputer technology, they’ve shown that unbendable equations of highsymmetry account convincingly and in quantitative detail for the existence ofprotonsandneutrons,andfortheirproperties.They’vedemonstratedtheoriginoftheproton’smass,andtherebythelioness’sshareofourmass.Ibelievethisisoneofthegreatestscientificachievementsofalltime.

10

TheOriginofMass

Knowinghowtocalculatesomethingisnotthesameasunderstandingit.Havingacomputercalculatetheoriginofmassforusmaybeconvincing,butitisnotsatisfying.Fortunately,wecanunderstandittoo.

HAVING A COMPUTER SPIT OUT ANSWERS after gigantic and totallyopaquecalculationdoesnotsatisfyourhungerforunderstanding.Whatwould?

PaulDiracwasfamouslytaciturn,butwhenhespoke,whathesaidwasoftenprofound.Heoncesaid,“IfeelIunderstandanequation,whenIcananticipatethebehaviorofitssolutionswithoutactuallysolvingit.”

What’sthevalueofsuchunderstanding?

“Solving” equations is just one tool—an imperfect one—for working withthem.Thecalculationswediscussedintheprecedingchapterareaninstructiveexample.They showconclusively that the equations for quark andgluonGridaccuratelyaccountforthemassesofprotons,neutrons,andotherhadrons.Theyalso show that those equations keep quarks and gluons hidden. (You caninterpretthenonappearanceofisolatedquarksorgluonsasacalculationoftheirmass,whenyouincludetheirvirtualparticleclouds—theanswerisinfinity!)

Those are glorious results,won after heroic efforts by human andmachine.But the need for heroic efforts is one of the biggest drawbacks of “solving”equations.Wedon’twanttotieupexpensivecomputerresourcesandwaitalongtime for answers every time we ask a slightly different question. Even moreimportant,wedon’twanttotieupexpensivecomputerresourcesandwaitaverylongtimewhenweaskmorecomplicatedquestions.Forexample,we’dliketobeabletopredictthemassesnotonlyofsingleprotonsandneutronsbutalsoofsystemscontainingseveralprotonsandneutrons—atomicnuclei.Inprinciplewehavetheequationstodoit,butsolvingthemisimpractical.Forthatmatter,we

haveequationsadequatetoansweranyquestionofchemistry, inprinciple.Butthat hasn’t put chemists out of business or replaced them with computers,becauseinpracticethecalculationsaretoohard.

In both nuclear physics and chemistry, we are happy to sacrifice extremeprecision for ease of use and flexibility. Rather than brutally “solving” theequationsbycrunchingnumbers,wemakesimplifiedmodelsandfindrulesofthumb that can give us practical guidance in complicated situations. Thesemodelsandrulesofthumbcangrowoutofexperienceinsolvingtheequations,andtheycanbecheckedbysolvingtheequationswhenthat’spractical,buttheyhave a life of their own.This remindsmeof the distinctionbetweengraduatestudents andprofessors: a graduate student knows everything about nothing, aprofessor knows nothing about everything. Solving the equations is whatgraduatestudentsdo,understandingthemiswhatprofessorsdo.

Weareas faraswecanbe fromunderstanding,whensolving theequationsreveals behavior that’s totally unexpected and appears miraculous. Thecomputershavegivenusmass—andnotjustanymass,butourmass,themassofthe protons and neutrons we’remade from—from quarks and gluons that arethemselvesmassless(ornearlyso).TheequationsofQCDoutputMassWithoutMass.Itsoundssuspiciouslylikesomethingfornothing.Howdidithappen?

Fortunately, it’s possible get a rough, professor-like understanding of thatapparent miracle. We just have to put together three ideas we’ve alreadydiscussedseparately.Let’sbrieflyrecallandassemblethem.

FirstIdea:BlossomingStorms

Thecolor chargeof aquark creates adisturbance in theGrid—specifically, inthegluon fields—thatgrowswithdistance. It’s likea strange stormcloud thatblossoms from a wispy center into an ominous thunderhead. Disturbing thefieldsmeansputting them intoa stateofhigherenergy. Ifyoukeepdisturbingthefieldsoveraninfinitevolume,theenergycostwillbeinfinite.EvenExxonMobil wouldn’t claim that Nature has the resources to pay that price.39 Soisolatedquarkscan’texist.

SecondIdea:CostlyCancellations

Theblossomingstormcanbeshort-circuitedbybringinganantiquark,withtheoppositecolorcharge, close to thequark.Then the twosourcesofdisturbancecancel,andcalmisrestored.

If the antiquark were located accurately right on top of the quark, thecancellation would be complete. That would produce the minimal possibledisturbance in the gluon fields—namely, none.But there’s another price to bepaidforthataccuratecancellation.Itcomesfromthequantum-mechanicalnatureofquarksandantiquarks.

According the Heisenberg uncertainty principle, in order to have accurateknowledgeof thepositionof aparticle,youmust let thatparticlehaveawidespread inmomentum. Inparticular, youmust allow that theparticlemayhavelarge momentum. But large momentum means large energy. And the moreaccuratelyyou fix thepositionof theparticle (“localize” it, in the jargon), themoreenergyitcosts.

(It’s also possible to cancel the color charge of a quark using thecomplementary color charges of two other quarks. This is what happens forbaryons, including the proton and neutron—as opposed to mesons, based onquark-antiquark.Theprincipleisthesame.)

ThirdIdea:Einstein’sSecondLaw

Sotherearetwocompetingeffects,whichpullinoppositedirections.Tocancelthefielddisturbanceaccuratelyandminimizethatenergycost,Naturewantstolocalize the antiquark on the quark. But tominimize the quantum-mechanicalcostoflocalizingaposition,Naturewantstolettheantiquarkwanderabit.

Nature compromises. She finds ways of striking a balance between thedemands of the gluon fields that don’twant to be disturbed, and those of thequarks and antiquarks that want to roam free. (You might think of a familygathering where the gluon fields are the old curmudgeons, the quarks andantiquarksaretherambunctiouskids,andNatureistheresponsibleadult.)

As with any compromise, the result is—well, a compromise. Nature can’t

makebothenergieszerosimultaneously.Sothetotalenergywon’tbezero.

Actually therecanbedifferentaccommodations thataremore-or-less stable.Each will have its own nonzero energy E. And thus, according to Einstein’ssecondlaw,eachwillhaveitsownmass,m=E/c2.

And that is theoriginofmass. (Or at least of 95%of themassof ordinarymatter.)

Scholium

Suchaclimaxdeservessomecommentary.Indeed,itdeservesascholium,whichissimplyLatinfor“commentary”butsoundsmuchmoreimpressive.

1.Nothinginthisaccountoftheoriginofmassreferredto,ordependedon,thequarksandgluonshavinganymass.WereallydogetMassWithoutMass.

2. It wouldn’t work without quantummechanics. You cannot understandwhereyourmasscomesfromifyoudon’ttakequantummechanicsintoaccount. Inotherwords,withoutquantummechanicsyou’redoomed tobealightweight.

3.Asimilarmechanism,thoughmuchsimpler,worksinatoms.Negativelycharged electrons feel an attractive electric force from the positivelychargednucleus.Fromthatpointofview,they’dliketosnugglerightontop of it. Electrons are wavicles, though, and that inhibits them. Theresult,again,isaseriesofpossiblecompromisesolutions.Thesearewhatweobserveastheenergylevelsoftheatom.

4.ThetitleofEinstein’soriginalpaperwasaquestion,andachallenge:

DoestheInertiaofaBodyDependonItsEnergyContent?

If the body is a human body, whose mass overwhelmingly arises from theprotons and neutrons it contains, the answer is now clear and decisive. Theinertiaofthatbody,with95%accuracy,isitsenergycontent.

11

MusicoftheGrid:APoeminTwoEquations

Themassesofparticlessoundthefrequencieswithwhichspacevibrates,whenplayed.ThisMusicoftheGridbetterstheoldmysticmainstay,“MusicoftheSpheres,”bothinfantasyandinrealism.

LETUSCOMBINEEinstein’ssecondlaw

(1)

withanotherfundamentalequation,thePlanck-Einstein-Schrödingerformula

(2)

The Planck-Einstein-Schrödinger formula relates the energy E of a quantum-mechanicalstatetothefrequencyνatwhichitswavefunctionvibrates.HerehisPlanck’s constant. Planck introduced it in his revolutionary hypothesis (1899)that launched quantum theory: that atoms emit or absorb light of frequency νonlyinpacketsofenergyE=hν.Einsteinwentabigstepfurtherwithhisphotonhypothesis (1905): that light of frequency ν is always organized into packetswithenergyE=hν.FinallySchrödingermadeitthebasisofhisbasicequationfor wave functions—the Schrödinger equation (1926). This gave birth to themodern,universal interpretation: thewave functionof any statewithenergyEvibratesatafrequencyνgivenbyν=E/h.40

By combining Einstein with Schrödinger we arrive at a marvelous bit of

poetry:

The ancients had a concept called “Music of the Spheres” that inspiredmanyscientists (notably JohannesKepler) and evenmoremystics.Because periodicmotion(vibration)ofmusicalinstrumentscausestheirsustainedtones,theideagoes, the periodic motions of the planets, as they fulfill their orbits, must beaccompanied by a sort of music. Though picturesque and sound-scape-esque,thisinspiringanticipationofmultimedianeverbecameaverypreciseorfruitfulscientificidea.Itwasnevermorethanavaguemetaphor,soitremainsshroudedinquotationmarks:“MusicoftheSpheres.”

Our equation (∗) is a more fantastic yet more realistic embodiment of thesameinspiration.Ratherthanpluckingastring,blowingthroughareed,bangingonadrumhead,orclangingagong,weplaytheinstrumentthatisemptyspacebyplunkingdowndifferentcombinationsofquarks,gluons,electrons,photons,.. . (that is, theBits that represent theseIts)and let themsettleuntil theyreachequilibrium with the spontaneous activity of Grid. Neither planets nor anymaterialconstructionscompromisethepureidealityofourinstrument.Itsettlesinto one of its possible vibratory motions, with different frequencies ν,depending on how we do the plunking, and with what. These vibrationsrepresentparticlesofdifferentmassm,accordingto(∗).ThemassesofparticlessoundtheMusicoftheGrid.

12

ProfoundSimplicity

Ourbesttheoriesofthephysicalworldappearcomplicatedanddifficultbecausetheyareprofoundlysimple.

EINSTEINISOFTENQUOTEDforhisadviceto“Makeeverythingassimpleaspossible,butnotsimpler.”AfterstudyingeitherEinstein’sgeneralrelativity,orhis theoryoffluctuations instatisticalmechanics—twoofhismore intricatecreations—youmightwellwonderwhetherheheededhisownadvice.Certainlythosetheoriesarenot“simple”intheusualsenseoftheword.

ModernphysicistsconsiderQCDanalmost ideallysimple theory,yetwe’veseen how complicated it is to describe QCD in everyday words, and howchallengingitistoworkwith(andnotsolve)thattheory.LikeBohr’sprofoundtruth, profound simplicity contains an element of its opposite, profoundcomplexity.Thisisaparadox,butitsresolutionisprofoundlystraightforward,aswe’llnowexplore.

PerfectionSupportingComplexity:Salieri,JosephII,andMozart

I learned what perfection means from the notoriously mediocre composerAntonioSalieri.41Inoneofmyfavoritescenesfromoneofmyfavoritemovies,Amadeus,Salierilookswithwide-eyedastonishmentatamanuscriptofMozart’sand says, “Displace one note and therewould be diminishment.Displace onephraseandthestructurewouldfall.”

In this, Salieri captured the essence of perfection.His two sentences definepreciselywhatwemean by perfection inmany contexts, including theoreticalphysics.Youmightsayit’saperfectdefinition.

A theorybegins tobeperfect if anychangemakes itworse.That’sSalieri’sfirstsentence,translatedfrommusictophysics.Andit’srightonpoint.Butthereal genius comeswith Salieri’s second sentence. A theory becomes perfectlyperfect if it’s impossible tochange it significantlywithout ruining itentirely—thatis,ifchangingthetheorysignificantlyreducesittononsense.

In the samemovie, Emperor Joseph II offersMozart somemusical advice:“Yourworkisingenious.It’squalitywork.Andtherearesimplytoomanynotes,that’sall.Justcutafewanditwillbeperfect.”Theemperorwasputoffbythesurface complexity ofMozart’s music. He didn’t see that each note served apurpose—tomakeapromiseorfulfillone,tocompleteapatternorvaryone.

Similarly, at first encounter people are sometimes put off by the superficialcomplexityoffundamentalphysics.Toomanygluons!

Buteachoftheeightcolorgluonsisthereforapurpose.Together,theyfulfillcompletesymmetryamongthecolorcharges.Takeonegluonaway,orchangeitsproperties,andthestructurewouldfall.Specifically,ifyoumakesuchachange,then the theory formerly known as QCD begins to predict gibberish; someparticles are producedwith negative probabilities, and others with probabilitygreater than1.Such a perfectly rigid theory, one that doesn’t allowconsistentmodification,isextremelyvulnerable.Ifanyofitspredictionsarewrong,there’snowheretohide.Nofudgefactorsortweaksareavailable.Ontheotherhand,aperfectlyrigidtheory,onceitshowssignificantsuccess,becomesverypowerfulindeed.Becauseifit’sapproximatelyrightandcan’tbechanged,thenitmustbeexactlyright!

Salieri’s criteria explain why symmetry is such an appealing principle fortheory building. Systems with symmetry are well on the path to Salieri’sperfection. The equations governing different objects and different situationsmustbestrictlyrelated,orthesymmetryisdiminished.Withenoughviolationsall pattern is lost, and the symmetry falls. Symmetry helps us make perfecttheories.

Sothecruxofthematterisnotthenumberofnotesorthenumberofparticlesor equations. It is the perfectionof the designs they embody. If removing anyone would spoil the design, then the number is exactly what it should be.Mozart’sanswertotheemperorwassuperb:“Whichfewdidyouhaveinmind,Majesty?”

ProfoundSimplicity:SherlockHolmes,NewtonAgain,andYoungMaxwell

Onesurewaytoavoidperfection is toaddunnecessarycomplications. If thereareunnecessarycomplications,theycanbedisplacedwithoutdiminishmentandremovedwithoutdestruction.Theyalsodistract,as in this story toldofmastersleuthSherlockHolmesandhisfriendDr.Watson:

SherlockHolmesandDr.Watsonwereonacampingtrip.Afterpitchingtent beneath a skyful of stars, theywent to sleep. In themiddle of thenightHolmesshookWatsonawake,andaskedhim,“Watson,lookupatthestars!Whatdotheytellus?”

“Theyteachushumility.Theremustbemillionsofstars,andifevenasmallfractionofthosehaveplanetslikeEarth,therewillbehundredsofplanetswithintelligentbeings.Someofthemareprobablywiserthanweare.TheymaybelookingthroughtheirgreattelescopesdownatEarthasitwasmany thousands of years ago. Theymay bewonderingwhetherintelligentlifewilleverevolvehere.”

After a moment, Holmes replied, “Actually,Watson, those stars aretellingusthatsomeonehasstolenourtent.”

Passingfromtheridiculoustothesublime,youmayrecallthatSirIsaacNewtonwasnotsatisfiedwithhistheoryofgravity,whichfeaturedforcesactingthroughemptyspace.Butbecausethat theoryagreedwithallexistingobservationsandhecouldnotdiscoveranyconcreteimprovement,Newtonputhisphilosophicalreservations aside and presented it unadorned. In the concluding GeneralScholiumtohisPrincipia,hemadeaclassicdeclaration:42

Ihavenotasyetbeenabletodiscoverthereasonforthesepropertiesofgravityfromphenomena,andIdonotfeignhypotheses.Forwhateverisnotdeducedfromthephenomenamustbecalledahypothesis;andhypotheses,whethermetaphysicalorphysical,orbasedonoccultqualitiesormechanical,havenoplaceinexperimentalphilosophy.

The key phrase “I do not feign hypotheses” is Hypothesis non fingo in theoriginal Latin.Hypothesis non fingo is the legend that Ernst Mach enshrinedbelow the portrait of Newton in his influential Science of Mechanics. It isfamousenoughtohaveitsownWikipediaentry.Itmeans,simply,thatNewton

refrainedfromloadinghistheoryofgravitywithspeculationfreeofobservablecontent. (In his private papers, however,Newtonworked obsessively to try todiscoverevidenceforamediumfillingspace.)

Of course, the easiest way to avoid unnecessary complications is to saynothing at all. To avoid that pitfall, we need a dose of young Maxwell.Accordingtoanearlybiographer,asasmallboyhewasalwaysasking,“intheGallowegianaccentand idiom,”“What’s thegoo’ that?”and,on receivinganunsatisfactoryanswer,asking,“Butwhat’stheparticulargoo’that?”

In other words, we must be ambitious. We must keep addressing newquestions and strive for specific, quantitative answers. The phrase scientificrevolution has been used for so many things that it has been devalued. Theemergence of ambition tomake precisemathematicalworld-models, and faiththatonecouldsucceed,wasthedecisive,inexhaustibleScientificRevolution.

Thereiscreativetensionbetweentheconflictingdemandsofeconomizingonassumptions and providing particular answers to many questions. Profoundsimplicityisstingyontheinputside,generousontheoutputside.

Compression,Decompression,and(In)Tractability

Data compression is a central problem in communication and informationtechnology.Ithinkitgivesusafreshandimportantperspectiveonthemeaningandimportanceofsimplicityinscience.

When we transmit information, we want to take best advantage of theavailable bandwidth. So we boil down the message, removing redundant orinessentialinformation.AcronymssuchasMP3andJPEGarefamiliartousersofiPodsanddigitalcameras;MP3isanaudiocompressionformat,andJPEGisanimagecompressionformat.Ofcourse,thereceiverattheotherendhastotaketheboiled-downdataandunpackittoreproducetheintendedmessage.Whenwewant to store information, similar problems arise. We want to keep the datacompact,butreadytounfold.

From a larger perspective, many of the challenges humans face in makingsense of the world are data compression problems. Information about theexternal world floods our sensory organs. We must fit it into the availablebandwidthofourbrains.Weexperiencefartoomuchtokeepaccuratememory

ofitall;so-calledphotographicmemoryisrareandlimited,atbest.Weconstructworkingmodelsandrulesofthumbthatallowustousesmallrepresentationsofthe world, adequate to function in it. “There’s a tiger coming!” compressesgigabytes of optical information, plus perhaps megabytes of audio from thetiger’sroar,andmaybeeven—thismeanstrouble—afewkilobytesofherodorandthewindshestirsup,intoatinymessage.(Forexperts:23bytesinASCII.)A lotof informationhasbeensuppressed,butwecanunfoldsomeveryusefulconsequencesfromthelittlethat’sthere.

ConstructingprofoundlysimpletheoriesofphysicsisanOlympian43gameindatacompression.Thegoal is to find theshortestpossiblemessage—ideally,asingleequation—thatwhenunpackedproducesadetailed,accuratemodelofthephysicalworld.LikeallOlympiangames, thisonehas rules.Twoof themostimportantare

•Stylepointsaredeductedforvagueness.•Theoriesthatmakewrongpredictionsaredisqualified.

Once you understand the nature of this game, some of its strange featuresbecomelessmysterious.Inparticular:fortheultimateindatacompression,wemust expect tricky and hard-to-read codes. For example, consider “Take thissentenceinEnglish.”Eliminatingthevowels,wemakeitshorter:

Tkthssntncnnglsh.

This is harder to read, but there’s no real ambiguity about what sentence itrepresents.Accordingtotherulesofthegame,it’sastepintherightdirection.Wemightgofurther,eliminatingthespaces:

Tkthssntncnnglsh.

Thatstartstogetmorequestionable.Itcouldbemistakenfor

Tookthoseeasynotnicenineogles,he.

Of course, English is so quirky that this kind of code loses heavily on stylepoints, for vagueness. It’s hard to be sure exactlywhat counts as a legitimatesentence. In the game of profound simplicity, wemust do our decompressionusing precisely defined mathematical procedures. But as this simple examplesuggests, we must expect that short codes will be less transparent than theoriginalmessage,andthatdecodingthemwillrequireclevernessandwork.

After centuries of development, the shortest codes could become quiteopaque.Itcouldtakeyearsoftrainingtolearnhowtousethem—andhardworkto readanyparticularmessage.Andnowyouunderstandwhymodernphysicslooksthewayitdoes!

Actually,itcouldbealotworse.Thegeneralproblemoffindingtheoptimalwaytocompressanarbitrarycollectionofdataisknowntobeunsolvable.Thereason is closely related to Gödel’s famous Incompleteness Theorem, and(especially) to Turing’s demonstration that the problem of decidingwhether aprogramwillsendacomputerintoaninfiniteloopisunsolvable.Infact,lookingfortheultimateindatacompressionrunsyoustraightintoTuring’sproblem:youcan’t be surewhether your latestwonderful trick for constructing short codeswillsendthedecoderintoaninfiniteloop.

ButNature’sdatasetseemsfarfromarbitrary.We’vebeenabletomakeshortcodesthatdescribelargepartsofrealityfullyandaccurately.Morethanthis:inthepast,aswe’vemadeourcodesshorterandmoreabstract,we’vediscoveredthat unfolding the new codes gives expanded messages, which turn out tocorrespondtonewaspectsofreality.

WhenNewtonencodedKepler’s three lawsofplanetarymotion intohis lawofuniversalgravity,explanationsof the tides, theprecessionof theequinoxes,and many other tilts and wobbles tumbled out. In 1846, after almost twocenturies of triumph upon triumph for Newton’s gravity, small discrepancieswereshowingupintheorbitofUranus.UrbainLeVerrierfoundthathecouldaccountforthesediscrepanciesbyassumingtheexistenceofanewplanet.Andloandbehold,whenobservers turnedtheir telescopeswherehesuggestedtheylook, therewasNeptune!(Today’sdark-matterproblemisanuncannyecho,aswe’llsee.)

Ever more compressed, profoundly simple equations to start, ever more

complexcalculationstounfoldthem,everricheroutputthattheworldturnsouttomatch.This,Ithink,isadown-to-earthinterpretationofwhatEinsteinmeantinsaying,“Subtle is theLord,butmaliciousHe isnot.” Instriving for furtherunification,we’rebettingthatourluckwillcontinue.

PARTII

TheFeeblenessofGravity

IN ASTRONOMY, gravity is the most important force. But fundamentally,actingbetweenelementaryparticles, gravitational forces are ridiculously smallcomparedtoelectricorstrongforces.Thatdisparityposesabigchallengetotheidealofaunifiedtheory,whichseekstoputalltheforcesonthesamefooting.Ournewunderstandingoftheoriginofmasssuggestsananswer.

13

IsGravityFeeble?Yes,inPractice

Whenfairlycompared,initsactionbetweenbasicparticles,gravityisridiculouslyfeeblerthantheotherfundamentalforces.

IFYOU’VEJUSTSTRUGGLEDtohaulyourbodyoutofbed,orifyou’vejustthankfullycollapsed intoaneasychairwithagoodbookaftera longday,youmightfindithardtoacceptthatgravityisfeeble.Nevertheless,atafundamentallevel,itis.Ridiculouslyfeeble.

Herearesomecomparisons.

Atoms are held together by electric forces. There is electrical attractionbetween the positively charged atomic nucleus and the negatively chargedelectrons.Let’simaginethatwecouldturnoff theelectricforces.Therewouldstillbegravitationalattraction.Howtightlycouldgravityhold thenucleusandelectronstogether?Howbigwouldagravitationallyboundatombe?Asbigasaflea?No.Amouse?No.Askyscraper?No,keepgoing.Earth?Notevenclose.AnatomheldtogetherbygravitywouldhaveahundredtimestheradiusofthevisibleUniverse.

The deflection of light by the Sun is a celebrated gravitational effect. Itsobservation, by the British expedition of 1919, was a triumph for generalrelativity,andestablishedEinsteinasaworldcelebrity.ThewholeSun,actingona nearby photon, deflected its path by 1.75 minutes of arc—about 3% of 1degree.Nowcomparethattohowthestrongforceactsongluons.Afewquarksdeflect the gluon’s straight-line path so severely that within the radius of aproton,thegluonturnsaroundcompletelyandstaysinside.

We can also do a numerical comparison. Because both electric andgravitationalforcesfalloffinthesamewaywithdistance(namely,astheinversesquare),we’llgetthesameratioatanydistance.Let’scomparetheelectrictothe

gravitationalforcebetweenaprotonandanelectron.Theelectricalforceisabout10,000,000,000,000,000,000,000,000,000,000,000,000,000 times stronger. Inscientific notation, that’s 1040. (You see why scientists prefer scientificnotation.) “Bogus!” carps the critic. “Protons are complicated objects. Youshouldbecomparingtheforcesbetweenbasic,elementaryobjects.”Fine,wiseguy—thatonlymakesitworse!Ifwecomparetheforcesbetweenelectrons,wegetanevenbiggernumber—about1043—becauseanelectron’smassissmallerthanaproton’s,butthemagnitudeofitselectricchargeisthesame.

Whenyou riseoutofbed,youovercome thegravitationalpullof theentireEarth,usingasmallpartofthechemicalenergyderivedfromlastnight’sdinner.Asanyonewho’striedtoburncaloriesbyfightinggravity(liftingweights,doingcalisthenics)canattest,gravitydoesn’tputupmuchofafight—afewcaloriesgoaverylongway.

Anothermeasureofthefeeblenessofgravity:Electromagneticradiationistheworkhorseofmodernastronomy,fromradiodishestoopticaltelescopestox-raysatellites.It isalsotheworkhorseofmoderncommunicationstechnology,fromconventionalradiotosatellite(microwavedishes)toopticalfibers.Gravitationalradiation,bycontrast,hasneveryetbeendetected,despiteheroicefforts.

Gravity is the dominant force in astronomy, but only by default. Otherinteractions are far stronger, but they feature both attractions and repulsions.Normally matter reaches an accurate equilibrium, with the forces cancelled.Temporary imbalances (small ones) among electric forces lead to lightningstorms; small temporary imbalances among strong forces induce nuclearexplosions.Grossbreakdownsofequilibriumcannotstand.Gravity,however,isalways attractive. Though feeble at the level of individual basic particles,gravitationalforcesinexorablyaddup.Themeekinheritthecosmos.

14

IsGravityFeeble?No,inTheory

Gravityisauniversalforce.Itshapesthebasicstructureofspaceandtime.Itisfundamental.Soweshouldusegravityasthemeasureofotherthings,andnotuseotherthingsasthemeasureofgravity.Gravity,therefore,can’tbefeebleinanabsolutesense—itjustiswhatitis.Thefactthatgravityappearsfeebleisconfoundingtotheory.Italsoputsamajorhurdleonthepathtounification.

EINSTEIN’STHEORYOFGRAVITY, general relativity, ties the existence ofgravity to the structure of space and time. The effect we see as the force ofgravity, according to this theory, is simply bodies doing their best to travel instraight lines through the curved landscape of space-time. Bodies also causespace-timetocurve.ThecurvaturecausedbybodyBaffectsthemotionofbodyA to produce what in Newtonian language we would call the “force ofgravity.”44

Afar-reachingconsequenceofEinstein’spictureofgravityistheuniversalityofthatforce.Anybody,doingitsbesttotravelinastraightlinethroughcurvedspace-time,will follow the samepath any other bodywould.The best path isdeterminedby thecurvatureof space-time,notbyanyspecificpropertyof thebody.

InfacttheobserveduniversalityofgravitywasabigpartofwhatledEinsteinto his theory. In Newton’s account of gravity, the universality was anunexplainedcoincidence (or ratheran infinitenumberofcoincidences,one foreach body). On the one hand, the gravitational force felt by a body isproportionaltoitsmass.Ontheother,theaccelerationabodyfeelsinresponseto a given force is inversely proportional to mass. (That’s Newton’s secondsecondlawofmotion.HisoriginalsecondlawofmotionisF=ma;thisisa=

F/m.) Clapping those two hands together, we discover that the gravitationalaccelerationofabody—theactualdisturbanceofitsmotion—doesn’tdependonitsmassatall!

And that is what’s observed: motion independent of mass. The observedbehaviorisuniversal:allbodiesaccelerateinthesamewayundergravity.ButinNewton’s account there’s no reasonwhy it had to occur. It’s another of thosethingsthatworksinpracticebutnotintheory.Thegravitationalforceonabodydidn’thavetobeproportionaltothebody’smass.Wecertainlyknowofforces,suchaselectricforces,thataren’tproportionaltomass.

Einstein’s theory explains the gravitational “coincidence.” Or rather,transcendsit:wedon’thavetospeakseparatelyaboutaforceandaresponsetoforce, that happen to depend onmass in opposite ways.We just have bodiesdoing their best to keep going straight through curved space-time. This isprofoundsimplicityatitsbest.

UniversalityandUnification

Whenwecome to seekaunified theory includingall the forcesofnature, thecombination of gravity’s universality and its (apparent) feebleness poses greatdifficulties.Herearethealternatives:

•Gravitymightbederivedfromtheotherfundamentalforces.Becauseitisa small (feeble) effect, maybe gravity is a byproduct, a small residualafterthenear-cancellationofeffectsofoppositeelectricorcolorcharges,or something more exotic. But then why should it be universal? Theotherforcesaredefinitelynotuniversal:quarksbutnotelectronsfeelthestrongforce;electronsandquarks,butnotphotonsorcolorgluons,feeltheelectromagneticforce.It ishardtoimagineasimpleuniversalforcethat has the same consequences for all particles arising from suchlopsidedingredients.

•Theotherforcesmightbederivedfromgravity.It’seasytoimaginehownonuniversal forcesmight arise out of a universal one.There could beseveral different solutions of the universal equations with energyconcentratedinsmallregionsofspace;we’dinterpretthosesolutionsasparticles with different properties. (Apparently Einstein himself had

hopesofconstructingatheoryofmatteralongtheselines.)Butitishardtoseehowanextravagantlyfeebleforcecanspinoffmuchlargerones.

•All the forcesmight appear on the same footing, as different aspects—perhapsrelatedbysymmetry—ofasinglewhole,likedifferentsidesofadie.Butagain,itishardtomakethisideaconsistentwithgravitybeingmuchfeeblerthantheotherforces.

Turningitaround:Faithinthepossibilityofunificationdrivesusintoastateofdenial.Wecan’tacceptthatgravityreallyisfeeble,eventhoughitappearsthatway.Appearances—orrather,ourinterpretationofthem—mustbedeceptive.

15

TheRightQuestion

Theoretically,gravityshouldn’tbefeeble.Inpractice,itis.Thecoreofthisparadoxisthatgravitycertainlyappearsfeebletous.What’swrongwithus?

WEMEASURE GRAVITY through its effect on matter. The strength of thegravitationalforceweobserveisproportionaltothemassofthebodiesweusetoobserveit.Themassofthosebodiesisdominatedbythemassoftheprotonsandneutronsthey’remadefrom.

So if gravity appears feeble—as we’ve seen it does—we can either blamegravity itself for beingwimpy, or blame the protons (and neutrons) for beinglightweights.

Hightheorysuggeststhatweshouldregardgravityasfundamental.Fromthatperspective,gravityjustiswhatitis—itcan’tbeexplainedintermsofanythingsimpler. So if we’re to reconcile theory and practice, the question we mustansweris

Whyareprotonssolight?

Asking the rightquestion isoften thecrucial step towardunderstanding.Goodquestionsarequestionswecancometogripswith.Becausewe’vedevelopedaprofoundunderstandingoftheoriginoftheproton’smass,“Whyareprotonssolight?”isaquestionwe’rereadyfor.

16

ABeautifulAnswer

Whyareprotonssolight?Becauseweunderstandhowthemassofaprotonarises,wecangiveabeautifulanswertothatquestion.Theanswerremovesamajorbarriertoaunifiedtheoryoftheforces,andencouragesustoseeksuchatheory.

LET’S BRIEFLYRECALL how the proton got its mass, with an eye towardfindingsomethingintheprocessthatmakesthemasssmall.(ThisrecapitulatespartofChapter10.)

Aproton’smass isacompromisebetweentwoconflictingeffects.Thecolorchargecarriedbyquarksdisturbsthegluonfieldsaroundthem.Thedisturbanceissmallatfirstbutgrowsasyougetfartherfromthequark.Thesedisturbancesin thegluonfieldcostenergy.Thestablestateswillbe thosewith thesmallestpossibleenergy,sowehavetocancel thesecostlydisturbances.Thedisturbinginfluence of the quark’s color charge can be nullified by an antiquark of theopposite charge nearby, or—the way it’s done in protons—by two additionalquarkswithcomplementarycolors.Putthenullifyingquarkspositionedrightontop of the original quark, and there’d be no disturbance left. That, of course,wouldleadtothe(null)disturbancewiththelowestpossibleenergy(zero).

Quantum mechanics, however, imposes a different energetic cost, whichforces a compromise. Quantum mechanics says that a quark (or any otherparticle)doesnothaveadefiniteposition.Ithasaspreadofpossiblepositions,described by itswave function.We sometimes speak of “wavicles” instead ofparticles, to emphasize that fundamental aspect of quantum theory.To force awaviquarkintoastatewithasmallspreadinpositions,wemustallowitalargeenergy.Inshort,ittakesenergytolocalizequarks.Thecompletenullificationweconsidered in the previous paragraphwould require that the nullifying quarks

havepreciselythesamepositionsastheoriginalquark.Thatwon’tfly,becauseitscostinlocalizationenergyisprohibitive.

So theremust be a compromise. In the compromise solution, there will besomeresidualenergyfromthenot-completely-canceleddisturbanceinthegluonfields, and some residual energy from the not-quite-completely-unlocalizedpositionsofthequarks.FromthetotalEoftheseenergiestheprotonmassarises,accordingtoEinstein’ssecondlawm=E/c2.

Inthisaccount,thenewestandtrickiestelementisthewaythedisturbanceinthegluonfieldgrowswithdistance.Itiscloselyrelatedtoasymptoticfreedom,adiscoverythatrecentlygotthreeluckypeopleNobelPrizes.Asymptoticfreedomisasubtlefeedbackeffectfromvirtualparticles,asIexplainedearlier.Itcanbethoughtofasaformof“vacuumpolarization,”inwhichtheentitywecallemptyspace, the Grid, antiscreens an imposed charge. The Grid Strikes Back, TheRunaway Grid,Grid Gone Wild—it has the makings of a thinking person’shorrormovie.

But the reality is subdued. Antiscreening builds up gradually, especially atfirst. If the seed (color) charge is small, its effecton theGrid startsout small.TheGriditself,byantiscreening,buildsuptheeffectivecharge,sothenextstepin the buildup is a little quicker, and so on.Eventually, the disturbancegrowslargeandthreateningandmustbecanceledoff.Butthatmighttakeawhile—thatis,youmighthavetogetratherfarfromtheseedquarkbeforeithappens.

Ifthedisturbanceisslowtobuild,thenthepressuretolocalizethenullifyingquarksiscorrespondinglymild.Wedon’thavetolocalizeverystrictly.Thustheenergies involved in both the disturbance and the localization are small—andthereforesoisthemassoftheproton.

Andthat’swhyprotonsaresolight!

What I’ve just given you iswhatwe call ahand-wavingexplanation . Youcouldn’tseeme,butwhileIwastypingitIkeptinterruptingmyselftosketchoutcloudswithmy hands, showingmy Italian side. Feynmanwas famous for hishand-waving arguments.Oncehe explainedhis theoryof superfluidhelium toPauli using such arguments. Pauli, a tough critic, was unconvinced. Feynmankept at it, and Pauli stayed unconvinced, until Feynman, exasperated, asked,“Surelyyoucan’tbelieve that everything I’ve said iswrong?”TowhichPaulireplied,“Ibelievethateverythingyou’vesaidisnotevenwrong.”

To make an explanation that might be wrong we have to get much morespecific. When we say protons are light, how light is light? What are thenumbers? Can we really explain the ridiculous feebleness of gravity, which,you’llremember,involvedfantasticallysmallnumbers?

Pythagoras’Vision,Planck’sUnits

Suppose you had a friend in theAndromeda galaxywhom you could contactonly by text-messaging. How would you transmit your vital statistics—yourheight, weight, and age? This friend doesn’t have access to Earth’s rulers orscalesorclocks,soyoucan’tjustsay,“I’mso-and-soinchestall,such-and-suchpounds,andthis-and-thatyearsold.”Youneeduniversalmeasures.

In 1899 and 1900, Max Planck was deeply immersed in the research thatinauguratedthequantumtheory.TheclimaxcameinDecember1900,whenheintroduced the famous constant h—Planck’s constant—that appears in thefundamentalequationsofquantummechanicsweusetoday.Justbeforethat,hegaveanaddresstotheaugustPrussianAcademyofSciencesinBerlin,inwhichheposedessentiallythequestionabove.(Thoughhedidn’tphraseitintermsoftext-messaging.) He called it the challenge of defining absolute units. WhatexcitedPlanck about his researchwas not any sense that hemight unlock thesecrets of the atom, overthrow classical logic, or level the foundations ofphysics.Allthatcamemuchlater,andfromothers.WhatexcitedPlanckwasthathesawawaytosolvetheproblemofabsoluteunits.

The problem of absolute unitsmight sound academic, but it is close to theheartsofphilosophers,mystics,andphilosophicallymindedscientificmystics.

Themanifestooftwentieth-(andtwenty-first-)centurypost-classicalphysicswasissuedlongbeforePlanck,inaround600BCE,whenPythagorasofSamosproclaimed an awesome vision. By studying the notes sounded by pluckedstrings, Pythagoras discovered that the human perception of harmony isconnectedtonumericalratios.Heexaminedstringsmadeofthesamematerial,havingthesamethickness,andunderthesametension,butofdifferentlengths.Under these conditions, he found that the notes sound harmonious preciselywhentheratioofthelengthsofstringcanbeexpressedinsmallwholenumbers.Forexample, the length ratio2:1soundsamusicaloctave,3:2amusical fifth,

and 4:3 a musical fourth. The maxim “All things are number” sums up hisvision.

At this remove, it’s hard to be sure exactly what Pythagoras had in mind.Probablypartofitwasaformofatomism,basedontheideathatyoucouldbuildupshapesfromnumbers.Today’sterminologyofsquaresandcubesofnumbersdescends from that shape building. Our construction of “Its fromBits” richlyfulfillsthepromisethat“Someimportantthingsarenumber.”Inanycase,ifwetakeitliterally,Pythagoras’smaximsurelygoestoofar.Abstractnumberssuchas“3”don’thavealength,amass,oradurationintime.Numbersbythemselvescan’tprovidephysicalunitsformeasurement;theycan’tmakerulersorscalesorclocks.

Planck’s problem of absolute units takes aim at precisely this issue. In thisdigital age we are used to the idea that information, as it appears in text-messaging, can be encoded in a sequence of numbers (indeed, 1s and 0s). SoPlanckwasasking,ineffect:Arenumberssufficient,ifnottoconstructthenatleast to describe every physically meaningful aspect of a material body—inother words, “all things” about it? Specifically, can we convey measures oflength,mass,andtimeusingjustnumbers?

Planck noted that although the Andromedans wouldn’t have access to ourrulers,scales,orclocks,theywouldhaveaccesstoourphysicallaws,whicharethesameastheirs.Theycouldmeasure,inparticular,threeuniversalconstants:

c:Thespeedoflight.

G:Newton’sgravitationalconstant.InNewton’stheory,thisisameasureofthestrengthofgravity.Tobeprecise, inNewton’s lawofgravity, thegravitationalforcebetweenbodiesofmassesm1,m2separatedbydistancerisGm1m2/r2.

h:Planck’sconstant.

(ActuallyPlanckusedaslightlydifferentquantityfromthemodernh,whichhehadn’tinventedyet.)

Fromthesethreequantities,bytakingpowersandratios,onecanmanufactureunitsoflength,mass,andtime.TheyarecalledPlanckunits.Heretheycome:

LP:ThePlancklength.Algebraically,itis .Numerically,itis1.6×10-33

centimeter.

MP :ThePlanckmass.Algebraically, it is .Numerically, it is 2.2×10-5

gram.

TP :ThePlanck time.Algebraically, it is .Numerically, it is5.4×10-44

second.

Obviously Planck units are not very handy for everyday use. The length andtimesareridiculouslytiny,evenfordoingsubatomicphysics.ThePlancklength,for example, is 1/100,000,000,000,000, 000,000 (10-20) times the size of aproton. The Planckmass, 22micrograms, is not entirely impractical. Vitamindosages, for example, are oftenmeasured inmicrograms. So youmight go toyourhealthfoodstoreandlookforpillswithaPlanckmassofvitaminB12.Forfundamentalphysics,however,thePlanckmassisridiculouslybig;itisroughlythemassof10,000,000,000,000,000,000(1019)protons.

Despite their impracticality, Planck was proud that his units are based onquantities thatappear in(presumably)universalphysical laws.Theyare, inhisterms,absoluteunits.Youcanusethemtosolvethatpressingproblemof text-messagingyourvitalstatisticstoafriendinAndromeda.Youjustexpressyourlength,mass,anddurationintime(thatis,yourage)as—big!—multiplesoftheappropriatePlanckunits.

Overthetwentiethcentury,asphysicsdeveloped,Planck’sconstructiontookon ever greater significance. Physicists came to understand that each of thequantities c,G, and h plays the role of a conversion factor, one you need toexpressaprofoundphysicalconcept:

• Special relativity postulates symmetry operations (boosts, a.k.a.Lorentztransformations) thatmixspaceandtime.Spaceandtimearemeasuredindifferentunits,however,soforthisconcepttomakesense,theremustbeaconversionfactorbetweenthem,andcdoesthejob.Multiplyingatimebyc,oneobtainsalength.

•Quantum theory postulates an inverse relation betweenwavelength andmomentum,andadirectproportionalitybetween frequencyandenergy,as aspects of wave-particle duality; but these pairs of quantities aremeasured in different units, andh must be brought in as a conversionfactor.

• General relativity postulates that energy-momentum density inducesspace-timecurvature,butcurvatureandenergydensityaremeasured indifferentunits,andGmustbebroughtinasaconversionfactor.

Within this circle of ideas, c,h, andG attain an exalted status. They are theenablers of profound principles of physics that couldn’t make sense withoutthem.

UnificationScorecard

WiththehelpofPlanck’sunits,wecanassesshowwellourunderstandingoftheoriginoftheproton’smassaccountsforthefeeblenessofgravity,andwhetheritremovesthebarriertounificationthatgravity’sfeeblenessseemedtopresent.

If we are going to produce a unified theory in which special relativity,quantum mechanics, and general relativity are primary components, then weshouldfindthatthemostbasic,underlyinglawsofphysicsappearnaturalwhenexpressedinPlanckunits.Noverylargeorverysmallnumbersshouldoccurinthem.

TherootoftheourtroublewiththeapparentfeeblenessofgravityisthattheprotonmassisverysmallinPlanckunits.Butwe’vecometounderstandthattheprotonmassisnotadirectreflectionofthemostbasiclawsofphysics.Itcomesfroma compromisebetweengluon field energy andquark localization energy.The basic physics behind the proton’s mass—the phenomenon that gets theprocessgoing—istheunderlyingbasicunitofcolorcharge.Thestrengthofthatseed(color)chargedetermineshowfastthegrowingbloomofgluonfieldenergybecomes threatening; and thus how much of a hit, in quantum localizationenergy, quarks must take to cancel it; and thus the value of proton mass,accordingtoEinstein’ssecondlaw.

Isitpossiblethatareasonableseedchargeleadstotheactual,verysmall—inPlanckunits—valueoftheprotonmass?Toanswerthisquestion,ofcourse,wehave to specify what we consider a reasonable value of the seed charge. Tomeasure the strength of the basic seed charge, we need to consider the basicphysicaleffectsitcauses.Wecouldconsideranyofseveraleffects:theforceitgenerates,thepotentialenergy,or(forexperts)thecross-section.Aslongaswemeasureeverythingat thePlanckdistanceusingPlanckunits,we’llgetsimilaranswerswhatevermeasureweuse.Sinceit’sthemostvividandfamiliareffect,let’sfocusontheforce.

So according to Planck, the seed charge is reasonable if it leads to a forcebetween quarks separated by a Planck length that is neither terribly small norterriblylargewhenmeasuredinPlanckunits.Ofcoursehewouldsaythat.ThepointisnottheprestigeofPlanck’sauthoritybuttheidealhisunitsembody:theidealthatspecialrelativity,quantummechanics,andgravity(generalrelativity)canbeunifiedwiththeotherinteractions.We’returningitaroundandaskingif,byassumingthatideal,weareledtoaconsistentunderstandingofwhyprotonsarelight,andthusalsoofwhygravityisfeebleinpractice.

Finally, then, it all boilsdown to avery concretenumericalquestion: Is themagnitude of the seed strong force between quarks, at the Planck length,expressedinPlanckunits,closeto1?

To answer that questionwemust extrapolate the laws of physics we knowdown to distances far smaller than where they have been checkedexperimentally.ThePlanck length isverysmall.Many thingscouldgowrong.Nevertheless, in the spirit of our Jesuit Credo, “It is more blessed to askforgivenessthanpermission,”let’sjustdoit.

The required calculation is actually quite a simple one by the standards ofmoderntheoreticalphysics.We’vediscussedallthenecessaryideasinwords.Itbreaksmyheartnottodisplaythealgebra,butI’mamercifulman,andbesidesmypublisherwarnedmeagainstit.SoI’lljuststatetheresult:

We find that the seed strong force between quarks, at the Planck scale,measured inPlanckunits, isabout1/25.That’squitean improvementover the1/10,000,000,000,000,000,000,000,000,000, 000,000,000,000 discrepancy wethoughtwehad!

Thus we’ve explained the (apparent) feebleness of gravity starting fromfundamental, new, yet firmly based physics. And we’ve overcome a major

obstacleblockingthepathtowardaunifiedtheoryoftheforces.

NextSteps

Ihopeyou’llagreethatit’saprettystory,andithangstogether.Declarationsof“missionaccomplished”havebeenbasedonmuchless.

But it’s unnerving to draw grand conclusions from such a narrow base. It’slikeconstructinganinvertedpyramidbalancedononepoint.Tofirmitup,weneedabroaderbase.

There’snomoreconvincingwaytodemonstratethatyou’veclearedahurdlethantofinishthecourse.Thepathtounificationopensbeforeus.Let’sfollowit.

Plate 1 Photograph taken at the Large Electron-Positron collider (LEP) thatoperated at CERN, nearGeneva, through the 1990s. The jets of particles thatemergefromthiscollisionfollowtheflowpatternspredictedtheoreticallyforaquark,anantiquark,andagluon.Jetsgiveoperationalmeaningtothoseentities,whichcannotbeobservedasparticlesintheusualsense.

Plate2Atwo-jetprocess,whichweinterpretasmanifestationofaquarkandanantiquark.

Plate3Symmetry in science, art, and reality, illustrated through icosahedra. a.Anicosahedronhas20equalsides;allareequilateral triangles.Anicosahedronsupports59distinct symmetryoperations; that is, thereare59distinct rotationsthattakeanicosahedronintoitself(whileinterchangingsomeofthesides).Thiscompares with 2 distinct symmetry operations for an equilateral triangle.Metaphorically,thesymmetryofQCDstandstothatofQEDasthesymmetryof

anicosahedronstandtothatofasingletriangle.b.Enormoussymmetryallowsonetospecifyelaboratestructuresusingsimplecomponents,afeatureviralDNA(or RNA) exploits. Shown here is a virus for the common cold. Note thesimilaritytoa.!

Plate4DeepstructureofthequantumGrid.Thisisatypicalpatternofactivityinthe gluon fields of QCD. These patterns of activity are at the heart of oursuccessfulcomputationofhadronmasses,asdiscussedinChapter9,sowecanbeconfidentthattheycorrespondtoreality.ThisbeautifulimagewascomputedbyDerekLeinweber,UniversityofAdelaide.

Plate5Endresultofaheavyioncollision—aminiatureversionofthebigbang.

Plate6AdisturbanceintheGrid.Attheleft,aquarkandanantiquarkhavebeeninjected. They soon establish a dynamic equilibrium, with the energy of the

disturbanceconfined toa small spatial region,moving through time.TheGridfluctuationshavebeenaveragedover,leavingonlythenetdistributionofexcessenergy.Bytakingaslice,wefindtheenergydistributioninsidetheparticlebeingreproduced: in this case, a πmeson.The total energy gives themass of the πmeson,accordingtoEinstein’ssecondlaw.

Plate7TheSiren’salluringsongasksus to leavecomfortablecertaintybehindand to meet her on a dubious shore. In return, she promises beauty andillumination.Issheteaching,orteasing?

Plate 8Viewof theLHC from the air. The JuraMountains andLakeGenevaframe a mystic scene. Some image processing has been committed here; inrealitythemachineisunderground.

Plate9TheATLASdetectorfor theLHC, inanearlystageofconstruction. Inthefinal,operationalformofthedetector,thisgiganticframeworkgetsdenselypackedwithmagnets,sensors,andultrafastelectronics.Thisiswhatit takestomakeacameracapableofresolvingtimesoforder10-27secondanddistancesof10-17centimeter!

Plate 10 Darkness visible. Dark matter does not emit light; it’s “seen” onlythrough its gravitationalinfluence on the motion of ordinary matter. Throughimageprocessingwecanletoureyesseetheworldasgravitonsdo.ThisROSAT

pictureshowsconfinedhotgashighlightedinfalsepurplecolor.Itprovidesclearevidence for gravity exceeding that exerted by the galaxies inside. The extragravity is attributed to darkmatter. Ideas to improve the equations of physicspredict new forms of matter whose properties make them good dark mattercandidates. Soon we may learn which, if any, of those ideas correspond toreality.

Plate11TheauthorwithnotedbloggerBetsyDevineinsideapieceoftheothermain detector for the LHC,whose acronym is CMS - for Compact (!)Muon

Solenoid.

PARTIII

IsBeautyTruth?

WE’VE FOUND AN EXPLANATION for the feebleness of gravity that islogicalandbeautiful.Butisittrue?Toestablishitstruthandfertility—ornot—we need to embed it in a wider circle of ideas, and draw out testableconsequences.

Natureseemstobehintingthataunifiedtheoryofthefundamentalforcesispossible.Our explanationof the feebleness of gravity fits very comfortably inthat framework. But to consummate the unification fully, in detail, we mustpostulate the existence of a new world of particles. Some of those particlesshouldmaterializeatthegreatLHC(LargeHadronCollider)accelerator,locatednearGeneva.Oneof themmightalsopervade theUniverse,providing itsdarkmatter.

17

Unification:TheSiren’sSong

Theknownparticlesandinteractionspresentafragmentarypattern.Anexpandedtheory,basedonthesameprinciplesbutfeaturinglargersymmetry,bringsthemtogether.

WE’VESEEN thatby following somewell-established lawsofphysicswheretheyleadus,wearriveataprofoundexplanationofoneofthesubject’sclassicproblems:Whyisgravitysofeeble?

Unfortunately, toget to thatanswerwehadtoproject thosewell-establishedlawsdowntodistancesfarsmallerthanthosewecanhopetoexaminedirectly.Equivalently,45wehadtoprojectthelawswehaveuptoenergiesfarlargerthananywecanhopetoexaminedirectly—energiesliterally“millionsofbillions”(1015)timesthosethatthelatestandgreatest,multibillion-euroacceleratorLHCis built to achieve. Thus our explanation is firmly based—on an untestedfoundation!

Weneednotacceptthissituationpassively.Wecansearchforotherwaystoaccess the physics of unification, and to look into ultrashort distances andultrahighenergies.Thedirectpathisblocked.Wecannot,asapracticalmatter,accelerateparticles and smash them together at the required energies.Wecan,however, look for additional signs of unification—unexplained patterns in theworldwedohaveaccessto.

Figure 17.1 The organization of particles and interactions in the Core. Whatleapstotheeyeisthatthequarksandleptonsfallintosixdistinctgroups,andtheinteractionsfallintothreedistinctparts.

Suchpatternsarethere.PleasetakealookatFigures17.1and17.2.

Figure17.1 presents the organization of particles aswe find them—the so-calledstandardmodel(includingQCD).Standardmodelisagrotesquelymodestname for one of humankind’s greatest achievements. The standard modelsummarizes,inremarkablycompactform,almosteverythingweknowaboutthefundamental laws of physics.46 All the phenomena of nuclear physics,chemistry, materials science, and electronic engineering—it’s all there. AndunlikeFeynman’sjocularU=0ortheverbalgymnasticsofclassicalphilosophy,thisfigurecomeswithdefinitealgorithmsforunfoldingsymbolsintoamodelofthephysicalworld. Itallowsyoutomakesurprisingpredictionsand todesign,for example, exotic lasers, nuclear reactors, or ultrafast ultrasmall computermemorieswithconfidence.Notbeinggrotesquelymodest,IwillhenceforthrefertothestandardmodelastheCoretheory.

Figure17.2Theorganizationof thesameparticlesandinteractions,plusmore,into a unified theory.What leaps to the eye is that the quarks and leptons areunifiedintoonewhole,asaretheinteractions.

It would be hard to exaggerate the scope, power, precision, and provenaccuracy of theCore. So Iwon’t even try. TheCore is close toNature’s lastword. It will provide the core of our fundamental description of the physicalworldforalongtime—possiblyforever.

Figure17.2presentsanorganizationofthesameparticlesandtheirpropertiesin a unified theory. It is far fromautomatic that the (established)Core can besubsumedinthe(hypothetical)unifiedtheory.IfthelopsidedshapesthatappearintheCorepatternorthefunnynumbersthathangfromthemweredifferent,itwouldn’t work. You wouldn’t be able to unify them (at least not so neatly).Reading it the otherway: by assuming unification,we explain those lopsidedshapesandfunnynumbers.

Natureissingingaseductivesong.Let’slistenmoreclosely...

TheCore:ChoiceBits

Inearlierchapters,wediscussedthestronginteractionanditstheory—quantumchromodynamics, or QCD—quite a lot. The modern quantum theory ofelectricity and magnetism—quantum electrodynamics, or QED—is both thefatherand thebabybrotherofQCD.Thefather, in thatQEDcameearlierandprovidedmanyoftheconceptsfromwhichQCDgrew;thebabybrother,inthattheequationsofQEDareasimpler,lessformidableversionoftheequationsofQCD.We’vealsodiscussedQEDquitealot.

Intheordinarycourseofnature,thestronginteraction’smainroleistobuildprotonsandneutronsoutofquarksandgluons.Thisalmostneutralizesthecolorcharges,butremainingimbalancesgenerateresidualforcesthatbindprotonsandneutrons together into atomic nuclei. The electromagnetic interaction in turnbinds electrons to those nuclei, producing atoms. This almost neutralizes theelectriccharges,butremainingimbalancesgeneratetheresidualforcesthatbindatomsintomoleculesandmoleculesintomaterials.QEDalsodescribeslightandall its cousin forms of electromagnetic radiation: radio, microwave, infrared,ultraviolet,x-ray,γ-ray.

ThethirdmajorplayerintheCoreistheweakinteraction.Itsroleinnatureismore subtle, but also crucial. The weak interaction performs alchemy. Moreprecisely, it morphs different flavors of quarks into one another, and alsodifferentkindsofleptonsintooneanother.InFigure17.1, theweak interactionmakes transformations in the vertical direction. (The strong interactionmakestransformations in the horizontal direction.) When you change one of the uquarks in a proton into ad quark, the proton becomes a neutron. So changeswrought by theweak interaction transform an atomic nucleus of one elementinto the atomic nucleus of another. Reactions based on weak interaction“alchemy” (a more respectable name is nuclear chemistry) can releaseenormously larger energies than ordinary chemical reactions. Stars live onenergyderivedfromsystematicallybakingprotonsintoneutrons.

Before going into more details about the core of the Core—the strong,electromagnetic, and weak interactions—let me make a few comments aboutwhat I’m (temporarily!) leaving out. There are two big items: gravity andneutrinomasses.

•Aswe’vealreadydiscussed, theapparent feeblenessofgravityprobably

hasmoretodowithourspecialperspectivethanwithgravityitself.Andaswe’llseeoverthenextfewchapters,Natureencouragesustoincludegravitywiththeotherinteractions,asanequalpartnerinunification.

There isnodifficulty, inpractice, includinggravitational interactionsinto the Core. There is a unique, straightforward way to do it, and itworks.(Forexperts:UsetheEinstein-Hilbertactionforthemetricfield,use minimal coupling to the matter fields, and quantize around flatspace.)AstrophysicistsusegeneralrelativitytogetherwiththerestoftheCore routinely, andquite successfully, in their everydaywork.SodoesanyonewhousesGPS.

Inshort:TheusualconventionofseparatinggravityfromtheCoreishandy,butprobablysuperficial.

•Thatneutrinoshavenonzeromasswasestablishedin1998,althoughtherewerehintsgoingback to the1960s.Thevaluesofneutrinomasses areverysmall.Theheaviestofthethreetypesofneutrinoshasnomorethana millionth the mass of the next-lightest particle we know about, theelectron.Neutrinosarefamouslyelusiveandghostly.Roughly50trillionof them pass through each human body every second, without ournoticing.JohnUpdikewroteapoemaboutneutrinos,whichbegins:

Neutrinostheyareverysmall.TheyhavenochargeandhavenomassAnddonotinteractatall.TheearthisjustasillyballTothem,throughwhichtheysimplypass

Nevertheless, by heroic efforts experimentalists have been able to study thepropertiesofneutrinosinconsiderabledetail.47

TheCorewas happywith zero neutrinomasses,which fit into its structureverynaturally.Toaccommodatenonzeroneutrinomasseswemust add innewparticles, with exotic properties, for which there’s no other motivation orevidence.WhenweextendtheCore,tomakeaunifiedtheory,thingswilllookverydifferent.Thenwe’llrecognizethenewparticlesaskinofthoseweknow—prodigalsreturninghome,completingthefamily.Andtheirexoticbehaviorwillhintofadventuresinfar-off,romanticlocales.

Therearealso twocomplications that I’mmostlygoing toglossover.They’rediversions frommycentralmessage, but itwouldbe improper not tomentionthem.Pleasedon’tbeintimidatedorputoffbythesesuperficialcomplications:wemustacknowledgetheirexistence,butwewon’tallowthemtoconfuseourview.

Thefirstcomplicationisthemassesandmixingsofgaugebosons.Inthebasicequations, there are three groups of gauge fields. There are eight color gluonfields,whichyou’vebecomefamiliarwith.Anotherthreeareassociatedwiththeweakinteractionsymmetry.TheyarecalledW+,W-,andW0,andtheyareallsymmetricwithoneanother.Finally, thereisoneisolated“hypercharge”gaugebosonB0.GridsuperconductivitygivesnonzeromassestotheparticlescreatedbyW+,byW-,andbyacertainmixtureofW0andB0.Disturbances in thatmixtureproducethemassiveparticlescalledZbosons.Disturbancesinanothercombination ofW0 and B0 (for experts: the orthogonal combination) remainmassless.ThatmasslesscombinationofW0andB0isthephoton.

Tosummarize:Fromthepointofviewof themathematicsofsymmetry, theW0andB0fieldsarethemostnatural.Butthedisturbanceswithdefinitemass,onceGridsuperconductivityis takenintoaccount, involvemixturesofW0andB0.OnetypeofdisturbanceistheZboson,withnonzeromass;theotheristhephoton,withzeromass.

It is sometimes said the Core unifies electromagnetism and the weakinteraction.Thatismisleading.Therearestilltwodistinctinteractionsinvolved,associatedwithdifferentsymmetries.Theyaremixed,ratherthanunified,intheCoretheory.

The second complication is the masses andmixings of quarks and leptons.Theseparticlescomeinthreedifferentvarieties,or“families.”Thusbesidesthelightest family,whichcontainsuanddquarks, theelectrone, and theelectronneutrinoν , thereare twoheavierones.The second familycontains thecharmandstrangequarkscands, themuonμ,andthemuonneutrinoνμ.Finally, thethirdfamilycontainsthetopandbottomquarkstandb,thetauleptonτ,andtheτneutrinoντ.

Like the gauge bosons, all these particles would be massless but for Grid

superconductivity. But Grid superconductivity gives them mass48 and alsoallows the heavier ones to mix with, and thereby decay into, lighter ones incomplicated ways. These masses and mixings are extremely interesting toexperts, and understanding their values is an unmet challenge for theoreticalphysics.Alsonotunderstoodatallisthesimplerquestion:Whyaretherethreefamiliestobeginwith?

Because Idon’thaveanyverygood ideasabout those issues, Iwon’twastewordsbyinsistingontheirdetails.TheywouldonlyadddistractingnoisearoundthegoodideasIdowanttodiscuss.SoI’llkeepthingsassimpleaspossible—ormaybe even a little simpler. Tolstoy’s Anna Karenina famously opens, “Allhappyfamiliesarehappyinthesameway.”Thatbeingthecase,we’llfocusonjustone.

Phew! It’sacomplicatedbusiness,getting to simplicity.Butafterwe’veputthosetwooddgiftsofgravityandneutrinomassesintotemporarystorageintheattic, tidiedupafter themix-upsmadebyGrid superconductivity, anddecidedthatonefamilyisenough,aclearandunclutteredimageemerges.ItiswhatyouseeinFigure17.1.ThisisthecoreoftheCore.

Therearethreesymmetries,SU(3),SU(2),andU(1).Theycorrespond to thestrong,weak,andelectromagneticinteractions,49respectively.

SU(3) is a symmetry among three kinds of color charge, as we’ve alreadydiscussed.Itcomestogetherwitheightgaugebosonsthatchangeorrespondtothecolorcharges.ItactsinthehorizontaldirectioninFigure17.1.

SU(2) isasymmetryamongtwoadditionalkindsofcolorcharges. Itacts intheverticaldirectioninFigure17.1.

You’llnoticethateachoftheparticlesontheleftislistedtwice.EachoccursonceinagroupwiththesubscriptLandonceinagroupwiththesubscriptR.Thesesubscriptsrefertothehandedness,orchirality,oftheparticles:Lforleft-handed,Rforright-handed.ThehandednessofaparticleisdefinedasinFigure17.3. Left-handed and right-handed particles interact differently. This fact iscalledparityviolation.ItwasfirstrealizedbyT.D.LeeandC.N.Yangin1956,andthatdiscoveryearnedthemaNobelPrizeintheleastpossibletime,in1957.

Figure17.3Thehandedness,orchirality,ofaparticleisdeterminedbydirectionofitsspinrelativetoitsdirectionofmotion.

U(1)dealswithonlyonekindofcharge.Wespecifyitsactiononthedifferentparticles according to how strongly, and with what sign, its one boson—essentially,thephoton—couplestoeach.Thelittlenumbersdanglingfromeachgroupingofparticlesspecifyexactly that, for theparticles in thegrouping.Forexample, theright-handedelectronhasa-1becauseitselectricchargeis-1(inunitswheretheproton’schargeis+1).Thebiggestgrouping,withsixmembers,hasu and d quarks with each of the three color changes. The u quarks haveelectriccharge⅔, thedquarkshaveelectriccharge—⅓,so theaverageelectricchargewithinthegroupis1/6,whichisthenumberyousee.

Andthat’sit.AsIsaidbefore,itwouldbedifficulttooverstatethepowerandscopeoftheCore.Therulesmightappearalittlecomplicatedatfirst,butthosecomplicationsarenothingcomparedto(forinstance)theconjugationsofafewirregularverbsinLatinorFrench.Andunlikethelatter,thecomplicationsoftheCorearenotgratuitous.Theyareforcedonusbyexperimentalrealities.

Critique

ThescoreofNature’ssong,aswehearit,isFigure17.1.We’verecordedit,andwe’vebeenabletocompresstherecordingintoanextremelycompactform.It’sagreatachievementsummingupcenturiesofbrilliantwork.

Judgedbythehighestestheticstandards,however,there’splentyofroomforimprovement. Salieri, looking at this score,would definitely not bemoved toexclaim, “Displace one note and there would be diminishment.” More likelyhe’dsay,“Interestingsketch,butitneedswork.”

Orperhaps,knowingthathewasviewingtheworkofamaster,Salierimightexclaim,“NaturecertainlyleftHerworkwithaquirkycopyist!”

First of all, there are three unconnected interactions.They are based on thesameprinciplesofsymmetryandresponsetocharges,butthechargesinvolvedfall into threedistinctgroups thatcan’tbe transformedintooneanother.Therearetransformations(involvingthecolorgluonsofQCD)thattransformthered,white, and blue color charges among themselves, and there are separatetransformations (involving theW andZ bosons) that transform the green andpurple color charges into one another. And electric charge is a separate thingaltogether.

Worse,thedifferentquarksandleptonsfallintosixunrelatedclusters.Andtheclusters aremostly unimpressive: one contains 6members, but the others aremere hints of motifs, with 3, 3, 2, 1, and 1 members, respectively. Mostdiscordant are those funny numbers, the average electric charges attached toeachcluster.Theyseemprettyrandom.

TheChargeAccount

Fortunately, the Core contains the seeds of its own transcendence. Its rulingprinciple is symmetry, and symmetry is a concept we can build on by purethought,justusingournoodles.Wecanplaywiththeequations.

For example,we can imagine that there are transformations that turn strongcolorchargesintoweakones,andviceversa.Thiswillgeneratebiggerclustersof relatedparticles,andmaybe they’ll click intoattractivepatterns. In thebestcase,wemighthopethatthethreedistinctsymmetrytransformationsofSU(3)×SU(2)×U(1) aredifferent facetsofone larger,master symmetry that includesthemall.

Themathematicsofsymmetryiswelldeveloped,sotherearepowerfultoolsfor thiskindofpatternrecognitiontask.Therearen’tmanypossibilities,sowecantrythemoutsystematically.

The master symmetry I find most convincing is based on a group oftransformations known as SO(10). All the attractive possibilities are minorvariantsofthisone.

Mathematically, SO(10) consists of rotations in a ten-dimensional space. Ishouldemphasizethatthis“space”ispurelymathematical.It’snotaspacethatyou could move around in, even if you were very small. Rather, the ten-dimensional space of SO(10), the master symmetry that absorbs the SU(3) ×SU(2)×U(1) of theCore—that unifies, inotherwords, the strong,weak, andelectromagneticinteractions—isahomeforconcepts.Inthisspace,eachofthecolorchargesoftheCore(red,white,blue,green,andpurple)isrepresentedbyaseparatetwo-dimensionalplane(sothereare5×2=10dimensionsaltogether).Becausetherearerotationsthatmoveanyplaneintoanyother,theCorechargesandsymmetriesgetunifiedandexpandedinSO(10).

Mathematicalsophisticateswillnotfind itsurprising thatsymmetriescanbecombined into larger symmetries. As I said, the tools for doing that are welldeveloped.Whatismuchlessautomatic,andthereforemuchmoreimpressive,isthat the scattered clusters of quarks and leptons fit together. This is what isdisplayedinFigure17.2.ItiswhatIliketocalltheChargeAccount.

IntheChargeAccount,allthequarksandleptonsappearonanequalfooting.Anyof themcanbe transformed into anyother.They fall into a very specificpattern, theso-calledspinor representationofSO(10).Whenwemakeseparaterotations in the two-dimensional planes, corresponding to the red,white, blue,green, and purple charges,we find in each case that half the particles have apositiveunitofcharge,halfanegativeunit.Theseappearasthe+and-entriesin the Charge Account. Each possibility for combinations of + and - occursexactlyonce,subjecttotherestrictionthatthetotalnumberof+chargesiseven.

Theelectriccharges,whichwithintheCoreappeartoberandomdecorations,become essential elements in the harmony of unification. They are no longerindependentoftheothercharges.Theformula

expresseselectriccharge—moreprecisely,hypercharge—intermsoftheothers.Thusthetransformationsassociatedwithelectricchargerotationturneachofthefirstthreeplanesthroughsomecommonangle,andturnthelasttwothrough3/2-biganangle,intheoppositesense.

To accomplish this degree of unification,wemust realize that right-handedparticles can be regarded as the antiparticles of their own (left-handed)antiparticles. For example, the right-handed electron is the antiparticle of theleft-handedpositron.Thesedescriptionshavethesamephysicalcontent,becausebothaparticleanditsantiparticleareexcitationsinthesamefield,anditisthefield that appears in the primary equations. Symmetry transformations amongthe fields relate excitationsof the samehandedness, so to findall thepossiblesymmetries, we deal with left-handed excitations only (even if that meansworkingwithantiparticles).

When we descend from Charge Account to Core, we must realize thatcomplementary color charges cancel. Equal amounts of red, white, and bluecharge—orequalamountsofgreenandpurplecharge—canceltonothing.Thus,for instance, the three equal (+) red,white, andblue color chargesof the left-handed electron e cancel. They cancel in the right-handed electron, which isrepresented in the Charge Account by its left-handed antiparticle ec as well.ElectronsofeithersortareinvisibletothecolorgluonsofQCD.Inotherwords,electronsdonotparticipateinthestronginteraction.

Themost singular entry in the ChargeAccount is the last one,N. Both itsstrong color charges and itsweak color charges cancel. Thus it is invisible toboththestrongandtheweakinteractions.Itselectricchargeisalsozero.Sothisparticledoesn’t respond to anyof theconventionalCore forces.Thatmakes ithopelesslydifficulttodetect—worsethanneutrinos,whichatleastparticipateinthe weak interaction. (N does both feel and exert gravity, but for practicalpurposes the gravity of individual particles is ridiculously feeble, as we’vediscussed.)

Sureenough,Nhasnotbeenobserved.Howcoulditbe?Ifweobserveit, itcan’t beN, which by definition is unobservable! That “triumph” of theory ishollow,ofcourse.ButN iswelcomeforamorepositivereason. It is theextraparticleνR that, when added to theCore, allows the neutrino to have its tinymass.50

The left-hand column of the Charge Account specifies the names of theparticles—the quarks and leptons—thatwe use to construct theCore, and theworld.Butreally,wecoulddeletethatcolumn.Ifwedidn’tknowthenamesofthose particles or anything about their properties, and had only the unlabeledChargeAccount,nothingwouldbelost.Wecouldreconstruct thepropertiesofalltheparticles,fromtheinformationintheChargeAccount(andofcoursetheirnamesarejustaconvenience).

Conversely, if theCoreclustershadslightlydifferentshapes,or if thefunnynumbersthatdangledfromthemweredifferent,thepatternwouldfail.

TheChargeAccountmapsthemathematicallyidealtothephysicallyreal.ItisfullyworthyofSalieri’shighestaccolade:“Displaceonenoteandtherewouldbediminishment.Displaceonephraseandthestructurewouldfall.”

TheSiren’sSong

The Sirens ofmyth sing entrancing songs from rocky coasts, luring sailors toshipwreck and destruction. Their song promises knowledge of secrets, of thepastandofthefuture.Theypromise“allthatcomestopassonthefertileearth,weknowitall!”JaneEllenHarrisoncomments,“ItisstrangeandbeautifulthatHomershouldmaketheSirensappealtothespirit,nottotheflesh.”

We’veheardaSiren’ssongofunification.

18

Unification:ThroughaGlass,Darkly

Thehighersymmetrythatunifiesthebasicparticlesalsopredictsequalityamongthedifferentbasicinteractions.Thatprediction,onthefaceofit,isquitewrong.ButwhenwecorrectforthedistortingeffectofGridfluctuationsitcomesclose.

WE’VEHEARDASIREN’SSONGOFUNIFICATION.Nowit’stimetoopenoureyes,toseewhetherwecannavigatetherockycoastswhereshedwells.

SymmetryNot

Theenhancedsymmetryofunificationdoessomegreatthings.Itassemblesthescattered pieces of the Core into well-proportioned wholes. Once our visionaccommodatestothatdazzlingfirstimpression,however,andwebegintolookmorecarefully,thingsdon’tseemright.

In fact, somethingverybasic appears to bewrong. If the strong,weak, andelectromagnetic forces are aspects of a commonunderlyingmaster force, thensymmetry requires that theyshouldallhave thesamestrength.But theydon’t.Figure18.1showsthis.

Figure 18.1 Perfect symmetry would require the strong, weak, andelectromagnetic forces to have equal strengths. They don’t. For laterconvenience, here I’ve used the inverse square of the couplings as thequantitativemeasureoftheirrelativepower.Sothestronginteraction,whichisthestrongest,appearsonthebottom.

There’s a reason why the strong interaction is called strong and theelectromagnetic interaction isn’t.Thestrong interaction really is stronger!Onemanifestationof thedifferenceis thatatomicnuclei,boundtogetherbystrong-interaction forces, are much smaller than atoms, held together byelectromagneticforces.Thestrongforcesholdnucleitogethermoretightly.

Themathematics of theCore theory enables us to give a precise numericalmeasureoftherelativestrengthofdifferentinteractions.Eachofitsinteractions—strong, weak, electromagnetic—has what we call a coupling parameter, orsimplyacoupling.

In termsofFeynmangraphs, the coupling is a factorbywhichwemultiplyeachhub. (Theseuniversal,overallcouplingfactorscomeon topof thepurelynumerical values of the color or electromagnetic charges of the particularparticles involved, as encoded in the Charge Account.) So each time a colorgluonappearsinahub,wemultiplythecontributionoftheprocessdepictedbythe strong coupling; each time a photon appears, we multiply by theelectromagnetic coupling. The basic electromagnetic force comes fromexchanging a photon (Figure 7.4), so it has the square of the electromagneticcoupling.Similarly,thebasicstrongforcecomesfromexchangingagluon,soithasthesquareofthestrongcoupling.

Complete symmetry among the forces requires every hub to be related toevery other. It leaves no room for differences among the couplings. Theobserved differences, therefore, pose a critical challenge to thewhole idea ofachievingunificationthroughsymmetry.

CorrectingOurVision

AgreatlessonfromtheCoreisthattheentityweperceiveasemptyspaceisinreality a dynamic medium full of structure and activity. The Grid, as we’ve

called it, affects thepropertiesofeverythingwithin it—that is, everything.Weseethingsnotastheyare,butasthroughaglass,darkly.Inparticular,theGridisaboil with virtual particles, and these can screen or antiscreen a source. Thatphenomenon, for the strong force, was central to the stories that unfolded inPartsIandII.Itoccursfortheotherforcestoo.

Sothecouplingvaluesweseedependonhowwelook.Ifwelookcrudely,wewill not discern the basic sources themselves, but will see their image asdistorted by the Grid. We will, in other words, see the basic sources mixedtogetherwith the cloud of virtual particles that surround them, unresolved.Tojudge whether perfect symmetry and unity of the forces occurs, we shouldcorrectforthedistortions.

Toseedownto thebasics,wemayneed to resolveveryshortdistancesandveryshorttimes.That’sanoft-repeatedlesson,fromvanLeeuwenhoekandhismicroscopes, to Friedman, Kendall, and Taylor using their ultrastroboscopicnanomicroscope at SLAC to look inside protons, to experimenters using thecreativedestructionmachineLEPtodigintoGrid.Aswesawinconnectionwiththosetworecentprojects,toresolveextremelyshortdistancesandtimes,wherequantum theory comes into play, it’s necessary to use probes that activelytransfer large amounts of momentum and energy to the object being probed.That’swhyhigh-energyaccelerators,despite theirexpenseandcomplexity,aretheinstrumentsofchoice.

ANearMiss

AswediscussedinChapter16,thevirtualparticlecloudscanbeslowtobuild.For the cloud around a quark to grow from a reasonable-sized seed tothreateningproportions,ithadtoevolvefromthePlancklengthtotheproton’ssize:afactorof1018indistance!

Given that experience,we should not be surprised to find that to get to thebasics—to see down to the distanceswhere unificationmight take place—wemightneed to transferoutlandishamountsofmomentumandenergy.Thenextgreat accelerator, the LHC,will give us ten times better resolution—that is, afactorof101—atacostofroughlytenbillioneuros.Andafterthat,itgetsreallydifficult.

Figure18.2CorrectingforGriddistortions,toseewhethertheforcesunify.Ifweplotthingsinthisway—withinversecouplingssquaredascendingintheverticaldirectionversuslogarithmofenergyor(equivalently)ofinversedistanceinthehorizontal direction—then the corrected couplings, viewed at better and betterresolution,trackstraightlines.Thesizeoftheexperimentalerrorsisindicatedbythewidthofthelines.Italmostworks,butnotquite.

So we have to use our noodles instead. Though not as foolproof, they’rerelativelycheap,andreadyathand(sotospeak).Withafewstrokesofapen,wecancalculatetheeffectsofGriddistortionandcorrectforthem.

TheresultisdisplayedinFigure18.2.

AsHomerSimpsonmightsay:

D’Oh!

Itdoesn’tquitework.Close,butnocigar.

Whattodo?

19

Truthification

Whenanattractiveideaisclosetobeingright,wetrytofindwaystomakeitright.Welookforwaystotruthify.

THEFAMOUSPHILOSOPHERKARLPOPPERemphasizedtheimportanceoffalsifiabilityinscience.Themarkofscientifictheories,accordingtoPopper, isthat theymakestatements—predictions—thatmightbefalse.IsPopper’sclaimtrue?Well,canyoufalsifyit?

Maybe it’s a profound truth. Reppopism—the opposite of Popperism—saysthatthemarkofagoodscientifictheoryisthatyoucantruthifyit.Atruthifiabletheorymightmakemistakes,butif it’sagoodtheorythey’remistakesyoucanbuildon.

In a crucial way, falsifiability and truthifiability are two sides of the samecoin.Bothvaluedefiniteness.Theworstkindoftheory,onbothaccounts,isnotatheorythatmakesmistakes.Mistakes,youcanlearnfrom.Theworstkindoftheoryisatheorythatdoesn’teventrytomakemistakes—atheorythat’sequallyreadyforanything. Ifeverything isequallypossible, thennothing isespeciallyinteresting.

In terms of our Jesuit Credo, “It is more blessed to ask forgiveness thanpermission,” a falsifiable theory asks permission, a truthifiable theory asksforgiveness—andanunscientifictheoryhasnosenseofsin.

The ideas of pattern recognition and description compression that wediscussed earlier give a different perspective on these issues (and, I think, godeeper).Iftheprocessingofeverypixelresultsinamiddlingshadeofgray,noimagewillemergefromarawexposure.Similarly,inordertorecognizepatternsinourexposuretothephysicalworld,againstthebackgroundofeverythingthatcould be imagined, our candidate theories must distinguish possible from

impossible (according to the theory).Only thencanwecolor themdifferently,and only then will our observations give us a picture we can work with—apicturewithcontrast.

Ifwearedefiniteandmanagetogetalotofpixelsright,ausefulimagecanemerge even if there are a few mistakes too. (We can touch it up withPhotoshop.)Thus there’sapremiumonambition—that is,onbringinga lotofpixelsintothepicture(or,inourmetaphor,alotoffactstobear)—aswellasonaccuracy. Enough metaphors and generalities! On to a case study intruthification.

UppingtheAnte:MoreUnification

Our ambitious attempt to unify the strong, electromagnetic, and weakinteractionsdidn’tquitework.Wesucceededinproducingatheorythatwasnotjut falsifiable but outright false. Very scientific, says Sir Karl Popper. Butsomehow,wearenotleftfeelinggratified.

Whensuchanattractiveandnearlysuccessfulideadoesn’tseemquiteright,itmakessensetotrytorescueit.Welookforwaystotruthifyit.

Maybe, inourquestforunification,wehaven’tbeenambitiousenough.Thesoulofourunificationofdifferentchargesisthis:

(1)

This still leaves the building blocks of the world divided into two separateclasses.Canwegofurther?Canwedothis?

(2)

Let’stry.

20

Unification♥SUSY

Whenweexpandtheequationsofphysicstoincludesupersymmetry,weenrichtheGrid.ThuswemustrecalibrateourcalculationofhowtheGriddistortsourviewofunification.Whenwemakethecorrection,asharpimageofunificationcomesintofocus.

BYPERFECTINGOUREQUATIONS,weenlargetheworld.

Inthe1860s,JamesClerkMaxwellassembledtheequationsforelectricityandmagnetism as they were understood at the time, and found that they led tocontradictions.51Hesawthathecouldmakethemconsistentifheaddedanewterm.Thenewterm,ofcourse,correspondstoanewphysicaleffect.Someyearsbefore,MichaelFaraday (inEngland)andJosephHenry (in theUnitedStates)had discovered that whenmagnetic fields change in time, they create electricfields. Maxwell’s new term embodied the converse effect: changing electricfieldsproducemagneticfields.Combiningthoseeffects,wegetadramaticnewpossibility: changing electric fields produce changing magnetic fields, whichproducechangingelectricfields,whichproducechangingmagneticfields,....You can have a self-renewing disturbance that takes on a life of its own.Maxwellsawthathisequationshadsolutionsofthiskind.Hecouldcalculatethespeedatwhichthesedisturbanceswouldmovethroughspace.Andhefoundthattheymoveatthespeedoflight.

Being a very bright fellow, Maxwell leaped to the conclusion that theseelectromagnetic disturbancesare light.That idea has held up to this day,withmany many fruitful applications. It remains the foundation of our deepestunderstandingofthenatureoflight.Butthere’smore.Maxwell’sequationsalsohave solutions with smaller wavelengths than those of visible light, and withlarger wavelengths. So the equations predicted the existence of new kinds of

things—newkindsofmatter,ifyoulike—thatweren’tknownatthetime.Thesearewhatwenowknowasradiowaves,microwaves,infrared,ultraviolet,x-rays,γ-rays—each a significant contributor tomodern life, each an immigrant fromconceptworldtophysicalworld(c-worldtop-world).

In the late 1920s, Paul Dirac was working to improve the equation thatdescribes electrons in quantum mechanics. A few years before, ErwinSchrödingerhadformulatedanelectronequationthatworkedverywellinmanyapplications. But theoretical physicists were not entirely satisfied withSchrödinger’selectronequation,because itdoesnotobeythespecial theoryofrelativity.Itisaquantum-mechanicalversionofNewton’sforcelaw;itobeystheoldmechanicalrelativityratherthanEinstein’selectromagneticrelativity.Diracfoundthattomakeanequationconsistentwithspecialrelativity,hehadtousealarger equation than Schrödinger’s. Like Maxwell’s perfected equations forelectricity and magnetism, Dirac’s perfected equation for electrons had newkinds of solutions: besides the solutions that correspond to electrons movingwithdifferentvelocitiesandspinning indifferentdirections, therewereothers.Aftersomestrugglesandfalsestarts,andwithsomehelpfromHermannWeyl,by1931Dirachaddecipheredthemeaningofthesestrangenewsolutions.Theyrepresentanewkindofparticle,withthesamemassastheelectronbutoppositecharge. Just such a particle was discovered soon thereafter, in 1932, by CarlAnderson.Wecallittheantielectron,orpositron.Nowadaysweusepositronstomonitor what’s happening inside brains (via the PET scan, a.k.a. positron-electrontomography).

Therearemanyotherrecentexampleswherenewformsofmatterappearedinourequationsbefore theyappeared inour laboratories. In fact, it’sbecometheusualcase.Quarks(bothasageneralconcept,andthespecificc,b,andtflavorvarieties),colorgluons,WandZbosons,andall threekindsofneutrinoswereseenfirstassolutionsofequations,andonlylaterasphysicalrealities.

The search is on for other talented inhabitants of c-world thatwe’d like torecruitintop-world,notablyHiggsparticlesandaxions.Itbreaksmyheartnottodescribethemindetailhere,butthatwouldrequiretwomajordigressions, justaswe’rebuildingtoaclimax.Youcanfindmoreinformationandreferencesonthemintheglossaryandendnotesand,fortheHiggsparticle,alsoinAppendixB.

For our story, the most important proposed expansion of the equations of

physics is supersymmetry, often fondly called SUSY. Supersymmetry, as thenamesuggests,proposesthatweshoulduseequationswithlargersymmetry.

SUSY’snewsymmetryisrelatedtotheboostsymmetryofspecialrelativity.Asyoumayrecall,boost symmetrysays that thebasicequationsdon’tchangewhen you impart a common, constant velocity to all the components of thesystemyou’redescribing.(DirachadtomodifySchrödinger’sequationtogiveitthat property.) Supersymmetry likewise says that the equations don’t changewhenyouimpartacommonmotiontoallthecomponentsofthesystemyou’redescribing.Butit’saverydifferentkindofmotionfromwhat’sinvolvedinboostsymmetry. Instead ofmotion through ordinary spacewith a constant velocity,supersymmetryinvolvesmotionintonewdimensions!

Before you get carried away with visions of spirit worlds and wormholesthroughhyperspace, letmehasten toadd that thenewdimensionshaveaverydifferent character from the familiar dimensions of space and time. They’requantum dimensions.What happens to a bodywhen itmoves in the quantumdimensionsisn’tthatitgetsdisplaced—there’snonotionofdistanceoutthere—instead,itsspinchanges.The“superboosts”turnparticleswithagivenamountof intrinsic spin into particles with a different amount of spin. Because theequations are supposed to stay the same, supersymmetry relates properties ofparticleswithdifferentspin.SUSYallowsus tosee themas thesameparticle,movingindifferentwaysthroughthequantumdimensionsofsuperspace.

YoucanvisualizethequantumdimensionsasnewlayersoftheGrid.Whenaparticlehopsintotheselayersitsspinchanges,andsodoesitsmass.Itscharges—electric,color,andweak—staythesame.

SUSYmightallowustocompletetheworkofunifyingtheCore.Unificationofthedifferentcharges,usingthesymmetrySO(10),unitedallthegaugebosonsintoacommoncluster,andallthequarksandleptonsintoacommoncluster.Butnoordinarysymmetryiscapableofjoiningthosetwoclusters,fortheydescribeparticles with different spins. Supersymmetry is the best idea we have forconnectingthem.

CorrectingtheCorrection

Afterexpandingtheequationsofphysicstoincludesupersymmetry,wefindthat

theyhavemoresolutions.JustaswithMaxwell’sandDirac’sequations,thenewsolutions represent new forms of matter—new kinds of fields and, as theirexcitations,newkindsofparticles.

Supersymmetryrequiresus,roughlyspeaking,todoublethenumberoffieldswe have in our equations. Alongside every field we know about, off in thequantumdimensions,isanewpartnerfielddescribingactivityinthenewlayerofGrid.Theparticlesassociatedwiththesenewfieldshavethesamecharges(ofallkinds)astheirknownpartners,butdifferentmassesandspins.

Itmaysoundrecklessandextravaganttoinferadoublingoftheworldbasedonestheticconsiderations.52Maybeitis.ButDirac’sintroductionofantimatterinvolved a similar doubling, andMaxwell’s enlargement of theworld of lightfrom the visible band to the infinite expanse of the electromagnetic spectrumwasevenlarger.Bothwere—atthetimeoftheirconception—essentiallyestheticgambits. So physicists have learned to be bold. It is more blessed to askforgivenessthanpermission.Thusendeththeapology;nowbacktobusiness.

Thenew,partnerparticlesmustbeheavierthantheirobservedsiblings,orelsethey’dalreadyhavebeenobserved.Butwe’llassumethatthey’renottoomuchheavier,andseewherethatleads.53

Fluctuations in these new fields permeate theGrid. They are new kinds ofvirtualparticles,whichcontribute to thescreeningandantiscreeningofstrong,weak, and electromagnetic sources. To see our way to the basics, at shortdistancesorhighenergy,wehavetocorrectourvision,toremovethedistortingeffect of that bubbly medium.We tried to make such a correction before, inChapter18,without takingintoaccount thesepossiblenewcontributions.Nowwemustcorrectthecorrections.

Figure20.1displaystheresult.WithSUSYonboard,itworks.

GravityToo

We can also bring gravity into the game. Gravity, as we’ve seen, starts outridiculously feebler than the other forces. Looking at Figure 20.1, at the left-handside,correspondingtothedistancesandenergieswecanaccessinpractice,we see that the difference in power between the strong and electromagnetic

forces is roughly a factor of 10. So they fit easily, together with the weakinteraction, into a nice tidy plot. Gravity doesn’t come close to fitting in.Becauseit’sfeeblerandwe’replottinginversepower,gravityshouldappearuphigher than the others. But to include it at this scale,we’d need tomake ourfigurefarlargerthantheknownuniverse!

Figure 20.1 Supersymmetry requires expanding the equations of physics toincludenewfields.Gridfluctuationsduetothesenewfieldsdistortourviewofthe most basic, underlying physical process. After we correct for thosedistortions, we find accurate unification at short distances or, equivalently, athighenergies.

Ontheotherhand...

For the Core forces—the strong, weak, and electromagnetic forces—thecorrections as we go to the right, toward much shorter distances or higherenergies, are fairly modest (and remember, each tick on the horizontal axisrepresents a factor of 10). Those corrections, after all, arose from a subtlequantum-mechanical effect: screening (or antiscreening) due to Gridfluctuations.Whenwe look at gravity at very short distances, by transferringverylargeamountsofenergy,thechangeismuchmoredrastic.AswediscussedwaybackinChapter3,gravityrespondsdirectlytoenergy.Itspower,asdefined

here,isproportionaltoenergysquared.Allowingforthateffect,wecancalculatethepowerofgravityatshortdistancesandcompareitwiththeotherinteractions.Figure 20.2 displays the result. From well outside the known universe, theinversepowerofgravitydescendstojointheotherinteractions,prettynearly.

Figure20.2Gravitystartsridiculouslyfeeble,butatshortdistancesitapproachestheotherinteractionsinpower;andtheyallcometogether,prettynearly.

21

AnticipatingaNewGoldenAge

We’vemadeourcaseforunification.NowitgoesouttoNature,theultimatejury.Weawaitverdictsfromaccelerators,fromthecosmos,andfromdeepunderground.

WE’VESEENTHATTHETHEORIESoftheCoreforces,eachdeeplybasedonsymmetry,canbecombined.ThethreeseparateCoresymmetriescanberealizedaspartsof a single, all-encompassing symmetry.Moreover, that encompassingsymmetrybringsunityandcoherencetotheclustersoftheCore.Fromamotleysix,weassemble the faultlessChargeAccount.Wealsodiscover thatoncewecorrectforthedistortingeffectofGridfluctuations—andafteruppingtheantetoincludeSUSY—thedifferentpowersoftheCoreforcesderivefromacommonvalueatshortdistances.Evengravity, thathopelesslyfeeblemisfit,comesintothefold.

To reach this clear and lofty perspective, we made some hopeful leaps ofimagination. We assumed that the Grid—the entity that in everyday life weconsider empty space—is a multilayered, multicolored superconductor. Weassumed that the world contains the extra quantum dimensions required tosupportsupersymmetry.Andweboldlytookthelawsofphysics,supplementedwith these two “super” assumptions, up to energies and down to distances farbeyondwherewe’vetestedthemdirectly.

Fromtheintellectualsuccesssofarachieved—fromtheclarityandcoherenceof this vision of unification—we are tempted to believe that our assumptionscorrespondtoreality.Butinscience,MotherNatureistheultimatejudge.

Afterthesolarexpeditionof1919confirmedhispredictionforthebendingoflightbytheSun,areporteraskedAlbertEinsteinwhatitwouldhavemeantiftheresult had been otherwise.He replied, “ThenGodwould havemissed a great

opportunity.”Naturedoesn’tmiss suchopportunities. I anticipate thatNature’sverdicts in favor of our “super” ideas will inaugurate a new golden age infundamentalphysics.

TheLHCProject

NearGeneva,at theCERNlaboratory,protonswillracearounda27-kilometercircumference tunnel at 0.999998 times the speed of light. There will be twotight beams flowing in opposite directions. Theywillmeet at four interactionpoints,where detectors the size of five-story office buildingswillmonitor theexplosiveoutputofcollisions.ThisistheLargeHadronCollider(LHC)project.Togetanimpressionofthesizeoftheacceleratorandakeydetector,seeColorPlates8,9,and11.

Insheersize,theLHCisourcivilization’sanswertothepyramidsofancientEgypt.Butitisanoblermonumentinmanyways.Itisbornoutofcuriosity,notsuperstition.Itisaproductofcooperation,notcommand.

And LHC’s gigantic scale is not an end in itself, but a side effect of itsfunction.Indeedtheoverallphysicalscaleoftheprojectisnotitsonly,orevenitsmost,impressivedimension.Insidethelongtunnelareexquisitelymachinedand aligned superconducting magnets. Each of these powerful giants is 15meters long, yet built to submillimeter tolerances. Precise timing is alsoessential, in the electronics. In separating the collisions and tracking theparticles,nanosecondscount.

The flowof raw information that gushes out is not onlymind-boggling butcomputernetwork-boggling.ItisestimatedthatLHCwillproduce15petabytes(1.5×1015bytes)ofinformationperyear.Thisisequaltothebandwidthallotedhalf a million telephone conversations running all at once, nonstop. Newarchitectures thatallowthousandsofcomputersaround theworld todivide theloadarebeingdevelopedtocopewithit.Thisisthe(computer)Gridproject.

TheLHCwillachieveconcentrationsofenergy largeenough to testbothofourtwo“super”assumptions.

Wecanmakeaprettyreliableestimateofwhatittakestoknocklooseapieceof the condensate responsible for the Grid’s (electroweak) superconductivity.

Theweak force is short-ranged,butnot infinitely so.TheWandZ bosons areheavy, but not infinitely so.The observed rangeof the force, andmass of theforce carriers, give us good handles on the stiffness of the condensateresponsibleforthoseeffects.Knowingthestiffness,wecanestimatehowmuchenergyweneedtoconcentrateinordertobreakoffindividualpieces(quanta)ofthe condensate—or, in more prosaic terms, to make the Higgs particle orparticles or sector or whatever kind of new stuff it is that makes the Grid acosmic superconductor. Unless our ideas are somehow very wrong, the LHCshouldbeuptothejob.

It’s a similar story for supersymmetry. We want the Grid fluctuationsassociatedwiththenewSUSYpartnerfieldstobringtheunificationofcouplingpowers into line. If they’re todo that job, then the excitations associatedwiththose fields can’t be too stiff. Some of their excitations—some new SUSYparticles,partnersofparticlesthatweknow—mustbeproducedanddetectedatLHC.

IfSUSYpartnerparticlesdoshowup, they’llgiveusnewwindowsinto thephysicsofunification.Themassesandcouplingsoftheseparticles,likethebasiccouplings of the Core interactions, will be distorted by effects of Gridfluctuations. But the details of the distortion are predicted to be different, inspecificways.Ifallgoeswell,thesuccessful(butisolatedandtenuouslybased)unificationcalculationwehavetodaycouldblossomintoa thrivingecologyofmutuallysupportiveresults.

DarkMatterintheBalance

Towardtheendofthetwentiethcentury,physicistsconsolidatedtheirextremelysuccessful theory of matter: the Core. The Core’s compact yet remarkablycompleteandaccurateaccountofthebasiclawsofmattercrownedcenturiesofwork.

But just as thatwas happening, astronomersmade startling newdiscoveriesthat restoredourhumility.Theydiscovered that thematterwe’vebeendealingwith all those centuries—the kind of matter we study in biology, chemistry,engineering, and geology, the kind of matter we’re made from, the kind weunderstand profoundly with our Core theory54—that stuff, normal matter,

contributesonlyabout5%ofthemassoftheuniverseasawhole!

Theremaining95%containsatleasttwocomponents,calleddarkenergyanddarkmatter.

Dark energy contributes about 70% of themass. It has been observed onlythrough its gravitational influence on themotion of normalmatter. It has notbeen observed to emit or absorb light; it is not dark in the usual sense, buttransparent. Dark energy seems to be uniformly distributed throughout space,withadensitythatisalsoconstantintime.Thetheoryofdarkenergyisinbadshape.It’saproblemforthefuture.

Darkmattercontributesabout25%ofthemass.Ittoohasbeenobservedonlythroughitsgravitationalinfluenceonthemotionofnormalmatter.Darkmatteris not uniformly distributed in space, nor is its density constant in time. Itclumps,thoughnotastightlyasnormalmatter.Aroundeverygalaxythat’sbeencarefully studied, astronomers have found an extended halo of dark matter.Thesehaloesarediffuse—theirdensityistypicallyamilliontimeslessthanthatofnormalmatter,inregionswheretheyoverlap—buttheyextendoverfarlargervolumes than normalmatter.Rather than speaking of galaxies as objectswithhaloes,itmightbemoreappropriatetospeakofthenormal-mattergalaxyasanimpurityinthedarkmatter.

Thedark-matterproblem,Ithink,isripeforsolution.

Among the new partner particles predicted by SUSY, one is special: thelightest. Its properties depend on details that we don’t have convincing ideasabout (especially, the specific values of all the SUSY partnermasses). Sowehave to try all thepossibilities.We find that inmanycases the lightestSUSYpartner is extremely long-lived (longer than the lifetime of the universe) andinteractsveryweaklywithnormalmatter.Themoststrikingthing,though,isthatwhenwerunourequationsthroughthebigbangtoseehowmuchofthisstuffwould have survived to the present day, we find that it’s roughly the rightamounttoaccountforthedarkmatter.Naturally,allthissuggeststhatthelightestSUSYpartneristhedarkmatter.

So it’s quite possible that by investigating the basic laws of physics atultrashortdistances,we’llsolveamajorcosmologicalriddle,andbegintoshedsomeofthatirksomehumility.Ifacandidateparticletoprovidethedarkmatterdoesemerge,itwillbeagreatenterprisetocheckwhetherthatcandidatereallydoesthejob.Onthetheoryside,we’llneedtopindownallthereactionsrelevant

toitsproductioninthebigbangandrunthenumbers.Ontheexperimentalside,we’llwanttocheckthatthecandidatereallyiswhat’soutthere.Onceyouknowexactlywhatyou’relookingfor,itbecomesmucheasiertofindit.

There’sanotherpromisingideaaboutwhatthedarkmatteris,whichemergesfrom a different proposal for improving the equations of physics. As we’vediscussed,QCDisinaprofoundandliteralsenseconstructedastheembodimentofsymmetry.Thereisanalmostperfectmatchbetweentheobservedpropertiesof quarks and gluons and the most general properties allowed by local colorsymmetry, in the frameworkof special relativity andquantummechanics.TheonlyexceptionisthattheestablishedsymmetriesofQCDfailtoforbidonesortofbehavior that isnotobserved tooccur.Theestablishedsymmetriespermitasortofinteractionamonggluonsthatwouldspoilthesymmetryoftheequationsof QCD under a change in the direction of time. Experiments provide severelimits on the possible strength of that interaction. The limits are much moreseverethanmightbeexpectedtoariseaccidentally.

The Core theory does not explain this “coincidence.” Roberto Peccei andHelenQuinnfoundawaytoexpandtheequationsthatwouldexplainit.StevenWeinbergandI,independently,showedthattheexpandedequationspredicttheexistence of new, very light, very weakly interacting particles called axions.Axionsarealsoseriouscandidates toprovide thecosmologicaldarkmatter. Inprincipletheymightbeobservedinavarietyofways.Thoughnoneiseasy,thehuntison.

It’s also possible that both ideas are right, and both kinds of particlescontributetothetotalamountofdarkmatter.Wouldn’tthatbepretty?

OneShoeHeardFrom;ListeningforOthers

Unification of the Core forces brings in a larger symmetry, and the largersymmetry brings in additional forces. We postulate a second, stiffer layer ofcosmicsuperconductivityintheGridtoexplainhowtheadditionalforces,whichhavenotbeenobserved,aresuppressed.55Butwedon’twanttosuppressthemcompletely. At the unification scale—at high energy or, equivalently, shortdistance—andbeyond,thesenewinteractionsareunitedwiththeCoreandhavethesamepower.

Quantum fluctuations—virtual particles—that reach those extraordinaryenergiesareextremelyrare,buttheydooccur.Correspondingly,theeffectsthatthosefluctuationscatalyzearepredictedtobeverysmall,butnotzero.Twooftheseeffectsare sounusual andotherwiseunexpected that they’re regardedasclassicsignsofunificationphysics.

•Neutrinosshouldacquiremass.•Protonsshoulddecay.

We’ve heard the first of those shoes drop.Asmentioned before, neutrinos dohaveverysmall,butnonzero,masses.Theobservedvaluesofthosemassesarebroadlyconsistentwithexpectationsfromunification.

We’rewaitingfor theothershoe.Deepunderground,giantphotoncollectorsmonitorhugevatsofpurifiedwater,lookingforflashesthatwillsignalthedeathofprotons.Our estimates for the rate suggest that discovery shouldnot be faroff. If so, itwill open yet another entry into unification physics—perhaps themostdirectandpowerful.Forprotonscandecayinmanyways,andtheratesforthe different possibilities directly reflect the new interactions arising fromunification.

Unification of our theories of the Core interactions—strong, weak, andelectromagnetic—intoasingleunifiedtheoryinvolvessomeguesswork,buttheprinciplesareclear.Quantummechanics,specialrelativity,and(local)symmetryfit together smoothly. Using them, we can make definite suggestions forexperimentalexploration,includingquantitativeestimatesofwhattoexpect.

Unification with gravity also looks good, at the level of comparing thefundamentalstrengthofalltheinteractions,aswe’veseen.Butwithgravityourideasaboutwhattheunifiedtheoryisarenowherenearasconcrete.Thefermentof ideasaroundsuperstring theory seemspromising,butnoone’sbeenable topull these ideas together enough to suggest specifically what new effects toexpect.What shoes will unification including gravity drop? Any that we canhopetohear?Thattooisaquestionforthefuture.

Epilogue

ASmoothPebble,aPrettyShell

[T]omyselfIseemtohavebeenonlyaboyplayingonthesea-shore,divertingmyselfinnowandthenfindingasmootherpebbleoraprettiershellthanordinary,whilstthegreatoceanoftruthlayallundiscoveredbeforeme.—IsaacNewton

HAVING SCALED OUR THIRD PEAK, we’ve reached a natural stoppingpoint.It’stimetocometorest,lookback,andscanthescenery.

Lookingdownonthevalleyofeverydayreality,weperceivemuchmorethanbefore. Beneath the familiar, sober appearances of enduring matter in emptyspace, our minds envision the dance of intricate patterns within a pervasive,ever-present,effervescentmedium.Weperceivethatmass,theveryqualitythatrendersmattersluggishandcontrollable,derivesfromtheenergyofquarksandgluonsevermovingatthespeedoflight,compelledtohuddletogethertoshieldoneanother from thebuffetingof thatmedium.Oursubstance is thehumofastrange music, a mathematical music more precise and complex than a Bachfugue,theMusicoftheGrid.Through patchy clouds, off in the distance, we seem to glimpse a

mathematical Paradise, where the elements that build reality shed their dross.Correcting for thedistortionsof our everydayvision,we create in ourminds avision of what they might really be: pure and ideal, symmetric, equal, andperfect.Orhaveourimaginationsmadetoomuchofawispychimera?Wepointour

telescope,andwaitforthecloudstoclear.

OwningUponMass

Aheadlieothermountains,whosepeakswecan’tyetdiscern.

Aspromised,I’veaccountedfor95%ofthemassofnormalmatterfromtheenergy of massless building blocks, using and delivering on the promise ofEinstein’ssecond law,m=E/c2.Nowit’s timeforme toownup towhat I’vefailedtoexplain.Themass of the electron, although it contributesmuch less than 1% of the

totalmassofnormalmatter,isindispensable.Thevalueofthatmassdeterminesthesizeofatoms.Ifyoudoubledtheelectron’smass,allatomswouldcontracttohalf their size; if you halved the electron’s mass, all atoms would expand totwicetheirsize.Otherthingswouldhappen,too,thatcouldmakelifeinanythingliketheformweknowitimpossible.Ifelectronswereheavierbyafactorof4orso, then itwould be favorable for electrons to combinewith protons tomakeneutrons,emittingneutrinos.ThatwouldbeR.I.P.forchemistry,tosaynothingof biology, because neither electrically charged nuclei nor electronswould beavailabletobuildatomsandcomplexmolecules.Andyetwehavenogoodidea(yet)aboutwhyelectronsweighwhattheydo.

There’snoevidencethatelectronshaveinternalstructure(andalotofevidenceagainst it), so thekindof explanationwearrivedat for theproton, relating itsmass to internalenergy,won’twork.Weneedsomenewideas.Atpresent, thebest we can do is to accommodate the electron’s mass as a parameter in ourequations—aparameterwecan’texpressintermsofanythingmorebasic.It’sasimilarstoryforthemassesofourfriendstheupanddownquarks,uand

d.Theymakeaquantitativelysmallbutqualitativelycrucialcontributiontothemassesofprotonsandneutrons,andhenceofnormalmatter.Iftheirvaluesweresignificantly different, lifemight become difficult or impossible.Yetwe can’texplainwhytheyhavethevaluestheydo.Wealsodon’tunderstand thevaluesof themassesof theelectron’sheavier,

unstable clones—that is, the muon (μ) and tau (τ) leptons, which are,respectively,209and3478timesheavier thanelectrons.Wedon’tknowwherethosenumbers209and3478comefrom.Dittofortheheavier,unstableclonesofthe up quark—that is the charm (c) and top (t) quarks—and for the heavier,unstableclonesofthedownquark,strange(s)andbottom(b).Theonlygoodnewsinthisdebacleisthatallthesequarksandleptonsappear

tobeclosely related tooneanother,both in termsof theirobservedpropertiesandtheoretically,withintheunifiedtheorieswediscussedinpreviouschapters.Soifwemanagetounderstandone—andiftheunifiedtheoriesareright!—it’llteachusaboutalltheothers.Thefact thatweremainsoignorantabout theoriginofquarkmassesmeans

thatmy explanation for the feebleness of gravity, based on the proton’s beinglightcomparedtothePlanckmass,isn’tcomplete.Itookitforgrantedthatmostof themass of the proton arises from the energy of the quarks and gluons itcontains,accordingtoEinstein’ssecondlaw.AndthatisactuallytrueinNature:theuanddquarksdoinfacthaveonlytinymasses,muchsmallerthanthemassoftheproton,sotheirdirectcontributiontotheproton’smassisverysmall.Butif you ask mewhy those quark masses are tiny, I don’t have a solid answer(thoughIcouldspinoutsometales).Thenthere’stheHiggsparticle,sometimessaidtobe“theoriginofmass”or

even “the God particle.” In Appendix B, I’ve sketched a wonderful circle ofideascenteredaroundtheHiggsparticle.Inbrief,theHiggsfield(whichismorefundamentalthantheparticle)enablesustoimplementourvisionofauniversalcosmic superconductor and embodies the beautiful concept of spontaneoussymmetrybreaking.These ideasaredeep,strange,glorious,andveryprobablytrue. But they don’t explain the origin of mass—let alone the origin of God.Although it’s accurate to say that the Higgs field allows us to reconcile theexistence of certain kinds of mass with details of how the weak interactionswork, that’s a far cry from explaining the origin ofmass orwhy the differentmasseshavethevaluestheydo.Andaswe’veseen,mostofthemassofnormalmatterhasanoriginthathasnothingwhatsoevertodowithHiggsparticles.Wealsodon’treallyunderstandthemassesofneutrinos.Andwereallydon’t

understand themasses of a welter of particles that appear in our theories buthaven’t yet been observed, including the Higgs particle or particles, all theparticlesassociatedwithsupersymmetry,axions,....Ashorterwaytosummarizethesituationwouldbetosaythattheonlycasein

whichwedounderstandtheoriginofmassistheoneI’vetoldyouaboutinthisbook.Happily,thatunderstandingcoversthelion’sshareofthemassofnormalmatter—themattermadeofelectrons,photons,quarks,andgluons—thekindofmatterthatdominatesourimmediateenvironment,thatwestudyinbiologyandchemistry,andthatwe’remadeof.

DarknessRevisited

Itwasagreatdiscoveryofastronomy(perhapsitsgreatest)thatdistantstarsandnebulaearemadefromexactly thesamesortofmatteraswefindonEarth.Inrecentdecades,however,astronomershavepartlyundiscoveredthatbasictruth.

They’vefoundthatthebulkofthemassoftheUniverse,about95%,comesfromsomethingelse.Newformsofmatter,notmadefromelectrons,photons,quarks,andgluons,areresponsiblefor95%ofthemassoftheuniverse.

The new stuff comes in at least two varieties, called dark matter and darkenergy.Thosearen’tverygoodnames,becauseoneofthefewthingsweknowabout this stuff is that it isn’t dark: it doesn’t absorb light to any detectableextent.Norhas itbeenobserved toemit light. It appearsperfectly transparent.Norhasitbeenobservedtoemitprotons,electrons,neutrinos,orcosmicraysofany kind. In short, both the dark matter and the dark energy interact withordinarymatteronlyveryfeebly,ifatall.Theonlywaytheyhavebeendetectedis through their gravitational influence on the orbits of ordinary stars andgalaxies,thethingswedosee.We know very little for sure about dark matter. It might be made from

supersymmetricparticles,asIdiscussedbefore,orfromaxions.(I’mveryfondofaxions,inpartbecauseIgottonamethem.Iusedthatopportunitytofulfilladreamofmyyouth.I’dnoticedthattherewasabrandoflaundrydetergentcalled“Axion,” which sounded to me like the name of a particle. So when theoryproducedahypotheticalparticlethatcleanedupaproblemwithanaxialcurrent,Isensedacosmicconvergence.Theproblemwas toget itpast thenotoriouslyconservative editors of Physical Review Letters. I told them about the axialcurrent,butnotthedetergent.Itworked.)Heroicexperimentsareunderwaytotest these possibilities and others, andwith any luckwe’ll havemuch clearerideasaboutwhatthedarkmatteriswithinafewyears.We know even less about dark energy. It seems to be spread out perfectly

evenly, with the same density everywhere and everywhen, as if it were anintrinsicpropertyof space-time.Unlike anyconventionalkindofmatter (evensupersymmetricparticlesoraxions),thedarkenergyexertsnegativepressure.Ittriestopullyouapart!Fortunately,althoughdarkenergysuppliesabout70%ofthemassoftheuniverseasawhole,itsdensityisonlyabout7×10-30timesthedensity of water, and its negative pressure cancels only about 7 × 10-14 ofnormalatmosphericpressure—less thanapart ina trillion. Idon’tknowwhenwe’llhaveclearerideasaboutwhatthedarkenergyis.I’dguessnotverysoon.IhopeI’mwrong.

LastWords

I’ve shown you my choicest smooth pebble, my prettiest shell, and anundiscoveredocean.Ihopeyou’veenjoyedthem.Afterall,they’reyourworld.

Acknowledgments

THISBOOKCAMEINLARGEPARToutofthepubliclectures“TheUniverseIsaStrangePlace,”“TheWorld’sNumericalRecipe,”“TheOriginofMassandtheFeeblenessofGravity,”and“ThePersistenceofEther”thatI’vegivenoverthe last few years at many institutions. I’d like to thank my hosts for theopportunitytogivethelectures,andtheaudiencesformanyinterestingquestionsandusefulfeedback.

I’dliketothankMITforcontinuoussupport;Norditaforhospitalitythroughthe bulk of the writing; and Oxford University for hospitality during thecompletionofthisbook.I’d like to thank Betsy Devine and Al Shapere for close readings of the

manuscriptthatresultedinmanyimportantimprovements.I’dalsoliketothankCarol Breen for her comments on themanuscript, and especially for her helpwithanearlyversionofChapter6.I’dliketothankJohnBrockmanandKatinkaMatsonforurgingmetowrite

thebook,andBillFrucht,SandraBeris,andthepeopleatPerseusforlotsofhelpandencouragement.Betsy’ssupportandinputhavebeenanessentialinspirationtomethroughout.

AppendixA

ParticlesHaveMass,theWorldHasEnergy

ASWEDISCUSSEDINCHAPTER3,E=mc2holdsforisolatedbodiesatrest.Formovingbodies,thecorrectmass-energyequationis

wherevisthevelocity.Forabodyatrest(v=0),thisbecomesE=mc2.When a body—for example, a proton or an electron—is accelerated, v

generally changes, butm stays the same. Therefore, the equation tells us, Echanges.Atfirsthearing,thatmightsoundlikejusttheoppositeofwhatwediscussed

inthemaintext.Wesaidthatenergyisconserved,butmassisnot.Whatgives?Conservationofenergyappliestosystems,nottoindividualbodies.Thetotal

energyofasystemofbodiesincludescontributionsfrombothenergyofmotion(given by the formula above) and “potential energy” terms that reflect theinteractions among the bodies. The potential energy terms are given by otherformulas, which depend on the distances between the bodies, their electriccharges,andperhapsotherthings.Itisonlythetotalenergythatisconserved.Anisolatedbodyhasaconstantvelocity.That’sNewton’sfirstlawofmotion,

which,unlikehiszerothlaw,stillappearstobevalid.Whenabodyisisolated,we can regard it as a systemunto itself. So the energy of the body should beconserved—and,fromtheformula,itis.Conversely,whenabody’svelocitychanges,thatverychangeisasignalthat

thebodyisnotisolated.Someotherbodyhastobeactingonit toproducethechangeinvelocity.Theactionofonebodyonanothergenerallytransfersenergybetweenthem.Onlythetotalenergyisconserved,nottheenergyofeachbodyseparately.

When we make a proton out of quarks and gluons, these concepts cometogether. From a fundamental perspective, a proton at rest is a complicatedsystem of interacting quarks and gluons. The quarks and gluons individuallyhave very little mass. That doesn’t, however, prevent the whole system fromhavingenergy.Call thatenergyE. It’sconserved in time,as longas thewholesystem—that is, the proton—is isolated. Alternatively, we can consider theisolated proton as a black box: a “body” with massm. These two quantities,whichariseinthealternativedescriptions,arerelatedbyE=mc2(orm=E/c2).InChapter2,weconsideredadramaticviolationofconservationofmass.An

electronandapositronannihilate,andoutcomeacollectionofparticleswhosetotal mass is 30,000 times larger. Nevertheless, energy is conserved. Thevelocities of the initial electron and positron were very close to the speed oflight.Therefore,accordingtothegeneralmass-energyequation, theirenergyisverylarge—muchlargerthanmc2.Theparticlesthatemergefromthecollision,althoughtheyaremoremassive,moveabitmoreslowly.Whenyouadduptheirenergies,calculatedusing themass-energyequation, the summatches the totalenergy of the original electron and positron. (Once the particles fly out andseparate,theinteraction,orpotential,energybecomesnegligiblysmall.)Finally,tocompletethisdiscussionoftherelationbetweenmassandenergy,

we must consider the special case of particles with zero mass. Importantexamples includephotons, colorgluons, andgravitons.Suchparticlesmoveatthespeedoflight.Ifweattempttoputm=0andv=c intoourgeneralmass-equation equation, both the numerator and the denominator on the right-handsidevanish,andwegetthenonsensicalrelationE=0/0.Thecorrectresultisthatthe energy of a photon can take any value. Photons of different energy differneither in theirvelocity,which isalways the speedof lightc,norofcourse intheir mass, which always vanishes, but in their frequency (that is, the rate atwhichtheunderlyingelectricandmagneticfieldsoscillate).TheenergyEofaphoton is proportional to the frequency ν of the light it represents. Moreprecisely, theyarerelatedbythePlanck-Einstein-SchrödingerequationE=hν,wherehisPlanck’sconstant.Forphotons in thevisible range,wesense thatdistinctionasadifference in

color:photonsattheredendofthespectrumhavethesmallestenergy,photonsat theblueend the largest.Goingdown inenergy,beyond thevisiblewemeetinfrared,microwave,andradiowavephotons.Movingup,wemeetultraviolet,x-rays,andγrays.

AppendixB

TheMultilayered,MulticoloredCosmicSuperconductor

Weliveinsideanexoticsuperconductorthathidesthesymmetryoftheworld.

THEMOSTFUNDAMENTALPROPERTYof superconductors isn’t that theyconduct electricity extremely well (although they do). The most fundamentalpropertywasdiscoveredbyWaltherMeissnerandRobertOchsenfeldin1933.ItiscalledtheMeissnereffect.WhatMeissnerandOchsenfelddiscoveredisthatmagnetic fields cannot penetrate into the interiors of superconductors, but areconfined to a thin surface layer. Superconductors can’t abidemagnetic fields.Thatistheirmostfundamentalproperty.Superconductors get their name from a more obvious and spectacular

property,theirspecialtalentforsustainingelectriccurrents.Superconductorscancarry electric currents that flow without resistance and therefore persistindefinitely,evenwithoutabatterytodrivethem.Here’stheconnectionbetweentheMeissnereffectandsuchsuper(b)conductivity:If we expose a superconducting body to an external magnetic field, then

according to the Meissner effect, that body must find a way to cancel themagneticfield,sothatthere’snonetfieldinside.Thebodycanonlyensuresuchcancellationbygeneratinganequalandoppositemagneticfieldofitsown.Butmagnetic fields are generated by currents. To generate a magnetic field thatkeeps the net field zeroed, the superconducting bodymust be able to supportcurrentsthatpersistindefinitely.Thus the possibility of “super” flow of electric current follows from the

Meissnereffect.TheMeissnereffectismorefundamental.Itisthetruemarkofasuperconductor.TheMeissnereffectappliesnotonlytorealmagneticfieldsbutalsotothose

thatariseasquantumfluctuations.Thusthepropertiesofvirtualphotons,whichare fluctuations in electric and magnetic fields, get modified inside a

superconductor.Thesuperconductordoesitsbesttocanceloutthosefluctuatingmagneticfields.Asaconsequence,virtualphotons insideasuperconductorarerarerandextendoversmallerdistancesthaninempty56space.In theGrid view of theworld, electric andmagnetic forces result from the

interplaybetweenchargedsourcesandvirtualphotons,a.k.a.fieldfluctuations.Particle A affects the field fluctuations around it, which also affect anotherparticle,B.ThisisourmostfundamentalpictureofhowaforcearisesbetweenAandB.ItiswhatyouseedepictedinthebasicFeynmandiagram,Figure7.4.So the fact that field fluctuations inside a superconductor become rare and

short-ranged means that the corresponding electric and magnetic forces areeffectively enfeebled. Especially, those forces cease to operate over longdistances.Thefield-nullifyingsupercurrentsalsomakelifeharderforrealphotonsinside

superconductors.Ittakesmoreenergytomakeself-renewingfielddisturbances,which,we’velearned,iswhatphotonsare.Intheequations,thiseffectshowsupas a nonzero mass for photons. In short: inside superconductors, photons areheavy.

CosmicSuperconductivity:ElectroweakLayer

Theweakinteractionisashort-rangeforce.Thefieldsresponsibleforthisforce,theWandZ,aresimilarinmanywaystotheelectromagneticfield.Theparticlesthat arise as disturbances in these fields (the W and Z particles) resemblephotons.Likephotons,theyarebosons.Likephotons,theyrespondtocharges—notelectricchargestobesure,butwhatwe’vecalledgreenandpurplecharges,withsimilarphysicalproperties.TheirmostobviousdifferencefromphotonsisthatWandZareheavyparticles. (Eachweighsaboutasmuchasonehundredprotons.)Short-range force. Heavy particles. Sound familiar? It should. Those are

exactly the properties of electromagnetic forces and photons insidesuperconductors.The modern theory of electroweak interactions is heavily invested in the

analogy between what happens to photons inside superconductors and theobservedpropertiesofWandZbosonsinthecosmos.Accordingtothispartofthe Core theory, the entity we perceive as empty space—the Grid—is asuperconductor.

Even though the conceptual andmathematical parallels run very deep,Gridsuperconductivity differs from conventional superconductivity in four mainways:

Occurrence Conventional superconductivity requires special materialsandlowtemperatures.Eventhenew“high-temperature”superconductorsmaxoutatlessthan200Kelvin(roomtemperatureisabout300Kelvin).Gridsuperconductivityiseverywhere,andhasneverbeenobservedto

breakdown.Theoretically,itshouldpersistuptoabout1016Kelvin.Scale The photon mass inside a conventional superconductor is 10-11protonmasses,orless.TheWandZmassesareabout102protonmasses.

What Flows The supercurrents of conventional superconductivity areflows of electric charge. They cause electromagnetic fields to becomeshort-range,andphotonstoacquiremass.The supercurrents of Grid superconductivity are correlated flows of

muchlessfamiliartypesofcharge:purpleweakchargeandhypercharge.WandZfieldscanbegeneratedbythoseflows,sotheforcesthatWandZgeneratebecomeshort-range,andtheWandZparticlesacquiremass.SubstrateAlthoughmanydetails remainmysterious,weunderstand inbroad terms how conventional superconductors work. (For manysuperconductingmaterials,wehavequiteadetailedandaccuratetheory;forothers,includingtheso-calledhigh-temperaturesuperconductors,it’sa work in progress.) Specifically, we know what their superflows aremadefrom.Thesupercurrentsareflowsofelectrons,organizedintowhatarecalledCooperpairs.By contrast, we don’t have a reliable theory for what the Grid

superflowsaremadefrom.Noneofthefieldswe’veobservedtodatehastherightproperties.Theoretically, it’spossiblethat thejobisdonebyasingle new field, the so-called Higgs field, and its attendant Higgsparticle.It’salsopossiblethatseveralfieldsareinvolved.Inthetheoriesfeaturing SUSY, which figured heavily in our ideas for achievingunification, there are at least two fields contributing to the superflows,and at least five particles associated with them. (In the language ofChapter8 thereare twocondensates, and fivedistinctivekindsof fielddisturbances.)Thingscouldbeevenmorecomplicated.Wedon’tknow.A major goal of the LHC project is to address these questions

experimentally.

Gridsuperconductivitydoesn’tinvolvestrongcolorcharges,sothestrongcolorgluonsremainunsuppressed,withzeromass.Nordoesitaffectphotons.UnlikeWandZ,whichhavetheirinfluencelargelysuppressedandrenderedshort-rangebyfield-cancelingsupercurrents,photonsremainmassless.Fortunatelyforus—giventhatourelectricalandelectronictechnology,nottomentionourchemicalbeing, relies on vigorous electromagnetic forces—Grid supercurrents areelectricallyneutral.

CosmicSuperconductivity:StrongweakLayer

Wecantaketheseideasaveryimportantstepfurther.ThecentralachievementofGridsuperconductivity,fortheCoreelectroweak

theory,istoexplainwhytheweakforceappearsmuchweakerandmoreobscurethantheelectromagneticforce,eventhoughtheyappearonverynearlythesamefooting in the fundamental equations. (Indeed, as we’ve discussed, the weakforce is, fundamentally, slightly more powerful.) In terms of the Coresymmetries,itshowsushowtoexplainthereduction

from the fundamental Core symmetries (strong ×weak × hypercharge) to theonesthathavelong-rangeconsequences(strong×electromagnetic).Inourunifiedtheoriesweworkwithmuchlargersymmetrygroupsthanthe

CoreSU(3)×SU(2)×U(1),suchasSO(10).Withmoresymmetry,youhavemorepossibilitiesfortransformationsamongthedifferentkindsofcharges,andmorekinds of gluon/photon/W,Z-like gauge particles that implement thosetransformations.Theadditionalgaugeparticlesarecapableofdoingthingsthatrarely,ifever,

happeninreality.Bytransforming,forexample,aunitofweakcolorchargeintoa unit of strong color charge, we can change a quark into a lepton, or anantiquark. The Charge Account is full of such possibilities. So we can easilygenerate,forexample,thedecay

ofprotonsintopositronsandphotons.Ifthisdecayoccurredwithanythinglikeatypicalweakinteractionrate,thedecaywouldoccurwithinasmallfractionofasecond.We’dbeinserioustrouble,becauseourbodieswouldquicklyvaporizeintoelectron-positronplasma.We can suppress the unwanted processes, while retaining the underlying

unificationsymmetry,usinganew layerofGridsuperconductivity.Thenwe’llhave, as we proceed from very small to longer distances, the active(unsuppressed)fieldsreducedaccordingto

Thesecondstepiswhatwealreadyhad,intheCore.Forthefirststep,weneedmuchmoreefficientGridsupercurrents.Theymust

mightilysuppresstheunwantedstrong↔weakcolorchargetransformations.Ofcourse, thismeans that the supercurrents themselveswouldbe flows involvingbothstrongandweakcolorcharges.Noknownformofmattercansupplysuchsupercurrents.Ontheotherhand,

it’seasytoinventnewHiggs-likefieldsthatdothejob.Peoplehaveplayedwithother ideas, too. Maybe these currents arise from particles racing around inadditional,tinycurled-upspatialdimensions.Maybethey’revibrationsofstringsthat wrap around additional tiny curled-up spatial dimensions. Because theconcentratedenergies required toprobedistances this small lie far, farbeyondwhatwecanachieveinpractice,thesespeculationsarenoteasytocheck.Fortunately, just as in the Core electroweak theory, we can make good

progressbytakingthesupercurrentsasgiven,withoutfingoinghypothesesaboutwhatthey’remadeof.That’sthephilosophyIadoptedinPartIIIofthisbook.Itled us to some encouraging successes, and to some specific predictions. If itsurvives further scrutiny, we’ll be able to assert with confidence that we livewithinamultilayered,multicoloredcosmicsuperconductor.

AppendixC

From“NotWrong”to(Maybe)Right

SAVASDIMOPOULOSISALWAYSENTHUSIASTICaboutsomething,andinthespringof1981itwassupersymmetry.HewasvisitingthenewInstituteforTheoreticalPhysicsinSantaBarbara,whichIhadrecentlyjoined.Wehititoffimmediately—hewasburstingwithwildideas,andIlikedtostretchmymindbytryingtotakesomeofthemseriously.Supersymmetrywas(andis)abeautifulmathematicalidea.Theproblemwith

applyingsupersymmetryisthatit istoogoodforthisworld.Wesimplydonotfindparticlesof thesort itpredicts.Wedonot, forexample,seeparticleswiththesamechargeandmassaselectrons,butadifferentamountofspin.However, symmetryprinciples thatmighthelp tounify fundamentalphysics

are hard to come by, so theoretical physicists do not give up on them easily.Basedonpreviousexperiencewithotherformsofsymmetry,wehavedevelopedafallbackstrategy,calledspontaneoussymmetrybreaking.Inthisapproach,wepostulatethat thefundamentalequationsofphysicshavethesymmetry,butthestable solutions of these equations do not. The classic example of thisphenomenonoccursinanordinarymagnet.Inthebasicequationsthatdescribethephysicsofa lumpof iron,anydirection isequivalent toanyother,but thelumpbecomesamagnetwithsomedefinitenorth-seekingpole.A familiar, simple example of spontaneous symmetry breaking is the

conventionfordrivingononesideof theroad.Itdoesn’tmatterwhichsideofthe road people drive on, as long as everybody does the same thing. If somepeopledriveontheleftandothersontheright,it’sanunstablesituation.Sothesymmetry between left and right must be broken. Of course in differentuniverses,callthemU.S.andU.K.,thechoicemaydiffer.Surveying the possibilities opened by spontaneously broken supersymmetry

requiresmodelbuilding—thecreativeactivityofproposingcandidateequationsandanalyzing their consequences.Buildingmodelswith spontaneouslybrokensupersymmetrythatareconsistentwitheverythingelseweknowaboutphysicsis a difficult business. Even if youmanage to get the symmetry to break, the

extraparticlesarestill there(justheavier)andcausevariousmischief.Ibrieflytriedmyhandatmodelbuildingwhensupersymmetrywasfirstdevelopedinthemid-1970s,butaftersomesimpleattemptsfailedmiserably,Igaveup.Savas was a much more naturally gifted model-builder, in two crucial

respects: he did not insist on simplicity, and he did not give up. When Iidentified aparticular difficulty (let us call itA) thatwasnot addressed inhismodeldujour,hewouldsay,“It’snotarealproblem,I’msureIcansolve it.”And the next afternoon he would come in with a more elaborate model thatsolveddifficultyA.ButthenwewoulddiscussdifficultyB,andhewouldsolvethatonewithacompletelydifferentcomplicatedmodel.TosolvebothAandB,youhad to join the twomodels,andsoon todifficultyC,andsoon thingsgotincrediblycomplicated.Workingthroughthedetails,wewouldfindsomeflaw.ThenthenextdaySavaswouldcomein,veryexcitedandhappy,withanevenmorecomplicatedmodel that fixedyesterday’s flaw.Eventuallyweeliminatedallflaws,usingthemethodofproofbyexhaustion—anyone,includingus,whotried to analyze themodelwouldget exhaustedbefore theyunderstood itwellenoughtofindtheflaws.WhenItriedtowriteupourworkforpublication,therewasacertainfeeling

ofunrealityandembarrassmentabout thecomplexityandarbitrarinessofwhatwe had come up with. Savas was undaunted. He even maintained that someexisting ideas about unification using gauge symmetry, which to me seemedgenuinely fruitful, were not really so elegant if you tried to be completelyrealistic and work them out in detail. In fact, he had been talking to anothercolleague, Stuart Raby, about trying to improve those models by addingsupersymmetry!Iwasextremelyskepticalaboutthis“improvement,”becauseIwascertain that theaddedcomplexityofsupersymmetrywouldspoil thehard-wonsuccessofgaugesymmetryinexplainingtherelativevaluesofthestrong,electromagnetic,andweakcouplingconstants.Thethreeofusdecidedtodothecalculation,toseehowbadthesituationwas.Togetorientedandmakeadefinitecalculation,westartedbydoingthecrudestthing,whichwastoignorethewholeproblem of breaking supersymmetry. This allowed us to use very simple (butmanifestlyunrealistic)models.The resultwasamazing, at least tome.The supersymmetricversionsof the

gaugesymmetrymodels,althoughtheywerevastlydifferentfromtheoriginals,gaveverynearlythesameanswerforthecouplings.Thatwastheturningpoint.Weputasidethe“notwrong”complicatedmodels

with spontaneous supersymmetry breaking andwrote a short paper that, taken

literally (with unbroken supersymmetry),waswrong.But it presented a resultthat was so straightforward and successful that it made the idea of puttingunification and supersymmetry together seem (maybe) right. We put off theproblemofhowsupersymmetrygetsbroken.Andtoday,althoughtherearesomegoodideasaboutit,thereisstillnogenerallyacceptedsolution.After our initialwork,more precisemeasurements of the couplingsmade it

possible to distinguish between the predictions of models with and withoutsupersymmetry. The models with supersymmetry work much better. We alleagerly await operation of theLargeHadronCollider atCERN, theEuropeanparticlephysicslaboratory,where,iftheseideasarecorrect,thenewparticlesofsupersymmetry—or, youmight say, the new dimensions of superspace—mustmaketheirappearance.This little episode, it seems to me, is 179º or so out of phase with Karl

Popper’s idea that we make progress by falsifying theories. Rather, in manycases, including someof themost important,we suddenly decide our theoriesmightbetruebyrealizingthatweshouldstrategicallyignoreglaringproblems.It was a similar turning point when David Gross and I decided to proposequantumchromodynamics(QCD)basedonasymptoticfreedom,puttingofftheproblemofquarkconfinement.Butthatisanotherstory....

Glossary

Acceleration

Rateofchangeofvelocity.Accelerationisthereforetherateofchangeoftherateofchangeinposition.Newton’scentraldiscoveryinmechanicswasthatthelawsgoverningaccelerationsareoftensimple.

Amplitude(quantum)

Quantummechanicssuppliespredictionsfortheprobabilityofvariousevents,buttheequationsofquantummechanicsareformulatedusingamplitudes,whichareasortofpre-probability.Moreprecisely,theprobabilityisthesquareoftheamplitude.(Forthecogniscienti:amplitudesaregenerallycomplexnumbers,andtheprobabilitiesarethesquareoftheirmagnitudes.)Thetermamplitudeisusedtodescribetheheightsofwavesofmanykinds,suchasoceanwaves,soundwaves,andradiowaves.Quantum-mechanicalamplitudesareessentiallytheheightsofquantum-mechanicalwavefunctions.Forfurtherdiscussionandexamples,seeChapter9.[Seealso:Wavefunction.]

Antimatter

Thematterweordinarilyencounter—andaremadeof—isbasedonelectrons,quarks,photons,andgluons.Mattermadefromthecorrespondingantiparticles,namelyantielectrons(a.k.a.positrons),antiquarks,photons,andgluons,isoftencalledantimatter.(Notethatphotonsandgluonsaretheirownantiparticles.Moreaccurately,someofthegluonsareantiparticlesofotherones;alleightgluonsmakeacompleteset,whichgoesoverintoitselfwhenyoutaketheantiparticleofeverything.)[Seealso:Antiparticle.]

Antiparticle

Theantiparticleofagivenparticlehasthesamemassandspinasthatparticle,buttheoppositevalueofelectricchargeandotherconservedquantities.Thefirstantiparticlesdiscovered,historically,wereantielectrons,

alsoknownaspositrons.TheywerepredictedtheoreticallybyDirac,andsubsequentlyobservedbyCarlAndersonincosmicrays.Adeepconsequenceofquantumfieldtheoryisthatforeverykindofparticlethereisacorrespondingantiparticle.Thephotonisitsownantiparticle;thisispossiblebecausephotonsareelectricallyneutral.

Particle-antiparticlepairscanhavezerovaluesofallconservedquantumnumbers;thustheycanbeproducedfrompureenergy,andcanalsoarisespontaneouslyasquantumfluctuations(virtualpairs).

Antiscreening

Theoppositeofscreening.[See:Screening.]Whereasscreeningdiminishestheeffectivestrengthofagivenelectriccharge,antiscreeningenhancestheeffectofacolorcharge.Thusantiscreeningallowsafeebleseedcolorchargetobecomepowerfulfaraway.Antiscreeningofcolorchargeistheessenceofasymptoticfreedom,akeyfeatureofQCD.[Seealso:Colorcharge,QCD.]

Asymptoticfreedom

Theconceptthatstronginteractionbecomesweakeratshortdistances.Morespecifically,effectivecolorcharges,whichgovernthepowerofthestronginteraction,becomesmalleratshortdistances.Readingittheotherway,thepowerofagiven,isolatedcolorchargeisenhancedfaraway.Physically,thishappensbecausethesourcechargeinducesacloudofvirtualparticlesthatenhancesorantiscreensit.Aconsequenceofasymptoticfreedomisthatradiationbyafast-movingcolorchargethatmovesinthesamedirection(“soft”radiation)iscommon,whereasradiationthatchangestheoveralldirectionofflowisrare.Thesoftradiationsuppliesquarkswithmatestheycanjoinupwithtoformhadrons;yettheoverallflowfollowsthepatternsetbytheunderlyingquarks(andantiquarksandgluons).Sowegetto“see”quarksandgluonsnotasindividualparticles,butthroughthejetstheytrigger.Wecaneat

ourquarksandhavethemtoo.[Seealso:ChargeWithoutCharge,Jets.]

Axion

HypotheticalparticlepredictedinaclassoftheoriesthatfixanestheticflawoftheCoretheory(fortherecord:thestrongP,Tproblem).Axionsarepredictedtointeractveryweaklywithordinarymatter,andtohavebeenproducedduringthebigbangwithroughlytherightdensitytoprovidethedarkmatter.Thereforeaxionsareawell-motivateddark-mattercandidate.

Baryon

Oneofthetwobasicbodyplansforstronglyinteractingparticles(hadrons).Baryonscanbeconsidered,roughly,asbeingformedfromthreequarks.Moreaccurately,theyresultfromlettingthreequarkscomeintoequilibriumwiththeGrid.Thecompletewavefunctionforabaryoncontains,inadditiontothreequarks,arbitrarynumbersofquark-antiquarkpairsandgluons.Protonsandneutrons,thebuildingblocksofatomicnuclei,arebaryons.[Seealso:Hadron.]

Boost

Atransformationthatcausesasystem,includingallitscomponents,tomoveataconstantvelocity.Amodernperspectiveonspecialrelativityisthatitpostulatesboostsymmetry.Thusthelawsofphysicsaresupposedtolookthesameaftertheapplicationofaboost.Asaconsequence,there’snowaytomeasure,bystudyingphysicalbehaviorpurelywithinaclosed,isolatedsystem,howfastit’smoving.

Boson

Quantumtheory,andmoreparticularlyquantumfieldtheory,bringssharpnewmeaningtotheconceptoftwoobjectsbeingabsolutelythesame,orindistinguishable.Ifonehas,say,twophotonsinstatesAandBatagiventime,andtwophotonsinstatesA’,B’atalatertime,onecannotsaywhetherthetransitioninvolvedwasA→A’,B→B’orA→B’,B→A’.Onemustconsiderbothpossibilities.Forbosonsoneaddstheiramplitudes,forfermionsonesubtracts.Photonsarebosons.A

consequenceisthatphotonsliketoenterthesamestate,forthenthetransitionamplitudesaredoubled.Lasersexploitthiseffect.Alongwithphotonsthemselves,gluons,W,andZarebosons,asaremesonsandthehypotheticalHiggsparticle.WeoftensaythatbosonsobeyBosestatistics,orBose-Einsteinstatistics,afterpioneerphysicistswhoclarifiedtheimplicationsofthisbehaviorforsystemscontainingmanyidenticalparticles.

Charge

Inelectrodynamics,chargeisthephysicalattributetowhichelectricandmagneticfieldsrespond.(Magneticfieldsrespondonlytomovingcharges.)Inthequantumversion,QED,wecansimplysaythatchargeisthethingthatphotonscareabout.Chargecanbeeitherpositiveornegative.Particlescarryingelectricchargeofthesamesign(eitherbothpositiveorbothnegative)repel,whereasparticlescarryingelectricchargesofoppositesignattract.Animportantpropertyofchargeisthatit’sconserved.Eachkindoffundamentalparticlecarriesanamountofcharge—possiblyzero—that’sastablecharacteristicofthatkindofparticle.Forexampleallelectronshavethesamequantityofcharge,usuallydenoted-e.(Confusingly,someauthorsusee,withouttheminussign.There’snoagreed-uponconvention,asfarasIknow.)Protonshavechargee,theoppositeofelectrons.Thetotalchargeofasystemissimplythesumofthechargesofeverythinginit.Thusatomsthatcontainanequalnumberofprotonsandelectronshavezerochargeoverall.Inthetheoryofthestronginteraction,threeadditionalkindsofcharges,calledcolorchargesorsimplycolor,playacentralrole.Colorchargeshavepropertiessimilartoelectriccharge;forexample,theyareconserved.InQCD,colorchargeiswhatgluonscareabout.[Seealso:Field,Electrodynamics,Color,Chromodynamics.]

ChargeAccount

Whimsicalnameforaunifiedaccountofquarksandleptonsthatfullyexplainsthepatternoftheirstrong(color),weak,andelectromagneticcharges.The

mathematicalstructureinvolvedisthespinorrepresentationofSO(10),togetherwithaspecificchoiceofanSU(3)×SU(2)×U(1)subgroup.ThechoiceofsubgroupspecifieshowtheCoretheorysitswithintheunifiedtheory.Ifweallowonlythetransformationsoftheestablished,smallerCoresymmetry,theunifiedChargeAccountbreaksintosixdisconnectedpieces,andthepeculiarpatternofelectriccharges(or,equivalently,hypercharges)isnotexplained.[Seealso:Unifiedtheory.]

ChargeWithoutCharge

Aconceptualconsequenceofasymptoticfreedom.Theeffectivecolorchargeofagivensourcedecreaseswithdistance.Anonzero,finitevalueofthechargeatnonzerodistancecorrespondstozerochargeinthemathematicallimitofzerodistance.ThusapointsourcegeneratesChargeWithoutCharge.It’safeatworthyoftheCheshirecat.

Chromodynamics

Theorythatdescribestheactivityofcolorgluonfields,includingtheirresponsetocolorchargesandcurrents(flowsofcharge).Itistheacceptedtheoryofthestrongforce.Mathematically,chromodynamicsisageneralizationofelectrodynamics.Becausequantumtheoryisimportantinallapplicationsofchromodynamics,itisoftenreferredtoasquantumchromodynamics,orQCDforshort.[Seealso:Strongforce.]

Color

1.Afundamentalphysicalattribute,analogoustoelectriccharge,butdifferent.Therearethreekindsofcolorcharge,herecalledred,white,andblue.Aquarkcarriesaunitofoneofthesecolorcharges.Gluonscarrybothapositiveunitandanegativeunitofcolorcharge,possiblyfordifferentcolors.2.Ineverydaylife,ofcourse,colormeanssomethingcompletelydifferent.Namely,coloristhefrequencyofelectromagneticradiation,whenthatfrequencyfallswithinanarrowbandthatcorrespondstothepeakradiationfromour

Sun.That’sajoke,sortof.Actually,everydayuseofcolorisprescientific.Itreferstooureyes’andbrains’responsetosuchelectromagneticradiation.[Seealso:Charge,Chromodynamics.]

Confinement

Thefactthatquarksareneverobservedinisolation.Moreprecisely,foranyobservablestate,thenumberofquarksminusthenumberofantiquarksisamultipleof3.(Notethat0isamultipleof3.)Confinementisamathematicalconsequenceofchromodynamics,butnotonethatiseasytodemonstrate.

Conservationlaw

Aquantityisconservedifitsvalue,foranisolatedsystem,doesnotchangewithtime.Charge,energy,andmomentumareimportantexamplesofconservedquantities.Conservationlawsareextremelyimportant,fortheyprovidestablelandmarksamidtheincessantfluxofquantumGrid.

Core

Ourworkingtheoryofstrong,electromagnetic,weak,andgravitationalinteractions.Itisbasedonquantummechanics,threesortsoflocalsymmetry—specifically,thetransformationgroupsSU(3),SU(2),U(1)—andgeneralrelativity.TheCoretheorygivespreciseequationsgoverningallelementaryprocessesthatarepresentlyknowntooccur.Itspredictionshavebeentestedinmanyexperimentsandprovedtobeaccurate.TheCoretheorycontainsestheticflaws,sowehopeitisnotNature’slastword.(Infactitcan’tbe,becauseitdoesn’tdescribethedarkmatter.)

Cosmologicalterm

Alogicalextensionoftheequationsofgeneralrelativity.Ingeometriclanguage,thecosmologicaltermencourages(dependingonitssign)eithertheuniformexpansionorcontractionofspacetime.Alternatively,thecosmologicaltermcanbeinterpretedasrepresentingtheinfluenceofaconstantdensityofenergy(positiveornegative)onmetricfield.Thatdensityρisaccompaniedbyapressureprelatedtoitbythe“well-tempered

equation”ρ=-p/c2.

Darkenergy

AstronomicalobservationsindicatethatalargeportionofthemassoftheUniverse,around70%ofthetotal,isuniformlydistributedandveryaccuratelytransparent.Other,independentobservationsindicateanacceleratingexpansionoftheuniverse,whichwecanascribetonegativepressure.Themagnitudesandrelativesignoftheseeffectsareconsistentwiththewell-temperedequation.Thustheobservations,sofar,canbedescribedbyacosmologicalterm.Itislogicallypossible,however,thatfutureobservationswillrevealthatthedensityand/orpressurearenotconstant,orthattheyarenotrelatedbythewell-temperedequation.Thetermdarkenergywasintroducedtoavoidprejudgingtheseissues.

Darkmatter

Astronomicalobservationsindicatethatalargeportionofthemassoftheuniverse,around25%ofthetotal,isdistributedmuchmorediffuselythanordinarymatterandisveryaccuratelytransparent.Galaxiesofordinarymatteraresurroundedbyextendedhalosofdarkmatter.Thehaloweighs,intotal,aboutfivetimesasmuchasthevisiblegalaxy.Theremayalsobeindependentcondensationsofdarkmatter.Interestingcandidatestoprovidedarkmatterincludeweaklyinteractingmassiveparticles(WIMPS),associatedwithsupersymmetry,andaxions.[Seealso:Supersymmetry,Axions.]

Diracequation

InventedbyPaulDiracin1928,itisamodificationofSchrödinger’sequationforthequantum-mechanicalwavefunctionofelectrons,designedtobeconsistentwithboostsymmetry(thatis,specialrelativity).TheDiracequationis,roughlyspeaking,fourtimesasbigastheSchrödingerequation.Moreprecisely,itisasetoffourinterconnectedequations,governingfourwavefunctions.ThefourcomponentsoftheDiracequationautomaticallyincorporatespin(upordown)forbothparticlesandantiparticles,whichaccountsforfourcomponents.WithminormodificationstheDirac

equationisalsousedtodescribequarksandneutrinos.Intoday’sphysicsweinterprettheDiracequationasanequationforthefieldthatcreatesanddestroyselectrons(or,equivalently,destroysandcreatespositrons),ratherthanasanequationforthewavefunctionofindividualparticles.

Electrodynamics

Theorythatdescribestheactivityofelectricandmagneticfields,includingtheirresponsetochargesandcurrents(flowsofcharge).Itcanalsobeconsideredthetheoryofthephotonfield.Lightinallitsforms,including(forinstance)radiowavesandx-rays,isnowunderstoodtobeactivityinelectricandmagneticfields.ThebasicequationsforelectrodynamicswerediscoveredbyMaxwellandperfectedbyLorentz.[Seealso:Charge,Maxwellequations.]

Electron

Afundamentalconstituentofmatter.Electronscarryallthenegativeelectricchargeinnormalmatter.Theyoccupythebulkofthespaceinatoms,outsidetheatoms’smallnuclei.Electronsareverylightandmobilecomparedtonuclei,sotheyaretheactiveplayersinmostofchemistryandofcourseinelectronics.

Electroweaktheory

Themoderntheorygoverningboththeweakinteractionsandelectromagneticinteractions.Itissometimesalsocalledthestandardmodel.Therearetwoleadingideasintheelectroweaktheory.Oneisthatitsequationsaregovernedbylocalsymmetry,leadingtotheequationsofMaxwellandYang-Mills.Theotheristhatspaceisanexotickindofsuperconductor,which—roughlyspeaking—shortsoutsomeoftheinteractions,hidingtheireffects.(Anotherimportantideaisthattheinteractionsarechiral.Thisisrathermoretechnical,andIwon’ttrytodescribeithere.Itsmostdramaticconsequenceisthattheweakinteractionsviolateparity—thatis,thesymmetrybetweenleftandright.)ItissometimessaidthattheelectroweaktheoryunifiesQEDandtheweak

interactions,butitwouldbemoreaccuratetosaythatitmixesthem.[Seealso:Weakforce.]

Energy

Acentralconceptinphysics.Givenitsimportance,itissurprisinghowsubtleandunpromisingthedefinitionofenergyatfirstappears.Indeed,itwasonlyinthemid-nineteenthcenturythatthemodernconceptofenergyanditsconservationbegantoemerge.Theoriginalandmostobviousformofenergyiskineticenergy,whichisenergyrelatedtomotion.(Inpre-relativisticmechanicsthekineticenergyofabodywasidentifiedasone-halfitsmasstimesthesquareofitsvelocity.Therelativisticformulas,whichincluderestenergy,arediscussedinAppendixA.)Thekineticenergyofabodygenerallychangeswhenforcesactuponit,butforcertainkindsofforces(so-calledconservativeforces)itispossibletodefineapotentialenergyfunction,dependingonlyontheposition,suchthatthetotalofkineticandpotentialenergiesisconstant.Moregenerally,forsystemsofbodies,andacertainclassofforces,thesumofalltheirkineticenergies,plusapotentialenergydependingontheirpositions,isconserved.Thefirstlawofthermodynamicsassertsthatenergyisconserved,althoughitcanbehiddenasheat,whichisamanifestationofverysmall-scale,hard-to-observemotionwithinbodies.Ineffect,thefirstlawofthermodynamicsassertsthatthefundamentalforcesofnaturewillalwaysbefoundtobeconservative.Thatboldhypothesis,putforwardlongbeforethenatureofthefundamentalforceswasatallclear,isjustifiedbythesuccessofthermodynamics.[Seealso:JesuitCredo.]Inmoderntheoriesofphysics,energyappearsasaprimaryconcept,onthesamefootingastime,towhichitisdeeplyrelated.Forexample,thetimeTittakesfortheoscillatingelectricdisturbanceswithinaphotontogothroughonecompletecycleisrelatedtothephoton’senergyEthroughET=h,wherehisPlanck’sconstant.Withinthesetheories,conservationofenergyfollowsfromsymmetryoftheequationsundertimetranslation—

or,incommonEnglish,thefactthatthelawsdon’tchangeovertime.

Youmightwonder:ifthefundamentallawsofphysicsensureconservationofenergy,whyarepeopleurgedtotakemeasurestoconserveenergy?Afterall,thelawsofphysicsaresupposedtobeself-enforcing!Thepointisthatsomeformsofenergyaremoreusefulthanothers;inparticular,randomjiggling(heat)isnotreadilyavailabletodousefulwork.Itwouldbebetterphysicstoaskpeopletominimizetheirentropyproduction.[Seealso:Entropy.]

Entropy

Ameasureofdisorder.[Seeabookonthermodynamics,orconsultWikipedia.]

Ether

Aspace-fillingmaterial.Beforephysicistsgotcomfortablewiththeconceptoffieldsasfundamentalcomponentsofreality,theytriedtomakemechanicalmodelsofelectricandmagneticfields.Theyspeculatedthatelectricandmagneticfieldsdescribedthearrangementsofmorebasicparticle-likeobjects,muchasthedensityandflow-fieldsofliquidsdescribearrangementsandrearrangementsofatoms.Thosemodelsgotcomplicatedandneverworkedverywell,sothattheconcept“ether”gotabadreputation.Inmodernphysics,however,aspace-fillingmediumistheprimaryreality.Thismediumhasverydifferentpropertiesfromtheclassicalether,soI’vegivenitanewname:theGrid.

Fermion

Quantumtheory,andmoreparticularlyquantumfieldtheory,bringssharpnewmeaningtotheconceptoftwoobjectsbeingabsolutelythesame,orindistinguishable.Ifonehas,say,twoelectronsinstatesAandBatagiventime,andtwoelectronsinstatesA’,B’atalatertime,onecannotsaywhetherthetransitioninvolvedwasA→A’,B→B’orA→B’,B→A’.Onemustconsiderbothpossibilities.Forbosonsoneaddstheiramplitudes,forfermionsonesubtracts.Electronsarefermions.A

consequenceisthePauliexclusionprinciple:twoelectronscannotgetintothesamestate,forthentheamplitudescancelcompletely.Pauliexclusioninducesaneffectiverepulsionbetweenelectrons(quantumstatisticalrepulsion),whichisresponsibleforthefactthatdifferentelectronsinatomsmustoccupydifferentstates,whichinturnislargelyresponsibleforthefactthatchemistryisarichandcomplicatedsubject.Notonlyelectrons,butallleptonsandquarks,andtheirantiparticles,arefermions.Soareprotonsandneutrons,whichisabigreasonwhynuclearchemistryisarichandcomplicatedsubject.WeoftensaythatfermionsobeyFermistatistics,orFermi-Diracstatistics,afterpioneerphysicistswhoclarifiedtheimplicationsofthisbehaviorforsystemscontainingmanyidenticalparticles.

Feynmangraph(alsocalledFeynmandiagram)

Feynmangraphsareapictorialshorthandforprocessesdescribedbyquantumfieldtheory.Theyconsistoflinesconnectedathubs(alsocalledvertices).Thelinesrepresentfreemotionofparticlesthroughspacetime;thehubsrepresentinteractions.Withthisinterpretation,theFeynmangraphdepictsapossibleprocessinspacetime:some(realorvirtual)particlesinteract,andtheirquantumstatemaychangeasaresult.TherearepreciserulesforassigningprobabilityamplitudestotheprocessdepictedinagivenFeynmangraph.Thesquareoftheamplitude,accordingtotherulesofquantumtheory,istheprobabilityoftheprocess.

Field

Aspace-fillingentity.Thefieldconceptenteredphysicsinthenineteenthcentury,throughtheworkofFaradayandMaxwellonelectricityandmagnetism.Theydiscoveredthatthelawsofelectricityandmagnetismcouldbeformulatedmosteasilyifoneintroducedtheideathatthereare(invisible)electricandmagneticfieldsfillingallspace.Theforcefeltbyanelectricchargeatapointgivesameasureofthestrengthoftheelectricfieldatthatpoint;butintheFaraday-Maxwellconcept,thefieldisthere,whetherornotthereisachargedparticle

aroundtosenseit.Thusfieldshavealifeoftheirown.Thefruitfulnessofthisconceptsoonemerged,whenMaxwelldiscoveredthatself-renewingdisturbancesinelectricandmagneticfieldscouldbeinterpretedaslight,withnoreferencetomaterialchargeorcurrentswhatsoever.

Inthequantumversionofelectrodynamics,electromagneticfieldscreateanddestroyphotons.Moregenerally,thekindsofexcitationswesenseasparticles(electrons,quarks,gluons,etc.)arecreatedanddestroyedbyvariousfields(electronfields,etc.),whicharetheprimaryobjects.Thisprovidesourmostfundamentalunderstandingofthevitalfactthatanytwoelectrons,anywhereintheuniverse,haveexactlythesamebasicproperties.Bothweremadebythesamefield!

Sometimesphysicistsorengineerswillmakestatementslike“I’vereducedtheelectricandmagneticfieldstozeroinsidemyspeciallyshieldedlaboratory.”Don’tbefooled!Whatthismeansisthattheaveragevalueofthosefieldshasbeenzeroed;nevertheless,theelectromagneticfield,asanentity,isstillpresent.Inparticulartheelectromagneticfieldwillstillrespondtochargecurrentsinsidetheshielding,anditstillboilswithquantumfluctuations—thatis,virtualphotons.Similarly,theaveragevaluesofelectricandmagneticfieldsindeepouterspacearezero,ornearlyso,butthefieldsthemselvesextendthroughout,andsupportthepropagationoflightraysoverarbitrarilylargedistances.(Thefielddestroysaphotonatonepoint,andanewoneiscreatedatthenextpoint,....)[Seealso:Quantumfield.]

Fitzgerald-Lorentz

Theeffectthatstructureswithinamovingbodyappeartoastationaryobserverascontracted(shrunk)inthedirectionofmotion.FitzgeraldandLorentzpostulated

contraction suchaneffectinordertoexplainsomeobservationsintheelectrodynamicsofmovingbodies.EinsteinshowedthattheFitzgerald-LorentzcontractionisalogicalconsequenceofboostsymmetryintheformsuggestedbyMaxwell’sequations—thatis,ofspecialrelativity.

Flavor

Intoday’sphysics,apoorlyunderstoodthree-valuedattributeofquarksandleptons,independentoftheircharges.Forexample,therearethreedistinctflavorsofUquarks—u(up),c(charm),andt(top).Eachhasthesameelectriccharge,2e/3,andoneunitofcolorcharge(red,white,orblue).Inaddition,therearethreeflavorsofDquarks—d(down),s(strange),andb(bottom),alsoeachinthreecolors,withelectriccharge-e/3.Similarly,therearethreeflavorsofleptons—e(electron),μ(muon),andτ(taulepton)—thathaveelectriccharge-eandnocolorcharge,andfinally,threekindsofneutrinoswithneitherelectricnorcolorcharge.Withineachofthesegroups,theparticlesofdifferentflavorhaveidenticalCoreinteractions.Theydifferinmass,sometimesbylargefactors(forexample,tisatleast35,000timesheavierthanu).Theweakinteractionsallowtransformationsamongthedifferentflavors.Thereisnogoodtheoreticalexplanationofwhythemassesarewhattheyare.

AlthoughWbosonsacttochangeflavors,itwouldbewrongtothinkthatflavorplaysthesameroleinweakinteractionsascolorplaysinthestronginteraction.Wbosonsdonotresponddirectlytotheflavorproperty,buttoyetanotherpairofcharges,whatI’vecalledweakcolorcharges.TheWbosonschangeflavorsforsport,sotospeak;itisnotwhatdrivesthem.Thetriplicationofparticleswithidenticalarraysofchargesandtherulesoftheflavor-changinggamethatWbosonsplayremainmysteries.

1.InNewtonianphysics,forceisdefinedtobean

Force influencethat,whenactingonabody,causesittoaccelerate.Thisdefinitionwasfruitful,andremainsuseful,becauseinmanycasesforcesturnouttobesimple.Forexample,anisolatedbodyfeelsnoforces—astatementequivalenttoNewton’sfirstlawofmotion,whichsaysthatanisolatedbodymoveswithconstantvelocity.2.Inmodernfundamentalphysics—and,specifically,intheCoretheoryanditsunifiedextensions—theoldforceconceptislessuseful.Itisstillcommontouseexpressionssuchas“thestrongforce,”“theweakforce,”andsoon,butamongthemselvesphysicistsusuallyrefer,moreabstractly,to“thestronginteraction.”I’vegenerallyusedtheonesyllableversioninthisbook.

Gaugesymmetry

[See:LocalSymmetry.]

Generalrelativity

Einstein’stheoryofgravity,basedontheideaofcurvedspacetimeor,alternatively,themetricfield.Inthefieldformulation,generalrelativitybroadlyresembleselectromagnetism.Butwhereaselectromagnetismisbasedontheresponseofelectricandmagneticfieldstochargesandcurrents,generalrelativityisbasedontheresponseofmetricfieldtoenergyandmomentum.[Seealso:Metricfield.]

Gluon

Anyofasetofeightparticlesthatmediatethestrongforce.Gluonshavepropertiessimilartothoseofphotons,buttheyrespondto(andchange)colorchargesratherthanelectriccharge.Theequationsforgluonshavetremendouslocalsymmetry,whichlargelydeterminestheirform.[Seealso:Chromodynamics,LocalSymmetry,Yang-Millsequations.]

Grid

Theentityweperceiveasemptyspace.Ourdeepestphysicaltheoriesrevealittobehighlystructured;indeed,itappearsastheprimaryingredientofreality.Chapter8isallabouttheGrid.

Hadron

Aphysicalparticlebasedonquarksandgluons.(Quarksandgluonsthemselvesdon’tcount,becausetheycan’texistinisolation.)Twobasickindsofhadronshavebeenobserved:mesonsandbaryons.MesonsaremadebylettingaquarkandanantiquarkcomeintoequilibriumwiththeGrid.BaryonsaremadebylettingthreequarkscomeintoequilibriumwiththeGrid.Manydozensofdifferentmesonsandbaryonshavebeenobserved.Nearlyallarehighlyunstable.“Glueballs,”initiatedbytwoorthreegluons,mayalsoexist.Thereissomecontroversyaboutwhetherglueballshavebeenobserved—theparticleswediscoverdon’tcomeclearlylabeled!

Higgsparticle

Excitationinthe(sofar,hypothetical)fieldthatmakesemptyspaceacosmicsuperconductorfortheweakforce.

Hub

Aspacetimepointatwhichparticles(realorvirtual)interact.InFeynmangraphs,hubsaretheplaceswherethreeormore

linesmeet.Theoriesofparticleinteractionssupplyrulesforwhatkindsofhubsarepossible,andthemathematicalfactorsassociatedwiththem.Inthetechnicalliterature,hubsareusuallycalledvertices.[Seealso:Feynmangraph.]I

Hypercharge

Theaverageelectricchargeofseveralparticlesrelatedbysymmetry.Inthecontextofunifiedtheories,hyperchargeismorefundamentalthanelectriccharge;thedistinction,however,arisesatafinerleveloftechnicaldetailthanI’veattemptedinmostofthisbook.

JesuitCredo

“Itismoreblessedtoaskforgivenessthanpermission.”Thisisaprofoundtruth.

Jet

Aclearlyidentifiablegroupofparticlesmovinginnearlythesamedirection.Jetsofparticlesarefrequentlyobservedasproductsofhigh-energycollisionsat

accelerators.Asymptoticfreedomallowsustointerpretjetsasthevisiblemanifestationofunderlyingquarks,antiquarks,andgluons.

LEP

AcronymforLargeElectron-Positroncollider.LEPoperatedatthegreatEuropeanlaboratoryCERN,nearGeneva,throughthe1990s.Roughlyspeaking,ittookpicturesofemptyspace,atevenhigherresolutionsthanSLAC.Todothis,electronsandtheirantiparticles(positrons)wereacceleratedtoenormousenergiesandthenmadetoannihilate,producinganintenseflashofenergywithinanextremelysmallvolume.LEPwasamachineforcreativedestruction.ExperimentsatLEPtestedandestablishedtheCoretheorywithextraordinaryquantitativeprecision.[Seealso:SLAC.]

Lepton

Anyoftheparticlese(electron),μ(muon),andτ(taulepton)ortheirneutrinos.Theseparticlescarryzerocolorcharge.e,μ,andτallcarrythesameelectriccharge,-e.(Yes,Irealizethatthesamesymbolisbeingusedfordifferentthings.Sorry,butlettersoftenare,ifyouthinkaboutit.)Neutrinoscarryzeroelectriccharge.Theyallparticipateintheweakinteractions.

Thereareverygood(butnotperfect)conservationlaws,accordingtowhichthetotalnumberofelectrons-antielectronsplusthetotalnumberofelectronneutrinos-electronantineutrinosstaysconstantintime(eventhoughtheseparatenumbersmaychange)—andsimilarlyforμandτ.Forexample,inmuondecaytheendproductisanelectron,amuonneutrino,andanelectronantineutrino.Boththeinitialstateandthefinalstatehavemuonicleptonnumberoneandelectronicleptonnumberzero.These“lawsofconservationofleptonnumber”areviolatedbythephenomenonofneutrinooscillations.Smallviolationofleptonnumberconservationwaspredictedbyunifiedtheories.Itsobservationencouragesustothinkthatthosetheoriesareontherighttrack.[Seealso:Neutrino.]

LHC

AcronymforLargeHadronCollider.TheLHCoccupiestheoldLEPtunnelatCERN.Itusesprotonsinsteadofelectronsandpositrons,andattainshigherenergies.Itwillbesurprisingifgreatdiscoveriesdon’toccurattheLHC.Ataminimum,weshouldfindoutwhatmakestheGridanexoticsuperconductor.

Localsymmetry(alsoknownasgaugesymmetry)

Symmetrysupportingindependenttransformationsindifferentspacetimeregions.Localsymmetryisaverypowerfullrequirement,whichfewequationssatisfy.Conversely,byassuminglocalsymmetry,weareledtoveryspecificequations,oftheMaxwellandYang-Millstype.ExactlytheseequationscharacterizetheCoretheoryandtheworld.Localsymmetryisalsocalledgaugesymmetry,forinterestingbutobscurehistoricalreasons.[Seealso:Symmetry,Maxwellequations,Yang-Millsequations.]

Mass

Apropertyofaparticleorsystem,whichisameasureofitsinertia(thatis,aparticle’smasstellsushowdifficultitistochangetheparticle’svelocity).Forcenturiesscientiststhoughtthatmassisconserved,butnowweknowthatitisnot.

MassWithoutMass

Theconcept,realizedinmodernphysics,thatobjectswithnonzeromasscanemergefrombuildingblocksofzeromass.

Maxwellequations

Thesystemofequationsgoverningthebehaviorofelectricandmagneticfields,includingtheirresponsetoelectricchargesandcurrents.Maxwellarrivedatthefullsetofequationsin1864,bycodifyingallthemutualinfluencesamongelectricity,magnetism,charge,andcurrentknownatthetime,andinadditionpostulatinganeweffect,whichmadethesystemconsistentwithconservationofcharge.Maxwell’soriginalformulationwassomewhatmessy,sotheunderlying(profound)simplicityandsymmetryoftheequationswerenot

evident.Later,physicistsincluding(notably)Heaviside,Hertz,andLorentzcleanedthingsupandgaveustheMaxwellequationsasweknowthemtoday.Theseequationshavesurvivedthequantumrevolutionintact,althoughtheinterpretationofelectricandmagneticfieldshasevolved.[Seealso:Field.]

Meson

Atypeofstronglyinteractingparticle,orhadron.[See:Hadron.]

Metricfield

Afieldthatcanberegardedasspecifying,ataspacetimepoint,theunitsformeasuringtimeanddistance(inalldirections).Thusspaceitselfcomessuppliedwithmeasuringrodsandclocks.Ordinaryrodsandclockstranslatethisunderlyingstructureintoaccessibleforms.Matteraffectsthemetricfield,andviceversa.Theirmutualinteractionisdescribedbythegeneraltheoryofrelativityandgivesrisetotheobservedforceofgravity.[Seealso:Generalrelativity.]

Momentum

Acentralconceptinphysics.Theoriginalandmostobviousformofmomentumiskineticmomentum,associatedwiththemotionofparticles.Inpre-relativisticmechanics,thekineticmomentumofabodywasidentifiedasitsmasstimesitsvelocity.Newtoncalledmomentum“quantityofmotion,”anditappearsinhissecondlaw:therateofchangeofmomentumofabodyisequaltotheforceactingonit.Inspecialrelativity,momentumiscloselyrelatedtoenergy.Underboosts,energyandmomentummixwithoneanother,justastimeandspacedo.Thetotalmomentumofanisolatedsystemisconserved.

Inmoderntheoriesofphysics,momentumappearsasaprimaryconcept,onthesamefootingasspace,towhichitisdeeplyrelated.Forexample,thedistanceDthatittakesforthespatiallyperiodicelectricdisturbanceswithinaphotontogothroughonecompletecycleisrelatedtothephoton’smomentumPthroughPD=h,

wherehisPlanck’sconstant.Withinthesetheories,conservationofmomentumfollowsfromsymmetryoftheequationsunderspatialtranslation—or,incommonEnglish,fromthefactthatthelawsarethesameeverywhere.[Compare:Energy.]

Neutrino

Akindofelementaryparticlethathasneitherelectricchargenorcolorcharge.Neutrinosarespin½fermions.Neutrinoscomeinthreeseparatetypes,orflavors,associatedwiththethreeflavorsofchargedleptons(electronse,muonsμ,andtauleptonsτ).Inweakinteractionprocesses,chargedleptonsandtheirantiparticlescanbetransformedintoneutrinosandtheirantiparticles,butalwaysinsuchawaythattheleptonnumbersareconserved.[Seealso:Leptons.]NeutrinosareemittedabundantlybytheSun,buttheirinteractionsaresofeeblethatnearlyallofthempassfreelythroughtheSun,nottomentionEarthiftheyhappentopointourway.Nevertheless,somerepresentativesofthesmallfractionthatdointeracthavebeendetected,inheroicexperiments.Recentlyitwasestablishedthatthedifferenttypesofneutrinos,astheytraveloverlongdistances,oscillatefromoneformintoanother(forexample,anelectronneutrinomightmorphintoamuonneutrino).Suchoscillationsviolatetheleptonconservationlaws.Theirexistenceandroughmagnitudeisconsistentwithexpectationsfromunifiedtheories.

Neutron

Areadilyidentifiablecombinationofquarksandgluons,andanimportantcomponentofordinarymatter.Individualneutronsareunstable;theydecayintoproton,electron,andelectronantineutrinowithalifetimeofaboutfifteenminutes.Neutronsboundintonucleicanbestable,however.[Compare:Proton.]

Normalmatter

Thephysicalsubstancestudiedinbiology,chemistry,materialsscienceandengineering,andmostofastrophysics.Itis,ofcourse,thesubstancehumans,and

theirpetsandmachines,aremadeof.Ordinarymatterismadefromuanddquarks,electrons,gluons,andphotons.Wehaveaprecise,accurate,andremarkablycompletetheoryofnormalmatter:thekerneloftheCore.

Nucleus

Smallcentralpartofanatom,whereallthepositivechargeandalmostallthemassisconcentrated.

Particle

LocalizeddisturbanceintheGrid.

Photon

Minimalexcitationoftheelectromagneticfield.Aphotonisthesmallestunitoflight,sometimescalledthequantumoflight.(Bytheway,aquantumleapisaverysmallleap.)

Planck’sconstant

Aphysicalconstantthatplaysacentralroleinquantumtheory.Itappears,forexample,intherelationshipE=hνbetweentheenergyofaphotonandthefrequencyνofthelightitrepresents,ortherelationshipp=h/λbetweenthemomentumofaphotonandthewavelengthλofthelightitrepresents.

Planckunits

Unitsoflength,mass,andtimederivedfromthevaluesofquantitiesthatappearinphysicallaws,ratherthanfromreferenceobjects.Thusonedoesn’tneedastandardized“meterstick”(orroyalextremity)tocomparelengths,noraspinningEarthtofixtheunitoftime,noraprototypekilogram.Instead,Planckunitsareconstructedbytakingsuitablepowersandratiosofthespeedoflightc,Planck’sconstanth,andNewton’sconstantGthatappearsintheequationsforgravity.Planckunitsarenotusedinpracticalwork:thePlancklengthandtimeunitsareabsurdlysmall;thePlanckmassunitisabsurdlylargeonatomicscales,butawkwardlysmallonhumanscales.Planckunitsareimportanttheoretically,however.Theyposethechallengeofcomputingsuchpurelynumericalquantities

astheprotonmassinPlanckunits(whereasthereisnopossibilityofcomputingthemassofastandardkilogram,sothe“problem”ofcomputingtheprotonmassinkilogramsispoorlyposed).

Ifweextrapolatetheexistinglawsofphysicsfarbeyondwherethey’vebeentested,wefindthatquantumfluctuationsinthemetricfieldonlengthandtimescalesbelowthePlancklengthandtimearesoimportant,comparedtoitsaveragevalue,thattheoperationalmeaningoflengthandtimebecomesunclear.Asdiscussedinthisbook,therearesignificantindicationsthatthedifferentforcesofnaturebecomeunified—inparticular,thattheirpowersbecomeequal—whenmeasuredinPlanckunitsatthePlanckscaleofdistance.

Proton

Averystablecombinationofquarksandgluons.Protonsandneutronswereoncethoughttobefundamentalparticles;nowweunderstandthattheyarecomplexobjects.Onecangetausefulmodelofatomicnucleiusingtheideathattheyareboundsystemsofprotonsandneutrons.Protonsandneutronshavenearlythesamemass;neutronsareabout0.2%heavier.Protonshaveelectricchargee,equalinmagnitudebutoppositeinsigntothechargeofelectrons.Thenucleiofhydrogenatomsaresingleprotons.Protonsareknowntohavelifetimesofatleast1032years(muchlongerthanthelifetimeoftheuniverse),butunifiedtheoriespredictthattheirlifetimecannotbemuchlongerthantheexistinglimit,andimportantexperimentsareunderwaytotestthisprediction.

QCD

Shortforquantumchromodynamics.[Seealso:Chromodynamics.]

QED

Shortforquantumelectrodynamics.Itis,ofcourse,theversionofelectrodynamicsincorporatingquantumtheory.Thefieldsnowhavespontaneousactivity(virtual

photons),andtheirdisturbancescomeindiscrete,particle-likeunits(realphotons).[Seealso:Electrodynamics,Photon,Quantumfield.]

Quantumfield

Aspace-fillingentitythatobeysthelawsofquantumtheory.Quantumfieldsarethelegitimatechildrenofthemarriagebetweenquantummechanicsandspecialrelativity.Quantumfieldsdifferfromclassicalfieldsinthattheyexhibitspontaneousactivity,alsoknownasquantumfluctuationsorvirtualparticles,atalltimesandthroughoutspace.TheCoretheory,whichsummarizesourbestcurrentunderstandingoffundamentalprocesses,isformulatedintermsofquantumfields.Particlesappearassecondaryconsequences;theyarelocalizeddisturbancesintheprimaryentities—thatis,inquantumfields.

Somegeneralconsequencesofquantumfieldtheorythatdonotfollowfromquantummechanicsorclassicalfieldtheoryseparatelyare:theexistenceofparticletypesthatarethesamethroughouttheuniverseandforalltime(forinstance,allelectronshaveexactlythesameproperties);theexistenceofquantumstatistics[See:Boson,Fermion];theexistenceofantiparticles;theinevitableassociationofparticleswithforces(forexample,fromtheexistenceofelectricandmagneticforcesonededucesphotons);theubiquityofparticletransformation(quantumfieldscreateanddestroyparticles);thenecessityofsimplicityandhighsymmetryforconsistentlawsofinteraction;andasymptoticfreedom[see:Asymptoticfreedom].Alltheseconsequencesofquantumfieldtheoryareprominentaspectsofphysicalrealityaswefindit.

Quarks

Togetherwithgluons,theplayersinthestrongforce(experimentalaspect)or,alternatively,QCD(theoreticalaspect).Theyarespin½fermions.TherearethreedistinctflavorsofUquarks—u(up),c(charm),andt(top)—andeachhasthesameelectriccharge,2e/3,and

oneunitofcolorcharge(red,white,orblue);inadditiontherearethreeflavorsofDquarks—d(down),s(strange),andb(bottom),alsoeachinthreecolors,withelectriccharge-e/3.Weakinteractionprocessescantransformthevariousflavorsintooneanother.Thus(color)gluonschangethecolorchargeofaquark,butnotitsflavor,whereasWbosonschangeflavor,butnotcolor.Quarksarenotobserveddirectly,butleavetheirsignatureinjets(experimentalaspect)andareusedasbuildingblockstoconstructtheobservedhadrons(theoreticalaspect).AlltheCoreinteractionsconservethetotalnumberofquarksminusantiquarks.This“conservationofbaryonnumber”ensuresprotonstability.Unifiedtheoriesgenerallypredicttheexistenceofinteractionsthatchangequarksintoleptonsandcouldcauseprotonstodecay.Sofar,nosuchdecayhasbeenobserved.[Seealso:Alltheunderlinedterms.]

RHIC

AcronymforRelativisticHeavyIonCollider.RHIClivesonLongIsland,attheBrookhavenNationalLaboratory.CollisionsatRHICreproduce,inaverysmallvolumeandforverybriefperiods,extremeconditionsthelikeofwhichwerelastseenintheearliestmomentsofthebigbang.

Schrödingerequation

Anapproximateequationforthewavefunctionofanelectron.electron.TheSchrödingerequationdoesnotsatisfyboostsymmetry,whichistosayitisnotconsistentwithspecialrelativity.Butitgivesagooddescriptionofelectronsthatarenotmovingtoofast,anditiseasiertoworkwiththanthemoreaccurateDiracequation.TheSchrödingerequationisthefoundationformostpracticalworkinquantumchemistryandsolid-statephysics.

Screening

Apositiveelectricchargeattractsnegativecharges,whichtendtocancel(screen)it.Thusthefullstrengthofapositivechargewillbefeltonlycloseby;faraway,its

influenceisdiminishedbytheaccumulatednegativecharge.Screeningisveryimportantinthetheoryofmetals,whichcontainmobileelectrons.Itisalsoimportantfor“emptyspace,”i.e.,theGrid.Inthatcase,thenegativechargesaresuppliedbyvirtualparticles.Althoughparticularvirtualparticlescomeandgo,thetotalpopulationissteadyandmakestheGridadynamicmedium.[Seealso:Antiscreening,Grid,Virtualparticle.]

SLAC

AcronymforStanfordLinearAcceleratorComplex,afacilitythatplayedakeyroleinestablishingtheCoretheory.HereFriedman,Kendall,Taylor,andtheircollaboratorstooktheirhigh-resolution,short-exposurepicturesofprotoninteriors,whichputusontheroadtoQCD.Thetwo-mile-longelectronacceleratortheyusedprovided,ineffect,anultrastroboscopicnanomicroscope.

Spin

Thespinofanelementaryparticleisameasureofitsangularmomentum.Angularmomentum,inturn,isaconservedquantitythathasmuchthesamerelationtorotationsinspaceas(ordinary)momentumhastotranslationsinspace.[Seealso:Momentum.]Inclassicalmechanics,theangularmomentumofabodyisameasureoftheangularmotionofthatbody.Thespinofanelementaryparticleiseitherawholenumberorawholenumber+½timesh/2π,wherehisPlanck’sconstant.Themagnitudeofspinisastablecharacteristicofeachparticletype.Leptonsandquarksaresaidtohavespin½,becausetheirspinis½timesh/2π.Protonsandneutronsalsohavespin½.Photons,gluons,andWandZbosonshavespin1.πmesonsandthehypotheticalHiggsparticlehavespin0.Thepolarizationoflightisaphysicalmanifestationofthephoton’sspin.

Theangularmomentumofanisolatedbodyisconserved.Tochangeanangularmomentum,onemustapplyatorque.Rapidlyspinninggyroscopeshavelarge

angularmomentum,andthisfactislargelyresponsiblefortheirunusualresponsetoforces.

Spontaneoussymmetrybreaking

Whenthestablesolutionsofasetofequationshavelesssymmetrythantheequationsthemselves,wesaythatthesymmetryisspontaneouslybroken.Notably,thiscanhappenifitisenergeticallyfavorabletoformacondensateorbackgroundfield,as

Strongforce

Oneofthefourbasicinteractions.Thestrongforcebindsquarksandgluonsintoprotons,neutrons,andotherhadrons,andholdsprotonsandneutronstogethertoformatomicnuclei.Mostofwhatisobservedathigh-energyacceleratorsisthestrongforceinaction.

Superconductor

Somematerials,whentheyarecooledtoverylowtemperatures,transitionintoaphasewheretheirresponsetoelectricandmagneticfieldsexhibitsqualitativelynewfeatures.Theirelectricresistancevanishes,andtheylargelyexpel—thatis,cancelout—appliedmagneticfields(thisistheMeissnereffect).Wesaytheyhavebecomesuperconductors.Theelectromagneticbehaviorofsuperconductors,whenanalyzedmathematically,indicatesthatwithinsuperconductorsphotonshaveacquirednonzeromass.

Althoughtheyresemblephotonsinmanyways—theyarespin1bosons,theyrespondto(weakcolor)charges—WandZbosonshavenonzeromass.Onthefaceofit,thatnonzeromasswouldruleouttheotherwiseattractiveideathatWandZbosons,likephotons,obeyequationswithlocalsymmetry.Superconductivityshowsthewayforward.Bypostulatingthatspaceisasuperconductor,notforelectriccharge,butforthechargesthatWandZbosonscareabout,wegivethoseparticlesnonzeromass,whilemaintainingthelocalsymmetryoftheunderlyingequations.Thisisacentralideaofmodernelectroweaktheory,anditseemstodescribeNatureverywell.MorespeculativeideaspostulateanadditionallayerofGrid

superconductivity,togiveverylargemassestotheparticlesthatmediatequark-leptontransitions.

Superstringtheory

Acollectionofideasforextendingthelawsofphysics.Ithasinspiredbrilliantworkbybrilliantpeople,resultinginimportantapplicationstopuremathematics.Atpresent,superstringtheorydoesnotprovideequationsthatdescribeconcretephenomenainthenaturalworld.Specifically,theCoretheory,whichaccuratelydescribessomuchaboutthephysicalworld,hasnotbeenshowntoemergeasanapproximationtosuperstringtheory.

TheideasofsuperstringtheoryarenotnecessarilyinconsistentwiththeCoretheory,orwiththeideasforunificationadvocatedinthisbook.Buttheideasdiscussedheredidnotarise,historically,fromsuperstringtheory,norhavetheybeenderivedfromsuperstringtheory.Theiroriginis,asI’veexplainedatlength,partlyempiricalandpartlymathematical/esthetic.

Supersymmetry(SUSY)

Anewkindofsymmetry.Supersymmetrymakestransformationsamongparticlesthathavethesamecharges,butdifferentspins.Inparticular,itallowsustoseebosonsandfermions,despitetheirradicallydifferentphysicalproperties,asdifferentviewsofasingleentity.Supersymmetrycanberealizedasaboostsymmetryinsuperspace,anextensionofspacetimetoincludeadditionalquantumdimensions.

OurpresentCoreequationsdonotsupportsupersymmetry,butitispossibletoexpandthemsothattheydo.Thenewequationspredicttheexistenceofmanynewparticles,noneofwhichhasbeenoberved.OnemustpostulatesomeformofGridsuperconductivitytomakemanyoftheseparticlesheavy.Thegoodnewsisthatthenewparticles,intheirvirtualform,supportasuccessful,quantitativeunificationoftheforces,asdescribedinChapter20.Oneofthenewparticlescouldbeagoodcandidatetosupplythedarkmatter.TheLHC

shouldbepowerfulenoughtoproducesomeofthenewparticles,iftheyexist.

Symmetry

Symmetryexistswhentherearedistinctionsthatdon’tmakeanydifference.Thatis,anobject—orasetofequations—exhibitssymmetrywhentherearethingsyoucandotoitthatmighthavechangeditbutinfactdonot.Thusanequilateraltrianglehassymmetryunderrotationby120°arounditscenter,whereasalopsidedtriangledoesnot.

Timedilation

Theeffectthat,viewedfromtheoutside,theflowoftimewithinamovingsystemappearstoslowdown.Timedilationisaconsequenceofspecialrelativity.

Unifiedtheory

ThedifferentcomponentsoftheCoretheoryarebasedoncommonprinciples—quantummechanics,relativity,andlocalsymmetry—butwithintheCoretheorytheyremainseparateanddistinct.OnehasseparatesymmetrytransformationsforthecolorchargesofQCD,theweakcolorchargesofthestandardelectroweaktheory,andhypercharge.Underthesetransformations,thequarksandleptonsfallintosixunrelatedclasses(actuallyeighteen,countingflavortriplication).Allthisstructurebegsustoconsiderthepossibilityofalarger,encompassingsymmetry.Uponexploringthemathematicalpossibilities,onefindsthatmanythingsclickintoplacequitenicely.Arelativelysmallexpansionoftheequationsenablesonetoviewalltheknownsymmetriesaspartsofasatisfyingwhole,andtobringthescatteredquarksandleptonstogether.Asabonus,gravity,whichseemedhopelesslyfeeblerthantheotherfundamentalforces,comesintofocusaswell.Tomaketheideasworkinquantitativedetail,itappearswemustalsoincludesupersymmetry.Theexpandedequationspredicttheexistenceofmanynewparticlesandphenomena.AsexplainedinChapters19–21,thejuryisoutonthesetheories,butsomeverdictsshouldbecominginsoon.

Velocity Rateofchangeofposition.

Vertex [See:Hub.]

Virtualparticle

Spontaneousfluctuationinaquantumfield.Realparticlesareexcitationsinquantumfieldsthathavesomeusefuldegreeofpermanenceandcanbeobserved.Virtualparticlesaretransients,whichappearinourequationsbutnotinexperimentaldetectors.Bysupplyingenergy,itispossibletoamplifythespontaneousfluctuationsabovethreshold,aneffectthatmakes(whatwouldhavebeen)virtualparticlesintorealones.

Wavefunction

Inquantumtheory,thestateofaparticleisnotspecifiedbyaposition,oradefinitedirectionforspin;instead,theprimarydescriptionofthestateinvolvesitswavefunction.Thewavefunctionspecifies,foreachpossiblepositionanddirectionofspin,acomplexnumber,theso-calledprobabilityamplitude.The(absolute)squareoftheprobabilityamplitudegivestheprobabilityoffindingtheparticleatthatpositionwiththatdirectionofspin.Forsystemsofmanyparticles,orfields,thewavefunctionsimilarlyspecifiesamplitudesforallpossiblephysicalbehaviorsthatyoumightfind,uponmakingameasurement.Asimple,butnottoosimple,exampleofwavefunctionsatworkisdiscussedinChapter9.

Weakforce(orinteraction)

Togetherwithgravity,electromagnetism,andthestrongforce,oneofthefundamentalinteractionsofNature.Alsoknownastheweakinteraction.Themostimportanteffectoftheweakinteractionistosupporttransformationsamongdifferenttypesofquarksanddifferenttypesofleptons(butnotofquarksinto

Well-temperedequation

ρ=-p/c2[Seealso:Cosmologicalterm,Darkenergy.]

Yang-Millsequations

GeneralizationsofMaxwell’sequations,whichsupportsymmetryamongseveralkindsofcharges.Speakingroughlyandcolloquially,wecansaythattheYang-MillsequationsaretheMaxwellequationsonsteroids.Today’stheoriesofthestrongandoftheelectroweakinteractionsarelargelybasedontheYang-Millsequations,forthesymmetrygroupsSU(3)andSU(2)×U(1),respectively.

Notes

Chapter1

Ashortandveryaccessible,thoughnowinpartsdated,introductiontophysicsbyagrandmasterisTheCharacterofPhysicalLawbyRichardFeynman(MIT).The Feynman Lectures on Physics (3 volumes) by Richard Feynman, RobertLeighton, and Matthew Sands (Addison-Wesley) was prepared with Caltechundergraduatesinmind,buttheearlypartsofeachbookandofmanyindividualchaptersareconceptual,colloquial,andfrequentlybrilliant.

Chapter2

11 the monumental work that perfected classical mechanics: The classicanalysisofthefoundationsofclassicalmechanicsisTheScienceofMechanicsby ErnstMach (Open Court). Einstein read this book carefully in his studentdays,anditscriticaldiscussionoftheNewtonianconceptsofabsolutespaceandtimehelpedhim toward the relativityconcept.Hewrote, “Even [JamesClerk]Maxwell and [Heinrich] Hertz, who in retrospect appear as those whodemolishedthefaithinmechanicsasthefinalbasisofallphysical thinking, intheirconsciousthinkingadheredthroughouttomechanicsasthesecuredbasisofphysics. It was ErnstMachwho, in his history ofmechanics (Geschichte derMechanik),shookthisdogmaticfaith.Thisbookexercisedaprofoundinfluenceupon me in this regard while I was a student. I see Mach’s greatness in hisincorruptible skepticism and independence.” For Newton’s own views, in hisownwords, see especiallyNewton’s Philosophy of Nature (Hafner). For otherhistorical and philosophical perspectives, see The Concept of Mass by MaxJammer(Dover).

Chapter3

The Principle of Relativity (Dover) is an indispensable collection of classicpapers on relativity. It contains papers by Lorentz, Einstein, Minkowski, andWeyl. Both of Einstein’s two original special relativity papers and hisfoundationalpaperongeneralrelativityareincluded.ThefirsthalfofEinstein’sfirstspecialrelativitypaperisalmostfreeofequations,andit’sajoytoread.Theearlypartsofhis firstpresentationofgeneral relativityarealsoaccessibleandinspiring. (For students of physics: that paper as a whole remains the bestintroduction to general relativity, inmyopinion.)TheEvolution ofPhysicsbyEinsteinandLeopoldInfeld(Touchstone)isacharmingpopularizationnotonlyofrelativityitselfbutalsoofitsintellectualbackgroundinelectromagnetismandofthefoundationsoffieldphysics.TwogoodmodernintroductionstorelativityareSpacetime Physics by Edwin Taylor and JohnWheeler (Freeman) and It’sAboutTime:UnderstandingEinstein’sRelativitybyDavidMermin(Princeton).

Chapter4

2395%of themass:Aswe’ll see,mostof themassofnormalmattercanbecalculated within a theory whose building blocks are massless gluons andmasslessuanddquarksandnothingelse(thetheoryIcallQCDLite).QCDLitetruly generatesMassWithoutMass. It is, however, not a complete theory ofnature.Lotsofthingsareleftout:electromagnetism,gravity,electrons,thesmallintrinsicmassesofuanddquarks,andmore.Fortunately,wecanestimatehowmuch the things we’ve left out or idealized away affect the mass of normalmatter—and we can check our estimates, using the sorts of calculationsdescribed inChapter9.Tomakea longstoryshort, the left-outeffectschangethingsbylessthan5%.(Forexperts:themostimportanteffectcomesfromthesquark.Itistooheavytotreatasmassless,butnotsoheavythatwecanintegrateitoutcleanly.)

Chapter5

RichardRhodes’sbookTheMakingoftheAtomicBomb(Simon&Schuster)isnot only a masterpiece of history and of literature, but also an excellentintroductiontonuclearphysics.

Chapter6

51thetheorywecallquantumchromodynamics,orQCD:Alivelyhistoricalaccount of the ideas and experiments leading to QCD is The Hunting of theQuarkbyMichaelRiordan(Touchstone).Twogood,accessibleaccountsofthephysics of QCD and the standard model of electroweak interactions are TheTheoryofAlmostEverythingbyRobertOerter(PiPress)andTheNewCosmicOnionbyFrankClose(TaylorandFrancis).Unique,andamust, isFeynman’spresentation of QED from scratch: QED: The Strange Theory of Light andMatter(Princeton).

33aclassofequations...byChenNingYangandRobertMills:50YearsofYang-Mills Theory, edited by G. ‘t Hooft (World Scientific), is an importantcollectionofarticlesby leadingexpertson thephysics that’sgrownoutof theYang-Millsequations.

34Theclaimwithouthavingtosupplysamplesormakeanymeasurementsis a (remarkably slight) exaggeration. Itwould be true if all quarks had eitherzeromassor infinitemass.Finite,nonzerovaluesof theirmasscancomeonlyfrommeasurementsorsamples.InNaturetheuanddquarkshavealmostzeromass,relativetothemassofprotonsorneutrons,whereasthec,b,andtquarksare so heavy that they play very little role in the structure of protons andneutrons,evenasvirtualparticles.Thestrangequarks is intermediate: itplayssomerole in thestructureofprotonsandneutrons, thoughnota largeone.Wecanget agoodapproximate theoryofprotonsandneutronsbypretending thattheuanddquarkshavezeromass,whereas theothershave infinitemass,andcan therefore be ignored. I call this approximate theory “QCDLite.” InQCDLite,youreallydon’thavetomakeanymeasurementsorsupplyanysamples.

Einstein emphasized the ideal of purely conceptual theories, which do notrequire measurements or samples as input, in his Autobiographical Notes: “Iwouldliketostateatheoremwhichatpresentcannotbebaseduponanythingmorethanuponafaithinthesimplicity,i.e.,intelligibility,ofnature:therearenoarbitraryconstants . . . that is tosay,nature is soconstituted that it ispossiblelogicallytolaydownsuchstronglydeterminedlawsthatwithintheselawsonlyrationally completely determined constants occur (not constants, therefore,whosenumericalvaluecouldbechangedwithoutdestroyingthetheory).”QCD

Lite is a rare exampleof apowerful theoryof thatkind. (For experts: anotherexample is the theory of structural chemistry based onSchrödinger’s equationwith infinitely heavy nuclei.) This issue is closely related to the question offixing parameters that arises in Chapter 9, and to thephilosophical/methodologicaldiscussionsinChapters12and19.Becausequarksdonotappearasisolatedparticles,theconceptoftheirmass

requiresspecialconsideration.Forshorttimesanddistances,quarksmoveasiftheyarefree(asymptoticfreedom).Wecancalculatesomeconsequencesofsuchmotion,whichofcoursedependonwhatvalueweassign to thequarks’mass.Then,whenwecomparecalculationstoexperiment,wedeterminethevalueofthemass.Thisworkswellfortheheavierquarks.Forthelighterquarks,amorepracticalway is to calculate the contribution of theirmass to themass of thehadronsthatcontainthem,asdescribedinChapter9.Intuitively,whatwemeanbyaquark’smassisthemassofthebarequark,strippedofitscloudofvirtualparticles.

43 strictly identical conditions assumes that there are no hidden variablesdescribingprotons—thatis, that theironlydegreesoffreedomarepositionanddirection of spin. All applications of Fermi statistics to protons rely on thisassumption.Theirsuccessthereforeprovidesoverwhelmingevidenceforit.

45nointernalstructurebringsupaveryinterestingandimportantissue,whicharises not only for quarks but also for protons, nuclei, atoms, andmolecules.Let’s discuss it for protons. As I mentioned in the preceding note, there isoverwhelmingevidencethat thestateofaprotoniscompletelyspecifiedbyitspositionandspin.Yetourbesttheoryofprotonsconstructsthemascomplicatedsystemsofquarksandgluons,or,moreaccurately(lookingaheadtoChapters7and 8), as complicated patterns of disturbance in theGrid. How does all thatstructure get hidden? If there’s all that stuff rattling around inside, why can’tdifferent protons have a large variety of different states, depending on whatexactlythatstuffinsideisdoing?

Inclassicalphysics,therewouldbemanypossibleinternalstates—or,ifyoulike, many “hidden variables.” But those states are removed by the QuantumCensor.Inquantumtheory(lookingahead,again,toChapter9)welearnthattheproton—oranyquantumsystem—supportsallitspossibleinternalstatesatonce,with different probability amplitudes. To get the lowest-energyquantum state,theprotoncombinesmanyclassicalstates,eachwithanappropriateamplitude.The next-best quantum state has a completely different set of amplitudes and

muchhigherenergy.Asaconsequence,youhavetodisturbtheprotonquitealotto change its internal structureatall. Small disturbances don’t supply enoughenergytorearrangetheamplitudes.Soforsmalldisturbances there isalwaysaunique set of amplitudes; variations are censored. The internal structure is, ineffect,frozenout.Itissimilartothewayasnowballactsasahard,rigidsphere,eventhoughit’smadefromlotsofmoleculesthat,athighertemperatures,wouldflowasliquidwater.An even closer analogy, mathematically, is to the physics of musical

instruments. If you play a flute properly, itwill sound a definite, desired tone(dependingonthefingering,ofcourse).Onlyifyoublowtoohard,orerratically,willitstarttosoundovertonesandscreeches.Thedesiredtonecorrespondstoaparticular—in detail, quite complex—vibration pattern of air in the flute. Theovertonecorrespondstoadistinctlydifferentpattern.Inthequantumtheorywehavevibratingwavefunctionsinsteadofvibratingair,buttheconceptsandthemathematicsarecloselysimilar.Indeed,whenthe“new”quantumtheoryusingwavefunctionswasdiscovered,physicistswentbacktotheirtextsonacousticsformathematicalguidance.It is because of theQuantumCensor that seemingly radical ideas about the

deep structure ofmatter can turn out to have little practical consequence. Forexample,itiswidelyspeculatedthatquarksaresecretlystrings.Yetwehaveanaccurate theory, QCD, which covers many precise experiments (so far, all ofthem),buttakesnoaccountofthatpossibility.Howisthispossible?Ifaquarkissecretlyastring,thenthequantum-mechanicalwavefunctionfor

the quark will support configurations of the underlying string with manydifferent sizes and shapes, weighted by their amplitudes. As time progresses,those different configurations evolve into one another, but the overalldistributionwillremainconstant.Aslongasthedistributionofstringconfigurationamplitudesstaysthesame,

it’s inert and undetectable. And it might cost a lot of energy to change thedistribution.Theinternal,stringdegreesoffreedomareinvisibletoexperimentsthatdonotreachthatcriticalenergy.Forpracticalpurposestheymightaswellnotexist.Nobody’ssurewhat thecriticalenergyforquarkstringvibrations is,but it must be considerably larger than what any existing accelerator hasattained.

55 soft radiation is common . . . A more refined account of the distinctionbetween soft and hard radiation is based on the connection between themomentumofagluonandthewavelengthofitswavefunction.Lowmomentum

correspondstolongwavelength.Longwavesdonotresolvethefinestructureofthequark’scloud,sotheyrespondtothecloudasawhole,withitsamplificationof color charge through antiscreening. Short waves do resolve the internalstructure.Theupsanddownsofthesewavestendtocancelouttheirinteractionwith the cloud, leaving the contribution of the seed charge, which is nowresolved.

Chapter7

58 symmetry is a word that’s in common use: A classic introduction tosymmetry,byagreatpioneerofthemathematicsofthesubjectandaprofoundlyculturedhumanbeing,isHermannWeyl’sSymmetry(Princeton).EugeneWignerbrought group theory into modern physics in a big way, and his thoughtfulessays in Symmetries and Reflections (Ox Bow) are interesting from manyangles.

69 Grooks: Piet Hein’s witty Grooks are collected athttp://www.chat.carleton.ca/~tcstewar/grooks/grooks.html.

72textbooks:Thenitty-grittyofquantumfieldtheoryisnotforsissies.Ifyou’dliketogodeeperintothesubject,I’drecommendstartingwithFeynman’sQED,mentionedearlier,andmyreviewarticleQuantumFieldTheorywrittenfor the100thanniversaryoftheAmericanPhysicalSociety,reprintedinMoreThingsinHeavenandEarth,ed.Bederson(Springer).Itisalsopostedatitsfrombits.com.ForsomeyearstheleadingtextbookhasbeenAnIntroductiontoQuantumFieldTheorybyMichaelPeskinandDanielSchroeder(Addison-Wesley);anexcellentnewcontenderisQuantumFieldTheorybyMarkSrednicki(Cambridge).TonyZee’s Quantum Field Theory in a Nutshell (Princeton) treats many unusualaspectsof thesubject inabreezystyle.Finally, thetrilogyQuantumTheoryofFields(Cambridge)byStevenWeinbergisamagisterialstatementfromagrandmaster,butasidefromthehistoricalintroductioninVolume1,nonprofessionalsarelikelytofinditveryhardgoing.

Chapter8

BiographyofEinstein:TherearemanybiographiesofEinstein.Twosuperbones, which emphasize his science, are his own Autobiographical Notes inAlbertEinstein ,Philosopher-Scientist, editedbyP.Schilpp (LibraryofLivingPhilosophers), andSubtle Is theLord byAbrahamPais (Oxford). Paiswas aneminentphysicistinhisownright.BiographyofFeynman:Feynmandidn’twriteasystematicautobiography,but

his personality shines through in his collections of anecdotes Surely You’reJoking, Mr. Feynman! (Norton) andWhat Do You Care What Other PeopleThink? (Norton).Genius by JamesGleick (Pantheon) is awell-written, deeplyresearchedaccountofFeynman’scolorfullife.

78 inconsistent: Inconsistent with what? Conservation of charge. Maxwellappliedtheknownequationstoa“thought-circuit”includingwhatwe’dnowcalla capacitor and found they required electric charge to appear from nowhere.Because the experimental evidence for conservation of charge under allcircumstancesseemedverystrong,Maxwellmodifiedtheequationsaccordingly.

85“...searchinginthedark...”QuotefromanaddressattheUniversityofGlasgow,1933.The“simultaneity”quoteisfromhisAutobiographicalNotes.

88inevitabilityofafield:Inthisdiscussionofthenecessityoffields,Irefertoauniversal valueof “now,” solving for the fields in the future in termsof thefields now, and so on. How can that be legitimate, given the demise ofsimultaneity?

Technical answer: In a boosted frame, the horizontal slice “now” will getchangedintoatiltedslice.Butbecausetheequationstakethesameform,itwillstillbepossibletocalculatethevalueofthefieldsofftheslice,intermsoftheirvalueson theslice. (Strictlyspeaking,youhave toknowthevaluebothof thefieldsandoftheirtimederivatives.)Inshort:different“now,”sameargument.Nevertheless there is an important tension here, whichmakes it difficult to

marryquantumtheoryandrelativity.Intheequationsofquantumtheory,andintheirinterpretation,timeappearsinaverydifferentwayfromspace.Butintheequations of relativity, time and space get mixed up. So when we’re doingquantummechanicswemakeaverystrongdistinctionbetweentimeandspace,

butwehavetoshow—ifwebelieveinrelativity—thatintheenditdoesn’tmakea difference. Fundamentally, this is why it’s difficult to construct quantumtheoriesthatareconsistentwithspecialrelativity.Theonlywayweknowhowtodoitusestheelaborateformalismofquantumfieldtheory(orpossiblytheevenmore elaborate—and still incomplete—formalism of superstring theory). Theflip sideof thedifficulty is thatwe’re led to avery tight, specific framework:(for experts: local) quantum field theory. Thankfully, this turns out to be theframework thatNature uses in ourCore theory of physics.Going back to themarriagemetaphor:ifyou’repickyaboutwhatyou’llacceptinapartner,thenifyoufindoneatallit’slikelytobeagoodone!

94 so-called weak interaction: The books by Close and Olmert mentionedpreviouslycontainextensivediscussionsoftheweakinteraction.

97maps of the world:Lectures on Classical Differential Geometry by DirkStruik (Dover) contains a nice discussion of themathematics ofmapmaking.ThestandardreferenceemphasizingthegeometricapproachtogeneralrelativityisGravitationbyCharlesMisner,KipThorne,andJohnWheeler(Freeman).Aclassic presentation emphasizing the field approach is Gravitation andCosmology by StevenWeinberg (Wiley). I should emphasize that there is nocontradictionbetweentheseapproaches,andgoodphysicistskeepbothinmind.

102Superstringtheory:TheElegantUniversebyBrianGreene(Vintage) isapopular,enthusiasticpresentationofstringtheory.

102apromisingopportunity:RecentdevelopmentsincosmologyincreasinglysuggestthattheUniverseunderwentaperiodofveryrapidexpansion,knownasinflation,earlyinitshistory.TheInflationaryUniversebyAlanGuth(Perseus)isanexcellentpopularaccountoftheunderlyingtheory,byitsfoundingfather.Amongthethingsthatgetinflated,accordingtotheory,arequantumfluctuationsin themetric field.Those fluctuations,magnified to cosmological dimensions,might be detectable today. Ambitious experiments to look for this effect areplanned.

Theprecisecauseofinflation(ifindeeditoccurred)isunknown.Butalikelyculpritemergesfromcombiningtwooftheideasdiscussedinthischapter:

•Wediscussedhowempty space is presently filledwithvariousmaterialcondensates. At extremely high temperatures these condensates could“melt” or otherwise change their character. We say there is a phasetransition, conceptually similar to the familiar phase transitions (solid)

ice→(liquid)water→(gas)steam;butherewe’retalkingcosmicphasetransitions.Becausespaceitselfchangesproperties,ineffectthelawsofphysicschange.

•One of the things that changes, in such cosmic phase transitions, is theenergy of the condensate. As we’ll discuss very shortly, this changeshowsupasacontribution to thedarkenergy.Veryplausibly, then, theveryearlyuniversemighthavecontainedamuchhigherdensityofdarkenergythanweseetoday.Today’sdarkenergyiscausingtheexpansionoftheuniversetoaccelerate,butonlygently.Amuchlargerdensityearlyonwouldhavetriggeredmuchmorerapidacceleration.

Andthat’showinflationmightarise.

108 The Extravagant Universe by Mark Kirshner (Princeton) is a personalaccountoftheobservationsbyoneoftheleadingastronomers.

110Apopularspeculation:TheseideasareclearlyexplainedandadvocatedinTheCosmicLandscapebyLeonardSusskind(TimesWarner).

Chapter9

113ourclassicalcomputers:These stepsdescribewhat’s involved in solvingthe equations straightforwardly. There are clever tricks that sidestep some ofthem in special cases. They go by names like Euclidean field theory,Green’sfunctionMonte Carlo, stochastic evolution, and so forth. It’s a very technicalsubject,waybeyondthescopeofthisbook.Progressinsolvingtheequationsofquantum mechanics could change the world, by allowing us to replaceexperiments in chemistry and material science with calculations. Progress incomputing aerodynamics has largely accomplished this program for aircraftdesign, so that newdesigns can be tried out numerically, bypassing rounds ofprototypingandwindtunneltesting.

114 quantum computers: Two directions of spins—up or down—can beinterpretedas1sand0s,sotheycanbeinterpretedasbits.But,aswe’lldiscussindetailoverthenextfewpages,thequantumstateofasetofspinscandescribemany arrangements of the spins simultaneously. Therefore, it’s possible toimagineoperatingonmanydifferentbitconfigurationsat thesame time. It’sakindofparallelprocessingenabledbythelawsofphysics.Natureappearstobeverygoodat it, solving theequationsofquantummechanicsveryquicklyandwithoutmuchapparenteffort.

We’re not so good, at least not yet. The problem is that the different spinconfigurationsinteractwiththeoutsideworldindifferentways,andthatdisruptsthe orderly parallel processing we’d like to do. The challenge of building aquantum computer is to findways of keeping spins from interactingwith theoutside world, or correcting for the interactions, or engineering objects lessdelicate than spins that obey similar equations. It’s an active area of research;there’snodesignthat’sanobviouswinner.

117thefamousEPRparadox:Sharper,quantitativeformsoftheEPRparadox,involving concepts such as Bell’s inequality and Greenberger-Horne-Zeilingerstates,aredescribedinbooksonthefoundationsofquantummechanics.AgoodclearoneisConsistentQuantumTheorybyRobertGriffiths(Cambridge).Thereis an enormous literature concerned with different interpretations of quantumtheory, tests of its elementary ingredients, and so forth. IMHO, if you see askyscraperstandingtallanderectfordecades,evenunderheavybombardment,

youshouldbegin tosuspect that its foundation isultimatelysound,even if it’snotclearlyvisible.Thenagain,conservationofmassoncelookedverysecureaswell....

118 a thirty-two-dimensional world: This note is strictly for experts. Theunnormalized amplitudes describe a space of thirty-two complex dimensions.Thiscorrespondstosixty-fourrealdimensions.Innormalizingthestate,welosetwoofthese.Soreallywe’redealingwithaspaceofsixty-twodimensions.

120highlyinfinite:Thequantumcontinuumissocomplicatedtoconstructthatit’stemptingtothinkthatweshouldsomehowgetridofit.EdwardFredkinandStevenWolframareprominentadvocatesofthisview.

Crude attempts certainly don’twork.Without entering into debates, I’ll justsay—without fear of contradiction—that nothing remotely approaching thecompleteness,precision,andaccuracyoftheCoretheoryhasemergedfromanysignificantlydifferentrivalideas.Ontheotherhand,itisdisconcertingtohavelimiting processes (and therefore calculations that are, in principle, infinitelylong) appearing in the most basic formulation of physical laws. But do they,really?It’snotcleartomethatgenuineinfinitiesariseifweonlyaskthetheoryto answer questions thatwe can also pose experimentally. Experimentally,wehave a limited amount of time and energy available, and we can only makemeasurementsof limitedprecision.Andapproximatecalculationsdon’t requirethatweactuallytakethelimit!Thisnoteismakingmedizzy,soI’dbetterenditnow.

122 the errors will be small: I’d like to devote this short and skippableparagraphtoavery important, thoughslightly technical,conceptualpoint.Youmightworry about the errors introduced replacing continuous space-time by adiscrete lattice. Inmany scientificproblems, suchaspredicting theweatherormodelingclimate, that’sahuge issue.Buthere, thanks toasymptotic freedom,it’snotsobad.Becausethequarksandgluonsinteractweaklyatshortdistances,you can calculate analytically—that is, with pen and paper—the effect ofreplacingthetrueactivitiesbytheirlocalaverages,trackedatthelatticepoints.Thenyoucancorrectforit.

124theoryisnot...predicting...justaccommodating:Themassmπofthepionisthemostsensitivetomlight;themassmKoftheK-mesonKisthemostsensitivetoms,andtherelativemassΔM1Pofthe1Pbottomoniumstateisthe

most sensitive to thecoupling strength, soweuse themeasuredvaluesofmπ,mK,andΔM1Ptofixthoseparameters.

127Thereisnoreallypopular-levelaccountofnumericalquantumfieldtheory(a.k.a.latticegaugetheory),andprobablythereneverwillbe.Althoughsomeofits results can be described fairly simply, as I’ve done here, the nitty-gritty isgraduate school material. A solid introduction at an unbeatable price can befoundhere:http://eurograd.physik.uni-tuebingen.de/ARCHIV/Vortrag/Langfeld-latt02.pdf.

Chapter10

130 ominous thunderhead: To minimize the energy the disturbance actuallyself-organizesintoatube,andtheenergyisproportionaltothelengthofthetube(asisitsmass,accordingtoEinstein’ssecondlaw).Thetubetrackstheinfluenceofthequark’scolorcharge,soitcan’tend(exceptonanantiquark),anditspriceinenergyisinfinite.

Chapter11

The Physics of Musical Instruments by David Lapp,http://www.tufts.edu/as/wright$\_$center/workshops/workshop_archives/physics_2003_wkshp/book/pom_book_acrobat_7.pdf,isaneat,short,mostlynon-mathematicalintroductionto the physics of sound and musical instruments with lots of pictures. Twomaster-worksareOntheSensationsofTonebyHermannHelmholtz(Dover)andTheTheoryofSound(2volumes)byLordRayleigh(Dover).Onlyprofessionalswouldwanttoreadthesetomesfromcovertocover,andpartsofHelmholtzareobsolete, but just thumbing through them is an inspiration. They’ll make youproudtobehuman.

Chapter12

136Salieri . . . says:Actually, of course, it’s the screenwriterwho says thesethings!

137“Actually,Watson...”:ThisjokeisadaptedfromQuirkologybyRichardWise-man(Macmillan).

138 According to an early biographer:http://www.sonnetusa.com/bio/maxbio.pdf contains The Life of James ClerkMaxwell,withaselectionfromhiscorrespondenceandoccasionalwritingsanda sketch of his contributions to science, by Lewis Camp-bell and WilliamGarnett.ThisisanextraordinaryresourceoneverythingMaxwell.Inadditiontoagoodold-fashionedbiography,itoffersanexcellentaccountofhisscienceandagenerousselectionofhisdrawingsandletters—andevenafewofhissonnets.

139 removing redundant or inessential information: Several otherconsiderations enter into the design of good data compression, besides thesimplegoalofkeepingthemessageshort.Wemightwanttoallowsomekindsofmistakes,aslongastheydon’tspoilthingstoomuch.JPEG,forexample,breaksacontinuousimageintodiscretepixels,andcompromisesoncoloraccuracy,butusuallyproducesgood-looking“reproductions.”Orwemightwanttobuildsomeredundancyintothetransmittedmessage,evenatthecostofmakingitlonger,ifaccuracy is precious and the channel is noisy. Reports ofmeasurements fromastronomicalorGPSsatellitesget this treatment.Similarly,whenpeoplemakemathematicalmodels inengineeringoreconomics, forexample, theymightbeveryconcernedtohaveequationsthatareforgivingoferrorsinmanufactureordata, and that accommodate as much empirical input as possible. Theoreticalphysics,however,putsoverwhelmingemphasisoncompressionandaccuracy.

141 for theultimate indata compression:On the conceptual foundations ofmodern data compression, I recommend Information Theory, Inference, andLearningAlgorithmsbyDavidMacKay(Cambridge).Forconnectionstotheory-building, and to the work of Gödel and Turing, see An Introduction toKolmogorov Complexity and Its Applications by Ming Li and Paul Vitányi(Springer).

141assuming theexistenceofanewplanet:Thehistoryof thediscoveryof

Neptune is complicated and, I understand, somewhat controversial. AlexisBouvard had already in 1821 suggested that some “dark matter” could beperturbing Uranus (anticipating Bart Simpson). But without a mathematicaltheory,hecouldnotsuggestwheretolook.JohnCouchAdamsdidcalculationssuggestingthatanewplanetcouldresolveproblemswithUranus’sorbitin1843,and supplied coordinates, but he did not publish his work or persuade anyobserverstofollowup.

Chapter13

146namely, as the inverse square:That is true atmacroscopicdistances.Atultrashort distances two new effects come into play, and the force laws aredifferent.We’vealreadydiscussedhowGridfluctuationscanmodifytheforce,astheeffectofvirtualparticlesdiminishes(screens)orenhances(antiscreens)it.Another effect we’ve discussed is that in quantum mechanics, probing smalldistances necessarily involves large momenta and energies. This affects thepower of gravity, because gravity responds directly to energy. Thesemodificationsoftheforcelawsareall-importantintheideasaboutunificationofforceswe’llbediscussinginPartIII.

146 Gravitational radiation . . . has never yet been detected: Althoughgravitationalradiationitselfhasneverbeendetected,oneofitsconsequenceshasbeenseen.PrecisionstudiesofthebinarypulsarPSR1913+16overlongperiodsoftimeindicatethatitsorbithasbeenchanginginawaythatisconsistentwiththe calculated effect of loss of energy due to gravitational radiation. In 1993RussellHulseandJosephTaylorwontheNobelPrizeforthiswork.

Chapter14

148Anybody . . .will follow the same path: Just as an infinite number ofstraight lines pass through a given point, an infinite number of “straightest”paths, with different slopes, pass through a given point of space-time. Theycorrespondtothetrajectoriesofparticleswithdifferentstartingvelocities.Sotheaccuratestatementofuniversalityisthatbodiesstartingatthesamepositionandvelocitywillmoveinthesamewayundertheinfluenceofgravity.

Chapter16

153 three luckypeople:DavidGross,DavidPolitzer, and I shared theNobelPrize in 2004 “for the discovery of asymptotic freedom in the stronginteraction.”

154myItalianside:That’smymom.Myfather’ssideisPolish.

154“Everythingyou’vesaidisnotevenwrong”:TheFeynman-Paulistoryiswell-establishedfolkloreinthephysicsworld.Idon’tknowwhetheritactuallyhappened,andtobehonestIdon’twanttoknow.It’sbetterleftnotevenwrong.

159seed strong force: The choice of force as ameasure of the power of thecoupling is somewhat arbitrary. Perhaps a more fundamental measure is thenumberthatappearsmultiplyingthehubsinFeynmangraphs,whentheprocessinvolvesparticleswiththePlanckenergyandmomentum.Thatnumberisevenclosertounity;it’sabout1/2.Anyreasonablemeasurewillgivearesultclosetounity—certainlymuchcloserthan10-40!

Chapter17

Ideas to unify theCore by enlarging its local symmetrywere pioneered byJogeshPatiandAbdusSalamandbyHowardGeorgiandSheldonGlashow.TheSO(10) symmetry and classification emphasized in this chapter were firstproposedbyGeorgi.GrandUnifiedTheoriesbyGrahamRoss(Westview)andUnification and Supersymmetry by Rabindra Mohapatra (Springer) are solidbook-lengthaccounts.

166Itwillprovidethecore...possiblyforever:Idon’tmeantoclaimthattheCorewon’tbesuperseded.Ihopeitwillbe,andI’mabouttodescribewhyandhow. But just as Newton’s theory of mechanics and gravity remains thedescriptionweuseformostapplications, theCorehassuchaprovenrecordofsuccessoveranenormousrangeofapplicationsthatIcan’timaginepeoplewillever want to junk it. I’ll go further: I think the Core provides a completefoundationforbiology,chemistry,andstellarastrophysicsthatwillneverrequiremodification. (Well, “never” is a long time.Let’s say for a fewbillionyears.)TheQuantumCensor,mentionedinanearliernote,protectsthesesubjectsfromwhateverwildstuffisgoingonatultrashortdistancesandultrahighenergies.

166theweakinteraction:WeakInteractionsofLeptonsandQuarksbyEugeneComminsandPhilipBucksbaum(Cambridge)containsextensivediscussionofastrophysicalapplications.NeutrinoAstrophysicsbyJohnBahcall (Cambridge)isanauthoritativetreatmentbyagrandmasterofthefield.

167 stars live on energy . . .: The nuclear transformations fromwhich starsderive their energy also include fusion reactions that don’t require changingprotons intoneutrons,suchas theprocessbywhich threealphaparticles (eachconsistingoftwoprotonsandtwoneutrons)combineintoacarbonnucleus(sixprotons and sixneutrons).Such reactionsdonot involve theweak interaction,butonlystrongandelectromagneticinteractions.Theyareespeciallyimportantinthelaterstagesofstellarevolution.

170 left-handedandright-handedparticles:Really, I should say left-handedandright-handedfields.

Aparticlewithnonzeromassmovesat less than thespeedof light,and thatraises the following problem: You can imagine making a boost so fast as to

overtake the particle. To the boosted observer, it will appear to be movingbackwards—that is, in the direction opposite to the direction it was movingaccording to the stationary observer.Because the spin direction still looks thesame,aparticlethatlooksright-handedtothestationaryobserverwilllookleft-handedto themovingobserver.Butrelativitysaysbothobserversmustseethesame laws. Conclusion: the laws can’t depend directly on the handedness ofparticles.The correct formulation ismore subtle.We have quantum fields that create

left-handed particles, and separate quantum fields that create right-handedparticles. The equations for those underlying fields are different. But once aparticle (ofeitherkind) iscreated, its interactionswith theGridcanchange itshandedness.Intheelectroweakstandardmodel,interactionsofparticleswiththeHiggscondensatedojustthat.We can make a strict (that is, boost-invariant) distinction between left-and

right-handed formassless particles, or using quantum fields.The fact that oursuccessfulequationsfortheweakinteractionsrelyonthisdistinctionshowsthatNatureprefersmasslessparticlesandquantumfieldsasherprimarymaterials.

176TheSirensofmyth:J.Harrison,“TheKerasSiren,”Prolegomena to theStudyofGreekReligion(3rded.,1922:197-207)p.197.ThisbitisherebecauseIhopedtouseTheSirenbyJohnWilliamWaterhouseasacover.Alas,itwasnottobe.ButyoucanseethepictureasColorPlate7.

Chapter18

Howard Georgi, Helen Quinn, and Steven Weinberg first calculated thebehaviorofthethreeforcesatshortdistances,toseeiftheymightunify.(Forthestrongforce,ofcourse,thisisjusttheGross-Politzer-Wilczekcalculation.)

178thequantitivemeasureoftheirrelativepower:Notethatatafundamentallevel—intermsofthenumbersmultiplyinghubsinFeynmangraphs—theweakcoupling is actually bigger than the electromagnetic (for experts: here readhypercharge) coupling. Grid superconductivity renders the weak force short-range,however,soitspracticaleffectsareusuallymuchsmaller.

178atomic nuclei . . . aremuch smaller than atoms: The contrast betweenatomic sizes and nuclear sizes is only partly due to the relative weakness ofelectromagneticforces.Thesmallnessoftheelectron’smass,relativetothatofprotons and neutrons, is also an important factor.We can understandwhy byrecallingthelogicofpoint3intheScholiumthatconcludesChapter10.Thesizeofatomsisdeterminedbyacompromisebetweencancelingoutelectricfieldsbyputting electrons right on top of protons, and respecting the wave nature ofelectrons.Thesmallerthemassoftheparticle,themoreitswavefunctionwantstospread,andsothesmallmassof theelectronskewsthecompromise towardlargersizes.

Chapter19

182ThefamousphilosopherKarlPopper:FormuchmoreonPopperandhisphilosophy, see The Philosophy of Karl Popper (2 volumes), ed. P. Schilpp(OpenCourt).

Chapter20

The effect of supersymmetry on the evolution of couplings was firstconsidered by Savas Dimopoulos, Stuart Raby, and me. For a personalrecollectionseeAppendixC.

187Higgsparticles:You’llfindmoreonHiggsparticlesinthe(popular-level)Oerter and Close books referenced earlier, and more technical discussions inPeskinandSchroeder,andSrednicki.

187 supersymmetry:Supersymmetry:Unveiling theUltimate Laws of NaturebyGordonKane(Perseus)isapopularaccountbyaprominentcontributortothefield.

188thebestidea...forconnectingthem:Supersymmetrydoesn’tconnectthedifferentpartsoftheCoredirectly.Noneofthepresentlyknownparticleshastheright properties to be the supersymmetric partner of any other. Only byconsideringbothchargeunificationandsupersymmetrysimultaneouslycanwebringeverythingtogether.

189not toomuch: SUSYmust be broken, but there’s evenmore uncertaintyabout how this occurs than about the related questions of cosmicsuperconductivity discussed in Chapter 8 and Appendix B. Howeversupersymmetrybreakingoccurs, thenet resultmustbe that thepartnersof theparticles we know about are significantly heavier. If they’re too heavy, theywon’tcontributeenoughtotheGridfluctuations,andwe’llrollbacktothenear-missofChapter18.

There are other, independent reasons to suspect that the supersymmetricpartnersaren’ttooheavy.Themostimportantoneisthis:IfyoucalculatetheeffectofvirtualparticlesonthemassoftheHiggsparticle

inaunifiedtheory,youfindthattheytendtopullthatmassuptotheunificationscale.Thisistheessenceofwhat’softencalledthehierarchyproblem.Youcancancelofftheseeffectswiththestrokeofapenbyhavingthestartingmassbejustenoughtocancelthevirtual-particlecontributionsalmostprecisely,butmostphysicists find such “fine-tuning” repellant—they call it unnatural. Withsupersymmetrythecorrectionscancel,andnotsomuchfine-tuningisrequired.Butifsupersymmetryisbadlybroken—i.e.,ifthepartnersaretooheavy—we’re

backinthesoup.

189Nowwemust correct the corrections: In this calculation, I include theeffects of only the particles necessary to implement supersymmetry. (Forexperts: I’m dealing with the minimal supersymmetric standard model, orMSSM.) Additional (much heavier) particles necessary to make a completeunifiedtheoryhavenotbeenincluded.Thatiswhythecouplings,afterunifyingathighenergies,divergeagain.Inthefulltheory,oncetheycometogethertheywillstaytogether.Butsincewedon’tknowenoughtopindownrelevantdetailsofthefulltheory,Ioptedtotakethingsastheycome.

191 they all come together, pretty nearly: Since we don’t have a reliabletheoryofhowgravitybehavesatshortdistancesI’vejustsketchedinthegravitylineroughly.

Chapter21

FormoreinformationontheLHCproject,includingthelatestnews,youcanvisit the CERN website http://public.web.cern.ch/Public/Welcome.html andfollowlinksfromthere.PerspectivesonLHCPhysics,editedbyG.Kane(WorldScientific), isacollectionofarticlesby leadingexperts. I also recommendmyscientific paper “Anticipating a New Golden Age.” You can find it atitsfrombits.com.

196Thedark-matterproblem:QuintessencebyLawrenceKrauss(Perseus)isagoodpopularaccountofthedarkmatter,darkenergy,andmoderncosmologyingeneral.

198protonsshoulddecay:Itsinsensitivitytodetailsisboththestrengthandtheweaknessofourcalculationshowingthat(low-energy)SUSYprovidesaccurateunification of the forces. A new particle’s contribution screening (orantiscreening) kicks in only at energies larger than the rest energymc2 of theparticle.Becausethechangescrucialtounificationaccumulateoveravastspanof energies, it doesn’tmuchmatter exactlywhere they begin, so the particle’scontributiondependsonlymildlyonitsmass.Thustheresultofourunificationcalculationwouldn’tbemuchaffectedifthemassesofthenewSUSYparticleswere(say)todoubleortohalve.Theresultisstiff:itcan’tbebenteasily.Protondecay,however,doesdependonthedetails.

198whatneweffectstoexpect:Stringtheoryhasinspiredspeculationabouttheexistenceofextraspatialdimensions.Theextradimensionsmustbeeitherverysmall (folded up) or highly curved and difficult to penetrate; otherwise we’dhave noticed them. Maybe a closer look, using the LHC, will reveal them.Hiding in theMirror by Lawrence Krauss (Viking) andWarped Passages byLisaRandall(HarperPerennial)givepopularaccountsoftheseideas.

Epilogue

202 that’s a far cry from explaining: According to the ideas described inAppendixB,theHiggscondensateisdirectlyresponsibleforthemassofWandZ bosons, through a form of cosmic superconductivity. So if those ideas areright, once we figure out what the Higgs condensate is, we’ll understand theoriginofthoseparticularmasses.

AppendixB

215Sowecaneasilygenerate...thedecay:Youcancheckthatbyemittingabosonthatcarriesoffaunitofredchargeandbringsinaunitofpurplecharge(thatis,carriesoffanegativeunitofpurplecharge),theuquarkinthetoplinewillchangeintotheantielectroneconthefifteenthline.(The+and-entriesarehalf-unit charges.)By absorbing the sameboson, thed quark on the fifth linewillchangeintotheanti-uquarkontheninthline.IntheChargeAccount,theseguysarerelatedbyflipping+and-signsbetweenthefirstandlastcolumns.Soby emitting and absorbing this particular color-changing boson, as a virtualparticle,wegettheprocess

u+d→uc+ec

Nowweadda spectatoru quark toboth sides:u +u +d→u+uc + ec, andwe’re almost home. We just have to recognize that the u + u + d are theingredientsofaproton,andthatu+uccanannihilateintoaphoton.Finallythenwearriveattheprotondecayprocess

p→γ+ec

aspromised.

IllustrationCredits

Figures

Figure7.3isbasedonadrawingthatfirstappearedinmyarticle“QCDMadeSimple”inPhysicsToday,53N822-28(2000),andisusedwithpermission.Figure8.1 isbasedonan illustration thatappeared indocumentationfor the

ArcInfoWorkstationfromESRI,andisusedwithpermission.Figures9.1,9.2,and9.3arebasedonanupdatedversionofworkreportedby

the MILC collaboration, which appeared in Physical Review D70, 094505(2004)(Figure17),andisusedwiththeirpermission.

ColorPlates

Plates1,2,8,and9aretakenfromtheCERNimagelibrary,andareusedwithpermission.Plate 3a is based on the paintingThe Library of aMathematician byAldo

Spizzichino,andisusedwithhispermission.Plate3bisbasedontheworkofMichaelRossmanandhisgroup,reportedin

Nature317,145-153(1985),andisusedwithhispermission.Plate4isduetoDerekLeinweber,CSSM,UniversityofAdelaide,andisused

withhispermission.Plate 5 is based on work of the STAR collaboration, and is reproduced

CourtesyofBrookhavenNationalLaboratory.Plate6isbasedonworkofGregKilcupandhisgroup,andisusedwithhis

permission.Plate 7 is a reproduction of the painting The Siren by John William

Waterhouse(circa1900).Plate10isduetoRichardMushotzky,andisusedwithhispermission.

AppendixC

Appendix C is based on my article of the same name that first appeared in

Nature428,261(2004),andisusedwithpermission.

Index

AbsoluteunitsAccelerators.SeeLargeElectron-PositronCollider;LargeHadronColliderAmplitude,probabilityAnderson,CarlAntielectron.SeePositronAntimatterAntiparticlesAntiquarkcancelingquarkscoreprocessflavorsandcolorsprotoninteriorssoftandhardradiationSeealsoQuark;Quark-antiquarkpairsAntiscreening.SeealsoAsymptoticfreedomAristotleAsymptoticfreedomcalculatingenergyandmomentuminjetscoreprocessnamingpartonmodelandquarkmodelofinteractionAtomicmodelAtomicnucleichangesinweakinteractionneutronsstrongforcestructureofAtomicspectroscopyAtomsbuildingblocksofmattergravity,electromagneticforceandimportanceofelectronmass

spectrumofSeealsospecificparticlesAugustine(Saint)Axion

BaryonsBentley,RichardBerra,YogiBjorken,JamesBlackholesBlackbodyradiationBohr,NielsBoostsymmetryconstantdensitylocalcolorsymmetryandrelativityandsupersymmetryuniversalmeasureunitsSeealsoFitzgerald-LorentzcontractionBosonsBottomquarkBrookhavenNationalLaboratory

CERNlaboratory.SeeLargeHadronColliderChadwick,JamesChaostheoryCharge.SeeColorcharge;ElectricchargeChargeAccountCharmquarkChekhov,AntonChemicalreactionsChiralsymmetry-breakingcondensate

ChiralityofparticlesChromodynamics.SeeQuantumchromodynamics(QCD)ClassicalmechanicsColeman,SidneyColorchargeasymptoticfreedomandchangingChargeAccountconservationofCoresymmetryflavorsandgluondisturbanceincreasingwithdistanceGridsuperconductivityincreasingstrengthwithdistancelocalsymmetrymetricfieldprotonmassQED,QCD,andColorgluon.SeeGluonColorsingletColor-flavorlockedsuperconductorComplexityComputationLHCdatamappingquarkandgluonfieldsportraitofaprotonCondensatesConfessions(Augustine)ConservationofcolorchargeConservationofenergyConservationofmassconservationofenergyandEinstein’sfirstequationandLavoisier’sverificationofmissingmassproblemsNewton’szerothlaw

ConservationofmomentumCoretheoryChargeAccountdarkmattergaugebosonsgravitationalforceneutrinomassesparticlesandinteractionsintheCorestructureandactivityintheGridsymmetryandthestrong,weak,andelectromagneticforcesweakinteractionCosmicmassdensityCosmicpressureCosmologicalconstantCosmologicaltermCosmologyCouplingparameterCurvatureofspace-time

DarkenergyDarkmatterDatacompressionanddecompressionDensitycosmologicalconstantdarkmatterGriddensityuniversaldensityDescartes,RenéDimopoulos,SavasDirac,PaulDownquark

Einstein,AlbertblackbodyradiationandthephotoelectriceffectconservationofmassconstantdensitydevelopmentofspecialrelativityetherandrelativitygravitybendinglightquarkmodelofahadronsecondlawandoriginofmasstheoryofgravityEinstein’ssecondlawElectricchargeCoretheorypartonmodelandquarkmodelprotonsandneutronsQED,QCD,andvirtualparticlesElectricfieldschangingmagneticfieldsElectromagneticforceblackbodyradiationandthephotoelectriceffectCoretheoryunifyingelectromagneticandweakforcesCoretheory’ssymmetryfailurefeeblenessofgravityandhyperchargeMaxwell’sequationsMeissnereffectmetricfieldQEDandrelativitytheoryofSO(10)transformationspecialrelativitystrengthofstrongforce,weakforce,andunificationincorporatingElectronsatomicstructure

coreprocessimportanceofmassphotographingprotoninteriorsquarksandElectroweaktheoryEmptyspace.SeeGridEnergyconservationofdarkenergyEinstein’ssecondlawandtheoriginsofmassEinstein’ssecondlawandthePlanck-Einstein-Schrödingerequationofquark-antiquarkpairsoriginsofprotonmasspartonanalysisphotographingprotoninteriorsquantumstatesupersymmetryandgravityEPR(Einstein-Podolsky-Rosen)paradoxEquationoftheUniverseEtherblackbodyradiationandthephotoelectriceffectcondensatesEinstein’sdifficultiesindiscardinghistoryofMaxwell’sadvancementsonworld-stuffcharacteristicsExpansionoftheuniverse,accelerationof

FalsifiabilityofatheoryFaraday,MichaelFeigninghypothesesFermi,EnricoFeynman,Richardconstantdensityproblem

constructionofmatterdifficultieswithfieldsEquationoftheUniverseexaminingprotoninteriorshand-wavingexplanationsFeynman,Richard(continued)partonsthecosmologicalconstantFieldsEinstein’sdifficultyoverEinstein’sfield-basedtheoryofgravityMaxwell’sadvancementsonMeissnereffectspecialrelativityandsupersymmetryrevealingnewparticlesandfieldsworld-stuffcharacteristicsFitzgerald-LorentzcontractionFlavors,quarkForceclassicalmechanicseffectofthemetricfieldmasslessquantitiesNewtonianplanetarymotionquarkmodelofhadronsstrongforceSeealsoElectromagneticforce;Gravity;Strongforce;WeakforceFouriertransformsFriedman,JeromeFriedman-Kendall-TaylorexperimentsFundamentalspinFuture,predicting

Galilei,GalileoGaugebosons

Gell-Mann,MurrayGeneralrelativityconstantdensityproblemcurvedspace-timeandgravityetheranduniversalmeasureunitsSeealsoGravityGeodesicsGlashow,SheldonGlashow-Weinberg-SalammodelGlobalsymmetryGluonasembodiedideascoreprocessgluondisturbanceincreasingwithdistancelocalsymmetrymetricfieldoriginsofmasspartonsprofoundsimplicityprotoninteriorsQEDandQCDstrongforceaffectingsymmetryamongGodGoogolGravityCartesianframeworkofthenaturalworldconstantdensityproblemCoretheorycosmologicalconstantcurvedspace-timeEinstein’sfield-basedtheoryfeeblenessofincreasingrateoftheexpansionoftheuniversemasslessquantities

measuringthemagnitudeofNewton’sgravitationaldiscrepanciesoriginofmasssupersymmetryunificationincorporatinguniversalityofworld-stuffcharacteristicsGriddensitygluonsandmanifestationofmattermaterialGridmetricfieldpandemoniumspecialrelativitystructureandactivityGrooks(Hein)Gross,David

Hadrons.SeealsoGluon;QuarkHandednessofparticlesHand-wavingexplanationsHardradiationHarmonyHein,PietHeisenberguncertaintyprincipleHenry,JosephHertz,HeinrichHertzHiggs,PeterHiggscondensateHiggsparticleHolmes,SherlockHubble,EdwinHubs

HyperchargeHypothesisnonfingo

IdealistviewofmatterInteractionscolorgluonsandphotonsdarkmatteranddarkenergy’slackofdistanceandNewtonianplanetarymotionparticleactivityresponsibleforphysicalforcesparticlesandinteractionsinaunifiedtheoryQCDandstronglyinteractingparticlesItsfromBits

JesuitCredoJets

Kendall,HenryKepler,JohannesKineticenergyKing,Alan

Lagrange,JosephLamb,WillisLaplace,Pierre-SimonLargeElectron-PositronCollider(LEP)LargeHadronCollider(LHC)Lavoisier,AntoineLeVerrier,Urbain

Lee,T.D.Leeuwenhoek,AntonievanLength:PlanckunitLeptonsCoretheoryunifyingelectromagneticandweakforcesparticlesandinteractionsinaunifiedtheoryparticlesandinteractionsintheCoreSO(10)transformationLightdarkmatteranddarkenergygravitybendinglightquantamatterandMaxwell’sequationsreconcilingelectricandmagneticfieldsmetricfieldandspectrumofanatomLimitingvelocityLocalsymmetryLorentz,HendrikLorentztransformationsLucretiusLuminiferousether

MagneticfieldchangingelectricfieldsMeissnereffectSeealsoElectromagneticforceMalley,JamesMapsMassatomicnucleicentralityofconservationofdarkenergy

Einstein’ssecondlawandtheoriginsofGriddensityimportanceofelectronandquarkmassmasslessquantitiesMusicoftheGridneutrinomassesandCoretheoryNewton’szerothlawnormalmatteroriginsofPlanckunitsupersymmetryaffectinguniversalityofgravityWandZbosonsMasswithoutMassMasslessparticlesMathematicalPrinciplesofNaturalPhilosophy(Newton)MatteratomicmodelofCartesianprimaryqualitiesconservationofmassdarkmatterdeconstructingGridcharacteristicsmetaphoricaluseofnormalmatterworld-stuffcharacteristicsMaxwell,JamesClerkambitionandcuriosityelectromagneticeffectexpansionoftheelectromagneticspectrumfieldviewofemptyspaceQEDMechanics,relativitytheoryofMeissner,WaltherMeissnereffectMesons

MetricfieldMills,RobertMinkowski,HermannMissingmassproblemMistakesMomentumconservationofHeisenberguncertaintyprinciplepartonanalysisMotionMozart,WolfgangAmadeusMuonsMusicMusicoftheGridMusicoftheSpheres

Naturalworld,searchingformeaninginNeutrinosNeutronsNewton,Isaacconstantdensityproblemcurvedspace-timeandgravityfeigninghypothesesgravitationdiscrepanciesportendingdiscoverygravitationalconstantondiscoveryplanetarymotionandspecialrelativityanduniversalityofgravityzerothlawNewton’slawsofmotionNobelprizeEinsteinFeynman

Friedman-Kendall-TaylorGlasgow-Salam-WeinbergGross-Politzer-WilczekLambLee-YangNordstrom,GunnarNormalmatter.SeealsoMatterNuclearforces.SeealsoStrongforce;Weakforce

Ochsenfeld,RobertOldRegime,Newton’s“OntheElectrodynamicsofMovingBodies”(Einstein)Opticks(Newton)Orbits

ParityviolationParticletheoryParticles-189.SeealsoVirtualparticles;specificparticlesPartonsPast,reconstructingPatternsPeccei,RobertoPerfectionPeriodicmotionPhilosophyPhotoelectriceffectPhotonasbuildingblockconservationofmassandenergycoreprocessphotographingprotoninteriorsPlanck-Einstein-Schrödingerequation

QEDandQCDspecialrelativitysuperconductivityandmassPlanck,MaxPlanckunitsPlanck-Einstein-SchrödingerequationPlanck’sconstantPlanetarymotionPoincaré,HenriPolitzer,DavidPopper,KarlPositronPotentialenergyPressurePrimaryqualitiesofthenaturalworldPrincipleofConfinementProbabilityamplitudeProtonconservationofenergyandmassgravity’sfeeblenessandmeasuringnuclearforcesneutronsandoriginsofmasspartonsphotographinginteriorsofQCDcomputationoftheportraitofstudyingdecayofPythagoras

QuantityofmatterQuantumactivity,world-stuffandQuantumchromodynamics(QCD)computingtheportraitofaphotondarkmatter

masslessmassmetricfieldprofoundsimplicityofQEDandquarkflavorsandcolorssupersymmetryandgravityvacuumpolarizationweakforceQuantumelectrodynamics(QED)QuantummechanicsasymptoticfreedomblackbodyradiationandthephotoelectriceffectenergyofquantumstatesfluctuationsinthemetricfieldlocalsymmetryoriginsofmassoriginsofprotonmasspartonanalysisprotoninteriorsquarksSeealsoQuantumtheoryQuantumreality,modelingQuantumtheoryEinstein’srefusaltoacceptPlanck-Einstein-SchrödingerequationpredictingthefuturerethinkingmatterandlightuniversalmeasureunitsSeealsoQuantummechanicsQuarkcondensateformationCoretheoryunifyingelectromagneticandweakforcesdistanceandinteractionflavorsandcolorsimportanceofmassisolated

localsymmetryoriginsofmassparticlesandinteractionsinaunifiedtheorypartonspropertiesofprotoninteriorsSO(10)transformationsoftandhardradiationQuarkmodelQuark-antiquarkpairsQubitQuinn,Helen

Raby,StuartRadiationRealistviewofmatterRealityRelativisticheavyioncollider(RHIC)RelativisticquantumfieldtheoriesReligionRotationtransformation

Salam,AbdusSalieri,AntonioSchrödinger,ErwinScienceofMechanics(Newton)ScientificRevolutionScreeningSeedchargeSensesSideways-pointingspinSimplicity

SingularitypointsSO(10)transformationSoftradiationSpace-timeSpecialrelativityboostsymmetrycosmologicaltermether,blackbodyradiation,andthephotoelectriceffectfieldsFitzgerald-LorentzcontractionGridmodelmetricfieldSchrödinger’selectronequationsymmetryanduniversalmeasureunitsSpectrumofanatomSpeedoflight(c)SpinmeasuringnuclearforcesquantumrealitymodelquarkflavorsandcolorssupersymmetryaffectingSpontaneoussymmetrybreakingStandardmodel.SeealsoCoretheoryStanfordLinearAccelerator(SLAC)StrangequarkStrongforceCoretheoryCoretheory’ssymmetryfailureLagrangianformnuclearforcesPlanckscaleSO(10)transformationsupersymmetryandgravityunificationincorporatingSuperconductivity

CoretheoryandmasslessparticleselectroweaktheoryMeissnereffectphotonbehaviorpostulatingcosmicsuperconductivitySupernovaeSuperstringtheorySupersymmetrydarkmattergravityandLHCdatarevealingnewparticlesandfieldssymmetryexpansionSymmetryChargeAccountcolorsymmetryCoretheorydistinctionwithoutadifferenceperfectionandQCDandQEDquarksandgluonsrelativitytheoriesofmechanicsandelectromagnetismspontaneoussymmetrybreakingstrong,weak,andelectromagneticforcesuniversalmeasureunitsSeealsoBoostsymmetry

TauleptonsTaylor,RichardTheologyTime:PlanckunitTimedilationTopquarkTractability

Treiman,SamTriangleworldTruthTuring,Alan

UnificationtheoriesUniversalconstantsUniversalmeasuresUpquarkUpdike,John

VacuumpolarizationVelocityVirtualparticlesVoltaire

WbosonsWatson,Dr.WavefunctionsWaviclesWeakforceCoretheoryCoretheory’ssymmetryfailureelectroweaktheoryLHCdatapartonmodelandquarkmodelSO(10)transformationsupersymmetryandgravitytheoryofunificationincorporatingWeinberg,Steven

Well-temperedequationWeyl,HermannWheeler,JohnWilczek,FrankWorld-modelsWorld-stuff,propertiesandcharacteristicsof

Yang,ChenNingYang-Millsequations

ZbosonsZerothlaw,Newton’sZweig,GeorgeZwicky,Fritz

1

Istilldo!

2

Starting here, and until Chapter 8, Iwill drop the adjectivenormal in talkingabout normalmatter, and just saymatter.Wewon’t revisit the dark side untilthen.

3

Toward the end of this book, I’ll discuss other strange ideas, for which theevidenceisasyetmuchlessconvincing.Iwantyoutoappreciatethedifference!

4

Bothprotonsandneutronsarealways spinning:wesay theyhavean intrinsic,fundamental spin. We’ll have much more to say about the property offundamentalspinlater.Itplaysacrucialroleinmodernideasabouttheultimateunificationofforces.

5

Notatypo.

6

The flavors of quarks should not be confused with their color charges. Colorcharge isadifferent,additionalproperty.Thereareuquarkswithaunitof redcolorcharge,uquarkswithaunitofbluecolorcharge,andsoforth.Thuswith3flavorsand3colors,wehave3×3=9kindsaltogether.

7

Strictly speaking, the laws of quantummechanics are universal: they apply tomacroscopic star systems just as well as tomicroscopic ones like atoms. Formacroscopic systems, however, the quantum restrictions on orbits have nopracticalsignificance,becausethespacingbetweenallowedorbitsisminuscule.

8

Actually, a very few extremely smart quantum-mechanicians, most notablyJamesBjorken,hadevenmoresophisticatedarguments indicating that itmightworkafterall.

9

Thus the force falls off faster than1over thedistance squared, asyou’dhavewithoutscreening.

10

WhenGrossandIdiscoveredasymptoticfreedomwewereyoungandnaive,andwedidn’tfullyappreciatetheimportanceofnamingthingsincatchyways.IfIhad it to do over, I’d call asymptotic freedom something sexy, like “ChargeWithout Charge.” “Asymptotic freedom” was suggested by my good friendSidneyColeman,whomIforgive.

11

They were much more challenging in 1973 than they are today, becausetechniquehasimproved.

12

It’snotaquantumleap:quantumleapsaresmall.

13

Ofcourse,“simple”isacomplicatedconcept.SeeChapter12.

14

This is because the total momentum is conserved. It was zero at the start,becausetheelectronsandpositronsweremovingatthesamespeedinoppositedirections. So it must still be zero at the end, as is observed. Of course, inprinciple wemight discover experimentally that momentum is not conserved,but then we’d really need to backtrack, all the way to unlearning first-yearphysics.

15

Forthisexample,you’resupposedtoignorethefactthatthethreetrianglesareindifferentplaces.Ifthatbugsyou,youcanimaginethatthey’reinfinitelythintrianglesstackedontopofoneanother.

16

Therewon’tbeaquiz.

17

IoncehadaveryinterestingconversationaboutthatwithFeynmanhimself.Hetold me that he had originally hoped to remove vacuum processes from thetheory,andwasverydisappointed to find thathecouldn’tdo it inaconsistentway.I’lltellyoumoreaboutthatconversationinChapter8.

18

EarlierImentionedathirdquarkflavor,thestrangequarks.Therearealsothreemorequark flavors: charmc, bottomb, and top t. These are even heavier andmoreunstablethans.We’llignorethemallfornow.

19

Theboostsymmetryofspecialrelativitychangestheenergyofparticles—butitalsochangesthebehaviorofthescalesyou’dusetoweighthem,injustsuchaway that there’s no net detectable effect. Our local color symmetry, on thecontrary,makesnochangeinnormalscales(suchasyoufindingrocerystores),whichhavezerooverallcolorcharge.Sotheywillregisterthechangedweight,andwe’restuckwithit.

20

Aswe’lldiscusslater.

21

Inhissecondpaper,hederivedEinstein’ssecondlaw.

22

Italicsadded.

23

Actually,deepQueens;FeynmanwasfromFarRockaway.

24

Nopunintended.Nope,nopunhere,folks.

25

Thatis,toagoodfirstapproximation.

26

Forexperts:theydecoupleatlowenergies,aswell.

27

For more details on the weak interaction, see the glossary, Chapter 17, andAppendixB.

28

That is, the ones I think aremost promising—the oneswe’ll be discussing inChapters17-21.

29

Technical point: Tomeasure the length of a path that goes in directions otherthan the localnorth-southoreast-west,youbreak thepath into littlesteps,usePythagoras’theoremoneachone,andaddupthelengths.Thesmallerthesteps,themoreaccuratethemeasurement.

30

Mathematicians andphysicists usually call themx1,x2,x3—less quaint,moreopaque.

31

ButI’veadvertisedapromisingopportunityintheendnotes.

32

Toavoid introducing toomanycomplicationsatonce, I’vedeferreddiscussionofanotherextremelyinterestingastronomicaldiscovery,“darkmatter.”We’llgettoitlater.

33

We’ll be discussing supersymmetry in more depth later, in connection withunification.Themain thing tonotehere is that it suggests a ridiculously largecontributiontothedensity,justlikeeverythingelse.

34

Ofcourseitis.

35

If you’rewilling to takemyword for it, andwould rather avoid the dizzyingdetails,youcanproceeddirectlytothesection“TheBig(Number)Crunch.”

36

Toavoidpossibleconfusion: in thiswayofcounting,northandsouthcountasjustonedirection—stepping1milesouthisthesameassteppingminus1milenorth.

37

Oneforeachfinger.

38

Atleast,that’sagoodworkinghypothesis,andit’sjustifiedbyitssuccess.

39

MaybeI’mbeingnaïvehere.

40

AttentivereaderswillrecognizethisasSchrödinger’ssecondlaw.

41

Salieri’s mediocrity is debated by serious music critics. Regardless, he’snotoriousforbeingmediocre.

42

Warning:mayinducedéjàvu.Iquotedthisbefore,inChapter8.

43

It’s not in the Olympics, of course, so it’s not an Olympic event. But as achallengeworthyoftheGreekgodsandgoddesses,it’sOlympian.

44

More precisely, Newton’s theory describes the results of general relativityapproximately.Newton’stheoryworksbestwhenthebodiesareslowlymoving,comparedtothespeedoflight,andarenottoolargeordense.

45

We’vediscussedthecloseconnectionbetweenultrashortdistancesandultralargeenergies previously. See the endnotes for pointers and some additionalcomments.

46

I’llgettotheexceptionsshortly.

47

Wholebookshavebeenwrittenaboutneutrinosand theirproperties. (Theydointeract,afterall—justveryrarely.)Becausethesubjectishighlytechnicalandsomewhattangentialtoourmaintopics,I’vebeenveryselectiveandtelegraphicin this discussion. For a few more details, and further references, see theendnotes.

48

Theneutrinosareaspecialcase,aswejustdiscussed.

49

Strictly speaking, electromagnetism is a mixture involving pieces from bothSU(2)andU(1),aswejustdiscussed.SotheU(1)isnotquiteelectromagnetism.Ithasitsownpropername,hypercharge.ButI’llgenerallyusethemorefamiliar,not-quite-pedantically-correctnameforit.

50

Moreonthislater,inChapter21.

51

Imentionedthisbefore,inChapter8.

52

Reinforcedbyastrikingnumericalsuccess—descriptionupcoming.

53

Formoreonthequantitativeaspects,seethefollowingchapterandtheendnotes.

54

Thekindofmattermadefromphotons,electrons,quarks,andgluons.

55

Foradeeperdiscussionofthesematters,seeAppendixB.

56Thatis,“empty.”

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