Contents

AbouttheBookAbouttheAuthorAlsobyJonButterworthTitlePageDedicationANoteontheMapsPrologue:TheJourneyBegins

ExpeditionI:SeaLegs

1.SettingSail2.TheOceanWave…3.…OrParticle?4.TravellingintheQuantumField

ExpeditionII:AtomLand

5.Atoms6.GoingSubatomic:TheElectron7.NuclearOptions8.TheSourceofChemistry

ExpeditionIII:TheIsleofLeptons,andRoadsOnwards

9.Electromagnetism10.InvarianceandRelativity11.TheGoodShipDirac12.SpinandAntimatter13.TheElectron’sOverweightSiblings

RestStopGravity:ADistantDiversion

TheWeakestForcePlanesandRoundabouts

Different,YetSomehowtheSameRipplesintheSpace–TimeContinuum

ExpeditionIV:GreatTrainJourneys

14.Protons,NeutronsandtheNucleus15.Hadrons16.QuarksandtheStrongForce17.LifeBeyondtheBridge18.FlavoursandGenerations

ExpeditionV:TheIslesbyAir

19.TheWeakForce20.Parity,HelicityandChirality21.MixedMessages22.NorthfromSouth

ExpeditionVI:TheRemoteNeutrinoSector

23.MasslessMatter?24.TheStandardModelisDead–LongLivetheStandardModel!25.NeutrinoBadlands

ExpeditionVII:IntoBosonia

26.SymmetryandConservation27.SymmetryandBosons28.VirtualParticlesandtheDefenceAgainstInfinity29.MassandHiddenSymmetry30.ElectroweakSymmetryBreaking31.HuntingtheHiggs

ExpeditionVIII:FarEast

32.WhyGo?33.CluesandConstraints34.SeaMonstersandDarkMatters35.Supersymmetry36.IntoAnotherDimension?37.OvertheEdge38.AFifthForce

39.IntotheCosmos

FurtherReadingAcknowledgementsCopyright

AbouttheBook

Whatistheuniversereallymadeof?Howdoweknow?Followthemapoftheinvisibletofindout…

Over the last sixty years, scientists around theworld haveworked together toexplorethefundamentalconstituentsofmatter,andtheforcesthatgoverntheirbehaviour.Theresult,sofar, is the‘StandardModel’ofelementaryparticles:atheoreticalmapofthebasicbuildingblocksoftheuniverse.Withthediscoveryof theHiggs boson in 2012, themap aswe know it was completed, but alsoextendedintostrangenewterritory.

AMap of the Invisible is an explorer’s guide to the StandardModel and theextraordinaryrealmsofparticlephysics.Aftershrinkingusdowntothesizeofasub-atomicparticle,pioneeringphysicistJonButterworthtakesusonboardhisresearch vessel for a journey in search of atoms and quarks, electrons andneutrinos,andtheforcesthatshapetheuniverse.Stepbystep,wetravelintotheworld of the unseen, discovering phenomena bothweird andwonderful, fromatoms to blackholes anddarkmatter, andbeyond, to the outer reaches of thecosmosandthefrontiersofhumanknowledge.

Beautifullyillustrated,withgraduallyevolvingmapsofferinganinventivevisualglossaryasthejourneyprogresses,AMapoftheInvisibleprovidesanessentialintroductiontoourworld,andtoparticlephysics.Itisalandmarkworkofnon-fictionbyoneofthegreatscientistsandsciencewritersoftoday.

AbouttheAuthor

JonButterworthiscurrentlyHeadoftheDepartmentofPhysicsandAstronomyatUCLandworksontheATLASExperimentatCERN'sLargeHadronCollider.HestudiedattheUniversityofOxford,receivingaDPhilinparticlephysicsin1992.HeistheauthorofSmashingPhysics,andofthe‘LifeandPhysics’blogfortheGuardian.HelivesinLondon.

AlsobyJonButterworth

SmashingPhysics

AMAPOFTHEINVISIBLEJourneysintoParticlePhysics

JonButterworth

ToAnnandKeith

ANoteontheMaps

THEMAPSWITHIN this book should be seen as an aid tomemory, rather than adetailed representation of particle physics. There is a rough direction ofincreasing energy (and decreasing size) from west to east, and increasingcomplexity from south to north, but there are grey areas and ambiguities.Sometimes the energy scale is binding energy, sometimesmass, and there areunavoidable inconsistencies even so. For example, the photon belongs onBosoniaintheeast,eventhoughitspresenceisfeltfartothewest.Thetauandmuonshouldarguablybefurthereast than theup,downandstrange,basedontheirmasses,althoughonedoesreallyhavetocrossLamdbaQCDtogettothequarks. Allegory and analogy can help understanding, but are misleading ifpushedtoofar.Enjoyyourselfbuttreadwithcare.

PROLOGUE

TheJourneyBegins

CONSIDERATHOUGHTexperiment: takeanappleandcut it inhalf, thencut it inhalfagain,andagain,andkeepdoingthat.Whatwillyouendupwith?Or, less destructively, peer more and more closely into an apple: what

structure is revealed? Is everything made up of a small set of commonconstituents–callthemelements,oratoms–arrangedinvariousdifferentways?Ifso,whathappensifIlookmorecloselyatthoseconstituents?Aretheymadeofsomethingevensmaller?Whatiseventuallyrevealedisalandscape.Alandscapeinhabitedbystrange

andwonderful particles. In this landscape are islands of complexity linked bynetworks of communication, emerging from the oceans of our ignorance. Thelandscapestartsfromeverydaylife,withanapple,forexample,andextendstothewildfrontierofthealmostimpossiblysmall.Togetfromanappletotheimpossiblysmall,wewillneedtosetsail.Wewill

needaboat,acraftwhichwillstandforthemicroscopes,acceleratorsandothermachinerythatextendourvisionbeyondthecapacityofthenakedeyeandintotheheartof theatomandbeyond.Howfarcanwesail?Is thereanendto thisinvisible world? Are there indivisible particles, of which everything else ismade,orcanwecarryonforever,findingever-smallerstuff,sailingeverfurthereastwards?These questions have beendiscussed formillennia, and addressingthemisoneof thegoalsofphysics.Theanswers,asfarasweknowthem,arefound in the strange, invisible landscape thatwewill explore andmap in thisbook.

TheNameoftheGame

The science of the very smallest things is commonly called ‘particle physics’.Nonameisperfect,andthisoneisconfusinginanumberofways.The word ‘particle’ is potentially misleading. Physicists study particles of

sand,pollutants,dust–inspaceandintheatmosphere–andothersmallclumps

of stuff, which have nothing directly to do with the ultimate constituents ofmatter.Sometimes particle physics is called ‘elementary particle physics’ to

distinguish it from the study of these composite particles.But this isn’tmuchhelp, since protons and neutrons – important, tiny particles which are crucialfeatures in the landscapeof the subject–aren’t elementary.At somepointwemayeven findout that the fundamentalparticlesofour current theories aren’telementary either, although studying them is definitely ‘particle physics’.Elementaryparticlephysicsisalsodisfavouredasatermforresearchgroupsoruniversitycoursesbecause itmakes thesubject sound tooeasy.Astudentwhoenrolled on an ‘Elementary Particle Physics’ course might get a shock whenconfrontedwiththeequationsrelatingtotheparticleswewillbesearchingfor.High-energy physics is a commonly used alternative, and it is true that the

directapproachtoparticlephysics–basically,smashingthingstogetherinhugecolliders to seewhat happens– involves a lot of energy.But someof thekeyexperiments actually rely on hunting for very, very rare, very low-energyparticles. Physicists hide their detectors deep underground to try to evadetinyamountsofnoise,andeveryultra-low-energyjitter isacauseforannoyanceorexcitement. Indirectly, theseexperimentsdo tellussomethingaboutwhatgoesonathighenergies,butcallingthem‘high-energyphysics’somehowseemsabitinappropriate.Another problem with ‘high-energy physics’ as a name is that nuclear

physicists, astrophysicists, plasma physicists and many more all deal withenergies that are much higher than those used to probe the limits of particlephysics. The energy of a collision in theLargeHadronCollider,which at thetimeofwritingisthehighest-energyparticlecollidereverbuilt,istinycomparedto the energy that is released in a functioning nuclear reactor, which itselfdoesn’tevenregisterwhencomparedtoanexplodingstar.Whatever thenamewegive the subject, the investigation is apracticalone,

liberated from the realmsof speculativephilosophybyexperiments,beginningwiththehumaneye,thenthemicroscope,andcontinuingwithpowerfulparticleaccelerators and other precision instruments. Each new generation ofexperimentsopensuptohumanenquirynewlandscapesoftheverysmall,andletsusmakemapstoguidethewaydeeperintotheheartofmatter.Butintheend,thequestionisthesame,thenandtoday:whatistheuniverse

madeof,really,whenyougetrightdowntoit?

TheStandardModel

Thecurrentanswerisencapsulatedinatheorygoingbytheunderstated(frankly,dull)nameof the‘StandardModel’,whichsummarises thecurrentstateofourknowledge of the fundamental forces and constituents ofmatter – the area ofsciencegenerallyknownasparticlephysics.Thisisatheory(itisreallymoreofa theory than a model, although the terms mean different things to differentpeople) that is the product of many decades of work and research, andsuccessfullydescribesavastrangeofphysicalphenomena.When I was growing up it was quite common for Indian or Pakistani

restaurants to call themselves ‘Standard’, as in StandardTandoori or StandardBaltiPalace.GiventhatIgrewupinManchester,homeoftheRusholme‘CurryMile’, the ‘standard’was extremely high, andwas something towhich a newrestaurantwould aspire. I think the StandardModel should be seen in similarterms.Themodestname is amarkofquality.Anynew theory thatmaycomealonghasahighstandardtomeet.AnexampleofthepoweroftheStandardModelisthesuccessitachievedin

2012withthediscoveryofthelong-predictedHiggsboson.Thisisanewkindofobject, unprecedented in nature, and it is essential to the mathematicalconsistencyofthetheory.Butfornowitisenoughtosaythatthediscoveryofthe Higgs boson was an amazing vindication of the ideas behind the theory.Remarkably,wenowhaveaself-consistenttheoryinwhichthesmallestobjectsare indeed infinitely small. This theory can describe phenomena over anenormous range of energies and distances, a range that was dramaticallyextendedbythediscoveryoftheHiggsboson.The ideas behind the Standard Model are elegant and mathematical, and

consideringtheenormousrangeofobservationsitcandescribe,itisremarkablycompact and simple. Each individual idea going into it can be understood, inoutlineatleast,byanyone.Butthereareseveralimportantandunfamiliarideas,andbuildinguptheoverallpicture,thewayitallfitstogether,ischallenging.TheStandardModelisnecessarilydynamic.Itmayneedtobechangedwhen

newdatacomesalong.Thatflexibilitydoesnot,however,alterthefactthatitisaneffectivetheory,beautifullydescribingavastarrayofdata.Itcontainstruth–justnotallthetruth.Thisbookisaquestforthetruth.Oraquestforasmuchtruthasweknow.Itwill take you on eight,maybe eight-and-a-half, expeditions deep into the

heartofthematerialuniverse.Theseexpeditionswilltogetherrevealandexplorethesmallestconstituentsofmatter,examinehowtheybehave(theyoftenbehavequite strangely) and identify the forces that bind and break them. This is thestoryofourworld,andindeedouruniverse.Itisfromthesebuildingblocksthat

themoleculesandmaterialsofeverydaylife,andthestarsandgalaxiesbeyond,areformed.Asweexplorenewterritoryontheedgeofphysicalknowledge,thelandswe

discoverwill benamed, and located in relation to eachother.Quarks, bosons,hadronsandtherestwillbesetdowninwhatisineffectanillustratedglossarythatalsoprovidesaframeworkinwhichtheideasoftheStandardModelcanbeplaced.The featuresweencountermayappeara littlearbitrarysometimes,buttheyreflectthebestevidencewehavesofar.Andwhile–asfarasweknow–someofthefeaturesoftheStandardModelareinfactarbitrary,othershavedeepexplanations, and the whole structure has a high degree of elegance andeconomy,atleastcomparedtoanyprecedingtheory.Beforeembarkinguponourjourney,itisaswelltonotethatthisisonlyone

possiblejourneytothefrontiersofscience.Itisareductionistapproach,andweknowthatitwillnotrevealthewholestory,inthesensethat,evenifitweretorevealaso-called‘theoryofeverything’(whichmayormaynotfitonaT-shirt),thatwouldstillleavealotunknown.Whatevertinyconstituentsarerevealedbyparticle physics, we already know that their interactions – and the ways theybehave in large numbers – reveal deep underlying principles and complexbehaviours which aren’t necessarily obvious from the so-called ‘fundamental’laws.Thereisnewphysics–nottomentionchemistry,biologyandtherest–tobe found here as well. However, knowledge of the structure of matter at thesmallestaccessibledistancesisimportant,andissurelyoneofthemostexcitingfrontiersofscience,andthat’swherewearegoing.Themapswemakewillalsorevealsomeofthosestartlingandbeautifulprinciplesthatseemtoapplyfarandwideacrossnature.And,likeanyearlyexplorers’maps,thereareedges.TheStandardModelmay

becomplete,butourunderstandingofphysicsisnot.Thefinalvoyagewilltakeusoff into theunknown,waryof seamonsters and thedistracting calls of thesiren,insearchofmoreanswers.

EXPEDITIONI

SeaLegs

Aboat,andwhatit’smadeof–Gulls,dolphinsandinterference–Alessonfromthepilot–Somescepticalcrew,impatienttosail– The pilot goes on and on, with lasers – The crew areconvinced–Notyourusualkindoffield–Shortdistances,highenergiesandtherelationshipbetweenthem–Theimportanceofchoosingyourpath.

1

SettingSail

HAVING OBTAINED A small but seaworthy vessel, with a scratch crew ofprofessional physicists and curious amateurs, we set sail. The hold containsprovisions,amixofscientificequipmentandaguitar.Wehavesometheoriestotest, andweneeddata.Wehope, likeDarwinon thevoyageof theBeagle, tofindthatwewillbeimprovedbyajourneytodistantcountries.Weenterthemysteriousseascapeoftheinvisiblysmallfromthewest.Onour

map,thewesternfringesareobjectsatahumanscale.Aswesaileastwardswewill shrink further, gazing from the bowsof our boat into the heart ofmatter,mappingtheotherwiseinvisible.Most things aremade of smaller things. Our boat ismade ofwood,metal,

fibreglass.Itdoesn’ttakemuchefforttoseethatthesematerialsarethemselvesmade of smaller stuff: splinters of wood, glass fibres, plastic. The glass fibrestrands, the thickness of cotton thread, are made of silica. Each one of thesestrands is made of silicon atoms bound to oxygen atoms, with two atoms ofoxygen for each of silicon – silicon dioxide.A silicon atom is a billion timessmallerthanthethicknessofthethread.Ifeachsiliconatomwerethesizeofoneofthepeasintheship’sgalley,thefibreswouldhaveadiameterclosetothatoftheEarth.Eachatomconsistsofanucleussurroundedbyfourteenelectrons,eachwitha

negativeelectriccharge.Thenucleushasapositiveelectricchargeof fourteentimes that of the electron, which is why fourteen electrons are attracted to it.Thatisafamiliarkindofconfiguration.Thesolarsystemhaseightplanets(andsomerocksandrejects)inorbitaroundthecentralsun.Itistemptingtopicturethe silicon atom as a tiny Solar System, with fourteen little electron-planetsorbitingthenucleus.Butaswewilldiscover,electronsarenotlittleplanets,theyareinrealitysomethingquitenewanddifferent.Asourboatsailseast,andweshrinktoever-smallersize,theworldaroundus

changes.Mostofthepredictablelawsgoverningthelandswetravelturnouttobeobeyedonlyonaverage,andelectronsandtheotherobjectsweencounterareradicallydifferentfromthefeatureswearefamiliarwithinthewest.

Forreasonsconnectedwiththis,inwayswhichshouldbecomeclearerduringthis voyage, the ability to see smaller and smaller pieces of matter requiresparticle beams –microscopes, effectively – of higher and higher energy. Thismeans that the frontier of the very small also becomes the frontier of high-energy. The important point of high energy in particle physics is theconcentration of the energy into a small space, or equivalently into a smallnumberofparticles.Becauseofthis,amapofhighenergiesandshortdistancesalso informs us about the physics of the very early universe: the hot, densemomentsjustaftertheBigBang.Inthosefirstfewmoments,theenergyinanygivenvolumeofspacewassohighthatthesmallestconstituentsofmatterwerelaidbare.Tounderstandallofthat,wefirstneedtofindoutwhatinhabitsthisstrange

newworld.Whatmightwefindinsideanatom?Fornow,allweknowisthatthethingswe findwill be very small, and thatwe need a lot of energy to accessthem.Butwherearewegoing?Whatstrangeseasarewesailing,andwhatlaws,ifany,apply?Theplacetostartourfirstexpeditionisinthefirstrelativelysafeharbour we spot in the distance – Port Electron, on the strange shores of anunknownisland.

2

TheOceanWave…

FROMOURHARBOURofPortElectron,wewanttochartacoursetowardsthecoastwesee faintlyon thehorizon.The localpilotwehaveengaged is impatient tosteerusoutoftheharbour,throughthecalmofthebayandaroundthepatchesofchoppy water we can see by the harbour’s entrance. But our navigator andcaptainarecautious.Consciousofthechallengesahead,theywanttounderstandwhat causes the choppiness, and how to steer the boat safely themselves.Thepilotshrugs,andstartstalkingaboutparticles.Particle-likebehaviourissomethingwearequitefamiliarwith.Ifyoushoota

gun, the bullet will travel onwards in a straight line until some force acts tochangeitsdirectionorslowitdown.Sandwilltricklethroughyourfingersandformneatpiles.Theseparticle-likethingswillnottravelinanythingotherthanastraightlineunlesstheyricochetoffsomething,orsomeotherforceactsonthemtobendtheirpath.Theywillalsostaythesameshapeastheytravel.Toproperlydescribeaparticleandpredictitsbehaviour,weneedtoknowitssize,speedandmass.Wethinkof themoleculesinagasasparticles,bouncingoffeachother,andwiththatpicturewecanunderstandtemperature,pressureandquiteanarrayof interesting anduseful behaviour, including convection currents that transferheat energy around the cabin. Particles also provide a way of transferringinformation.Thelettersthecrewsenthomebeforewesetoffonourjourneyareparticles too, inasense–discretepacketsofstuff, travelling inawell-definedpathfromsendertorecipient.Waves provide a very differentway of transferring information and energy.

Theship’sradio(emergencyuseonly)sendssignalsbacktobase,andtheship’smicrowaveheatsupthecaptain’ssoup.Mostofwhatweknowabouttheworldaround us comes from waves – generally light waves and sound waves ineveryday life, but also radio, X-rays and more esoteric forms once we bringscientific instruments into play. The physics of waves is in many ways moreinterestingandmorecomplex than thephysicsofparticles,andgives rise to arichermixofeffects,includingthechoppyandcalmpatchesthecaptainsawaswearrived.

To properly describe awave,wemust know itswavelength, frequency andamplitude.Travellingwaveshavepeaksandtroughsthatmoveastheygo.Butwhatisactuallytravelling?Thepilotdrawsourattentiontoaseagull,sittingonthewaterofthebay,asripplesintheotherwisecalmseapassbyandlapattheshoreline.Thegullbobsupanddownasthewavespass,butdoesnototherwisemove.Thoughwavesaretravellingacrossthebaytotheshore,theseagull,andindeed thewater throughwhich thewaves are transmitted, onlymove up anddown:theydonottravelalongthesurface.Itisonlythe‘up-and-down’motion,thedisplacement,whichissomehowtravellingacrossthebay.Theheightofthe‘up’,orthedepthofthe‘down’,comparedtothesurfaceof

theundisturbedbay,iswhatiscalledthe‘amplitude’ofthewave.Anywavehasanamplitudeof somekind– thedisplacement that it causes from theaverage.Anamplifierinasoundsystemissocalledbecauseitincreasestheamplitudeofawave–itamplifiesit,andthesoundgetslouder.As the ripples continue – perhaps a dolphin is having a good time nearby,

splashingaround–thenthegullwillkeeponbobbingupanddown.Thenumberoftimesitbobsinagivenperiodoftimeisknownasthefrequencyofthewave–thenumberofpeaksortroughspassingagivenpointinacertaintimeinterval.Usuallyitismeasuredinhertz(Hz),aslightlyoddunitwhichshouldreallybecalled‘persecond’.Ifthewaveinthebayhasafrequencyof2Hz,thegullwillbobupanddowntwiceeverysecond.The wavelength, on the other hand, is simply the distance between two

neighbouringpeaks in the seriesof ripples.And since thedisplacementhas totravel a distance of one wavelength each time the gull bobs, the speed withwhichthewavetravelsacrossthepondisquiteeasilycalculatedbymultiplyingthefrequencywiththewavelength.Soifweknowtheamplitude,thewavelengthandthefrequencyofawave,we

alsoknowitsspeed,andthatspecifiesallofitsmostimportantproperties.Howis the behaviour of waves any more interesting in any sense than the wayparticlesbehave?Well,consider this.Twodolphinsaresplashingaround indifferentplaces in

thebay,makingwaveswith thesameamplitude, frequencyandwavelengthaseachother,but travelling indifferentdirections.Thingsmightbe lookingabitturbulentforthegull.Butperhapsnot.Ifthepeaksoftwowavesarriveattheseagullatthesametime,thenindeed

thebirdisinforabumpyride.Theamplitudesofthewaveswilladdup,andthegullwill bob twice as high and dip twice as low. But, depending on how faraway each dolphin is from the gull, itmight be the case that the peak of onewavearrivesjustasthetroughofthewavefromtheotherdolphinturnsup.In

this case, the troughwill cancelout thepeak;or thinkingof it in termsof thewaterundertheseagull,theforcefromonewaveistellingittomoveup,whileanequalandopposite force fromtheotherwave is telling it tomovedown. Itwon’tmove.Thegullcanrelax.Thewaveswillcarryonpast it,but itwillbeleftinpeace.Such quiet spots are seenwhen all kinds of wavesmeet each other. Radio

waves andmicrowaves, suchas thosewhichcarryWi-Fi signals, exhibit themtoo.fn1 These effects, when waves come together, are known collectively as‘interference’.Whentwowavesarrivewiththepeaksofonehittingthetroughsof another, they are said to be ‘out of phase’.And obviously,when the peakscometogether,theyare‘inphase’.Phaseisanotherimportantpropertyofwaves,butitcanonlyreallybedefinedwhenyouhavetwowaves.Phasedifferences–suchaswhethertwowavesareinoroutofphase–havearealphysicaleffect.Inour example, the gull bobs up and down, or does not, depending upon therelative phase of the two waves. But phase has to be defined relative tosomething. If there is only one wave, we might decide to define the phaserelativetosomearbitrarytime–say,themomentwefirstsawthedolphin–butregardless,ifthereisonlyasingledolphinmakingasinglesetofwaves,thegullwillbobupanddownwhateverthephaseofthewavemightbe.Itisonlywhenwehavemultiplewaves,withphasedifferencesbetweenthem,thatweseereallydifferent behaviour. This rather simple fact has surprisingly far-reachingconsequences.Thisinterferencebehaviourisverydifferentfromthemorefamiliarbehaviour

ofparticles.Whilebulletsfiredataseagullfromdifferentdirectionsmaycollide,thereisnowaythatfiringmoreshotscouldreducethenumberofbullets.fn2Butmakingmorewavesmightindeedmakeitspartofthebaycalmer.Waves do other interesting, non-particle-like things. The bay contains a

harbour, connected by a narrow channel.All the dolphin-and-seagull action ishappening in the bay, and some of thewaves impinge on the narrow channelleadingtotheharbour.Whathappens?Ifwavesbehavedlikeparticles,thenanythatweredirectedaccuratelyenough

at the channel would pass through, and travel in a straight line across theharbour,leavingmostofthesurfaceoftheharbourundisturbed.Butthisisnotwhathappens.Thewaveshitthechannel,andthechannelactsasthesourceofwavesintheharbour–asthoughadolphinhadactuallygotinthere.(Thisworksmosteffectivelyifthewidthofthechanneliscomparabletothewavelengthofthewaves,asinthatcaseitlookslikeasinglesourceofwaves,ratherthanarowof sources.)Waveswill spreadout from the channel concentrically, across thedolphin-freeharbour.Thisspreadingoutiscalleddiffraction;itallowswavesto

go round corners, without any bending force being applied. It’s another keyproperty which features in the quantum-particle-wave world of the StandardModel.One important practical consequence of this kind ofwave behaviour is that

there is a limit to the smallest structures they can be used to study. Roughlyspeaking, effects suchasdiffractionand interferencemean that awavecannotgiveusgoodinformationaboutobjectswhicharesmallerthanthewavelengthofthewave.Smallerthanthat,andthingsbecometooblurredandconfused.Inthecaseoftheharbourchannelabove,wavelengthsmuchshorterthanthewidthofthe channel lead to a tight beampointing back to the position of the channel.Wavelengthsthesamesizeasthechannelspreadoutandfilltheharbour;longerwavelengthswillnotevenpassthroughthegap.Any set-up which can support a wave has an equation behind it – a wave

equation,ofcourse–whichdescribeshowthewavewillwork.Thesurfaceofthebaywearesailingonisonesuchsystem.Anotherexampleistheair.Asmallregion of dense, high-pressure air will spread out, compressing neighbouringregions, which in turn compress their neighbours, and so on. A high-pressurepulsepropagatingthroughtheairlikethisisasoundwave,createdwhenairiscompressed somehow, say by a vibrating drum, or your larynx. Electric andmagnetic fields form another system, which is how light, radio and otherelectromagnetic waves travel. The important point here is that the generalbehaviourof thesesystemsissimilar insomeveryimportantways– includingthe fact that diffraction and interference occur – because the underlyingwaveequationsareverysimilar.Because theywillbesuchavitalnavigationalaid inourcomingvoyages, it

mightbeworthtakingamomenttoexaminewhyequationsaresoimportantinphysics.We won’t need to go into the detailed mathematics, and I won’t bewritingoutanyequationsexplicitly,buttherewillbeseveralmomentswhenanequationofsomekind issovital tonavigating thephysicalworld thatwewillneedtodiscussit.Anequationinmathematicsrelatesdifferentconceptstoeachother in an abstract, but completely definite, way.When used in physics, theconcepts on each side of the equation are physical objects, and an equationrelating themgivesnew insight into how those objects behave, and especiallyhowchangingoneofthemaffectstheothers.In the current case, a wave equation describes changes in some physical

quantity – the height of the water, the pressure of the air, the strength of theelectricfield.Itrelateshowtheychangeastimepassestohowtheychangewithposition.Specifically,thewaveequationforourbaytellsusthatiftheheightofthesurfaceisdifferentatdifferentpointsinthebay,thisimpliesthatthesurface

will also change with time. Imagine a wriggle from the tail of one of ourdolphinsthatraisesaregionofwatertobehigherthanitssurroundings.Thisisan unstable situation. The small hill of water created by the dolphin will bepulled down by gravity, and this will spread ripples across the surface, as atravellingwave. Thewave equation is simply themathematical description ofhow this happens. It tells us how differences in the height of the water atdifferentplacesleadtochangesintheheightatdifferenttimes.Itcanbeusedtopredict howwaveswill travel and interact –waterwaves, soundwaves, radiowaves–orquantumwaves.Our boat heads out of the harbour in a straight, particle-like line, the crew

cheeredbyourpilot’sinstructionandbuoyedbythewaves.Wenowknow,andhopefully understand, two distinct behaviours – particle-like and wave-like.Theydifferfromeachotherprofoundly,andit isveryhardtoseehowthetwocouldeverbemixedtogether.Butwearesailingunchartedanddangerousseas,and we should expect surprises. And, to the frustration of some of the moreimpatientcrewmembers,ourpilotisnotdoneyet.

3

…OrParticle?

BEFOREWETRAVELon,weneedtoreallyunderstandthemediumwearemovingin.Ifwedon’tdothis,thepilotassuresus,wewillunderstandlittleofwhatwesee,andinparticular the interiorofAtomLand, the targetofournextvoyage,willbeanimpenetrablejungle.Thecoastlinealreadyappearscloser,thoughwehavebarelyleftport.Whatthepilothastotellusissoweirdthatheknowswemaynotbelievehim,

soheurgesthecaptaintodropanchorandassemblethecrewbelowdecksforademonstration.Afterafewmoments’preparation,inthepitch-blackholdofourship,thepilotfiresabeamoflaserlightatascreenwithtwosmallslitsinit.Onthe other side of the screen is a detector, to monitor the light that makes itthroughtheslits.Thefirstthingtonoteisthatlightbehaveslikeawave.Iftheslitsarenarrow

enough, theslits themselvesstartactingas sourcesofwaves.That is, the lightdiffracts as it passes through the slits, just like thewaterwaves in the narrowchannel in theharbour.This indicates that the lighthasawavelength,whichissimilarinsizetothewidthofeachslit,justasthewaterwavesthatdiffractedthemosthadwavelengthssimilartothewidthoftheharbourentrance.Furthermore,wewillseeapatternofbrightanddarkbandswithourdetector.

Ateachpositiononourdetector,lightisbeingreceivedfromtwosources–thetwo slits, like the two splashing dolphins near the harbour. For points exactlyhalfwaybetweentheslits,thelighttravelsthesamedistancefromeachslit,andthe peaks of waves from each slit will arrive together, in phase. The peaksreinforceeachother,asdothetroughs,leadingtoastrongwaveandthusabrightlight.Foranyotherpoint,thelighttravelsadifferentdistancefromoneslitthanthe other, and the ‘adding up’ is not guaranteed. If the difference in distancetravelledisawholenumberofwavelengths,thepeakfromonesourcewillarrivewith a different peak from the other, and things will still add up. But if thedifference is awhole number plus a half, the peakof onewill arrivewith thetroughofanother.Thewavesareinantiphase.(Thesearethedarkbands,where

thepeaksandtroughscanceleachother).Thedetectorwillremaindark,justastheseagullrestedatpeaceinthebay.Thisseemsprettyconclusive.Diffractionand interferencearegoingon,and

theyonlyhappenwithwaves.Wewouldnot see thisbehaviourwithparticles.Wecanevenworkout thewavelengthof thewaves,notsomethingthatmakesanysenseforaclassicalparticle.Lightisawave.Endofstory.Butitisnottheend.Thereisatwist.Animportanttwist.Thepiloturgesustolookabitmorecarefullyatthedetectorthatismeasuring

the light once it has passed through the slits, creating the bright and darkinterference bands.The detector in our experiment relies on the ‘photoelectriceffect’;thatis,whenlighthitsthedetector,itreleaseselectrons,whichcanthencarryanelectriccurrent.TheexplanationforthisbehaviourliesonthecoastofAtomLand,but fornowwesee thatbyapplyingavoltage to thedetector,wecanmakethecurrentflow,anddetectthefreedelectrons.Thisishowweknowwhenlighthitsthedetector,andthuswherethebrightbandsare,andwhereitisdark.Wavesmoveenergyaround.That’swhatmakestheseagullmove,andthat’s

whatreleasestheelectronsinourdetector.Andwithwaves,therearetwowaysthe amountof energycanbe increased.Youcan increase the amplitudeof thewave,whichmakesthegullbouncehigher.Oryoucanincreasethefrequencyofthewave,whichwillmakeitbounceupanddownmoreoften.Thesameistruewith light.Thepowerof a laser canbe increasedeitherbymaking itbrighter,moreintense,orbyincreasingthefrequency.Frequencyforlightcorrespondstocolour,soincreasingfrequencymightmeanmovingfromredlighttobluelight,say.Inourexperiment,however,thesetwodifferentwaysofincreasingthepower

haveverydifferentimpactsonourlightdetector.fn1Onewouldexpectthenthatwhen the amount of light shining on a photoelectric material, such as ourdetector, is increased, theelectriccurrentwouldalso increase; and this is true,undersomecircumstances.Butitdoesn’talwaysworklikethat.Say, for example, that the light we are using is blue. This means it has a

wavelength of 475 billionths of ametre, corresponding to a frequency of 650terahertz (650 trillion oscillations per second). The light detector registers thelight, producing our lovely interference pattern of bright and dark bands, andclearlydemonstratingthewavenatureoflight.Ifweincreasethepowerofourbluelaser,theintensityofthelightregisteringinthedetectoralsoincreases.Allwellandgood.However,wenowtune thefrequencyofour laser.Wereduce it,making the

lightfirstgreen, thenred.For thisparticulardetector,as thefrequencyreduces

intothered,theelectriccurrentsuddenlydiesawayandwecannolongerdetectthelight.Aswe reduce the frequency,we are reducing the power of the laser. If this

werethewavesinthebayweweredealingwith,wewouldbemakingthegullbouncelessoften.Soitisnotsurprisingthatwegetlesscurrent,thoughitisabitsurprisingthatitdropssosuddenly.No matter, we can compensate by turning up the intensity of the light –

correspondingtomakingthegullbouncehigher,evenifitisbouncinglessoften.Whatwewouldseeisdisappointing.Infactwewouldseenothing.Oncethefrequencyhasdroppedbelowacertainvalue(whichdependsonthe

detectorwehaveandexactlywhatitismadeof)wehavenoelectriccurrent,nomatter how highwe turn up the intensity. This is impossible to explain usingcontinuouswaves of light. The energy is there –why does it not free up anyelectrons?This can only be explained if light comes not as a continuouswave, but in

littlepackets,orquanta,ofenergy,morelikethelettersthecrewsenthomethantheradiowavesweuseinemergencies.Forlight,thepacketsarecalledphotons.Asinglephotonisaquantumoflight.ThisistheexplanationEinsteinputinabreakthroughpaperof1905.fn2Theenergyofan individualphotondependsonits associated frequency – blue photons havemore energy that red ones. Thetotalamountofenergyinthelaserbeamisthenumberofphotonsmultipliedbytheenergyofeachphoton.Whenweturnupthepoweroftheredlaser,weareincreasingtherateatwhichphotonsareemitted,buttheenergyofeachphotonremainsthesame,becausethefrequencyofthelightdoesnotchange.Conversely, as we turn down the power of the blue laser, we reduce the

numberofphotons,butnottheenergyofeachphoton,andso,asEinsteinsaidinhispaper,thereisindeed‘nolowerlimit…fortheintensityoftheexcitinglightbelow which the light would be unable to act as an exciter’. Acting as an‘exciter’ in our case means releasing an electron and thus registering in ourdetector.ThisispresumablymoreelegantlyputintheoriginalGerman,buttheresultagreeswithexperimentandisexciting,inanysense.Whatismeantisthatevenalaserturnedrightdownuntilitemitsonlyonephotonayearwouldstill,eventually,builduptheinterferencepatternoflightanddarkbands–onespotata time.Lightcomes indiscretepackets,as thoughitconsistedofparticles,butexhibitsinterference,asthoughitwereawave.Puttogether,thefactsthatontheonehandlightexhibitswave-likeproperties

suchasinterference,butontheotherhandalsocomesindiscretepacketswithanenergy that depends on the frequency, tell us that it is neither a wave nor aparticle, as we know them classically. It is something else entirely. At low

intensitiesandhighfrequencies,wehaveenteredanewregimeofphysicsandwe need a new set of concepts to describe it. Photons are excitations in a‘quantumfield’.Thequantumfieldistheseathatwearesailingon.Thepilotislookingquitesmugatthisstage,andhasmadeacaptiveaudience

of the crew. His demonstration has got our attention, and got us closer tounderstandingwhataquantumfieldis,andhowitworks.Butweneedtoknowmore.Andhe’sonlytoohappytotellus.

4

TravellingintheQuantumField

A‘FIELD’INphysicsisanyquantitythathasavalueforanygivenpointinspace.Forexample,amagneticfieldhasastrengthatallpointsnearamagnet,whichyou canmeasure by the effect it has on small pieces of iron.TheEarth has agravitationalfielddefinedatanygivenpoint,whichcanbeobservedbyitseffecton any piece of matter placed at that point. It keeps our boat firmly on thesurface of the sea, andmakes the rain fall downwards from the clouds above.Indeed,withoutgravitywecan’tevendefine‘down’and‘up’.Aquantumfieldtakesthisideaofafieldintotherealmoftheverysmall.Backto theexperimentwith thelaser, the twoslitsandthedetector,andthe

quantum field can describe what is going on. Themagnitude of the quantumversionof theelectricandmagnetic fields tellsushow likelyweare to findaphoton present. This quantum field spreads and travels like a wave, it has afrequency and wavelength, and can exhibit interference and other wave-likeeffects,butitistellingustheprobabilityofaparticle(aphoton)beingpresentatanygivenplace.Theenergiesandthemomentaofthosephotonsaredeterminedby the frequency andwavelengthof thequantum field.Thisway, thedetectorcan register individualphotonsone at a time,but their distribution, over time,willbuildupthepatternoflightanddarkbandsthatweobserve.The quantum field theory that does this for us is called ‘quantum

electrodynamics’ – QED – and was developed by Richard Feynman, JulianSchwingerandSin-ItiroTomonagainthe1940s.Thenameisdescriptive–thetheorytreatslightascarriedbythephoton(aquantum)butdescribesthemotionof electric and magnetic fields (electrodynamics). It constitutes the first solidcomponentofwhatbecametheStandardModelofparticlephysics,andwewillseealotmoreofitonourtravels.As well as describing the apparent contradictions of our experiment, the

conceptofaquantumfieldhasevenmoretooffer.Electronsarealsoexcitationsinaquantumfield.Assuch, theyalsohavewave-likeproperties.Thesewave-likepropertiesareseenininterferenceexperimentsjustliketheonewecarriedout above for photons. It will turn out that these properties are also what is

neededinordertounderstandtheinteriorofAtomLand,whenwegetthere,andthechemistryoftheelements.Quantumfieldtheoryalsoexplainsthedoublemeaninginthelongitudescale

ofthemapwehavestartedtodrawonourtravels.Aswegofromlefttoright,westtoeast,wealsogoupinenergy,anddowninsize.Thisseemsodd–highenergy means high mass, which usually means ‘bigger’. It is true that ineveryday life, heavy things are often (though not always) bigger than lightthings.fn1But for fundamental particles in quantum field theory, it is the otherwayaround.Highenergycorrespondstoahighfrequency,whichcorrespondstoa shortwavelength.Andaswesaw in theharbour, thewavelengthdeterminesthesmallestthingthatcanbeobserved.Thus,toobservesmallerobjects,moreenergy is needed. And this means there is a sense in which the objects wediscover as we travel east, which have higher and higher masses, areneverthelesssmallerandsmallerthantheobjectstothewest.Theincorporationofparticle-likeandwave-likepropertiesintoanewkindof

object, with the properties required to describe nature, is the achievement ofquantumfieldtheory.Thepilothas finishedhisexposition,and returns to thewheel,asweweigh

anchorandgetunderway.Thecrewarestillabsorbingwhattheyhavelearned.Quantumfieldtheoryisverymuchcountertoourintuitionabouthowphysicalobjectsshouldbehave,andthereisanotherusefulwaytotrytounderstandwhatis going on. Richard Feynman, one of the originators of QED, was a greatexplainer, and he used an idea called a ‘path integral’, not only to build themathematicsofhistheory,butalsotodescribeittonon-specialists.fn2He talked about particles travelling along all possible routes between two

points,butcarryingwiththemarotating‘phase’,whichhevisualisedasalittlearrow.Thearrowsrotateastheparticletravels,andthenumberofrotationspersecond is the ‘frequency’ associated with the particle. Rather like our boat,sailingoneofmanypossiblepathsbetweenPortElectronand theapproachingshoresofAtomLand,withtheship’sclocktickingthesecondsandminutesaswetravel.Unlikeourboat, theparticles thatFeynmandescribesarequantumparticles,

and individually they potentially travel all over the place, randomly, in alldirections. To calculate the probability of a particle actually getting from anyplaceA to another positionB, quantum field theory says that all the possibleroutes betweenA andB have to be taken into account. Every possibleway aparticlecouldleavepointAandarriveatpointBhastobesummedup,togettheactualprobabilityofaparticlegettingthere.Ifthatseemsweird,wellitis,butitisthewaythingsare,sobearwithit.Thisiswherethequantumindeterminacy

of very small things enters in. This ‘summing over all paths’ is called a pathintegral.The key is that the sum takes into account the direction of the arrows.

Rememberthearrowsrotateastheparticlesmove,likethehandsoftheclockonourboat,soforroutesofdifferinglength,thearrowwillingeneralbepointinginadifferentdirectionbythetimetheparticlegetstoB,becauseitwillhavehadmore,or less, time to rotate.Thedirectionof thearrow is like theheightof awaveintheharbour.Iftwoarrowspointinthesamedirection,theyadduptoasingle longer arrow.But if they point in opposite directions, they cancel eachother out and the sum is zero. This is where the wave-like aspect comes in,becausethiscancellingisjustlikethepeakandthetroughofwavesarrivingatthesametime,cancellingeachotherout(andleavingtheseagullinpeace).In general there are so many possible routes from A to B (including ones

whereparticleschangemass,andeven routes thatgobackwards in time!) thatfor anygiven route, there isusuallyanother route that endsupwith thearrowpointing in the opposite direction, and cancels it out. It is possible to pair uproutes like this and show that theymake little or no contribution to the finalprobabilityoftheparticlearrivingatB.Theonlyplacewherethisdoesn’tworkisforpathswhichareclosetotheshortestpossiblepathbetweenAandB.Thisistheroutewheretheparticleundergoesthefewestnumberofturnsofitsarrowas it travels, and all the possible routes similar to this one will have arrowspointinginthesamedirection.fn3Because thearrowsarepointing innearly thesamedirection,theyaddup,andthenetresultofsummingoverallthepathsisdominatedby these fewpathsaddingup togetherstrongly,whileall theotherscanceleachotherout.This tellsus themost likelywayaparticlewillbehave,andwhatthechancesareofmakingitfromAtoB.Ifweobstruct theshortestpath,forexamplebythescreenwithslitsinitinourexperiment,wehavetoredothe sum – the path integral – and we get new behaviour, which includesinterference patterns, and diffraction and other wave-like effects, exactly asobserved. Making the calculations this way gives results that agree withmeasurements that include not only thesewave-like aspects, but also particle-likeaspectssuchasthephotoelectriceffect.This is a lot to absorb, and the crew go about their various tasks with

thoughtful looks on their faces, once the pilot has seen us out of the bay anddeparted. In the landswe are exploring, the objectswewill encounter are notreallywavesorparticlesinthewaywethinkofthosethingsineverydaylife.Butthenwhyshouldtheybe?Wearesailingintonewterritory.Wewillcontinuetousethewords‘particle’and‘particlephysics’,butitisaswelltorememberthatwewillnotbeencounteringparticlesasweknowthem.Theyareexcitationsof

energy in quantum fields. The quantum field is all-pervasive in our currentunderstanding of the map of physics. It is now the ocean surrounding andconnectingthedifferentlandscapesofphysicswewillexplore.The boat is just a boat of course, and behaves like a big particle, not a

quantum excitation. If it goes by some strange route, it isn’t going to getcancelledoutbysomeotherquantumversionofitselfonwhichtheship’sclockshowsadifferenttime.Nevertheless,thenavigatorisconcentratingveryhardontakingtheshortestpathtoAtomLand.

EXPEDITIONII

AtomLand

Landfall amongst the atoms – Dead mice, the sun and theStandardModelofChemistry– (Don’tmention themoles)–Abrieftripbackwards–Attentiontotheelectron,andavoidingthepilot– IntoAtomLand–Puddingsorplanets?–ThemusicofAtomLand–Aguitarlesson,shellsandSchrödinger.

5

Atoms

HAVINGPREPAREDOURSELVESforthefactthattheobjectsweencounterwillbeastrange amalgam of wave and particle, we approach the shore of Atom Landwithconfidenceandexcitement,eagerand,we think,wellprepared toexploretheinterior.Wedisembarkandheadoffonfoot.An atom is the smallest indivisible fragment of a chemical element. Think

back to the fibreglass of our boat, and the silicon the fibres aremade of.Wealready peered briefly inside the silicon atom, observing the nucleus andespecially the electrons around it. Ifwewere to break up an atom of silicon,what wewould getmight be interesting,fn1 but it wouldno longer be silicon.Everydaymaterialsconsistofdifferentchemicalelements,eachoneofwhichisadifferentkindofatom,sometimesboundtogetherasmolecules.Theideathatthereareindivisiblebuildingblockstomattermaydatebackto

the ancient Greeks, but the knowledge that atoms are real was the result ofcarefulexplorationoverthelasttwocenturies.Muchofthatexplorationwasnotdone directly with high-resolution instruments probing tiny structures: it wasdone by observing the properties of different materials, identifying how theycombineandreactwithoneanother,andweighing themprecisely.Mostof theelementswerediscoveredbetween1745and1869,bymanydifferentexplorersusing a wide variety of inventive techniques, including tasting, smelling,weighing or simply observing the properties of various materials and theproductsofvariousreactionsbetweenthem.For example, several scientistsworking independently in the 1760sworked

outthataircontainstwomajorcomponents,oneofwhichwouldallowflamestoburn, andmakemicemore active and healthy, while the other would put outflamesandsuffocatemice.Inthe1770sthemouse-friendlygas–whichwasalsoproducedbyheatingmercuryoxide–was identifiedas theelementoxygen.AScottish student, Daniel Rutherford, guessed that the mouse-killing gas wasanotherelement,nitrogen,inhis1772doctoralthesis.Astronomy was also employed, being responsible for the observation that

therewasanewelementpresentintheSun,notpreviouslyknownonEarthbut

identifiedbythedistinctivefrequenciesoflightitemitted.Itwasnamedhelium,afterHelios,theGreekgodoftheSun,andwaslateridentifiedingasesemittedby Mount Vesuvius. In 1895, Swedish chemists Per Teodor Cleve and NilsAbraham Langer noted that the same gas was produced by dissolving certainmineralsinacid,andmanagedtoisolateenoughofitthattheycouldmeasureitsatomicmass.JohnDalton,achemist,physicistandmeteorologistworkinginthenineteenth

centuryinManchester,conductedaseriesofenormouslycarefulexperimentsfn2–combining, reacting and weighing various gases and other substances – andestablished that somematerials involved in various chemical reactions alwayscombinedinfixedratios.Hehypothesisedthatthiswasduetothefactthatthereactionwasactuallytakingplacebetweentinyfractionsofeachmaterial.Thesetiny building blocks possessed, he believed, certain well-defined ways ofcombining and recombining to make new stable building blocks of a newmaterial.Carbondioxide,forexample,couldbemadefromcombiningtwopartsoxygen with one part carbon. Water could be made by combining two partshydrogenwithonepartoxygen.Ifyougettheratioright,alltheinitialmaterialswillturnintothefinalproduct.Ifyougetitwrong,youwillfindthatyouhavesomethingleftover.In1869,theRussianchemistDmitriMendeleevarrangedtheknownelements,

accordingtotheirchemicalproperties,intothePeriodicTable.Thisismorethanjustaneatwayofarrangingthings.Groupingtheelementsbytheirreactivityandmasses in the way that Mendeleev did reveals a pattern which reflects theinternal structure of the atoms, and which had predictive power. Gaps in hisoriginal table suggested ‘missing’ elements, all of which have since beendiscovered. It is the ‘StandardModel’ of chemistry, in a sense, and it pointsratherdirectlytowardsthebeginningsoftheStandardModelofparticlephysics.OurexplorationofAtomLandhasshownusacomplexandbeautifularrayof

features, the building blocks of everyday materials. They exhibit some fascinatingbehaviour,whichwewould like tounderstandbetter.But everywherewegoinAtomLand,everyoneweasktellsusthattounderstandtheeconomyandecologyoftheplace,grasphowitsdenizensreallyinteractwitheachother,wemustreturntoPortElectron.

6

GoingSubatomic:TheElectron

ASHORTSEAtriplater,retracingourpreviouspath,wepullintothebayagainatPort Electron. Despite the lessons from the garrulous pilot, our brief visit toAtomLandhasshownusthatweneedmoreanswersfromherebeforeheadinginto the interior.We disembark, hoping to avoid meeting the same pilot, andspreadouttoexplore.Thisiswhatwefindout.The electron was the first subatomic particle to be discovered. These tiny

objects were first observed as beams of so-called ‘cathode rays’, a strangeradiationemittedbymetalswhentheywereheated.Somethoughttheraysweremade up of particles,while others thought theywerewaves in the ether. Twodecadesaftertheirinitialdiscovery,J.J.Thomson,workinginCambridge,intheUK,in1897,appearedtosettlethematterinfavourofparticles.Particleshaveadefinitemass,andadefiniteelectriccharge,whichalsomeans

that the ratio of the mass and the charge has a definite value. To prove thatcathode raysweremadeof particles, one thingThomsonneeded to dowas toshow that this ratio was always the same, whatevermaterial was used as thesource of the cathode ray. This would meet the criteria for calling them‘particles’.Thefirstkeyevidenceisthefactthatcathoderaysaredeflectedinelectricand

magnetic fields in just theway thatwouldbe expected for a beamof chargedparticles.Nowaveknownatthetimecarriedcharge,sothismightbeconsideredstrongcircumstantialevidenceinfavouroftheparticlehypothesis.ThesecondpieceofevidenceThomsonacquiredcamefromfinelybalancing

the electric and magnetic fields he applied to a beam of cathode rays as ittravelled through a vacuum.Hewas able to arrange it so that the forces fromeachfieldcancelledeachothercompletely,andtherewasnonetforce.Fromthisset-up, the speedof the beamcanbeworkedout.fn1Finally, once the speed isknown,themagneticfieldcanbeturnedoff,andtheamountthebeamdeflectsintheelectricfieldallowstheratioofthechargeandthemasstobedetermined.fn2As Thomson observed, the ratio for the electron is about two thousand timeshigher than it is for the hydrogen ion, which is a single proton – the lightest

particleknownatthetime.Thismeantthateitheranelectroncarriedenormouslymorechargethanaproton,orithadmuchlessmass.Therearelotsofwaysofworkingoutwhichoftheseoptionsistrue.Probably

themostannoyingway,whichthepilotwoulddoubtlessbeeagertodemonstrateifwehadn’tmanagedtoavoidhimthistime,istosuspendsmallchargedspheresin an electric field. The electrostatic force on the sphere depends both on thestrengthoftheelectricfieldandontheelectricchargethathappenstobeonthesphere. If the sphere is stationary – not falling or rising – this forcemust beexactlycancellinggravity,whichdependson themassof the sphere.So if thefield strength and the mass of the sphere are known, the charge can becalculated.Doingthismanytimesshowsthatthechargeisalwaysamultipleofasmall unit, whichwe call e. Spheres can carry a charge of e, or two or threetimese,orahundred timese,butneverahalfe,oranyfraction.Thise is thechargeoftheelectron.fn3Theresultofallthisevidenceisthatthereisatinyparticle,theelectron,with

a definitemass and definite charge. Since electrons are somuch smaller thanatoms,itisasensibleguesstoassumetheyarepresentsomewhereinsideatoms,beforebeingsplitouttoformcathoderays.AtthispointwearetrulyreadytoreturnoncemoretoAtomLand,andbegin

theexplorationoftheinterior.

7

NuclearOptions

THEKNOWLEDGEGAINEDinPortElectronallowsustolandagainontheshoresofAtomLandwithconfidence, ready tounderstandsomeof the featureswefindthere. But there must certainly be other stuff inside the atom, in addition toelectrons. Electrons are so light compared to atoms that something has toaccountformostofthemass.Also,atomsareelectricallyneutral,sotheremustbesomethingintherecarryingapositivecharge,tobalancethenegativechargeoftheelectrons.Whatmightthisotherstuffbe,andhowareelectronsdistributedamongstit?The first tools needed to explore further into the territory of the atomwere

providedbythediscoveryofradioactivity.AtomLandliessomewhattotheeast;togothere,andexploreinland,weneedhigherenergiesthanourgentlecathoderays can provide. Luckily, for reasons that will become clearer later, someelements naturally give off radiation which has much higher energy thananythingseensofar.ThisisthevehiclethatwillallowustopenetratetheterrainofAtomLand.One of themost common forms of naturally produced radiation consists of

‘alphaparticles’.fn1A landingpartyofHansGeiger,WaltherMüllerandErnestRutherford(inManchesteragain)madethemostdecisiveearlydiscoveryoftheinterior of Atom Land. They used a beam of alpha particles, produced inradioactive decays of the quite newly discovered element radon, to bombardgold atoms. The relatively high energy of the alpha particles meant that theyshouldinprinciplehavetheresolvingpowertoseetiny,subatomicfeatures.Theideawasthatthealphaparticleswouldbedeflectedbysuchfeaturesinsidethegoldatoms,andbyanalysingtheanglesatwhichtheyscattered,andhowoftentheydidso,detailsoftheinternalstructurecouldbeworkedout.Noonehadbeenabletolookinsidetheatombefore,andthereweredifferent

hypotheses as towhatmight be going on in there.Onemodel for the internalstructure of atoms, apparently favoured by Rutherford himself, was thatelectrons were distributed throughout the atom like raisins through a plumpudding.Surprisingly,plumpuddingsdon’tcontainanyplums,fn2but this isas

nothingtothesurprisethatGeiger,MüllerandRutherfordgotwhentheyfiredabeamofalphaparticlesatgoldfoil.Inaplum-puddingatom,thealphaparticlesshouldhavesmashedthroughwithonlyminordeflections.Butwhilemostofthealpha particles passed through almost unperturbed, some of them actuallybouncedrightbackagain,andothersweredeflectedthroughmuchbiggeranglesthanshouldhavebeenpossibleforadiffuse,pudding-likedistributionofmatterinside the atom.Rutherford famously described this result as like firing a 15-inchshellatapieceoftissuepaperandhavingitreboundingtohityou.This remarkable message from the interior can only be explained if the

overwhelming majority of the positively charged mass of the atom isconcentratedinavolumethousandsoftimessmallerthantheatomitself.This,wenowknow,istheatomicnucleus.Thevastmajorityofthemassofanyatomisconcentratedinaboutathousand-trillionth(10–15)ofthevolumeoftheatomitself.Thisconcentrationiswhyitcanbouncealphaparticlesbackthewaytheycame.Thebasicstructureofeveryatomisaveryheavynucleussurroundedbyacloudof lighterelectrons.Thenextpartofour journeywillexplorehowthoseelectronsareboundtothenucleus,andthefar-reachingconsequencesofthat.

8

TheSourceofChemistry

OUREXPLORATIONSSOfartellusthatthevastmajorityofthemassofanatomisconcentratedinthenucleus.Themuchlighterelectronsbuzzaroundthenucleus,constrained to stay in the neighbourhood by the electromagnetic attractionbetweenthenegativechargetheycarryandthepositivelychargednucleus.Thisisreminiscentofamini-SolarSystem,withlighterplanetsinorbitaroundamoremassive star in the centre. However, we already know that electrons are notclassical particles. This is another point at which their quantum-mechanicalnaturemakesahugedifference.Inthiscase,itdictatesthewayatomsbindandreact to form molecules and compounds, and explains the structure ofMendeleev’sPeriodicTableitself.Thereactivityofthedifferentelementsdependsuponhowtightlyboundtothe

nucleus are the electrons they contain. As we tour Atom Land and visit theatomsofvariousdifferentelements,we find theycontaindifferentnumbersofelectrons–enoughtobalancethepositivechargeofthedifferentnuclei.Butwealsofindthattheseelectronscannothaveanyoldarbitraryenergy.Theyhaveaspecific set of binding energies, characteristic to the atoms of each element.Thesecharacteristicenergiesarewhatdeterminetheabilityoftheatomtoformmoleculesandotherassociationswithneighbouringatoms.Theyareresponsibleforthewholeofchemistry,andeverythingthatfollowsfromit.Likeanycuriousexplorer,weneedtounderstandhowthisallworks:whatfixestheseenergies?Anelectronofaparticularenergyhasaparticularwavelengthassociatedwith

it,aswesawonourpreviousvoyage.Whentravellingaroundfreelycrossingtheoceansofourmap,electronscanhaveanywavelength,andthereforewhateverenergy, no restrictions.Butwhen they are confinedwithinAtomLand, boundclosetoanatomicnucleus,thatthisisnolongertrue.Thefactthatonlycertainenergiesareallowed implies thatonlycertain,veryparticular,wavelengthsareallowed.This– the fixedwavelengths – iswherewe can start to understandwhat is

goingonwiththeelectrons.Thereareothersituationswhereonlyafewspecialwavelengths are allowed. One example is the harmonics on a guitar string.

Luckily, we have a guitarist on our boat, who will help illustrate this. In aclearinginoneoftheforestsofAtomLandwemakecamp,buildafire,andsitourselvesaroundittohearwhatshehastosay,astheduskdrawsinandthetinyelectronsbuzzaroundthetreetopsaboveus.Each note that a musical instrument makes corresponds with a particular

wavelengthof sound.Aguitar stringofacertain lengthwillmakeaparticularnote, determined by the fact that an exact number of half-wavelengthscorrespondingtothatnotehavetofit intothespaceallowedonthestring.Theendsofaguitarstring,at thebridgeandthenut(oratafretwhentheguitaristholdsthestringdown),arefixed.Theycan’tvibrateliketherestofthestring.Soawave on the stringmust have fixed points at each end, points atwhich theamplitudeoftheoscillationiszero.Thishastheconsequencethatnotallwavelengthswork.Awavelengthaslong

at thestring isok– itwouldhaveafixedpointateachend,andanotherfixedpointinthemiddle,withthepeakandthetroughaquarterandthree-quartersofthewayalong,swappingsidesasthewavebouncesbackandforth.Awavelengthtwicethelengthofthestringalsoworks,withthemiddleofthe

stringoscillatingupanddown.Thiswouldactuallybethebassharmonicofthestring,theopennoteaguitarplays.Theimportantpointisthatanywavelengththatdoesn’tallowstationarypointsateachendofthestringisforbidden.That iswhathappenswithelectronstoo,whentheyareconfinedclosetoan

atomicnucleus.Thelimitsoftheelectrons’distancefromthenucleusarelikethebridgeandnutoftheguitar–theydefinefixedpointswhichtheelectroncannotgobeyondandwhere thewaveassociatedwith the electron is stationary.Thismeans only certainwavelengths are allowed, and that in turnmeans that onlycertainenergiesarepossible,andthat,inturn,explainsthepeculiarstructuresinwhichelectronsareboundtothenucleusoftheatomswehaveencountered.fn1Thereisafinalpieceofinformationweneedtomakesenseoftheemerging

internalarrangementsofAtomLand.There isadefinite listofallowedenergylevelsforelectronsboundinsideanatom–theharmonicsoftheirorbitsaroundthemassivecentralnucleus.Butonemightexpectthatthemoststablesituationforanatomisthatall theelectronssinktothelowestenergylevel;allofthemplaythebassnote.Thisisnotwhatwesee.Eachenergylevelallowsonlytwoelectronstooccupyit,andisthenfull.The‘NoVacancies’signsgoupforanyfurtherelectrons,whichwillthenhavetomakedowiththenext-lowestenergylevel,fn2whichcanthenonlytaketwoofthem,pushingthereststillhigher,andso on. An atom in its lowest-energy state has all its electrons in the lowestavailablelevels,withallthehigherlevelsempty.Sobacktosilicon,thefourteenelectronsareinthesevenlowestenergylevels,twoofthemineach.Sodiumhas

elevenelectrons.Theywill fill the lowest five energy levels, leaving the sixthonehalf-filled;oneelectronandonevacancy.Inthisway,theatomsbuildup‘shells’ofelectrons,withenergylevelsinside

theshellfilledandthoseoutsideempty,withsometimesavacancyontheedge.Thisintricatestructureofelectronsandenergylevelsdeterminesthesizeoftheatom,anditspropensitytoreactandformmolecules.There are a lot of questions that can be asked here. For example,why two

electronsperenergylevel,notjustone–orasmanyaswewant?Wedonotyetknow.Butitisdifficulttooverstatetheimpactofthediscoveryitself.Thefactthattheenergylevelsaredistinctanddifferentforeachtypeofatom,andevenfor different molecules when the atoms bind together, provides a way ofidentifyingtheconstituentpartsofmaterialswithouttouchingthem.Whenelectronsjumpaboutbetweenthedifferentenergylevels,theyemitor

absorb characteristic amounts of energy, as photons of light. The science ofmeasuringand identifying these iscalledspectroscopy,and it is the reasonweknowwhat the Sun, the other stars, and the dust between them aremade of.Becauseonlycertaindiscontinuousenergylevelsareallowed,onlycertainjumpsin energy are allowed. So only certain energies of photon can be absorbed oremitted,andtheseshowupeitherasdarklinesinthespectrumoflightpassingthroughamaterial,wherethosewavelengthsofphotonhavebeenabsorbed,orasbrightlinesinthelightgivenoffbyamaterialwhenitisheated,suchasthecharacteristicyellowlinesinasodiumlamp.Theexactyellow,whenmeasuredpreciselyinaspectrometer,isenoughtoidentifysodiumasthemaincomponentofoneofthoselamps.Similarly,thelinesinthespectrumfromothermaterialsallow us to seewhat kinds of atom are present. This explains the ‘distinctivefrequencies of light’ responsible for the discovery of helium in the Sun, forexample.Theelectronicstructureofatomsandmolecules– thedetailedgeographyof

Atom Land – was discovered at energy scales of a few hundred or thousandelectronvolts.fn3Itwascrucialinestablishingthequantumnatureofelectronsandphotons,aswellastellinguswhatelementsarepresentinthestarsanddustofdistant galaxies. It provides much inspiration, and information, for furtherexploration.Thetheoryofhowelectronsandphotonsinteract–QED–wasthefirst part of the Standard Model of particle physics to be developed, andprecision atomic physics measurements played a critical role in thatdevelopment,aswewillseeaswevoyageonwards.AtomLand,andthequantumtheorywepickedupalongtheway,isthepoint

ofdepartureforthefarreachesofparticlephysics.Thenextstepofthatjourneytakesusbackoncemoretowardstheislandonwhichwefirstlanded,theisland

containingPortElectron.ForaswereachthesouthofAtomLand,wediscoverthereisabridge,aswellasacarrentalshop.Wecrossthebridge,hireacar,andheadoffbyroadtoexplorethenewterritoryinthehinterlandofPortElectron.

EXPEDITIONIII

TheIsleofLeptons,andRoadsOnwards

Hitting the road –Maxwell – A unification of forces, with thepower to travel –Plus ça change, plus c’est lamême chose –Relativity, quantummechanics, and a powerful new vessel forthejourneysouth–Solvinganoldpuzzleanddiscoveringanewworld–Roadtripstotheeast.

9

Electromagnetism

THEFORCECONNECTING theelectron, theatomicnucleus,andmanyof theotherfeatures on our map is electromagnetism. Electromagnetism is described byQED,thequantumfieldtheoryofFeynman,SchwingerandTomonagawhichwehave encountered already. It plays avital role inholdingAtomLand together,andprovidestheverybridgewecrossedtogethere,aswellastheroadnetworkwearenow travelling.Theelectromagnetic force is carriedby thephoton, thequantumoflightthatwehavealreadycomeacross.AsweexploretheislandforwhichPortElectronwasour first point of entry,wewill have time to look inmoredetailathowitworks.Thiswillbeasurprisingexploration,andonethatwillchangethewayweseespaceandtime.On our expedition intoAtomLand,we saw that electrons are bound to the

nucleus,inacomplexseriesofenergylevels,becausetheyarequantumparticleswithnegative charge and thenucleushas apositive charge.Toget far enougheastwardtoseethenucleus,weneededalpha-particleenergiesofafewmillionelectronvolts.Toseetheelectronaroundthenucleus,lessenergyisneeded–afewthousandelectronvoltsisenough.Thisisroughlythe‘bindingenergy’oftheelectronsinatypicalatom.Bindingenergyisanimportantconceptthatwillfeatureoftenonourmap.Itis

thedifferenceinenergybetweenseparatedparticles,andtheenergyofthesameparticles stuck together. It is alwayspresent in anycompositeobject. Itmeansthattopulltheobjectapart,energyhastobeadded.Youcaneventhinkofthelaunchofaspacecraftfromaplanetinthisway.Thespacecraftandplanetareaboundsystem.Toseparatethem,youneedtoputinalotofenergy,releasedfromrocketfuel,toreachescapevelocity.Likewise,toremoveelectronsfromanatom–toioniseit,oreventuallycreateaplasmawhereelectronsandionsbuzzaroundfreely – energymust be added. If youwant to release one of themost tightlyboundelectronsfromanatom,youhavetogiveitenergy,otherwisethenucleuswillclingontoit.ThisbindingenergydeterminesthelongitudeofAtomLandonourmap.Theattractivepowerofelectromagnetism is the force responsibleforthebinding.

Infacttheinteractionwenowcallelectromagnetismistheunificationoftwoforcespreviouslythoughttobedistinct.Thereistheelectrostaticforce,bywhichtwoelectricallychargedobjectswillattractorrepeleachother.Iftheyarebothnegativelycharged,orbothpositivelycharged,theywillrepeleachother.Ifoneisnegativeandone ispositive, theywillattracteachother.Mostmaterialsareelectrically neutral, because the positive charge of the atomic nuclei exactlybalances, and so cancels out, the negative charge of the electrons. However,rubbingaballoononyourhair, for example, can transfer someelectrons fromonetotheother,leadingtoanimbalanceofchargeandthereforeanelectrostaticattraction.Inadditiontotheelectrostaticforce,ifthetwoelectricallychargedobjectsare

inmotion relative to each other – say electrons carrying a current in oppositedirections in two wires – they will also experience a magnetic force, whichdependsnotjustontheirchargebutontheirspeed.fn1ThemagneticforcefieldoftheEarthwillbendelectriccurrents,andiscausedbytheflowofcurrentsinsidethecore.There are many questions about these forces though. Both the electric and

magneticforcesdependontheelectriccharge,sosurelytheymustberelatedtoeach other. But how? And is the force between the charged particlesinstantaneous, or does something carry it? If so, what, and how fast does ittravel?Howdoesthatforcebehavewhenthedistancebetweenchargeschanges,orwhenthechargesaremoving,orspinning?These are not obscure details. They go to the heart of physics. And the

importanceofhavingagoodunderstandingofthemliesnotjustinthefactthat(as usual) we want to know what is going on, but also because the detailedbehaviourofelectronsunderthisforceisthekeytomuchofthenaturalworld,aswellasthemoderntechnologicalworld.Leavingasidethebiologyfornow,thebilgepumpsofourlittleboatchugged

away using an electric motor. On our journey we are navigating using acompass.Aswedoso,Iammakingnotesonalaptop,stuffedfullofelectronictechnology.WhenI’vefinishedmyaccountIwillemailittomypublisher,usingWi-Fiormaybeamobile-phonesignal.Anyonecomingaftermewill read thewordswiththehelpoflight,unlesstheyhaveabrailleoranaudioversion.Allofthose things, even light itself, are understood in terms of the relationshipsbetweenelectricalcharges,andelectricandmagneticfields.All of this is electromagnetism, and the original equations that unified the

electric andmagnetic forces, that led toQED, andexplainedoptics, radio andWi-Fi, are Maxwell’s equations, published by Scottish physicist James ClerkMaxwellinthePhilosophicalTransactionsoftheRoyalSocietyin1865.fn2

Maxwell’s equations relatemagnetic andelectric fields to eachother and toelectrical charge and current. They encapsulate the fact that electric andmagneticfieldsmakeelectricchargesmove;thatelectricchargescauseelectricfields, but that there are no magnetic charges; and that changes in magneticfieldscauseelectricfields,andviceversa.Theequationsspecifypreciselyhowall this happens. They also encode the fact that the only way to change theamountofelectricchargeinagivenvolumeistohaveanelectriccurrenttakeitawayorbring it in.Chargenever justvanishes,orappearsfromnowhere; it isconserved.The equations seem to have been very much a bottom-up affair, in that

Maxwellcollectedtogetheranumberofalready-knownlawswhichwereusedtodescribevariousexperimentalresults.Forexample,MichaelFaradayworkingattheRoyal Institution inLondon in1831haddiscovered thatmovingamagnetthrougha loopofwirecausedanelectriccurrent to flow–aneffectknownaselectromagnetic induction.MaxwellbuiltFaraday’s lawof induction intowhatwas effectively a ‘grand unified theory’ of electricity and magnetism,encapsulating thewaychargesattractoneanotherandhowamagnetic field isgenerated by an electrical current. While collecting together and unifyingexistinglawssuchasFaraday’s lawof induction,Maxwellalsointroducedonenew term of his own. This term describes the way in which a change in anelectric field gives rise to a magnetic field, even if no electrical charges orcurrentsarepresent.Maxwellfittedthiswiththeotherequationsintoaunifiedframework.Whatisamazingishowmuchthatframeworkthenreveals,bothintermsofdeepphysicalprinciples,andrichphysicalphenomena.Crucially,theequationsshowthatelectricandmagneticfieldscanexisteven

in the absenceof electric charges.Achanging electric field causes a changingmagnetic field,whichwillcausemorechanges in theelectric field,andsoon.Mathematicallythisisexpressedinthefactthattheequationscanberearrangedandcombinedtogetawaveequation–aformulatodescribeatravellingwave,of the kindwemet beforewhenwatching the seagull in the bay.Because theelectricandmagneticfieldscansupporttravellingwaves,theycancarryenergyandinformation.Thespeed of thesewaves can be obtained from the equation, and it is 300

millionmetrespersecond–thespeedoflight!Thesewavesare,infact,light–electromagneticradiation;inquantumlanguage,theyarephotons.Theycomeinmanydifferentforms–visiblelight,radio,Wi-Fi,X-raysandmore.Allinteractdifferentlywithmatter – being absorbed and reflected differently by differentmaterials–butthesedifferencesareentirelyduetothefactthatthewavelengths–thedistancebetweensuccessivepeaksofthewave–differ.Photonswillstay

withusaswe travel from the lowestenergies in thewest to thehighest in thesouth; they are our road network on the map which connects everything thatcarrieselectriccharge.Theymayappearverydifferentlysometimes;visiblelightdoesnotseemmuchlikeagammaray.ButfromthepointofviewofMaxwell’sequations,andofQED,theyareallwavesintheelectromagneticfield.

10

InvarianceandRelativity

IN OUR EXPLORATION of the landscape of the invisible, equations are a keyresource.They relatedifferentobjects in the landscape toeachother, andgivenew insight into how those objects behave – as we already saw with waveequations.Nowhere is thismore true thanon the roadsweare travellingnow.Maxwell’s equations are such apowerful new resource theywill reward somedeepinterrogationtoseewhatelsetheycontain.The equations work in three dimensions, and they relate fields pointing in

different directions to each other. So the electric field in the north–southdirection depends upon what the magnetic field in the east–west direction isdoing, for example. Maxwell wrote it all out component-by-component,direction-by-direction, in twenty separate equations.Maybe that’swhy it tookLordKelvinawhiletoreadthepaper.Thereisamoreelegantwayofwritingdownthesameinformation,andthis

also reveals important features which will be an essential instrument for ournavigationofthemapofphysics.Theequationscanbewrittendownsimply,injustfourshortlines,fn1intermsofmathematicalobjectscalledvectors.A number is a basicmathematical concept that can be used to describe the

size,orvalue,ofsomething.Theweightofthevehiclewearetravellingin,forexample.The temperatureof theengineas it strugglesupahill.Avector is amathematical concept that candescribeobjectswhichhaveboth a size and anorientation, like an arrow.Velocity is a vector, for example. Instead of sayinghowfastourvehicle is travelling in termsofanorth–southcomponentandaneast–west component, we can give a vector. The length of the vector is ourspeed, and the angle specifies our direction. Similarly, an electric field has amagnitudeandadirection,andcanbedescribedbyavector.Aswell as being economicalwith ink, expressing the equations in termsof

vectorsmakes it obvious that they possess a certain symmetry: like a sphere,theyarethesamefromanyangle.IfIrotatethedirectionsofthevectorssothatnorth becomes east, or south-west, or whatever, so long as I rotate all thedirections,alltheaxes,together,nothingchanges.Thesameequationsstillwork.

A physicist, or a mathematician, would say the form of the equations is‘invariant’ under rotations.fn2 If we turn, from driving east to driving north,Maxwell’sequationsstaythesame.Lookingforinvariancesandsymmetrieslikethisisoneofthesurestguidesto

finding a sensible route aroundourmapof the invisible.And there is anotherinvariance hidden inMaxwell’s equations, in addition to rotational invariance.Theequationsstay thesameif Ichangespeed.It isnotatallobvious that thisshould be the case. For example, the equations relate how moving electriccharges (acurrent)createamagnetic field. If Ichangemyspeed, Ichange theapparent speedof the current. I could even catch it up, so that frommypointview there is no current! So what do Maxwell’s equations tell me about themagneticfieldinthiscase?On our evolvingmap, the road connections represent electromagnetism. So

let’sperformatest,orathoughtexperiment.Aseriesofcarsispassingus,at50km/h, each carrying a large box of electrons, and therefore a negative charge.Thestreamofcarsisthereforeanelectriccurrent,soMaxwell’sequationstellusweshouldseeamagneticfieldduetothatcurrent,aswellasanelectricfieldduetothechargeoftheelectrons.Wedo,andwecanmeasurethemboth.Now, imagineweaccelerate toaspeedof50km/h, in thesamedirectionas

the series of cars.We are now travelling with them. Relative to us, they arestationary, so there isno longeranelectriccurrent.Andso there shouldbenomagneticfield.Hasphysicsreallychangedjustbecausewespedup?Fromthepointofview

of someone by the roadside, there is still a current, and so according toMaxwell’s equations nothing changed – there is still amagnetic field.DoweeachneedourownversionofMaxwell’sequations?Whataboutathirdpersonmovingwithadifferentspeed,maybetravellingin theoppositedirectionat50km/hsotheyseeastrongercurrent?TheansweristhatweallusethesameversionofMaxwell’sequations.They

stillwork,becausetheyareinvariantunderchangesofspeed.Indeedforusthemagneticfieldwilldisappear,becausethecurrentvanishes,buttheelectricfieldchangessubtlytocompensate,andintheendtherelationshipsbetweenmotionsand forces on any electric charge all stay the same, in a way which appearsalmostmiraculousbutwhichisentirelyprescribedbyMaxwell’sequations.Theelectricandmagneticfieldsaresaid tobe‘covariant’– theyvary together inawaywhichkeepstheformoftheequationsinvariant.Weonlyneedoneversionofphysics,nomatterhowfastwemaybemovingrelativetoeachother.This has very far-reaching consequences. Remember, Maxwell’s equations

couldbeusedtogetthewaveequationforelectromagneticwaves,andtherefore

the speedof light. If theequationsare the samenomatterhow fastwe travel,thensoisthespeedoflight.Thespeedoflightisaninvariant.The fact that the speed of light is always the same for everyone, nomatter

whattheirownspeedis,isafoundingprincipleofEinstein’srelativity.Relativityisneededtodescribethefast-movingandhigh-energyparticleswewillmeetonourtravels,anditalsocontainsthefactthatenergy(E)andmass(m)arerelatedbythefamousequationE=mc2,wherecisthespeedoflight–thespeedofthewavesoriginallyderivedfromMaxwell’sequations.Thisisalottogetoutofonesetofnineteenth-centuryequations.Bykeeping

the electrons bound to the nucleus, they are holdingAtomLand together.Allparticles that have electric charge can pass photons back and forth, eitherattracting or repelling each other; an important road network connecting upmany of our islands of knowledge. In addition to all this, the equations haveshown us a tool kit of general rules and ideas, like invariance and relativity,whichwillhelpustoexplorefurther.

11

TheGoodShipDirac

EXPLORINGMAXWELL’SEQUATIONShasfilledinsomeofthephysicsbehindQED,andbuilta roadnetworkforus thatbridgesAtomLand to theelectron. Itwillallowustotravelthroughtheinterioroftheislandswediscoveronourvoyages.IthasalsobroughtEinstein’s relativity intoview.ButMaxwell’sequationsarenotquantummechanical,andwealreadyknowthatwithoutquantummechanics,AtomLandmakesnosense.ThereisahugeandunexpectedrewardtobehadbylookingathowrelativityandquantummechanicscometogetherinQED.We’ve seen thewave-likenatureof theelectronsaroundatoms,which is an

essential featureofchemistryandphysics.Thiswave-likebehaviourhas tobegovernedbysomekindofwaveequation,becausethat’showwaveswork.ThesimplestequationthatcanbeusedtodothiswasderivedbyErwinSchrödingerin1925.Ittakestheclassicalrelationshipbetweentheenergyofaparticleanditsmomentum,fn1andbysomeingenioussleightofhandmakesawaveequationoutofit.Thewaythisisdoneistoredefinetheenergyandmomentumofaparticleasbeingpropertiesofanunderlyingquantum‘state’,anewkindofunderlyingobject that contains all possible information about the particle. The energy isrelated tohowthestatechangeswith respect to time,and themomentumwithhowitchangeswithrespecttodistance.Butthisisnolongergoodenough.Weneedtotakerelativityonboard.Itisalittleasthoughwehaveanexcellentlittleboatforchuggingaroundthe

coastlines of our islands, hugging the shore of Atom Land. But we needsomethingmorepowerfulandheavy-duty to takeus further.Weneedabiggerboat.That’swheretheDiracequationcomesin.The classical, pre-relativity relationship between energy and motion dates

back to IsaacNewton and others in the seventeenth century. It states that thekinetic energy – the energy ofmotion – is one half times themass times thesquare of the speed. After Schrödinger’s trick, this becomes a wave equationwhichtellsushowaquantumparticlemoves.Thatequationworksverywellinpredictingthebehaviourofelectronsandotherparticles,includingmanysubtlequantumeffects–forexample,withtheenergylevelsoftheelectronsaroundan

atomthatwealreadyexplored.But theenergy-and-momentumrelationshipwestartedwithisonlyvalidatspeedsmuchsmallerthanthespeedoflight.Itdoesnot incorporate the lessons of relativity. So as we explore the behaviour ofparticles at higher energies (and higher speeds), we need to improveSchrödinger’sequationtotakeintoaccountrelativisticeffects.Taking a similar recipe to that used by Schrödinger to obtain his wave

equation,theobviousthingistouseEinstein’snewrelationbetweenenergyandmomentumandmakethesamereplacements.Thatis, theenergytellsusaboutthe time dependence of the quantum state, the momentum tells us about thedependenceonposition,andweshouldgetanewwaveequationthatworksevenatspeedsclosetothespeedoflight.The complete form of Einstein’s E = mc2 includes the momentum of the

particleaswellasitsenergyandmass,andrelatesthesquareoftheenergytothesquare of the mass and the square of the momentum.fn2 And that presents aproblem when we try to turn it into a quantum wave equation. Equationsinvolving squares generally have two solutions. If I know that the square ofsomenumberisfour,whatdoIknowaboutthenumber?Itmightbetwo,sincethesquareoftwo–twotimestwo–isfour.Butitcouldalsobeminustwo,sinceminus two timesminus two is also four.Likewise,–Emultipliedby–E is thesameasEmultipliedbyE.Itwouldseemthatournewequationsallownegativeenergyparticles.That isnotaneasythingtomakesenseof.What isaparticlewith a negative energy, or even negativemass? This turns out to be quite animportantquestion.Remember that toget therightanswersaboutquantumparticles–howthey

move,wheretheygo,howtheyinteractorbindtogether–wehavetoincludeallthepossibilitiesforhowtheymightmove,andwheretheymightendup.Onlythendoweget thepropermixofwave-like andparticle-likebehaviour that isseen in nature. This means we can’t pick and choose solutions to our waveequation.Allpossiblesolutionshavetobetakenintoaccount,andthatmeanswewouldhavetoallowelectronstohavenegativeenergy–lotsofit.Andwedon’tseethoseelectronsaroundinnature.Worse,thosenegativeenergystateswouldallowpositiveenergyelectronsto

sort of sink into them and vanish. The number of electrons would not beconserved; very bad news for conservation of electric charge, and totallyincompatiblewithMaxwell’sequations.None of this matches the way electrons actually behave. So, at least for

electrons, thedefault recipe formakingaquantumwaveequation fails.Wedoindeedneedabiggerboat.

The negative solutions are allowed because the energy is squared in theequation.Whatisreallyneededisanequationwhereenergyappearsonlyonce,notsquared.fn3So, to summarise the problem: to carry us any further in understanding

particles,weneedanequationwhich isconsistentwith relativity,but inwhichtheenergyandmomentumarenotsquared,somethinglikeenergyisequaltoAtimes the mass plus B times the energy, where A and B are some unknownnumbersweneed toworkout.This is thekindof thingwedo inmathematicsveryoften.FindAandBandwe’reontheway.Theproblem is, therearenonumbers thatwork ifwe substitute them forA

andB.Tomake theequationwork,youneedAandB tobeobjects that don’t‘commute’.Thisdoesn’tmean thatAandBwork fromhome,or liveover theshop.Commuting in this contextmeans thatA timesB is the same thing asBtimesA.That’strueforallnumbers.Themultiplicationtableslearnedatschoolallshowcommutation,inthatifweknowfivetimessixisthirty,weknowthatsixtimesfiveisalsothirty.Evenimaginarynumberssuchasthesquarerootofminus one, which you might think would be weird enough to do just aboutanything, commute and therefore don’t help us towards the relativistic waveequationweneed.fn4At thispoint itmightbe tempting togiveup, and leave the restof themap

blank. Maybe the behaviour of subatomic particles is just not susceptible tomathematics. Perhaps there is no wave equation that can properly describeelectronsandatthesametimeagreewithrelativity.Maybethesewatersaretooroughforus,andtheroadstoodifficulttopass.NotforPaulDirac.Hemetthechallenge–tofindanequationthatdescribes

the motion of a quantum particle moving at relativistic speeds – in 1928. Itinvolvedastrangeformofmathematicsnotusedsofar inthisexploration,butluckily,waitingthereinourtoolkittobeused.Theimportantfirststepistonotethattherearemathematicalobjectsthatdo

not commute. One such type of object is called a matrix. In mathematics, amatrixisanarrayofnumbersarrangedinrowsandcolumns,governedbyrulesdictatinghowtheyshouldbemultipliedtogetherandsoon.fn5Mathematiciansdothiskindofthingquitealot–definingsomenewabstractmathematicalobjectwith some specified behaviour, and then playing around to see what theconsequencesare.Fromthepointofviewof themathematics, itmattersnotatallwhether there is anycorrespondencebetween thenew toyand thephysicalworld.But from the point of viewof a physicist looking for some things thatdon’t commute, to helpmakemore sense of the map of physics, it can be atreasure trove. Matrices can slot in there instead of numbers in the trial

relativisticwaveequationweare trying tobuild.Theymake itwork,and thenthemathematicsofmatricescanhelpusseewhatthephysicalpredictionsoftheequationmightbe.InDirac’scase,theyaredramatic.ThesimplestmatricesthatcanmaketheDiracequationworkarearrangedin

fourcolumnsandfourrows,offournumberseach.Thesemultiplythequantumfielddescribingaparticle, just like the terms in theSchrödinger equation.Butthe rules of thematrix gamemean that the objects theymultiply can also nolonger be simplynumbers.Theyhave to have four components, arranged in alittlecolumn.Onceyouhavedecidedyouneedmatrices,youneedfourquantumfieldstodescribeaparticle,notjustone.Asonemightexpect,thefactthattherearefourcomponents to thequantumfieldhasrealphysicalconsequences.Thiswillallowustotravelintothedeepsouth,andalsoexplainoneofthemysteriesweencounteredlongago,backinAtomLand.

12

SpinandAntimatter

FROMTHESOUTHcoastoftheisland,theweathertothesouth-eastlooksgrimandforbidding.Themoresuperstitiouscrewmembersfearthatwewillbelostinthedeeps,orevenofftheedgeoftheworld,ifwesetoutinthatdirection.Butwiththe Dirac equation, and its matrices and its vectors containing four quantumfieldswhereweused tohaveone,wehaveconstructedavesselworthyof thejourney, and it will take us on one of themost remarkable expeditions in thelandscapeofparticlephysics.One thingwhichgivesusconfidence inournewvesselisthat,indevelopingit,wehavesolvedanoldpuzzlewecameacrossinAtomLand.Onthatexpeditionwemadetheobservationthattheelectronsboundtoatoms

wereconfinedtoparticularenergylevels.Acuriousfactthatwasalsonotedwasthat each level could only hold two electrons. There’s no argument about thisfact–thewholeofchemistryandspectroscopybackitup.Butwhytwo?Evenifwe accept that there is some limited occupancy, that we can’t stuff lots ofelectronsintothesameenergylevel,thentwoseemsastrangenumbertoallow.Whynotjustone?Whynotten?The ‘exclusion principle’ behind this is built deeply into the quantum field

theoryweusetodescribeelectrons,andindeedallquantumparticles,andasisveryoftenthecase,itcomesdowntoasymmetry.Inthiscaseitisasymmetryunderswappingpairsofidenticalparticles.That’s a fairly trivial-sounding symmetry. One would think that swapping

pairsofidenticalparticlesmakesnodifferencetoanything,bydefinition–theyareidentical.Butinquantummechanicsthat’snotquitetrue.Theprobabilityofmeasuring a real physical property depends on themagnitude of the quantumfield,notonitssign.Minusoneandonebothhavethesamemagnitude–one!So swapping over two identical particles will obviously have no effect onphysicalobservablesifithasnoeffectonthequantumfield(that’strivial),butitwillalsohavenoeffectevenifitflipsthesignofthefieldtominuswhatevertheoriginalvaluewas.Quantumparticlesseemtoexploitallavailableopportunitiestobeweird,andsomeparticlesbehaveinthefirstway(nochangeinthefieldor

the observable physics)whereas others behave in the secondway (change thesignofthefield,butstillnochangetotheobservablephysics).Thefirstkindofparticlesarecalledbosons,thesecondarefermions.Nowwhatisthechanceofhavingtwoormoreidenticalelectronsinthesame

energylevelinanatom?Wehaveto,asusualinquantummechanics,sumupallthe different possible ways. Electrons are fermions, so there are two possibleways according to this exchange symmetry – onewith the particles swapped,one un-swapped. But these have identical quantum fields behind them, apartfromadifferentsign.Theywillcancelout,justlikethewavesinthebaycouldarrive out of phase and leave the seagull becalmed. If they cancel out, theprobabilityofhavingtwoidenticalelectronsinthesameenergyleveliszero.That’stheexclusionprinciple.Itshowshowtheenergylevelscangetfull,but

it does not yet explain why there are two electrons in each energy level.Accordingtotheexclusionprinciple,therecanbeonlyone.Unless… the electrons are not identical. And the Dirac equation has just

shown us that the electron has to correspond to four quantum fields. Two ofthese explain the double occupancy of the energy levels inAtomLand. Theycorrespond to different ‘spins’ of the electron. Spin is an intrinsic angularmomentumthatelectronshave,almostasthoughtheywerereallyspinning.Itisa very important property of a particle, dictating a lot about how it behaves.Electronshavehalfaunitofspin,whichcanpointinoneoftwodirections–say,clockwiseoranticlockwise.Thespinmeanselectronsgeneratea tinymagneticfield,aswellastheelectricfieldduetotheircharge.Thismagneticfieldaffectshowtheybindtoatomicnuclei.Itcanbemeasured–forexample,ifanatomisplaced in a strong magnetic field, each energy level splits into two, becausewhenthemagneticfieldduetothespinisalignedwiththestrongmagneticfield,ithasadifferentenergytothatwhichithaswhenitisanti-aligned.Thesesplitsinenergylevelshavebeenpreciselymeasured.TheDiracequationtellsuswhytheyhappen.Theexclusionprinciple,andwhetheraparticleisabosonorfermion,isinfact

intimatelywrappedupinthematterofspin.Fermions,suchastheelectron,havehalf-integerspin.Bosons,suchasthephoton,haveintegerspin.ButwhatoftheothertwocomponentsintheDiracequation?Thisiswherewe

launchournewboatandheadsouth,intothosestorms.AtthetimeofDirac’sresult,therewasnophysicalproperty,likespin,waiting

tobeexplainedby thesecomponents.They lookabit like thenegativeenergysolutions thatplaguedusearlier,but rather thannegativeenergy, theydescribeparticlesthathavetheoppositechargetoelectrons,andidenticalmass.

Nopositivelychargedelectronswereknown.ThiswasaproblemforDirac,andhewronglysuggestedthattheprotonmightbetheso-called‘antiparticle’ofthe electron, even though their masses are very different. He did not need toworry.Physicistswerebusilyphotographingthefragmentsproducedwhenhigh-energyparticlesfromspacehittheEarth’satmosphere.Withinaveryfewyearsof Dirac’s prediction, tracks were seen in these photographs which indicated,fromthedistancetheytravelledandthewaytheycurvedinamagneticfield,thattheyhadthesamemassastheelectron,butwerepositivelycharged.Theywerenamed positrons – the antiparticle of the electron. As we have built betterdetectors and high-energy accelerators, antiparticles for all the other particlesdescribedbytheDiracequationhavesincebeenfound.Thisiswhatwefindaswesailsouth.Theworldisaglobe,notaflatplane.

There is an equator, and sailing over it reveals a whole new landscape. Thehemispheresouthof theequator isantimatter,and thenewvessel that takesusthere is the Dirac equation, powered by mathematics, relativity and quantummechanics. Every type of particle we discover north of the equator has itssouthern, antimatter equivalent. Positrons for the electron, antiprotons for theproton,andsoon.Antimatterisoneofthemoreastonishingconceptsinthelandscapeofparticle

physics.Insciencefictionitappearsasaweaponofawesomepower,destructiveorotherwise, largelybecausewhenmatterandantimattermeet, theyannihilateoneanotherinablazeofreleasedenergy.Inreallifeithas,perhapssurprisingly,beenputtouseinmedicinebeforewarfare.Itwasastunningpredictionofnewphysics, pulled right out of human imagination and reason, shortly beforeexperiment would reveal it to be correct. For all its starring roles in sciencefiction,antimatterissciencefact.Awholenewhemisphereofphysicswasmadeaccessible by the exploratory power of some rather esotericmathematics. Themathematicstoldussomethingstartlinglynewaboutnature,butperhapsanevenmore profound shock is what the observable existence of antimatter tells usabouttheconnectionbetweenabstractmathematicsandphysicalreality.Thefactthatthevesselswebuilthavesuchrangeandpowerisastonishing.Toaddtheicingonthecake,justbeforeweturnbacktowardstheislandon

whichPortElectron is found,anothercoastlinedriftspast in themurk.OneofthemoreexperiencedsailorsinformsusthatthisisthelandofBosonia,anditistherethatthephotonswehavecomeacrosssooftenontheroadoriginate.Thisisclearlyacountrytobevisitedonafuturetrip.Fornow,wehavebusinessbacknearPortElectronagain.

13

TheElectron’sOverweightSiblings

DIRAC’SEQUATION,MAXWELL’SequationsandrelativityareallbroughttogetherinQED,thequantumfieldtheorywehavealreadybeenusingtonavigateonlandusing ourmap.Back from the south and armedwith our new knowledge,wenowlandyetagainatPortElectron,andsetofftoexploretheinlandareaaroundit,whichweneglectedearlierwhenwewereintentonsailingforAtomLand.Weknowquitealotabouttheelectronbynow.Weknowithasasmallmass.

We know its connection toAtomLand, and the fact that it has a spin and anantiparticle.WhatelsemightbelyinghithertoundiscoveredinthehinterlandofPortElectron?Thereare stories.The locals refer to thecountryas the ‘IsleofLeptons’.Whenaskedwhatthismeans,theysaythatbecauseit issolight, theelectron is called a lepton, from the Greek for ‘small’. But the question thatposesitselfthenis–arethereotherleptonsabout?A rapid trip on the excellent highways in our increasingly fast and road

worthy vehicle reveals that yes, there are. Two other particles exist on thisisland,whichareidenticalineverywaytotheelectron,exceptforthatfactthattheyaremoremassive.Theparticlesbothcarryelectricchargeliketheelectron,sotheyinteractviatheelectromagneticforce–wecangettothembyroad,onourmap.Theyalsocarryhalfaunitofspin:theyarefermions.Sofar,somuchlike the electron.Theirgreatermass,however, is a significantdifference,withmajorconsequences.Becausetheyaremassive,theyareabletodecaytolighterparticles.Particles

decay whenever they can, in general. Because mass is a form of energy, aparticle is really a very, very dense clump of energy, which, if it can, willnaturally tend to spread out, to distribute itself more evenly, by decaying tolighter particles. Imagine if Iwere to superheat a cubic centimetre of air in aroom.Thatwouldbea concentrationofheat energy,but itwouldn’t last long.Thehotairwouldspreadoutthroughtheroomalmostimmediately.Theoveralltemperature would rise slightly, but rather quickly there would be no sign ofwherethehotcubiccentimetrewas.Inasimilarway,particlesdecayandspread

out their energy.And themoremassive they are, themoreways they have ofdoingthis,becausetherearemoreoptionsoflighterparticlesopentothem.The electron has no options. It is the lightest electrically charged particle.

Electric charge is conserved, and there is nothing it candecay towhich couldcarrythecharge,soitdoesnotdecay.Someway to the east on the Isle of Leptons, however, lies themuon. The

muonismorethantwohundredtimesmoremassivethananelectron.Thatisahugeconcentrationofenergywhichwillspreadoutveryrapidly if itcan.Andthereis,ofcourse,alighterparticlethatcancarryawaythechargeofthemuon–theelectronitself.Thisistheonlydecayavailabletothemuon(intheStandardModel, anyway). It decays to an electron, plus a neutrino and an antineutrino,whicharevery lightandcarrynoelectriccharge.Theyoccupyadifferentandvery inaccessible part of the Isle of Leptons, and so far we have only heardrumoursof them.Theaverage timeamuonexistsbefore itdecays thisway isjustover twomicroseconds.For this reason,muonsplayno significant role inAtomLand,althoughitispossibletoformshort-lived‘muonic’atoms,inwhichone of the electrons bound to the nucleus is replaced by a muon. The mostcommonsourceofmuonsistheupperatmosphere,wherehigh-energyparticlesfromspace–cosmicrays–collidewith theoxygenandnitrogenmoleculesoftheplanet’sprotectiveblanket.Furtherondowntheroadeastwardisthetaulepton.Thisisheavierstill,with

amass nearly seventeen times that of themuon.Because of this, it hasmoredecay options open to it (always with at least one neutrino involved). Theaveragetimeataustayswithusbeforeitdecaysisjustonethirdofamillionthofamicrosecond.Thisisjustaboutlongenoughforthedecaysoffast-movingtaus,produced inhigh-energycollisions inparticlecolliders, tobeobserved inparticle detectors, but it is not long enough for them to form any bondswithatoms,orwithanythingelse.There ismore tobe learnedbystudying thesenewleptonsmoreclosely.As

weknowfromQED,magneticfieldsarecreatedwheneverelectricchargemovesaround.Sobecauseoftheirspinandtheirelectriccharge,electrons,muonsandtausare tinymagnets.Theyhave twopoles,northandsouth, like theEarthoranyothermagnet.Thestrengthof themagneticdipoleofaparticle isan importantquantity to

measure. It depends on the spin, the electric charge, themass, and a constantwhichisconventionallycalled‘g’.Thevalueofgtellsusalotabouttheparticleinquestion.Foraclassical,everydayparticle,gisequaltominusone.Imagineaspinning

ball, with an electric charge equally spread throughout its volume. If we use

Maxwell’sequations tocalculate themagnetic fielddue to thatchargemovingaroundtheaxisofrotation,wearriveatminusone.Wealwayswill.However,electronsandmuonsarenotclassical,everydayparticles.Theyare

quantum particles, or fermions, described by the Dirac equation, as we havealreadyseen.Aspartofthewaytheequationintroducesaspinofhalfaunit,italsopredictsthatgshouldbeminustwo.Comparedtomeasurementsofg,thisisnearlyright.Theactualanswerforthe

electronis–2.00231930436152,withanuncertaintyof0.00000000000054.Thatmakesg one of the most precisely measured and calculated quantities in theworld.Thevalueforthemuonisverysimilar:−2.00233184178withanuncertainty

of about 0.0000000012. It is less preciselymeasured than the electron, as onemight expect since muons are less common than electrons, and because theydecay so quickly. But more interestingly, the theory and the most recentmeasurements disagree in the case of the muon, by about 3.4 standarddeviations, which is about a 3-in-10,000 chance that the theory and theexperimentarebothcorrect.Thatisenoughofadiscrepancytomotivatelotsofeffortbothtocalculateandtomeasurethevaluemoreprecisely.The reasons for these tinydifferences fromtheDiracpredictionof two,and

thereasonfortheinterestinmeasuringthispropertyoftheparticlesoprecisely,arethesame:quantumcorrections.Several timesonour travelswehavecomeacross the idea that, inquantum

field theory,allpossibilitieshave tobe taken intoaccount.This ishowwegetthe rightanswer for the interferencepatternswhenparticlespass throughslits.This iswhyelectronsaroundatomsareconfined tospecificenergy levels,andwhyeachlevelcancontainonlytwoelectrons.Andweneedtodothisevenforaparticlethatisjustonitsown,mindingitsownbusiness.Imaginethatwepausebytheroadsideandwatchaparticle,sayanelectronor

amuon.Theparticleisthereonemoment,and…continuestobetherethenext.Thesimplestpossibilityisthatnothinghappens.Butthereisalsothepossibilitythatinthatmoment,itbrieflykickedoffaphoton,whichsprungawayandthencame back again, so that at the end of the moment it is as though nothinghappened. That possibility needs to be taken into account in calculating theproperties of the particle, such as its magnetic dipole. There are even moreesoteric possibilities. The photon might have split into a particle–antiparticlepair, which then annihilated with each other back to a photon, which is thenreabsorbed by the original particle, so that again it is as though nothinghappened.Thatpossibilityneedstobetakenintoaccount,ifyouwantapreciseenoughanswer.

Itisthesetinyquantumloopsandcorrectionsthat,ridiculousthoughtheymaysound,actuallyhaveaneffectong, thenumberthatcharacterisesthemagneticmoment, and are the reason it is not exactly two. The mass of the originalparticlealsoaffectsthem,whichiswhygisslightlydifferentfortheelectronandthemuon.The reason that knowing these values so precisely is interesting is that the

tiny, transient loopsmight contain new, unknown particles, not present in theStandardModel.Tantalisingly, thismightbe the reason that, for themuon, themeasurement does not agree with the theory. Perhaps mysterious unknownparticles, not present in theStandardModel andnotyet directlyobserved, aregoing round those loops, and affecting the value of g. If, with more precisemeasurements, the disagreement between the data and the Standard Modelgrows,thismaybeadefinitesignposttowhatisgoingoninthefareastofourmap.Lookingindetailat theinhabitantsoftheIsleofLeptonscouldhavefar-reachingconsequences.

RESTSTOP

Gravity:ADistantDiversion

Interlude inaplayground–Pretentious forces–Thegeodesic,straight lines that loop – Black hole mergers waving from adistance–Apredictionvindicated.

TheWeakestForce

WEHAVEMADEalotofprogressinourexplorations.StartingfromPortElectron,we have surveyed the interior lives of atoms – discovering the nucleus andunderstanding the arrangement of the electrons that are bound to it – in ourtravels through Atom Land.We have found the muon and tau – two heaviercopiesof theelectron–andexploredthewesternendof theIsleofLeptonsindetail. And we have worked out how the electromagnetic force operates,followedtheroadnetworkandevenspottedthehomeofthephotononthewestcoastofBosonia,althoughwedidnotlandthere.Therearemore journeys tocome,andmore toberevealed.But there isone

vitalpieceofphysicswhichisoperatinginthebackgroundofallthis,whichisapparent in everyday life, even to the farwest of ourmap, andwhichwe aregettingnoclosertounderstandingbytravellingfurther.Theforceofgravityisfeltbyallmatterandenergy,andisthemostobvious

force ineveryday life. In fact it is soubiquitous,andsuchanacceptedpartofeverydaylifethat–astheapocryphalstoryofNewtonbeinginspiredbyafallingappleindicates–evennoticingitasaforceissomethingofabreakthrough.Wegetmost excitedwhenwe appear to escape the force of gravity.An astronautorbiting in free fall is ahugenoveltywhennormal life is spentpressed to thegroundinsideagravitywell.Itisabitofasurprisethentofindthat,ofallthefundamentalforces,gravity

istheonewiththemosttenuousconnectiontoourmapofphysics.Thereisn’treallya‘GravityIsland’oranythingsimilartoexplore.Sowewillsitourselvesdown in a park, somewhere in the suburbs of Port Electron on the Isle ofLeptons,haveacupofteaandthinkaboutit.Thereareafewreasonsforthedistancebetweengravityandanythingelseon

ourmap.Themostobviousisthestrengthoftheforce.Gravityhasanoticeableeffect becausewe live next to an enormousmass (the Earth) which orbits aneven bigger mass (the Sun). We are continually under the influence of thecumulativeattractionofallthebillionsoftrillionsofatomsinthosebodies.ButthosebodiesexistfartothewestofAtomLand,faroffthemap,toolargeanddiffuseforitsscope.

Thus,gravityisthestrongestnetforceactingonusbyfar.Somethingtothinkaboutaswepourourselvesthatcupoftea.Andaswedoso,andwhenweraiseourcupstodrink,ourarmiscounteringthegravitationalattractionoftheentireEarth. In fact,we areovercominggravity all the time,wheneverwe standup,breathe,andjustgenerallydon’tcollapseintoanunstructuredjelly.fn1Theforcethat allows us to do this is the electromagnetic force governing the chemicalinteractions in our bodies – the bonds that keep our bones rigid, the energytransfersthatmakeourmusclescontractandexpand.Unlike gravity, which is always attractive, electromagnetism can be both

repulsiveandattractive;therearebothpositiveandnegativecharges.SincetheEarth, and our bodies, both contain equal amounts of positive charge (in theatomicnuclei) andnegative charge (the electrons), the attractive and repulsiveforcescanceleachother.Evenaverysmall,localimbalanceinthiscancellationleadstosignificanteffects.Lightningisadramaticexample,whereanimbalancebuildsupintheatmosphereandisrestoredinaviolentflash.Thiscancellationiswhywedon’tfeelelectromagneticforcesasobviouslyas

we feel the force of gravity. But down at the subatomic level, theelectromagnetic force between a proton and an electron is about 1043 (onefollowedbyforty-threezeros,ortenmillionbillionbillionbillionbillion)timesstronger than thegravitational force.Considering this hugedifference, particlephysicistscanignoregravityintheircalculations.fn2

PlanesandRoundabouts

THE OTHER WAY in which gravity is different from the forces of the StandardModelisrelatedtothewayitisunderstoodwithinEinstein’stheoryofGeneralRelativity.Inthistheory,itisquestionablewhetherweshouldevencallgravityaforceatall.WhengettingtogripswiththeDiracequationforourjourneysacrossthemap,

wesawthatthe‘special’theoryofrelativityariseswhenyouinsistthatthelawsof physics are the same for all ‘inertial observers’ – observers travellingwithconstant speed in a constant direction. The laws of physics includeelectromagnetism,sothatmeansthatthespeedoflightmustbethesameforallthoseobservers,andonceyou insiston that,all theweirdeffectsonhow timepassesandhowspacecontractsfollow.Asdoesthefamousequivalenceequationbetweenenergyandmass,E=mc2.Toget suchastoundingnewphysics fromsuchageneralprincipleisremarkable.But what about other observers? Most of the time we are not ‘inertial

observers’. Surely the laws of physics should not change just becausewe areacceleratingordecelerating?Itiscertainlytemptingtoinsistthatphysicsshouldbe the same for all observers, even ‘non-inertial’ ones, if onlybecausewegotsuch a lot of new and correct physical understanding from doing that for theinertialones.Anyway,itseemsintuitivelyright,somehow.ThatisthechallengeEinsteinaddressedwithhisgeneraltheoryofrelativity–

‘general’becauseitappliestoallobservers,notjusttothespecialcaseofinertialonesconsideredinhispreviousmasterpiece,theSpecialTheoryofRelativity.Whataretheeffectsofacceleration?Thereisanairportnotsofarawayfrom

us–wewillvisitthissoononourtravels.Inanaeroplaneacceleratingdowntherunwayfortake-off,thepassengersfeelthemselvespressedbackintotheirseats.From their point of view this feels like a force, and that’s why they are notinertialobservers. Imagineyourself in theirplace.Thewaterbottleyouleftonthe floor beneath your seat rolls backwards as though someone is pushing it.Objects inyour frameof referencedonotmovewith constant speeds, as theyshould for an inertial observer. From your point of view, objects acceleratebackwards.Frommypointofview,watchingfromthepark,youareacceleratingforwardsandleavingthembehind.

Howdoes thisconnect togravity?Well, imagineit isnight. It ispitchblackoutside.Youarepressedbackinyourseatastheplaneaccelerateshorizontally.Butcouldyou tell thedifferencebetween thissituationand thepossibility thattheaeroplanemightbeflyingupwardsatsomeangleandaconstantspeed?In both cases the bottle (or carelessly stowed laptop) would accelerate

backwardsuntil ithits something,maybe thebackof thecabin.Einstein’skeyobservation was to notice that it is difficult, perhaps impossible, to tell thedifference between a framewhich is non-inertial because it is experiencing agravitational force (the climbing aeroplane) and a framewhich is non-inertialbecauseitisaccelerating(thehorizontalaeroplanespeedingup).Similarly,aframewhichisfallingfreelyundergravitylooksverymuchlike

aninertialframe,inwhichnogravityacts.Infact,theonlyframeswe’refamiliarwithwhich really look inertialare those in free fall;mostobviously the framemovingalongwiththeInternationalSpaceStation(ISS),continuallyfreefallingalongitsorbitroundtheEarth.It is worth thinking about the situation of something in orbit like the ISS,

compared to someone or something on, for example, the roundabout in thechildren’splaygroundwe’vejustnoticedacrosstheparkfromus.FromthepointofviewofsomeoneonEarth,theISSismovingquickly,andit

wouldmoveinastraightline,accordingtotheconservationofmomentum,butforthegravitationalattractionbetweenitandtheEarth.Thegravitationalforceplaysthesameroleasthearmsofachildholdingontotheroundabout,spinningintheplaygroundwecansee.Byholdingon,thechild’sarmsexertaforcethatpullsthemcontinuallytowardsthecentreoftheroundaboutandsokeepsthemturningaroundit.Likewise,ifgravitysuddenlystoppedworking,theISSwouldflyoffintoouterspace.Butgravitykeepsitcirclinginorbit.Gravityprovidesacentripetalforce,directedtowardsthecentreoftheEarth.Buttherearesomebigdifferencesbetweenthesituationofthechildandthe

ISS,apartfromtheobviousonesinvolvingspacesuitsandstuff.On the roundabout, the child experiences a centrifugal ‘pseudoforce’. They

definitely are not in an inertial frame. Anything they drop will fly off theroundabout, away from the axis of rotation in themiddle.Yet on the ISS, theastronauts seem to experience fewer forces acting. Not only do they notexperienceacentrifugalpseudoforce,buttheyseemtobeweightless.The reason is that in orbit, your weight and the centrifugal pseudoforce

completely cancel, leavingyou in free fall.This is averydifferent experiencefrombeingflungaroundaroundabout,fortwomainreasons.Firstly, gravity acts on yourwhole body, and indeed allmatter, equally and

simultaneously, so you don’t have to grab on to a handle and then have your

armspull the restofyou round thecircle.Yourarms, legsand the rest are allbeingactedonbygravity.ThesecondreasongoestotheheartofGeneralRelativityandthereasonyou

are,ontheISS,infactinaninertialframe.Mass appears in two important equations – force is mass multiplied by

acceleration,fn1 and the force of gravity is proportional to mass. GeneralRelativityworksbecausethemassinthosetworelationsisidentical.Onthefaceofitthereisnoreasonthatthisshouldbeso,butinGeneralRelativityitisbuiltin.ThatwasanotherofEinstein’sgreatinsights.ThismeansthatinyourISSreferenceframe,thecentrifugalpseudoforcecan

be cancelled by the force of gravity, not just for one particular massapproximately,butforallmasses,exactly,allthetime,leavingyouinaninertialframe.Infact,becauseitcancelsapseudoforceinthisway,itislegitimatetosaythat the General Relativity reduces the ‘force of gravity’ to the status of justanotherpseudoforce.Theprincipleofconservationofmomentum,usedtodefineaninertialframe,

stillappliesandstilldefinessucha frame,but inertial framesnowincludeanyframe falling freelyundergravity.Bodies falling freely like thisare said tobetravellingalonga‘geodesic’,whichisaredefinitioninspaceandtimeofwhatconstitutesastraightline,theshortestroutebetweentwopoints.In the absence of a gravitational field, a geodesic is a straight line in the

‘Euclidian’ sense. Euclid was the first person we know of to define rules forgeometry.Amongst these rules, or axioms, is the statement that themaximumnumberoftimesapairofstraightlinescancrosseachotherisonce,andparallelstraight lines never meet each other. If there is no gravitational field around,geodesics are straight lines, and General Relativity, Special Relativity andNewton’slawsofmotionallagreethatfreelymovingbodieswilltravelalongastraightlineataconstantspeed.But near a large mass, General Relativity states that geodesics bend into

curves, or even into the closed ellipse of an orbiting ISS. Space and time,definedbygeodesics,arenolongerEuclidian.Theverymeaningofa‘straightline’haschanged.Maybe theeasiestway togetan ideaofwhat isgoingon is to imagine two

people at the equator a fewmiles apart, setting off due north, parallel to eachother.Though they set off parallel andkeep travelling in the samedirection–duenorth–theywilleventuallymeet,attheNorthPole,becausethesurfaceoftheEarthiscurved,anddefinesanon-Euclidiantwo-dimensionalgeometry.Nearalargemass,spaceiscurvedinthreedimensions,and‘straightlines’–

geodesics–canbecomeorbits.Thiscurvatureiswhatwe,andallothermasses,

experience as gravitational force. This is why gravity is, in some sense, apseudoforce.Itisaneffectgeneratedbycurvesinthegeometryofspace–time.This is a very differentway of thinking about a ‘force’ fromhowwe think

about the forces in theStandardModel. Ifwe think of particles and forces asactorsonthestageofspace–time,gravityisn’tjustanotheractor,itissomethingwhich bends the stage onwhich the others perform.Also, as is already beingdiscovered inourexploration, theother forcesare fullydeveloped inquantumfieldtheories,whilegravityisdefinitelynot.

Different,YetSomehowtheSame

THEREARE SOME things in common between gravity and the other forces. Theideas of symmetry play an important role in both. Any time we changesomething (say, rotate a shape) and it makes no difference (if the shape werotatedwas a sphere), there is a symmetry. In quantummechanics, there is asymmetry in that changing the phase of all quantumwaves at the same timemakes no difference to the physics. In General Relativity, moving aroundbetweendifferentacceleratingormovingframes,inoroutofgravitationalfields,makes no difference to the physics. A lot of theoretical effort has gone intotryingtoexploitsuchsimilarities,withsomeverypowerfulresults,butsofarnoonehasmanagedtomakeafullyStandardModel-likequantumtheoryofgravitywhichwouldworkatverysmalldistancesandhighenergies.Stepping back from the quantum world, however, there is a very simple

similaritybetweengravityandelectromagnetism.TheSunpullstheEarthtowardsitwithgravitationalforce.IftheEarthwere

twice as far away from the Sun, the forcewould be four timesweaker. If theEarthwerethreetimesnearertotheSun,theforcewouldbeninetimesstronger.This is the famous ‘inverse square’ law.Multiply thedistanceby two, and theforcegetsweakerbythesquareoftwo–thatis,byafactoroffour.Shrinkthedistancetoathird,andtheforcegetsstrongerbythesquareofthree,i.e.nine.It tickles me that even though the theories behind the forces are so very

different, the electric force does exactly the same thing.There is an attractionbetween a negatively charged electron and the proton in a hydrogen atom.Double the distance between them and the force drops by four; it follows aninversesquarelaw,justlikegravity.Thisisnocoincidence.Wecanthinkofamass,oranelectriccharge,asthe

sourceofaforce.Physicistsoftendrawthemaslinesofforce.fn1Thedensityofthelinesisproportionaltothestrengthoftheforce.Theforceisspreadoutoverabiggerandbiggersphereasyoumovefurtherandfurtherfromthesource.Ifthetotalnumberofforcelinesstaysthesame,thentheforceatanygivenpointwill drop as the area increases.The areaof a sphere is four timesπ times thesquareoftheradiusofthesphere,sotheamountofforceatanygivenpointonthesphereisdividedbythis.Themostimportantthinginthatexpressionisthe

radius.The force is divided by the radius squared.This is the ‘inverse squarelaw’, which works just as well for any long-range force, whether the theorybehinditisbasedonquantummechanicsorwarpedspace–time.This isagoodexampleof thefact thatsomeof thegeneral features thatwe

encounteronourtravelsacrossthemapareinasensemorefundamentalthanthedetails.Theprinciplesthatemergeareinsomewaysmorefundamentalthantheunderlyingtheory.Conservationlawsandsymmetriesareotherexamplesofthesameeffect.Youdon’tneedtoknowalltheinternaldetailsofwatermoleculestohave a good idea ofwhatwill happen if you boil a kettle.You don’t need tounderstandQED orGeneral Relativity to know that the inverse square law isprobablyagoodbettodescribehowtheforcefallsoffwithdistance.

RipplesintheSpace–TimeContinuum

CONTINUING THE ATTEMPT to find similarities between gravity andelectromagnetism, the first real theory of electromagnetism, encapsulated inMaxwell’s equations, is not a quantum theory either. It describes theelectromagnetic interactions in terms of continuous fields, just as GeneralRelativity talksaboutcontinuousspace–time.AndMaxwell’sequationspredictthe existence of electromagnetic waves – light, X-rays, radio, the wholespectrum – before we even start discussing quantum effects. Does GeneralRelativitydosomethingsimilar?Aretherewavesingravitationalfields?As far as the theory goes, the answer is decisively yes. After some early

uncertainty, Einstein and everyone else who looked into it agreed thatgravitationalwavesshouldexist.Theyhavetoexistinsomesense,becauseamovingmasswillcausechanges

inthegravitationalfield–changesinthecurvatureofspace–time–inmuchthesamewaythatthedolphinswesawearliercausedripplesinthebay.Accordingto relativistic principles, those changes cannot appear instantaneously all overspace. They can only spread around at the speed of light, and that implies aripple,awaveofcurvature,travellingawayfromthemovingmass.The waves warp distances in space, shortening them in one direction and

lengthening others perpendicular to them, the way that, if you squeeze thecircularrimoftheplasticcupcontainingyourteaandletgo,itwillsquashintoanellipsefirstoneway,thenbacktheotherway.UntilSeptember2015,gravitationalwaveswereexpected,butneverseen.To

see them would require something much more cataclysmic than squeezing aplastic teacup. Itwouldneedahugeastrophysical event– starsorblackholessmashingtogetherorexploding.Evenwithsuchahugeevent,itwouldrequirean unimaginably sensitive detector, simply because the force of gravity is soweak.According toGeneralRelativity, as twoobjects orbit eachother under their

mutual gravitational attraction, they radiate energy as gravitational waves.Losingenergy incredibly slowly, theywill spiralvery,verygradually inwards,withtheirratesofrotationspeedingupastheygo,untileventually,afterasuper-rapidwhizzaroundeachother,theycollideandeithermergeorsmasheachother

topieces.Whiletheendisrapidandviolent,thechangeinorbitearlyoninthisprocessissotinythatevenforenormousstarsorblackholes,thewavesaretoofainttodetect.Therewasevidencethattheywerethere,though.In1974,RussellHulseand

Joseph Taylor Jr at the University of Massachusetts published precisemeasurementsofthefirst‘binarypulsar’.Apulsarisastellarobject thatemitsregular pulses of electromagnetic radiation. In the Hulse–Taylor pulsar, thepulsesshowashiftintheirradiofrequency.Whenthesourceismovingtowardsus,theradiowaveshaveahigherfrequency,andwhenitmovesawaytheyhavea lowerfrequency.The twoorbitingbodiesareultra-dense,withradiiofabouttenkilometresbutmassescomparabletothatoftheSun.TheyareorbitingeachotheratadistanceofafewtimesthedistancebetweentheEarthandtheMoon–practically on top of each other in astronomical terms.And they complete anorbitinundereighthours,soaretravellingveryquickly.Even this gargantuan, high-speed cosmic roundabout does not make big

enough gravitational waves for them to be directly observed. However, whatcouldbeobserved,fromtheregularshiftinthefrequencies,wasthattheirrateofrotationisincreasingveryslowly.Thisishappeningataratepreciselyconsistentwith the rate expected inGeneralRelativity, due to the radiation of energy asgravitationalwaves.Thiswasahugeboost to thecredibilityof the idea thatgravitationalwaves

shouldexist.Butitisstillnotthesameasactuallymeasuringthem,andittellsyounothingabouthowtheytravel.The beautiful elegance of General Relativity is a little deceptive – actually

solvingEinstein’sequationtogetarealprediction,whichtellsyouwhatkindofexperiment you need to build to test the prediction, is a major mathematicalchallengeandatoweringachievementinitself.As gravitational waves pass through the Earth they distort distances,

compressing them in one directionwhile stretching them in the perpendiculardirectionliketherimofthecup.Theamountsofcompressionandstretchingaretiny though; less than the diameter of a proton over several kilometres. It isastonishing thatwe can even dreamofmeasuring suchminuscule effects.Butpeoplehavedoneso.Thekeyiswavesagain,andspecificallytheinterferenceeffectsthatwesaw

inthebay.Abeamoflightcanbesplit,andthetwohalvesmadetotraveldowndifferentpaths,thenbroughtbacktogetheragain.Ifthetwopathsarethesamelength,ordifferbyawholenumberofwavelengthsofthelight,thetwohalvesofthebeamwillbeinphase–thepeakswilllineupwitheachother,aswillthetroughs.Butifthereisadifferenceinthepathsofhalfawavelength,theywillbe

outofphaseandwillcanceleachotherout.Theobservedintensityofthelightisvery sensitive to fractions of a wavelength. An instrument which does this iscalledaninterferometer.Foropticalorinfraredlight,distancesofafewhundrednanometres(billionths

ofametre)couldbemeasured.Small,butnowherenearsensitiveenoughtoseegravitationalwaves.However, if thetwopathsthelighttakesarelongenough,and the light is reflectedbackand forthmany timesbymirrors, thesensitivitycanbeincreased.TheLaserInterferometerGravitational-WaveObservatory(LIGO)consistsof

twoenormousinterferometers,oneinHanford,WashingtonState,USA,andtheotherinLivingston,Louisiana.Eachhastwoperpendiculararms,4kmlong.Aninfraredlaserissplit,andhalfsentupeacharm.Thebeamisreflectedmorethan200times,andthesensitivityisdesignedtobeonetenthousandthofthewidthof the proton, or a ten billionth of a nanometre. The technology required –accurate,efficientmirrors;powerful,stablelaserandsoon–isformidable,buttheprincipleissimple.In February 2016,LIGO announced that they had seen gravitationalwaves,

consistentwithcomingfromthemergeroftwoblackholes.Furtherobservationshavebeenreportedsince.ThisisabigtriumphforGeneralRelativity.Everythingwecanseeaboutthe

wavesisaspredictedbythetheory,andtheyarenowbeingusedasanewmeansofobservingastrophysicalphenomena.Theyarelikelytotellusalotabouttheuniversearoundusoverthenextfewyears.Insummary,muchisknownaboutgravity.GeneralRelativitymakesprecise

predictions,correctlymatchingthemotionoftheplanetsandthefallofanapple,andtheexistenceofgravitationalwaves.Thesewavesaretheanalogueofradiowavesforelectromagnetism–describedbyMaxwell’sequationsbeforequantumelectrodynamicscamealong.Ifthereisaquantumparticlecarryinggravity–agraviton, thecousinof thephoton thatcarrieselectromagnetism– thesewavesarewhatitlookslikeinthelow-energy,classicallimit.Theytellusthegravitonismassless,ifitexistsasaquantumparticle.Buttheydonotgiveusaquantumtheoryofgravity;theydonotallowustofititintoourmapofparticlephysics.And aswewill see aswe travelmuch further east, there are other reasons toworryaboutgravityaswell.Talkingoftravellingthough,ourpicnicintheparkhasbeenlongenough.The

crewareeagertobeoff,andwehavebusinesswithnearerlandmasses.Itistimetofinishourtea,stopthespeculation,andheadoffonourtravelsoncemore.

EXPEDITIONIV

GreatTrainJourneys

Intothenucleus–Elementsandtheirisotopes–Aprofusionofhadrons and themeaning of the eightfoldway –An importantcrossing to a different kind of country – Various flavours –Followingthegluon

14

Protons,NeutronsandtheNucleus

WE ARE HEADING eastwards again. That means toward higher energies, andsmallerandmoremassiveparticles.Ourlastnewdiscoverywasthetaulepton,whichwevisitedbyroad,intheeastoftheIsleofLeptons.Thetauhasamassof about 1.8 GeV, nearly twice the mass of a hydrogen atom. Lookingnorthwardsfromthevantagepointofthetau,anewcoastlineloomsthroughthemist,ahithertounexploredlandmass.ThecoastlineofthissamelandmasswasalsovaguelyvisiblefromtheeastcoastofAtomLand,wherewediscoveredtheatomic nucleus and toyed briefly with alpha particles.We return to our boat,departing once more from Port Electron, but this time sailing east. Our nextjourneywilltakeusinsidetheatomicnucleus,andbeyond.DuringourexplorationofAtomLand,theatomicnucleuswasrevealedinside

theatombyanaturalbeamofparticles–alphaparticles–producedinthedecayof the radioactive element radon. To look inside the nucleus itself, artificiallyproduced beams of particles accelerated in electric and magnetic fields arerequired.Weknowfromourstudiesofquantumfieldsthathigh-energyparticleshave correspondingly short wavelengths, and that is exactly what we need toresolvetheinternalstructureofthenucleus.fn1Suchtechniquesrevealthatalphaparticlesthemselveshaveinternalstructure.

They are actually twoprotons and twoneutronsbound together, a particularlytightlybound,stableconfiguration.Itturnsoutthatallnucleiaremadeofsomenumberofprotonsandsomenumberofneutrons,with the singleexceptionofhydrogen, the lightest element, whose nucleus is a lonely proton with noneutrons.Thealphaparticle– twoprotons, twoneutrons– is thenucleusof ahelium

atom.HeliumissolightthatiteasilyescapesfromtheEarth’satmosphereandoutintospace.Theonlyreasonheliumisstillaroundinsignificantquantitiesisbecause it is constantly produced in the radioactive decay of heavy elements,suchastheradonusedbyRutherfordandhisteam.Yourpartyballoonsarefullofalphaparticles(withelectronsstucktothem).

Nucleiofdifferentelementsaredistinguishedfromeachotherbythenumberofprotonstheycontain.WewalkedaroundsiliconwhenexploringAtomLand,andsawthatthesiliconatomisthesmallestunitofsilicon.Thesameistrueforallelements.Althoughanatomofanyelementcanbebrokenintostillsmallerpieces–electrons,protonsandneutrons–at that stage itwillno longerbeanelement.Thesiliconnucleusconsistsoffourteenprotonsandsomeneutrons.Anything

withadifferentnumberofprotonsisnotsilicon.Thirteenwouldbealuminiumandfifteenwouldbephosphorus,bothofwhicharevery,verydifferentintheirbehaviours.The history of studying the nucleus emphasises an important fact about the

mapwearedrawingofthefundamentalstructureofmatter.Asmentioned,likemost scientific knowledge, the Standard Model is in some ways provisional.Whatwe now view as fundamental particles, the smallest things in existence,may simply be the smallest things we can measure so far, with the toolsavailable.Theremaybedeeperlayers.Thisisnottosaythetheoryisnot‘true’insomesense,justthatitmightnot

be thewhole truth, andaquote about thenucleus fromMaxPlanck, thegreatGerman physicist, one of the pioneers of quantum mechanics, illustrates thepoint. In his bookTheUniverse in the Light ofModern Physics (1931),fn2 heconfidentlyexplainsuraniumusingthepreferredmodelofthetime:

Uranium contains 238 protons and 238 electrons; but only 92 electronsrevolveroundthenucleuswhiletheothersarefixedinit…Thechemicalpropertiesofanelementdependnoton the totalnumberof itsprotonsorelectrons,butonthenumberofrevolvingelectrons,whichyieldtheatomicnumberoftheelement.

There is an interesting mixture of wrong and right in here. Planck did notknow about the neutron (discovered by James Chadwick the year after thistranslationappeared), sohisdescriptionof thenucleus iswrong.Uranium238has only 92 protons, matching the 92 ‘revolving’ electrons, but it has 146neutrons, nestled in the nucleus with the protons.We know that there are noelectrons in the nucleus, in the sense Planck meant. We also know that theelectronsaren’t‘revolving’inthesamewayplanetsorbit theSun.Thiswasanearlymodel of the atom, due toNielsBohr.Aswe have seen already on ourexploration, electrons are fundamentally quantum objects, not particles in thewayPlanckwouldhaveunderstooditatthattime.However,hewasabsolutelyright that there is a nucleus,with ninety-two electrons outside it.Hewas also

right that these ninety-two electrons determine the chemical properties of theelement. His model is useful, and would still work fine today as far as thechemistry of elements goes. But new data, from higher-energy experiments,surveyingtheareafurthereastinourmapthanphysicshadgoneinPlanck’sday,wouldshowthatsomeaspectsofitwerewrong,andneededtobechanged.This is another reminder that the StandardModelmay need to be changed

when new data comes along. For example, our confidence in the idea thatelectronsareinfinitelysmallobjectsisdeterminedbyourcurrenttechnologyandthe ingenuitywithwhichwecanuse it toprobe them.Anewexperimentmayone day show that the electron is not an infinitesimal point, and contains stillsmaller constituents. The StandardModel would then need to be changed. Intermsofourmap,anychangeswouldmost likelyextendeastwardsand revealnew features, although most of what we are exploring now would remainrecognisable.Changing the number of protons in a nucleus then changes the number of

electrons the atom will attract, and so changes the chemistry. It changes theelement.Changingthenumberofneutronshasalessdramaticimpact,however.Asiliconnucleususuallycontainsfourteenneutrons,butsometimestheycan

have fifteen or sixteen. All three versions have the same chemical properties.Theyareallsilicon.Differentversionsofthesameelementthatdifferonlyinthenumber of neutrons inside the nucleus like this are called ‘isotopes’. Someelements have many isotopes, and sometimes they are unstable; that is, theydecayradioactivelytootherelements.Althoughtheneutronsarenotascrucialasprotonsindefiningthebehaviour

ofanatom,theyareabsolutelyessentialinholdingittogether.Protonsallhavepositive electric charges, and since like charges repel each other, any pair ofprotonsupagainsteachotherinthetinyconfinesoftheatomicnucleusmustbeexperiencinghugerepulsiveforces.Weshouldexpectnucleitoflyapartbecauseofthis–orinfactnevertoforminthefirstplace.Thereasontheydon’tisthatthey are attracted to each other by a force strong enough to overpower theelectromagneticrepulsion.Butwhat is this force? It is a connectionbetween features of the landscape

thatwehavenotpreviouslyencountered.WelandatthePortofProton,ontheshore of this new eastern island, the target of this expedition.We are grantedaccessbecauseofourhigh-energyparticlebeams,poweringusfurthereast.Aswemoorupatthestrange,foreignharbour,welookforaroadtofollowinland.Butawhistleisheardfrominsidealargebuilding.Weapproachtoinvestigate,andnoticeapuffofsmokedriftingoutbehind thebuilding.Railsandsleepersemerge from the back, heading off into the interior of this new land. A sign

abovetherathergrandentrancesays‘HadronIslandRailways:ProtonCentral’.Wehavefoundthestrongforce,thebestwaytoexploreHadronIsland.

15

Hadrons

THEPORTOFProton,andthenearbyNeutron,arethefirsttwoexamplesofatypeof particle called a hadron. Hadrons are densely scattered throughout thelandscapewearenowtravellingbytrain.Innature,protonsandneutronsarethemostcommonhadrons:wealreadysawthattheymakeupalltheatomicnuclei,andsoitisfittingthattheyarethefirst,mostobviousthingswecomeacrossonHadronIsland.This is a land that is home to a complex network of structures, tightly

connected by railway lines. This is the strong force. The strong force is thesecondfundamentalforceoftheStandardModelwehaveencountered.Thereismuchtolearnaboutit,butthemostobviousfactrightnowisthatit

overcomes theelectromagnetic force, andholds thenucleus together.Thewaythismanifests itself, as with any attractive force, is that the total energy of acollectionofprotonsandneutrons–let’ssaytwoofeach–isreducedwhentheyarestucktogether.Thisisalsothecaseforelectronsboundtoanucleus:theystayboundbecause

theyhavelessenergythatway.Toreleasethem,energyneedstobeadded.Themain differencewith protons and neutrons bound in nuclei is that the bindingforceisenormouslystronger,andsotheenergiesinvolvedaremuchhigher.Weare,afterall,movingfurthereast.Thelargebindingenergiesinvolvedinholdingnucleitogetherareseeninthe

values of the masses of the nuclei. Since energy and mass are equivalent, alower-energy system has a lowermass. So themass of a helium nucleus, forexample,islessthantwotimesthemassofaneutronplustwotimesthemassofaproton.Again,thisisalsotrueofanyboundsystem:themassofaheliumatomisless

thanthemassofaheliumnucleusplustwicethemassoftheelectron,becauseoftheelectromagneticbindingenergy.But theelectromagneticmassdifference istiny compared even to themass of the electron. Themass differences due tonuclear binding energies are far more significant than this. This is why the

energy that canbe released innuclear reactions ismuchgreater than even themostenergeticchemicalreaction.The binding energy per proton or neutron for different nuclei is biggest for

elements around iron (twenty-six protons and around thirty neutrons). It dropsrapidly forelements lighter than iron,which iswhyenergycanbe releasedbyfusingthemtogether,ashappens,forexample,instarsandhydrogenbombsandhopefully– ifwecanmanage to compress andcontain the enormous energiesand densities required – in power stations one day. The energy also drops,althoughmoreslowly,asthemassofelementsincreasesaboveiron.Thismeansthat there is energy to be gained not just by fusing light elements together tobringtheirmassuptowardsthatofiron,butalsobybreakingdownelementsthatareheavierthanirontobringtheirmassdowntowardsit.Thisisnuclearfission,already useful as a terrestrial power source. In both fusion and fission,everythingheadstowardsiron,whichexplainswhyitissuchacommonelement,makingupthecoreofourplanet,forexample.Thebindingenergyhasanotherimportantimpact.Aneutronleftonitsownis

unstable.Onaverageafreeneutron,outsideanatomicnucleusandnotboundtoanyprotons,willdecayafteraboutaquarterofanhour.However,onceboundina nucleus, a neutron is protected by the binding energy. That is, if it were todecay,theresultingfragmentswouldhaveahighertotalenergythanthenucleusas a whole. Since decays must conserve energy, this is not possible, and thedecay does not happen. This is why, while there are plenty of single protonsaround in theuniverse, thereareno singleneutrons, even though theyexist inabundanceinpartnershipwithprotons,insidenuclei.All other known hadrons decay even more rapidly than neutrons. Most of

themonlylastfortinyfractionsofasecond.Thisiswhytheywerediscoveredlater–theirfleetingpresencefirstseeninthedebriswhenhigh-energyparticlesfrom space bombarded theEarth’s atmosphere.These days they are copiouslyproducedincollisionsathigh-energyparticleaccelerators.AswetraverseHadronIslandbytrain,itbecomesclearthattherearealotof

hadrons.Theydecayatdifferentratesandindifferentways,havedifferentspins,andhavemassesrangingfromthelightest–thepion,ataboutasixthofthemassoftheproton–uptoseveraltimestheprotonmass.Wecanalsonotethathadronscomeintwotypes,baryonsandmesons,with

baryonsbeinggenerallyheavierthanmesons.fn1Theprotonandtheneutronareexamplesofbaryons,buttherearemanymore,anddozensofmesonsconnectedas whistle-stops or major stations on the line. This plethora of particles isdisturbingifoneishopingforasimplesetofconstituentsformatter. Ifall thehadronswere‘fundamental’,thatwouldbeaconfusingarrayofbuildingblocks.

However,aswe travel the island, it isapparent that therearepatterns in thearrangement of hadrons. Much as the Periodic Table arranges elementsaccordingtotheirreactivity,themesonsandbaryonscanbearrangedintogroupsofeightor twelve (octets anddecuplets)basedon their spin, chargeandotherproperties.We see this aswe go down the line: equidistant stations, clusteredtogether at a similar longitude, and differing from each other in systematic,predictable ways. For example, we pass three almost identical hadrons, eachdifferingbyoneunitoftheirelectriccharge,clusteredwithanotherfivesimilarones differing by one unit of spin. This kind of pattern is repeated across thelengthandbreadthofHadronIsland.TheregularityofthePeriodicTableisabigclueastotheinternalstructureof

atoms.Aswesaw,thechemicalpropertiesoftheatomsaredrivenbyhowmanyelectronstheyhave,andhowtightlyboundtheyaretothenucleus.Similarlytheoctets and decuplets of Hadron Island betray the internal composition ofhadrons.

16

QuarksandtheStrongForce

THEANALYSISOFthepatternsofhadronswehavenotedwassystematisedinthewhimsically named ‘eightfold way’ of US physicist Murray Gell-Mann, whointroducedtheconceptof‘quarks’.Allhadronsaremadefromquarks–baryonscontainthreequarks,andmesonscontainonequarkandoneantiquark.fn1The properties of hadrons come from the quarks they contain, and theway

theyareboundtogetherbythestrongforce.WhenGell-Mann,andtheRussian–American physicist George Zweig, first introduced the idea of quarks, all theknownhadronscouldbearrangedaccording to theoctetanddecupletpatterns,and where there were gaps in the patterns, the expected hadrons were lateridentifiedexperimentally.Thepositionofahadronintheeightfoldwaysimplyarisesfromwhichquarksitcontainsandinwhichdirectiontheyspin.Manyofthe fastest-decayinghadronsdo sobecause thequarks inside them flyapart indifferent,morestable,combinations.Allofthatsummarisessomeofthebestevidencefortheexistenceofquarks–

theycanbeusedtopredicttheexistenceofnewhadronswithaparticularcharge,spin,massandsoon.IthasbecomeclearthatHadronIslandisstronglylinkedtoanotherlandmasstothesouth-east.TheIsleofQuarksisournextdestination.Andwewill travel by train – the strong force takes us directly there, over animposingrailwaybridge.Justastheelectromagneticforceiscarriedbyphotons,originatinginBosonia

andtravellingtheroadnetworkfarandwide,thestrongforceisalsocarriedbyaboson. This boson, the trains on our tracks, is called the gluon – it glues thequarkstogetherinsidehadrons,andalsostickstheprotonsandneutronstogetherinside nuclei. It is this force which overcomes the electromagnetic repulsionbetweentheprotons.The strong-forceequivalentof electric charge is called ‘color’ charge,using

theUSspelling,sinceithasnothingtodowithopticalcolourandwasnamedinAmerica. Itwasnamed thiswaybecause there are three ‘colors’ofquark thatwhen mixed together leave no net color, just as three primary colours mixtogethertoformwhite.Quarkshavecolorcharge,andsodogluons.Inanalogy

with QED for electromagnetism, this theory of the strong force is calledquantumchromodynamics (QCD), and it iswithQCD that all thecalculationsandpredictionsforhadronicpropertiesandformostofthebehaviourofquarksandgluonshavetobemade.UsingQCD,it ispossibletocalculateimportantfeaturesofthestrongforce,

suchas theway itchangeswithdistance. It isalsopossible toget informationabout themasses of the hadrons.Thosemasses aremostly due to the bindingenergyofthequarksandgluons,andthefact that theyarewhizzingaroundsorapidlyinsidethehadrons.Not only is the strong force strong, it does not get weaker with increasing

distance.Theelectromagneticforceandgravitybothfallawayasthesquareofthedistance–soiftwoobjectsaremovedfurtherawaybyafactoroftwo,thegravitationalorelectromagneticforcewillfallbyafactoroffour.Notsoforthestrongforce.As two quarks are pulled apart, the strong force between them remains

constant.Thismeansahugeamountofpotentialenergybuildsupinthegap,andatsomepoint thereisenoughof it toproducenewquark–antiquarkpairs,as iffromnowhere.Thequantumvacuumcontainslittleloopsofparticle–antiparticlepairs, similar to thosewe saw affecting themagneticmoment of the electron.Makingsuchapairintoarealpairofaquarkandanantiquarkcanmeanthatthestrongforcehastostretchoverashorterdistance,andthatreducesthepotentialenergy. So, because quantum mechanics allows it and the result lowers thetension, these pairs will indeed be spontaneously created. This is weird, andimportant,becausethesenewparticlesthensticktotheoriginalquarks,makingnew hadrons. In other words, you have to put in somuch energy to separatequarksfromeachotherthatyouendupmakingmorequarks.Thatisfrustrating,ifyourgoal is to isolateaquark.Manyexperimentshavesearched invain forisolatedquarks.However, as two quarks get closer, the strength of the force between them

actually drops. This is what happens as we move eastwards across HadronIsland,upwardsinenergyscale–remember,shortdistancemeanshigherenergy.Atom Land was characterised by binding energies of several thousandelectronvolts.Thenuclearbindingenergieson thewestcoastofHadronIslandare thousands of times higher, many millions of electronvolts. Travellingeastwardsamongstthehadrons,wereachedanenergyscaleofgreatimportance,at around 200 million electronvolts. This was where we crossed the bridgebetweenHadronIslandandtheIsleofQuarks.Aroundthisenergyscale,whichisknowntothelocalsbythestrangenameof

‘Lambda QCD’, a change in physics takes place. On the north-western side,

quarksareeffectivelyinvisible,hiddeninsidehadronsbecauseoftheweirdpair-creationbehaviourasyoutrytopullthemapart.Buttothesouth-east,theenergylevel has increased to such an extent that we start being able to resolve thequarksinsidethehadrons,toseethemintheirnaturalhabitat.Andwhatweseeisthattheyaremovingaroundquitefreely,becausetheyareveryclosetogetherandtheforcebetweenthemisrelativelyweak.AswetraveleastandtheenergyscaleincreaseswellaboveLambdaQCD,the

strengthoftheforcecontinuestodecrease,andwecanbegintoexploretheIsleofQuarksinevermoredetail.

17

LifeBeyondtheBridge

THEISLEOFQuarksisaconfusingplace.Sincequarkscanneverbeisolated,theyneverdirectlyregisterinadetector,soitisreasonabletoaskhowweknowtheyare there at all. The patterns we saw amongst the hadrons, described by theeightfoldway,arecompelling,butabitmoreevidenceisrequired.Aretheunitsused in theeightfoldwaytoarrange thosepatternsactualphysicalparticles,orjustaconvenientmathematicaltrick?AswetravelintotheIsleofQuarks,therearetwoimportantanddirectways

inwhich theexistenceandbehaviourofquarksandgluonscanbeestablished.The first of these is the production, in high-energy particle collisions, ofdramatic features known as hadronic ‘jets’. The are sprays of hadrons, alltravellingtogetherinroughlythesamedirection,producedquiteoftenwhenthecollidingbeamshaveanenergywhichplacesthemeastofLambdaQCD.Jetsareseen,forexample,whenelectronsandpositronscollideandannihilate

athighenoughenergy,producingquarksandantiquarks.TheyareunderstoodinQCD–thetheoryofthestrongforce–asfollows:pairsofquarksandantiquarksflyapartfromeachother,carryingall thekineticenergyoftheinitialcollidingelectron and positron. At first, they are very close together, and the QCDinteractionbetweenthemisquiteweak.Thequarkandantiquarkwillbehaveasthoughtheyarefreeparticles.Butverysoonthetugofthestrongforcewillbefelt.Asisthecasewheneverquarkstrytoescape,thepotentialenergybetweenthemincreasesastheyseparate,andthisleadstothecreationofmorequarksandantiquarks.Thisprocesscanhappenseveraltimes,eachtimesuckingawaysomeof the energy of the initial quarks, and producing more quark and antiquarkpairs. In the end there are two sprays, or jets, ofmanyquarks and antiquarks,whichareheadingoffawayfromeachother,goinginroughlythedirectionsoftheinitialquarkandantiquark.Withinthesejets,thequarksaretravellingcloseenough to each other that they can bind together and form hadrons. The endresultisusuallytwojetsofhadrons,oneforthequark,andonefortheantiquark.Thesprays,orjets,ofhadronswillbecollimatedroughlyinthedirectionoftheinitialquarkandantiquark.Theenergiesanddirectionsoftheinitialquarkand

antiquark can be calculated in QCD, and the calculation agrees well withmeasurementsof the jets.Thisagreement is strongevidence thatquarks reallydoexist.Goodtoknow,asthestationsflyby.Jets also provide evidence for the existence of gluons. In some electron–

positron collisions, three jets are produced. This was first seen at the Petracollider in the DESY laboratory, Hamburg. The presence of these ‘three jet’eventsisexpectedinQCD,andisduetogluons.Whathappensisthatverysoonaftertheyareproduced(andwhiletheyarestillfeelingfree!)eitherthequarkorthe antiquark radiates ahigh-energygluon,Like thequarks, thegluonwill flyaway,andeventuallyturnintoajetofhadrons.Aswiththequarks,thepropertiesofthesejetscanbecalculatedinQCD,andthepredictionsagreewiththedata.Thisisstrongevidencethatgluonsarealsoreal,eventhoughtheytoocanneverbeisolated.Evidenceforpoint-likequarksinsidehadrons–ratherthanbeingproducedin

collisions–comesfromexperimentswhichscatterelectronsoffprotonsathighenergies.Abeamofelectronscanbefiredatstationaryprotons,aswasdoneinthe first such experiments, atStanford inCalifornia, or canbe collidedwith abeamofprotonstogetevenhigherresolution.Ineithercase,theexperimentisactingasasuper-high-resolutionmicroscope,probingtheinsidesoftheproton–and, unfortunately, smashing it to pieces in the process. A huge amount ofenergy and momentum is transferred between the electron and the proton,usuallyvia anexchangedphoton.Asusual, theenergyandmomentumset thewavelengthofthephoton,andthustheresolutionofthemicroscope.Whentheenergyishigh,thewavelengthissmall,sotheresolutionisgood.At low values of energy, well below the crucial Lambda QCD scale, the

microscope sees the whole proton. This is what happens if we perform theexperimentbackonHadronIsland.As theenergyincreases, thewavelengthofthephotonshrinks,andasmallerandsmallerpartoftheprotonisseen.Becauseof this, the probability of actually hitting the proton with the electron dropsratherquickly.However,inthefirstexperimentinStanford,andatotherexperimentssince,it

was seen that at some point, at energy transfers significantly above LambdaQCD,thescatteringprobabilitystopsfallingsofast.Infact,onceyoutakeintoaccount the fact that the photon keeps on getting smaller as you go higher inenergy,thescatteringprobabilityisalmostconstant.Thisiswhathappensifweperformtheexperimentnow,ontheIsleofQuarks.Thisiswhatwewouldexpectif thereweretiny,point-likequarksinsidethe

proton.Thequarksarealready infinitesimally small, and soevenby shrinkingthewavelength,wecan’tseeanevensmallerpartofthem.Thesituationisvery

similartoRutherfordandhisalphaparticles,discoveringthenucleuswaybackwestinAtomLand.Thesurprisinglyhighnumberofelectron–protonscattersathigh energy-transfers is the equivalent of alpha particles bouncing right backfromthegoldfoil,whichsoshockedRutherfordandhisteam.Fromobservationslikethis,andfromwheretheysitintheeightfoldway,we

know thatprotonsaremadeof twoquarks thatcarry two-thirdsof theelectricchargeoftheprotonandonequarkwhichcarries–onethird,addinguptoatotalof one, of course. However, the internal structure of a proton is much morecomplexthanjustthreequarkssittingnexttoeachother.Thequarksareboundtogetherinasmallspacebythestrongforce,whichmeanstheyareexchanginggluons frantically. At the shortest distances we can observe, the proton is acomplicatedobjectcontaininglotsofpoint-likequarksandgluons,splittingandradiating. In away, it is amazing that it is so stable; but it is. If protons everdecay,wehaveneverseenonedoso,despitesoverysensitivesearches.

18

FlavoursandGenerations

ALTHOUGH SIMILARLY COVERED in railway lines, the Isle of Quarks is nowherenearasdenselypopulatedasHadronIsland.Incontrast to themyriadhadrons,therearejustsixmajorcitieshere,dominatingthelandscape.TheseareUpandDown, Charm and Strange, Top and Bottom. The Top is the heaviest, on theeasterntipoftheisland,andtheDownandUparethelightest,furthestwest.The different types of quark are called ‘flavours’.fn1 We know from

measurement of the hadrons they form, andwhat they decay into, that down,strangeandbottomallcarryachargeofminusone-thirdoftheproton’scharge,and theotherscarryplus two-thirds.Strangewassocalledbecause itwasfirstnoticed as a constituent of some strange new particles seen in cosmic rays.fn2Charm solved someproblems caused by the lonely strange quark, and bottomandtopfn3mirrorthenamesofdownandup.A remarkable thing about the Isle ofQuarks is the distribution of the cities

from west to east. Even though the quarks are, as far as we know, allinfinitesimallysmall,theirmassesspanahugerange.Down and up are the constituents of protons and neutrons, and so between

themmakeupthenucleusofeveryatom.Theyeachhaveamassofacoupleofmillion electronvolts; only four times heavier than the electron.However, thatmass is swamped by the extra mass they get from the binding energy of thestrongforce,uptoafewhundredmillionelectronvolts.(Thisisonereasonthebaremass isnotveryaccuratelyknown.) Inprinciple, these twoquarks,alongwiththeelectron,couldmakeupeveryatomintheuniverse,soitissomethingofasurprisethatnaturehascopiedthem,athighermass,furthereast.Therearethree‘generations’ofmatter–threesetsofparticlesfollowingasimilarpattern.Up, down and the electron, along with a neutrino, constitute just the first ofthese.Thesecondgenerationconsistsof thestrangeandcharmquarks,alongwith

themuonanditsneutrino.Thesecond-generationquarksarehigher-masscopiesofthefirst,justasthemuonisahigher-masscopyoftheelectron.Thebaremass

of the strange quark is about 5 million electronvolts, and the charm is muchmoremassive,atabout1.3billionelectronvolts.Thethirdgenerationofquarksareheavierstill,withbottomhavingamassof

4.2 billion electronvolts. The top quark is a ridiculously massive 172 billionelectronvolts, the heaviest of all the fundamental particles in the StandardModel.Becauseofthishugemass,thetopquarkdecayssoquicklythatitneverhastimetobeboundupinsideahadron.Theratherodddistributionofquarkmasses–withup,downandstrangefairly

close,charmandbottomalsonotsofar fromeachother inmassdespitebeingdifferentgenerations,andtopbeingfarawaytotheeast–isnotunderstood.Thetop quark is a realmonster, nearly 200 times themass of the proton, and yetunlike the proton it is supposed to be fundamental, an infinitely small pointparticle.fn4Therearesometantalisingreasonstothinkthatthreegenerationsisaspecial

number,whichmay again be a natural consequence of a bigger, better theorybeyondtheStandardModel.Especially,threegenerationsisjustenoughtobreakthe symmetry between matter and antimatter in the theory – between thenorthernandsouthernhemispheresonthemap.Touring the IsleofQuarksby trainwasa rapidandquite luxurious journey.

Becausethegluoncarriescolorcharge,thereisevenarailbridgetoBosonia,alandwhichisfirmlyonourlistofplacestoexplore.AlsoinBosonia,however,isamajorairport.Theplaneswehaveoccasionallyseenoverheadoriginatehere,andweareofferedtantalisinglyrapidtransporttoalmostanywhereonourmap.Thisisanopportunityweoughttotake.

EXPEDITIONV

TheIslesbyAir

Particlesinpairsandfrequentflyers–Thelocationofairportsturns out to be important – Discussions with space aliens,physicsinamirrorandthemeaningofsouth.

19

TheWeakForce

THESTANDARDMODEL incorporatesthreefundamentalforces–threemethodsoftransportacrossthelandwehavebeenexploring.Wehavemadeuseoftwoofthem so far. Electromagnetism is our road network, connecting all electricallychargedparticles.ThestrongforceisthedenserailwaysystemspanningHadronIslandandtheIsleofQuarks.Theairlinesthatwehavejustcomeacross,attheirhubinBosonia,aretheweakforce.Theweakforcedoesnotmanifestitselfveryobviouslyineverydaylife.Itis

relativelyeasy tosee theeffectsofelectromagnetism– indeedweseewith thephoton, theboson that carries the electromagnetic force.Andwhile the strongforcemaynotbesovisible,itplaysaneasy-to-appreciate,vitalroleinholdingtogethertheatomicnucleus.It is abit harder topoint to the essential roleof theweak force. It operates

over such a short range that its influence is not felt directly, even at distancescomparable to the radiusof aproton.Becauseof the short distances involved,gaininganunderstandingof theweakforcehas requireda journeyfurthereastthanmosthaveundertakensofar:theairlinehubisalmostattheboundaryofthemap.Nevertheless,itisacrucialpartoftheStandardModel.Withouttheweakforce,quarkscannotchangeflavour.Thatmeansthatneutronscannottransforminto protons. That means that the Sun could not shine, since it relies on thefusionoffourprotonsintohelium,inwhichtwoofthembecomeneutrons.So,weakthoughitsinfluenceis,thisforceisanessentialcomponentofourworld.Theweak force does not really bind anything together, in theway roads or

railwaysdo.IthasnodomainequivalenttoAtomLandorHadronIsland.Astheairline network on our map, it makes tenuous but ubiquitous connections toanywhereanaeroplanecanland.Thebosonswhichruntheairline,carryingtheforce,aretheWandtheZ.TheWhasanelectriccharge,whichcanbepositive(W+)ornegative (W-).TheZ is electrically neutral.Like gluons (which carrycolorcharge)butunlikethephoton(whichiselectricallyneutral),theWandZdocarrytheweak-forceequivalentofcharge,or‘weakcharge’.

Every settlementon themap–every fundamentalparticle–has anairfield.Allofthemexperiencetheweakforce.Butsomearebusierthanothers.Andinparticular,theairwaysbetweensomepairsofparticlesareespeciallybusy.Thisis one of several striking features of the weak force which sets it apart fromelectromagnetismandthestrongforce.Electromagnetism – QED – tells us how an electron (or any particle with

electric charge) canemit aphoton.The theoryof theweak interaction tellsushowanelectron(oranyparticlewithaweakcharge)canemitaZoraW.Ittellsus thatemittingaZ ismuch likeemittingaphoton.ButwhenaWisemitted,thingsaresomewhatdifferent,becausetheWhasanelectriccharge.Sowhenanelectron emits aW, it loses its electric charge, and turns into a neutrino. PortElectronanditsmysteriousneutrinohavethisdedicatedairroutebetweenthem;they form a pair, or doublet. Similarly, amuon can emit aW and turn into amuonneutrino,andataucandothesameandturnintoatauneutrino–allbyemitting aWboson.Note that electric charge is conserved – in each case thelepton’s negative charge is carried off by theW, and the neutrino, in a ratherinaccessiblemountainousregionoftheIsleofLeptons,isneutral.From the air, the samepattern is seen on the Isle ofQuarks.Emission of a

negativelychargedWwillturnadownquarkintoanupquark,becausetheyareinadoublettogether.Itwillalsoturnastrangequarkintoacharmquark,andabottomquarkintoatop.Thisabilitytotransformparticleswithindoubletsintooneanotherisuniqueto

the weak force, and it is important. Without it, for example, the top quarkscreatedattheBigBangwouldstillbewithus.Therewouldbenowayofgettingrid of them.fn1 The weak force is also responsible for the fact that isolatedneutronsdecayafterafewminutes–inthiscasetheunderlyingprocessinvolvesa down quark transforming into an up quark, by emitting a W. The W thendecaystoanelectronandanelectronantineutrino.

20

Parity,HelicityandChirality

THEPROCESSBYwhichaneutronconvertsintoaprotoniscalled‘betadecay’.Itwasinbetadecaythattheweakforcesprangitsbiggestsurprise.Theweakforceinteractswithallthequarksandleptons,butatthesametime

itonlyinteractswithhalfofthem,inasense.Putanotherway,everycityontheIsleofLeptonsandtheIsleofQuarkshasanairport,butonlyhalftheinhabitantseverfly.Perhapstheyarefrightened,orworriedaboutclimatechange.Ormaybeairport security are very picky.Whatever the reason, it is a puzzling fact. Toworkoutwhatitmeans,weneedtounderstandaconceptknownaschirality.A chiral object is one which is not identical to its mirror image. It is also

sometimes called ‘handedness’. Some molecules are chiral, having a right-handed version and a left-handed version. This is true of many biologicalmolecules;DNA is chiral, for example, the twist in thedoublehelixgoes inaparticular direction. So are sugars. Usually only one of the two possiblechiralitiesisactuallyuseablebylivingorganisms.Theparticlesofourmap, too,arechiral,andonlyoneof thosechiralities is

affectedbytheweakforce.Spinningparticlescanbedividedintotwoclassesbasedonwhethertheirspin

is pointing in the direction the particle is travelling, or opposite to it. This iscalled the helicity.fn1 These are the only two possibilities for the helicity of aquantumparticlewithaspinofhalfaunit,suchasthequarksandleptonsoftheStandardModel.Ifyouimaginetheparticlecomingtowardsyou,youcanthinkof the two helicities as corresponding to seeing the spin turning clockwise oranticlockwise, just as the twist of theDNAhelix goes in one direction or theother. For a massless particle, these two helicities define the two possiblechiralitiesoftheparticle.This is strange behaviour. The fact that there are two chiralities is not so

surprising. Since we know that most particles have spin, there will be ahandedness associated with the sense in which they spin, clockwise oranticlockwise,similartothehandednessofthetwistinthedoublehelixofDNA.WhatissurprisingisthattheWandZbosons,whichcarrytheweakforce,‘see’

only one of those chiralities. Amassless particlewith its spin pointing in theoppositedirectiontotheparticle’sdirectionofmotionwillfeeltheweakforce;amasslessparticlewhichhasitsspinpointinginthesamedirectionasitsmotionwill be invisible to theweak force. The inverse is true for antiparticles: thosewithspinpointinginthesamedirectionastheirmotionfeeltheforce;thosewithitpointingagainstdonot.Thefactthatinnature,plantsandanimalsproduce,andmakeuseof,onlyone

chirality of some molecules is presumably down to random chance – somecommonancestorhappenedtomakeanduseoneofthem,andthesuccessofthatancestorhasmeantthattheoriginalchoicehasbeen‘lockedin’eversince.ButwhyfundamentalparticlesshouldhavesuchastrongbiastowardsoneofthetwochiralitiesisfarfromobviousandisnotunderstoodwithintheStandardModel.Whateverthereasonforit,thischiralitybiashasprofoundconsequences.Beforethispropertyoftheweakforcewasestablished,physicistshadthought

thattheuniversewascompletelysymmetricunderreflectionsinamirror.Ortoput it anotherway,we thought that the fundamental forces of physics did notdistinguish between left and right. But the weak force does. If you imaginereflectingaspinning,masslessparticleinamirror–anoperationcalledaparityinversion–youflipitschirality,whichwillturntheweakforceonoroff.Thatcan completely change the energy of the particle, or of any other particlesnearby, and completelybreaks the symmetry. Itmeans ‘left’ and ‘right’ arenolongerarbitrarylabels–adifferencebetweenthemisbuiltintothestructureofphysics.Agoodwayofthinkingaboutitistoimaginecommunicatingremotelywitha

differentcivilisationonafarplanet.Therewouldbemanychallenges,butlet’simaginethateventuallyweestablisharudimentarycommonvocabulary,wherewecanchatreasonablyfluently.Wefindtheyarealsoacarbon-basedlifeform.Theydon’tcall itcarbon,ofcourse,butweagreeonwhatatomsare,and thatcarbon is the one with six protons and six neutrons in the nucleus, with sixelectronsboundtoit.fn2Sowewanttosendthemaboxofchocolatesasagestureof goodwill. But we are worried that theymay use sugar molecules with theoppositechiralitytoours.Ifthiswerethecase,theywouldnotbeabletodigestour chocolates,which could be awkward, diplomatically speaking.Howcouldwetellinadvance?Wecouldaskthem,butweneedtoagreeonadefinitionofwhatwecallright

or left, clockwise or anticlockwise. Images are no good becausewe can’t tellwhetherwehavedecoded themwith thecorrectchirality.There isnophysicalreferencepossiblebasedonelectromagnetism,becauseelectromagnetismtreatsleft and right identically. The same goes for the strong interaction. Theweak

interactionprovidestheonlyway.fn3Whatwemightendupdoing,laboriously,inourpainstakinglybuiltupcommonlanguage,isexchanginginstructionsonhowtobuildanatomicparityexperiment.In 1957,Chien-ShiungWu and her teamatColumbiaUniversity conducted

the experiment which proved that the weak force does indeed violate paritysymmetry.Thisseminalexperimentinvolvedtakingatomicnucleithatundergobeta decay – a process governed by theweak interaction – and aligning themwith a magnetic field, so that their spins point along the direction of themagnetic field. A reflection in a mirror will not affect the magnetic field –electromagnetismconservesparity–butitwillflipthespin.Measuring the electrons from the beta decay shows that they are mostly

emitted in the opposite direction to that in which the spin of the nucleus ispointing.Sotheywillbepointingoppositetothemagneticfield.Thismeanswecan agree with our space alien friend that ‘anticlockwise’ corresponds to thedirectionofrotationofthespinoftheelectronasseenwhenlookingalongthemagneticfield,andclockwiseistheopposite,ofcourse.Fromthat,leftandrightcanbeunambiguouslydefined,andwecanworkoutwhetherourchocolateswillgodownwellornot.The weak interaction changed our assumptions about physics for ever. It

connectseverycityonourmapbyair,eventheinaccessibleneutrinos.Butnoteveryoneinthosecitiesusestheairport.Alltheright-handedbitsareunabletofly.Anddespitebeingsomewhatobscureineverydaylife,theweakforcehasasurprisinglypervasive,indeedcritical,influenceonwhytheuniverseisthewayit is. ItallowstheSuntoburn,andtheheavygenerationsofparticles todecayintoeverydaymatter.Italsohasotheruniquequalities,whichwewillinvestigatefurtheraswehoparoundourmapbyair.

21

MixedMessages

STUDYING THE FLIGHT paths of theweak force across the Isles of Leptons andQuarkshasrevealedthefactthatasfarastheweakforceisconcerned,particlescomeinpairs,ordoublets.Eachleptonsharesadoubletwithaneutrino,theupquarkisinadoubletwiththedownquark,andsoonforcharmandstrange,topandbottom.TheWbosonprovidesdirectconnectionsbetweenthetwoparticlesinadoublet,andthisallowsthetopquarktodecaytothebottomquark,andtheneutron to decay into a proton by the conversion of a down quark into an upquark.Sofarsogood.Butaswebecomeseasonedfrequentflyers,moresubtleeffectsstarttobecomeevident.Thetopquarkdecaystoabottomquark,becauseitisinthesamedoublet.But

the bottom quark also decays to even lighter quarks, even though they are indifferentdoublets.Sodoalltheheavierquarksandleptons.Thestablematteroftheuniverse consists ofup anddownquarks inside every atomicnucleus, andelectrons.Thismakessense,becauseheavyparticleswilldecaytolighteronesiftheycan,aswehavenotedbefore.Butthekeyis‘iftheycan’.Whatisprovidingtherouteswestwards thatallowthis?It is theweakforce,again,but inquiteasubtlefashion.Aswetravelaround,itbecomesclearthattheairportsatwhichtheweakforce

landsarenotexactly in thecities.This isn’tunusual: it’safairlyshort journeyfromtheairportnearthestrangequarktothecityofStrangeitself,andthat’sthewaymostofthetrafficgoes.However,itispossibletogodirectlytothedownquark from there too, or even to the bottom quark. Itmay be a bit of a longtransit,andmostpassengersdon’tdothis,theyflytotheStrangeairportandgostraight into town.But it ispossible togo instead toDownorBottomdirectlyfromStrangeairport,andsomedoso.Intermsofourmap,therearetwowaysoflookingatthesettlementsonthe

IslesofLeptonsandQuarks.Fromthepointofviewoftheinhabitants,themostimportant thing is the cities. On the Isle of Quarks, these would be Up andDown,CharmandStrange,TopandBottom.Eachofthesequarkshasadefinitemass,withtopbeingtheheaviestanddownandupthelightest.

Butfromthepointofviewofanairlinepilot,oraWbosonoftheweakforce,amoresensiblewaytothinkaboutitmightbeintermsoftheairports.AndforDown,StrangeandBottom,theairportisnotinquitethesameplaceasthecity.Theyarenearby,butaswe’venoted,onecanflyintotheairportnearDownandtraveldirectlyontoStrangeorBottom.Tomakeitcleartheyareneartowns,theairports are called Down-prime, Strange-prime and Bottom-prime. The airlineconnects these locations, rather than the cities of Down, Strange and Bottomthemselves.This is crucial to understandingwhy the stablematter of the universe only

containsupanddownquarks.Togetattherealitybehindthisairportplacement,weneedtoreturntotheideaofaquantumstate.Aquantumstateis theobjectthatcarriesalltheinformationaboutaparticle,orsetofparticles.Itispossibleto extract that information in several different ways, which sometimes seemcontradictory.Differentwaysoflookingataquantumstatecanevendisagreeonwhat kind of particles it describes. In terms of themap, looking at the islandfrom the point of view of the cities or the airports is the equivalent: you stillcover thewhole island. The StandardModel really does the same thing withquarks.Ifyouhaveaquantumstatedescribingsomequarks,youcananalyseitasbeingacertainamountofdown,afractionofstrangeandabitofbottom.Thismakessense,andsincethosequarkshavedifferentmasses,thatishowtheywillappear inhadrons, too.However, that is not how theweak force (awkward asever)seesthem.Theweakforcesplitsthequantumstateadifferentway,intoadifferentsetof‘primary’particles.ThesearethedifferentflavoursofquarkthatcanbeproducedwhenaWbosondecays,andwecallthemd′(down-primed),s′andb′.Theydon’thavedefinitemasses,buttheyaretheparticlestheweakforcesees.Wedon’tknowwhyitdoesthis(anymorethanweknowwhyitonlyseesleft-handedparticles!)butthat’sthewayitis,anditisagoodthingtoo,asithasimportantconsequences.Thestrange-primequarkisnearlythesameasthestrangequark,butithasa

smalladmixtureofdownandbottomtoo.ItisasthoughwetakeaselectionofpeopleinthecityofStrange,andaskthemwheretheylive.TheyallsayStrange.But then we ask themwhat airport they landed at. Sensibly enough, most ofthemsaytheyflewintothenearbyStrange-prime.ButafewcameintoBottom-prime,andafewcameintoDown-prime.Likewise,ifwesurveyaplanefullofpassengerslandingatStrange-prime,andaskthemwhichcitytheyareheadingto,mostwill say StrangeCity, but a fewwill sayBottom and a fewwill sayDown.When a quark travels through space and forms a hadron, a particularmassisselected;thisisthecityitbelongsto.ButaWbosonwhichdecayswillnotproducepurestrangequarks–itwillproducestrange-primequarks,whichis

the airport it lands at.And the strange-prime quark has a small probability ofbeingadownquark,orabottomquark–thatis,someofthepeoplelandingatStrange-primeairportactuallyliveinthecitiesofDownorBottom.Thisistherealitybehindwhatweobservedonourmap,thatevenifwelandattheStrange-prime airport, we could (sometimes, not often) travel straight to the city ofDown,orBottom,insteadofStrange.These crucial small probabilities are what allow the weak force to

communicatebetweenthegenerations.Thisiswhatallowstheheavierparticlesof the second and third generation to eventually (or sometimes quite rapidly)decay to the lightest, first generation. This is how the weak force provides aroutewestfromTop,Bottom,CharmandStrangeallthewaytoUpandDown.Andthatiswhywedon’thaveauniversefilledwithatomscontainingcharmorstrangequarksinsidetheirnuclei.

22

NorthfromSouth

ONOURMAP, thenorthernhemisphere ismatter, and the southern is antimatter.Wehavebeen travellingalmostentirelyaround thenorth,but thesouthwouldlookverysimilar,ifnotidentical.Ormaybewearetravellinginthesouth,really,not the north? Could we even tell? Does the differencematter, or is it just aconvention?Nowwehaveanairlineatourdisposal,wecantaketheviewfrom10,000m.In a sense, very often, it does notmatter at all. According to the Standard

Model,theelectromagneticforcebetweenanelectronandaprotonisexactlythesame as the forcebetween their antiparticles, a positron and an antiproton.Sowhilewewouldobviouslynotice(briefly,beforewewereannihilatedinaburstofphotons)ifhalftheworldweremadeofmatterandtheotherhalfantimatter,wouldwebeabletotellif,inaninstant,allmatterwereswappedforantimatter,andviceversa?Frommeasurementsofelectromagnetism,orthestrongforce,orgravity,wecouldnot–atleast,asfarasweknow.Thisissimilartotheconundrumwehadwithparity,andtryingtoexplainleft

andrighttoourspacealienfriend.Wewouldhaveverysimilarproblemstryingtoworkoutwhethertheyweremadeofmatterorantimatter.Thisisanimportantquestion to resolve before setting up a diplomatic mission. Since matter andantimatterannihilate,anerrorwouldbecatastrophicforanydiplomaticvisit.Theoperationofswappingallparticlesfortheirantiparticlesandviceversais

called charge conjugation. We saw that the weak force violates a similarsymmetry, the left–right symmetry of parity, since it only affects left-handedparticles,andright-handedantiparticles.Thismeans that isalsobreakscharge-conjugationsymmetry,sinceifwecharge-conjugatedaleft-handedelectron,wewouldgetaleft-handedanti-electron.Theformerexperiencestheweakforcebutthelatterdoesnot.Intermsofourmap, inthesouthernhemisphereadifferenthalfofthepopulationareafraidtofly.However, ifwesimultaneouslycharge-conjugateeverythingandat thesame

timereflectitinamirror,wemaybeOK.Theleft-handedelectron(whichfeelstheweakforce)becomesaleft-handedpositron(whichdoesnot)undercharge-

conjugation,but thenbecomesa right-handedpositronunder reflection (whichagainfeelstheweakforce).Thinking back to the parity discussion, and trying to communicate with a

distantspacealientodefineleftandright,wehaveaproblem.Ifthespacealienismadeofantimatter,notmatter,wewillgetthewronganswer.Ourneattrickwith theWuexperimentdoesn’twork,because if theyaremadeofantimatter,their magnetic field will point in the opposite direction, so there are twoconfigurationswhichgivethesameresult.Eithertheyaremadeofmatterandweuse the samedefinitionofhandedness,or theyaremadeofantimatterandusetheoppositehandednessdefinitiontous.Wecan’ttellthesetwoscenariosapartusingtheWuexperiment.The weak force again provides a way out of the impasse. There is still a

measurementthatwecanperformtodecidewhetherornotitissafetomeetthealien. The weak force violates the combined symmetry of charge-conjugationandparity inaverysubtle fashion,away that is intimately related to that factthatwehavethreegenerationsofmatter,andtothewaytheweakforceconnectstheprimedobjects(theairports)ratherthanthemassivequarksthemselves(thecities).We have to quantify the relationship between the airports and the cities –

betweentheprimedandunprimedversionsofthequarks.Wecandothisusingamatrix,anarrayofnumberswhichencodeshowmuchdown,strangeandbottomaremixedintoeachofthedown-prime,strange-primeandbottom-primestates.Thismatrixwill tellyouexactlyhow likelyapassenger landingat theDown-primedairportistogotoeachoftheDown,StrangeorBottomcities–thereisanumberinthematrixforeachpossibility.Thepresenceof thismixingmatrix iswhat introduces thepossibility of the

violationofthecombinedcharge-conjugationandparitysymmetry.Thatiswhatweneedtoallowustocommunicatewithourspacealienfriendandbesureweagreeonwhat ismatterandwhat isantimatterandwhat is left and right.Thepossibilityarisesasfollows.Thematrixcancontaina term thataffects thephaseof thequarks’quantum

state.Remember,fromtheearlypreparationforourjourney,thatthephaseofawave is just the stage it isat in itsoscillation, thepositionofFeynman’s littlerotating arrow. Phase itself is not physically measurable, but differences inphasesare.Thisiswhyviolationofthecharge-conjugationandparitycombinedsymmetryisasubtleeffect.Thematrixallowsmixingbetweendifferentflavoursofquarks,andwhenthey

areboundtogetherinhadrons,thismayalsoallowmixingbetweenparticlesandantiparticles.

For example, there is a hadron (called a ‘neutral kaon’, one of the manyhadronswewhizzedpastonHadronIsland)whichcontainsadownquarkandastrangeantiquark.Sincethedownquarkhasachargeofminusone-third,andthestrangeantiquarkhasplusone-third,thehadronhasatotalchargeofzero.Theantiparticle of the hadron also has zero charge, but is made up of a downantiquark, and a strange quark.By exchangingWbosons between the quarks,which involves the mixing matrix, the neutral kaon can transform into itsantiparticle, and back again, ‘silently’, oscillating between particle andantiparticleasittravelsthroughspace.Sofar,soweird,butthisinitselfisnotaviolationofthecombinedsymmetry.Infacttherearetwopossiblewaysforthekaontotransformbetweenparticle

and antiparticle – two differentways theWbosons can be exchanged. So thephysicalresultinvolvesthesumofboththeseways.Andthephaseterminthematrix affects these two ways differently. This introduces a phase differencebetween the two,which can bemeasured by precise detection of the particlesthatareproducedwhenkaonsdecay.Ithasbeenmeasuredthisway,andisfoundtobedifferentifthehadronisgoingfromparticletoantiparticle,fromwhenitisgoingfromantiparticletoparticle.That’swheretheviolationofthecombinedsymmetrycomesin.Notonlyisit

possible in the Standard Model, it actually happens. It is a small but verysignificanteffect.Itwouldbealongconversation,explainingtoaspacealienwhatspecialkinds

ofhadronsareneeded,howtomakethemandwhatpropertiestomeasure.Butintheendwecoulddoit,andcouldthenbesurewhethertheyweremadeofmatterorantimatter,andthenalsoagreeonleftandright.Wehavediscovered,by lookingcarefullyenoughat theairline trafficof the

Isle ofQuarks, that nature does not respect the symmetry betweenmatter andantimatter,orbetween leftandright,or thecombinationof the two.There isarealdifferencebetweenthephysicsofthenorthernandsouthernhemispheresonourmap.Thereareseveraloddthingsabout this.Firstly,only theweakforceviolates

thesesymmetries.Whywouldthatbe?Onceyouhaveestablishedthattherecanbedifferences,itwouldbeveryeasy,forexample,forthestrongforcetoshowthem too, but it does not appear to. Once you know that one force of natureviolates the symmetry, the fact that the strong force conserves it is actually apuzzle.Itisoneofthepossiblehintsastowhatmaybegoingoninthefareastofourmap.Secondly,thecombinedsymmetrycanonlybeviolatedinthematrixifthere

are three ormore generations ofmatter.Twowould not be enough. So nature

seems to have the minimum number of generations required to allow thisdistinctionbetweenleftandright,andmatterandantimatter,tobedrawn.Thoseextra quarks and leptons may be there for a reason after all! Yet within theStandardModel, this looks like a coincidence. Maybe it is another clue to abettertheory,againinthefareast,wherethisisallobviousandnecessary?Finally, it is obvious that the universe around us is not symmetric between

matter and antimatter, just as it is obvious on the real globe that the southernhemisphere is different from the north. There is much more matter thanantimatterintheuniverse.YetthesymmetryviolationintheStandardModelissuchatinyeffect,nooneknowshowtobuildatheoryinwhichitleadstosuchabig imbalance in the universe today. This again may be a clue to wild andwonderfulthingsofftotheeast.

EXPEDITIONVI

TheRemoteNeutrinoSector

Ashortbutarduoustriparoundsomeroughterrain–Abudgetairline–Moremixing–Whenisaparticleanantiparticletoo?

23

MasslessMatter?

PORTELECTRON,ONtheIsleofLeptons,wasourveryfirststop,andsubsequentlywediscoveredandvisited theMuonand theTau lepton, important featuresonthe same island. These places are easy to get to by sea and road – they areelectrically charged, so electromagnetism gives us easy access. But studyingtheirairports,learningabouttheweakforce,wehaveseveraltimescomeacrossrumoursofneutrinos.WehaveseendepartureboardslistingflightstoElectronNeutrino,MuonNeutrinoandTauNeutrino,andwehaveseenpeoplegettingonandoff theseflights,sopresumably thedestinationsexist.Butsofarweknownext to nothing about these mysterious settlements. They are inaccessible byroad or rail – the electromagnetic and strong forces just don’t go there – andwhiletheweakforcecangetustherebyair,sofarwehavehadlittlemorethanahigh-altitudefly-by.Enoughtoseethattheyareacrucialpartofourlandscape,andwehaveseenthattheyareimportantplayersinbetadecayandthereactionsthat keep the Sun burning, but little else. The difficulty of the terrainnotwithstanding,itistimetorectifythat.Neutrinos were first postulated in 1930, by Austrianfn1 theoretical physicist

WolfgangPauli.fn2 Famously and rather shamefacedly, he said, ‘I have done aterriblething,Ihavepostulatedaparticlethatcannotbedetected.’The reasonhedid thiswas todowithbetadecay.Aswehaveseen, inbeta

decay,adecayingnucleusemitsanelectron.Theseelectronscanbedetectedandtheirenergycanbemeasured.Oneofthebasiclawsofphysicsisthatenergyandmomentumarebothconserved.Thetotalsbeforethedecaywillbethesameasthetotalsafterwards.Wecanusethattomakesomepredictions.Imagine the nucleus is stationary before it decays. The total momentum is

zero. So after the decay, the total momentum must also be zero, since totalmomentum is conserved. This means that if the electron moves off in onedirection, the nucleus must recoil in the opposite direction, to cancel out theelectron’smomentum,andleavingthetotalaszero.Likewise, energy is conserved. The electron and the recoiling nucleus have

somekineticenergy,andthefinalmassofthenucleuswillhavereducedslightly

during the decay, by an amount exactly sufficient to provide the mass of theproducedelectronandthatkineticenergy.Ifyouputall that together, it ispossible tosolve theconservationequations

and predict exactly the unique momentum the electrons must all have. Othertypesofradiation(alphaandgamma)bearthisout.Alphaparticlesandgammarayshavea fixedenergy for agivennucleardecay.But forbeta radiation, theanswer is … wrong. The electrons have a spread of momenta and energies,alwayslessthantheprediction.Thisisaproblem.Thereareonlytwooptions.Eitherenergyandmomentumconservationdon’t

workinbetadecays(whichwasproposedasasolutionbyDanishphysicistNielsBohr), or we are missing something in the decay. Pauli went for the latter,inventing the neutrino, which could carry off variable amounts of energy andmomentum and thus balance the nucleus and the electron. Energy andmomentumwouldstillbeconserved,buttheelectroncouldnowhavearangeofenergies, as observed, with the maximum occurring when the neutrino hadalmostzeroenergy,andtheminimumoccurringwhentheneutrinocarriedawaythemaximumitpossiblycould.Alltheenergiesintherangewouldbeconsistentwith conservation of momentum, and they would be distributed randomlyaccordingtotheprobabilisticnatureofquantummechanics.Fromourpointofviewasexplorers,wearesittinginthearrivalshallofthe

airportneartheupquark.Weseemorepassengerslandingthatareemerginginthe arrivals hall. Either some passengers are vanishing (whichwould be verydisturbing), or they are transferring to connecting flights onwards to theneutrino.Thankfully, the latter is the case. Pauliwas right about the existence of the

neutrino.Buthewaswrongabouttheimpossibilityofdetection.GettingtotheNeutrinoSectoroftheIsleofLeptonsisverydifficult,butitcanbedone.IntheoriginalconceptionoftheStandardModel,neutrinoswereinaunique

position–theonlymasslessmatterparticle.Thereasonforthiswastodowiththeweakforce,theonlyforcetheyexperience.Aswe saw studying the airlines on ourmap, theweak force interactswith

onlyonechirality:left-handedparticlesandright-handedantiparticles.Sincetheonlyforcetheneutrinosexperienceistheweakforce,thismeansthattheright-handedneutrinoand the left-handedantineutrinoare totally inaccessible in theStandardModel.There isnoaccessby road, railor air.Electromagnetism, thestrong force and the weak force do not connect to them! It would be lessdisturbingifsuchparticlesdidn’tevenexist–afterall,howcouldweeventelliftheydid?

HowdoesthisrelatetothemasslessnessofneutrinosintheoriginalStandardModel?ThereisafascinatingconnectioninvolvingbothrelativityandquantumfieldtheorythatwewillhavetonegotiateinordertoaccessandunderstandtheNeutrinoSectorproperly.Whenlookingatthestrangeasymmetricbehaviouroftheweakforce,andthe

wayitaffectsonlyleft-handedparticlesandright-handedantiparticles,weonlydiscussedmasslessparticles,forgoodreason.Becauseonceaparticlehasmass,thedefinitionof left-andright-handedparticlesgetsa littlemorecomplicated.Thehelicity–thedirectionofspinrelativetothedirectionofmotion–nolongerdefinesthechirality.Itisstillpossibletodefinechiralityasthefeaturethattheweakforcecaresabout,butforamassiveparticle,chiralityisnolongerexactlythesamethingashelicity.If you think about it, this has to be true, because the helicity of a particle

dependsupontherelativespeedof theobserverandtheparticle. Ifwechaseapositive-helicityparticleandovertakeit,thespindoesnotchangedirection,buttherelativemotiondoes,sothehelicitywouldflipover.Thisisthesameeffectas if we look at the hands of a clock from behind its face – they goanticlockwise.So by overtaking a particle, we alter the helicity. If this changed the weak

force, thatwouldbeunambiguouslyobservable,anditwouldgiveusawayofmeasuringabsolutespeed,inviolationofrelativity.Wecouldusethestrengthofthe weak force to define the absolute direction of travel of particles, withoutreference to anything else. Just as bad, saywe catch the particle up but don’tovertakeit,sothatrelativetousitisstationary.Forastationaryparticle,thereisnodirectionofmotion,sonodefinedhelicity.Sowhatdoestheweakforcedo?What doeshappen is thatwhen I catchupwith andovertake a particle, the

helicitychanges,butthechiralitydoesnotchange,andtheweakforcedoesnotchange.Masslessparticlesalltravelatthespeedoflight,anditisnotpossibletobring

them to restorovertake them. In this case, helicity andchirality are identical.Formassive particles, the helicity is still correlated to the chirality, but is notidenticaltoit.The upshot of this is that for massive particles, a particle with a definite

helicity does not have a definite chirality, and conversely a particle with adefinitechiralitydoesnothaveadefinitehelicity.Soifwecreateapurebeamofparticleswithadefinitehelicity, itmustcontainbothchiralities.Foramassiveparticle,bothchiralitiesmustexistinnature;butforamasslessparticle,wecangetawaywithhavingonlyonechirality.

Goingbacktotheideaofamasslessneutrinothen,iftheneutrinoismasslesswecanbuildatheorycontainingonlytheleft-handedneutrinosandright-handedantineutrinos.Only theparticles thatactually interactwith theStandardModelforces need to exist. The right-handed neutrinos and left-handed antineutrinosneedneverevenexist.AppealingtoOccam’srazor,nonsuntmultiplicandaentiasinenecessitate,fn3

or the simplest answer is usually the correct one. The Standard Model wasoriginallyconstructedsothatitdidnotcontainright-handedneutrinos,norleft-handedantineutrinos.Theywereablankspaceonthemap.Andthismeantthatthe neutrino had to be massless. What we are saying is that in the so-far-unchartedneutrinobadlands,whichcanonlybereachedbyair,onlytheairportsexist.Butisthisreallytrue?

24

TheStandardModelisDead–LongLivetheStandardModel!

ATLASTWE takea flight tooneof theneutrinos– theElectronNeutrino–andstarttoexplorethesurroundingterritory.AccordingtotheStandardModel,thistinyairport,andsimilaronesfortheMuonNeutrinoandTauNeutrino,shouldbeallthereistosee.Butdoubtscreepinwithfurtherexplorations.Apartfromthegeneralweirdnessofaparticlewhichcanonlyexistwithone

‘handedness’,amajorworryforphysicistsexploringthisterritorywasthe‘solarneutrino problem’, first observed in experiments led by American physicistsRaymondDavisJrandJohnBahcallinthelate1960sandearly1970s.The essence of the problem with solar neutrinos as Davis and Bahcall

understooditwasthatthereweren’tenoughofthem.OurknowledgeoftheSunandnuclear physics had led to a prediction that a certain number of neutrinosshould be being produced by the fusion reactions in theSun.Thesewould be‘electronneutrinos’,meaningtheyareproducedinassociationwithelectrons,asintheradioactivebetadecayofunstablenuclei.Since theyonlyexperience theweakforce,neutrinos interactvery rarely, so

areveryhardtodetect.Onethingtheycando,however,isscatteroffnucleiandproduce electrons. This involves the exchange of a W boson, which carrieselectric charge, and is called a ‘charged-current’ interaction. It is sort of theinverseoftheprocessbywhichtheneutrinoisoriginallycreated.Bahcall andDavis predicted howoften this should happen– in the specific

caseofneutrinosfromtheSunhittingchlorinenucleiandproducingargonplusanelectron–anddesignedandbuiltanextraordinaryexperimenttomeasureit.The experiment used 400 tonnes of perchloroethylene, a chemicalfn1

commonlyused indry-cleaning fluid.Neutrino reactionswithin this substanceproduceargon,byturningoneoftheneutronsinachlorineatomintoaproton.These reactions are so rare that the tank containing the fluid had to be buriedunderground to shield it from other particles. Davis used the Homestakegoldmine in South Dakota, USA. The argon produced was an isotope withnineteen neutrons inside the nucleus alongwith its eighteen protons,which is

unstablebutdecaysquiteslowly,withhalfoftheatomsinanysampledecayinginfiveweeks.Daviscollectedtheargoneveryfewweeksandcountedtheargonby detecting its decays. He found that the amount of argon was lower thanpredicted by Bahcall’s calculations based on our knowledge of the Sun. Thenumberofneutrinointeractionslookedtobelowerthanexpectedbyafactorofthree.Thismeantthatsomethingwaswrong.Eitherwedidn’tunderstandtheSun,or

wedidn’tunderstandnuclearphysics,ortheexperimentshadmadeamistake,ortheStandardModelofparticlephysicswaswrong.Theresultsweresogroundbreakingthatmanypeoplesuspectedtheproblem

must liewith theexperiment.ButDaviscontinuedcollectingdataandrefininghis experiment, and different experiments over several years repeated themeasurement.Thediscrepancyremained.If theproblemwerewith theSun,wecouldbe invery serious trouble.The

fusion reactionswhichpower theSunproduceneutrinosandphotons. It is thephotons that keep uswarm – they are sunlight! The neutrinos almost all passstraight throughtheEarth.AneutrinoproducedinsidetheSunwill reachus inaboutnineminutes,travellingatthespeedoflight.ButaphotonwillbedelayedintheSun,bouncingaroundamongsttheplasma,beingabsorbedandre-emittedmany times, over thousands of years, before eventually reaching the surface.Oncethere,itwillalsogethereinaboutnineminutes.Onepossiblereasonforthe lackofneutrinos is that thereare fewer fusion interactionsgoingon in theheart of theSun.Maybe, scientists thought, the experiments indicated that theSunwasrunningoutoffuel,alackthathasnotaffectedthelightandheatweseefrom it yet, because of the time-lag in photons getting to the surface.But theSun’sdays,oryearsatleast,wouldbenumbered.If theproblemwere indeedwithparticlephysics, thesolutionwouldbe less

threatening,butintriguingnonetheless.Thissolutionissuggestedbythefactthatthe experimentallymeasured number of neutrinoswas too low by a factor ofthree.Weknowthereare threedifferentkindsofneutrinos in theStandardModel:

the electron neutrino, the muon neutrino and the tau neutrino, each one in adoubletwithitspartnerchargedlepton,andeachinteractingwiththatleptonviatheW boson of theweak force. These are the airports, the onlyway into theNeutrinoSectoroftheIsleofLeptons.However,theexperimentswereabletodetectonlythefirstkind,theelectron

neutrino.TheneutrinosfromtheSunshouldbeproducedaselectronneutrinos,because that is how nuclear physics told us those fusion reactions work. ButwhatiftheychangedonthewayfromtheSuntotheEarth?Whatiftheneutrino

types mixed themselves up, so that by the time it reached us the beam ofneutrinos contained an equal amount of all three types? That would neatlyexplain the discrepancy, since two-thirds of them would be invisible to thedetector.Thereisalreadyawayofchangingthetype,orflavour,ofmatterparticlesin

theStandardModel.WesawitalreadyontheIsleofQuarks.Thedefinitemassversionsofquarksdonotexactlylineupwiththeversionswhichareproducedby theweak force–onourmap, the airports arenot in the sameplace as thecities – so quarks can change flavour as they travel, and oscillate betweenflavours. Could the same thing be happeningwith neutrinos? If the neutrinoswere tomix flavourson theirway from theSun to theEarth, thenonaveragetherearelikelytobeequalamountsofthethreekindsarrivingatthedetectors.Twooutof threeof thesewouldbecompletely invisible,and thus thedetectorwouldmeasureananswerwhichwastoolowbyafactorofthree,asobserved.FollowingthesituationweobservedontheIsleofQuarks,weknowhowto

handlethis.Weneedasituationwheretheairportsdon’texactlylineupwiththecities,andweneedtoquantifytheeffectusingamixingmatrixfortheneutrinos,similartotheonewehaveforthequarks.Butinordertodothis,weneedthreeneutrinocitiestoexist,justasthequarkshavecitiesdistinctfromtheairports.Thedistinguishing featureof the cities, though, is their definite anddistinct

masses.Thiswon’tworkifalltheneutrinoshavethesamemass!Ifwearetouseneutrinomixingtosolvethesolarneutrinoproblem,theneutrinoshavetohavedifferentmasses from each other.And specifically, thatmeans at least two ofthem(andprobablyallthree)musthavenon-zeromasses.We know that has a serious impact though. Following our examination of

helicity and chirality, a non-zero neutrino mass means that the left-handedneutrino can also become right-handed, and we can no longer get away withhavingonly left-handedneutrinosand right-handedantineutrinos.Therehas tobe a right-handedneutrino.Wemust introduce anewparticle,whichdoesnotinteractwithanyoftheforcesoftheStandardModel!Sorting out what is really going here requires data from a definitive

experiment: thedefinitiveexpedition to reallyworkouthowthe land lies.TheSudburyNeutrinoObservatory–SNO–wasjustthat.Thekeyideawastodesignanexperimentthatcoulddetectneutrinosofany

flavour, bymeasuring the ‘neutral current’ interaction. In this interaction, a ZbosonisexchangedinsteadofaW.BecausetheZcarriesnoelectriccharge,theneutrinobreaksupanucleus,but remainsaneutrino.Noelectron (ormuonortau) is produced.Theonly sign that itwas therewouldbe a fewhadrons, theshatteredproductsofthebrokennucleus.

Detecting these hadrons required detectors of unprecedented sensitivity. Toconfidently detect the tiny signal of a broken nucleus, all other extraneousradioactivity has to be reduced to the lowest possible level, and measuredprecisely.To do this, theSNOcollaboration borrowed1,000 tonnes of ‘heavywater’ from theCanadian atomic energy programme.Heavywater is just likenormalwater,twohydrogenatomsboundtoanoxygenatom,butoneorbothofthehydrogenatomsarereplacedbyaheavyisotopeofhydrogen–deuterium–which has a nucleus of one neutron and one proton, as opposed to a normalhydrogen,whichhas just a singleproton.Thismakes thewater 5–10per centheavierthannormalwater.Otherthanthat,itisjustlikenormalwater.Youcouldswiminitortakeasipofit,althoughexperimentswithmiceindicatethatmorethanabout20percentofheavywaterinyourdrinkisverybadforyouandmorethanabout50percentisprobablyfatal.TheSNOheavywaterwasstoredinanacrylicvesselsurroundedbynormal

water,andwatchedcarefullywithanarrayofhighlysensitivephotondetectors.Three different things can happen in SNO when a neutrino interacts. One

thing is that they convert a neutron into a proton – the charged-currentinteraction – and produce an electron.Only electron neutrinos can do this.Ortheycanbreakthedeuteronupintoaneutronandaproton–theneutral-currentinteraction. This reaction is possible regardless of the neutrino flavour –electron, muon and tau neutrinos all do it. Neutrinos may also scatter off anelectron via the neutral current interaction; again, all neutrino flavours can dothis,althoughelectronneutrinosareaboutsixtimesmorelikelytodosothantheotherflavours.The different kinds of collisions leave different patterns of light in the

detectors. Counting the rates for the neutral-current interactions told thephysicistsatSNOthetotalnumberofneutrinoscomingfromtheSun,regardlessofwhethertheyoscillatedbetweendifferentflavoursornot.Therateofcharged-currentinteractionsofelectronneutrinostoldthemhowmanyelectronneutrinoswere arriving at theEarth.Thedifferencebetween the twomeasurements toldthemhowmanyneutrinoshadchangedflavourontheway.Theresultwasspectacular.ThetotalnumberofneutrinosarrivingattheEarth

from theSunwasbangon theexpectation; theSunwas fine,andweproperlyunderstoodthefusionreactionsdrivingit.Thenumberofelectronneutrinoswastoosmall,byafactorofthree.Thoseearly,immenselychallengingexperimentsbyDaviesetal.werevindicated,atveryhighprecision.TheStandardModelhadtobechanged–neutrinosaredefinitelychangingflavourbetweentheSunandtheEarth.Therefore,theyhavemass.

Infact,whileSNOsettledthesolarneutrinoproblemonceandforall,anotherexperiment,Super-KamiokandeinJapan,hadalreadymadebiginroadsintotheneutrinowildernessoftheIsleofLeptons,andshowninadifferentmeasurementthatneutrinoshadmass.TheSuper-Kamiokandeconsistedofanundergroundpoolof50,000tonnesof

purifiedwater, surroundedbyphotondetectors.Thekeymeasurement itmadewasofmuonneutrinos.Theseareproducedwhenhigh-energyparticleshit theupperatmosphereof theEarth.Theparticlescomefromalldirections,and theneutrinoswillpassthroughtheatmosphere,andindeedpassthroughtheEarth.So in thisquiet,undergroundpoolunderamountain in Japan,muonneutrinoswere expected to arrive from all directions equally. They did not. Super-Kamiokandeshowed thatonlyabouthalfasmanyarrivedfrombelowas fromabove,suggestingthatsomeofthemwerechangingintotauneutrinos,towhichSuper-Kamiokandewasinsensitive.Subsequentdetailedanalysisoftheangulardistributionconfirmedthis.Thisshowedthatneutrinosdidhavemass;andSNOshowedthatthis(inthe

formofelectronneutrinoflavour-changing)wasindeedthesolutiontothesolarneutrinoproblem.ConsideringthedifficultyofgettingtotheNeutrinoSectoroftheIsleofLeptons,thiswasamazingprogress.Itwasthefirst,andsofaronly,fundamental change forced on to the Standard Model since its inception. Itmeans that the neutrino territory is more complicated and interesting that wethought,andtheremightbemuchmoretobelearnedfromexploringit.

25

NeutrinoBadlands

SO LET US exit the tiny airport we landed at and head out to explore thesurroundingNeutrinoSectoronfoot.Thefactthatneutrinoshavedifferentmasses,andmix,indicatesthatthereis

indeed amixingmatrix for leptons, just as there is for quarks. Sowe shouldexpectthattheairportsontheIsleofLeptonsaresomewhatdisplacedfromthepopulation centres, just as the Down-prime, Strange-prime and Bottom-primeairportsaredisplaced.Thisisthecase,butthepictureisratherdifferent.On the Isle of Quarks, the two different versions of down quark, with and

withouttheprime,arecloseenoughthatitisobviousthattheybelongtogether.However, for theneutrinos, themixingmatrix isverydifferent.Toexplain theobservations,themixingmustbemuchlargerthanontheIsleofQuarks.Theonlywaywehaveof fullyexploring theNeutrinoSector isbyair.The

weakinteractionconnectsthreeairports:ElectronNeutrino,MuonNeutrinoandTau Neutrino. SNO and Super-Kamiokande – and other experiments atacceleratorsandreactorsthathavefollowedthem–haveidentifiedthefactthattheseairportsarenot thewholestory; therearecitieswhich theairportsserve.Theseareversionsoftheneutrinoswithdefinitemass.Buttheweakinteractionseems to be running a budget airline into the Neutrino Sector. The cities aremilesawayfromtheairports,andinfactwestillaren’tevensurewheretheyareexactly.Thisisnotaverysatisfactorystateofaffairs.Thereisaninterestingpossibilityherethough.Remember,themixingmatrix

forthequarksbreaksthecombinedsymmetryofcharge-conjugationandparity,introducingarealdistinctionbetweenthenorthernandsouthernhemispheresofourmap,betweenmatterandantimatter.Thematrixwehavejustbeenforcedtointroduceforneutrinosalsoincludesthispossibility.Inthequarkcase,thiseffecthasbeenmeasured.Neutrinosarehardertostudy,

becausetheyinteracttoorarely,andthisaspectofthemixingmatrixhasnotyetbeenmeasured.Ifitturnsoutthereisalargeeffect,itcouldhelpexplainhowtheuniverseevolvedtobemostlymadeofmatter,notantimatter.

Ourexplorationof theNeutrinoSectorof the IsleofLeptonshasbeenveryfruitful, but theremight be stillmore out there.There are still other explorersbravingthewilderness,tryingtoestablishwhethertheneutrinoiseventhesamekindofparticleasalltheotherleptons,whethertheDiracequationevenappliestoitatall,orwhetheritdancestoadifferentdrum.Theneutrinohasastartlingpossibility open to it, unavailable to the othermatter particles. Itmight be itsownantiparticle.Wemighthave the IsleofLeptonswrong.ThewildernessoftheNeutrino Sectormight extend right down to the equator –we still do notknow,butwearetryingtofindout.Matter is the sameas antimatter except that all the ‘charges’– thequantum

numbersthatdeterminetheinteractionswiththeforces–aretheopposite.Sotheelectron is negatively charged, and its antiparticle, the positron, is positivelycharged and therefore obviously different from the electron. Likewise, for aquark carrying a color charge (call it ‘blue’), the corresponding antiquarkwillcarry the opposite charge (antiblue, or yellow if you want to stick with theanalogytorealcolours).Before we knew they had mass, we knew that neutrinos don’t feel the

electromagneticorstrongforces.Andeventheweakforceactsonlyontheleft-handed neutrinos. Back when neutrinos were thought to have zero mass, theStandardModelonlycontainedthose left-handedneutrinos.Butnowweknowtheyhavemass,thatdoesn’tworkanymore.Themassimpliesthatright-handedneutrinosmustexisttoo,mixedupwiththeleft-handedones.Theseright-handedneutrinoshavezerochargewithrespecttoalltheforces–noelectriccharge,nocolorcharge for thestrongforce,andnoweakcharge.So inverting thechargemakesnodifference–minuszeroisthesameaspluszero!Thereforethereisapossibility – andmany theoristswould say a highprobability – that the right-handedneutrinoandtheleft-handedantineutrinoarethesameparticle,withjustthehelicityflipped.Thiskindofparticlewouldappear in theequationsofphysics inadifferent

way from the quarks and the other leptons; especially, the way their massappearsisdifferent.fn1TheNeutrinoSectoriscurrentlybeingscouredforsuchaso-far-hypothetical particle. The search focuses on some very rare and specialnucleardecayswhich,ifobserved,wouldhavehugeimplicationsforphysicsandcosmology.Theraredecayinquestionis‘neutrinolessdouble-betadecay’.Wehavecome

acrossbetadecayalready.Itistheprocessinwhicheitheraneutronbecomesaproton,oraprotonbecomesaneutron, insideanatomicnucleus,changing theatomicnumberby+1or−1respectively.Theprocesswasfirstobservedaround

theendofthenineteenthcentury,andthe‘betaparticle’whichisemittedisnowknowntobeanelectroninthefirstcase,andapositroninthesecond.Remember, beta decay provided the first indication of the existence of

neutrinos.Theemissionofaneutrino,evenifunobserved,allowstheelectronorpositronthatisemittedtohaveaspectrumofenergiesratherthanafixedvalue,asmeasuredinexperiments.Asthenamesuggests,indouble-betadecaytwoneutronsorprotonstransform

atonce, twoelectronsorpositronsareemitted,alongwith twoneutrinos.Thissoundsunlikely,but forsomenuclei theenergybalance issuch that this is theonly way they can decay. The process is rare, but has been observed andmeasuredinseveraldifferentisotopes.Theexistenceofnucleiwhichundergodouble-betadecayopensupanewand

intriguingpossibility.Emittingaparticleisinmanysensesthesameasabsorbinganantiparticle.Soiftheneutrinocanmixwithitsantiparticle,thesameneutrinocouldbebothabsorbedandemittedinadouble-betadecay,meaningthatoverallnoneutrinosgoinorout.Thiswouldbeneutrinolessdouble-betadecay.Inthiscasethepairofelectronswouldcarrythefixedenergyofthedecay–justastheelectroninsingle-betadecaywouldhavehadafixedenergyifnoneutrinowereemitted.Ifneutrinolessdouble-betadecayweretobeobserved,itwouldshowthatthe

neutrino is, at least in part, its own antiparticle, because it would have to beemittedbyonebeta-decayingneutronasaparticle,andabsorbedbytheotherasanantiparticle.ThiswouldmakeitafundamentallydifferentkindofobjectfromalltheotherparticlesoftheStandardModel.Thatcouldleadtoanunderstandingofwhyneutrinomassesaresosmall.Itcouldalsoprovidestillanothersourceofviolation of the combined charge-conjugation and parity symmetry, helping toexplainwhytheuniversecontainssomuchmorematterthanantimatter.Itwouldcertainlygivesomeimportantpointersastowhatliesinthefareast,offtheedgeofourcurrentmap.Thechallengeforexperimentssearchingforraredecaysistoeliminate,asfar

aspossible, thenoisefromnaturalbackgroundradiation.Everycomponenthastobescreenedfor tracesofnatural radioactivity(mostlyuraniumandthorium)usingspecialisedinstruments.Thedetectorconstructionmustbecarriedoutinacarefully controlled, clean environment to avoid any contamination duringassembly. Unsurprisingly building such an instrument takes a long time. Theexperimentsthenhavetobeinstalledfarunderground,andwatchedcarefullyforalongtime.Severalgroupsarebuildingandrunningexperimentsrightnow.Wehavelearnedmuchmorethanonemighthaveexpectedfromexploringthe

NeutrinoSector: it forceda significantchange in theStandardModel, itholds

out a possible new source of matter–antimatter asymmetry, and it may havegivenussomeimportantcluesastowhatishappeningfarintheeast,atenergiesbeyondour current reach.Thevoyagesof exploration anddiscovery continue,deepintotheNeutrinoSector.Itmaynotbewildernessforlong.Butwhatliesinstore forourbandofexplorers rightnow isa long-haul flightbackeast to theairline hub. The land of Bosonia, home of theW, the Z, the photon and thegluon,requiresourattention.Andamysteryliesatitsheart.

EXPEDITIONVII

IntoBosonia

Thebenefitsofairportcoffee–Thoughtsonafrozenwindscreen–Volcanoesandhowtoavoidthem–Carnivorousparticles–Atriumphandawelcome.

26

SymmetryandConservation

ARESTLESSRED-EYEflightandabumpylandinglater,andwearereadytoembarkonthethoroughexplorationofthelastknownmajorlandmassonourmap–theenigmaticlandofBosonia.ThisiswheretheW,theZ,thegluonandthephotonareallbased. It iswhere thecars, trainsandaeroplanes that connect theotherislandsoriginate–alltheforcesoftheStandardModel.Andintheheartofitsinteriorliesanenigma.Thisisournextgoal.Bosons are different. All the matter particles we have encountered – the

electron,muon and tau, the quarks, even the neutrinos – have been fermions,meaningthattheycarryahalf-integerunitofspin.Bosonscarryanintegerunit,andthischangestheirbehaviourprofoundly.Ratherthanfillingupenergylevelsandexcludingotherparticles–astheelectronsdoaroundatoms,forexample,inlinewith theexclusionprinciple–bosonsgangup togetherandaremore thancontenttocrowdintothesamespace.ThisisjustonewayinwhichBosoniaisapeculiarplace.Beforestrikinginland,weneedtoproperlyequipourselves.Thewomanattheinformationdeskattheairportinformsus,innouncertainterms,that one of the important things to take with us is a better understanding ofsymmetry.Understandingsymmetry,sheassuresus,willactuallyallowustoseewheretheforcesoftheStandardModel,andhencethebosons,comefrom.Shehandsusanexplanatoryleaflet.We have stumbled across symmetry several times already, in

electromagnetism, in relativity, in the discovery of antimatter and the ideas ofparityandcharge-conjugation.Itisacrucialideainphysics:itliesbehindbasiclawssuchas theconservationofenergy,andbehind theforcesof theStandardModel,aswellasgravity.Sowebelievewhatthewomanatthedesktoldus:weneedtomakesureweknowwhatwearedoingbeforewesetoff.Otherwisewemayloseourselvesinthewildterraininland.Weretiretoanearbycoffeebartoreadcarefullytheleafletweweregiven.Itbeginsratherphilosophically.Thereasonthatsymmetryissopowerfulinsolvingproblemsinphysicsisthat

itisconnectedtotheattempttobeobjective.Insomesense,theuseofsymmetry

allows us to askwhether things would be the same if wewere looking fromsomewhereelse,otherthanourownpointofview.Tosaythatsomephysicalsystemrespects‘translationalsymmetry’istostate

that the laws of physics are the samewherever you happen to be. Rotationalsymmetrymeanstheangleyoulookfromdoesn’tmatter.Aswewillsee,thesesymmetries are connected to fundamental physical laws. But it is also moremetaphoricallytrue.Whatwouldphysicslooklikeifwegrewuponadifferentplanet?Or ifwewere allmade of antimatter instead ofmatter?Or…? If thephysical laws that we discover really do describe the objective nature of theuniverse,thentheyoughttobethesame,whateveroursubjectivepointofviewandwhereverwetravel,onourallegoricalmaporonarealone.Ifsomephysicalobject,oranequationdescribingsomephysics,issymmetric

undersomehypotheticalchange,thatmeansitlooksthesameafterthechangeasitdidbefore.Sothechangeis,insomesense,nochangeatall.Forexample,acircleissymmetricwithrespecttorotationsarounditscentre–itlooksthesamenomatterwhatangleyourotateitthrough.Asquareisalsosymmetric,butonlyunderquarter-rotations–thatis,rotations

through 90, 180, 270 or 360 degrees. For any other angle the sideswill havechangeddirection:theywon’tlineupwiththeoriginal.Sotheperfectrotationalsymmetryofthecircleisbroken.This idea can be generalised to other transformations, andwe have already

foundsomeoftheseonourjourneys.Paritysymmetryistheideathattheworldissymmetricunderreflection:thatreflectingeverythinginamirrorwouldleavephysicsjustthesame.Weknowthatthisisnotactuallytrue,becausetheweakforcebehavesdifferentlyforparticlesofdifferenthandedness.Likewise,charge-conjugation symmetry would hold if the transformation of all particles intoantiparticlesandviceversaleftphysicsthesame.Again,theweakforcemessesthis up, as well as in a small way breaking the combined transformation ofcharge-conjugationandparityatthesametime.Itisasthoughthecirclehasanimperfectionintherim,aglitch,whichallowsustellwhenithasbeenturned.Themajor impactofsymmetrieson the lawsofphysics isencapsulated ina

theoremprovedbytheGermanmathematicianEmmyNoetherin1915.Omittingtechnical qualifiers, Noether’s theorem states that for every continuoussymmetry in nature, there exists a conserved quantity, something which canneitherbecreatednordestroyed.Ifsomephysicalsystemhasa‘continuoussymmetry’,thatmeansthatthereis

a variable that canbe changed to anyvaluewithout affecting the system.Therotationofacircleisanexample–anyangleofrotationisfine,sothesymmetryis continuous. For a square, only four angles are valid, so the symmetry is

discrete,instead.Anexampleofacontinuoussymmetrythatwethinkappliestothelawsofphysicsis‘translationalsymmetry’:thefactthatthelawsofphysicsdon’t depend on where you are, they are the same everywhere. This is acontinuous symmetry with respect to changes of location. Noether’s theoremsaysthatbecauseofthis,theremustbeaconservedquantity.The conserved quantity in this case is momentum: we have seen the

conservationofmomentuminactionalready,butnowwecanseewhereitcomesfrom.Fromanassumption that the lawsofphysicsare thesamewhereveryouare,Noether’s theoremallowsus toprove theconservationofmomentum,andthus start deriving the laws of motion. This is a very powerful tool in ourexplorer’s toolbox, andwe are going to be applying it to the photon, our firststoppingpointinBosonia.Thereisacontinuoussymmetryinelectromagnetism.Itisapparentinthefact

thatelectriccurrentflowsfromhighvoltagestolowervoltages,butonlyvoltagedifferencesmatter.Theabsolutevoltagehasnomeaning.Thisiswhybirdscansit on high-voltage electric cableswithout turning into tasty fried snacks. Thewiresareatahighvoltage,butaslongasthebirdsareatthesamevoltageasthewires,noelectriccurrentflowsandnoharmisdone.This means that if we could, hypothetically, change all the voltages

everywhereintheworldatonce,itwouldmakenodifferencetoanything.Infactfor allyouknow, it justhappened then,whileyouwere reading that sentence.Invarianceunderchangesofvoltageisacontinuoussymmetryoftheequations.InQED, the quantum theory of electromagnetism, the electron is awave-likequantumstate,andthevoltagesymmetryisnowmanifestasthefactthatphysicsis invariant when the phase of this quantum state is changed. Remember, thephase just specifies the absolute position of the peaks and troughs of theassociatedwave.Onlydifferencesinphasematter–thevalueofthephaseitself,just like the value of voltage, makes no difference to anything. Noether’stheoremtellsusthatthereshouldbeaconservedquantitycorrespondingtothissymmetry.Thereis.Theconservedquantityiselectriccharge,whichwealreadysawfromMaxwell’sequationscannotbecreatedordestroyed.Thefieldofmathematicsthatdealswithsymmetriesiscalled‘grouptheory’.

A‘group’inthemathematicalsenseisthelistofallthedifferentpossibleactionsthat satisfy a given symmetry. So the group of possible rotations of a squarewouldhavefourmembers:therearefouranglesyoucanrotateitthroughwhichpreserveitunchanged.Forthecircle,andforanyothercontinuoussymmetry,therelevantgrouphasaninfinitenumberofmembers.Fromthepointofviewofphysics,oneofthestrengthsofmathematicsisthat

ifyoulearnsomepieceofmathsonce,itwillveryoftencropupoverandover

again in different bits of physics. This happens here, in that the samemathematical symmetry groups crop up in a variety of circumstances, and tohelp recogniseanddiscuss them,mathematicianshavegiven themnames.Therelevantgroup for thephase-invariancesymmetryseen inQEDiscalledU(1),wherethe‘1’comesfromthefactthatthephaseisjustonenumber(othergroupswemeetwill havemore) and ‘U’ stands for unitary, which is a property thatguarantees theconservationofcharge, in that ifwestartwithoneelectronandmoveitaboutinthegroup,we’llalwayshaveoneelectron,albeitwithdifferentphases.Wefinishourcoffees.Thiswasclearlyamoreimportant tourist information

leafletthanmost.Thebackgroundbriefingithasprovided,identifyingtheglobalU(1) symmetry of QED and its connection with the conservation of electriccharge,getsustothepointthatwearereadytotakeonthemissiontoexploreBosonia.Over to thecar rental stand tohirea4×4.Weareheading into someverychallengingterrain.

27

SymmetryandBosons

ASWEPULLoutoftheairportcarparkandheadforthehillsofBosonia,westillclutch the leaflet we got from the information desk. It is satisfying and, theleaflet assures us, important to know that there exists a mathematical proofconnecting the fact that charge is conserved, with the fact that under asimultaneous phase rotation everywhere in the universe, nothing changes.Conservationofchargeisverypractical,andisabsolutelykeytotheoperationofvast amounts of our technology. The phase of a quantum field seems ratherdistantandabstract.Butmathematicstellsusthatoneimpliestheother.Sofarsogood,butitisnotatallobvioushowthisconnectswiththebosons

which carry the fundamental forces, and hence the terrainwe are planning totraverse.Thatsaid,theideaofsimultaneouslychangingeverythingeverywhereseemsa

bit unphysical.We know that instantaneous communication is not possible. Inrelativity,theveryideaof‘simultaneous’eventsissubjective,anddependsuponthe speed of the observer. People travelling at different relative speeds willdisagreeonwhetherornoteventsoccuratthesametime.Maybewe should insist that physics remains the sameunder all changesof

phase,fn1 even if there aredifferent changes indifferentplaces?Thiswouldbecalledalocalsymmetry,whereasbeforewehadaglobalone.Ifwedoenforcethissymmetrylocally,allowingourselvestomakedifferent

changes to the phase of electrons at different points in space, somethingmarvellous happens. The need to retain the local symmetry means that extratermshavetobeaddedintheequationsthatdescribetheelectron.Thisisabitlike the terrainwe are driving across in our Jeep. The driver, who is slightlyobsessive,wantstomaintainaconstantspeed,sothatsheknowswewillkeeptoour demanding schedule. To keep a constant speed on a plain or plateau, sheneedsthesameamountofpowerfromtheengine.Whetherweareonthecoastalplane or a high plateau is irrelevant. Indeed, it wouldn’t matter if someonemysteriouslyraisedBosoniaahundredmetreshigherabovesealevel.Solongastheyraisedthewholecountryatonce,aplainorplateauwouldremainflat,and

theJeepwouldstayat thesamespeedwithout thedriverneeding tomoveherfooton the accelerator.However, if there are local changes inheight –hills –then to maintain constant speed, the force exerted by the engine has to bechanged. If we are going up, it has to increase, and going down, it needs todecrease.Theneedtochangethepowertotheengineistheanalogueoftheextraterms

we need to add to the equations of motion of the electron. These terms looksomewhatclunkyandawkwardatfirstsight,butinspectingthemproperly,andseeing what effect they have, reveals that they are exactly the quantummechanicalversionofMaxwell’sequations!This isphenomenal.WeenforcealocalU(1)symmetry,andindoingsoweproducetheequationsthatdescribethephoton,andthewholeofQED,asiffromnowhere!Justasthedriverhastouseforcetokeepthespeedconstantwhentheslopevaries,QEDappearsasaforceintheStandardModelwhenthephaseisallowedtovarylocally.Thisstartlingsuccessmakessomesenseinretrospect.Weknowthatthephase

symmetry is connected to conservation of charge, and we know that localdifferencesintheamountofelectricchargeleadtoelectromagneticforces.Buteven so, to derive the existence of the photon from a symmetry this way isbeautifulandremarkable,andisakeyinsightintothenatureofBosonia.The photon is the first boson we heard about on our travels – Photon is a

majorindustrialcityonthewestcoastofBosonia,whichmanufacturesthecarstravelling the road networks right across the Isles of Quarks and Leptons,HadronIslandandAtomLand.Itseemsclearnowwhythewomanontheinformationdeskwassoemphatic

that to properly explore Bosonia, we needed to be tooled up with a decentknowledge of symmetry. The whole of the road network and the PhotonindustrialzonecanbetracedbacktoalocalU(1)phasesymmetry.Itistemptingtowonderwhetheratrickasgoodasthatcanbetriedagain.TherearesymmetrygroupsotherthanU(1)available.Whatmighttheydoforus?They can do a lot, it turns out. There is a group known as SU(2), which

insteadoftheonephaseofU(1)hasalittlevectoroftwonumbers.fn2Enforcinglocalinvarianceunderthissymmetrygroup,justlikewedidwithU(1),givesussomethingverymuchliketheWandZbosonsoftheweakforce;wearecloserto understanding our airlines. And enforcing local symmetries for the groupknownasSU(3)producesthewholeofthestrongforce,therailwaynetworksofHadronIslandandtheIsleofQuarksandtheconnectingbridgetothegluononthewestcostofBosonia.Thismeansthatall theforcesof theStandardModelarerelatedtolocalinvarianceunderthesesymmetrygroups.

Symmetryisabeautifulandpleasingfeatureofnature,seeninthegrowthofplants, the arc of a rainbow and the flow of the seasons. But the closerelationshipbetweensymmetryandtheforcesoftheStandardModelturnsouttobemorethanjustanaestheticallypleasingcoincidence:itseemstobeessential.

28

VirtualParticlesandtheDefenceAgainstInfinity

LEAVINGPHOTONINourrear-viewmirrornow,weturnandheadeast,tocontinueourjourneyintocentralBosonia.Theroadsaregettingrougher,andthegeologyhasaruggedandunstablelooktoit.Therehavebeenstoriesofvolcanicactivityin the region, and the occasional geyser seems lends them credibility. SinceBosoniaiswherealltheforcesoriginate,perhapsweshouldexpectturbulence.As we have seen several times on our previous expeditions, an interaction

between two particles in the StandardModel is described by an exchange ofbosons. Electromagnetic attraction and repulsion involve the exchange ofphotons(ourroadnetwork);thestronginteractionismediatedbytheexchangeofgluons(railways),andtheweakforcebytheWandtheZ(thoseairlines,withtheirsometimesoddlyplacedairports).PartofthepoweroftheStandardModelisthatitcanprovideyouwithaquick

estimateofthepredictionforsomeprocess–sayforthechancesoftwoparticlesscattering off each other.And if you need amore precise answer you can domore work, more calculations, and gradually reduce the uncertainties in theprediction.Theroughanswerfortheprobabilityoftwoelectronsscatteringoffeachother

could be calculated by considering the chances that they exchange a singlephoton,becausethisisthesimplest,mostlikelywaysuchascattercouldoccur.Butifwewanttomaketheanswermoreaccurate,weshouldalsoconsiderthechancesthat twophotonsareexchanged.This is less likelytohappen,becauseeachtimeanelectronandaphotoninteract,weintroduceafactorofabout1/137(0.007orso)intotheprobability.fn1Butifwewantapreciseanswerweneedtoinclude it. Remember that all possibilities have to be taken into account inquantummechanics,soifwemisssomeout,wegetthewronganswer.Themoreweinclude,themoreaccurateourpredictionswillbe.Wecouldalsoincludethechanceofexchangingthree,fourormorephotons.

Each time we increase the number of photons, we decrease the size of thecontribution to the probability, making smaller and smaller corrections andconvergingonamorepreciseanswer.Thisideaofstartingwitharoughanswer

and systematically improving it with more sophisticated corrections is calledperturbationtheory.Theexchangedparticlesinallthesecasesarewhatwecall‘virtual’.Theyare

very ephemeral, and never directly observed. In fact we have met virtualparticlesbefore,goingroundtheloopsthataffectthemagneticmomentsoftheelectronandthemuon,andbubblinginthequantumvacuumwhilequarksturninto hadrons. Virtual particles are real in some sense, because if they are notincludedinourcalculations,theanswerscomeoutwrong.Andtheyhavesomerelation to real particles. For example, themass of a virtual particle does nothavetobethesameasthemasstheparticlewouldhaveifitwerereal.Virtualphotonscanhavenon-zeromass,while realonesarealwaysmassless.But thefurther the mass of a virtual photon is from zero, the less likely it is to beexchanged,andtheloweristheprobabilityofthescattering.Sothereisacloseconnectionbetweentherealandvirtualversionofthephoton,orindeedtherealand virtual versions of any particle. In the end, all that actually registers in adetector are the real particles that go into a scatter, and the real particles thatcome out, but the properties of the virtual particles critically influence wheretheygo,andhowoften.Therearefurtherimplicationsofthevirtualparticleexchangesthough,aswe

lookcloserattheentitiesonourmap.AccordingtotheStandardModel,virtualparticlescanalsoformlittle loops,connectingbackon themselves,orsplittinginto little particle– antiparticle pairs before reforming. In any quantum systemthis kind of unruly behaviour is going on all the time, if you look closelyenough.Aswestudyitmorecarefully,weseethatevenanelectron,onitsown,is surrounded by a cloud of virtual particles, looping out and round andconnectingbackagaintotheelectron.Thisiswhatwesawwhenlookingatthequantumcorrectionsto‘g’andthemagneticmomentof theelectronandmuonthatweobservedonourtouroftheIsleofLeptons.Allthismayseemquitewildandabstract,butitworks.Theincrediblyprecise

calculationsofthemagneticmomentsoftheelectronandmuon,discussedwhenwe were exploring the Isle of Leptons, require virtual-particle loops. Theexistenceandmassofthetopquarkwerepredicted,beforeitsdiscovery,throughthe influence of its appearance in quantum loops contributing to preciselymeasuredquantitiesinelectron–protonannihilation.Sincetheparticlesgoingroundtheseloopscarryenergy,andsinceenergyis

massmultipliedby the speedof light squared, the loopswill contribute to themasswewillmeasureforaparticle,eveniftheloopsaretoosmallandquickforustosee.Itistemptingtohopethatitmightbepossibletocalculatethemassofaparticlefromtheenergyinallthepossibleloopsthatsurroundit.Maybethat

can even explain the curiousdistributionof themasses of leptons andquarks,scatteredfromwesttoeastonourmap,fromthesuper-lightneutrinostothetopquarkwithamassnearly200timesthatoftheproton?Sadly not.Evenworse, not only dowe fail to get the right answers for the

masses,wedon’tevengetsensibleanswers.Theresultcomesoutasinfinity.It’sas thoughwe are peering closely at one of the bosons by the roadside and avolcanosuddenlyerupts!This is not just wrong, it is silly. And a similar thing happens if we try to

calculatehowtheloopsaffectthechargeoftheelectron.Thisisbadnews.Ifourfancytheoryispredictingeverythingtobeinfinity, thisisagainstexperimentalevidence,toputitmildly.Andthisiswherethefactthattheforcesinvolvedinthesequantumloopsare

basedonsymmetriescomesbackintoplay,tosaveus.Weneedtopullintothesideoftheroadandpauseforamoment.Thistalkof

infinitiesandsuddenvolcanoesisunnerving.When confronted with an answer like infinity for the electron mass, a

physicistcould just take theview, ‘Well that’sobviouslynonsense,but Iknowwhattheanswershouldbereally,becauseIhavemeasuredit.’Wecouldtaketheequations behind the theory and, in all the places where the electron massappears,with its infinite loopcontributions,cross itoutandreplace itwith theactualmeasuredvalue.Thisisareasonable,pragmaticapproach,evenifitdoesfeel abit likecheating. It is called ‘renormalisation’,because the infinitiesarebeingnormalisedintosomethingsensible.Butevenasacheat,thisfallsflatonitsface,ingeneral.The problem with it is this idea that we can improve the precision of a

calculationbyaddingmore loopsandexchanges.Sowegetan infiniteanswerwhencalculatingallthepossibilitieswithoneloopinthem,thenwereplacethatbythemeasuredmass.Thenwetrytoimproveouraccuracybycalculatingthenext set of loops. Infinity again. Which means we have to fix it to themeasurementagain,andournewcalculationhasn’thelpedatall.Thishappenseverytimewetrytoimproveourcalculation.Itisfrustrating,anditmeansthatin the end the theory can’tmakeproperpredictions.Renormalisationdoesnotwork,ingeneral.However,thereisaclassoftheoriesforwhichnormalisationdoeswork,and

has been proved to work. If the theory is based on a local symmetry, thenreplacing the infinities by the measured values just once is all we need. Thesymmetries guarantee that the in finite bits of the quantum corrections canceleachotherout,leavingthefinitebitsthatdoindeedimprovetheaccuracyofthe

calculation.fn2 After that, no more of these impossible infinities crop up, nomatterhowmanyloopsweinclude.Toour immense relief, all the forcesof theStandardModel are constructed

thisway,withelectromagnetismbasedontheU(1)symmetry,theweakforceonSU(2)andthestrongforceonSU(3).Forthesetheories,renormalisationworks.We cheat once, and from then on the game is fair. This is probably not acoincidence.Maybebuildingatheoryonsymmetryistheonlywaytomakeonethatcanwithstandtheseinfinities.Thisismassiveprogress,andwestarttheengine,pullbackontotheroad,and

continueonourway,somewhatreassured.

29

MassandHiddenSymmetry

OUR JEEP BOUNCES along over the rock-strewn road, and the countryside getswilder and strangerwith everymile, aswe continue east.Weare lessworriedthanwewere thatwemight be abruptly immolated in an infinity of lava, butthereisstillsomethingamissintheinteriorofBosonia.Andassomanytimesbefore,itistheweakforcethatisresponsiblefortheweirdness.ThegroupSU(2)givesus‘somethinglike’ theWandZbosonsof theweak

force.Butnotexactlylikethem.ItgivesusaWandZwithzeromass.Thisisabigproblem.WelandedhereonBosoniaattheWandtheZ.Weknowtheyhavemass. But giving mass to bosons breaks the symmetry, and that threatens tounleashinfinitiesagain.Thisisnotaproblemforthestrongforce.Thegluonismassless,sotheSU(3)

symmetrycanhold,renormalisationworks,andtheinfinitiesintheloopscanbevanquished.Likewiseforelectromagnetism,thephotonhaszeromass,soU(1)isfine.TheW andZ bosons, however, are both verymassive. They are dozens of

timesmoremassivethantheproton.Thosemassesarenotaminormatter.Theyare the very reason the weak force is weak and short-range. Plus, W and Zbosons have been produced in particle colliders, and their masses have beenmeasureddirectly, so there isnodoubtabout them.They lie to theeastof thephotonandgluon.ButtheWandZmassesbreaktheSU(2)symmetry,whichonthe face of it means that renormalisation does not work, the infinities arerampant,andthetheoryisuseless.Luckily,therearewaysofhidingsymmetries.Ithappensquitealotinnature,

notjustintheesotericreachesoftheeastofourmap.Forexample,thinkoftheformationofacrystalfromagasoraliquid.Thegasorliquidisfeatureless–itlooksthesamefromanyangle,andfromanypositioninsidetheliquid.For several kilometres we have been climbing a steep mountain road, and

drivingthroughadownpour.RainbatterstheroofandbonnetofourJeep.Onthefrontwindscreen, thewipers are sweeping frantically, and the sidewindow, aswepeeroutinanattempttoseewhereweare,isbasicallyasheetofwater.As

wecontinuetoclimb,thecloudsthin,theraineases,andthetemperaturedropsdramatically.Thewateronthewindscreenbeginstofreezeaswewatch.Imagineatinyphysicistonthewindscreen,insidethesheetofliquid,looking

around.Theyareso tiny that thewindowappearsasan infinitesurfacewithadeeppoolofwatercoveringit.Theycan’ttellwheretheyare,orwhichdirectiontheyarefacing,italllooksthesame.Thentheliquidcondenses,andstartstoformcrystals.Delicatefern-leavesof

ice spread across thewindow.Now, not all directions are the same. Some areparallel to the crystal fronds of the fern, and some are not. The tiny physicsgnome can see all thewatermolecules lining up in planes and rows, and candefinedifferentanglesrelativetothoseplanes.Similarly,while thegnomestillcannotsaywhereexactlytheyareonthewindow,theycancertainlysaywhethertheyareonaplaneofwatermoleculesinthecrystal,orbetweenplanes.Notallpositionsarethesameanymore.Beingaphysicist,thegnomewillknowtheimportanceofthis,asshouldwe.

Asymmetrythatwaspresentintheliquid,andwhichisinfactstillpresentintheunderlying theory governing the interactions between the water molecules(electromagnetismagain) is notpresent in the crystal. It hasbeenhidden.Theliquidwaterisinahigher-energystatethantheicecrystals,andthesymmetryishiddenbecausetheorderlycrystalisalower-energystate.Astheyloseenergytotheir surroundings, the atoms arrange themselves into positions that minimisetheirtotalenergy.Thatenergyismadeupoftheirenergyofmotion(theslowertheymove, the lesskineticenergytheyhave)andtheirpotentialenergy,whichtheyhavebecauseoftheforcesbetweenthem.Theresultiscondensationintoacrystal,which,whilestillquitesymmetric,andratherpretty,haslesssymmetrythantheinitialsheetofwater.The second law of thermodynamics, one of those general principles which

seem to apply right across our map and beyond, states that entropy alwaysincreases.Entropy isaquantity thatmeasuresdisorder in somesense.Entropyincreaseswhenaparticledecays,forexample,becauseauniquedistributionofenergy–allofitinoneparticle–convertsintoseveralparticlesinwhichenergycan be distributed in several differentways. The result is a less unique,moredisordered state. This is why, as we saw earlier in our travels, particles willalwaysdecayiftheycan–itincreasesentropy.Given all this, one might worry about how a more orderly state can

spontaneously arise from a less orderly one, as seems to happen incrystallisation.However, theredistributionof theenergy to theenvironmentasthe liquidcoolsmeans that theoverall state (includingboth thecrystal and itssurroundings)hashigherentropy than thestarting liquid.For the same reason,

evolutionfromprimevalsludgetohomosapiensdoesnotviolatethesecondlawof thermodynamics, once you take into account the fact that there is a nearbythermonuclearreactor(thesun)madlyredistributingenergywhichcandrivetheprocess.Bothcrystallisationandevolutionarevastlycomplexanddifficulttopredict.

Physics is easier – all we need to know is that cooling and redistribution ofenergy can hide symmetries. Even if we have a symmetrical theory for theinteraction between particles, it is still possible that those particles form low-energystatesthatdonotshowallthesamesymmetries.ThisisapointertowardswhatisgoingoninthemiddleofBosonia,andthesolutiontotheproblemofWandZbosonmass.This ideaofhidden symmetry is just as important as the idea of symmetry,

whichgivesusconservationlawsandkeepsinfinitiesatbay.Itisfundamentaltophysicsthattherearesymmetries,presentintheunderlyinglawsgoverningthebehaviour of particles and forces, which are hidden in low-energy states,meaningthatingeneraltheyarenotapparentineverydaylife.Remember,wehadaproblemwith thebosonsof theweakforce.Toprotect

against infinities,weneedasymmetry tobepresent– thegroupSU(2) in thiscase. But we also know the W and Z bosons have mass, which breaks thatsymmetry. Freezing and crystallisation point to away out of this conundrum.Freezing a liquid into a crystal hides the rotational and translation symmetriesinherentinelectromagnetism,byarrangingtheatomsormoleculesofamaterialintoa lower-energystatewhichhappens tohavemoreorderand structure thatthehigher-energyliquidstate.Inaverysimilarway, theStandardModelhidesthesymmetriesinherentintheweakforce.Theenergyatwhichthishappensisavery significant longitude on our map, and it is this scale we have nowencountered aswe top the ridgeof themountainswehavebeen climbing andgazeoutacrosstheinteriorforestsandprairiesofcentralBosonia,rightacrosstotheeasterncoast.AsfarastheWandtheZ,andtherestoftheStandardModel,areconcerned,

‘everyday life’ corresponds to energies below this scale, behind us and to thewestonthemap.Backthere,theSU(2)symmetryoftheweakforcewashidden.Beyondthispoint,thingschange.Wehavereachedthe‘electroweaksymmetry-breakingscale’.

30

ElectroweakSymmetryBreaking

THE RIDGE OF mountains marking the Electroweak Symmetry Breaking Scalefollows a rift between continental plates which runs north–south across alllatitudesofourmap,evenintothesouthernhemisphere.Aswestarttodescendfromthepasswehavetaken,andintotheforestsbelowus,weexpectsurprises.Thesignificantchangesinphysicsat this longitudeaffectmanyexperiments

andmeasurements.Perhapstheclearestisintheprocessthatwelastencounteredon our train journeys around Hadron Island and the Isle of Quarks – thescatteringof electronsoff protons,which first revealed thepresenceof quarksinsidehadrons.In these experiments, a beam of leptons – usually electrons or positrons –

scatters off a hadron – usually a proton – and transfers so much energy andmomentum that the hadron shatters. Usually this is an electromagneticinteraction,meaningthatavirtualphotonisexchangedbetweentheelectronandaquark.However,electron–protoncollisionscanalsobemediatedbytheweakforce,

meaning theexchangeof theWor theZboson.Since theWcarriesaway theelectricchargeoftheelectron,inthoseeventstheemergingscatteredleptonisaneutrino.fn1Asmightbeexpected,these‘charged-current’eventsaremuchrarerthantheelectromagneticscatters,reflectingthefactthattheweakforceismuch…well,weaker,thantheelectromagneticforce.Astheenergyscaleincreases,andwemoveeastwards,theratesofthesetwo

differenttypesofscatteringconverge,until,aswedescend,theybecomeroughlyequal.Aswedescend the ridgeof theElectroweakSymmetryBreakingScale,theybecomeequal.And, ifwecanpull togetherwhatwehave learnedonourjourneyssofar,wealreadyknowenoughtounderstandwhy.In thewest, at lower energies,most of the difference in strength and range

betweenelectromagnetismandtheweakforceisduetothedifferentmassesofthe exchanged bosons. The photon has zero mass, while the W and Z havemasses of just below 1011 electrovolts – about a hundred times themass of ahydrogenatom.

The range and strength of the force depend on the mass of the exchangedparticlebecausetheparticlesintheseexchangesarevirtualanddonothavethecorrectmass.Infacttheycannothavethecorrectmass–thereisnowaythatanelectroncansuddenlyemitarealphoton,aWoraZ,andconserveenergy.Theonlyway thatcanwork is if theemittedparticlehas thewrongmass.Andwealready know that the further the virtual particle is from the correctmass, theloweristheprobabilityofitbeingemittedorexchanged.In the low energy interactions of Atom Land, and indeed everyday life

westward,themassiveWandZbosonsaremuchfurtherfromtheircorrectmassthan is the photon, so are much less likely to feature. This is why theelectromagneticforceisstronger,andmorecommonlyobserved.Gofurthereastthough,whereenergiesarehigher,andthedifferenceinmass

betweentheW,Zandphotonbecomeslessandlessrelevant,andtheweakforceandtheelectromagneticforcebecomeverysimilarinstrength.fn2Intermsofthetransportnetworkonourmap,beyondthisridgeofmountainsflyinghasbecomejust as commonas travellingby road,mainlybecause the roads are becomingmoredifficulttonegotiate.This serves tomake themass problem evenmore important. TheW andZ

massesplayanabsolutelycrucial role indetermining thecharacteristicsof theweak force, and we still have the problem that they ought to breakrenormalisation and let in the infinities. As indicated by clues on our frozenwindscreen, and the name of the Electroweak Symmetry Breaking Scalemountainswehavejustpassedthrough,abrokensymmetryisbehindthis.People suspected thismight be the case decades ago, before the rest of the

Standard Model was established and even before the Isle of Quarks wasdiscovered.Iffundamentalparticles–whatevertheymightturnouttobe–weretohavemass,somethinghadtobedone.Somethingstrangeanddifferenthastobegoingonintheforestswearenowentering.

31

HuntingtheHiggs

ATTHEBOTTOMofthemountainroad,wemakecampandasmallpartysetsofftoexploreonfoot,carefully,tostudythefloraandfaunaofthisnewland.Peeringfrombehindsomedensevegetation,acompellinganddramaticsightmeetsoureyes:somelargepredatorsarestalkingsomeevenlargergrazinganimals.Oneofourguidesrecognisesthespeciesandnarratesthesceneinahushedvoice:

Theweakbosonshaveformedasmallhuntingpack.Silently, stealthily, stalking through theundergrowth, theyapproach the

unsuspecting Goldstone bosons. One of the Goldstone bosons looks upsuddenly,perhapssensingsomething.The weak bosons pounce! Three of the Goldstone bosons are brought

down, messily devoured and digested. They will provide much neededlongitudinalpolarisation states for theweakbosons.But the fourth,morealert Goldstone boson escapes! Acquiring mass of its own, the spinlessparticlefleeseastwardstosafetyandhides,toliveanotherday…

ClearlyBosoniaisabrutalplace,butthatpieceofnaturalhistorycontainsthesolution to theproblemof theWandZmasses.The solution iswide-ranging,andrequiresafewsteps,afewadditionstotheStandardModelofphysicsthatwehavebeenexploring.To try to build a theorywhich can accommodate all this, the first step is a

dramaticone.Wemustinventanewquantumfieldpermeatingthewholeofourmap, thewholeof theuniverse,unlikeanyotherfieldwehaveencounteredsofar.Thisfieldcarriesnospin,andnocharge.For thesecondstep, this fieldhas tobesuch that ithasahiddensymmetry,

similartothefrozenwateronourwindscreenupinthemountains,butwithoneextra twist. Imagine thewatermolecules all carried amagnetic dipole. In theliquid, they will all point in different directions, and be continually knockingeachotherintodifferentalignmentsastheyjigglearoundenthusiastically.Thereisnooverallmagneticfield.Asthewatercoolsandfreezes,thejigglinglessens,andeventually themoleculeswill settledown to theextent thatall thedipoles

pointinthesamedirection,becausethatisthelowestenergyconfiguration.fn1Asthis cooling happens, an overallmagnetic field develops, because of the now-aligneddipoles.Thismagneticfieldbreaksthesymmetryofthesystemtoo–itchoosesaspecialdirectionfor thenorthandsouthpolesof themagneticfield,whenfortheliquidnosuchdirectionexisted.TodealwiththeWandZbosonmasses,wepostulateaquantumfieldintheuniversethatmimicsthisbehaviour.Whentheuniverseishotanddense,asymmetryispresentandthefieldhasanaveragevalueofzero.Aswereducetheenergy,downthroughtheelectroweaksymmetrybreakingscale,thefieldgetsanaveragevaluethatisnotzero.In the third step,wemake themassof the fundamental particles a property

they acquire by interaction with this non-zero value of the field. This can bearrangedmathematicallyforafield like this(withnospinandnocharge).Theadvantage we achieve by all of this, the goal of these three steps, is that thesymmetry isstillpresent in the theory,so the infinitiesarekeptatbay,but thesymmetryisabsentineverydaylife,sotheparticlescanhavemass.Thisisallveryneat.Alittlebittooneat.Whena symmetry ishidden like this, it leaves traces.Specifically, it leaves

newwaysof transmitting information, it leavesbehindnewparticles,masslessbosonsthatshouldbeseenwanderingaroundBosonia,thatshouldappearinthequantumloopsoftheStandardModel,andofwhichthereisnosignanywhere.Precisesurveysandmeasurementsleavenoroomforthemonourmap.Thisisabigproblemforourneatsymmetry-breakingtrick.There is even amathematical theorem, theGoldstoneTheorem,which says

that when a symmetry is hidden, such bosons must exist. In the physicalexampleswehavelookedat,youcanseethem.Onceacrystal,oraregulararrayof magnetic diploes, has been formed, there is a new way of transmittinginformation through the crystal. Displace an atom slightly from its site in thelattice,oradipole from its alignment, and theperturbationwill ripple throughthematerial.Thisripplecantransmitenergy,andinformation.Itistheclassicalanalogueofwhat,inthequantumfield,wouldbeanewmasslessboson.Onthefaceofit, thequantumfieldneededtogivemasstotheWandtheZ

givesrisetofoursuchmasslessbosons,andwehavecoveredenoughofthemaptoknowthattheyaren’tthere.Thisistheproblemthatwasbeinggrappledwithbyseveralphysicistsinthe1960s–notspecificallyfortheWandtheZ,whichweren’t known of then, but generally for the case of massive fundamentalparticles. In a nutshell the problem is: ifmassive bosons carry a force, then asymmetrymusthavebeenhidden.Butifasymmetryishidden,thereshouldbeGoldstonebosons.Sowherearethey?

Theanswerwasdiscoveredby twoBelgianphysicists,FrancoisEnglert andRobert Brout, and by Peter Higgs in Edinburgh, and it involves the kind ofcarnivorousbosonfoodchainwewitnessedinactiononourfirstforayintothewoodsabovetheElectroweakSymmetryBreakingScaleridge.Amasslessbosonthatcarriesasingleunitofspin,suchasthephotonorthe

gluon, has two possible orientations for its spin. The spin can point along itsdirectionofmotionoragainstit–thatdefinesthehelicity,whichwemetearlierwhendealingwithverydifferentparticles,theneutrinos.A massless particle has to travel at the speed of light, so the direction of

motionisalwayswelldefined.Thereisnoreferenceframeinwhichthebosonisstationary.Thiswouldalsobe true foramasslessWorZ.Butonce theyhavemass,itnolongerworks.Wheredoesthespinpointif thebosonisstationary?The upshot of this problem is that there needs to be an additional option formassivebosons, a so-called ‘longitudinal’ state, not present formassless ones,correspondingtothespinpointingperpendiculartothedirectionofmotionwhenitismoving.TheW and Z bosons appropriate three of theGoldstone bosons to provide

these longitudinal states,oneeach for theW+andW-, andone for theZ. In asense they devour them. Bosonia is a brutal place, althoughwatching all thishappen in the mathematics of the Standard Model is rather beautiful andinspiring,ratherlikeagorynaturalhistoryprogramme.The hunt for that more alert Goldstone boson, the one that got away, has

preoccupiedmuchofthelastcoupleofdecadesofparticlephysics.Itisascalarparticle–meaning itcarriesnospin, theonlysuch fundamentalparticle in theStandardModel–andithasnowacquiredmass.Itsexistenceispredictedbythetheoreticalmechanismwe have put together to explain electroweak symmetrybreaking. Ifwe find it inBosonia, then theweak force and those parts of ourmapmakesense.Ifnot,thenwehaveabigproblem.ItistheparticleweknowofastheHiggsboson.TrackingtheHiggsthroughtheundergrowthofBosonia,wehadseveralclues.

Precisemeasurementsof the topquark andWmasses at theTevatronproton–antiprotoncolliderinChicago,combinedwithevenmoreprecisemeasurementsof the Z bosons at CERN and at the Stanford Linear Collider in California,severelylimitedtheterritoryinwhichtheHiggsbosoncouldbefound.Again,ifit existed, virtual Higgs bosons should be contributing to already-measuredprocessesviaquantumloops.TheStandardModelalsopredictedexactlyhowaHiggsbosonshouldappear

in the experiment. It would be very short-lived, and would decay to otherStandardModel particles at different rates. These rates could be predicted for

anygivenmassoftheHiggsboson;butthemassitselfwasnotknownandnotpredicted, beyond the fact that it should be somewhere within reach of theelectroweaksymmetry-breakingscale.The final push, to cover all the territory on our map that might possibly

contain themissingHiggsbosonof theStandardModel, came from theLargeHadron Collider (LHC) at CERN. Colliding protons together head on atunprecedentedenergies, themachineis ineffect themostpowerfulmicroscopeeverbuilt.ItgivesusaccesstothewholeofBosoniaandbeyond.Andin2012theHiggswasindeedfinallyobserved,firstofalldecayingtopairsofphotonsand to pairs of virtualZbosons, but later in other decaymodes too. Itsmass,about125GeV,orabout130timesthemassoftheproton,putsitintheeasternreachesofBosonia,butwellwithintherangerequiredforittobeconsistentwiththeStandardModel.WeemergefromtheforestsofBosoniaandreachtheeastcoast.Higgsbosons

arebeingstudiedingreatdetailinthelivelyandbuzzingmaritimecitywefindhere; yet people are still thrilled to hear that we saw a Higgs in its naturalhabitat.Theamazingbosonicecosystemprobablystillhasthingstoteachus.Thisculminationofourjourneywasaremarkabletriumph,notonlyforusas

explorers but also for the predictive cartography of the theory. With theknowledgethattheHiggsbosonexists,wenowhaveatheorywhichallowstheWandZtohavemassesasobserved,butwhichstillcontainsthesymmetriesweneed to keep infinities at bay. This means the theory is capable of makingpredictions at energies far above the electroweak scale, far into the unknowneast.

EXPEDITIONVIII

FarEast

Taking stock –Dinner anda decision–The fascinationof theeast, storiesandspeculations–Jigsawsanda seamlessweb–Shipssettingsail.

32

WhyGo?

WE STANDON the eastern shore ofBosonia, gazing out at the oceanhorizon infrontofusandthinkingbackoverthelandswehaveexploredintheprecedingexpeditions.There is somedebate.Shouldwe, canwe, continue,or is this theend?Shouldweputourfeetupandstayhere?Thereisarathernice-lookingfishrestaurant off the promenade,with a terrace overlooking the beach.We find atablefordinner,anddiscussfutureplans.Over the aperitif and starters, we relive our recent travels and discoveries.

Predicting, hunting and finding the Higgs boson was a singular triumph. Aproblem in the theory led to thepostulationof a qualitativelynewanduniqueobject in nature: a fundamental particle with zero spin. Such triumphs occurmuch more rarely than you might think in physics: Dirac’s prediction ofantimatterprobablymatchesit,butnotmuchelsecomesclose.TheStandardModel stands tall, then.Thedifferentelementsofourmapall

connectupandfittogetherself-consistently.Atom Land has its orderly array of elements, each containing a nucleus

surroundedbyelectrons;quantumparticlesboundtogetherbythesophisticatedroadnetworkofelectromagnetism.Those electrons abide on the Isle of Leptons, alongwith their two easterly

allies,Muon andTau, also connected by road, plus theNeutrino Sector awaydowntothesouthandwest,accessibleonlybyair,theweakforce,which,albeittenuously,connectsallthelandswecomeacross.East of Atom Land, we entered the nucleus, and Hadron Island. Protons,

neutronsandtheotherhadronsareconnectedbythesophisticatedrailnetworkofthe strong force, which also takes us into the Isle of Quarks, with its Down,Strangeandtherest,withtheirprimedairportsnearby.And inBosoniawemadesenseof the transportnetworks,andhunteddown

theHiggsneartheElectroweakSymmetry-BreakingScale.TheremightbeabitofawildernessleftoverintheNeutrinoSector,butpretty

much everything works.Without the discovery of the Higgs, our map wouldhave just been a rough outline, and would definitely have failed around the

mountainousElectroweakSymmetryBreakingScaleridge.WiththeHiggs,thesymmetries hang together, infinities are vanquished, and yet the fundamentalparticleshavemass.Withasmallnumberoffundamentalobjectsandprinciples,the Standard Model describes and predicts an enormous variety of physicalphenomena, over energy scales ranging from zero up to several 1012electronvoltsandpotentiallyfarbeyond,farintotheeastofourmap.Thereisamoodamongstsomeofourlittlebandthatthisisenough.Whyexplorefurther?Asthemaincoursearrives,othersarguebackstronglythatweshouldnotbe

toosmugandcomplacentaboutthepowerandsubtletyoftheStandardModel,and neither shouldwe despair that there is nothing left to discover. There aresomeimportantfactorstoconsider.Itisworthrememberingthatouroverallmapfails entirely to incorporate one of the fundamental forces.Aswe sawon ourdigression, gravity is described by the general theory of relativity, and in thatcontextitisaconsequenceofthecurvatureofspace–timeratherthanaforcelikethose in theStandardModel,mediated bybosons.For the regions covered byourmap, this isgoodenough.It isevenpossible tomakeaquantumtheoryofgravity thatworks in theseregions,although it isnot renormalisable,whichaswesawonour last tripmeans it isnotprotectedagainst infinity,soweshouldexpect trouble. Far enough east, at high enough energies, trouble does indeedhappen.BecausegravityisnotproperlyincludedintheStandardModel,ifwewereto

go far enough east, there is definitely a distance scale, corresponding to anenergyofaround1027eV,beyondwhichthingsdefinitelygowrong.ThisisthePlanck scale. Gravity at this scale becomes as strong as the other forces.Singularitiesandinfinitiesbreakoutallovertheplace,andwehavenowayofunderstanding, or predicting, what might happen. This is a very significantfailureintheambitiontodescribenaturalphenomenainasingleframework.TheStandardModel is very clearly not a theory of everything, even if it co-optsGeneralRelativityasapartner.Worse, even at lower energies, the partnership between theStandardModel

andGeneralRelativityisinadequate.The amazing breakthrough of gravity is that the same theory describes the

wayobjects fall to thegroundon theEarthaswellas theorbitsof theplanetsandmoons inspace.This isaclassicsuccessofphysics–asinglesetofrulesdescribing awide rangeof phenomena.Newton’s gravitywas a breakthrough,thoughyouneedGeneralRelativitytogettheplanetaryorbitsexactlyright(andto predict the timing and orbit of a satellite well enough to make the GlobalPositioningSystemworkaccurately).

As accurate measurements of more distant astrophysical objects – stars,galaxies, clusters of galaxies – aremade, the expectation is that our theory ofgravityshouldworkforthemtoo.Specifically,lookattheorbitofstarsaroundthecentresofgalaxies,comparedtotheorbitofplanetsaroundthecentreoftheSolarSystem.ForeachplanetaryorbitintheSolarSystem,thereisapredictedspeedfor theorbit.Thishas tobethecase,becausethegravitationalattractionbetween the Sun and the planet has to exactly match the required centripetalacceleration of the orbit. The same applies to stars orbiting the centre of thegalaxy.IntheSolarSystem,GeneralRelativitygetsitright.Butforthestarsinthegalaxy, theanswerdoesnotmatch theobservation.Thestarsare travellingfartoofast–theirorbitalspeedsaretoohigh.Thespeedofthestarshasbeenmeasuredaccuratelyusingthesametechnique

ofspectroscopyencounteredinourexpeditionthroughAtomLand.Atomsgiveoff, or absorb, light in characteristic patterns, dictated by the jumps in energythat their electrons are allowed to make. These patterns allow us to usespectroscopytoidentifytheelementsinstars,aswesawwhenexploringAtomLand.Butwecanalsoobservethatsometimestheyareshifted,becausethestariseitherrecedingorapproaching.Justaswiththeclassicexampleofapassingsiren, approaching makes the frequency higher – blue shift, for light – andrecedingmakesitlower–redshift,whichismoreusualasonaveragestarsarereceding.Precisemeasurementsoftherotationalspeedofgalaxies,madebytheastronomer Vera Rubin and her team using this technique, convinced peoplethereisabigproblem.Thestarsaregoingtoofast,andthegalaxiesoughttoflyapart.Therearetwowaysofsolvingthisconundrum.Eitherourtheoryofgravityis

wrong,orourestimateofthemassofthegalaxiesiswrong.Ifthemassofthegalaxiesweretobemuchbigger,byafactoroffourorfive

on average, than the mass of stars and gases that we can see, then thecalculationscouldworkagain.Thatwouldexplainthespeedofthestars.Thoughthemissingmass,ifitisthere,doesn’tseemtobemadeofanyknownparticleintheStandardModel.Asaplace-holder,wecall it ‘DarkMatter’.Whatever thesolution,theproblemisagoodargumenttocarryonexploring.Anothergravity-relatedproblemissomethingcurrentlylabelledDarkEnergy.

Frommeasurementsoftheredshiftandbrightnessofsupernovae,itseemsthatnotonlyistheuniverseexpandingoutwardfromtheBigBang,butthattherateofexpansionisincreasing.Gravityonitsownwouldslowtheexpansion,asthestarsandgalaxiesattracteachother.Soanewingredientisneededtoexplaintheacceleration.Wedon’tknowwhatthisnewingredientis,butDarkEnergyisthenamewe give to our ignorance. ‘Dark’ presumably comes from analogywith

DarkMatterfn1and‘Energy’comesfromthefactthatitneedstobesomeformofeffectiveenergydensitywhichisconstantthroughoutallspace(unlikematterorphotons,whichgetmorespreadoutasspaceexpands).ThequantumloopsoftheStandard Model actually predict the existence of a vacuum energy like this.Unfortunately itgets theanswerwrongbya factorof10120– ten followedby120zeroes,anumbersobigIamnotevengoingtotrytospellitoutinwords.Itissuchanenormousnumberthatevensomecosmologistshavetroubleignoringit.Again,maybetheanswerliestotheeast.The discussion continues as we eat, assembling the possible reasons for

exploring furthereast.Another reason for further exploration isbrought to thetableasthedessertsarrive.Whataboutmatterandantimatter?AsweexploredtheIsleofQuarkswediscoveredthatthesymmetrybetween

matter and antimatter is broken,meaning there is a real difference between aworldmadeofmatterandonemadeofantimatter.However,thetinyviolationsofmatter–antimattersymmetrythatweknowofseemfartoosmalltoexplaintheabsolutelygrossasymmetryweseearoundus.Matteriscommon,andantimatteris extremely rare. Expeditions into theNeutrino Sector of the Isle of Leptonsmay show up a source of matter–antimatter asymmetry that could be fittedwithin theStandardModel.Butunless there is somethingnewgoingon there,beyondtheStandardModel,thissourceofasymmetryalsolookstoosmall.Anexampleof‘somethingbeyondtheStandardModel’whichcouldbediscoveredthere would be that the neutrinos turn out to be their own antiparticles, apossibilitywealreadydiscussedonthatexpedition.Suchadiscoverywouldalsohave implications for the far east of our map, meaning there might besupermassiveneutrinostobefoundoutthere.Afinal,verygeneralargumentisbroughtupovercoffees.Itisapparentfrom

our explorations so far that, elegant and economical though it is compared towhatwentbefore, theStandardModelcontains rathera lotofparameterswithseeminglyarbitrary,butsuggestive,values.For example, themasses of the particles are distributed over a huge range,

from theneutrinos in thewest to the topquark in theeast (not tomention themassless photon, gluon and possible graviton). Are they really randomlyscattered,or is thereapattern in there somewhere?Thereare somesuggestiverelationships – for example, the sum or the squares of all the boson masses(Higgs,W,Z)isroughlythesameasthesumofthesquaresofall thefermionmasses(quarksandleptons).Isthatjustacoincidence,orisitaclue?The Higgs mass is especially troubling. We know all particles get infinite

contributions to their masses from quantum loops, and those are removed byinsertingthemeasuredmassintotheequations,atechniquewhichreliesonthe

symmetrybehindtheforcetoprotectitfrominfinities.ButwiththeHiggsbosonmass,becauseofthefactthatithaszerospin,theloopcorrectionsareenormous.Noinfinities,theprotectionstillworks,butifyouwanttheHiggsmasstohaveareasonable value both at the electroweak scale (which is where it is) andonwards into the east to another energy scale, say the Planck scale, thecancellation of those corrections has to be ridiculously ‘fine-tuned’. It is asthough the Higgs balances on a knife-edge over many orders of magnitude,where a slip to either side would make nonsense of the Standard Model. Afavourite analogy is a bank account with credits and debits (the quantumcorrections)ofbillionsofpoundsoccurringseeminglyrandomlythroughoutthemonth,yetonthelastdayofeachmonththeaccountmagicallycontainsexactly£125.Thiswouldseemtobetoomuchofacoincidence.Theremustsurelybeanaccountantpayingattention–or, inthecaseofphysics,maybeabiggertheorypullingthestringsoftheStandardModel.Even the number of generations of matter looks suspicious. Just the first

generationwouldseemtobeperfectlyadequatetomakeupalltheelements.Aswe saw, three is theminimum number to allow a real distinction to bemadebetween matter and antimatter, which seems significant. But perhaps we justhaven’texploredfarenougheast.Maybetherearefour,fiveorevenaninfinitenumberofgenerations?Tothereliefofthewaiters,wepayourbillsandleavetherestaurant.Butthe

discussiondoesnotdiedownaswestrollalong theseafrontback towardsourhotel.

33

CluesandConstraints

THECOMMENTABOUTextragenerationsofmatter,madeaswelefttherestaurant,leads toa robust response.While it isnot easy to ruleout anything if it is farenougheastward,wearenotincompleteignoranceeither,evenifwehavenotvisitedit.Wedoknowthatanypossiblefurthergenerationsofmattercannotbevery similar to the first three – specificallywe know that they do not containlow-massneutrinos,astheotherthreedo.WeknowthisfromourdetailedexplorationsofBosonia,especiallystudiesof

the Z boson, produced in electron–positron collisions at the Large ElectronPositronCollideratCERN,andtheStanfordLinearColliderinCalifornia.ThoseexperimentsproducedtheZbosonintheannihilationofelectronsand

positrons.TheZbosonwilldecayveryrapidly,intolessmassiveparticles,sowedon’tdetectitdirectly:itisoneofthosevirtualparticlesthatdonothavetohaveexactlytherightmass.However,arealZwouldhaveamassof91GeV,andifyoutuneupyourbeamenergiesto45.5GeVeach,thecentre-of-massenergyisjustrighttoproducerealZbosons.Thisiswhattheexperimentsdid,andatthatvalue,thereisabigpeakintheprobabilityoftheelectron–positronannihilation,justbecausetheZexists.Still,theZcanbevirtualtoo,inwhichcaseitdoesnothavetohaveexactly

the right mass, and if the beam energies are moved gradually away from theoptimalvalue,theprobabilitydropsrelativelyslowly–itdoesnotfallinstantlyto zero. Virtual Z bosons can still be exchanged. The rate at which theprobability drops on either side of the peak defines what we call the ‘decaywidth’oftheZ.The decay width can be thought of as an uncertainty in mass, or energy.

Heisenberg’suncertaintyprincipleisreasonablywellknownforstatingthatwecannot know both the position and themomentum of a particlewith absolutecertainty.Themorepreciselyweknowthemomentum,thelesscertainwecanbeof theposition,andviceversa.Thesameprincipleapplies to timeandenergy.Theuncertaintyinenergyisrelatedtotheuncertaintyintime.Iftheuncertaintyintimeisshort,theenergycannotbepreciselyknown,whereasiftheenergyis

preciselyknown, thecorresponding time is long.What thismeans for theZ isthat if its lifetime is short, its decay width is large. (For stable particles, thelifetime is infinitely long, and the decaywidth is zero – they have a definitemass.)Howdoes this tell us anything about the number of generations? It does so

becausetherateatwhichtheZbosondecaysdependsonhowmanyparticlesitcandecayto.SometimestheZdecaystoneutrinos,whichwereinvisibletothedetectorsatCERNandStanford.ButthenumberoftypesofneutrinotheZcandecaytoaffectsitslifetime,andthusitswidth.Themoreneutrinos,thefasteritdecays,andthebroaderthewidth.Andthedecaywidthcanbemeasuredusingvisibleparticles–electrons,muonsorquarks.Itisfromthismeasurementthatweknowthattherearethree,andonlythree,

types of neutrino, and thus only three generations. Of course, that is on theassumption thatallneutrinos interact in thesamewaywith theZ.Therecouldalwaysbemoregenerationswithweirdneutrinos:almostanythingcanhappenout east.But anynewgenerationsofmatterwouldnot really be copies of thethreeweknowof;theywouldbeverydifferentindeed.More apparently arbitrary features can be seen in the StandardModel. For

example,theoreticallyitwouldbeveryeasyforthestronginteractiontoviolatethematter–antimattersymmetry,but itdoesnot.Whyis that?Issomethingwedon’tknowaboutforcingthestrongforcetorespectthissymmetry?It is very tempting to think that these arbitrary features and parameters are

fixed inevitably by some so-far-unknown symmetry or principle inherent in alarger theory, ofwhich the StandardModel is just a part, inwhich ourwholemapisjustthewesternregionofamuchbiggerlandscape.Wearetiredbynow.Manyweeksonthemovehavetakentheirtoll,ashasa

gooddinnerandaheateddiscussion.Therearedefinitelygoodreasonstothinkthat thereare importantand interestingdiscoveriesstill tobemade in theeast,butthereisnoconsensusonwhereexactlytogo,whattolookforfirst,orhowtotravel.Weresolve towaitawhile in this ratherpleasant seaside townforotherexplorers to report, before we plan new expeditions. We will frequent theharbour bars and pubs, and listen to stories. And while we do that, thecartographersinourgroupwillhavefunimaginingwhatmightbeoutthere.Thefinalexpeditionofthisguideisanexpeditionoftheimagination.Whatmonstersmightliebeyondourcurrentmap,andwhatprinciples,ifany,mightguideusoutthere?

34

SeaMonstersandDarkMatters

THEORETICALPHYSICISTSARE the imaginativecartographersofphysics.Theyarethe fillers-in-of-gaps-with-dragons, the extrapolators of hint and rumour, andextravagant-tale-tellersoftheoceanports.GiventhenumberofopenquestionstheStandardModelleavesthemtochewon,itisnosurprisethattheeasternseasof the imagination are populated with a menagerie of fantastical beasts, ofvaryingdegreesofplausibility.Inthis‘expedition’wewillstayinthepubsalongthe shoreline and hearwhat they have to say, in the hope that itmay provideguidanceforfuturetravels.Thebestpubisrightonthedockside,ontheeasternshoresofBosonia.There

aresometelescopesofvariablequalityinthewindows,andalotofdrinkbehindthedark,oakbar.Theoristsloungeorslouchoncouchesandbenches,chattingtoeachotherandcomparingtales.Occasionallyaseafarer,oratleastsomeonewhoclaims to have been to sea, staggers in, and is immediately surrounded, pliedwith drinks, and pumped for any information they may have about the landsbeyondthehorizon.Many of the stories, dreams and even (later in the evenings) songs revolve

aroundthefactwediscussedoverdinnerthateitherourunderstandingofgravityiswrong,orthemajorityofthematterintheuniverseissomeunknownformofDarkMatter–probablysomeparticlewhichliesbeyondtheStandardModel.Peopleexploreboththosepossibilities,butcurrentlythemostpopularoption

isthesecond–DarkMatter.WewoulddearlyliketocomeacrossDarkMatterinourjourneyeastwards,andthereareanumberofwaysthiscouldhappen.There is a chance that the LHC will manage to produce Dark Matter and

(indirectly)observeit.Anyobservationwillhavetobeindirect,becausebyitsnaturetheDarkMatterwillnotinteractwiththedetectorssurroundingthepointswheretheprotonscollide.However,becausethedetectorssurroundthecollisionpoint, if something energetic and invisible is produced, they will measure amomentumimbalance.ThatwouldbetraythepresenceofDarkMatter,muchasthemissingmomentuminbetadecaysledPaulitopostulatetheexistenceoftheneutrino, all that way backwest. Neutrinos are also produced at the LHC, of

course, and like Dark Matter they also lead to apparent missing momentum.However, theStandardModel canpredict howmanyof those collision eventsthereshouldbe,andwhattheyshouldlooklike.AnyanomaliescouldbeasignofDarkMatterproduction.One thing we know about Dark Matter is that if it exists, it interacts

gravitationally.Thereforeitprobablycollectstogethernearlargemasses,suchastheblackholesatthecentreofgalaxies,orevenintheheartsofstars.Intheseregionsof relativelyhighDarkMatterdensity, itmaybe thatoccasionally twoDarkMatterparticlesmeetand,dependingonwhatkindofDarkMattertheyaremade of, annihilate and produce high-energy photons, neutrinos or otherStandard Model particles. There are telescopes looking for signs of theseproductsofDarkMatterannihilation,includinginstrumentsonsatellites,wherethe Earth’s atmosphere doesn’t confuse matters. There are even experimentswhichusetheiceofAntarcticaasaneutrinodetector–hopingtospottherareoccasions when a very-high-energy neutrino collides with water molecules,convertingintoamuonoranelectronandeventuallyradiatinglight,radiowavesorotherelectromagneticwavelengths.Sensitiveexperimentsarealsobuiltunderground,awayfromtheinfluenceof

cosmicrays,searchingforDarkMatterinteractingdirectlywiththedetector.Weknow thatbillionsofunseenparticlespass throughuseverymoment–wearebathedinneutrinosfromtheSun,andinlow-energyphotonsleftoverfromtheBigBang.Both types of particle are vital ingredients in our understanding ofphysicsandtheuniverse,andbothhavebeenmeasured–eventually–byhighlyspecialiseddetectors. IfDarkMatter is there, itmay also interactwithnormalmatterviatheweakforceasitpassesthroughtheEarth–orastheEarthpassesthroughthecloudofDarkMatterparticlescentredonourgalaxy.In this case, therewould be a generic kind ofDarkMatter particle called a

WIMP–WeaklyInteractingMassiveParticle.ThisisalsothemostlikelytypeofDarkMattertobeseenattheLHC.WIMPspresentmoreofachallengetodetectthanneutrinos,partlybecausetheyareslower,andpartlybecausewedon’tknowwhattheyreallyare,so(unlikeneutrinos)theStandardModeldoesn’ttellustheinteraction probability. So the experiments have to do their best to scan anunknownparameterspace,usuallymappedoutintermsoftheWIMPmassandthechancesofitinteractingwithanatomicnucleus.Oneof themost sensitive experiment scanning this parameter space to date

wascalledLUX(LargeUndergroundXenon).fn1LUXwasdesignedtomeasureboth the light and electrons thatwould be produced if aDarkMatter particleglancedoffthenucleusofaxenonatom.Itdidnotseeanything,whichisabitofadisappointment.However,moresensitiveexperimentsareunderconstruction.

Thevoyagecontinues.And thenegativeornull resultsarenotworthless: theyare filling regions of the map which were previously blank. True, they aregenerally filling in themapwith featureless seascape,but even so, at leastweknowtherearenodragonsthere.In importantways, the significanceofanull result like thisdependsupona

robust theoretical framework. If there isno theoreticalexpectation to test, thensometimesanullresultreallytellsyouverylittle,anditmaybeyoujustdidaboring experiment. You believed a drunken sailor with a reputation for crazystories, you left the pub and sailed out there, and confirmed he was talkingnonsense.Frustrating,especiallyifittookalotoftimeandmoney.Butwitharobustframework–acrediblestoryteller–anullresultcanbevery

important.ThiswasthecasewhentheLHCwassearchingfortheHiggsboson,for example. If the boson had not been found, that would have broken theStandardModel,averyrobusttheorywhichhassurvivedfordecades,withmanyprecise predictions to its credit. So a null result would in fact have beenextremelyinteresting.

35

Supersymmetry

THERE ISA particularlycommonand–at leastuntil recently–widelybelievedseafarers’talewhichmaybeheardeverywherefromthemostnoisomeseafrontdives to the elegant drawing rooms of the ship-owning aristocracy. This is‘supersymmetry’. It is a seductive story. It offersmany things to the excitabletraveller,andoneofthethingsitoffersisDarkMatter.Supersymmetry builds on the extraordinary success, seen throughout our

travels, of symmetry principles in physics. It does this by introducing anothersymmetry,thistimebetweenthebosonswhichcarrytheforces,andthefermionswhich make up matter. For every spin-one boson, there is a spin-half‘superpartner’–aphotinoforthephoton,agluinoforthegluon,azinofortheZandtheratherunfortunatewinofortheWboson.fn1Thefermionshavespin-zeropartners–selectrons,smuons,squarksandsoon.Supersymmetry cannot be an exact symmetry, because we know that (for

example)ifaselectronexists, itsmassisnotthesameastheelectronmass.Infact nearly all these new particles have to be far enough east – that is, highenoughinmass–thatwehaven’tbeenabletofindthemyet.Anythatarelowermasshavetobedeeplyhiddeninmountainsor junglessomewhereelseonourmap. That means that supersymmetry has to be at least slightly broken, orhidden.Butweknowthatevenhiddensymmetriescanbeveryimportant.One advantage of supersymmetry is that it solves the ‘fine-tuning’ problem

with theHiggsmass.Remember the bank accountwith big credits and debitsthat alwaysmysteriouslycancelledout to£125? In thequantumcorrections totheHiggsmass,eachfermionisadebitandeachbosonisacredit.Therefore,ifyou have an equal number of bosons and otherwise identical fermions,cancellation is guaranteed. The account comes to zero. Supersymmetry is thehidden accountant. Even though it has to be hidden, if themasses of the newsupersymmetric particle are not too far away east, the cancellation is goodenoughtosolvetheproblemwiththeHiggsquantumcorrections.Supersymmetryisn’treallyasingletheory,itisasymmetrywhichcanbeused

tobuildmanydifferenttheories.That’sonereasonitfeaturesinsomanyofthe

rumours we hear on the dockside. Inmany of these theories, supersymmetricparticles carry a conserved quantity, called R-parity. Conservation of R-parityhas the consequence that supersymmetric particles can only decay into othersupersymmetric particles, and that in turn means that the lowest masssupersymmetricparticle (sparticle, youguessed it)mustbe stable.Thatmeanslotsof themshouldbe leftoverafter theBigBang,andthatmakes themgoodcandidatesforDarkMatterWIMPs.Unfortunately, at the time of writing, no sparticles have been found. For

severalyears, supersymmetry theoristshavebeensayingwe justneed tosailalittlefurthereastandtheywillshowup.TheLHCopenedupanotherbigareaofthe map, and there were high hopes that sparticles would be discovered.However,nonehasbeenseensofar.Maybewejustneedtogostillfurthereast.Ormaybeweneedtolookforothersolutions,tolistentootherstories.

36

IntoAnotherDimension?

ONCUE,ANOTHER travellerstaggersintothebar,shakingthesea-sprayfromhershoulder-length, straw-coloured hair and orders a large gin. She will relateanother common yarn, not quite as respectable as supersymmetry but told bysomeloudandconvincingtravellers–thetaleofextradimensions.Thisistheideathatspacedoesn’tjusthavethethreedimensionsthatwecan

see, but several more, which are only accessible at high energies. Extradimensionsarereallyodd,inthattheyarefairlyeasytodescribeinmathematics,butareprettymuchimpossibletoimagine.Intheequationsofphysicsweoftencount over three dimensions of space, essentially length, breadth and depth.Momentum has three components, for example, which a physicist wouldnormally labelwithx,y and z, or simply1, 2 and3.Each component tells ushow fast an object is moving in one of those three dimensions. For somepurposes we can even count to four dimensions, treating time as the fourth.Mathematicallyitiseasyenoughtoextendthattocountoverfive,sixormore–just keep counting. From a mathematical point of view, it would seem a bitarbitraryifthingsonlyworkedwiththreeorfourandstopped.Mathematics deals with abstract concepts and doesn’t care about physical

reality,ofcourse.Physicscares.Fromthepointofviewofphysics,whatwouldextradimensionsmeanforthenaturalworld?Theonlywayofgettinganyideaistoreducethenumberofdimensionsandworkbyanalogy.So for example, imagine that the whole three-dimensional universe is

embedded in some bigger, multidimensional space. To picture this, I have todropourthree-dimensionaluniversedownadimensiontotwo,soitisasortofsurface,amembrane–orbraneforshort–inathree-dimensional‘bulk’space.Oneoftheideasfloatingaroundthedocksideisthatgravityspreadsoutoveralldimensions,whiletheStandardModelisconfinedtoalower-dimensionalbrane.Gravityisthenverydilutedandthatexplainsitsweaknesscomparedtotheotherforces.In some tales of extra dimensions, they are very tiny and curled up. The

travellerstellustoimaginewaves,vibrationsinastring.Asfarasthesewaves

areconcerned,thestringisone-dimensional,becausethethicknessofthestringis negligible compared to the wavelength of the waves. But as the waves gohigher in energy they go smaller in wavelength, and at some point thewavelengthiscomparabletothethicknessofthestring.Atthatpointwavescangoaroundthestring,notjustalongit–anewdimensionhasopenedup.Inmoststories,thishappenssoimpossiblyfareastthatourfastestshipscanneverhopetoreachit.Thoughsomeofthebolderseafarerswhojointhestory-tellingassureusthatsomethingsimilarcouldhappenatahigh-energycollider,muchnearertohome.Modelswithadditionalspace–timedimensionswereevenproposedasaway

toavoidtheneedforaHiggsboson,beforeitwasdiscovered.AlltheproblemswithWandZmassesthatariseintheStandardModel,andwhichrequiredtheHiggsbosontoexistatLHCenergies,wouldhavebeensubsumedintotheotherchanges to physicswhich happenedwhenwe started to be able to resolve theextra dimensions. There would be a need for all the electroweak symmetry-breakingstuff,andthereforenoHiggs.One manifestation of the ‘changes to physics’ that such extra dimensions

couldcausewouldbetheproductionof‘blackholes’.Aswetraveleast,wearegoing to higher energies and shorter distances, concentrating more and moreenergy into a smaller and smaller space. The point of particle colliders, themachinesthatgetusthere,isthattheyconcentrateenergylikethis.AprotonintheLHChasatinyenergycomparedtoaping-pongball.Ifallthekineticenergyof an LHC protonwere transferred to a ping-pong ball, the ball wouldmoveabout1mmeverytenseconds.However,thereareabout1023protonsinaping-pongball,sothat’squiteimpressivereallywhenyouthinkaboutit.If enough energy is concentrated in one place, then the gravitational field

close to it becomes very strong, eventually even stronger than the StandardModelforces.Strongenough,eventually,topreventevenlightescapingfromitsgrip.This iswhenablackhole is formed; the super-highdensityofmass andenergywarpsspaceandtimesomuchthatnothingcanescape.Theconcentrationofenergyrequiredtodothisinathree-dimensionaluniverseiswaybeyondthecapability of theLHC.But in a universewith extra dimensions, thismight bepossible.fn1NowweknowtherereallyisaHiggsboson,themotivationforthiskindofmodelissomewhatreduced,buttherearestilloldsea-handswhotellthetales,and theycan’tbecompletelydismissed.However,wewillmoveonnowandlistenintoanotheragitatedgroup,clusteredaroundatablebythefireplace.

37

OvertheEdge

THISECCENTRICGROUParetellingstoriesofactionouteastthatisstillwithintheStandardModel.ArmedwiththenewlydiscoveredHiggsboson,theStandardModelcannow

makepredictionsformulti-TeVscalephysics–1012eVandbeyond,wellabovethe electroweak symmetry-breaking scale. Making these predictions in thisqualitativelynewregimebringsnewchallengesthough.As the energy of a collision increases, so do the possibilities for the

productionofhigh-energyobjectssuchashigh-momentumleptonsandphotons.Increasing the energy far above the electroweak scalemeans that objectswithmasses around that scale can be produced with high energies, and in highnumbers.SeveraltopquarksandW,ZorHiggsbosonsmaybeproducedinthesame collision – something we have never seen before. Describing suchcollisions with any degree of precision requires innovative calculationaltechniques.Given that the necessary theoretical advances aremade (and they are being

made), the experiments can make precise and detailed measurements to testthem. The number, reach and precision will increase as long as the LHCcontinuestoprovidedata.And the Standard Model itself may contain some fantastical beasts. An

exampleofoneoftheseisthesphaleron.SphaleronsareaveryexoticpredictionoftheStandardModel,notsomething

beyondit.AndnowweknowtheHiggsexists,weknowtheyshouldexisttoo.Weevenknowtheirlongitude,roughly.Theyoughttolieatabout1012eV.Thisis higher than we can observe in LHC collisions, because even though theproton–protoncollisionenergyishigherthanthat,theenergyofthecollisionisshared betweenmany quarks and gluons, and so not all of it is available formakingnewobjects. (Remember,collidersareallaboutconcentratingenergy).Buttheenergyatwhichsphaleronsshouldappearisnotridiculouslyhigh.To get an idea of what a sphaleron is, you have to think of the way we

describe quantum particles. We use something called ‘perturbation theory’,

where we take something which is approximately correct and add smallcorrections to improve it, piecebypiece.We first cameacross this ideawhenimaging one, two or more photons being exchanged between particles. Butperturbationtheoryhasitslimits.Trythis.Grabasoupbowlwitharoundedbasefrom behind the bar. Place an olive in the bottom of the bowl.fn1 Imagine theemptyuniverse,withnoenergy,istheolive,sittingatthebottomofthebowl.Addingabitofenergycorrespondstoshakingthebowlslightlyfromsideto

side.Theolivewill rollup thesideof thebowlabit. If theenergy issmall, itwill roll back down again, go up the other side, and oscillate like that. Theseoscillationscorrespondtoparticlesinperturbationtheory,ripplingalongthroughspace– time in theirmerryquantumway.Addingabit of energy like this is asmall perturbation on the ‘still olive’ scenario, andwe can calculate its effectwithperturbationtheory.Butifyouaddalotofenergy,theolivecanzipovertherimofthebowl,into

another bowl which we placed next to it to avoid olive-related chaos. Thatphenomenon,ofleapingoverthehillfromonebowltothenext,isasphaleron,sortof.It’sapointatwhichperturbationtheorybreaksdown.Sphaleronswouldhavebeenaroundintheearlyuniverse,becausetheenergy

densitywasveryhighthen.Andtheyseemtohaveplayedacrucialroleinthecreationofmatterasweknowit.There are various things that don’t change in perturbation theory, quantities

that are conserved. One thing, in our olive-in-a-bowl universe, is the averagepositionoftheolive.Itspendsasmuchtimeononesideofthebowlasontheother;theaverageisthebottomofthebowl.Butiftheolivesphaleronsitswayoverthelipintothenextbowl,itsaveragepositionhasmoved–tothecentreofthenextbowl.Theconservationlawhasbeenviolated.Sphaleronsintheearlyuniverseviolateconservationlawstoo,andonethattheyviolateisthenumberofparticles. They can add more quarks and leptons to the universe. This is anessentialpartofhowthestuffwearemadeofgothereatall.There are other exotica which are sometimes recounted around the less

respectablediveson thedockfront,mostof thembeyondtheStandardModel,somewithinitbutweirdandsofarunobserved.Wedowelltorememberinthecold light of day that there is no direct experimental evidence that any of theexotic theories expounded in the dockside pubs is correct. They are all juststories – dreams, or nightmares. But this does not mean they are completelywild,orcompletelyworthless.Thefactthattheoriessuchassupersymmetry,forexample,canconnectsuch

disparateobservationsas therateofneutrinosmeasured in theAntarctic to theresults of experiments at the LHC to the observations of galactic rotations,

showstheirusefulnessasanaidtoexploration.Beingabletodisplaydatafromsuch different experiments on the same graph, to discuss them in the samecontextandmeasurethemagainstacommonscale,isimportantingaugingtheirrelativesensitivitytotheunknown,andinhuntingforinconsistencies–or,inthecaseof adiscovery, for consistency. In the absenceofobservationaldata, it isterriblyhardtodistinguish,inthesaloonbarofourdocksidepub,theramblingsof fantasists from the reasonable guesses of intelligent explorers. Drawing adistinctionisimportantifyouaretryingtodecidehowmuchtimeandmoneytoput intochasingdownthefactsbehindastory.Forafinalcoupleofwild talesfrom the edgesof themap,we return togravity, and also illustrate oneof thewaysinwhichsuchdecisionsaremade.

38

AFifthForce

ATENACIOUSDREAMER,proppedupagainstapillarbythepooltable,remindsusthat it is alsopossible thatwhatwe thinkof as fundamental forces just aren’t.The quarks, leptons and bosons of the Standard Model may contain smallerconstituents, just as the atoms of the PeriodicTable turned out to bemade ofother things.Thesolutions to theoutstandingproblemsof theStandardModelmightthenbefoundintheinteractionsofthesenew,evensmaller,pieces.Again,this was partly motivated as a way to avoid the need for a Higgs boson.However, therearestillversionsaroundinwhichtheHiggstooisacompositeparticle,madeupofevensmallerthings.Sucha scenariowould involvenew fundamental forces, andprobablymean

that the forceswe currently think of as fundamental are not, but emerge fromsomehigher-energy,smaller-distancetheorywhichlivesoutinthefareast.Therearealsoideasinwhichthecurrentforcesremain,butweaddanewone,

or change an existing one. Since gravity is a common thread inmany of theproblemswithphysics–DarkMatter,DarkEnergy,thelackofquantumgravityinthefirstplace–itisveryreasonabletoexpectthatGeneralRelativityneedstobemodifiedinsomeway.That’sathoughtthathasoccurredtomanyphysicists.However,GeneralRelativityissosubtle,andso,well,general,thatreplacingit,orevensuccessfullytweakingit,isaveryhardthingtodo.Still,physicistsarepersistent,andtherearenewideascomingforwardallthe

time. One possible tweak is to postulate a new particle which carries a ‘fifthforce’ontopofelectromagnetism,theweakandstronginteractions,andgravity.Maybeoutinthefareastthereissomeotherformoftransport,beyondourroad,railandairways,anddistinctfromgravity?ToexplainDarkEnergy, this forcehas toaffectallmatter–asgravity itself

does – and operate over large distances. Such forces have been looked foralready, and if they affect the motion of the planets in the Solar System, forexample, they have to be enormouslymore feeble than gravity, otherwise wewouldhaveseenthemalready.Butiftheyareenormouslymorefeeblethanthe

gravitationalforcebetweenstarsandgalaxies,theywon’tmakeanydifferencetotheDarkEnergyorDarkMatterproblems,sothat’sawasteoftime.Onepossibleway around this conundrum is a process called ‘screening’, in

which thestrengthofa forcedependsupon theenvironment it is in. It isevenpossible that such a force is screened by matter itself. It is possible to buildtheorieswhereby indenseregionsof theuniverse (like theEarth, for instance)theforcecanbehidden,whileinemptyspacetheforcecanoperate.InthecaseoftheDarkEnergyproblem,whichiswhatsomesuchtheoriesare

aimingtosolve,thiscanprovideexactlywhatthedataneed.Theforcecanmaketheuniverseaccelerateatlargedistances,whilehavingnomeasurableeffectontheorbitof theplanets.Asabonus, thisnewforcecanalsohavea significantimpact on the way galaxies rotate, which might at least partially address theDarkMatterissueaswell.ThewaythisnewforceworksisreminiscentofthewaythetheoryofBrout,

EnglertandHiggsgivesmasstofundamentalparticles.Itinvolvesascalarboson–aparticleliketheHiggsboson,whichhasnospin–anditinvolvestheideaofsymmetry breaking. If that isn’t familiar enough to you to help, consider apointillist painting, in which an image, and even the colour mix within it, iscomposedofmanytinydots.Whenaveragedoverdenseregionsofspace,asymmetryhidesthefifthforce.

Thisislikelookingatthepicturefromametreorsoaway.Thedotsarehiddeninthecoloursandlandscapeofthepainting.Closetothepainting,thedotsarevisible.Inthesameway,forthingsthesize

ofatomsorsmaller, theaveragingdoesn’thappen,sothefifthforcemayshowup.Andonverylongdistancescales,spaceisveryempty,so thedensity is low

andagaintheforcereappears.Similarly,averylongwayfromthepainting,itisjustasingledotagain.By the standards ofwild yarns, this idea seems at least to be testable in an

excitinglywiderangeofexperiments.Upcomingobservatorieswillcharacterisegravity and Dark Energy on astrophysical scales. Precise atomic physicsexperimentscouldmeasure theeffectof thefifthforceonatoms,andtheLHCmay also produce, or rule out, some varieties of these weird, so-calledchameleonparticles.A theoretical framework, such as is provided by supersymmetry, or the

StandardModelofparticlephysics,playstheroleofthepictureontheboxofajigsawpuzzle.fn1Whenlookingatajigsawpiece,thepicturegivesyouanideaofwhereitmightfit,andhowitmightconnecttotheothers.Tryingtodoajigsaw

puzzlewithout looking at the picture on the box is enormouslymore difficultthatlookingatthebigpicture.Ofcourse,onceyouseewhereapiecemightfitin,youstillhavetotryitto

seeifitreallydoesso.Andinthescienceversionofthispuzzle,wealsohavetobearinmindthatourpictureisalmostcertainlyincomplete(forexampleinthecaseoftheStandardModel,whichdefinitelydescribeslotsofdata)andpossiblycompletely wrong (for example, supersymmetry or extra dimensions, wherethere is currentlynodata).But to someextent anypicture isbetter thannone,and anywaywe don’t havemuch choice.At some pointwemight fit enoughpiecestogethertorealiseitwaswrong,throwitoutandtryanewpicture.AsortofparadigmshiftthatwouldseeajigsawpuzzlemanufacturergooutofbusinessundertheweightofreturnedChristmaspresents.The framework provided by a good theory, or collection of theories, gives

focus to research andmakes it harder for a new theory to gain acceptance.Amaverick new theory – and there aremany around –must either fit with theexisting picture, or replace it completely. In the latter case, it has toaccommodateallthejigsawpiecesthatarealreadysnuglyinterlocked.This,notaconspiracyoflizardsorilluminati(orevenhide-boundconservatives),iswhyadramatic‘Einsteinwaswrong’typeofideaisunlikelytobetakenveryseriouslywithouta lotof supportingevidence, and theability toaccommodatepreviousevidence that he was pretty much right. It will generally not just postulatemonstersouteast,itwillprobablycontradictthingswealreadyknowaboutlandswehavealreadyexploredindetail.In the sense that it emphasises the importance of the whole, and the

interdependenciesoftheparts,theapproachdescribedaboveisaholisticviewofscience. Inanessayentitled ‘WhenScientistsGoAstray’, thegreat theoreticalphysicistPhilipW.Andersondescribesthisasa‘seamlessweb’:

a bodyof firmly established theory, now extending fromphysics throughmolecular biology, which inmany situations, traps dubious observations.Already known laws, like conservation of energy, quantum mechanics,relativity,andthe lawsofgenetics,constrain theexplanationofanygivenresultinafashionwhichcanbeunique,ornearlyso,andmakeserrorseasytospot.Muchofscienceis‘overdetermined’inthissense.

Itisbynomeansinfalliblebutitisthebestwehave.

39

IntotheCosmos

LASTORDERSHAVErungatthebar.Beforeweleave,afinalstory–anexampleofa borderline case, which is not completely discredited but which mostrespectableexplorerswouldprobablydismiss.Ameasurementoftheelectricchargeofantihydrogenwaspublishedin2016

by theAlphaexperimentatCERN.Thecharge isexpected tobezero,and themeasurement confirms that, tohighprecision.That is an important step in themain goal of the experiments, which is tomeasure for the first timewhetherantimatterexperiencesthesamegravitationalforceasmatter.Accordingtothe‘seamlessweb’oftheory,itshould.Buttheforcehasnever

beenmeasured,sofromapurelyobservationalpointofview,wedon’tknow.Itcould even be that antimatter experiences the opposite gravitational force tomatter,whichwouldmeanmatterandantimatterrepeleachothergravitationally–thatis,antimattermayexperienceantigravity.This brings in another wild tale, the so-called ‘Dirac–Milne’ universe, in

which matter and antimatter do indeed gravitationally repel each other. Thiswould be a very different picture on the jigsaw box, and it is sort of hard tobelieve that it could describe the observationswe alreadyhave.These includemeasurementsofparticlesincolliders,ofthedistributionofmatterinthegalaxy,of the radiation leftover from theBigBang,andmore.All theseobservationshavedrivenus toour currentpictureofphysics andcosmology,knownas the‘concordance’model,which describes how the universe evolved after theBigBangandincludesDarkMatterandDarkEnergy.Ontheotherhand,aswehaveseen,ourcurrentpicturehassubstantialgaps.TheDirac–Milnemodel claims to address all these problems, and to agree

withthedata(andtheconcordancemodel)onsomeimportantfeaturessuchasthe abundance of light elements in the universe and the main feature of thecosmic microwave background. Whether it can be accommodated with theseamless web of current knowledge – and thus profoundly change it – maydepend upon whether enough people take it seriously enough to do thecalculations and follow through the consequences. Or, as Douglas Adams’

fictionaldetectiveDirkGentlymightputit,howmuchtimewilltheytake,inaDirac–Milne model, ‘detecting and triangulating vectors of theinterconnectednessofallthings’.Thesameappliestotheotherstoriesoftheoldseadogsandyoungidealists

clusteredon theeastern shoresofBosonia.One thing is certain– if andwhensomeone really measures antigravitational forces acting on antimatter, orchameleonparticles,orsparticles,oranythinginsideaquark,ortheHiggsdoingsomething reallyodd, or just something that reallydoesn’t fitwith the currentcoveronthepuzzlebox,someonewilldefinitelyhavetopickupthatstoryandtry.Meanwhile,aswewanderbackalongthedocktowardourhotelonelasttime,

ships areputtingout to seaon the tide.Thevoyages theyaremaking into theeastern oceans will report back and tell us whether or not the ideas andknowledgewehavegainedoutwestareagoodguidetotheeast.Wehaveourmap of the invisible, featuring the quarks and leptons – fundamental particlesaccordingtotheStandardModel–derivingtheirmassesfromtheBrout-Englert-Higgs mechanism and interacting via the electromagnetic, strong and weakforcesby theexchangeofphotons, gluons andWandZbosons to formmorecomplexobjects – hadrons, atoms and eventually the visibleworld aroundus.We have good reason to know this is not the whole story. But are any newislandswithin reach?Or are the landmasses of ourmap isolated? Is there anexpanseofemptyoceanforgreatdistanceseastwards?Oraretherenewislands,continentseven, justoutofsightwaiting tobediscovered?Perhapsoneof theshipssettingsailrightnowwillanswerthequestion.Rightnow,itmaybetimeforarest,agoodnight’ssleep,toabsorbwhatwe

havelearned,andwhattheremightstillbetolearn.Butitisgoodtoknowthataswesleep,newshipsaresettingsail.Andtheywillkeepsettingsail,aslongasenoughofuswanttoknowwhatliesoutthere,beyondourcurrenthorizon.

FurtherReading

HOPEFULLYTHISBOOKwhetsyourappetiteformoreadventure.Ifso,thenhereareafewsuggestions:Ifyoustillhaveshakysealegs,ChadOrzell’sHowtoTeachQuantumPhysics

toyourDogwillgiveyoumuchmoreonwavesversusparticlesandallthat.ThedescriptionofQEDinExpeditionIIIowesadebttoashortpopularbookbyoneofitsdiscoverers:RichardFeynman’sTheStrangeTheoryofLightandMatteriswellworthreadingifyouwanttohearmore,fromthehorse’smouth.Janna Levin’s Black Hole Blues and Other Songs from Outer Space is a

gripping account of the people (and the persistence) behind the discovery ofgravitational waves described in Gravity: A Distant Diversion. GrahamFarmelo’s biographyofPaulDirac,TheStrangestMan, is full ofmoving andenthralling insights into a great breakthrough and a too-little-known genius.BrianCoxandJeffForshaw’sWhydoesE=mc2? isagreatwaytoget togripswithmore of the ideas behind relativity, andUniversalwill showyouhow tobeginexpeditionsofyourown,evenwithoutaLargeHadronCollidertohand.Sean Carroll’s Particle at the End of the Universe gives a good account ofparticlephysicsup toand including thediscoveryof theHiggs,asdoesGavinHesketh’sTheParticleZoo(andofcourseSmashingPhysicstellsyouabitmoreabout the discovery itself). Finally, Lisa Randall’s Dark Matter and theDinosaurshasthetrueflavourofsomeofthestoriesweheardinthedocksidebars.

Acknowledgements

THE IDEAFOR themapsstartedwitha talk Igaveat theRoyalSociety,butwasdeveloped further in discussionswith TomAvery andChrisWormell. ThanksalsotoTomforpatienceandsuggestionsonthetext,andChrisforpatiencewithmysuggestionsonthemaps.Itwasapleasureworkingwithbothofyou.ThesupportofDianeBanksandherteamcontinuestobeoutstanding.IamprivilegedtobepartofUCL,auniversitywhichsupportsandencourages

an amazing diversity of ideas and activities, in research, teaching and in thewritingofbookslikethis.Iamgratefultomycolleaguesthere,aswellastomycolleaguesinthegreatinternationalcommunityofparticlephysics.Theloveandencouragementofmyfamily is thecrust,mantleandcore that

supportstheentiremapofmyworld.

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2:TheOceanWave…

fn1IthinkthereissuchaquietspotinmyofficeatCERNwhichiswhy,inthebirthplaceoftheworldwideweb,Istillstruggletogetontotheinternetsometimes.Therearejusttoomanywaves,arrivingatthewrongtimes,andhappeningtocanceleachotheroutinthevicinityofmydesk.fn2Iapologisetotheseagull.Thatgotunexpectedlyviolent.

3:…OrParticle?

fn1Thisdifferencespurredthedevelopmentofquantummechanics,andinspiredabreakthroughresultfromAlbertEinstein,whichresuscitatedtheideaoflightasaparticle.fn2AnnalenDerPhysik17(1905)pp.132–48.Seehttp://einsteinpapers.press.princeton.edu/

4:TravellingintheQuantumField

fn1Thisiswhyonsomephysicswallcharts,heavyparticlesareshownasbigblobscomparedtosmallerblobsforlighterparticlessuchastheelectron.fn2QED:TheStrangeTheoryofLightandMatter,1985.fn3Thisisthesameeffectasminimumheightofthelandinavalley.Onthesidesofavalley,adjacentpositionshavedifferentheightsduetotheslope,butatthebaseofthevalley–theminimumheight–thegroundisalmostflatandadjacentpointshavealmostthesameheight.Inthesameway,pathsneartheminimumnumberofturnshaveaverysimilarnumberofturnstoeachother,sotheyaddup.

5:Atoms

fn1Itis.fn2ItistemptingtothinkthatthesemusthavebeenawelcomebreakfromstudyingtheMancunianweather.

6:GoingSubatomic:TheElectron

fn1Themagneticforceonaparticledependsonbothitschargeanditsspeed,whereastheelectricforcedependsonlyonitscharge.Sowhenthesearemadetobeequal,withabitofalgebratheunknownchargecanbecancelledout,andthespeedcanbecalculated.fn2Knowingthespeediscrucial,becausethattellsyouhowlongtheelectricforceactsontheelectronsasthebeampassesbetweentheplates.Theimpulsefromtheforcedeflectsthebeambyanamountdependingonthecharge(highchargemeansalargerforce,soalargerdeflection)andtheinverseofthemass(highmassmeansmoreinertia,sosmallerdeflection).Theresultisthatthedeflectiondependsontheratioofthechargeandthemass.fn3Thisisaverypainstakingexperiment,evenmoresowhencarriedoutwithoildropsinsteadofstandardspheres,asitwasoriginallyin1910bytheAmericanphysicistRobertMillikan.Theexperimentisstillcarriedout,largelywithoutsuccess,infartoomanyundergraduatephysicslaboratoriesbysquintingandimpatientstudents.

7:NuclearOptions

fn1Theothercommonformsarebetaparticles,whichareelectrons,andgammarays,whicharephotons.fn2Apparentlythere’sagoodhistoricalraisinforthis.

8:TheSourceofChemistry

fn1TheequationwhichdescribesthesewavesistheSchrödingerequation.Lessfamousthanhiscatbutmuchmoreuseful.fn2Thisunfriendlybehaviouristhe‘exclusionprinciple’discoveredbyWolfgangPauli,oneofthefirstexplorersofourlandscapewhowewillmeetagainbeforetoolong.fn3Oneelectronvolt(eV)istheenergyofmotionthatanelectronacquiresifitisacceleratedthroughonevoltofelectricpotential.Soa12-voltbatterycanaccelerateanelectrontoanenergyof12eV.TogettomillionsofeVwouldrequireseveralhundredthousandsofsuchbatteries.Orthenuclearpowerofonedecayingnucleus.

9:Electromagnetism

fn1RecallthatitwasbybalancingthesetwoforcesthatJ.J.Thomsondiscoveredtheelectron.fn2Theoriginalmanuscriptwassubmittedin1864,but,inasituationfamiliartoscientistseverywhere,wasthenheldupinpeerreview.There’saletter,datedMarch1865,fromWilliamThomson(laterLordKelvin)sayinghewassorryforbeingslow,thathe’dreadmostofitanditseemedprettygood(‘decidedlysuitableforpublication’).

10:InvarianceandRelativity

fn1ThisisthewaytheyappearatthefootofthestatueofMaxwellneartheRoyalSocietyofEdinburgh.fn2Thisisactuallywhytheysaveonink–whenweclumpthecomponentstogetherintovectorsandwritetheequationsthatway,theabsolutedirectionsofthevectorsdon’tevenappearintheequations.Thephysicsdoesnotdependonthem.

11:TheGoodShipDirac

fn1Energyisequaltothesquareofthemomentumdividedbytwicethemass,E=p2/(2m),whichisequivalenttothepossiblymorefamiliarexpressionforkineticenergy,E=½mv2,wherevisthevelocity.fn2Ifyouwanttoknow,thefullexpressionisE2=m2c4+p2c4,whereEistheenergy,misthemassandpisthemomentum.Forzeromomentum,thisreducestoE2=m2c4,andtakingthesquarerootofbothsidesgetsusthefamiliarE=mc2.AndpossiblyE=–mc2too(seetext).fn3ThisistrueinSchrödinger’sequation.Butbecauseofthewayrelativitymixesupenergyandmomentum(andspaceandtime),themomentummustappeartothesamepowerastheenergy.IntheSchrödingerequation,themomentumappearssquared,whichwon’tdo.fn4Youdon’tneedtounderstandexactlyhowthisworksinordertocontinueourexploration,butifyou’d

liketoseeit,heregoes.WewantanequationlikeE=Am+Bp,butwhichisalsoconsistentwithE2=m2c4

+p2c4.Ifwesquarethefirstequationwehavetomultiplyallthetermsbyeachother,sowegetE2=A2m2

+(Am×Bp)+(Bp×Am)+B2p2.NowwehavetwoexpressionswhichoughttobothequalE2,sotheymustequaleachother:m2c4+p2c4mustequalA2m2+(Am×Bp)+(Bp×Am)+B2p2,foranyvaluesofmandp.IfweletA2andB2bothbeequaltoc2,thattakescareofthetermsinvolvingthesquareofthemassandthesquareoftheenergy.Butweareleftwiththeotherbit(Am×Bp)+(Bp×Am).Thiscanonlybezero(forallvaluesofpandm,becausewewantanequationwhichworksforallparticles)ifA×BisequaltothenegativeofB×A.Butforallnumbers,A×BequalsB×A.SoAandBcannotbenumbers.fn5Fromthepointofviewofmathematicsthenumberscanbeprettymuchanythingyoulike,althoughifwewanttousethemtohelpusunderstandphysics,theytakeonspecificmeaning.Forexample,thenumbersinamatrixcanencodehowthedifferentcomponentsofamagneticfieldchangewhenwerotateitthroughsomeangleaboutsomedirection.

TheWeakestForce

fn1MostdaysexceptMonday,infact.fn2Though,disappointingly,notintheirpersonallives.

PlanesandRoundabouts

fn1Newton’slaw,F=ma.

Different,YetSomehowtheSame

fn1AninnovationduetoMichaelFaraday’sveryearlythoughtsaboutelectricityandmagnetism.

14:Protons,NeutronsandtheNucleus

fn1Ortoputitanotherway,theycansmashitup.fn2G.Allen&Unwin,Limited,atranslationoftheoriginal“DasWeltbildderneuenPhysik”(1929)

15:Hadrons

fn1Aswithleptons,thisisfromtheGreekbarus(heavy)andmeso(intermediate).

16:QuarksandtheStrongForce

fn1Veryrecently,newstructureshavebeenfounddeepintheinterioroftheisland,withtwoquarksandtwoantiquarks(tetraquarks)andfourquarksandanantiquark(pentaquarks).Extremelyephemeral,theinternalstructureoftheseobjectsisthesubjectofongoingexploration.

18:FlavoursandGenerations

fn1Thesamewordisusedtodescribethedifferenttypesoflepton–electron,muonandtau.fn2AlsoinManchester,in1947–tenyearsafterthefirstcurryhouse,accordingtoareportintheManchesterEveningNews.fn3Theyhavealternativenames–beautyandtruth–buttheyaretoopretentiousformostphysicists.fn4ThispeculiarhierarchyofmassesmaywellbeoneofthebiggestcluestowhatliesbeyondtheStandardModel–certainly,thetopquarkplaysquiteaspecialroleinmanyspeculativenewtheories.

19:TheWeakForce

fn1Unlessanduntiltheymeetwithatopantiquarkandareannihilated.

20:Parity,HelicityandChirality

fn1Fromthesamerootas‘helix’.Thetipofaspinningarrowwilldescribeahelixastheparticlemovesalongthroughspace.fn2Theirmapofphysicsshouldbethesameasours,afterall,eveniftheyusedifferentwordstodescribeit.fn3Apartfrom,presumably,saying,‘Seethatfunny-lookinggalaxyoverthere?That’sonourleft.’

23:MasslessMatter?

fn1AndSwiss.AndAmerican.fn2HealsodevelopedtheexclusionprinciplewediscoveredinAtomLand.fn3Entitiesmustnotbemultipliedbeyondnecessity.

24:TheStandardModelisDead–LongLivetheStandardModel!

fn1C2Cl4–twocarbonswithfourchlorines.

25:NeutrinoBadlands

fn1TherelevantequationswerefirstwrittendownbyItalianphysicistEttoreMajorana,andsothiskindofparticleisoftencalledaMajoranaparticle,leadingtounexpecteddrugreferencesinmanyphysicspresentations.

27:SymmetryandBosons

fn1Thatis,rotationsintheU(1)group.fn2The‘S’meansitisaspecialsubgroupofabiggerU(2)group.

28:VirtualParticlesandtheDefenceAgainstInfinity

fn1Thisnumbercharacterisesthestrengthoftheinteraction,anddependsonthechargeoftheelectron–ifthechargewerehigher,thenumberwouldbehigher.fn2TheproofthatthisisthecasewaspublishedbyDutchphysicistsGerardus’tHooftandMartinusVeltmanin1971.

30:ElectroweakSymmetryBreaking

fn1ThisistheWbosonplayingitstrickofswitchingparticlesaroundwithindoublets,whichwenotedwhenwefirststudiedtheweakforce.fn2Theforcesdon’texactlyunify(theystillcomefromdistinctsymmetries,U(1)andSU(2))butitturnsoutthereisamixingbetweentheneutralbosons.ThephotonisnotexactlytheneutralbosonyouwouldexpectfromU(1),andtheZisnotpurelyfromSU(2).Theyarebothamixtureoftheneutralbosonsonewouldexpectfromthetwodifferentsymmetries.

31:HuntingtheHiggs

fn1Thisistruefortypesofmaterialsknownasferromagnets.

32:WhyGo?

fn1Which,asUSphysicistLisaRandallhaspointedout,wouldbebetternamedTransparentMatter,really,sinceitisinvisibleratherthanopaque.

34:SeaMonstersandDarkMatters

fn1Asmightbeexpected,itwaslarge,underground(intheSanfordUndergroundResearchFacilityinSouthDakota),andmademostlyofxenon.

35:Supersymmetry

fn1TheHiggs,whichisalwaysspecial,hastohaveatleastfourextraHiggsbosons,aswellassuperpartners.

36:IntoAnotherDimension?

fn1ThereisnochancethatblackholesproducedthiswaycoulddestroytheEarth,bytheway,otherwisethiswouldhavehappened,andbehappening,alreadyandallovertheplace,becauseoftheveryhighcosmic-raycollisionsthatgoonaroundus.

37:OvertheEdge

fn1Thebarismakingahalf-heartedattempttobeagastropub,soithasbiggreenolivesinajar,aswellasabottleofbalsamicvinegarandsomebasketswithbreadin.Theregularsareignoringallofthisandstickingtotheirdrinksandstories,sonoonewillmindifweusethemtotrytoillustratesphalerons.

38:AFifthForce

fn1Incaseyouwerewondering,yes,thisisthekindofpubwhichhasjigsawpuzzlesonashelfintheloungebar,alongwithbackgammonandaScrabblesetwiththeQ,Xandthreevowelsmissing.