Carlo Rovelli - Web Education
Transcript of Carlo Rovelli - Web Education
![Page 1: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/1.jpg)
![Page 2: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/2.jpg)
![Page 3: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/3.jpg)
CarloRovelli
REALITY IS NOT WHAT IT SEEMS
TheJourneytoQuantumGravity
TranslatedbySimonCarnellandEricaSegre
![Page 4: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/4.jpg)
Contents
AuthorâsNotePreface:WalkingalongtheShore
PARTONERoots
1Grains2TheClassics
PARTTWOTheBeginningoftheRevolution
3Albert4Quanta
PARTTHREEQuantumSpaceandRelationalTime
5SpacetimeisQuantum6QuantaofSpace7TimeDoesNotExist
PARTFOURBeyondSpaceandTime
8BeyondtheBigBang9EmpiricalConfirmations?10QuantumBlackHoles11TheEndofInfinity12Information13Mystery
NotesAnnotatedBibliographyFollowPenguin
![Page 5: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/5.jpg)
ABOUTTHEAUTHOR
CarloRovelliisatheoreticalphysicistwhohasmadesignificantcontributionstothephysicsofspaceandtime.HehasworkedinItalyandtheUS,andiscurrentlydirectingthequantumgravityresearchgroupoftheCentredePhysiqueThĂŠoriqueinMarseille,France.HisSevenBriefLessonsonPhysicsisaphenomenalinternationalbestsellertranslatedintoforty-onelanguages.
![Page 6: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/6.jpg)
AuthorâsNote
Duringmyentireresearchlife,friendsandcuriouspeoplehaveaskedmetoexplainwhatwasgoingoninquantumgravityresearch.Howwasitpossibletostudynewwaysofthinkingaboutspaceandtime?OverandoveragainIhavebeenaskedtowriteapopularaccountofthisresearch.Whilebooksoncosmologyorstringtheoryabound,abookdescribingtheresearchonthequantumnatureofspaceandtime,andonloopquantumgravityinparticular,didnotyetexist.Ihavelonghesitated,becauseIwantedtoconcentrateonresearch.Someyearsago,aftercompletingmytechnicalbookonthesubject,Ifeltthatthecollectiveworkofmanyscientistshadmovedthetopictoastagematureenoughforapopularbook.Thelandscapeweareexploringisenchanting:whykeepithidden?ButIstilldelayedtheproject,becauseIcouldnotâseeâthebookinmyhead.Howtoexplaina
worldwithoutspaceandtime?Onenightin2012,duringalongsolitarydrivefromItalytoFrance,Irealizedthattheonlywaytoexplaininacomprehensiblemannertheongoingmodificationsofthenotionsofspaceandtimewastotellthestoryfromthebeginning:startingfromDemocritus,allthewaythroughtothequantaofspace.Afterall,thisishowIunderstandthestory.Ibegantodesigntheentirebookinmymindwhiledriving,andgotincreasinglyexcited,untilIheardapolicecarâssirenstellingmetopullover:Iwasdrivingfarabovethespeedlimit.TheItalianpolicemenaskedmepolitelyifIwascrazytodriveatthatspeed.IexplainedthatIhadjustfoundtheideaIâdbeenseekingforsolong;thepolicemanletmegowithoutaticket,andwishedmegoodluckwiththebook.Thisisthebook.ThisbookwaswrittenandfirstpublishedinItalianatthebeginningof2014.Shortlyafterwards,I
wroteafewarticlesonfundamentalphysicsforanItaliannewspaper.AprestigiousItalianpublisher,Adelphi,askedmeforanextendedversionofthesearticles,toappearasasmallbooklet.ThisistheoriginoftheshortbookSevenBriefLessonsonPhysics,whichtomyimmensesurprisehasbecomeaninternationalbestsellerandhasopenedabeautifulchannelofcommunicationbetweenmeandsomanywonderfulreadersallovertheworld.TheSevenLessonswerethuswrittenafterthisbook,andtosomeextenttheyareasynthesisofsomeofthetopicsyoufindhere.IfyouhavereadSevenBriefLessonsonPhysicsandwanttoknowmore,tojourneydeeperintothestrangeworldthatbooksketched,hereyoucanfindmore.WhiletheaccountofestablishedphysicsIgivehereispresentedfromthepeculiarperspectivein
whichIunderstandit,itislargelyuncontroversial.However,thepartofthisbookthatdescribescurrentresearchinquantumgravityismyownpersonalunderstandingofthestateoftheart.Thisistheregionattheboundarybetweenwhatwehaveunderstoodandwhatwedonotyetunderstand,andisstillfarfromachievingconsensus.SomeofmyphysicistcolleagueswillagreewithwhatIwritehere;otherswonât.Thisistrueforallpresentationsofongoingresearchatthefrontiersofknowledge,butIprefertostateitupfrontandclearly.Thisisnotabookaboutcertainties:itisabookabouttheadventureofmovingtowardstheunknown.Asawhole,thisisatravelbookdescribingoneofthemostspectacularjourneysthathumanityhas
taken:ajourneyoutofourlimitedandparochialviewsofreality,towardsanincreasinglyvastunderstandingofthestructureofthings.Amagicaljourneyoutofourcommon-senseviewofthings,farfromcomplete.
Marseille,4May2016
![Page 7: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/7.jpg)
Preface:WalkingalongtheShore
Weareobsessedwithourselves.Westudyourhistory,ourpsychology,ourphilosophy,ourgods.Muchofourknowledgerevolvesaroundmanhimself,asifwewerethemostimportantthingintheuniverse.IthinkIlikephysicsbecauseitopensawindowthroughwhichwecanseefurther.Itgivesmethesenseoffreshairenteringthehouse.Whatweseeouttherethroughthewindowisconstantlysurprisingus.Wehavelearnedagreat
dealabouttheuniverse.Inthecourseofthecenturieswehavecometorealizejusthowverymanywrongideaswehad.WethoughtthattheEarthwasflat,andthatitwasthestillcentreofourworld.Thattheuniversewassmall,andunchanging.Webelievedthatmanwasabreedapart,withoutkinshiptotheotheranimals.Wehavelearnedoftheexistenceofquarks,blackholes,particlesoflight,wavesofspace,andoftheextraordinarymolecularstructuresineverycellofourbodies.Thehumanraceislikeagrowingchildwhodiscoverswithamazementthattheworldconsistsnotjustofhisbedroomandplayground,butthatitisvast,andthatthereareathousandthingstodiscover,andinnumerableideasquitedifferentfromthosewithwhichhebegan.Theuniverseismultiformandboundless,andwecontinuetostumbleuponnewaspectsofit.Themorewelearnabouttheworld,themoreweareamazedbyitsvariety,beautyandsimplicity.Butthemorewediscover,themoreweunderstandthatwhatwedonâtyetknowisgreaterthan
whatweknow.Themorepowerfulourtelescopes,thestrangerandmoreunexpectedaretheheavenswesee.Thecloserwelookattheminutedetailofmatter,themorewediscoverofitsprofoundstructure.TodayweseealmosttotheBigBang,thegreatexplosionfromwhich,14billionyearsago,allthegalaxieswerebornâbutwehavealreadybeguntoglimpsesomethingbeyondtheBigBang.Wehavelearnedthatspaceiscurved,butalreadyforeseethatthissamespaceiswovenfromvibratingquantumgrains.Ourknowledgeoftheelementarygrammaroftheworldcontinuestogrow.Ifwetrytoput
togetherwhatwehavelearnedaboutthephysicalworldinthecourseofthetwentiethcentury,thecluespointtowardssomethingprofoundlydifferentfromwhatweweretaughtatschool.Anelementarystructureoftheworldisemerging,generatedbyaswarmofquantumevents,wheretimeandspacedonotexist.Quantumfieldsdrawspace,time,matterandlight,exchanginginformationbetweenoneeventandanother.Realityisanetworkofgranularevents;thedynamicwhichconnectsthemisprobabilistic;betweenoneeventandanother,space,time,matterandenergymeltinacloudofprobability.Thisstrangenewworldisslowlyemergingtodayfromthestudyofthemainopenquestionposed
infundamentalphysics:quantumgravity.Itâstheproblemofcoherentlysynthesizingwhatwehavelearnedabouttheworldwiththetwomajordiscoveriesoftwentieth-centuryphysics:generalrelativityandquantumtheory.Toquantumgravity,andthestrangeworldthatthisresearchisunfolding,thisbookisdedicated.Thebookisalivecoverageoftheongoingresearch:whatwearelearning,whatwealreadyknow,
andwhatwethinkwearebeginningtounderstand,abouttheelementarynatureofthings.ItstartsfromthedistantoriginofsomekeyideasthatweusetodaytoorderourunderstandingoftheworldanddescribesthetwogreatdiscoveriesofthetwentiethcenturyâEinsteinâsgeneralrelativityandquantummechanicsâtryingtoputintofocusthecoreoftheirphysicalcontent.Ittellsofthepictureoftheworldwhichisemergingtodayfromresearchinquantumgravity,takingintoaccountthelatestindicationsgivenbynature,suchastheconfirmationofthecosmologicalstandardmodelobtainedfromthePlancksatelliteandthefailureatCERNtoobservethesuper-symmetricparticlesthatmanyexpected.Anditdiscussestheconsequencesoftheseideas:thegranularstructureofspace;thedisappearanceoftimeatsmallscale;thephysicsoftheBigBang;theoriginofblack-holeheatâuptotheroleofinformationinthefoundationofphysics.InafamousmythrelatedbyPlatointheseventhbookofTheRepublic,somemenarechainedat
thebottomofadarkcaveandseeonlyshadowscastuponawallbyafirebehindthem.Theythinkthatthisisreality.Oneofthemfreeshimself,leavesthecaveanddiscoversthelightoftheSun,andthewiderworld.Atfirstthelight,towhichhiseyesareunaccustomed,stunsandconfuseshim.Buteventuallyhecansee,andreturnsexcitedlytohiscompanionstotellthemwhathehasseen.Theyfindithardtobelieve.Weareallinthedepthsofacave,chainedbyourignorance,byourprejudices,andourweak
sensesrevealtousonlyshadows.Ifwetrytoseefurther,weareconfused:weareunaccustomed.Butwetry.Thisisscience.Scientificthinkingexploresandredrawstheworld,graduallyofferingusbetterandbetterimagesofit,teachingustothinkinevermoreeffectiveways.Scienceisa
![Page 8: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/8.jpg)
continualexplorationofwaysofthinking.Itsstrengthisitsvisionarycapacitytodemolishpreconceivedideas,torevealnewregionsofreality,andtoconstructnovelandmoreeffectiveimagesoftheworld.Thisadventurerestsupontheentiretyofpastknowledge,butatitsheartischange.Theworldisboundlessandiridescent;wewanttogoandseeit.Weareimmersedinitsmysteryandinitsbeauty,andoverthehorizonthereisunexploredterritory.Theincompletenessandtheuncertaintyofourknowledge,ourprecariousness,suspendedovertheabyssoftheimmensityofwhatwedonâtknow,doesnotrenderlifemeaningless:itmakesitinterestingandprecious.Ihavewrittenthisbooktogiveanaccountofwhatformeisthewonderofthisadventure.Iâve
writtenwithaparticularreaderinmind:someonewhoknowslittleornothingabouttodayâsphysicsbutiscurioustofindoutwhatweknow,butalsowhatwedonâtyetunderstand,abouttheelementaryweaveoftheworldâandwherewearesearching.AndIhavewrittenittotrytocommunicatethebreathtakingbeautyofthepanoramaofrealitywhichcanbeseenfromthisperspective.Iâvealsowrittenitformycolleagues,fellowtravellersdispersedthroughouttheworld,aswellas
fortheyoungwomenandmenwithapassionforscience,eagertosetoutonthisjourneyforthefirsttime.Iâvesoughttooutlinethegenerallandscapeofthestructureofthephysicalworld,asseenbythedoublelightsofrelativityandofquantumphysics,andtoshowhowtheycanbecombined.Thisisnotonlyabookofdivulgation;itâsalsoonewhicharticulatesapointofview,inafieldofresearchwheretheabstractionofthetechnicallanguagemaysometimesobscurethewide-anglevision.Scienceismadeupofexperiments,hypotheses,equations,calculationsandlongdiscussions;buttheseareonlytools,liketheinstrumentsofmusicians.Intheend,whatmattersinmusicisthemusicitself,andwhatmattersinscienceistheunderstandingoftheworldwhichscienceprovides.TounderstandthesignificanceofthediscoverythattheEarthturnsaroundtheSun,itisnotnecessarytofollowCopernicusâscomplicatedcalculations;tounderstandtheimportanceofthediscoverythatalllivingbeingsonourplanethavethesameancestors,itisnotnecessarytofollowthecomplexargumentsofDarwinâsbooks.Scienceisaboutreadingtheworldfromagraduallywideningpointofview.Thisbookgivesanaccountofthecurrentstateofthesearchforournewimageoftheworld,asI
understandittoday.ItisthereplyIwouldgivetoacolleagueandfriendaskingme,âSo,whatdoyouthinkisthetruenatureofthings?â,aswewalkalongtheshore,onalongmidsummerâsevening.
![Page 9: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/9.jpg)
![Page 10: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/10.jpg)
PartOne
ROOTS
ThisbookbeginsinMiletus,twenty-sixcenturiesago.Whybeginabookaboutquantumgravitywithevents,peopleandideassoancient?Ihopethereadereagertogetontoquantaofspacewillnotholdthisagainstme.Foritiseasiertounderstandideasbystartingwiththerootsfromwhichtheyhavegrown,andanimportantnumberoftheideaswhichturnedouttobeeffectiveforunderstandingtheworldoriginatedovertwothousandyearsago.Ifwebrieflyretracetheirbirth,theybecomeclearer,andthelaterstepsturnouttobesimplerandnatural.
Butthereâsmore.Certainproblemsfirstposedinantiquitycontinuetobecrucialtoourunderstandingoftheworld.Someofthemostrecentideasaboutthestructureofspaceutilizeconceptsandissuesintroducedthen.Inspeakingofthesedistantideas,Iputontothetablequestionswhicharegoingtobecentraltoquantumgravity.Thismakesitalsopossible,whentreatingofquantumgravity,todistinguishbetweentheideaswhichgobacktotheveryoriginofscientificthought,evenifweareunfamiliarwiththem,andthosewhichareradicallynew.Theconnectionbetweenproblemsposedbythescientistsofantiquity,andsolutionsfoundbyEinsteinandquantumgravity,is,asweshallsee,surprisinglyclose.
![Page 11: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/11.jpg)
1.Grains
Accordingtotradition,intheyear450BCE,amanembarkeduponashiptravellingfromMiletustoAbdera.Itwastobeacrucialjourneyforthehistoryofknowledge.
ThemanwasprobablyfleeingpoliticalturmoilinMiletus,wherethearistocracywasviolentlyseizingbackpower.MiletushadbeenaprosperousandflourishingGreekcity,perhapstheprincipalcityoftheGreekworldbeforethegoldenageofAthensandSparta.Ithadbeenabusycommercialhub,dominatinganetworkofalmostahundredcoloniesandcommercialoutposts,stretchingfromtheBlackSeatoEgypt.CaravansfromMesopotamiaandshipsfromallovertheMediterraneanarrivedatMiletus,andideascirculated.
Figure1.1ThejourneymadebyLeucippusofMiletus,thefounderoftheatomistschool(circa450BCE).
Duringtheprecedingcentury,arevolutioninthinkingwhichwouldprovefundamentaltohumanityhadtakenplaceinMiletus.Agroupofthinkershadreformulatedthewayquestionswereaskedabouttheworld,andthewayanswersweresought.ThegreatestofthesethinkerswasAnaximander.
Fromtimeimmemorial,oratleastsincehumanityhadleftwrittentextswhichhavecomedowntous,menhadaskedthemselveshowtheworldhadcomeintobeing,whatitwascomposedof,howitwasordered,andwhynaturalphenomenaoccurred.Forthousandsofyearstheyhadgiventhemselvesanswerswhichallresembledoneanother:answerswhichreferredtoelaboratestoriesofspirits,deities,imaginaryandmythologicalcreatures,andothersimilarthings.FromcuneiformtabletstoancientChinesetexts;fromhieroglyphicwritinginthePyramidstothemythsoftheSioux;fromthemostancientIndiantextstotheBible;fromAfricanstoriestothoseofaboriginalAustralians,itwasallacolourfulbutbasicallyquitemonotonousflowâofPlumedSerpentsandGreatCows,ofirascible,litigious,orkindlydeitieswhocreatetheworldbybreathingoverabysses,utteringâFiatluxâ,oremergingoutofastoneegg.
Then,atMiletus,atthebeginningofthefifthcenturybeforeourera,Thales,hispupilAnaximander,Hecataeusandtheirschoolfindadifferentwayoflookingforanswers.Thisimmense
![Page 12: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/12.jpg)
revolutioninthoughtinauguratesanewmodeofknowledgeandunderstanding,andsignalsthefirstdawnofscientificthought.
TheMilesiansunderstandthatbyshrewdlyusingobservationandreason,ratherthansearchingforanswersinfantasy,ancientmythsorreligionâand,aboveall,byusingcriticalthoughtinadiscriminatingwayâitispossibletorepeatedlycorrectourworldview,andtodiscovernewaspectsofrealitywhicharehiddentothecommonview.Itispossibletodiscoverthenew.
Perhapsthedecisivediscoveryisthatofadifferentstyleofthinking,wherethediscipleisnolongerobligedtorespectandsharetheideasofthemasterbutisfreetobuildonthoseideaswithoutbeingafraidtodiscardorcriticizethepartthatcanbeimproved.Thisisanovelmiddleway,placedbetweenfulladherencetoaschoolandgenericdeprecationofideas.Itisthekeytothesubsequentdevelopmentofphilosophicalandscientificthinking:fromthismomentonwards,knowledgebeginstogrowatavertiginouspace,nourishedbypastknowledgebutatthesametimebythepossibilityofcriticism,andthereforeofimprovingknowledgeandunderstanding.ThedazzlingincipitofHecataeusâsbookofhistorygoestotheheartofthiscriticalthinking,includingasitdoestheawarenessofourownfallibility:âIwrotethingswhichseemtruetome,becausetheaccountsoftheGreeksseemtobefullofcontradictoryandridiculousthings.â
Accordingtolegend,HeraclesdescendedtoHadesfromCapeTenaro.HecataeusvisitsCapeTenaro,anddeterminesthatthereisinfactnosubterraneanpassageorotheraccesstoHadesthereâandthereforejudgesthelegendtobefalse.Thismarksthedawnofanewera.
Thisnewapproachtoknowledgeworksquicklyandimpressively.Withinamatterofafewyears,AnaximanderunderstandsthattheEarthfloatsintheskyandtheskycontinuesbeneaththeEarth;thatrainwatercomesfromtheevaporationofwateronEarth;thatthevarietyofsubstancesintheworldmustbesusceptibletobeingunderstoodintermsofasingle,unitaryandsimpleconstituent,whichhecallsapeiron,theindistinct;thattheanimalsandplantsevolveandadapttochangesintheenvironment,andthatmanmusthaveevolvedfromotheranimals.Thus,gradually,wasfoundedthebasisofagrammarforunderstandingtheworldwhichissubstantiallystillourowntoday.
SituatedatapointofconjunctionbetweentheemergentGreekcivilizationandtheancientempiresofMesopotamiaandEgypt,nourishedbytheirknowledgebutimmersedinthelibertyandthepoliticalfluiditywhichistypicallyGreek;inasocialspacewithoutimperialpalaces,orpowerfulpriestlycastes,whereindividualcitizensdiscusstheirdestiniesinopenagoras,Miletusistheplacewhere,forthefirsttime,mendecidecollectivelytheirownlaws;wherethefirstparliamentinthehistoryoftheworldgathersâthePanionium,meeting-placeofthedelegatesoftheIonianLeagueâandwhereforthefirsttimemendoubtthatonlythegodsarecapableofaccountingforthemysteriesoftheworld.Throughdiscussion,itispossibletoreachthebestdecisionsforthecommunity;throughdiscussion,itispossibletounderstandtheworld.ThisistheimmenselegacyofMiletus,cradleofphilosophy,ofthenaturalsciences,andofgeographicalandhistoricalstudies.Itisnoexaggerationtosaythattheentirescientificandphilosophicaltradition,Mediterraneanandthenmodern,hasacrucialrootinthespeculationsofthethinkersofMiletusinthesixthcenturyBCE.1
ThisluminousMiletusshortlyafterwardscametoacalamitousend.ThearrivalofthePersianEmpire,andafailedanti-imperialrevolt,ledtoaferociousdestructionofthecityin494BCEandtotheenslavementofalargenumberofitsinhabitants.InAthens,thepoetPhrynichuswritesthetragedyTheTakingofMiletus,whichsodeeplymovestheAtheniansthatitsre-stagingisprohibited,onaccountofitcausingtoomuchdistress.Buttwentyyearslater,theGreeksrepelthePersianmenace;Miletusisreborn,repopulated,andreturnedtobeingacentreofcommerceandideas,radiatingitsthoughtandspiritoncemore.
Thepersonwithwhomwebeganthischaptermusthavebeenmovedbythisspiritwhen,in450,accordingtotradition,heembarkedfromMiletusforAbdera.HisnamewasLeucippus.Littleisknownabouthislife.2HewroteabookentitledTheGreatCosmology.OnhisarrivalinAbdera,hefoundedascientificandphilosophicalschooltowhichhesoonaffiliatedayoungdisciple,Democritus,whoselongshadowwastobecastoverthethoughtofallsubsequenttimes.
Together,thesetwothinkershavebuiltthemajesticcathedralofancientatomism.Leucippuswastheteacher.Democritus,thegreatpupilwhowrotedozensofworksoneveryfieldofknowledge,andwasdeeplyveneratedinantiquity,whenpeoplewerefamiliarwiththeseworks.âThemostsubtleoftheAncientsâ,Senecacalledhim.3âWhoistherewhomwecancomparewithhimforthegreatness,notmerelyofhisgenius,butalsoofhisspirit?âasksCicero.4
What,then,hadLeucippusandDemocritusdiscovered?TheMilesianshadunderstoodthattheworldcanbecomprehendedusingreason.Theyhadbecomeconvincedthatthevarietyofnaturalphenomenamustbeattributabletosomethingsimple,andhadtriedtounderstandwhatthissomethingmightbe.Theyhadconceivedofakindofelementarysubstanceofwhicheverythingwasmade.Anaximenes,amongtheMilesians,hadimaginedthissubstancecouldcompressandrarefy,thustransformingfromonetoanotheroftheelementsofwhichtheworldisconstituted.Itwasafirstgermofphysics,roughandelementary,butintherightdirection.Anideawasneeded,agreatidea,agrandvision,tograspthehiddenorderoftheworld.LeucippusandDemocrituscameupwiththisidea.
![Page 13: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/13.jpg)
Figure1.2DemocritusofAbdera.
TheideaofDemocritusâssystemisextremelysimple:theentireuniverseismadeupofaboundlessspaceinwhichinnumerableatomsrun.Spaceiswithoutlimits;hasneitheranabovenorabelow;iswithoutacentre,oraboundary.Atomshavenoqualitiesatall,apartfromtheirshape.Theyhavenoweight,nocolour,notaste.âByconventionissweet,byconventionbitter,byconventionhot,byconventioncolour;butbyverityatomsandvoid.â5
Atomsareindivisible;theyaretheelementarygrainsofreality,whichcannotbefurthersubdivided,andeverythingismadeofthem.Theymovefreelyinspace,collidingonewithanother;theyhookontoandpushandpulleachother.Similaratomsattracteachotherandjoin.
Thisistheweaveoftheworld.Thisisreality.Everythingelseisnothingbutaby-product,randomandaccidental,ofthismovementandthiscombiningofatoms.Theinfinitevarietyofthesubstancesofwhichtheworldismadederivessolelyfromthiscombiningofatoms.
Whenatomsaggregate,theonlythingthatmatters,theonlythingthatexistsattheelementarylevel,istheirshape,theirarrangement,andtheorderinwhichtheycombine.Justasbycombiningthelettersofthealphabetindifferentwayswemayobtaincomediesortragedies,ridiculousstoriesorepicpoems,soelementaryatomscombinetoproducetheworldinitsendlessvariety.ThemetaphorisDemocritusâsown.6
Thereisnofinality,nopurpose,inthisendlessdanceofatoms.We,justliketherestofthenaturalworld,areoneofthemanyproductsofthisinfinitedance.Theproduct,thatis,ofanaccidentalcombination.Naturecontinuestoexperimentwithformsandstructures;andwe,liketheanimals,aretheproductsofaselectionwhichisrandomandaccidental,overthecourseofeonsoftime.Ourlifeisacombinationofatoms,ourthoughtsaremadeupofthinatoms,ourdreamsaretheproductsofatoms;ourhopesandouremotionsarewritteninalanguageformedbycombinationsofatoms;thelightwhichweseeiscomprisedofatomswhichbringusimages.Theseasaremadeofatoms,asareourcities,andthestars.Itâsanimmensevision;boundless,incrediblysimpleandincrediblypowerful,oneonwhichtheknowledgeofacivilizationwouldlaterbebuilt.
OnthisfoundationDemocrituswrotedozensofbooksarticulatingavastsystem,dealingwithquestionsofphysics,philosophy,ethics,politicsandcosmology.Hewritesonthenatureoflanguage,onreligion,ontheoriginsofhumansocieties,andonmuchelsebesides.(TheopeningofhisLittleCosmologyisimpressive:âInthisworkItreatofallthings.â)Allofthesebookshavebeenlost.Weknowofhisthoughtonlythroughthequotationsandreferencesmadebyotherancientauthors,andbytheirsummariesofhisideas.7Thethoughtwhichthusemergesisakindofintensehumanism,rationalistandmaterialist.8Democrituscombinesakeenattentiontonature,illuminatedbyanaturalisticclarityinwhicheveryresidualsystemofmythicideasisclearedaway,withagreatattentiontohumanityandadeepethicalconcernforlifeâanticipatingbysometwothousandyearsthebestaspectsoftheeighteenth-centuryEnlightenment.TheethicalidealofDemocritusisthatofaserenityofmindreachedthroughmoderationandbalance,bytrustinginreasonandnotallowingoneselftobeoverwhelmedbypassions.
![Page 14: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/14.jpg)
PlatoandAristotlewerefamiliarwithDemocritusâsideas,andfoughtagainstthem.Theydidsoonbehalfofotherideas,someofwhichwerelater,forcenturies,tocreateobstaclestothegrowthofknowledge.BothinsistedonrejectingDemocritusâsnaturalisticexplanations,infavouroftryingtounderstandtheworldinfinalistictermsâbelieving,thatis,thateverythingthathappenshasapurpose;awayofthinkingthatwouldrevealitselftobeverymisleadingforunderstandingthewaysofnatureâorintermsofgoodandevil,confusinghumanissueswithmatterswhichdonotrelatetous.
AristotlespeaksextensivelyabouttheideasofDemocritus,andwithrespect.PlatonevercitesDemocritus,butscholarssuspecttodaythatthiswasoutofdeliberatechoiceandnotforlackofknowledgeofhisworks.CriticismofDemocritusâsideasisimplicitinseveralofPlatoâstexts,asinhiscritiqueofâphysicistsâ,forexample.InapassageinhisPhaedo,PlatohasSocratesarticulateareproachtoallâphysicistsâwhichwillhavealastingresonance.HecomplainsthatwhenâphysicistsâhadexplainedthattheEarthwasround,herebelledbecausehewantedtoknowwhatâgoodâitwasfortheEarthtoberound;howitsroundnesswouldbenefitit.PlatoâsSocratesrecountshowhehadatfirstbeenenthusiasticaboutphysics,buthadcometobedisillusionedbyit:
IhadexpectedtobefirsttoldthattheEarthwasflatorround,butalsothat,afterwards,thereasonforthenecessityofthisshapewouldbeexplainedtome,startingfromtheprincipleofthebest,provingtomethatthebestthingfortheEarthistohavethisshape.AndifhehadsaidthattheEarthwasatthecentreoftheworld,thentoshowmehowbeingatthecentrewasofbenefittotheEarth.9
HowcompletelyofftrackthegreatPlatowashere!
Istherealimittodivisibility?Thegreatestphysicistofthesecondhalfofthetwentiethcentury,RichardFeynman,wroteatthebeginningofhiswonderfulintroductorylessonsonphysics:
If,insomecataclysm,allscientificknowledgeweretobedestroyed,andonlyonesentencepassedontothenextgenerationofcreatures,whatstatementwouldcontainthemostinformationinthefewestwords?Ibelieveitistheatomichypothesis,ortheatomicfact,orwhateveryouwishtocallit,thatallthingsaremadeofatomsâlittleparticlesthatmovearoundinperpetualmotion,attractingeachotherwhentheyarealittledistanceapart,butrepellinguponbeingsqueezedintooneanother.Inthatonesentenceyouwillseeanenormousamountofinformationabouttheworld,ifjustalittleimaginationandthinkingareapplied.10
Withoutneedinganythingfrommodernphysics,Democritushadalreadyarrivedattheideathateverythingismadeupofindivisibleparticles.Howdidhedoit?
Hehadargumentsbaseduponobservation;forexample,heimagined,correctly,thatthewearingdownofawheel,orthedryingofclothesonaline,couldbeduetotheslowflightofparticlesofwoodorofwater.Buthealsohadargumentsofaphilosophicalkind.Letâsfocusonthese,becausetheirpotencyreachesallthewaytoquantumgravity.
Democritusobservedthatmattercouldnotbeacontinuouswhole,becausethereissomethingcontradictoryinthepropositionthatitshouldbeso.WeknowofDemocritusâsreasoningbecauseAristotlereportsit.11Imagine,saysDemocritus,thatmatterisinfinitelydivisible,thatistosay,itmaybebrokendownaninfinitenumberoftimes.Imaginethenthatyoubreakupapieceofmatteradinfinitum.Whatwouldbeleft?
Couldsmallparticlesofextendeddimensionremain?No,becauseifthiswerethecasethepieceofmatterwouldnotyetbebrokenuptoinfinity.Therefore,onlypointswithoutextensionwouldremain.Butnowletustrytoputtogetherthepieceofmatterstartingfromthesepoints:byputtingtogethertwopointswithoutextensionyoucannotobtainathingwithextension,norcanyouwiththree,orevenwithfour.Nomatterhowmanyyouputtogether,infact,youneverhaveextension,becausepointshavenoextension.Therefore,wecannotthinkthatmatterismadeofpointswithoutextension,becausenomatterhowmanyofthesewemanagetoputtogether,weneverobtainsomethingwithanextendeddimension.Theonlypossibility,Democritusconcludes,isthatanypieceofmatterismadeupofafinitenumberofdiscretepieceswhichareindivisible,eachonehavingfinitesize:theatoms.
Theoriginofthissubtlemodeofargumentationpre-datesDemocritus.ItcomesfromtheCilentoregioninthesouthofItaly,fromatownnowcalledVelia,whichinthefifthcenturyBCEwasaflourishingGreekcolonycalledElea.Parmenideslivedthere,thephilosopherwhohadtakentotheletterâperhapstoomuchâtherationalismofMiletusandtheideaborntherethatreasoncanrevealtoushowthingscanbeotherthantheyappear.Parmenideshadexploredanavenuetotruthviapurereasonalone,apathwhichledhimtodeclarethatallappearancesareillusory,thusopeningadirectionofthinkingthatwouldprogressivelymovetowardsmetaphysicsanddistanceitselffromwhatwouldcometobeknownasânaturalscienceâ.HispupilZeno,alsofromElea,hadbroughtsubtleargumentstobearinsupportofthisfundamentalistrationalism,whichrefutesthecredibilityofappearancesradically.AmongtheseargumentstherewasaseriesofparadoxesthatbecamecelebratedasâZenoâsparadoxesâ;theyseektoshowhowallappearanceisillusory,arguingthatthecommonplacenotionofmotionisabsurd.12
ThemostfamousofZenoâsparadoxesispresentedintheformofabrieffable:thetortoisechallengesAchillestoarace,startingoutwithaten-metreadvantage.WillAchillesmanagetocatch
![Page 15: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/15.jpg)
upwiththetortoise?Zenoarguesthatrigorouslogicdictatesthathewillneverbeabletodoso.Beforecatchingup,ineffect,Achillesneedstocoverthetenmetres,andinordertodothishewilltakeacertainamountoftime.Duringthistime,thetortoisewillhaveadvancedafewcentimetres.Tocoverthesecentimetres,Achilleswillhavetotakealittlemoretimebut,meanwhile,thetortoisewillhaveadvancedfurther,andsoon,adinfinitum.Achillesthereforerequiresaninfinitenumberofsuchtimestoreachthetortoise,andaninfinitenumberoftimes,arguesZeno,isaninfiniteamountoftime.Consequently,accordingtostrictlogic,Achilleswilltakeaninfinitetimetoreachthetortoise;orrather,wewillneverseehimdoso.Since,however,wedoseetheswiftAchillesreachingandovertakingasmanytortoisesashelikes,itfollowsthatwhatweseeisirrational,andthereforeillusory.
Letâsbehonest:thisishardlyconvincing.Wheredoestheerrorlie?OnepossibleansweristhatZenoiswrongbecauseitisnottruethatbyaccumulatinganinfinitenumberofthingsoneendsupwithaninfinitething.Thinkoftakingapieceofstring,cuttingitinhalf,andthenagaininhalf,andagain,adinfinitum.Attheend,youwillobtainaninfinitenumberofsmallpiecesofstring;thesumofthese,however,willbefinite,becausetheycanonlyadduptothelengthoftheoriginalpieceofstring.Hence,aninfinitenumberofstringscanmakeafinitestring;aninfinitenumberofincreasinglyshorttimesmaymakeafinitetime,andthehero,evenifhewillhavetocoveraninfinitenumberofdistances,eversmaller,willtakeafinitetimetodoso,andwillendupcatchingthetortoise.
Itseemsthattheparadoxisresolved.Thesolution,thatis,isintheideaofthecontinuumâarbitrarilysmalltimesmayexist,aninfinitenumberofwhichmakeupafinitetime.Aristotleisthefirsttointuitthispossibility,whichwassubsequentlydevelopedbyancientandmodernmathematics.fn1
Butisthisreallythecorrectsolutionintherealworld?Doarbitrarilyshortstringsreallyexist?Canwereallycutapieceofstringanarbitrarynumberoftimes?Doinfinitelysmallamountsoftimeexist?Thisispreciselytheproblemthatquantumgravitywillhavetoface.
Accordingtotradition,ZenohadmetLeucippusandhadbecomehisteacher.LeucippuswasthereforefamiliarwithZenoâsriddles.Buthehaddevisedadifferentwayofresolvingthem.Maybe,Leucippussuggests,nothingarbitrarilysmallexists:thereisalowerlimittodivisibility.
Theuniverseisgranular,notcontinuous.Withinfinitelysmallpoints,itwouldbeimpossibleevertoconstructextensionâasinDemocritusâsargument,reportedbyAristotleandmentionedabove.Therefore,theextensionofthestringmustbeformedbyafinitenumberoffiniteobjectswithfinitesize.Thestringcannotbecutasmanytimesaswewant;matterisnotcontinuous,itismadeofindividualâatomsâofafinitesize.
Whetherthisabstractargumentiscorrectornot,itsconclusionâasweknowtodayâcontainsagreatdealoftruth.Matterdoesindeedhaveanatomicstructure.IfIdivideadropofwaterintwo,Iobtaintwodropsofwater.Icandivideeachoneofthesetwodropsagain,andsoon.ButIcannotcontinuetoinfinity.AtacertainpointIhaveonlyonemolecule,andIhavefinished.Nodropsofwaterexistsmallerthanasinglemoleculeofwater.
Howdoweknowthistoday?Evidencehasaccumulatedovercenturies,muchofitfromchemistry.Chemicalsubstancesaremadeupofcombinationsofafewelementsandareformedbyproportions(ofweight)givenbywholenumbers.Chemistshaveconstructedawayofthinkingaboutsubstancesascomposedofmoleculesmadeupoffixedcombinationsofatoms.Water,forexampleâH2Oâiscomposedoftwopartshydrogenandonepartoxygen.
Buttheseareonlyclues.Stillatthebeginningofthelastcenturynumerousscientistsandphilosophersdidnotconsidertheatomichypothesistobecredible.AmongthemwastherenownedphysicistandphilosopherErnstMach,whoseideasonspacewouldcometohavegreatimportanceforEinstein.AttheendofalecturebyLudwigBoltzmannattheImperialAcademyofScienceinVienna,Machpubliclydeclared,âIdonotbelievethatatomsexist!âThiswasin1897.Many,likeMach,understoodchemicalnotationonlyasaconventionalmethodofsummarizinglawsofchemicalreactionsânotasevidencethatthereactuallyweremoleculesofwatercomposedoftwoatomsofhydrogenandoneofoxygen.Youcanâtseeatoms,theywouldsay.Atomswillneverbeseen,theywouldsay.Andthen,theyasked,howbigwouldanatombe?DemocrituscouldnevermeasurethesizeofhisatomsâŚ
Butsomebodyelsecould.Thedefinitiveproofoftheâatomichypothesisâhadtowaituntil1905.Itwasfoundbyarebellioustwenty-five-year-old,whohadstudiedphysicsbuthadnotbeenabletofindemploymentasascientistandwasmakingendsmeetbyworkingasanemployeeinthepatentofficeinBerne.Iwillspeakalotaboutthisyoungmanintherestofthisbook,andaboutthethreearticleshesenttothemostprestigiousphysicsjournalofthetime,theAnnalenderPhysik.Thefirstofthesearticlescontainedthedefinitiveproofthatatomsexist,andcalculatedtheirdimensions,solvingtheproblemposedbyLeucippusandDemocritustwenty-threecenturiesearlier.
![Page 16: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/16.jpg)
Figure1.3AlbertEinstein.
Thenameofthistwenty-five-year-old,obviously,isAlbertEinstein.Howdoeshedoit?Theideaissurprisinglysimple.Anyonecouldhavearrivedatit,fromthetime
ofDemocritusonwards,ifhehadhadEinsteinâsacumenandasufficientmasteryofmathematicstomakewhatwasnotaneasycalculation.Theideagoeslikethis:ifweobserveattentivelyverysmallparticles,suchasaspeckofdustoragrainofpollen,suspendedinstillairorinaliquid,weseethemtrembleanddance.Pushedbythistrembling,theymove,randomlyzigzagging,andsotheydriftslowly,graduallymovingawayfromtheirstartingpoint.ThismotionofparticlesinafluidiscalledBrownianmotion,afterRobertBrown,abiologistwhodescribeditindetailinthenineteenthcentury.Thetypicaltrajectoryofaparticledancinginthismannerisillustratedinfigure1.4.Itisasifthesmallparticleisreceivingblowsrandomlyfromeachsideofit.Infact,itisnâtâasifâitwerebeinghit,itreallyishit.Ittremblesbecauseitishitbyindividualmoleculesofair,whichcollidewiththeparticleattimesfromtherightandattimesfromtheleft.
Figure1.4TypicalBrownianmotion.
![Page 17: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/17.jpg)
Thesubtlepointisthefollowing.Thereareanenormousnumberofmoleculesofair.Onaverage,asmanyhitthegranulefromtheleftasthosethathititfromtheright.Iftheairâsmoleculeswereinfinitelysmallandinfinitelynumerous,theeffectofthecollisionsfromrightandfromleftwouldbalanceandthuscanceloutateachinstant,andthegranulewouldnotmove.Butthefinitesizeofthemoleculesâthefactthatthesearepresentinfiniteratherthaninfinitenumberâcausestheretobefluctuations(thisisthekeyword):thatistosay,thecollisionsneverbalanceoutexactly;theyonlybalanceoutonaverage.Imagineforamomentthemoleculeswereveryfewinnumberandlargeinsize:thegranulewouldclearlyreceiveablowonlyoccasionally;nowoneontheright,thenoneontheleftâŚBetweenonecollisionandtheotheritwouldmovehereandtheretoasignificantdegree,likeafootballkickedbyboysrunningaroundaplayingfield.Thesmallerthemolecules,ontheotherhand,theshortertheintervalbetweencollisionsandthebetterthehitsfromdifferentdirectionsbalanceandcanceleachotherout.Andthelessthegranulemoves.
Itisindeedpossible,withalittlemathematics,toworkbackfromtheamountofmovementofthegranule,whichcanbeobserved,tothedimensionsofthemolecules.Einsteindoesthis,asImentionedabove,attheageoftwenty-five.Fromobservationsofgranulesdriftinginfluids,fromthemeasurementofhowmuchtheseâdriftââthatis,moveawayfromapositionâhecalculatesthedimensionsofDemocritusâsatoms,theelementarygrainsofwhichmatterismade.Heprovides,after2,300years,theproofoftheaccuracyofDemocritusâsinsight:matterisgranular.
ThenatureofthingsSublimeLucretiusâsworkwillnotdie,Untilthedaytheworlditselfpassesaway.
âOvid13
IoftenthinkthatthelossoftheworksofDemocritusintheirentiretyfn2isthegreatestintellectualtragedytoensuefromthecollapseoftheoldclassicalcivilization.Takealookatthelistofhisworksinthefootnote;itisdifficultnottobedismayed,imaginingwhatwehavelostofthevastscientificreflectionsofantiquity.
WehavebeenleftwithallofAristotle,bywayofwhichWesternthoughtreconstructeditself,andnothingbyDemocritus.Perhaps,ifalloftheworksofDemocritushadsurvived,andnothingofAristotleâs,theintellectualhistoryofourcivilizationwouldhavebeenbetterâŚ
ButcenturiesdominatedbymonotheismhavenotpermittedthesurvivalofDemocritusâsnaturalism.TheclosureoftheancientschoolssuchasthoseofAthensandAlexandriaandthedestructionofallthetextsnotinaccordancewithChristianideaswerevastandsystematic,atthetimeofthebrutalanti-paganrepressionfollowingfromtheedictsofEmperorTheodosius,which,in390â1declaredthatChristianitywastobetheonlyandobligatoryreligionoftheempire.PlatoandAristotle,paganswhobelievedintheimmortalityofthesoulorintheexistenceofaPrimeMover,couldbetoleratedbyatriumphantChristianity.NotDemocritus.
Butatextsurvivedthedisaster,andhasreachedusinitsentirety.Throughit,weknowalittleaboutancientatomismand,aboveall,weknowthespiritofthatscience.ItisthesplendidpoemDererumnatura(TheNatureofThings,orOntheNatureoftheUniverse),bytheLatinpoetLucretius.
LucretiusadherestothephilosophyofEpicurus,apupilofapupilofDemocritus.EpicurusisinterestedmoreinethicalthanscientificquestionsanddoesnothaveDemocritusâsdepth.HesometimestranslatesDemocriteanatomismalittlesuperficially.ButhisvisionofthenaturalworldissubstantiallythatofthegreatphilosopherofAbdera.LucretiusdecantsinversethethoughtofEpicurusandtheatomismofDemocritus,andinthiswayapartofthisprofoundphilosophywassavedfromtheintellectualcatastropheoftheDarkAges.Lucretiussingsofatoms,thesea,thesky,ofnature.Heexpressesinluminousversephilosophicalquestions,scientificideas,refinedarguments.
âŚIwillexplainbywhatforcesnaturesteersthecoursesofthesunandthejourneyingsofthemoon,sothatweshallnotsupposethattheyruntheiryearlyracesbetweentheheavenandearthoftheirownfreewillâŚorthattheyarerolledroundinfurtheranceofsomedivineplanâŚ14
Thebeautyofthepoemliesinthesenseofwonderwhichpervadesthevastatomisticvisionâthesenseoftheprofoundunityofthings,derivedfromtheknowledgethatweareallmadeofthesamesubstanceasarethestars,andthesea:
âŚweareallsprungfromheavenlyseed.Allalikehavethesamefather,fromwhomall-nourishingmotherearthreceivestheshoweringdropsofmoisture.Thusfertilized,shegivesbirthtosmilingcropsandlustytrees,tomankindandallthebreedsofbeasts.Sheitisthatyieldsthefoodonwhichtheyallfeedtheirbodies,leadtheirjoyouslivesandrenewtheirraceâŚ15
Thereisasenseofluminouscalmandserenityaboutthepoem,whichcomesfromunderstandingthattherearenocapriciousgodsdemandingofusdifficultthings,andpunishingus.Thereisavibrantandairyjoyfulness,beginningwiththemarvellousopeningversesdedicatedtoVenus,aradiantsymbolofthecreativeforceofnature:
Beforeyouthewindsflee,andatyourcomingthecloudsforsakethesky.Foryoutheoceanlevelslaugh,theskyiscalmedandglowswithdiffusedradiance.16
Thereisadeepacceptanceofthelifeofwhichweareanintegralpart:
![Page 18: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/18.jpg)
Doyounotseethatnatureisclamouringfortwothingsonly,abodyfreefrompain,amindreleasedfromworryandfearfortheenjoymentofpleasurablesensations?17
Andthereisasereneacceptanceoftheinevitabilityofdeath,whichcancelseveryevilandaboutwhichthereisnothingtofear.ForLucretius,religionisignorance;reasonisthetorchthatbringslight.
Lucretiusâstext,forgottenforcenturies,wasrediscoveredinJanuary1417bythehumanistPoggioBracciolini,inthelibraryofaGermanmonastery.Poggiohadbeenthesecretaryofmanypopes,andwasapassionatehunterofancientbooks,inthewakeofthecelebratedrediscoveriesmadebyFrancescoPetrarch.HisrediscoveryofatextbyQuintilianmodifiedthecourseofthestudyoflawthroughoutthefacultiesofEurope;hisdiscoveryofthetreatiseonarchitecturebyVitruviustransformedthewayinwhichfinebuildingsweredesignedandconstructed.ButhistriumphwasrediscoveringLucretius.TheactualcodexfoundbyPoggiohasbeenlost,butthecopymadebyhisfriendNiccolòNiccoli(nowknownastheCodexLaurenziano35.30)isstillpreservedinitsentiretyinFlorenceâsBibliotecaLaurenziana.
ThegroundwasalreadysurelypreparedforsomethingnewwhenPoggiogaveLucretiusâsbookbacktohumanity.Already,fromDanteâsgeneration,ithadbeenpossibletohearmarkedlynewaccents:
Youreyeswentshootingthroughmyhearttowakemydormantthought.Looknow,Iâmdesperateanddistraughtwithlovethattearsmylifeapart.18
ButtherediscoveryofDererumnaturahadaprofoundeffectupontheItalianandEuropeanRenaissance,19anditsechoresounds,directlyorindirectly,inthepagesofauthorsrangingfromGalileo20toKepler,21andfromBacontoMachiavelli.InShakespeare,acenturyafterPoggio,atomsmakeadelightfulappearance:
MERCUTIOO,thenIseeQueenMabhathbeenwithyou:Sheisthefairiesâmidwife,andshecomesInshapenobiggerthananagate-stoneOntheforefingerofanalderman,DrawnwithalittleteamofatomiesOvermenâsnosesastheylieasleepâŚ22
MontaigneâsEssaysincludeatleastahundredquotationsfromLucretius.ButthedirectinfluenceofLucretiusextendedtoNewton,Dalton,Spinoza,DarwinâandallthewayuptoEinstein.TheveryideaofEinsteinâsthattheexistenceofatomsisrevealedbytheBrownianmotionofminuteparticlesimmersedinafluidmaybetracedbacktoLucretius.HereisapassageinwhichLucretiusprovidesaâlivingproofâofthenotionofatoms:
Thisprocessisillustratedbyanimageofitthatiscontinuallytakingplacebeforeourveryeyes.Observewhathappenswhensunbeamsareadmittedintoabuildingandshedlightonitsshadowyplaces.Youwillseeamultitudeoftinyparticlesminglinginamultitudeofwaysintheemptyspacewithinthelightofthebeam,asthoughcontendingineverlastingconflict,rushingintobattlerankuponrankwithneveramomentâspauseinarapidsequenceofunionsanddisunions.Fromthisyoumaypicturewhatitisfortheatomstobeperpetuallytossedaboutintheillimitablevoid.Tosomeextentasmallthingmayaffordanillustrationandanimperfectimageofgreatthings.Besides,thereisafurtherreasonwhyyoushouldgiveyourmindtotheseparticlesthatareseendancinginasunbeam:theirdancingisanactualindicationofunderlyingmovementsofmatterthatarehiddenfromoursight.Thereyouwillseemanyparticlesundertheimpactofinvisibleblows,changingtheircourseanddrivenbackupontheirtracks,thiswayandthat,inalldirections.Youmustunderstandthattheyallderivethisrestlessnessfromtheatoms.Itoriginateswiththeatoms,whichmoveofthemselves.Thenthosesmallcompoundbodiesthatareleastremovedfromtheimpetusoftheatomsaresetinmotionbytheimpactoftheirinvisibleblowsandinturncannonagainstslightlylargerbodies.Sothemovementmountsupfromtheatomsandgraduallyemergestothelevelofoursenses,sothatthosebodiesareinmotionthatweseeinsunbeams,movedbyblowsthatremaininvisible.23
EinsteinresuscitatedtheâlivingproofâpresentedbyLucretius,andprobablyfirstconceivedofbyDemocritus,andmadeitsolidbytranslatingitintomathematicalterms,thusmanagingtocalculatethesizeoftheatoms.
TheCatholicChurchattemptedtostopLucretius:intheFlorentineSynodofDecember1516itprohibitedthereadingofLucretiusinschools.In1551,theCouncilofTrentbannedhiswork.Butitwastoolate.AnentirevisionoftheworldwhichhadbeensweptawaybymedievalChristianfundamentalismwasre-emerginginaEuropewhichhadreopeneditseyes.Itwasnotjusttherationalism,atheismandmaterialismofLucretiusthatwerebeingproposedinEurope.Itwasnotmerelyaluminousandserenemeditationonthebeautyoftheworld.Itwasmuchmore:itwasanarticulateandcomplexstructureofthinkingaboutreality,anewmodeofthinking,radicallydifferentfromwhathadbeenforcenturiesthemind-setoftheMiddleAges.24
ThemedievalcosmossomarvellouslysungbyDantewasinterpretedonthebasisofahierarchicalorganizationoftheuniversewhichreflectedthehierarchicalorganizationofEuropeansociety:asphericalcosmicstructurewiththeEarthatitscentre;theirreducibleseparationbetweenEarthandheavens;finalisticandmetaphoricalexplanationsofnaturalphenomena.FearofGod,fearofdeath;littleattentiontonature;theideathatformsprecedingthingsdeterminethestructureoftheworld;theideathatthesourceofknowledgecouldonlybethepast,inrevelationandtraditionâŚ
ThereisnoneofthisintheworldofDemocritusassungbyLucretius.Thereisnofearofthegods;noendsorpurposesintheworld;nocosmichierarchy;nodistinctionbetweenEarthandheavens.
![Page 19: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/19.jpg)
Thereisadeeploveofnature,asereneimmersionwithinit;arecognitionthatweareprofoundlypartofit;thatmen,women,animals,plantsandcloudsareorganicthreadsofamarvellouswhole,withouthierarchies.ThereisafeelingofdeepuniversalisminthewakeofthesplendidwordsofDemocritus:âToawiseman,thewholeearthisopen,becausethetruecountryofavirtuoussoulistheentireuniverse.â25
Thereis,too,theambitionofbeingabletothinkabouttheworldinsimpleterms.Ofbeingabletoinvestigateandunderstandthesecretsofnature.Toknowmorethanourparents.AndthereareextraordinaryconceptualtoolsonwhichGalileo,KeplerandNewtonwillbuild:theideaoffreerectilinearmotioninspace;theideaofelementarybodiesandtheirinteractions,outofwhichtheworldisconstructed;theideaofspaceasacontaineroftheworld.
Andthereisthesimpleideaofthefinitedivisibilityofthings.Thegranularqualityoftheworld.Theideawhichstopstheinfinitebetweenourfingers.Thisideaisattherootoftheatomichypothesis,butitwillalsoreturnwithaugmentedforcewithquantummechanics,andtodayisrevealingitselftobepowerfulagainâasthekeystoneofquantumgravity.
ThefirstpersontomakethepartsofthemosaicwhichbegintoemergefromRenaissancenaturalismcohereâandtoreprisetheDemocriteanvision,immenselyreinforced,placingitatthecentreofmodernthoughtâwillbeanEnglishman,thegreatestscientistofalltimeandthefirstprotagonistofthefollowingchapter.
![Page 20: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/20.jpg)
2.TheClassics
IsaacandthelittlemoonIfinthepreviouschapterIappearedtobesayingthatPlatoandAristotlehaveonlydoneharmtothedevelopmentofscience,Iwouldliketocorrectthisimpression.Aristotleâsstudiesofnatureâofbotanyandzoology,forexampleâareextraordinaryscientificworks,groundeduponmeticulousobservationsofthenaturalworld.Theconceptualclarity,theattentiontothevarietyofnature,theimpressiveintelligenceandtheopennessofmindofthegreatphilosophermadehimanauthorityforcenturiestocome.ThefirstsystematicphysicsthatweknowofisAristotleâs,anditisnotbadphysicsatall.
Aristotlepresentsitinabookentitled,precisely,Physics.Thebookdidnâttakeitstitlefromthenameofadiscipline:itwasthedisciplinewhichgotitsnamefromAristotleâsbook.ForAristotle,physicsworksasfollows.First,itisnecessarytodistinguishbetweentheheavensandEarth.Intheheavens,everythingismadeupofacrystallinesubstancewhichmovesinacircularmotionandturnseternallyaroundtheEarthingreatconcentriccircles,withthesphericalEarthatthecentreofeverything.OntheEarth,itisnecessarytodistinguishbetweenforcedmotionandnaturalmotion.Forcedmotioniscausedbyathrustandendswhenthethrustends.Naturalmotionisverticalâupwardsordownwardsâanddependsbothonthesubstanceandthelocation.Eachsubstancehasaânaturalplaceâ,thatistosay,aproperaltitudetowhichitalwaysreturns:earthatthebottom,wateralittlewayaboveit,airalittlehigherstill,andfireevenhigher.Whenyoupickupastoneandletitfall,thestonemovesdownwardsbecauseitwantstoreturntoitsnaturallevel.Airbubblesinwater,fireintheair;andchildrenâsballoonsmoveupwards,seekingtheirnaturalplace.
Donotsmileatthistheory,ordismissit,becauseitisverysoundphysics.Itâsagoodandcorrectdescriptionofthemotionofbodiesimmersedinafluidandsubjecttogravityandfriction,namely,therealthingswemeetinoureverydayexperience.Itâsnotwrongphysics,asisfrequentlysaid.fn3
Itâsanapproximation.ButthephysicsofNewton,too,isanapproximationofgeneralrelativity.Andprobablyeverythingthatweknowtodayaswellisanapproximationofsomethingelsewhichwedonâtyetknow.ThephysicsofAristotleisstillrough,itisnotquantitative(wecannotcomputewithit),butitiscoherentandrationalandenablescorrectqualitativepredictionstobemade.Itisnotfornothingthatitremainedforcenturiesthebestavailablemodelforunderstandingmotion.1
PerhapsevenmoreimportantforthefuturedevelopmentofscienceisPlato.ItishewhounderstoodthevalueoftheintuitionofPythagorasandPythagorism:thatthekeyto
movingforwards,togoingbeyondMiletus,wasmathematics.PythagoraswasbornonSamos,asmallislandnotfarfromMiletus.Hisfirstbiographers,
IamblichusandPorphyry,reporthowyoungPythagoraswasadiscipleofelderlyAnaximander.EverythingoriginatesinMiletus.Pythagorastravelledwidely,probablyinEgyptandasfarasBabylon,beforefinallysettlinginthesouthofItaly,atCrotone,wherehefoundedareligio-politico-scientificsectwhichplayedanimportantroleinthepoliticsofthelittletownbutleftamomentouslegacytotheentireworld:thediscoveryofthetheoreticalutilityofmathematics:âNumberââheissaidtohaveassertedââgovernsformsandideas.â2
PlatodivestedPythagorismofitscumbersomeanduselessmysticalbaggage.Heabsorbedanddistilleditsusefulmessage:mathematicsisthelanguagebestadaptedtounderstandanddescribetheworld.Thereachofthisinsightisimmense;itisoneofthereasonsforthesuccessofWesternscience.Accordingtotradition,Platocarvedonthedoorofhisschoolthephrase,âLetnooneenterherewhoisignorantofgeometry.â
Drivenbythisconviction,itwasPlatowhoposedthemomentousquestion:thequestionoutofwhich,afteralongdetour,modernsciencewouldemerge.Ofhisdiscipleswhostudiedmathematicsheaskediftheycouldfindthemathematicallawsfollowedbythecelestialbodiesvisibleintheheavens.Venus,MarsandJupitercanbeeasilyobservedinthenightsky.Theyseemtomovealittleatrandom,backandforthamongtheotherstars.Isitpossibletofindamathematicswhichisabletodescribeandpredicttheirmovements?
TheexercisebeginswithEudoxusinPlatoâsschool,andispursuedthroughoutthefollowingcenturiesbyastronomerssuchasAristarchusandHipparchus,bringingancientastronomyontoanextremelyhighscientificlevel.Weknowofthetriumphsofthissciencethankstoasinglebook,theonlyonetohavesurvived:theAlmagestofPtolemy.PtolemywasanastronomerwholivedinAlexandriainthefirstcenturyofourera,undertheRomanEmpire,whensciencewasalreadyin
![Page 21: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/21.jpg)
declineandabouttodisappearaltogether,overwhelmedbythecollapseoftheHellenisticworldandsuffocatedbytheChristianizationoftheempire.
Ptolemyâsbookisamajorworkofscience.Rigorous,precise,complex,itpresentsamathematicalsystemofastronomycapableofpredictingtheseeminglyrandommovementsoftheplanetsinthesky,withalmostcompleteprecision,giventhelimitationsofthehumaneye.ThebookistheproofthattheintuitionofPythagoraswascorrect.Mathematicsallowstheworldtobedescribedandthefuturetobepredicted:theapparentlywanderinganddisorderlymovementsoftheplanetscanbepreciselypredictedbyusingmathematicalformulaethatPtolemy,summarizingtheresultsofcenturiesofworkbyGreekastronomers,presentsinasystematicandmasterlyway.Eventoday,withalittlestudying,itispossibletoopenPtolemyâsbook,learnitstechniquesandcalculate,forexample,thepositionwhichMarswillhaveinafuturesky.Today:twothousandyears,thatis,afterthebookwaswritten.TherealizationthatworkingthismagicisreallypossibleisthebasisofmodernscienceandowesnotalittletoPythagorasandPlato.
Afterthecollapseofancientscience,noonethroughouttheMediterraneanwascapableofunderstandingPtolemyâoranyoftheothersmallnumberofmajorscientificworksthatsurvivedthecatastrophe,suchastheElementsofEuclid.InIndia,whereGreeklearninghadarrived,thankstorichcommercialandculturalexchanges,thesebookswerestudiedandunderstood.
FromIndiathisknowledgereturnedtotheWest,thankstolearnedPersianandArabscientistswhowereabletounderstandandpreserveit.Butastronomydidnottakeanyverysignificantstepforwardforoverathousandyears.
MoreorlessatthesametimeasPoggioBracciolinidiscoveredthemanuscriptofLucretius,theheadyatmosphereofItalianhumanismandtheenthusiasmforancienttextsalsointoxicatedayoungPolewhohadcometostudyinItaly,firstatBologna,thenatPadua.HesignedhimselfintheLatinmanner:NicolausCopernicus.TheyoungCopernicusstudiesPtolemyâsAlmagestandfallsinlovewithit.Hedecidestospendhislifedoingastronomy,followinginthefootstepsofthegreatPtolemy.
Thetimeisnowripeand,morethanathousandyearsafterPtolemy,CopernicusisabletomaketheleapforwardthatgenerationsofIndian,ArabandPersianastronomershadnotbeenabletomake:notsimplylearning,applyingandaddingsmallameliorationstothePtolemaicsystembutthoroughlyimprovingitâwiththecouragetochangeitindepth.InsteadofdescribingheavenlybodiesturningaroundtheEarth,CopernicuswritesasortofrevisedandcorrectedversionofPtolemyâsAlmagest,inwhichtheSunisatthecentreandtheEarth,togetherwiththeotherplanets,runsaroundit.
InthiswayâCopernicushopesâthecalculationswouldworkevenbetter.Inreality,theydidnotworkmuchbetterthanthoseofPtolemy;infact,intheend,theyturnedouttoworklesswell.Buttheideawas,nevertheless,sound:inthesucceedinggeneration,JohannesKeplershowsthattheCopernicansystemcanreallybemadetofunctionbetterthanPtolemyâs.Painstakinglyanalysingnew,preciseobservations,KeplershowsthatafewnewmathematicallawscandescribewithexactitudethemovementsoftheplanetsaroundtheSun,withadegreeofaccuracyevengreaterthananyobtainedinantiquity.Wearenowin1600,andforthefirsttimehumanityfindsouthowtodosomethingbetterthanwhatwasdoneinAlexandriamorethanathousandyearsearlier.
WhileKeplerinthecoldnorthcalculatesmovementsinthesky,inItalyitiswithGalileoGalileithatthenewsciencebeginstotakeoff.Exuberant,Italian,polemical,argumentative,highlycultured,exceptionallyintelligentandoverflowingwithinventiveness,GalileogetssentfromHollandanewinventionâthetelescopeâandmakesagesturewhichchangeshumanhistory.Hepointsittowardsthesky.
LikeRoyinBladeRunner,heseesthingswepeoplewouldnâtbelieve:ringsaroundSaturn,mountainsonthemoon,phasesofVenus,moonsorbitingJupiterâŚEachofthesephenomenarendersCopernicusâsideasmoreplausible.Scientificinstrumentsbegintoopenthemyopiceyesofhumankindontoaworldvasterandmorevariedthanithadasyetbeenabletoconceiveof.
ButGalileoâsgrandideaistomakethelogicaldeductionfromthecosmicrevolutionbroughtaboutbyCopernicus:convincedthattheEarthisaplanetlikeallothers,Galileoreasonsthat,ifmovementsintheheavensfollowprecisemathematicallaws,andiftheEarthisaplanetlikeallothers,andthuspartoftheheavens,thentheremustalsoexistprecisemathematicallawsgoverningthemovementsofobjectsonEarth.
ConfidentoftherationalityofnatureandofthePythagorean-Platonicvisionthatnatureisunderstandablethroughmathematics,GalileodecidestostudyhowobjectsmoveonEarthwhentheyaresetfreeâthatis,whentheyfall.Convincedthatarelevantmathematicallawmustexist,hesetsouttosearchforit,bytrialanderror.Forthefirsttimeinthehistoryofmankind,anexperimentismade.ExperimentalsciencebeginswithGalileo.Hisexperimentissimple:heletsobjectsfall;thatis,heletsthemfollowwhatforAristotlewastheirnaturalmovementandseekstomeasurepreciselytheirfallingspeed.
Theresultismomentous:objectsdonotfallalwaysataconstantspeed,aseverybodythought.Theirspeed,instead,graduallyincreasesduringtheearlypartofthefall.Inthisphase,whatisconstantisnotthespeedofthefallbutrathertheacceleration,thatistosay,therateatwhichspeedincreases.And,magically,thisaccelerationturnsouttobethesameforallobjects.Galileocompletesafirstroughmeasurementofthisaccelerationandfindsitconstant.Itsvalueis
![Page 22: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/22.jpg)
approximately9.8metrespersecondpersecond,whichistosaythatforeverysecondthatanobjectfalls,itsspeedincreasesby9.8metrespersecond.Keepinmindthisnumber.
Thisisthefirstmathematicallawdiscoveredforearthlybodies:thelawoffallingbodies.fn4Upuntilthispoint,onlymathematicallawsforthemovementsoftheplanetshadbeendiscovered.Mathematicalperfectionisnolongerconfinedtotheheavens.
Butthegreatestresultisstilltocome,anditwillbeIsaacNewtonwhowillattainit.NewtonstudiesindepththeresultsofGalileoandKeplerandbycombiningthem,findsthehiddendiamond.Wecanfollowhisreasoningintermsoftheâlittlemoonâ,ashehimselftellsitinTheMathematicalPrinciplesofNaturalPhilosophy,thebookthatformsthefoundationofmodernscience.
ImaginethattheEarth,writesNewton,hadmanymoons,likeJupiter.InadditiontotherealMoon,imagineothermoons,andinparticularalittlemoonwhichorbitstheEarthataminimaldistancefromit,justabovethemountainpeaks.Atwhatspeedwouldthislittlemoontravel?OneofthelawsdiscoveredbyKeplerrelatestheradiusoforbitwithperiod,namely,thetimetakentocompleteanorbit.fn5WeknowtheradiusoftheorbitoftherealMoon(Hipparchushadmeasureditinantiquity)anditsperiod(onemonth).Weknowtheradiusoftheorbitofthelittlemoon(theradiusoftheEarth,measuredbyEratosthenesinantiquity).Withasimpleproportionwecancomputetheperiodoftheorbitofthelittlemoon.Theresultisonehourandahalf.ThelittlemoonwouldcompleteitsorbitaroundtheEartheveryonehourandahalf.
Now,anobjectwhichorbitsdoesnotgostraight:itcontinuallychangesdirection,andachangeofdirectionisanacceleration.ThelittlemoonacceleratestowardsthecentreoftheEarth.Thisaccelerationiseasytocompute.fn6Newtonmakesthesimplecalculation,andtheresultisâŚ9.8metrespersecondpersecond!ThesameaccelerationasinGalileoâsexperimentsforfallingbodiesonEarth.
Coincidence?Itcanâtbe,reasonsNewton.Iftheeffectisthesameâadownwardsaccelerationof9.8metrespersecondpersecondâthecausemustbethesame.Andso:theforcewhichcausesthelittlemoontoturnarounditsorbitmustbethesameasthatwhichcausesobjectstofalltothegroundonEarth.
Wecalltheforcecausingobjectstofallgravity.NewtonunderstandsthatitisthissamegravitythatmakesthelittlemoonturnaroundtheEarth.Withoutthisgravityitwouldrunawayinastraightline.Butthen,also,therealMoonmustorbittheEarthbecauseofgravity!AndthemoonswhichorbitJupiterareattractedbyJupiter,andtheplanetswhichturnaroundtheSunareattractedbytheSun!Withoutthisattraction,everycelestialbodywouldmoveinastraightline.Sotheuniverse,then,isalargespacewherebodiesattractoneanotherbymeansofforces;andthereisauniversalforce:gravityâeverybodyattractseveryotherbody.
Animmensevisiontakesshape.Suddenly,aftermillennia,thereisnolongerseparationbetweentheheavensandEarth;thereisnoânaturallevelâforthings,asAristotlepresumed;thereisnocentretotheworld;thingsletfreenolongerseektheirnaturalplacebutmoveinastraightline,forever.
AsimplecalculationwiththelittlemoonallowsNewtontodeducehowtheforceofgravitychangeswithdistanceandtodetermineitsstrength,*givenbywhatwecalltodayNewtonâsconstant,indicatedbytheletterâGâforâgravityâ.OnEarth,thisforcecausesthingstofall;intheheavensitholdsplanetsandsatellitesontheirorbits.Theforceisthesame.
ItâsasubversionoftheconceptualstructureoftheAristotelianworld,thedominantvisionoftheworldthroughouttheMiddleAges.ThinkofDanteâsuniverse,forexample:justasforAristotle,Earthisaballatthecentreoftheuniverse,orbitedbythecelestialspheres.Notanymore.Theuniverseisanimmense,infinitespacestuddedwithstars,withoutlimitandwithoutcentre.Withinit,materialbodiesrunfreeandstraight,unlessaforce,generatedbyanotherbody,deviatesthem.ReferencetoancientatomismisclearinNewton,evenifstillformulatedinconventionalterms:
ItseemsprobabletomethatGod,inthebeginning,formedmatterinsolid,massy,hard,impenetrable,moveableparticles,ofsuchsizesandfigures,andwithsuchotherproperties,andinsuchproportionstospaceâŚ3
TheworldofNewtonianmechanicsissimple,andissummarizedinfigures2.1and2.2.ItistheworldofDemocritusreborn.Aworldmadeofavast,undifferentiatedspace,alwaysequaltoitself,whereparticlesrunforeverandactuponeachotherâandnothingelse.TheworldsungbyLeopardi:
âŚsittinghereandgazing,IfindthatendlessSpacesbeyondthathedge,andmore-than-humanSilences,andthedeepestpeaceandquietArefashionedinmythoughtâŚ4
ButnowthevisionisimmenselymorepowerfulthaninDemocritus,becauseitisnotjustamentalimagewithwhichtoordertheworld:itisnowcombinedwithmathematics,withthelegacyofPythagoras,andwiththemightytraditionoftheAlexandrianastronomersâmathematicalphysics.TheworldofNewtonistheworldofDemocritus,renderedmathematical.
![Page 23: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/23.jpg)
Figure2.1Whatistheworldmadeof?
Figure2.2TheworldofNewton:particleswhichmoveinspace,astimepasses,attractedbyforces.
Newtonacknowledgeswithouthesitationthedebtthatthenewscienceowestothescienceofantiquity.InthefirstlinesofhisTheSystemoftheWorld,forexample,heattributestoantiquity(correctly)theoriginsoftheideaatthebasisoftheCopernicanrevolution:âItwastheopinionoftheancientphilosophersthatinthehighestpartsoftheworldthestarsremainfixedandmotionless,andthattheEarthturnsaroundtheSunâ;althoughheisabitconfusedastowhodidwhatinthepast,andquotesâsometimesappositely,sometimesoutofcontextâPhilolaus,AristarchusofSamos,Anaximander,Plato,Anaxagoras,Democritusand(!)âthelearnedNumaPompilius,kingoftheRomansâ.
ThepowerofthenewNewtonianintellectualframe-workprovestobebeyondallexpectation.TheentiretechnologyofthenineteenthcenturyandofourownmodernworldrestslargelyuponNewtonâsformulae.Threecenturieshavepassed,butitâsstillthankstotheoriesbaseduponNewtonâsequationsthattodaywebuildbridges,trainsandskyscrapers,enginesandhydraulicsystems;thatweknowhowtoflyplanes,makeweatherforecasts,predicttheexistenceofaplanetbeforeseeingitandsendspaceshipstoMarsâŚThemodernworldwouldnothavebeenbornwithoutpassingbywayofNewtonâslittlemoon.
Anewconceptionoftheworld,awayofthinkingwhichraisedtheenthusiasmoftheEnlightenmentofVoltaireandKant,aneffectivewayforpredictingthefuture:thishasbeenandcontinuestobetheimmenselegacyoftheNewtonianrevolution.
Itseemedthusthatthefinalkeytounderstandingrealityhadbeendiscovered:theworldconsistsonlyofagreat,infinitespacewhere,astimepasses,particlesmoveandattractoneanotherbymeansofforces.Wecanwritepreciseequationsthatdescribetheseforces.Theseequationsprovetobeimmenselyeffective.Stillinthenineteenthcentury,peoplesaidthatNewtonwasnotonlyoneofthemostintelligentandfar-seeingofmenbutalsothemostfortunateâbecausethereisonlyonesystemoffundamentallaws,andhewasgiventhegoodfortuneofdiscoveringit.Everythingseemedclear.
Butisthatreallyall?
Michael:fieldsandlightNewtonknewthathisequationsdidnotdescribealltheforcesthatexistinnature.Thereareforcesotherthangravitythatactuponbodies.Thingsdonâtmovejustwhentheyfall.ThefirstproblemleftopenbyNewtonwastounderstandtheotherforcesthatdeterminewhathappensaroundus.Thishadtowaituntilthenineteenthcentury,anditledtotwosurprises.
Thefirstsurpriseisthatalmostallphenomenaweseearegovernedbyasingleforce,otherthangravity:theforcethattodaywecallelectromagnetism.Itisthisforcewhichholdstogetherthematterthatformssolidbodies;holdstogetheratomsinmolecules,andelectronsinatoms.Thisiswhatmakeschemistryandlivingmatterwork.Itisthisforcewhichoperatesintheneuronsofourbrainandgovernsourprocessingoftheinformationontheworldweperceive,andthewaywethink.Anditâsalwaysthisforcethatcreatesthefrictionwhichstopsaslidingobject,whichsoftensthelandingofaparachutist,whichturnselectricmotorsandcombustionengines,fn7orthatallowsustoturnonlightsandlistentotheradio.
Thesecondandbiggestsurprise,crucialtothestoryIâmtelling,isthatunderstandingthisforcerequiresanimportantmodificationtotheworldofNewton:themodificationoutofwhichmodern
![Page 24: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/24.jpg)
physicswasborn,andthemostimportantnotiontokeepinfocus,tounderstandtherestofthisbookâthenotionoffield.
TheunderstandingofhowelectromagneticforceworkswasmadebyanotherBriton,orratherbytwo:scienceâsoddestcoupleâMichaelFaradayandJamesClerkMaxwell.
MichaelFaradayisanimpoverishedLondonerwithoutformaleducation,whoworksfirstinabookbindery,theninalaboratory,whereheexcels,gainshismasterâsconfidenceandgrowsintothemostbrilliantexperimenterofnineteenth-centuryphysicsanditsgreatestvisionary.Withoutknowingmathematics,hewritesoneofthebestbooksofphysicseverwritten,virtuallydevoidofequations.Heseesphysicswithhismindâseye,andwithhismindâseyecreatesworlds.JamesClerkMaxwellisarichScottisharistocratandoneofthegreatestmathematiciansofthecentury.Despitebeingseparatedbyagulfinintellectualstyleaswellassocialorigin,theysucceedinunderstandingeachotherâand,together,combiningtwokindsofgenius,theyopenthewaytomodernphysics.
Figure2.3MichaelFaradayandJamesClerkMaxwell.
Whatwasknownaboutelectricityandmagnetismatthebeginningoftheeighteenthcenturyconsistedoflittleotherthanafewamusingsideshowtricks:glassrodswhichattractpiecesofpaper;magnetswhichrepelandattract.Thestudyofelectricityandmagnetismcontinuedslowlythroughouttheeighteenthcenturyandintothenineteenth,wherewefindFaradayworkinginaLondonlaboratoryfullofbobbins,needles,knivesandironcages,exploringhowelectricalandmagneticthingsattractandrepel.AgoodNewtonian,hetriestounderstandtheforcewhichactsbetweenchargedandmagneticthings.Butslowly,guidedbyhishands,inclosecontactwiththeseobjects,heisledtoanintuitionthatwillbecomethebasisofmodernphysics.Heâseesâsomethingnew.
Hisintuitionisthis:wemustnotthinkofforcesactingdirectlybetweendistantobjects,asNewtonpresumed.Wemustinsteadthinkthatthereexistsanentitydiffusedthroughoutspace,whichismodifiedbyelectricandmagneticbodiesandwhich,inturn,actsupon(pushesandpulls)thebodies.Thisentity,whoseexistenceFaradayintuits,istodaycalledthefield.
Whatisit,then,afield?Faradayseesitasformedbybundlesofverythinlines(infinitelythin),whichfillspace;aninvisible,giganticcobwebfillingeverythingaroundus.Hecallstheselinesâlinesofforceâbecause,insomeway,theselinesâcarrytheforceâ:theytransmittheelectricandthemagneticforcesfromonebodytoanother,asiftheywerecablespullingandpushing(figure2.4).
Anobjectwithanelectriccharge(arubbedglassrod,forinstance)distortstheelectricandmagneticfields(thelines)arounditself,andinturnthesefieldsproduceaforceoneachchargedobjectimmersedinthem.Thus,twodistantchargedobjectsdonotattractorrepeleachotherdirectlybutonlyviathemediuminterposedbetweenthem.
![Page 25: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/25.jpg)
Figure2.4Thefieldâslinesfillspace.Throughthem,twoobjectswithelectricalchargeinteract.Theforceofthetwoobjectsisâcarriedâbythefieldâslinesofforce.
Ifyoutaketwomagnetsinyourhandsandplaywiththem,bringingthemtogetherandapartrepeatedly,feelingtheforcewithwhichtheyattractandrepel,itisnotdifficulttoexperiencethesameintuitionasFaraday,toâfeelâviatheseeffectsthefieldinterposedbetweenthemagnets.
ThisisaradicallydifferentideafromtheNewtoniannotionofaforceactingbetweendistantbodies.ButitwouldhaveappealedtoNewton.Newton,indeed,wasperplexedregardingthisveryattractionatadistancethathehimselfhadintroduced.HowdoestheEarthmanagetoattracttheMoon,whichissodistant?HowcantheSunattracttheEarthwithoutcomingintocontactwithit?Hehadwritteninaletter:
Itisinconceivablethatinanimatebrutemattershould,withouttheinterventionofsomethingelsewhichisnotmaterial,operateuponandaffectothermatter,andhaveaneffectuponit,withoutmutualcontact.5
And,furtherdownthepage,weevenfind:ThatGravityshouldbeinnate,inherentandessentialtoMatter,sothatoneBodymayactuponanotherataDistancethroâaVacuum,withouttheMediationofanythingelse,byandthroughwhichtheirActionandForcemaybeconveyedfromonetoanother,istomesogreatanAbsurdity,thatIbelievenoManwhohasinphilosophicalMattersacompetentFacultyofthinking,caneverfallintoit.GravitymustbecausedbyanAgentactingconstantlyaccordingtocertainLaws;butwhetherthisAgentbematerialorimmaterial,IhavelefttotheConsiderationofmyReaders.6
Newtonisdeeminghisveryownmasterworktobeabsurdâtheverysameworkwhichwastobepraisedforcenturiestocomeastheultimateachievementofscience!Heunderstandsthatbehindtheactionatadistanceofhistheorytheremustbesomethingelse,buthehasnoideawhat,andleavesthequestionâŚâtotheConsiderationofmyReadersâ!
Itischaracteristicofgeniustobeawareofthelimitationsofitsownfindings,eveninthecaseofsuchmomentousoutcomesasNewtonâsdiscoveryofthelawsofmechanicsanduniversalgravity.Newtonâstheoryworkedsowell,itturnedouttobesouseful,thatfortwocenturiesnoonebotheredanylongertoquestionitâuntilFaraday,theâreaderâtowhomNewtonhadbequeathedtheunansweredquestion,foundthekeytounderstandinghowbodiescanattractandrepeleachotheratadistanceinareasonablemanner.EinsteinwilllaterapplyFaradayâsbrilliantsolutiontoNewtonâsowntheoryofgravity.
IntroducingthenewentityâthefieldâFaradaydepartsradicallyfromNewtonâselegantandsimpleontology:theworldisnolongermadeuponlyofparticlesthatmoveinspacewhiletimepasses.Anewactorâthefieldâappearsonthescene.Faradayisawareoftheimportanceofthestepheistaking.Therearebeautifulpassagesinhisbookwhereheaskswhethertheselinesofforcecouldbethingswitharealexistence.Afterdoubtsanddifferentconsiderations,heconcludesthathethinkstheyareindeedreal,butwithâthehesitationthatisnecessarywhenfacedwiththedeepestquestionsofscienceâ.7Heisconsciousthatheissuggestingnothinglessthanamodificationofthestructureoftheworld,aftertwocenturiesofuninterruptedsuccessesforNewtonianphysics(figure2.5).
![Page 26: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/26.jpg)
Figure2.5TheworldofFaradayandMaxwell:particlesandfieldswhichmoveinspace,withthepassageoftime.
Maxwellquicklyrealizesthatgoldhasbeenstruckwiththisidea.HetranslatesFaradayâsinsight,whichFaradayexplainsonlyinwords,intoapageofequations.fn8ThesearenowknownasMaxwellâsequations.Theydescribethebehaviouroftheelectricandthemagneticfields:themathematicalversionoftheâFaradaylinesâ.fn9
Today,Maxwellâsequationsareuseddailytodescribeallelectricandmagneticphenomena,todesignantennae,radios,electricenginesandcomputers.Andthisisnotall:thesesameequationsareneededtoexplainhowatomsfunction(theyareheldtogetherbyelectricalforces),andwhytheparticlesofthematerialthatformsastoneadheretogether,orhowtheSunworks.Theydescribeanamazingnumberandrangeofphenomena.Almosteverythingthatwewitnesstakingplaceâwiththeexceptionofgravity,butlittleelsebesidesâiswelldescribedbyMaxwellâsequations.
Butthereismore.Thereisstillwhatisperhapsthemostbeautifulsuccessofscience:Maxwellâsequationstelluswhatlightis.
MaxwellrealizesthathisequationspredictthatFaradayâslinescantrembleandundulate,justlikethewavesofthesea.HecomputesthespeedatwhichtheundulationsofFaradayâslinesmoveandtheresultturnsouttobeâŚthesameasforlight!Why?Maxwellunderstands:becauselightisnothingotherthanthisrapidtremblingofFaradayâslines!NotonlyhaveFaradayandMaxwellfiguredouthowelectricityandmagnetismworkbut,withthesamestroke,asacollateraleffect,theyhavefiguredoutwhatlightis.
Weseetheworldaroundusincolour.Whatiscolour?Putsimply,itisthefrequency(thespeedofoscillation)oftheelectromagneticwavethatlightis.Ifthewavevibratesmorerapidly,thelightisbluer.Ifitvibratesalittlemoreslowly,thelightisredder.Colour,asweperceiveit,isthepsychophysicalreactionofthenervesignalgeneratedbythereceptorsofoureyes,whichdistinguishelectromagneticwavesofdifferentfrequencies.
IwonderhowMaxwellfeltwhenherealizedthathisequationsâwrittentodescribebobbins,smallcagesandlittleneedlesinFaradayâslabâturnedouttoexplainthenatureoflightandcolourâŚ
LightisthusnothingmorethanarapidvibrationofthespiderwebofFaradayâslines,whichripplelikethesurfaceofalakeasthewindblows.ItisnâttruethatweâdonotseeâFaradaylines.WeonlyseevibratingFaradaylines.âToseeâistoperceivelight,andlightisthemovementofFaradaylines.Nothingleapsfromonelocationinspacetoanotherwithoutsomethingtransportingit.Ifweseeachildplayingonthebeach,itisonlybecausebetweenthemandourselvesthereisthislakeofvibratinglineswhichtransporttheirimagetous.Istheworldnotmarvellous?
Thediscoveryisextraordinary,butthereisevenmore.Theultimatecorollaryofthediscoveryhasaconcretevalueforusthatisunequalled.MaxwellrecognizesthattheequationsforeseethatFaradayâslinescanalsovibrateatmuchlowerfrequencies,thatistosay,moreslowlythanlight.Therefore,theremustbeotherwaveswhichnobodyhadyetseen,producedbythemovementofelectricalcharges,whichinturnmoveelectricalcharges.Itmustbepossibletoshakeanelectricchargehere,andtoproduceawavewhichwilldriveanelectriccurrentthere.Onlyafewyearslater,thesewaves,anticipatedtheoreticallybyMaxwell,willberevealedbytheGermanphysicistHeinrichHertz;andjustafewyearslaterstill,GuglielmoMarconibuildsthefirstradio.
Allmoderncommunicationstechnologyâradio,television,telephones,computers,satellites,wi-fi,theinternet,etc.âisanapplicationofMaxwellâsprediction;theMaxwellequationsarethebasisforallcalculationsmadebytelecommunicationsengineers.Thecontemporaryworld,basedoncommunications,emergesfromtheintuitionsofapoorLondonbookbinderâaskilfulexplorerofideaswithavividimaginationâwhosawsomelinesinhismindâseye;andtheworkofagoodmathematicianwhotranslatedthisvisionintoequations,understandingthatintheblinkofaneyethewavesoftheselinescancarrynewsfromonesideoftheplanettotheother.
![Page 27: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/27.jpg)
Figure2.6Whatistheworldmadeof?
Ourentirecurrenttechnologyisfoundedontheuseofaphysicalthingâelectromagneticwavesâwhichwasnotdiscoveredempirically:itwaspredictedbyMaxwell,simplybysearchingforthemathematicaldescriptionaccountingfortheintuitionFaradaygotfrombobbinsandneedles.Thisistheoutstandingpoweroftheoreticalphysics.
Theworldhaschanged:itisnolongermadeupofparticlesinspacebutofparticlesandfieldsinspace(figure2.6).Itseemsaminorchange,butafewdecadeslaterayoungJewishman,acitizenoftheworld,willdrawfromitconsequencesthatwillgofarbeyondMichaelFaradayâsalreadyfervidimagination,andwhichwillshakeNewtonâsworldevenfurthertoitscore.
*
![Page 28: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/28.jpg)
![Page 29: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/29.jpg)
PartTwo
THE BEGINNING OF THE REVOLUTION
Twentieth-centuryphysicshasradicallymodifiedtheNewtonianimageoftheworld.Thenewstepsarethebasisofagreatdealoftodayâstechnology.Thedeepeningofourunderstandingoftheworldisbasedontwotheories:generalrelativityandquantummechanics.Bothdemandadaringre-evaluationofourconventionalideasabouttheworld:spaceandtimeinrelativity;matterandenergyinquantumtheory.
InthispartofthebookIdescribethetwotheoriesinsomedetail,tryingtoclarifytheircoremeaningandhighlighttheconceptualrevolutiontheybroughtabout.Itâsherethatthemagicoftwentieth-centuryphysicsbegins.Studyingandtryingtounderstandthemindepthisabewitchingadventure.
Thesetwotheoriesârelativityandthequantaâprovidethebasisonwhichwearetodaybuildingaquantumtheoryofgravity.Theyarethegroundfromwhichwearetryingtomoveforwards.
![Page 30: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/30.jpg)
3.Albert
ThefatherofAlbertEinsteinbuiltpowerstationsinItaly.WhenAlbertwasayoungboy,theMaxwellequationswereonlyafewdecadesoldâbutItalywasenteringitsindustrialrevolution,andtheturbinesandtransformersthathisfatherconstructedwerealreadybasedonthem.Thepowerofthenewphysicswasobvious.Albertwasarebel.HisparentslefthiminGermanytoattendhighschool,buthefoundthe
Germanschoolsystemtoorigidandmilitaristic;hecouldnotstandtheauthorityoftheschoolandabandonedhisstudies.HejoinedhisparentsinItaly,inPavia,andspenthistimeloafing.Later,hewenttostudyinSwitzerland,initiallyfailingtogetintotheZurichPolytechnic,ashewished.Afterhisuniversityyearshecouldnotfindaresearchpositionand,inordertolivewiththegirlheloved,hefoundemploymentinthepatentofficeofBerne.Itwasnâtmuchofaprofessionforaphysicsgraduate,butitgaveAlberttimetothink,andtowork
independently.Andhedidthinkandwork.Afterall,thisiswhathehaddonesincehisearlyyouth:hewouldreadEuclidâsElementsandKantâsCritiqueofPureReasoninsteadofattendingtowhathewasbeingtaughtatschool.Youdonâtgettonewplacesbyfollowingestablishedtracks.Attheageoftwenty-five,EinsteinsendstotheAnnalenderPhysikthreearticles.Eachwasworthy
ofaNobelPrize,andmore.Eachoneofthethreeisapillarsupportingourunderstandingoftheworld.Ihavealreadyspokenofthefirstarticle,inwhichtheyoungAlbertcalculatesthedimensionsofatomsandproves,aftertwenty-threecenturies,thattheideasofDemocrituswerecorrect:matterisgranular.ThesecondarticleistheoneforwhichEinsteinismostfamousâthearticleinwhichheintroduces
thetheoryofrelativityâanditistothetheoryofrelativitythatthischapterisdevoted.Infact,therearetwotheoriesofrelativity.Theenvelopesentbythetwenty-five-year-oldEinstein
containedtheexpositionofthefirstofthese:thetheoryknowntodayasâspecialrelativityâ.Thisisanimportantclarificationofthestructureofspaceandtime,whichIillustrateherebeforeturningtotheother,andmostimportantofEinsteinâstheories:generalrelativity.Specialrelativityisasubtleandconceptuallydifficulttheory.Itismoredifficulttodigestthan
generalrelativity.Reader,donâtbecomedemoralizedifthenextfewpagessoundabitabstruse.Thetheoryshows,forthefirsttime,thatintheNewtonianvisionoftheworldthereisnâtjustsomethingmissing:rather,itmustberadicallymodifiedâinawaythatgoescompletelyagainstcommonsense.Itisthefirstrealleapintotherevisionofourmostintuitiveunderstandingoftheworld.
TheextendedpresentThetheoriesofNewtonandofMaxwellappeartocontradicteachotherinasubtleway.Maxwellâsequationsdetermineavelocity:thevelocityoflight.ButNewtonâsmechanicsisnotcompatiblewiththeexistenceofafundamentalvelocity,becausewhatentersNewtonâsequationsisacceleration,notvelocity.InNewtonâsphysics,velocitycanonlybevelocityofsomethingwithrespecttosomethingelse.GalileohadunderlinedthefactthattheEarthmoveswithrespecttotheSun,evenifwedonotperceivethismovement,becausewhatweusuallytermâvelocityâisvelocityâwithrespecttoEarthâ.Velocity,wesay,isarelativeconcept,thatis,thereisnomeaningtothevelocityofanobjectbyitself:theonlyvelocitywhichexistsisthevelocityofanobjectwithrespecttoanotherobject.Thisiswhatphysicsstudentslearnedinthenineteenthcentury,andwhattheylearntoday.Butifthisisso,thenthespeedoflightdeterminedbyMaxwellâsequationsisvelocitywithrespecttowhat?Onepossibilityisthatthereisakindofuniversalsubstratuminrelationtowhichlightmovesand
hasitsspeed.ButthepredictionsofMaxwellâstheoryseemtobeindependentofthissubstratum.TheexperimentalattemptstomeasurethespeedoftheEarthwithrespecttothishypotheticalsubstratumtriedattheendofthetwentiethcenturyallfailed.Einsteinhasclaimedthathewasnotputontherighttrackbyanyexperimentsbutonlyby
reflectingontheapparentcontradictionbetweenMaxwellâsequationsandNewtonâsmechanics.HeaskedhimselfwhethertherewasawayofrenderingNewtonâsandGalileoâscorediscoveriesandMaxwellâstheoryconsistent.Indoingso,Einsteinarrivesatastupefyingdiscovery.Tounderstandit,thinkofallthepast,
presentandfutureevents(withrespecttothemomentinwhichyouarereading)andimaginethemdistributedasinfigure3.1.Well,Einsteinâsdiscoveryisthatthisdiagramisincorrect.Inreality,thingsareactuallyasthey
aredepictedinfigure3.2.
![Page 31: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/31.jpg)
Betweenthepastandthefutureofanevent(forexample,betweenthepastandthefutureforyou,whereyouare,andintheprecisemomentinwhichyouarereading)thereexistsanâintermediatezoneâ,anâexpandedpresentâ;azonethatisneitherpastnorfuture.Thisisthediscoverymadewithspecialrelativity.
Figure3.1SpaceandtimebeforeEinstein.
Figure3.2Thestructureofâspacetimeâ.Foreveryobserver,theâextendedpresentâistheintermediatezonebetweenthepastandthefuture.
Thedurationofthisintermediatezone,fn10whichisneitherinyourpastnorinyourfuture,isverysmallanddependsonwhereaneventtakesplacerelativetoyou,asillustratedinfigure3.2:thegreaterthedistanceoftheeventfromyou,thelongerthedurationoftheextendedpresent.Atadistanceofafewmetresfromyournose,dearreader,thedurationofwhatforyouistheintermediatezone,neitherpastnorfuture,isnomorethanafewnanoseconds:nexttonothing(thenumberofnanosecondsinasecondisthesameasthenumberofsecondsinthirtyyears).Thisismuchlessthanwecouldpossiblynotice.Ontheothersideoftheocean,thedurationofthisintermediatezoneisathousandthofasecond,stillwellbelowthethresholdofourperceptionoftimeâtheminimumamountoftimeweperceivewithoursensesâwhichissomewhereintheorderofatenthofasecond.ButontheMoonthedurationoftheexpandedpresentisafewseconds,andonMarsitisaquarterofanhour.Thismeanswecansaythat,onMars,thereareeventsthatinthisprecisemomenthavealreadyhappened,eventsthatareyettohappen,butalsoaquarterofanhourduringwhichthingsoccurthatareneitherinourpastnorinourfuture.Theyareelsewhere.Wehadneverbeforebeenawareofthisâelsewhereâbecause,nexttous,this
âelsewhereâistoobrief;wearenotquickenoughtonoticeit.Butitexists,anditisreal.ThisiswhyitisimpossibletoholdasmoothconversationbetweenhereandMars.SayIamon
Marsandyouarehere.IaskyouaquestionandyoureplyassoonasyouâveheardwhatIsaid;yourreplyreachesmeaquarterofanhourafterIposedthequestion.Thisquarterofanhouristimethatisneitherpastnorfuturetothemomentinwhichyouâverepliedtome.ThekeyfactaboutnaturethatEinsteinunderstoodisthatthisquarterofanhourisinevitable:thereisnowayofreducingit.Itiswovenintothetextureoftheeventsofspaceandoftime:wecannotabbreviateit,anymorethanwecansendalettertothepast.
![Page 32: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/32.jpg)
Figure3.3Therelativityofsimultaneity.
Itâsstrange,butthisishowtheworldhappenstobe.AsstrangeasthefactthatinSydneypeopleliveupsidedown:strange,buttrue.Onegetsaccustomedtothefact,whichthenbecomesnormalandreasonable.Itisthestructureofspaceandtimethatismadelikethis.ThisimpliesthatitmakesnosensetosayofaneventonMarsthatitistakingplaceâjustnowâ,
becauseâjustnowâdoesnotexist(figure3.3).fn11Intechnicalterms,wesaythatEinsteinhasunderstoodthatâabsolutesimultaneityâdoesnotexist:thereisnocollectionofeventsintheuniversewhichexistânowâ.Thecollectionofalltheeventsintheuniversecannotbedescribedasasuccessionofânowâs,ofpresents,onefollowingtheother;ithasamorecomplexstructure,illustratedinfigure3.2.Thefiguredescribesthatwhichinphysicsiscalledspacetime:thesetofallpastandfutureevents,butalsothosethatareâneither-past-nor-futureâ;thesedonotformasingleinstant:theyhavethemselvesaduration.IntheAndromedaGalaxy,thedurationofthisexpandedpresentis(withrespecttous)2million
years.Everythingthathappensduringthese2millionyearsisneitherpastnorfuturewithrespecttoourselves.IfafriendlyadvancedAndromedacivilizationdecidedtosendafleetofspacecrafttovisitus,itwouldmakenosensetoaskwhetherânowâthefleethasalreadyleft,ornotyet.Theonlymeaningfulquestioniswhenwereceivethefirstsignalfromthefleet:fromthatmomentonânotearlierâthedepartureofthefleetisinourpast.ThediscoveryofthestructureofspacetimemadebytheyoungEinsteinin1905hasconcrete
consequences.Thefactthatspaceandtimeareintimatelyconnected,asinfigure3.2,impliesasubtlerestructuringofNewtonâsmechanics,whichEinsteinrapidlycompletesin1905and1906.Afirstresultofthisrestructuringisthat,asspaceandtimefusetogetherinasingleconceptofspacetime,sotheelectricfieldandthemagneticfieldsfusetogetherinthesameway,mergingintoasingleentitywhichtodaywecalltheelectromagneticfield.ThecomplicatedequationswrittenbyMaxwellforthetwofieldsbecomesimplewhenwritteninthisnewlanguage.Thereisanotherimplicationofthetheory,freightedwithheavyconsequences.Theconceptsof
âenergyâandâmassâbecomecombinedinthesamewayastimeandspace,andelectricandmagneticfields,arefusedtogetherinthenewmechanics.Before1905twogeneralprinciplesappearedcertain:conservationofmass,andconservationofenergy.Thefirsthadbeenextensivelyverifiedbychemists:massneverchangesinachemicalreaction.ThesecondâconservationofenergyâfolloweddirectlyfromNewtonâsequationsandwasconsideredoneofthemostincontrovertiblelaws.ButEinsteinrealizesthatenergyandmassaretwofacetsofthesameentity,justastheelectricandmagneticfieldsaretwofacetsofthesamefield,andasspaceandtimearetwofacetsoftheonething:spacetime.Thisimpliesthatmass,byitself,isnotconserved;andenergyâasitwasconceivedatthetimeâisnotindependentlyconservedeither.Onemaybetransformedintotheother:onlyonesinglelawofconservationexists,nottwo.Whatisconservedisthesumofmassandenergy,noteachseparately.Processesmustexistthattransformenergyintomass,ormassintoenergy.ArapidcalculationteachesEinsteinhowmuchenergyisobtainedbytransformingonegramof
mass.TheresultisthecelebratedformulaE=mc².Sincethespeedoflightcisaverylargenumber,andc²anevengreaternumber,theenergyobtainedfromtransformingonegramofmassisenormous;itistheenergyofmillionsofbombsexplodingatthesametimeâenoughenergytoilluminateacityandpowertheindustriesofacountryformonthsor,conversely,capableofdestroyinginasecondhundredsofthousandsofhumanbeings,inacitysuchasHiroshima.
![Page 33: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/33.jpg)
ThetheoreticalspeculationsoftheyoungEinsteinhadtransportedhumanityintoanewera:theeraofnuclearpower,aneraofnewpossibilities,andnewdangers.Today,thankstotheintelligenceofarebelliousyoungmanwhowouldnotabiderules,wehavetheinstrumentstobringlighttothehomesofthe10billionhumanbeingswhowillsooninhabittheplanet,totravelinspacetowardsotherstars,ortodestroyeachotheranddevastatetheplanet.Itdependsonourchoices;onwhichleaderswecallupontodecideforus.TodaythestructureofspacetimeproposedbyEinsteiniswellunderstoodandrepeatedlytestedin
laboratories;itisconsideredconclusivelyestablished.TimeandspacearedifferentfromthewaytheyhadbeenconceivedsinceNewton.Spacedoesnotexistindependentlyfromtime.Intheexpandedspaceoffigure3.2thereisnoparticularslicehavingabetterclaimthanotherstobecalledâspacenowâ.Ourintuitiveideaofthepresentâtheensembleofalleventshappeningânowâintheuniverseâisaneffectofourblindness:ourinabilitytorecognizesmalltemporalintervals.Itisanillegitimateextrapolationfromourparochialexperience.ThepresentisliketheflatnessoftheEarth:anillusion.WeimaginedaflatEarthbecauseofthe
limitationsofoursenses,becausewecannotseemuchbeyondourownnoses.Hadwelivedonanasteroidofafewkilometresindiameter,liketheLittlePrince,wewouldhaveeasilyrealizedwewereonasphere.Hadourbrainandoursensesbeenmoreprecise,hadweeasilyperceivedtimeinnanoseconds,wewouldneverhavemadeuptheideaofaâpresentâextendingeverywhere.Wewouldhaveeasilyrecognizedtheexistenceoftheintermediatezonebetweenpastandfuture.Wewouldhaverealizedthatsayingâhereandnowâmakessense,butthatsayingânowâtodesignateeventsâhappeningnowâthroughouttheuniversemakesnosense.ItislikeaskingwhetherourgalaxyisâaboveorbelowâthegalaxyofAndromeda:aquestionthatmakesnosense,becauseâaboveâorâbelowâhasmeaningonthesurfaceoftheEarth,notintheuniverse.Thereisnâtanâupâoraâdownâintheuniverse.Similarly,thereisnâteitheralwaysaâbeforeâandanâafterâbetweentwoeventsintheuniverse.Theresultingknittedstructurethatspaceandtimeformtogether,depictedinfigureslike3.2and3.3,iswhatphysicistscallâspacetimeâ(figure3.4).WhentheAnnalenderPhysikpublishedthearticlebyEinsteininwhichallthiswassuddenly
clarified,theimpactupontheworldofphysicswasmomentous.TheapparentcontradictionbetweentheequationsofMaxwellandNewtonianphysicswerewellknown,andnooneknewhowtoresolvethem.Einsteinâssolution,astonishingandextremelyelegant,tookeveryonebysurprise.ThestorygoesthatinthedimlylitoldhallsofCracowUniversity,anaustereprofessorofphysicscameoutofhisstudy,wavingaroundEinsteinâsarticle,screaming,âThenewArchimedesisborn!âButdespitetheoutcryprovokedbythestepforwardsmadebyEinsteinin1905,wearenotyetat
hismasterpiece.Einsteinâstriumphisthesecondtheoryofrelativity,thetheoryofgeneralrelativity,publishedtenyearslater,whenhewasthirty-five.
Figure3.4Whatistheworldmadeof?
Thetheoryofâgeneralrelativityâisthemostbeautifultheoryproducedbyphysics,andthefirstofthepillarsofquantumgravity.Itisattheheartofthenarrativeofthisbook.Here,therealmagicoftwentieth-centuryphysicsbegins.
ThemostbeautifuloftheoriesAfterpublishingthetheoryofspecialrelativity,Einsteinbecomesarenownedphysicistandreceivesoffersofworkfromnumerousuniversities.Butsomethingtroubleshim:specialrelativitydoesnotsquarewithwhatwasknownaboutgravity.Herealizesthiswhilewritingareviewonhistheory,andwonderswhetherthevenerabletheoryoftheâuniversalgravityâofthefatherofphysics,Newton,shouldnotbereconsideredaswell,tomakeitcompatiblewithhisrelativity.
![Page 34: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/34.jpg)
Theoriginoftheproblemiseasytounderstand.Newtonhadtriedtoexplainwhythingsfallandplanetsrevolve.Hehadimaginedaâforceâthatdrawsallbodiestowardsoneanother:theâforceofgravityâ.Howthisforcemanagedtodrawdistantthingstogetherwithoutanythingbetweenthemwasnotunderstood.Newtonhimself,aswehaveseen,hadsuspectedthatintheideaofaforceactingbetweendistantbodiesthatdonottouchtherewassomethingmissing;andthatinorderfortheEarthtoattracttheMoonsomethingthatcouldtransmitthisforcehadtobetherebetweenthetwo.Twohundredyearslater,Faradayhadfoundthesolutionânotfortheforceofgravity,butfortheelectricandmagneticforces:thefield.Electricandmagneticfieldsâcarryaroundâtheelectricandmagneticforce.Itâsclear,atthisstage,toanyreasonableperson,thattheforceofgravitymusthaveitsFaraday
linesaswell.Itâsclearalso,byanalogy,thattheforceofattractionbetweentheSunandtheEarth,orbetweentheEarthandfallingobjects,mustbeattributedtoafieldâinthiscase,agravitationalfield.ThesolutiondiscoveredbyFaradayandMaxwelltothequestionastowhatcarriestheforcemustreasonablybeappliednotonlytoelectricitybutalsotogravity.Theremustbeagravitationalfield,andsomeequationsanalogoustoMaxwellâs,capableofdescribinghowFaradayâsgravitationallinesmove.Inthefirstyearsofthetwentiethcenturythisiscleartoanysufficientlyreasonableperson;thatistosay,onlytoAlbertEinstein.Einstein,fascinatedsinceadolescencebytheelectromagneticfieldthatpushedtherotorsinhis
fatherâspowerstations,beginstolookintothisgravitationalfieldandsearchforwhatkindofmathscoulddescribeit.Heimmerseshimselfintheproblem.Itwouldtaketenyearstoresolve.Tenyearsofmanicstudies,attempts,mistakes,confusion,brilliantideas,wrongideas,alongseriesofarticlespublishedwithincorrectequations,furthermistakesandstress.Finally,in1915,hecommitstoprintanarticlecontainingthecompletesolution,whichhenamestheGeneralTheoryofRelativity:hismasterpiece.ItisLevLandau,themostoutstandingtheoreticalphysicistoftheSovietUnion,whocalleditâthemostbeautifuloftheoriesâ.Thereasonforthebeautyofthetheoryisnothardtosee.Insteadofsimplyinventingthe
mathematicalformofthegravitationalfieldandseekingtodevisetheequationsforit,EinsteinfishesouttheotherunresolvedquestioninthefurthestdepthsofNewtonâstheoryandcombinesthetwoquestions.NewtonhadreturnedtoDemocritusâsidea,accordingtowhichbodiesmoveinspace.Thisspace
hadtobealarge,emptycontainer,arigidboxfortheuniverse;animmensescaffoldinginwhichobjectsruninstraightlines,untilaforcecausesthemtocurve.Butwhatisthisâspaceâwhichcontainstheworldmadeof?Whatisspace?Tous,theideaofspaceseemsnatural,butitisourfamiliaritywithNewtonianphysicsthatmakes
itso.Ifyouthinkaboutit,emptyspaceisnotpartofourexperience.FromAristotletoDescartes,thatistosay,fortwomillennia,theDemocriteanideaofspaceasapeculiarentity,distinctfromthings,hadneverbeenseenasreasonable.ForAristotle,asforDescartes,thingshaveextension:extensionisapropertyofthings;extensiondoesnotexistwithoutsomethingbeingextended.Icantakeawaythewaterfromaglass,butairwillfillit.Haveyoueverseenareallyemptyglass?Ifbetweentwothingsthereisnothing,Aristotlereasoned,thenthereisnothing.Howcantherebe
atthesametimesomething(space)andnothing?Whatisthisemptyspacewithinwhichparticlesmove?Isitsomething,orisitnothing?Ifitisnothing,itdoesnâtexist,andwecandowithoutit.Ifitissomething,canitbetruethatitsonlypropertyistobethere,doingnothing?Sinceantiquity,theideaofemptyspace,halfwaybetweenathingandanon-thing,hadtroubled
thinkers.Democritushimself,whohadplacedemptyspaceatthebasisofhisworldwhereatomscourse,certainlywasnâtcrystalclearontheissue:hewrotethatemptyspaceissomethingâbetweenbeingandnon-beingâ:âDemocrituspostulatedthefullandtheempty,callingoneâBeingâ,andtheotherâNon-Beingâ,âsaysSimplicius.1Atomsarebeing.Spaceisnon-beingâaânon-beingâthat,nevertheless,exists.Itisdifficulttobemoreobscurethanthis.Newton,whoresuscitatedtheDemocriteanideaofspace,hadtriedtopatchthingsupbyarguing
thatspacewasGodâssensorium.NoonehaseverunderstoodwhatNewtonmeantbyâGodâssensoriumâ,perhapsnotevenNewtonhimself.Certainly,Einstein,whogavelittlecredittotheideaofaGod(withorwithoutasensorium),exceptasaplayfulrhetoricaldevice,foundNewtonâsexplanationofthenatureofspaceutterlyunconvincing.Newtonstruggledconsiderablytoovercomethescientistsâandphilosophersâresistancetohis
revivingtheDemocriteanconceptofspace;atfirstnobodytookhimseriously.Onlytheextraordinaryefficacyofhisequations,whichturnedouttopredictalwaysthecorrectoutcome,endedupsilencingcriticism.ButdoubtsconcerningtheplausibilityoftheNewtonianconceptofspacepersisted,andEinstein,whoreadphilosophers,waswellawareofthem.ErnstMach,whoseinfluenceEinsteinreadilyacknowledged,wasthephilosopherwhohighlightedtheconceptualdifficultiesoftheNewtonianideaofspaceâthesameMachwhodidnotbelieveintheexistenceofatoms.(Agoodexample,incidentally,ofhowthesamepersoncanbeshort-sightedinonerespectandfar-seeinginanother.)Thus,Einsteinaddressesnotonebuttwoproblems.First,howcanwedescribethegravitational
field?Second,whatisNewtonâsspace?
![Page 35: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/35.jpg)
AnditâsherethatEinsteinâsextraordinarystrokeofgeniusoccurs,oneofthegreatestflightsinthehistoryofhumanthinking:whatifthegravitationalfieldturnedoutactuallytobeNewtonâsmysteriousspace?WhatifNewtonâsspacewasnothingmorethanthegravitationalfield?Thisextremelysimple,beautiful,brilliantideaisthetheoryofgeneralrelativity.
Figure3.5Whatistheworldmadeof?
Theworldisnotmadeupofspace+particles+electromagneticfield+gravitationalfield.Theworldismadeupofparticles+fields,andnothingelse;thereisnoneedtoaddspaceasanextraingredient.Newtonâsspaceisthegravitationalfield.Orviceversa,whichamountstosayingthesamething:thegravitationalfieldisspace(figure3.5).But,unlikeNewtonâsspace,whichisflatandfixed,thegravitationalfield,byvirtueofbeinga
field,issomethingwhichmovesandundulates,subjecttoequationsâlikeMaxwellâsfield,likeFaradayâslines.Itisamomentoussimplificationoftheworld.Spaceisnolongerdifferentfrommatter.Itisoneof
theâmaterialâcomponentsoftheworld,akintotheelectromagneticfield.Itisarealentitywhichundulates,fluctuates,bendsandcontorts.Wearenotcontainedwithinaninvisible,rigidscaffolding:weareimmersedinagigantic,flexible
mollusc(themetaphorisEinsteinâs).TheSunbendsspacearounditself,andtheEarthdoesnotcirclearounditdrawnbyamysteriousdistantforcebutrunsstraightinaspacethatinclines.Itâslikeabeadwhichrollsinafunnel:therearenomysteriousforcesgeneratedbythecentreofthefunnel,itisthecurvednatureofthefunnelwallwhichguidestherotationofthebead.PlanetscirclearoundtheSun,andthingsfall,becausespacearoundthemiscurved(figure3.6).
![Page 36: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/36.jpg)
Figure3.6TheEarthturnsaroundtheSunbecausespacetimearoundtheSuniscurved,ratherlikeabeadwhichrollsonthecurvedwallofafunnel.
Alittlemoreprecisely,whatcurvesisnotspacebutspacetimeâthatspacetimewhich,tenyearspreviously,Einsteinhimselfhadshowntobeastructuredwholeratherthanasuccessionofinstants.Thisistheidea.Einsteinâsonlyproblemwastofindtheequationstomakeitconcrete.Howto
describethisbendingofspacetime?AndhereEinsteinislucky:theproblemhadalreadybeensolvedbythemathematicians.Thegreatestmathematicianofthenineteenthcentury,CarlFriedrichGauss,theâprinceof
mathematiciansâ,hadwrittenmathstodescribecurvedsurfaces,suchasthesurfacesofhills,orsuchastheoneportrayedinfigure3.7.
Figure3.7Acurved(bidimensional)surface.
Thenhehadaskedatalentedstudentofhistogeneralizethismathstocurvedspacesinthreeormoredimensions.Thestudent,BernhardRiemann,producedaponderousdoctoralthesisofthekindthatseemscompletelyuseless.Riemannâsresultwasthatthepropertiesofacurvedspace(orspacetime)inanydimensionare
describedbyaparticularmathematicalobject,whichwenowcallRiemanncurvatureandindicatewiththeletterâRâ.Ifyouthinkofalandscapeofplains,hillsandmountains,thecurvatureRofthesurfaceiszerointheplains,whichareflatââwithoutcurvatureââanddifferentfromzerowheretherearevalleysandhills;itisatitsmaximumwheretherearepointedpeaksofmountains,thatistosay,wherethegroundisleastflat,ormostcurved.UsingRiemannâstheory,itispossibletodescribetheshapeofcurvedspacesinthreeorfourdimensions.Withagreatdealofeffort,seekinghelpfromfriendsbetterversedinmathematicsthanhimself,
EinsteinlearnsRiemannâsmathsâandwritesanequationwhereRisproportionaltotheenergyofmatter.Inwords:spacetimecurvesmorewherethereismatter.Thatisit.TheequationistheanalogueoftheMaxwellequations,butforgravityratherthanelectricity.Theequationfitsintohalfaline,andthereisnothingmore.Avisionâthatspacecurvesâbecomesanequation.Butwithinthisequationthereisateeminguniverse.Andherethemagicalrichnessofthetheory
opensupintoaphantasmagoricalsuccessionofpredictionsthatresemblethedeliriousravingsofa
![Page 37: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/37.jpg)
madmanbutwhichhaveallturnedouttobetrue.Evenuptothebeginningofthe1980s,almostnobodytookthemajorityofthesefantasticalpredictionsentirelyseriously.Andyet,oneafteranother,theyhaveallbeenverifiedbyexperience.Letâsconsiderafewofthem.Tobeginwith,EinsteinrecalculatestheeffectofamassliketheSunonthecurvatureofthespace
thatsurroundsit,andtheeffectofthiscurvatureonthemovementsoftheplanets.HefindsthemovementsoftheplanetsaspredictedbyKeplerâsandNewtonâsequations,butnotexactly:inthevicinityoftheSun,theeffectofthecurvatureofspaceisstrongerthantheeffectofNewtonâsforce.EinsteincomputesthemovementofMercury,theplanetclosesttotheSunandhencetheoneforwhichthediscrepancybetweenthepredictionsofhisandNewtonâstheoriesisgreatest.Hefindsadifference:thepointoftheorbitofMercuryclosesttotheSunmoveseveryyear0.43secondsofarcmorethanthatpredictedbyNewtonâstheory.Itisasmalldifference,but,withinthescopeofwhatastronomerswereabletomeasure,andcomparingthepredictionswiththeobservationsofastronomers,theverdictisunequivocal:MercuryfollowsthetrajectorypredictedbyEinstein,nottheonepredictedbyNewton.Mercury,thefleet-footedmessengerofthegods,thegodofthewingedsandals,followsEinstein,notNewton.Einsteinâsequation,then,describeshowspacecurvesveryclosetoastar.Duetothiscurvature,
lightdeviates.EinsteinpredictsthattheSuncauseslighttocurvearoundit.In1919themeasurementisachieved;adeviationoflightismeasuredwhichturnsouttobeexactlyinaccordancewiththeprediction.Butitisnotonlyspacethatcurves:timedoes,too.EinsteinpredictsthattimeonEarthpasses
morequicklyathigheraltitude,andmoreslowlyatloweraltitude.Thisismeasured,andalsoprovestobethecase.Todaywehaveextremelypreciseclocks,inmanylaboratories,anditispossibletomeasurethisstrangeeffectevenforadifferenceinaltitudeofjustafewcentimetres.Placeawatchonthefloorandanotheronatable:theoneonthefloorregisterslesspassingoftimethantheoneonthetable.Why?Becausetimeisnotuniversalandfixed,itissomethingwhichexpandsandshrinks,accordingtothevicinityofmasses:theEarth,likeallmasses,distortsspacetime,slowingtimedowninitsvicinity.Onlyslightlyâbuttwotwinswhohavelivedrespectivelyatsea-levelandinthemountainswillfindthat,whentheymeetupagain,onewillhaveagedmorethantheother(figure3.8).Thiseffectoffersaninterestingexplanationastowhythingsfall.Ifyoulookatamapoftheworld
andtheroutetakenbyanaeroplaneflyingfromRometoNewYork,itdoesnotseemtobestraight:theaeroplanemakesanarctowardsthenorth.Why?Because,theEarthbeingcurved,crossingnorthwardsisshorterthankeepingtothesameparallel.Thedistancesbetweenmeridiansareshorterthemorenortherlyyouare;therefore,itisbettertoheadnorthwards,toshortentheroute(figure3.9).Well,believeitornot,aballthrownupwardsfallsdownwardsforthesamereason:itâgainstimeâ
movinghigherup,becausetimepassesatadifferentspeedupthere.Inbothcases,aeroplaneandballfollowastraighttrajectoryinaspace(orspacetime)thatiscurved(figure3.10).fn12
![Page 38: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/38.jpg)
Figure3.8Twotwinsspendtheirtimeoneatsea-levelandtheotherinthemountains.Whentheymeetupagain,thetwinwholivedinthemountainsisolder.Thisisthegravitationaldilationoftime.
Butthepredictionsofthetheorygowellbeyondtheseminuteeffects.Starsburnaslongastheyhaveavailablehydrogenâtheirfuelâthendieout.Theremainingmaterialisnolongersupportedbythepressureoftheheatandcollapsesunderitsownweight.Whenthishappenstoalargeenoughstar,theweightissostrongthatmatterissquasheddowntoanenormousdegreeandspacecurvessointenselyastoplungedownintoanactualhole.Ablackhole.
Figure3.9Thefurthernorthyougo,thesmallerthedistancebetweentwomeridians.
![Page 39: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/39.jpg)
Figure3.10Thehigherupsomethingis,themorequicklytimepassesforit.
WhenIwasauniversitystudent,blackholeswereregardedasascarcelycredibleimplicationofanesoterictheory.Todaytheyareobservedintheirhundredsandstudiedindetailbyastronomers.Oneoftheseblackholes,withamassamilliontimesgreaterthantheSun,islocatedatthecentreofourgalaxyâwecanobservestarsorbitingaroundit.Some,passingtooclose,aredestroyedbyitsviolentgravity.Furtherstill,thetheorypredictsthatspacerippleslikethesurfaceofthesea,andthatthese
ripplesarewavessimilartotheelectromagneticoneswhichmaketelevisionpossible.Theeffectsoftheseâgravitationalwavesâcanbeobservedintheskyonbinarystars:theyradiatesuchwaves,losingenergyandslowlyfallingtowardseachother.fn13GravitationalwavesproducedbytwoblackholesfallingintooneanotherweredirectlyobservedbyanantennaonEarthinlate2015,andtheannouncement,giveninearly2016,hasonceagainlefttheworldspeechless.Oncemore,theseeminglymadpredictionsofEinsteinâstheoryturnouttobepreciselytrue.Andfurtherstill,thetheorypredictsthattheuniverseisexpandingandemergedfromacosmic
explosion14billionyearsagoâasubjectIwilldiscussinmoredetailshortly.Thisrichandcomplexrangeofphenomenaâbendingofraysoflight,modificationofNewtonâs
force,slowingdownofclocks,blackholes,gravitationalwaves,expansionoftheuniverse,theBigBangâfollowfromunderstandingthatspaceisnotadull,fixedcontainerbutpossessesitsowndynamic,itsownâphysicsâ,justlikethematterandtheotherfieldsitcontains.Democritushimselfwouldhavesmiledwithpleasure,hadhebeenabletoseethathisideaofspacewouldturnouttohavesuchanimpressivefuture.Itistruethathetermeditnon-being,butwhathemeantbybeing(δÎν)wasmatter;andhewrotethathisnon-being,thevoid,neverthelessâhasacertainphysics(ĎĎĎΚν)andasubstantialityofitsownâ.fn14Howrighthewas.WithoutthenotionoffieldsintroducedbyFaraday,withoutthespectacularpowerofmathematics,
withoutthegeometryofGaussandRiemann,thisâcertainphysicsâwouldhaveremainedincomprehensible.Empoweredbynewconceptualtoolsandbymathematics,EinsteinwritestheequationswhichdescribeDemocritusâsvoidandfindsforitsâcertainphysicsâacolourfulandamazingworldwhereuniversesexplode,spacecollapsesintobottomlessholes,timeslowsdowninthevicinityofaplanet,andtheboundlessexpansesofinterstellarspacerippleandswaylikethesurfaceoftheseaâŚAllofthissoundslikeataletoldbyanidiot,fullofsoundandfury,signifyingnothing.Andyet,
instead,itisaglancetowardsreality.Orbetter,aglimpseofreality,alittlelessveiledthanourblurredandbanaleverydayviewofit.Arealitywhichseemstobemadeofthesamestuffourdreamsaremadeof,butwhichisneverthelessmorerealthanourcloudeddailydreaming.Andallthisistheresultonlyofanelementaryintuitionâthatspacetimeandthegravitationalfield
areoneandthesamethingâandasimpleequationwhichIcanâtresistcopyingouthere,evenifmostofmyreaderswillcertainlynotbeabletodecipherit.Idoso,anyway,inthehopethattheymightbeabletocatchaglimpseofitsbeautifulsimplicity:
In1915theequationwassimplerstill,becausetheterm+Îgab,whichEinsteinaddedtwoyearslater(andwhichIdiscussbelow)didnotyetexist.fn15RabdependsonRiemannâscurvature,andtogetherwith½Rgabrepresentsthecurvatureofspacetime;Tabstandsfortheenergyofmatter;GisthesameconstantthatNewtonfound:theconstantthatdeterminesthestrengthoftheforceofgravity.
![Page 40: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/40.jpg)
Thatâsit.Avisionandanequation.
Mathematicsorphysics?Iwouldliketopause,beforecontinuingwithphysics,tomakeafewobservationsaboutmathematics.Einsteinwasnogreatmathematician.Hestruggledwithmaths.Hesaysthishimself.In1943herepliedinthefollowingwaytoanine-year-oldchildwiththenameofBarbarawhowrotetohimaboutherdifficultieswiththesubject:âDonâtworryaboutexperiencingdifficultieswithmaths,Icanassureyouthatmyownproblemsareevenmoreserious!â2Itseemslikeajoke,butEinsteinwasnotkidding.Withmathematics,heneededhelp:hehaditexplainedtohimbypatientfellowstudentsandfriends,suchasMarcelGrossman.Itwashisintuitionasaphysicistthatwasprodigious.Duringthelastyearinwhichhewascompletingtheconstructionofhistheory,Einsteinfound
himselfcompetingwithDavidHilbert,oneofthegreatestmathematiciansofalltime.Einsteinhadgivenalecture,attendedbyHilbert,inGĂśttingen.HilbertimmediatelyunderstoodthatEinsteinwasintheprocessofmakingamajordiscovery,graspedtheideaandtriedtoovertakeEinsteinandbethefirsttowritethecorrectequationsofthenewtheoryEinsteinwasslowlybuilding.Thesprinttothefinishlinebetweenthetwogiantswasanail-bitingaffair,eventuallydecidedbyamatterofjustafewdays.Einstein,inBerlin,endedupgivingapubliclecturealmosteveryweek,eachtimepresentingadifferentequation,anxiousthatHilbertwouldnotgettothesolutionbeforehim.Theequationwasincorrecteverytime.Until,thatis,byahairâsbreadthâjustmarginallyaheadofHilbertâEinsteinfoundtherightone.Hehadwontherace.Hilbert,agentleman,neverquestionedEinsteinâsvictory,eventhoughhewasworkingonvery
similarequationsatthetime.Infact,heleftagentleandbeautifulphrasewhichcapturesperfectlyEinsteinâsdifficultrelationshipwithmathematics,and,perhaps,thedifficultrelationshipwhichexistsgenerallybetweenthewholeofphysicsandmathematics.Themathsthatwasnecessarytoformulatethetheorywasgeometryinfourdimensions,andHilbertwrites:
AnyyoungsteronthestreetsofGĂśttingenfn16understandsgeometryinfourdimensionsbetterthanEinstein.Andyet,itwasEinsteinwhocompletedthetask.
Why?BecauseEinsteinhadauniquecapacitytoimaginehowtheworldmightbeconstructed,toâseeâitinhismind.Theequations,forhim,cameafterwards;theywerethelanguagewithwhichtomakeconcretehisvisionsofreality.ForEinstein,thetheoryofgeneralrelativityisnotacollectionofequations:itisamentalimageoftheworldarduouslytranslatedintoequations.Theideabehindthetheoryisthatspacetimecurves.Ifspacetimehadonlytwodimensions,and
welivedonasortofplane,itwouldbeeasytoimaginewhatitmeanstosaythatâphysicalspacecurvesâ.Itwouldmeanthatthephysicalspaceinwhichweliveisnotlikeaflattablebutresemblesinsteadasurfacewithmountainsandvalleys.Buttheworldweinhabitdoesnothaveonlytwodimensions,ithasthree.Four,infact,whentimeisincluded.Toimagineacurvedspaceinfourdimensionsismorecomplicated,becauseinourhabitualperceptionwedonothaveanintuitionofaâlargerspaceâwithinwhichspacetimecancurve.ButEinsteinâsimaginationhadnodifficultyinintuitingthecosmicmolluscinwhichweareimmersed,whichcanbesquashed,stretchedandtwistedâandthatconstitutesthespacetimearoundus.ItisthankstothisvisionaryclaritythatEinsteinmanagedtobethefirsttowritethetheory.Intheend,adegreeoftensionbetweenHilbertandEinsteindiddevelop.Afewdaysbefore
Einsteinmadehissuccessfulequationpublic,Hilberthadsentanarticletoaperiodicalwhichshowsjusthowclosehehadcometothesamesolutionâandeventodayhistoriansofsciencearefacedwithdoubtswhentryingtoevaluatetherespectivecontributionsofthesetwogiants.Atsomepointtheirrelationscooled,andEinsteinfearedthatHilbert,moreseniorandpowerfulthanhim,wouldseektoattributetohimselftoomuchofthemeritfortheconstructionofthetheory.ButHilbertneverclaimedtobethefirsttodiscovergeneralrelativityâandinaworldsuchasthatofscience,whereoften,toofrequently,disputesoverprecedencebecomepoisonousâthetwogaveatrulywonderfulexampleofwisdom,clearingthefieldofallnegativetension.EinsteinwritesamarvellouslettertoHilbert,summarizingtheprofoundsenseoftheshared
coursetheyhadtaken:Therewasamomentinwhichsomethinglikeanirritationcamebetweenus,theoriginofwhichInolongerwanttoanalyse.Ihavefoughtagainstthebitternesswhichitprovokedinme,andhavesucceededcompletelyindoingso.Iagainthinkofyouwithuncloudedfriendship,andIaskyoutodothesameforme.Itisreallyapityifcompanionssuchasweare,whohavemanagedtoforgeapathasidefromthepettinessofthisworld,couldfindanythingotherthanjoyineachotherâscompany.3
ThecosmosTwoyearsafterthepublicationofhisequation,Einsteindecidestouseittodescribethespaceoftheentireuniverse,consideredatthelargestscale.Andherehehasanotherofhisamazingideas.Forthousandsofyears,menhadaskedthemselveswhethertheuniversewasinfinite,orhada
limit.Bothhypothesesentailthornyproblems.Aninfiniteuniversedoesnotseemtostandtoreason:ifitisinfinite,forexample,theremustexistsomewhereareaderjustlikeyouwhoisreadingthe
![Page 41: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/41.jpg)
verysamebook(infinityistrulyvast,andtherearenotsufficientcombinationsofatomstofillitwiththingsalwaysdifferentfromeachother).Infact,theremustbenotonlyonebutaninfiniteseriesofreadersidenticaltoyourselfâŚButifthereisalimittotheuniverse,whatisthatboundary?Whatsenseisthereinaborderwithnothingontheotherside?AlreadyinthefourthcenturyCE,inTaranto,thePythagoreanphilosopherArchytashadwritten:
IfIfoundmyselfinthefurthestsky,thatofthefixedstars,wouldIbeabletostretchmyhand,orarod,outbeyonditâornot?ThatIshouldnotbeabletoisabsurd;butifIamableto,thenanoutsideexists,beitofmatter,orspace.Inthiswayonecouldproceedeverfurther,towardstheend,fromtimetotimeaskingthesamequestion,astowhethertherewillalwaysbesomethingintowhichtoextendtherod.4
Thesetwoabsurdalternativesâtheabsurdityofaninfinitespace,andtheabsurdityofauniversewithafixedborderâdidnâtseemtoleaveanyreasonablechoicebetweenthem.ButEinsteinfindsathirdway:theuniversecanbefiniteandatthesametimehavenoboundary.
How?JustasthesurfaceoftheEarthisnotinfinitebutdoesnothaveaboundaryeither,whereitâendsâ.Thiscanhappen,naturallyenough,ifsomethingiscurved:thesurfaceoftheEarthiscurved.Andinthetheoryofgeneralrelativity,ofcourse,three-dimensionalspacecanalsobecurved.Consequently,ouruniversecanbefinitebutborderless.OnthesurfaceoftheEarth,ifIweretokeepwalkinginastraightline,Iwouldnotadvancead
infinitum:IwouldeventuallygetbacktothepointIstartedfrom.Ouruniversecouldbemadeinthesameway:ifIleaveinaspacecraftandjourneyalwaysinthesamedirection,IflyaroundtheuniverseandeventuallyendupbackonEarth.Athree-dimensionalspaceofthiskind,finitebutwithoutboundary,iscalleda3-sphere.
Figure3.11Aspherecanberepresentedastwodiscswhichinrealityaresmoothlyjoinedallalongtheiredges.
Tounderstandthegeometryofaâ3-sphereâ,letusreturntotheordinarysphere;thesurfaceofaball,ortheEarth.TorepresentthesurfaceoftheEarthonaplane,wecandrawtwodiscs,asiscustomarywhendrawingthecontinents(figure3.11).Noticethataninhabitantofthesouthernhemisphereisinacertainsenseâsurroundedâbythe
northernhemisphere,sinceinwhicheverdirectionshegoestoexitherhemisphere,shewillalwaysarriveintheotherone.Butthecontraryisobviouslytrueaswell:eachhemisphereâsurroundsâ,andissurroundedby,theother.A3-spheremayberepresentedinasimilarfashion,butwitheverythinggivenanadditionaldimension:twoballsstucktogetherallalongtheiredges(figure3.12).Whenweleaveoneballweenterintotheother,justaswhenweleaveoneofthediscsinthe
representationoftheglobeweenterintotheotherdisc.Eachballsurroundsandissurroundedbytheother.Einsteinâsideaisthatspacecouldbea3-sphere:somethingwithafinitevolume(thesumofthevolumeofthetwoballs),butwithoutborders.fn17The3-sphereisthesolutionwhichEinsteinproposesinhisworkof1917totheproblemoftheborderoftheuniverse.Thisarticleinitiatesmoderncosmology,thestudyoftheentirevisibleuniverse,studiedatthegrandestscale.Fromitwillarisethediscoveryoftheexpansionoftheuniverse;thetheoryoftheBigBang;theproblemofthebirthoftheuniverse,andmuchelsebesides.IspeakaboutallofthisinChapter8.
![Page 42: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/42.jpg)
Figure3.12A3-spherecanberepresentedastwoballsjoinedtogether.
ThereisonemoreobservationwhichIwouldliketomakeaboutEinsteinâs3-sphere.Howeverincredibleitmightseem,thesameideahadalreadybeenconceivedbyanothergenius,fromanentirelydifferentculturaluniverse:DanteAlighieri,Italyâsgreatestpoet.IntheParadiso,thethirdpartofhismajorpoem,theCommedia,Danteoffersagrandiosevisionofthemedievalworld,calquedontheworldofAristotle,withthesphericalEarthatitscentre,surroundedbythecelestialspheres(figure3.13).
Figure3.13TraditionalrepresentationofDanteâsuniverse.
Accompaniedbyhisshininglovedone,Beatrice,Danteascendsthesespheresinthecourseofafantastic,visionaryjourneyuptotheoutermostsphere.Whenhereachesit,hecontemplatestheuniversebelowhimwithitsrotatingheavensandtheEarth,veryfardown,atitscentre.Butthenhelooksevenhigherâandwhatdoeshesee?Heseesapointoflightsurroundedbyimmensespheresofangels,thatistosay,byanotherimmenseball,which,inhiswordsâsurroundsandisatthesametimesurroundedbyâthesphereofouruniverse!HereareDanteâsversesfromCantoXXVIIoftheParadiso.QuestaaltrepartedellâUniversodâuncerchioluicomprendesicomequestolialtri:âThis
![Page 43: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/43.jpg)
otherpartoftheuniversesurroundsthefirstinacirclelikethefirstsurroundstheothers.âAndinthenextcanto,stillonthelastâcircleâ,parendoinchiusodaquelchâelliinchiude:âappearingtobetobeenclosedbythosethatitenclosesâ.Thepointoflightandthesphereofangelsaresurroundingtheuniverse,andatthesametimetheyaresurroundedbytheuniverse!Itisanexactdescriptionofa3-sphere!TheusualrepresentationsofDanteâsuniversecommoninItalianschoolbooks(suchasfigure3.13)
placetheangelicspheresseparatefromthecelestialones.ButDantewritesthatthetwoballsâsurroundandaresurroundedbyâeachother.Dantehasacleargeometricalintuitionofa3-sphere.fn18ThefirsttonoticethattheParadisodescribestheuniverseasa3-spherewasanAmerican
mathematician,MarkPeterson,in1979.Ingeneral,scholarsofDantearenotveryfamiliarwith3-spheres.Today,everyphysicistandmathematiciancouldeasilyrecognizethe3-sphereinDanteâsdescriptionoftheuniverse.HowisitpossiblethatDantehadanideathatsoundssomodern?Ithinkitwaspossible,inthe
firstplace,duetotheprofoundintelligenceofItalyâsfinestpoet.ThisintelligenceisoneofthereasonswhytheCommediaissofascinating.ButitisalsoduetothefactthatDantewaswritingwellbeforeNewtonconvincedeveryonethattheinfinitespaceofthecosmoswastheflatoneofEuclideangeometry.DantewasfreeoftherestraintsuponourintuitionwehaveasaresultofourNewtonianschooling.Danteâsscientificculturewasbasedprincipallyontheteachingsofhismentorandtutor,Brunetto
Latini,whohasleftusasmall,enchantingtreatise,Litresor,whichisasortofencyclopaediaofmedievalknowledge,writteninadelightfulcombinationofoldFrenchandItalian.InLitresor,BrunettoexplainsindetailthefactthattheEarthisround.Buthedoesso,curiouslytotheeyesofamodernreader,intermsofâintrinsicâratherthanâextrinsicâgeometry.Thatistosay,hedoesnotwrite,âtheEarthislikeanorangeâ,astheEarthwouldlookifseenfromtheoutside,butwritesinstead,âTwoknightswhocouldgallopsufficientlyfarinoppositedirectionswouldmeetupontheotherside.âAnd:âIfhewerenotimpededbytheseas,amanwhosetouttowalkforeverwouldreturntothepointontheEarthfromwhichhedeparted.âInotherwords,headoptsaninternal,notanexternal,pointofview:theperspectiveofsomeonewhowalkstheEarth,notofsomeonewholooksatitfromafar.Atfirstglanceitmightseemlikeapointless,complicatedwayofexplainingthattheEarthisaball.WhydoesnâtBrunettosimplysaythattheEarthislikeanorange?But,onreflection:if,say,anantwalksonanorange,itwillatsomepointfinditselfupsidedown,andmustkeepitselfattachedbymeansofthetinysuctionpadsonitslegs,toavoidfallingoff.AndyetatravellerwhowalkstheEarthneverfindshimselfupsidedown,andneedsnosuctionpadsonhislegs.Brunettoâsdescriptionisnotsoquaintafterall.Now,thinkaboutit.Forsomeonewhohaslearnedfromhisteacherthattheformofthesurfaceof
ourplanetissuchthatbywalkingalwaysinastraightlinewereturntothepointwestartedfrom,itisperhapsnotsodifficulttotakethenextobviousstep,andimaginethattheformoftheentireuniverseissuchthat,flyingalwaysinastraightline,wereturntothesamepointofdeparture:a3-sphereisaspaceinwhichâtwowingedknightsthatcouldflyinoppositedirectionswouldmeetupontheothersideâ.Intechnicalterms,thedescriptionofthegeometryoftheEarthofferedbyBrunettoLatiniinLitresorisgivenintermsofintrinsicgeometry(seenfromtheinside)ratherthanextrinsic(seenfromtheoutside),andthisisexactlythedescriptionthatissuitabletogeneralizethenotionofâsphereâfromtwodimensionstothree.Thebestwayofdescribinga3-sphereisnottotrytoâseeitfromtheoutsideâ,butrathertodescribewhathappenswhenmovingwithinit.ThemethoddevelopedbyGausstodescribecurvedsurfaces,andgeneralizedbyRiemannto
describethecurvatureofspacesinthreeormoredimensions,basically,amountstoBrunettoLatiniâsway.Thatistosay,theideaistodescribeacurvedspacenotasâseenfromtheoutsideâ,statinghowitcurvesinanexternalspace,butinsteadintermsofwhatmaybeexperiencedbysomebodywithinthatspace,whoismovingandalwaysremainingwithinit.Forinstance,thesurfaceofanordinarysphere,asBrunettoobserves,isasurfacewherealltheâstraightâlinesgetbacktothestartingpointaftertraversingthesamedistance(thelengthoftheequator).A3-sphereisathree-dimensionalspacewiththesameproperty.Einsteinâsspacetimeisnotcurvedinthesensethatitcurvesâinanexternalspaceâ.Itiscurvedin
thesensethatitsintrinsicgeometry,thatistosay,thewebofdistancesbetweenitspoints,whichcanbeobservedbystayingwithinit,isnotthegeometryofaflatspace.ItisaspacewherePythagorasâstheoremisnotvalid,justasPythagorasâstheoremisnotvalidonthesurfaceoftheEarth.fn19Thereisawayofunderstandingthecurvatureofspacefromwithinit,andwithoutlookingatit
fromoutside,whichisimportantforwhatfollows.ImagineyouareattheNorthPoleandwalksouthwardsuntilyoureachtheequator,carryingwithyouanarrowpointingahead.Onceyoureachtheequator,turntotheleftwithoutchangingthedirectionofthearrow.Thearrowstillpointssouth,whichisnowtoyourright.Advancealittletowardstheeastalongtheequatorandthenturnagaintowardsthenorthâagainwithoutchangingthedirectionofthearrow,whichwillnowbepointingbehindyou.WhenyoureachtheNorthPoleagain,youhaveexecutedaclosedcircuitâaâloopâ,asit
![Page 44: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/44.jpg)
istermedâandthearrowdoesnotpointinthesamedirectionaswhenyoustartedout(figure3.14).Theanglethroughwhichthearrowhasturnedinthecourseoftheloopmeasuresthecurvature.Iwillreturnlatertothismethodofmeasuringcurvaturebymakingaloopinspace.Thesewillbe
theloopsthatgivethenametothetheoryofloopquantumgravity.
Figure3.14Anarrowcarriedparalleltoitselfalongacircuit(aloop)inacurvedspacearrivesbackrotatedatthepointofdeparture.
DanteleavesFlorencein1301,whilethemosaicsinthecupolaoftheBaptisteryarebeingcompleted.Themosaic,representingHell(theworkofCoppodiMarcovaldo,theteacherofCimabue),probablyterrifyingintheeyesofamedievalperson,hasoftenbeenindicatedasasourceofinspirationtoDante(figure3.15).Shortlybeforestartingtowritethisbook,IvisitedtheBaptisteryinthecompanyofEmanuela
Minnai,thefriendwhoconvincedmetowriteit.EnteringtheBaptisteryandlookingup,youseeashiningpointoflight(thelightsourcefromthelanternatthesummitofthecupola)surroundedbynineordersofangels,withthenameofeachorderwritten:Angels,Archangels,Principalities,Powers,Virtues,Domains,Thrones,CherubimandSeraphim.ThiscorrespondsexactlytothestructureofthesecondsphereofParadise.ImaginethatyouareanantontheflooroftheBaptisteryandareabletowalkinanydirection;regardlessofwhichdirectionyoufollowtoclimbthewall,youwouldreachtheceilingatthesamepointoflightsurroundedbyangels:thepointoflightanditsangelsbothâsurroundâandâaresurroundedbyâtherestofthedecoratedinterioroftheBaptistery(figure3.16).
![Page 45: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/45.jpg)
Figure3.15ThemosaicdepictingHell,byCoppodiMarcovaldo,intheBaptisteryofFlorence.
LikeeverycitizenofFlorenceattheendofthethirteenthcentury,Dantemusthavebeenprofoundlyawe-struckbytheBaptistery,thegrandiosearchitecturalenterprisehiscitywascompleting.IbelievethathemayhavebeeninspiredbytheBaptistery,notonlybyCoppodiMarcovaldoâsInferno,butalsobyitsoverallarchitecture,forhisvisionofthecosmos.TheParadisoreproducesitsstructureremarkablyprecisely,includingtheninecirclesofangelsandthepointoflight,justtranslatingitfromtwotothreedimensions.AfterdescribingthesphericaluniverseofAristotle,BrunettohadalreadywrittenthatbeyonditliestheplaceofdivinityâandmedievaliconographyhadalreadyimaginedParadiseasGodsurroundedbyspheresofangels.Intheend,DantedoesnomorethanmountthepiecesthatalreadyexistedintoacoherentarchitecturalwholewhichfollowsthesuggestivearchitectureoftheBaptisteryandresolvestheancientproblemofthebordersoftheuniverse.Insodoing,DanteanticipatesbysixcenturiesEinsteinâs3-sphere.
Figure3.16TheinterioroftheBaptistery.
IdonâtknowiftheyoungEinsteinhadencounteredtheParadisoduringhisintellectualwanderingsinItaly,andwhetherornotthevividimaginationoftheItalianpoetmayhavehadadirectinfluenceonhisintuitionthattheuniversemightbebothfiniteandwithoutboundary.Whetherornotsuchinfluenceoccurred,Ibelievethatthisexampledemonstrateshowgreatscienceandgreatpoetryarebothvisionary,andmayevenarriveatthesameintuitions.Ourcultureisfoolishtokeepscienceandpoetryseparated:theyaretwotoolstoopenoureyestothecomplexityandbeautyoftheworld.Danteâs3-sphereisonlyanintuitionwithinadream.Einsteinâs3-spherehasmathematicalform
andfollowsfromthetheoryâsequations.Theeffectofeachisdifferent.Dantemovesusdeeply,touchingthesourcesofouremotions.Einsteinopensaroadtowardstheunsolvedmysteriesofouruniverse.Butbothcountamongthemostbeautifulandsignificantflightsthatthemindcanachieve.Butletâsreturnto1917,whenEinsteintriestoinserttheideaofthe3-sphereintohisequations.
Hereheencountersaproblem.Heisconvincedthattheuniverseisfixedandimmutable,buthisequationstellhimthatthisisnotpossible.Itisnâtdifficulttounderstandwhy.Everythingattracts,thereforetheonlywayforafiniteuniversenottocollapseonitselfisforittobeexpanding:justas
![Page 46: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/46.jpg)
theonlywaytopreventafootballfromfallingtothegroundistokickitupwards.Iteithergoesup,orfallsdownâitcanâtstaystill,suspendedintheair.ButEinsteindoesnotbelievewhathisownequationsaretellinghim.Heevenmakesasilly
physicsmistake(hedoesnotrealizethatthesolutionheconsidersisunstable)justtoavoidacceptingwhathistheorypredicts:theuniverseiseithercontractingorexpanding.Hemodifieshisequations,tryingtoavoidtheimplicationthatitisexpanding.ItisforthisreasonthatheaddsthetermÎgabintheequationwrittenabove.Butitisafurthermistake:theaddedtermiscorrect,butitdoesnotchangethefactthattheequationpredictsthattheuniversemustbeexpanding.Forallhisbravery,Einsteinthegeniuslacksthecouragetobelievehisownequations.AfewyearslaterEinsteinisforcedtogiveup:itishistheorythatisright,nothisreservations
aboutit.Astronomersrealizethatallgalaxiesareindeedmovingawayfromus.Theuniverseisexpanding,exactlyastheequationspredicted.Fourteenbillionyearsago,theuniversewasconcentratedalmosttoasingle,furiouslyhotpoint.Fromthereitexpandedinacolossalâcosmicâexplosionâandherethetermâcosmicâisnotusedinanyrhetoricalsense:itis,literally,acosmicexplosion.ThisistheâBigBangâ.Todayweknowtheexpansionisreal.ThedefinitiveproofofthescenarioforeseenbyEinsteinâs
equationsarrivesin1964,whentwoAmericanradio-astronomers,ArnoPenziasandRobertWilson,discoverbyaccidentaradiationdiffusedthroughouttheuniversewhichturnsouttobepreciselywhatremainsoftheoriginalimmenseheatoftheearlyuniverse.Onceagain,thetheoryturnsouttohavebeencorrect,uptoitsmostamazingpredictions.
Figure3.17Einsteinâsworld:particlesandfieldswhichmoveonotherfields.
EversincewediscoveredthattheEarthisroundandturnslikeamadspinning-top,wehaveunderstoodthatrealityisnotwhatitseems:everytimeweglimpseanewaspectofit,itisadeeplyemotionalexperience.Anotherveilhasfallen.ButtheleapmadebyEinsteinisunparalleled:spacetimeisafield;theworldismadeonlyoffieldsandparticles;spaceandtimearenotsomethingelse,somethingdifferentfromtherestofnature:theyarejustafieldamongtheothers(figure3.17).In1953,aprimaryschoolchildwritestoAlbertEinstein,âOurclassisstudyingtheuniverse.Iam
veryinterestedinspace.Iwouldliketothankyouforallthatyouhavedonesothatwemightunderstandit.â5Ifeelthesameway.
![Page 47: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/47.jpg)
4.Quanta
Thetwopillarsoftwentieth-centuryphysicsâgeneralrelativityandquantummechanicsâcouldnotbemoredifferentfromeachother.Generalrelativityisacompactjewel:conceivedbyasinglemind,basedoncombiningprevioustheories,itisasimpleandcoherentvisionofgravity,spaceandtime.Quantummechanics,orquantumtheory,ontheotherhand,emergesfromexperimentsinthecourseofalonggestationoveraquarterofacentury,towhichmanyhavecontributed;achievesunequalledexperimentalsuccessandleadstoapplicationswhichhavetransformedoureverydaylives(thecomputeronwhichIwrite,forinstance);but,morethanacenturyafteritsbirth,itremainsshroudedinobscurityandincomprehensibility.
Thischapterillustratesthestrangephysicsofthistheory,relateshowthetheorycameintobeingandthethreeaspectsofrealityithasunveiled:granularity,indeterminismandrelationality.
AlbertagainItâssaidthatquantummechanicswasbornpreciselyin1900,virtuallyusheringinacenturyofintensethought.In1900theGermanphysicistMaxPlancktriestocomputetheamountofelectromagneticwavesinequilibriuminahotbox.Toobtainaformulareproducingtheexperimentalresults,heendsupusingatrickwhichdoesnotappeartomakemuchsense:heassumesthattheenergyoftheelectricfieldisdistributedinâquantaâ,thatistosay,insmallpackets,littlebricksofenergy.Thesizeofthepackets,heassumes,dependsonthefrequency(thatis,thecolour)oftheelectromagneticwaves.Forwavesoffrequencyν,everyquantum,oreverypacket,hasenergy
E=hνThisformulaisthefirstofquantummechanics;hisanovelconstantwhichtodaywecallthe
Planckconstant.Itfixeshowmuchenergythereisineachpacketofenergy,forradiationoffrequency(colour)ν.Theconstanthdeterminesthescaleofallquantumphenomena.
Theideathatenergycouldbemadeupoffinitepacketsisatoddswitheverythingthatwasknownatthetime:energywasconsideredsomethingthatcouldvaryinacontinuousmanner,andtherewasnoreasontotreatitasifitweremadeupofgrains.Forexample,theenergyofapendulummeasurestheamplitudeoftheswing.Thereseemstobenoreasonforapendulumtooscillateonlywithcertaindeterminedamplitudesandnotothers.ForMaxPlanck,takingenergyinfinite-sizepacketswasonlyastrangetrickwhichhappenedtoworkforthecalculationâthatis,toreproducelaboratorymeasurementsâbutforutterlyunclearreasons.
FiveyearslateritisAlbertEinsteinâhimagainâwhocomestounderstandthatPlanckâspacketsofenergyareinfactreal.ThisisthesubjectofthethirdofthethreearticlessenttotheAnnalenderPhysikin1905.Andthisisthetruedateofbirthofquantumtheory.
Inthearticle,Einsteinarguesthatlighttrulyismadeupofsmallgrains,particlesoflight.Heconsidersaphenomenonthathadbeenrecentlyobserved:thephotoelectriceffect.Therearesubstancesthatgenerateaweakelectriccurrentwhenstruckbylight.Thatistosay,theyemitelectronswhenlightshinesonthem.Todayweusethem,forexample,inthephotoelectriccellswhichopendoorswhenweapproachthembydetectingiflightarrives,ornot,inasensor.Thatthishappensisnotstrange,becauselightcarriesenergy(itwarmsus,forexample),anditsenergymakestheelectronsâjumpoutâoftheiratoms;itgivesthemapush.
Butsomethingisstrange:itseemsreasonabletoexpectthatiftheenergyoflightisscarceânamely,ifthelightisdimâthephenomenonwouldnottakeplace;andthatitwouldtakeplacewhentheenergyissufficientânamely,whenthelightisbright.Butitisnâtlikethis:whatisobservedisthatthephenomenonhappensonlyifthefrequencyoflightishighanddoesnothappenifthefrequencyislow.Thatistosay,ithappensordoesnâthappendependingonthecolouroflight(thefrequency)ratherthanitsintensity(energy).Thereisnowayofmakingsenseofthiswithstandardphysics.
EinsteinusesPlanckâsideaofthepacketsofenergy,withasizethatdependsuponfrequency,andrealizesthatifthesepacketsarereal,thephenomenoncanbeexplained.Itisnâtdifficulttounderstandwhy.Imaginethatthelightarrivesintheformofgrainsofenergy.Anelectronwillbesweptoutofitsatomiftheindividualgrainhittingithasagreatdealofenergy.Whatmattersistheenergyofeachgrain,notthenumberofgrains.If,asinPlanckâshypothesis,theenergyofeachgrainisdeterminedbyfrequency,thephenomenonwilloccuronlyiffrequencyissufficientlyhigh,
![Page 48: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/48.jpg)
thatistosay,iftheindividualgrainsofenergyaresufficientlylarge,independentlyfromthetotalamountofenergythatâsaround.
Itislikewhenithails:whatdetermineswhetheryourcarwillbedentedisnotthetotalquantityofhailthatfallsbutthesizeoftheindividualhailstones.Therecouldbeanenormousamountofhail,butitwilldonodamageifallthestonesaresmall.Inthesameway,eveniflightisintenseâwhichamountstosayingthatthereareagreatdealoflightpacketsâtheelectronswouldnotbeextractedfromtheiratomsiftheindividualgrainsoflightaretoosmall,thatis,ifthefrequencyoflightistoolow.Thisexplainswhyitisthecolourandnottheintensitywhichdetermineswhetherthephotoelectriceffectoccursornot.ForthissimplereasoningEinsteinwasawardedtheNobelPrize.Itiseasytounderstandthingsoncesomeonehasthoughtthemthrough.Thedifficultyliesinthinkingthemthroughinthefirstplace.
Todaywecallthesepacketsofenergyâphotonsâ,fromtheGreekwordforlight:ĎĎĎ.Photonsarethegrainsoflight,itsâquantaâ.InthearticleEinsteinwrites:
Itseemstomethattheobservationsassociatedwithblackbodyradiation,fluorescence,theproductionofcathoderaysbyultravioletlight,andotherrelatedphenomenaconnectedwiththeemissionortransformationoflightaremorereadilyunderstoodifoneassumesthattheenergyoflightisdiscontinuouslydistributedinspace.Inaccordancewiththeassumptiontobeconsideredhere,theenergyofalightrayspreadingoutfromapointsourceisnotcontinuouslydistributedoveranincreasingspacebutconsistsofafinitenumberofâenergyquantaâwhicharelocalizedatpointsinspace,whichmovewithoutdividing,andwhichcanonlybeproducedandabsorbedascompleteunits.1
Thesesimpleandclearlinesaretherealbirthcertificateofquantumtheory.NotethewonderfulinitialâItseemstomeâŚâ,whichrecallsthehesitationsofFaraday,orthoseofNewton;ortheuncertaintyofDarwininthefirstpagesofOntheOriginofSpecies.Truegeniusisawareofthemomentousnessofthestepsitistaking,andisalwayshesitantâŚ
ThereisaclearrelationbetweenEinsteinâsworkonBrownianmotion(discussedinChapter1)andhisworkonthequantaoflight,bothcompletedin1905.Inthefirst,Einsteinhadmanagedtofindademonstrationoftheatomichypothesis,thatistosay,ofthegranularstructureofmatter.Inthesecondheextendsthissamehypothesistolight:lightmusthaveagranularstructureaswell.
Atfirst,Einsteinâsideathatlightcouldbemadeupofphotonsisregardedbyhiscolleaguesasnomorethanyouthfulwaywardness.Everyonecommendshimforhistheoryofrelativity,buteverybodyjudgesthenotionofphotonstobeoutlandish.Scientistshadonlyrecentlybeenpersuadedthatlightwasawaveintheelectromagneticfield:howcoulditbemadeupofgrains?InaletteraddressedtotheGermanMinistry,recommendingthatEinsteinshouldhaveaprofessorshipinauguratedforhiminBerlin,themostdistinguishedphysicistsofthedaywritethattheyoungmanissobrilliantthatheâmaybeexcusedâcertainexcesses,suchastheideaofphotons.Notmanyyearslater,theverysamecolleaguesawardhimtheNobelPrize,preciselyforhavingunderstoodthatphotonsexist.Lightfallsonasurfacelikeagentlehailshower.
Tocomprehendhowlightmaybesimultaneouslyanelectromagneticwaveandaswarmofphotonswillrequiretheentireconstructionofquantummechanics.Butthefirstbuildingblockofthistheoryhasbeenestablished:thereexistsafundamentalgranularityinallthings,includinglight.
Niels,WernerandPaulIfPlanckisthebiologicalfatherofthetheory,Einsteinistheparentwhogavebirthtoandnurturedit.Butasisoftenthecasewithchildren,thetheorythenwentitsownway,barelyrecognizedbyEinsteinashisown.
Duringthefirsttwodecadesofthetwentiethcentury,itistheDaneNielsBohrwhoisresponsibleforguidingitsdevelopment.Bohrstudiesthestructureofatoms,whichwasbeginningtobeexploredattheturnofthecentury.Experimentshadshownthatanatomislikeasmallsolarsystem:themassisconcentratedinaheavycentralnucleus,aroundwhichlightelectronsrevolve,moreorlessliketheplanetsaroundtheSun.Thispicture,however,didnotaccountforasimplefact:matteriscoloured.
Saltiswhite,pepperisblack,chilliisred.Why?Studyingthelightemittedbyatoms,itisapparentthatsubstanceshavespecificcolours.Sincecolouristhefrequencyoflight,lightisemittedbysubstancesatcertainfixedfrequencies.Thesetofthefrequenciesthatcharacterizesagivensubstanceisknownastheâspectrumâofthissubstance.Aspectrumisacollectionoffinelinesofdifferenthues,inwhichthelightemittedbyagivensubstanceisdecomposed(forinstance,byaprism).Thespectraofafewelementsareshowninfigure4.2.
![Page 49: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/49.jpg)
Figure4.1NielsBohr.
Spectraofnumeroussubstanceshadbeenstudiedandcataloguedinmanylaboratoriesattheturnofthecentury,andnobodyknewhowtoexplainwhyeachsubstancehadthisorthatspectrum.Whatdeterminesthecolourofthoselines?
Figure4.2Thespectraofsomeelements:sodium,mercury,lithiumandhydrogen.
ColouristhespeedatwhichFaradayâslinesvibrate,andthisisdeterminedbythevibrationsoftheelectricchargeswhichemitlight.Thesechargesaretheelectronsthatmoveinsidetheatoms.Therefore,studyingspectra,wecanunderstandhowelectronsmovearoundnuclei.Theotherwayaround,wecouldpredictthespectrumofeachatombycomputingthefrequenciesoftheelectronscirclingtheirnucleus.Easytosay,butinpracticenobodywasabletodoso.Infact,thewholethingseemedimpossible,becauseinNewtonâsmechanicsanelectroncanrevolvearounditsnucleusatanyspeed,andhenceemitlightatanyfrequency.Butthenwhydoesthelightemittedbyanatomnotcontainallcolours,ratherthanjustafewparticularones?Whyareatomicspectranotacontinuumofcolours,insteadofjustafewseparatelines?Why,intechnicalparlance,aretheyâdiscreteâinsteadofcontinuous?Fordecades,physicistsseemedincapableoffindingananswer.
Bohrfindsatentativesolution,bywayofastrangehypothesis.Herealizesthateverythingcouldbeexplainediftheenergyofelectronsinatomscouldonlyassumecertainâquantizedâvaluesâcertainspecificvalues,justaswashypothesizedbyPlanckandbyEinsteinfortheenergyofthequantaoflight.Onceagain,thekeyisagranularity,butnotnowfortheenergyoflightbutratherfortheenergyoftheelectronsintheatom.Itbeginstobecomeclearthatgranularityissomethingwidespreadinnature.
Bohrmakesthehypothesisthatelectronscanexistonlyatcertainâspecialâdistancesfromthenucleus,thatis,onlyoncertainparticularorbits,thescaleofwhichisdeterminedbyPlanckâsconstanth.Andthatelectronscanâleapâbetweenoneorbitwiththepermittedenergytoanother.Thesearethefamousâquantumleapsâ.Thefrequencyatwhichtheelectronmovesontheseorbitsdeterminesthefrequencyoftheemittedlightand,sinceonlycertainorbitsareallowed,itfollowsthatonlycertainfrequenciesareemitted.
![Page 50: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/50.jpg)
ThesehypothesesdefineBohrâsâatomicmodelâ,whosecentenarywascommemoratedin2013.Withtheseassumptions(outlandish,butsimple)Bohrmanagestocomputethespectraofallatoms,andeventopredictaccuratelyspectranotyetobserved.Theexperimentalsuccessofthissimplemodelisastonishing.
Clearly,theremustbesometruthintheseassumptions,eveniftheyruncontrarytoallcontemporarynotionsofmatteranddynamics.Butwhyaretherealwaysonlyjustcertainorbits?Andwhatdoesitmeantosaythatelectronsâleapâ?
InBohrâsinstituteinCopenhagen,themostbrilliantyoungmindsofthecenturygathertotrytogiveordertothisjumbleofincomprehensiblebehavioursintheatomicworld,andtoconstructacoherenttheory.Theresearchisarduousandprotracted,untilayoungGermanfindsthekeytounlockthedoorofthemysteryofthequantumworld.
WernerHeisenbergistwenty-fiveyearsoldwhenhewritestheequationsofquantummechanics,thesameageasEinsteinwaswhenhewrotehisthreemajorarticles.Hedoessoonthebasisofdizzyingideas.
Figure4.3WernerHeisenberg.
TheintuitioncomestohimonenightintheparkbehindtheCopenhagenInstituteofPhysics.TheyoungWernerwalksaboutpensivelyinthepark.Itisreallydarkthere;wearein1925.Thereisonlyanoccasionalstreetlamp,castingdimislandsoflighthereandthere.Thepoolsoflightareseparatedbylargeexpansesofdarkness.Suddenly,Heisenbergseesafigurepassby.Actually,hedoesnotseehimpass:heseeshimappearbeneathalamp,thendisappearintothedarkbeforereappearingbeneathanotherlamp,andthenvanishingbackintothedarkagain.Andsoon,frompooloflighttopooloflight,untilheeventuallydisappearsaltogetherintothenight.Heisenbergthinksthat,âevidentlyâ,themandoesnotactuallyvanishandreappear:inhismind,hecaneasilyreconstructthemanâstrajectorybetweenonestreetlampandanother.Afterall,amanisasubstantialobject,bigandheavyâandbig,heavyobjectsdonotsimplyappearandvanishâŚ
Ah!Theseobjects,whicharesubstantial,largeandheavy,donâtvanishandreappearâŚbutwhatdoweknowaboutelectrons?Alightflashesoninhismind.Whyshouldsmallobjectssuchaselectronsdothesame?Whatif,effectively,electronscouldvanishandreappear?Whatifthesewerethemysteriousquantumleapswhichappearedtounderliethestructureoftheatomicspectra?Whatif,betweenoneinteractionwithsomething,andanotherwithsomethingelse,theelectroncouldliterallybenowhere.
Whatiftheelectroncouldbesomethingthatmanifestsitselfonlywhenitinteracts,whenitcollideswithsomethingelse;andthatbetweenoneinteractionandanotherithadnopreciseposition?Whatifalwayshavingaprecisepositionissomethingwhichisacquiredonlyifoneissubstantialenoughâlargeandheavylikethemanthatpassedbyalittlewhileago,likeaghostinthedark,andthendisappearedintothenightâŚ?
Onlysomeoneinhistwentiescantakesuchdeliriouspropositionsseriously.Youhavetobeatwenty-somethingtobelievethattheycanbeturnedintoatheoryoftheworld.Andperhapsyouhavetobethisyoungtounderstandbetterthananyoneelse,forthefirsttime,thedeepstructureofnature.JustasEinsteinwasinhistwentieswhenherealizedthattimedoesnotpassinthesamewayforeveryone,so,too,wasHeisenbergonthatCopenhagennight.Perhaps,itisnolongeragoodideatotrustyourintuitionsaftertheageofthirtyâŚ
![Page 51: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/51.jpg)
Heisenbergreturnshomegrippedbyfeverishemotion,andplungesintocalculations.Heemerges,sometimelater,withadisconcertingtheory:afundamentaldescriptionofthemovementofparticles,inwhichtheyaredescribednotbytheirpositionateverymomentbutonlybytheirpositionatparticularinstants:theinstantsinwhichtheyinteractwithsomethingelse.
Thisisthesecondcornerstoneofquantummechanics,itshardestkey:therelationalaspectofthings.Electronsdonâtalwaysexist.Theyexistwhentheyinteract.Theymaterializeinaplacewhentheycollidewithsomethingelse.Thequantumleapsfromoneorbittoanotherconstitutetheirwayofbeingreal:anelectronisacombinationofleapsfromoneinteractiontoanother.Whennothingdisturbsit,anelectrondoesnotexistinanyplace.Insteadofwritingthepositionandvelocityoftheelectron,Heisenbergwritestablesofnumbers(matrices).Hemultipliesanddividestablesofnumbersrepresentingpossibleinteractionsoftheelectron.And,asiffromthemagicalabacusofamagus,theresultscorrespondexactlywithwhatwasobserved.Thesearethefirstfundamentalequationsofquantummechanics.Fromhereon,theseequationswilldonothingbutwork,work,work.Upuntilnow,incredibleasitmayseem,theyhaveneverfailed.
Intheend,itisanothertwenty-five-year-oldwhopicksuptheworkinitiatedbyHeisenberg,takesthenewtheoryinhishandsandconstructsitsentireformalandmathematicalscaffolding:theEnglishmanPaulAdrienMauriceDirac,consideredbymanytobethegreatestphysicistofthetwentiethcenturyafterEinstein.
Despitehisscientificstature,Diracismuchlesswell-knownthanEinstein.Thisisdue,inpart,totherarefiedabstractionofhisscience,andpartlyduetohisdisconcertingcharacter.Silentincompany,extremelyreserved,incapableofexpressingemotions,frequentlyunabletorecognizethefacesofacquaintancesâincapableevenofconductinganordinaryconversation,orof,apparently,understandingsimplequestionsâheseemedvirtuallyautistic,andperhapsfellwithinthespectrumofthiscondition.
Figure4.4PaulDirac.
Duringoneofhislectures,acolleaguesaidtohim,âIdonâtunderstandthatformula.âAfterashort,silentpause,Diraccontinuedonregardless.Themoderatorinterruptedhim,askingifhewouldliketoreplytothequestion.Dirac,sincerelyastonished,replied,âQuestion?Whatquestion?Mycolleaguehasmadeanassertion.âAndso,inaverypedanticsense,hehad.Itwasnâtarrogance:themanwhocoulddiscoversecretsofnaturewhichhadeludedeveryoneelsecouldnotunderstandtheimplicitmeaningoflanguage,couldnotgraspitsnon-literalusage,andtookeveryphraseatfacevalue.2Andyet,inhishands,quantummechanicsistransformedfromajumbleofintuitions,half-bakedcalculations,mistymetaphysicaldiscussionsandequationsthatworkwell,butinexplicably,intoaperfectarchitecture:airy,simpleandextremelybeautiful.Beautiful,butstratosphericallyabstract.
ThevenerableBohrsaidofhim,âOfallphysicists,Dirachasthepurestsoul.âAnddonâthiseyes,infigure4.4showso?Hisphysicshasthepristineclarityofasong.Forhim,theworldisnotmadeofthings,itâsconstitutedofanabstractmathematicalstructurewhichshowsushowthingsappearandhowtheybehavewhenmanifestingthemselves.Itâsamagicalencounterbetweenlogicandintuition.Deeplyimpressed,Einsteinremarked,âDiracposesproblemsforme.Tomaintainanequilibriumalongthisvertiginouscourse,betweengeniusandmadness,isadauntingenterprise.â
![Page 52: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/52.jpg)
Diracâsquantummechanicsisthemathematicaltheoryusedtodaybyanyengineer,chemistormolecularbiologist.Init,everyobjectisdefinedbyanabstractspacefn20andhasnopropertyinitself,apartfromthosethatareunchanging,suchasmass.Itspositionandvelocity,itsangularmomentumanditselectricalpotential,andsoon,acquirerealityonlywhenitcollidesââinteractsââwithanotherobject.Itisnotjustitspositionwhichisundefined,asHeisenberghadrecognized:novariableoftheobjectisdefinedbetweenoneinteractionandthenext.Therelationalaspectofthetheorybecomesuniversal.
Whenitsuddenlyappears,inthecourseofaninteractionwithanotherobject,aphysicalvariable(velocity,energy,momentum,angularmomentum)doesnotassumejustanyvalue.Diracprovidesthegeneralrecipetocomputethesetofvaluesthataphysicalvariablecantake.fn21Thesevaluesareanalogoustothespectraofthelightemittedbyatoms.Todaywecallthesetoftheparticularvalueswhichavariablemayassumetheâspectrumâofthatvariable,byanalogywiththespectraintowhichthelightofelementsdecomposesâthefirstmanifestationofthisphenomenon.Forexample,theradiusoftheorbitalsofanelectronaroundanucleuscanacquireonlyspecificvalues,thosethatBohrhadhypothesized,whichformtheâspectrumoftheradiusâ.
Thetheoryalsogivesinformationonwhichvalueofthespectrumwillmanifestitselfinthenextinteraction,butonlyintheformofprobabilities.Wedonotknowwithcertaintywheretheelectronwillappear,butwecancomputetheprobabilitythatitwillappearhereorthere.ThisisaradicalchangefromNewtonâstheory,whereitispossible,inprinciple,topredictthefuturewithcertainty.Quantummechanicsbringsprobabilitytotheheartoftheevolutionofthings.Thisindeterminacyisthethirdcornerstoneofquantummechanics:thediscoverythatchanceoperatesattheatomiclevel.WhileNewtonâsphysicsallowsforthepredictionofthefuturewithexactitude,ifwehavesufficientinformationabouttheinitialdataandifwecanmakethecalculations,quantummechanicsallowsustocalculateonlytheprobabilityofanevent.Thisabsenceofdeterminismatasmallscaleisintrinsictonature.Anelectronisnotobligedbynaturetomovetowardstherightortheleft;itdoessobychance.Theapparentdeterminismofthemacroscopicworldisdueonlytothefactthatthemicroscopicrandomnesscancelsoutonaverage,leavingonlyfluctuationstoominuteforustoperceiveineverydaylife.
Diracâsquantummechanicsthusallowsustodotwothings.Thefirstistocalculatewhichvaluesaphysicalvariablemayassume.Thisiscalledâcalculationofthespectrumofavariableâ;itcapturesthegranularnatureofthings.Whenanobject(atom,electromagneticfield,molecule,pendulum,stone,star,andsoon)interactswithsomethingelse,thevaluescomputedarethosewhichitsvariablescanassumeintheinteraction(relationism).ThesecondthingthatDiracâsquantummechanicsallowsustodoistocomputetheprobabilitythatthisorthatvalueofavariableappearsatthenextinteraction.Thisiscalledâcalculationofanamplitudeoftransitionâ.Probabilityexpressesthethirdfeatureofthetheory:indeterminacyâthefactthatitdoesnotgiveuniquepredictions,onlyprobabilisticones.
ThisisDiracâsquantummechanics:arecipeforcalculatingthespectraofthevariablesandarecipeforcalculatingtheprobabilitythatoneoranothervalueinthespectrumwillappearduringaninteraction.Thatâsit.Whathappensbetweenoneinteractionandthenextisnotmentionedinthetheory.Itdoesnotexist.
Theprobabilityoffindinganelectronoranyotherparticleatonepointoranothercanbeimaginedasadiffusecloud,denserwheretheprobabilityofseeingtheparticleisstronger.Sometimesitisusefultovisualizethiscloudasifitwerearealthing.Forinstance,thecloudthatrepresentsanelectronarounditsnucleusindicateswhereitismorelikelythattheelectronappearsifwelookatit.Perhapsyouencounteredthematschool:thesearetheatomicâorbitalsâ.fn22
Theefficacyofthetheorysoonprovesextraordinary.Iftodaywebuildcomputers,haveadvancedmolecularchemistryandbiology,lasersandsemiconductors,itisthankstoquantummechanics.ForacertainnumberofdecadesitwasasifitwereChristmaseverydayforphysicists:foreverynewproblem,therewasananswerwhichfollowedfromtheequationsofquantummechanics,anditwasalwaysthecorrectanswer.Oneexampleofthiswillsuffice.
Themattersurroundingusismadeupofathousanddifferentsubstances.Duringthenineteenthandtwentiethcenturieschemistsunderstoodthatallthesedifferentsubstancesarejustcombinationsofarelativelysmallnumber(lessthanahundred)ofsimpleelements:hydrogen,helium,oxygen,andsoonâtouranium.Mendeleevputtheseelementsinorder(accordingtoweight)inthefamousperiodictablewhichispinnedtothewallsofsomanyclassroomsandwhichsummarizesthepropertiesoftheelementsofwhichtheworldismadeânotonlyonEarthbutallovertheuniverseinallgalaxies.Whythesespecificelements?Whatexplainstheperiodicstructureofthetable?Whydoeseachelementhavecertainpropertiesandnotothers?Why,forinstance,dosomeelementscombineeasily,whereasothersdonot?WhatisthesecretofthecuriousstructureofMendeleevâstable?
![Page 53: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/53.jpg)
Figure4.5Lightisawaveonafield,butithasalsoagranularstructure.
Well,taketheequationofquantummechanicsthatdeterminestheformoftheorbitalsofanelectron.Thisequationhasacertainnumberofsolutions,andthesesolutionscorrespondexactlytohydrogen,helium,oxygenâŚandtheotherelements!Mendeleevâsperiodictableisstructuredexactlylikethesetofthesesolutions.Thepropertiesoftheelements,witheverythingelse,followsfromthesolutionofthisequation.Quantummechanicsdeciphersperfectlythesecretofthestructureoftheperiodictableofelements.
PythagorasandPlatoâsancientdreamisrealized:todescribealloftheworldâssubstanceswithasingleformula.Theinfinitecomplexityofchemistry,capturedbythesolutionsofasingleequation!Andthisisjustoneoftheapplicationsofquantummechanics.
FieldsandparticlesarethesamethingShortlyaftercompletingthegeneralformulationofquantummechanics,Diracrealizesthatthetheorycanbedirectlyappliedtofieldssuchaselectromagneticones,andcanbemadeconsistentwithspecialrelativity.(Makingitconsistentwithgeneralrelativitywillprovemuchharder,andisthemainsubjectofthisbook).Indoingthis,Diracdiscoversanulterior,profoundsimplificationofourdescriptionofnature:theconvergencebetweenthenotionofparticlesusedbyNewtonandthenotionoffieldsintroducedbyFaraday.
Thecloudofprobabilitywhichaccompanieselectronsbetweenoneinteractionandanotherdoesresembleafield.FaradayandMaxwellâsfields,inturn,aremadeupofgrains:photons.Notonlyaretheparticlesinacertainsensediffusedinspacelikefieldsbutthefieldsinteractlikeparticles.Thenotionsoffieldsandparticles,separatedbyFaradayandMaxwell,endupmerginginquantummechanics.
Thewaythishappensinthetheoryiselegant:theequationofDiracdeterminesthevaluesavariablecantake.AppliedtotheenergyofFaradayâslines,theytellusthatthisenergycanonlytakeoncertainvalues,andnotothers.Sincetheenergyoftheelectromagneticfieldcantakeononlycertainvalues,thefieldbehaveslikeasetofpacketsofenergy.ThesearepreciselythequantaofenergyintroducedbyPlanckandEinsteinthirtyyearsearlier.Thecirclecloses,andthestoryiscomplete.Theequationsofthetheory,writtenbyDirac,accountforthegranularnatureoflight,whichPlanckandEinsteinhadintuited.
TheelectromagneticwavesarevibrationsofFaradayâslines,butalso,atasmallscale,swarmsofphotons.Whentheyinteractwithsomethingelse,asinthephotoelectriceffect,theymanifestthemselvesasparticles:tooureye,lightrainsinseparatedroplets,insinglephotons.Photonsarethequantaoftheelectromagneticfield.
ButtheelectronsandalltheotherparticlesofwhichtheworldismadeareequallyquantaofafieldâaâquantumfieldâsimilartoFaradayandMaxwellâs,subjecttogranularityandtoquantumprobability.Diracwritestheequationsforthefieldoftheelectronsandoftheotherelementaryparticles.fn23ThesharpdistinctionbetweenfieldsandparticlesintroducedbyFaradayvanishes.
Thegeneralformofquantumtheorycompatiblewithspecialrelativityisthuscalledquantumfieldtheory,anditformsthebasisoftodayâsparticlephysics.Particlesarequantaofafield,justasphotonsarequantaoflight.Allfieldsdisplayagranularstructureintheirinteractions.
![Page 54: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/54.jpg)
Duringthecourseofthetwentiethcenturythelistoffundamentalfieldswasrepeatedlyupdated,andtodaywehaveatheorycalledthestandardmodelofelementaryparticleswhichdescribesalmostallwesee,withtheexceptionofgravity,fn24inthecontextofquantumfieldtheory.Thedevelopmentofthismodeloccupiedphysicistsforagoodpartofthelastcentury,andrepresentsinitselfawonderfuladventureofdiscovery.Idonâtpresentthissideofthestoryhere:itisquantumgravitythatIwouldliketogetonto.Thestandardmodeliscompletedbythe1970s.Thereareapproximatelyfifteenfields,whosequantaaretheelementaryparticles(electrons,quarks,muons,neutrinos,Higgs,andlittleelse),plusafewfieldssimilartotheelectromagneticone,whichdescribeelectromagneticforceandtheotherforcesoperatingatanuclearscale,whosequantaaresimilartothephotons.
Thestandardmodelwasnottakenveryseriouslyatfirst,duetoitssomewhatcobbled-togetheraspect,sodifferentfromtheairysimplicityofgeneralrelativityandMaxwellâsorDiracâsequations.Againstexpectations,however,allofitspredictionshavebeenconfirmed.Formorethanthirtyyears,everysingleexperimentofparticlephysicshasdonenothingbutrepeatedlyreconfirmthestandardmodel.ArecentconfirmationwasthediscoveryoftheHiggsparticle,whichcausedasensationin2013.Introducedtorenderthetheorycoherent,theHiggsfieldseemedabitartificialâuntiltheHiggsparticle,thequantumofthisfield,wasactuallyobservedandfoundtohavepreciselythepropertiespredictedbythestandardmodel.fn25(ThefactthatithasbeencalledâtheGodparticleâissostupidastobeunworthyofcomment.)Inshort,despiteitsunjustlymodestname,thestandardmodelhasbeenatriumph.
Figure4.6Whatistheworldmadeof?
Quantummechanics,withitsfields/particles,offerstodayaspectacularlyeffectivedescriptionofnature.Theworldisnotmadeupoffieldsandparticlesbutofasingletypeofentity:thequantumfield.Therearenolongerparticleswhichmoveinspacewiththepassageoftime,butquantumfieldswhoseelementaryeventshappeninspacetime.Theworldisstrange,butsimple(figure4.6).
Quanta1:InformationisfiniteThetimehascometoattemptsomeconclusionsaboutwhatitis,precisely,thatquantummechanicstellsusabouttheworld.Itisnâtaneasytask,becausequantummechanicsisnotconceptuallyclearanditstruemeaningremainscontroversial;butitâsanecessaryexercise,togainclarityandgoforward.Ithinkthatquantummechanicshasrevealedthreeaspectsofthenatureofthings:granularity,indeterminacyandtherelationalstructureoftheworld.Letâslookateachofthesemoreclosely.
Thefirstistheexistenceofafundamentalgranularityinnature.Thegranularityofmatterandlightisattheheartofquantumtheory.ItisnâtthesamegranularityintuitedbyDemocritus,however.ForDemocritus,atomswerelikelittlepebbles,whereasinquantummechanicsparticlesvanishandreappear.Buttherootoftheideaofthesubstantivegranularityoftheworldisstilltobefoundinancientatomism,andquantummechanicsâstrengthenedbycenturiesofexperiments,bypowerfulmathematics,andbyitsextraordinarycapacityformakingcorrectpredictionsâisagenuinerecognitionoftheprofoundinsightsonthenatureofthingsreachedbythegreatphilosopherofAbdera.
![Page 55: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/55.jpg)
Saywemakemeasurementsonaphysicalsystemandfindthatthesystemisinaparticularstate.Forinstance,wemeasuretheamplitudeoftheoscillationsofapendulumandfindthatithasacertainvalueâsay,somewherebetweenfivecentimetresandsixcentimetres(nomeasurementisexactinphysics).Beforequantummechanicswewouldhavesaidthat,sincethereareaninfinitenumberofpossiblevaluesbetweenfiveandsixcentimetres(forinstance5.1or5.101or5.101001âŚ),thenthereareinfinitepossiblestatesofmotioninwhichthependulumcouldfinditself:theamountofourignoranceaboutthependulumstateisstillinfinite.
Instead,quantummechanicstellsusthatbetweenfiveandsixcentimetresthereisafinitenumberofpossiblevaluesoftheamplitude,henceourmissinginformationaboutthependulumisfinite.
Thisgoesforeverythingingeneral.fn26Therefore,thefirstmeaningofquantummechanicsistheexistenceofalimittotheinformationthatcanexistwithinasystem:alimittothenumberofdistinguishablestatesinwhichasystemcanbe.ThislimitationuponinfinityâthisgranularityofnatureglimpsedbyDemocritusâisthefirstcentralaspectofthetheory.Planckâsconstanthmeasurestheelementaryscaleofthisgranularity.
Quanta2:IndeterminacyTheworldisasequenceofgranularquantumevents.Thesearediscrete,granularandindividual;theyareindividualinteractionsofonephysicalsystemwithanother.Anelectron,aquantumofafieldoraphotondoesnotfollowatrajectoryinspacebutappearsinagivenplaceandatagiventimewhencollidingwithsomethingelse.Whenandwherewillitappear?Thereisnowayofknowingwithcertainty.Quantummechanicsintroducesanelementaryindeterminacytotheheartoftheworld.Thefutureisgenuinelyunpredictable.Thisisthesecondfundamentallessonlearnedwithquantummechanics.
Duetothisindeterminacy,intheworlddescribedbyquantummechanics,thingsareconstantlysubjecttorandomchange.Allthevariablesâfluctuateâcontinually,asif,atthesmallestscale,everythingisconstantlyvibrating.Wedonotseetheseomnipresentfluctuationsonlybecauseoftheirsmallscale;theycannotbeobservedatalargescale,aswhenweobservemacroscopicbodies.Ifwelookatastone,itstaysstill.Butifwecouldseeitsatoms,wewouldobservethemconstantlyspreadhereandthere,andinceaselessvibration.Quantummechanicsrevealstousthat,themorewelookatthedetailoftheworld,thelessconstantitis.Theworldisnotmadeupoftinypebbles.Itisaworldofvibrations,acontinuousfluctuation,amicroscopicswarmingoffleetingmicro-events.
Theatomismofantiquityhadanticipatedalsothisaspectofmodernphysics:theappearanceoflawsofprobabilityatadeeplevel.Democritusassumed(justlikeNewton)thatthemovementofatomswasrigorouslydeterminedbytheircollisions.Buthissuccessor,Epicurus,correctsthedeterminismofthemasterandintroducesintoatomismthenotionofindeterminacyâinthesamewayinwhichHeisenbergintroducesindeterminacyintoNewtonâsdeterminism.ForEpicurus,atomscanonoccasiondeviatebychancefromtheircourse.Lucretiussaysthisinbeautifulwords:thisdeviationoccursâincertotemporeâŚincertisquelociâ:3atanuncertainplace,atanuncertaintime.Thesamerandomness,thesameappearanceofprobabilityatanelementarylevel,isthesecondkeydiscoveryabouttheworldthatquantummechanicsexpresses.
So,howdowecomputetheprobabilitythatanelectroninacertaininitialpositionAwillreappear,afteragiventime,inoneoranotherfinalpositionB?
Inthe1950s,RichardFeynman,whoIâvealreadymentioned,foundasuggestivemethodofmakingthiscalculation:considerallpossibletrajectoriesfromAtoB,thatistosay,allpossibletrajectoriestheelectroncanfollow(straight,curved,zigzaggingâŚ).Eachtrajectorydeterminesanumber.Theprobabilityisobtainedfromthesumofallthesenumbers.Thedetailsofthiscalculationarenotimportant:whatmattersisthefactthatalltrajectoriesfromAtoBcontribute:itisasiftheelectron,inordertogofromAtoB,passedâthroughallpossibletrajectoriesâ,or,inotherwords,unfurledintoacloudinorderthentoconvergemysteriouslyonpointB,whereitcollidesagainwithsomethingelse(figure4.7).
![Page 56: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/56.jpg)
Figure4.7InordertomovefromAtoBanelectronbehavesasifpassingthroughallpossibletrajectories.
ThistechniqueforcomputingtheprobabilityofaquantumeventiscalledFeynmanâssumoverpaths,fn27andweshallseethatitplaysaroleinquantumgravity.
Quanta3:RealityisrelationalThethirddiscoveryabouttheworldarticulatedbyquantummechanicsisthemostprofoundanddifficultâandonewhichwasnotanticipatedbytheatomismofantiquity.
Thetheorydoesnotdescribethingsastheyare:itdescribeshowthingsoccurandhowtheyinteractwitheachother.Itdoesnâtdescribewherethereisaparticlebuthowtheparticleshowsitselftoothers.Theworldofexistentthingsisreducedtoarealmofpossibleinteractions.Realityisreducedtointeraction.Realityisreducedtorelation.4
Inacertainsense,thisisjustanextensionofrelativity,albeitaradicalone.Aristotlewasfirsttoemphasizethatweonlyperceiverelativespeed.Onaship,forexample,wetalkofourspeedrelativetotheship;onland,relativetotheEarth.GalileounderstoodthatthisisthereasonwhytheEarthcanmovewithrespecttotheSunwithoutusfeelingthemovement.Speedisnotapropertyofanobjectonitsown:itisthepropertyofthemotionofanobjectwithrespecttoanotherobject.Einsteinextendedthenotionofrelativitytotime:wecansaythattwoeventsaresimultaneousonlyrelativelytoagivenmotion(seehere).Quantummechanicsextendsthisrelativityinaradicalway:allvariableaspectsofanobjectexistonlyinrelationtootherobjects.Itisonlyininteractionsthatnaturedrawstheworld.
Intheworlddescribedbyquantummechanicsthereisnorealityexceptintherelationsbetweenphysicalsystems.Itisnâtthingsthatenterintorelationsbut,rather,relationsthatgroundthenotionofâthingâ.Theworldofquantummechanicsisnotaworldofobjects:itisaworldofevents.Thingsarebuiltbythehappeningofelementaryevents:asthephilosopherNelsonGoodmanwroteinthe1950s,inabeautifulphrase,âAnobjectisamonotonousprocess.âAstoneisavibrationofquantathatmaintainsitsstructureforawhile,justasamarinewavemaintainsitsidentityforawhilebeforemeltingagainintothesea.
Whatisawave,whichmovesonwaterwithoutcarryingwithitanydropofwater?Awaveisnotanobject,inthesensethatitisnotmadeofmatterthattravelswithit.Theatomsofourbody,aswell,flowinandawayfromus.We,likewavesandlikeallobjects,areafluxofevents;weareprocesses,forabrieftimemonotonousâŚ
Quantummechanicsdoesnotdescribeobjects:itdescribesprocessesandeventswhicharejunctionpointsbetweenprocesses.
Tosummarize,quantummechanicsisthediscoveryofthreefeaturesoftheworld:
Granularity(figure4.8).Theinformationinthestateofasystemisfinite,andlimitedbyPlankâsconstant.Indeterminacy.Thefutureisnotdeterminedunequivocallybythepast.Eventhemorerigidregularitiesweseeare,ultimately,statistical.Relationality.Theeventsofnaturearealwaysinteractions.Alleventsofasystemoccurinrelationtoanothersystem.
Quantummechanicsteachesusnottothinkabouttheworldintermsofâthingsâwhichareinthisorthatstatebutintermsofâprocessesâinstead.Aprocessisthepassagefromoneinteractionto
![Page 57: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/57.jpg)
another.Thepropertiesofâthingsâmanifestthemselvesinagranularmanneronlyinthemomentofinteraction,thatistosay,attheedgesoftheprocesses,andaresuchonlyinrelationtootherthings.Theycannotbepredictedinanunequivocalwaybutonlyinaprobabilisticone.
Figure4.8TheâlightboxâinEinsteinâsmentalexperiment,asdrawnbyBohr.
ThisisthevertiginousdivetakenbyBohr,HeisenbergandDiracâintothedepthofthenatureofthings.
Butdowereallyunderstand?Certainly,quantummechanicsisatriumphofefficacy.AndyetâŚareyousure,dearreader,thatyouhavefullyunderstoodwhatquantummechanicsrevealstous?AnelectronisnowherewhenitisnotinteractingâŚmmmâŚthingsonlyexistbyjumpingfromoneinteractiontoanotherâŚwellâŚDoesitallseemalittleabsurd?
ItseemedabsurdtoEinstein.Ontheonehand,EinsteinproposedWernerHeisenbergandPaulDiracfortheNobelPrize,
recognizingthattheyhadunderstoodsomethingfundamentalabouttheworld.Ontheother,hetookeveryopportunitytogrumblethat,however,noneofthismademuchsense
TheyounglionsoftheCopenhagengroupweredismayed:howcouldthiscomefromEinsteinhimself?Theirspiritualfather,themanwhohadthecouragetothinktheunthinkable,nowpulledbackandfearedthisnewleapintotheunknownâtheveryleapwhichhehadhimselftriggered.HowcoulditbethatthesameEinstein,whohadtaughtusthattimeisnotuniversalandthatspacebends,wasnowsayingthattheworldcouldnotbethisstrange?
NielsBohrpatientlyexplainedthenewideastoEinstein.Einsteinobjected.Bohr,intheend,alwaysmanagedtofindanswerstotheobjections.Thedialoguecontinuedforyears,bywayoflectures,letters,articlesâŚEinsteindevisedmentalexperimentstoshowthatthenewideaswerecontradictory:âImagineaboxfilledwithlight,fromwhichisletescapeforabriefinstantasinglephotonâŚâ:thusoneofthemostfamousexamplesofthesebegins(figure4.8).fn28
Duringthecourseoftheexchange,bothgreatmenhadtogiveway,toaltertheirideas.Einsteinwasobligedtorecognizethattherewasactuallynocontradictionwithinthenewideas.ButBohrhadtorecognizethatthingswerenotassimpleandasclearashethought.Einsteindidnotwanttorelentonwhatforhimwasthekeypoint:thenotionthatthereisanobjectivereality,independentofwhateverinteractedwithwhat.Herefusedtoaccepttherelationalaspectofthetheory,thefactthatthingsmanifestthemselvesonlythroughinteractions.Bohrdidnotwanttoconcedeonthevalidityoftheprofoundlynewwayinwhichtherealwasconceptualizedbythetheory.Ultimately,Einsteinacceptsthatthetheoryrepresentsagiganticleapforwardinourunderstandingoftheworld,andthatitiscoherent.Butheremainsconvincedthatthingscouldnotbeasstrangeasthistheoryproposedâandthat,âbehindâit,theremustbeafurther,morereasonableexplanation.
Acenturyhaspassed,andweareatthesamepoint.RichardFeynman,whomorethananyonehasknownhowtojugglewiththetheory,haswritten,âIthinkIcanstatethatnobodyreallyunderstandsquantummechanics.â
Theequationsofthetheoryandtheirconsequencesareuseddailyinawidevarietyoffields:byphysicists,engineers,chemistsandbiologists.Buttheyremainmysterious:theydonotdescribephysicalsystemsbutonlyhowphysicalsystemsinteractwithandaffectoneanother.Whatdoesthismean?
Physicistsandphilosopherscontinuetoaskthemselveswhattherealmeaningofthetheorymightbeand,inrecentyears,articlesandconferencesontheissuehaveproliferated.Whatisquantumtheory,acenturyafteritsbirth?Anextraordinarydivedeepintothenatureofreality?Ablunder
![Page 58: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/58.jpg)
thatworks,bychance?Partofanincompletepuzzle?Oracluetosomethingprofoundregardingthestructureoftheworld,whichwehaveyettofullydecipher?
TheinterpretationofquantummechanicswhichIhavepresentedhereistheonewhichseemsleastunreasonabletome.Itiscalledtheârelationalinterpretationâ,andithasbeendiscussedbyseriousphilosopherssuchasBasvanFraassen,MichelBitbolandMauroDorato.5Butthereisnoconsensusonhowtothinkaboutquantummechanics:thereareotherwaysofthinkingaboutit,discussedbyotherphysicistsandotherphilosophers.Weareonthebrinkofthatwhichwedonâtknow,andopinionsdiverge.
Quantummechanicsisonlyaphysicstheory:perhapstomorrowitwillbecorrectedbyanunderstandingoftheworldwhichisdifferentandevenmoreprofound.Somescientiststodaytrytoironitoutabit,torenderitmoreinkeepingwithourintuition.Inmyopinion,itsdramaticempiricalsuccessshouldcompelustotakeitseriously,andtoaskourselvesnotwhatthereistochangeinthetheoryâbutratherwhatislimitedaboutourintuitionthatmakesitseemsostrangetous.
Ithinkthattheobscurityofthetheoryisnotthefaultofquantummechanicsbut,rather,isduetothelimitedcapacityofourimagination.Whenwetrytoâseeâthequantumworld,weareratherlikemolesusedtolivingundergroundtowhomsomeoneistryingtodescribetheHimalayas.OrlikethemenimprisonedatthebackofPlatoâscave.
WhenEinsteindied,hisgreatestrival,Bohr,foundforhimwordsofmovingadmiration.When,afewyearslater,Bohrinturndied,someonetookaphotographoftheblackboardinhisstudy.Thereâsadrawingonit.ItrepresentstheâboxoflightâofEinsteinâsthoughtexperiment.Totheverylast,thedesiretodebate,tounderstandmore.Totheverylast,doubt.
Thispermanentdoubt,thedeepsourceofscience.
![Page 59: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/59.jpg)
![Page 60: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/60.jpg)
PartThree
QUANTUM SPACE AND RELATIONAL TIME
Ifyouhavefollowedmethisfar,younowhavealltheelementswithwhichtounderstandthecurrentimageoftheworldsuggestedbyfundamentalphysicsâitspower,itsweaknesses,itslimits.
Thereisacurvedspacetimeborn14billionyearsagoânobodyknowshowâandstillexpanding.Thisspaceisarealobject,aphysicalfieldwithitsdynamicsdescribedbyEinsteinâsequations.Spacebendsandcurvesundertheweightofmatterandplungesintoblackholeswhenmatteristooconcentrated.
Matterisdistributedin100billiongalaxies,eachcontaining100billionstars,andismadeupofquantumfieldswhichmanifestthemselvesintheformofparticles,suchaselectronsandphotons,oraswaves,suchastheelectromagneticonesthatbringustelevisionimagesandthelightoftheSunandthestars.
Thesequantumfieldsmakeupatoms,lightandthefullcontentsoftheuniverse.Theyarestrangeobjects:theirquantaareparticlesthatappearwhentheyinteractwithsomethingelse;leftalone,theyunfurlintoaâcloudofprobabilityâ.Theworldisaswarmingofelementaryevents,immersedintheseaofavastdynamicalspacewhichswayslikethewaterofanocean.
Withthisimageoftheworld,andthefewequationsthatmakeitconcrete,wecandescribealmosteverythingthatwesee.
Almost.Somethingismissing.Anditisthissomethingthatweareseeking.Therestofthebooktalksaboutthismissingpart.
Turningthepage,youpassfromwhat,forgoodorill,wecrediblyknowabouttheworld,towhatwedonâtyetknowbutaretryingtoglimpse.
Turningthepageislikeleavingthesecurityofoursmallspacecraftofnear-certaintiesandsteppingintotheunknown.
![Page 61: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/61.jpg)
5.SpacetimeisQuantum
Thereisaparadoxattheheartofourunderstandingofthephysicalworld.Generalrelativityandquantummechanics,thetwojewelsthatthetwentiethcenturyhasleftus,havebeenprolificingiftsâforcomprehendingtheworldandfortodayâstechnology.Fromthefirstofthese,cosmologyhasdeveloped,aswellasastrophysics,thestudyofgravitationalwavesandofblackholes.Thesecondhasprovidedthefoundationforatomicphysics,nuclearphysics,thephysicsofelementaryparticlesandofcondensedmatter,andofmuchelsebesides.Andyetbetweenthetwotheoriesthereissomethingthatgrates.Theycannotbothbetrue,at
leastnotintheirpresentforms,becausetheyappeartocontradicteachother.Thegravitationalfieldisdescribedwithouttakingquantummechanicsintoaccount,withoutaccountingforthefactthatfieldsarequantumfieldsâandquantummechanicsisformulatedwithouttakingintoaccountthefactthatspacetimecurvesandisdescribedbyEinsteinâsequations.Auniversitystudentattendinglecturesongeneralrelativityinthemorning,andotherson
quantummechanicsintheafternoon,mightbeforgivenforconcludingthathisprofessorsarefools,orthattheyhavenâttalkedtoeachotherforatleastacentury.Inthemorning,theworldisacurvedspacetimewhereeverythingiscontinuous;intheafternoon,theworldisaflatonewherediscretequantaofenergyleapandinteract.Theparadoxresidesinthefactthatboththeoriesworkremarkablywell.Witheveryexperimentandeverytest,naturecontinuestosayâyouarerightâtogeneralrelativity,
andcontinuestosayâyouarerightâtoquantummechanicsaswell,despitetheseeminglyoppositeassumptionsonwhichthetwotheoriesarefounded.Itisclearthatsomethingstilleludesus.Inmostsituationswecanneglectquantummechanicsorgeneralrelativity(orboth).TheMoonis
toolargetobesensitivetominutequantumgranularity,sowecanforgetthequantawhendescribingitsmovements.Ontheotherhand,anatomistoolighttocurvespacetoasignificantdegree,andwhenwedescribeitwecanforgetthecurvatureofspace.Buttherearesituationswherebothcurvatureofspaceandquantumgranularitymatter,andforthesewedonotyethaveanestablishedphysicaltheorythatworks.Anexampleistheinteriorofblackholes.AnotheriswhathappenedtotheuniverseduringtheBig
Bang.Inmoregeneralterms,wedonotknowhowtimeandspacebehaveatverysmallscale.Inalltheseinstances,todayâstheoriesbecomeconfusedandnolongertellusanythingreasonable:quantummechanicscannotdealwiththecurvatureofspacetime,andgeneralrelativitycannotaccountforquanta.Thisistheproblemofquantumgravity.Theproblemgoesevendeeper.Einsteinunderstoodthatspaceandtimearemanifestationsofa
physicalfield:thegravitationalfield.Bohr,HeisenbergandDiracunderstoodthatphysicalfieldshaveaquantumcharacter:granular,probabilistic,manifestingthroughinteractions.Itfollowsthatspaceandtimemustalsobequantumentitiespossessingthesestrangeproperties.What,then,isquantumspace?Whatisquantumtime?Thisistheproblemwecallquantum
gravity.Abandoftheoreticalphysicistsscatteredacrossfivecontinentsislaboriouslyseekingtosolvetheproblem.Theirobjectiveistofindatheory,thatistosay,asetofequationsâbut,aboveall,acoherentvisionoftheworldâwithwhichtoresolvethecurrentschizophreniabetweenquantaandgravity.Itisnâtthefirsttimethatphysicshasfounditselffacedwithtwohighlysuccessfulbutapparently
contradictorytheories.Theefforttosynthesizehasinthepastbeenrewardedwithgreatstridesforwardinourunderstandingoftheworld.NewtondiscovereduniversalgravitypreciselybycombiningGalileoâsphysicsofhowthingsmoveonEarthwithKeplerâsphysicsoftheheavens.MaxwellandFaradayfoundtheequationsofelectromagnetismbybringingtogetherwhatwasknownaboutelectricityandwhatwasknownaboutmagnetism.EinsteinfoundspecialrelativityinordertoresolvetheapparentconflictbetweenNewtonâsmechanicsandMaxwellâselectromagnetismâandthengeneralrelativityinordertoresolvetheresultingconflictbetweenNewtonâsmechanicsandhisownspecialrelativity.Theoreticalphysicistsarethusonlytoohappywhentheydiscoveraconflictofthistype:itisan
extraordinaryopportunity.Thequestiontoaskis:canweconstructaconceptualstructurecompatiblewithwhatwehavelearnedabouttheworldwithboththeories?Tocomprehendwhatquantumspaceandquantumtimeare,weneedoncemoretoreviseindepth
thewayweconceivethings.Weneedtorethinkthegrammarofourunderstandingoftheworld.JustashappenedwithAnaximander,whounderstoodthatEarthfliesinspace,andthatâupâandâdownâdonotexistinthecosmos;orwithCopernicus,whounderstoodthatwearemovingacrossthe
![Page 62: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/62.jpg)
heavensatgreatspeed;orwithEinstein,whounderstoodthatspacetimesquasheslikeamollusc,andtimepassesdifferentlyindifferentplacesâŚonceagain,inseekingacoherentvisionoftheworldinkeepingwithwhatwehavelearnedaboutit,ourideasaboutthenatureofrealityhavetochange.
Figure5.1MatveiBronĹĄtejn.
Thefirsttorealizethatourconceptualbasismustchangeinordertounderstandquantumgravitywasaromanticandlegendarycharacter:MatveiBronĹĄtejn,ayoungRussianwholivedduringtheStalineraanddiedtragically.
MatveiMatveiwasayoungerfriendofLevLandauâthescientistwhowouldgoontobecomethebesttheoreticalphysicistoftheSovietUnion.Colleagueswhoknewthembothwouldclaimthat,ofthetwo,Matveiwasthemorebrilliant.AtthepointwhenHeisenbergandDiracwereconstructingthebasesofquantummechanics,Landau,wrongly,thoughtthatfieldsbecameilldefinedduetoquanta:quantumfluctuationwouldpreventusfrommeasuringthevalueofacomponentofafieldatapoint(anarbitrarysmallregion)inspace.ThemasterlyBohrimmediatelysawthatLandauwaswrong,studiedtheissueindepthandwrotealonganddetailedarticletoshowthatfields,suchastheelectricone,remainwelldefinedevenwhenquantummechanicsisbroughttobear.1Landaudroppedtheissue.ButhisyoungfriendMatveiwasintrigued,realizingthatLandauâsintuition,thoughimprecise,
containedsomethingofimportance.HerepeatedthesamereasoningbywhichBohrhaddemonstratedthatthequantumelectricfieldwaswelldefinedatapointofspace,applyingitinsteadtothegravitationalfield,forwhichEinsteinhadjustafewyearspreviouslywrittentheequations.Andhereâsurprise!âLandauwasright.Thegravitationalfieldatapointisnotwelldefined,whentakingquantaintoaccount.Thereisanintuitivewayofunderstandingwhathappens.Supposewewanttoobserveavery,
very,verysmallregionofspace.Todothis,weneedtoplacesomethinginthisarea,tomarkthepointthatwewishtoconsider.Sayweplaceaparticlethere.Heisenberghadunderstoodthatyoucanâtlocateaparticleatapointinspaceforlong.Itsoonescapes.Thesmallertheregioninwhichwetrytolocateaparticle,thegreaterthevelocityatwhichitescapes.(ThisisHeisenbergâsuncertaintyprinciple.)Iftheparticleescapesatgreatspeed,ithasagreatdealofenergy.NowletustakeEinsteinâstheoryintoaccount.Energymakesspacecurve.Alotofenergymeansthatspacewillcurveagreatdeal.Alotofenergyinasmallregionresultsincurvingspacesomuchthatitcollapsesintoablackhole,likeacollapsingstar.Butifaparticleplummetsintoablackhole,Icannolongerseeit.Icannolongeruseitasareferencepointforaregionofspace.Icanâtmanagetomeasurearbitrarilysmallregionsofspace,becauseifItrytodothistheseregionsdisappearinsideablackhole.
![Page 63: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/63.jpg)
Thisargumentcanbemademoreprecisewithalittlemathematics.Theresultisgeneral:quantummechanicsandgeneralrelativity,takentogether,implythatthereisalimittothedivisibilityofspace.Belowacertainscale,nothingmoreisaccessible.Moreprecisely,nothingexiststhere.Howsmallisthisminimalregionofspace?Thecalculationiseasy:weneedonlytocalculatethe
minimumsizeofaparticlebeforeitfallsintoitsownblackhole,andtheresultisstraightforward.Theminimumlengthisaround:
Underthesignofthesquareroottherearethethreeconstantsofnaturewehavealreadyencountered:NewtonâsconstantG,discussedinChapter2,whichsetsthestrengthofgravity;thespeedoflightc,introducedinChapter3whendiscussingrelativity,whichopensuptheextendedpresent;andPlanckâsconstanth,foundinChapter4,whichdeterminesthescaleofthequantumgranularity.fn29Thepresenceofthesethreeconstantsconfirmsthefactthatwearelookingatsomethingwhichhastodowithgravity(G),relativity(c)andquantummechanics(h).ThelengthLP,determinedinthisfashion,iscalledthePlancklength.Itshouldbecalledthe
BronĹĄtejnlength,butsuchisthewayoftheworld.Innumericalterms,itisequivalenttoapproximatelyonemillionthofabillionthofabillionthofabillionthofacentimetre(10-33centimetres).So,thatistosayâŚsmall.Itisatthisextremelyminutescalethatquantumgravitymanifestsitself.Togiveanideaofthe
smallnessofthescalewearediscussing:ifweenlargedawalnutshelluntilithadbecomeasbigasthewholeobservableuniverse,wewouldstillnotseethePlancklength.Evenafterhavingbeenenormouslymagnifiedthus,itwouldstillbeamilliontimessmallerthantheactualwalnutshellwasbeforemagnification.Atthisscale,spaceandtimechangetheirnature.Theybecomesomethingdifferent;theybecomeâquantumspaceandtimeâ,andunderstandingwhatthismeansistheproblem.MatveiBronĹĄtejnunderstandsallofthisinthe1930sandwritestwoshortandilluminating
articlesinwhichhepointsoutthatquantummechanicsandgeneralrelativity,takentogether,areincompatiblewithourcustomaryideaofspaceasaninfinitelydivisiblecontinuum.2Thereis,however,aproblem.MatveiandLevaresincerecommunists.Theybelieveinrevolution
astheliberationofmankind,theconstructionofagenuinelybettersociety,withoutinjustice,withouttheimmenseinequalitieswhichwestillseegrowingsystematicallythroughouttheworld.TheyareenthusiasticfollowersofLenin.WhenStalinassumespower,theyarebothperplexed,thencritical,thenhostile.TheywritearticleswhicharemildlybutopenlycriticalâŚThiswasnotthecommunismtheywantedâŚButtheseareharshtimes.Landaugetsthroughthem,noteasily,buthesurvives.Matvei,theyear
afterhavingbeenthefirsttounderstandthatourideasonspaceandtimehadtochangeinaradicalway,isarrestedbyStalinâspoliceandcondemnedtodeath.Hisexecutiontakesplaceonthesamedayashistrial,18February,1938.3Heisthirtyyearsold.
JohnAfterMatveiBronĹĄtejnâsprematuredeath,manyofthecenturyâseminentphysiciststriedtosolvethepuzzleofquantumgravity.Diracdedicatedthefinalyearsofhislifetotheproblem,openingavenuesandintroducingideasandtechniquesonwhichagoodpartofcurrentworkonquantumgravityisbased.Itisthankstothesetechniquesthatweknowhowtodescribeaworldwithouttime,asIwillexplainfurtheron.Feynmantried,attemptingtoadaptthetechniqueshehaddevelopedforelectronsandphotonstothecontextofgeneralrelativity,butwithoutsuccess:electronsandphotonsarequantainspace;quantumgravityissomethingelse:itisnâtenoughtodescribeâgravitonsâmovinginspace,itisspaceitselfthathastobequantized.AfewNobelPrizeswereawardedtophysicistswhohappenedtoresolveotherproblems,almost
bymistake,duringthecourseoftheirattemptstodisentanglethepuzzleofquantumgravity.TwoDutchphysicists,GerardâtHooftandMartinusVeltman,receivedtheNobelPrizein1999forhavingshowntheconsistencyofthetheorieswhichtodayareusedtodescribenuclearforcesâapartofthestandardmodelâbuttheirresearchprogrammewasactuallyaimingtodemonstratetheconsistencyofatheoryofquantumgravity.Theywereworkingonthetheoriesoftheseotherforcesonlyasapreliminaryexercise.TheâpreliminaryexerciseâearnedthemaNobelPrize,buttheydidnotsucceedinshowingtheconsistencyoftheirversionofquantumgravity.
![Page 64: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/64.jpg)
Thelistcouldgoonandwouldreadlikearollofhonourofthecenturyâsoutstandingtheoreticalphysicists.Aswellaslikeacatalogueoffailures.Verygradually,though,overthecourseofdecades,ideaswereclarifiedanddeadendsexploredandusefullyclosedoff;techniquesandgeneralideaswerestrengthened,andresultsbegantobuild,onedevelopingfromanother.Tomentionherethenumerousscientistswhohavecontributedtothisgradual,slow-moving,collectiveconstructionwouldrequireatediouslistofnames,eachoneofwhomhasaddedagrainorastonetotheprocess.Iwouldliketomentionjustone,whoforyearsheldtogetherthethreadsofthiscollective
research:theremarkable,eternallyyouthfulEnglishmanâhalfphilosopherandhalfphysicistâChrisIsham.ItwaswhenreadingoneofhisarticlesreviewingthequestionofquantumgravitythatIfirstbecameenamouredwiththeproblem.Thearticleexplainedjustwhyitwassodifficult,howourconceptionofspaceandtimeneededtobemodified,andgavealucidoverviewofalltherouteswhichwerebeingfollowedatthetime,withtheresultsachieved,anddifficultiesentailed.Iwasinmythirdyearatuniversity,andthepossibilityofrethinkingspaceandtimefromsquareonefascinatedme.Thisfascinationhasneverdiminished.For,asPetrarchsings,âThewounddoesnothealduetotheweakeningofthebow.â
Figure5.2JohnWheeler.
ThescientistwhohasmostcontributedtoquantumgravityisJohnWheeler,alegendaryfigurewhohastraversedthephysicsofthepastcentury.ApupilofandcollaboratorwithNielsBohrinCopenhagen;acollaboratorwithEinsteinwhenEinsteinmovedtotheUnitedStates;ateacherwhocancountamonghisstudentsfiguressuchasRichardFeynmanâŚWheelerwasattheheartofthephysicsofthetwentiethcentury.Hewasgiftedwithafervidimagination.Itwashewhoinventedandmadepopularthetermâblackholeâ.Hisnameisassociatedwiththeearlyextendedinvestigationsâfrequentlymoreintuitivethanmathematicalâintohowtothinkaboutquantumspacetime.HavingabsorbedBronĹĄtejnâslessonthatquantumpropertiesofthegravitationalfieldimplyamodificationofthenotionofspaceatasmallscale,Wheelerlookedfornovelideastohelpconceiveofthisquantumspace.Heimagineditasacloudofsuperimposedgeometries,justaswecanthinkofaquantumelectronasacloudofpositions.Imaginethatyouarelookingattheseafromagreatheight:youperceiveavastexpanseofit,a
flat,ceruleantable.Nowyoudescendandlookatitmoreclosely.Youbegintomakeoutthegreatwavesswollenbythewind.Youdescendfurther,andyouseethatthewavesbreakupandthatthesurfaceoftheseaisaturbulentfrothing.Thisiswhatspaceislike,asimaginedbyWheeler.fn30Onourscale,immenselylargerthanthePlancklength,spaceissmooth.IfwemovedowntothePlanckscale,itshattersandfoams.Wheelersoughtawaytodescribethisfoamingofspace,thiswaveofprobabilityofdifferent
geometries.In1966,ayoungcolleagueofhiswholivedinCarolina,BryceDeWitt,providedthekey.4Wheelertravelledfrequently,andmetcollaboratorswhereverhecould.HeasksBrycetomeetatRaleighDurhamairport,inNorthCarolina,wherehehadafewhoursâwaitbetweenconnectingflights.Brycearrivesandshowshimanequationforâawavefunctionofspaceâ,obtainedbyusinga
![Page 65: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/65.jpg)
simplemathematicaltrick.fn31Wheelerisenthused.Fromthisconversationatypeofâequationoforbitalsâforgeneralrelativityisborn;anequationwhichshoulddeterminetheprobabilityofoneoranothercurvedspaces.Foralongtime,DeWittcalleditWheelerâsequationfn32âwhileWheelercalledittheDeWittequation.EveryoneelsecallsittheWheeler-DeWittequation.Theideaisverygood,andbecomesabasisfortheattemptstoconstructthefulltheoryof
quantumgravity.Buttheequationitselfisriddledwithproblemsâseriousones.Inthefirstplace,fromamathematicalpointofview,theequationisreallyquitebadlydefined.Ifwetrytouseittodocalculations,wesoonobtainresultsthatareinfinite,whichmakesnosense.Itmustbeimproved.Butitisalsodifficulttounderstandhowtointerpretthisequation,toknowwhatitmeans.Among
itsdisconcertingaspectsisthefactthatitnolongercontainsthetimevariable.Howcanitbeusedtocomputetheevolutionofsomethingwhichhappensintimeifitdoesnotincludeatimevariable?Dynamicalequations,inphysics,alwayscontainthevariablet,time.Whatdoesaphysicaltheorywithoutatemporalvariablesignify?Foryears,researchwillrevolvearoundsuchquestions,tryingtorevisetheequationindifferentmanners,inordertoimproveitsdefinitionandunderstandwhatitmightmean.
ThefirststepsoftheloopsThefogbeginstodissipatetowardstheendofthe1980s.Surprisingly,somesolutionsoftheWheelerâDeWittequationappear.DuringtheseyearsIfoundmyselffirstattheUniversityofSyracuse,inNewYorkState,visitingtheIndianphysicistAbhayAshtekar,andtheninConnecticut,atYaleUniversity,visitingtheAmericanphysicistLeeSmolin.Irememberaperiodofintensediscussionsandburningintellectualfervour.AshtekarhadrewrittentheWheelerâDeWittequationinasimplerform;andSmolin,togetherwithTedJacobsonoftheUniversityofMarylandinWashington,hadbeenthefirsttofindsomeofthesenewstrangesolutionsoftheequation.Thesolutionshadacuriouspeculiarity:theydependedonclosedlinesinspace.Aclosedlineisa
âloopâ.SmolinandJacobsoncouldwriteasolutiontotheWheelerâDeWittequationforeveryloop:foreverylineclosedonitself.Whatdidthismean?Thefirstworksofwhatwilllaterbecomeknownasloopquantumgravityemergefromthesediscussions,asthemeaningofthesesolutionsoftheWheelerâDeWittequationgraduallyclarify.Uponthesesolutions,littlebylittle,acoherenttheorybeginstobeerected,inheritingthenameâlooptheoryâfromthefirstsolutionsstudied.Todaytherearehundredsofscientistsworkingonthistheory,spreadthroughouttheworldfrom
ChinatoArgentina,fromIndonesiatotheUnitedStates.Whatisslowlybeingerectedisthetheorynowknownaslooptheory,orloopquantumgravity:thetheorytowhichthefollowingchaptersaredevoted.Itisnottheonlydirectionexploredinthesearchforaquantumtheoryofgravity,butitistheoneIconsiderthemostpromising.fn33
![Page 66: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/66.jpg)
6.QuantaofSpace
ThelastchapterclosedwiththesolutionsoftheWheelerâDeWittequationdiscoveredbyJacobsonandSmolin.Thesesolutionsdependonlinesthatcloseonthemselves,orloop.Whatdoesitallmean?
RememberFaradayâslinesâthelineswhichcarrytheelectricforceandwhich,inFaradayâsvision,fillspace?Thelinesfromwhichtheconceptofâfieldâoriginates?Well,theclosedlinesthatappearinthesolutionsoftheWheelerâDeWittequationareFaradaylinesofthegravitationalfield.
ButtwonewingredientsarenowaddedtoFaradayâsideas.Thefirstisthatwearedealingwithquantumtheory.Inquantumtheory,everythingisdiscrete.
Thisimpliesthattheinfinitelyfine,continuousspiderwebofFaradayâslinesnowbecomessimilartoarealspiderweb:ithasafinitenumberofdistinctthreads.EverysinglelinedeterminingasolutionoftheWheelerâDeWittequationdescribesoneofthethreadsofthisweb.
Thesecondnewaspect,thecrucialone,isthatwearespeakingofgravityand,therefore,asEinsteinunderstood,wearenotspeakingoffieldsimmersedinspacebutoftheverystructureofspaceitself.Faradayâslinesofthequantumgravitationalfieldarethethreadsofwhichspaceiswoven.
Atfirst,theresearchwasfocusedontheselinesandhowtheycouldâweaveâourthree-dimensionalphysicalspace.Figure6.1representsanearlyattempttogiveanintuitiveideaofthediscretestructureofspacewhichwouldresultfromthis.
Soonafter,thankstotheintuitionsandmathematicalabilityofyoungscientistssuchastheArgentineJorgePullinandthePoleJurekLewandowski,itbecameclearthatthekeytounderstandingthephysicsofthesesolutionsliesinthepointswheretheselinesintersect.Thesepointsarecallednodes,andthelinesbetweennodesarecalledlinks.Asetofintersectinglinesformswhatiscalledagraph,thatistosay,acombinationofnodesconnectedbylinks,asinfigure6.3.
Acalculation,infact,demonstratesthat,withoutnodes,physicalspacehasnovolume.Inotherwords,itisinthenodesofthegraph,notinthelines,thatthevolumeofspaceâresidesâ.Thelinesâlinktogetherâindividualvolumessittingatthenodes.
Gettingtoafullclarificationoftheresultingpictureofquantumspacetimetookyears.Itwasnecessarytotransformtheill-definedmathematicsoftheWheelerâDeWittequationintoastructuresufficientlywelldefinedtobeabletocomputewith.Withthis,itbecamepossibletoachievepreciseresults.Thekeytechnicalresultwhichclarifiesthephysicalmeaningofthegraphsisthecalculationofthespectraofvolumeandofarea.
Figure6.1ThequantumversionofFaradayâslinesofforce,whichweavespacelikeathree-dimensionalmeshofinterlinkedrings(loops).
![Page 67: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/67.jpg)
Figure6.2Thespectrumofthevolume:thevolumesofaregulartetrahedronthatarepossibleinnaturearelimitedinnumber.Thesmallest,atthebottom,isthesmallestvolumeinexistence.
SpectraofvolumeandareaTakeanyregionofspace,forexample,theroominwhichyouarereadingthis,ifyouareinaroom.Howbigisthisroom?Thesizeofthespaceoftheroomismeasuredbyitsvolume.Volumeisageometricalquantitywhichdependsonthegeometryofspace,butthegeometryofspaceâasEinsteinunderstood,andasIrecountedinChapter3âisthegravitationalfield.Volumeisthereforeapropertyofthegravitationalfield,expressinghowmuchgravitationalfieldthereisbetweenthewallsoftheroom.Butthegravitationalfieldisaphysicalquantityand,likeallphysicalquantities,issubjecttothelawsofquantummechanics.Inparticular,likeallphysicalquantities,volumemaynotassumearbitraryvaluesbutonlycertainparticularones,asIdescribedinChapter4.Thelistofallpossiblevaluesiscalled,ifyouremember,thespectrum.Hencethereshouldexistaâspectrumofthevolumeâ(figure6.2)
Diracprovideduswiththeformulawithwhichtocomputethespectrumofeveryvariable.Thecalculationtooktime,firsttoformulateitandthentocompleteit,andmadeussuffer.Itwascompletedinthemid-1990s,andtheanswer,asexpected(Feynmanusedtosaythatweshouldneverdoacalculationwithoutfirstknowingtheresult),isthatthespectrumofthevolumeisdiscrete.Thatis,thevolumecanonlybemadeupofâdiscretepacketsâ.Thesearesomewhatsimilartotheenergyoftheelectromagneticfield,whichisalsoformedofdiscretepackets:photons.
Thenodesofthegraphrepresentthediscretepacketsofvolumeand,asinthecaseofphotons,canonlyhavecertainsizes,whichcanbecomputedusingDiracâsgeneralquantumequation.fn34
Everynodeninthegraphhasitsownvolumevn:oneofthenumbersinthespectrumofthevolume.Thenodesaretheelementaryquantaofwhichphysicalspaceismade.Everynodeofthegraphisaâquantumparticleofspaceâ.Thestructurethatemergesistheoneillustratedinfigure6.3.
Figure6.3Ontheleft,agraphformedbynodesconnectedbylinks.Ontheright,thegrainsofspacewhichthegraphrepresents.Thelinksindicatetheadjacentparticles,separatedbysurfaces.
![Page 68: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/68.jpg)
AlinkisanindividualquantumofaFaradayline.Nowwecanunderstandwhatitrepresents:ifyouimaginetwonodesastwosmallâregionsofspaceâ,thesetworegionswillbeseparatedbyasmallsurface.Thesizeofthissurfaceisitsarea.Thesecondquantity,afterthevolume,whichcharacterizesthequantumwebsofspace,istheareaassociatedwitheachline.fn35
Thearea,justasinthecaseofthevolume,isaphysicalvariable,andhasaspectrumwhichmaybecalculatedusingDiracâsequation.*Areaisnotcontinuous,itisgranular.Thereisnosuchthingasanarbitrarilysmallarea.
Spaceappearscontinuoustousonlybecausewecannotperceivetheextremelysmallscaleoftheseindividualquantaofspace.JustaswhenwelookcloselyattheclothofaT-shirt,weseethatitiswovenfromsmallthreads.
Whenwesaythatthevolumeofaroomis,forexample,100cubicmetres,weareineffectcountingthegrainsofspaceâthequantaofthegravitationalfieldâwhichitcontains.Inaroom,thisnumberhasmorethanahundreddigits.Whenwesaythattheareaofthispageis200squarecentimetres,weareactuallycountingthenumberoflinksintheweb,orloops,whichtraversethepage.Acrossthepageofthisbook,thereisanumberofquantawithmoreorlessseventydigits.
Theideathatmeasuringlength,areaandvolumeisaquestionofcountingindividualelementshadbeenproposedinthenineteenthcenturybyRiemannhimself.Themathematicianwhohaddevelopedthetheoryofcontinuouscurvedmathematicalspaceswasalreadyawarethatadiscretephysicalspaceis,ultimately,morereasonablethanacontinuousone.
Tosummarize,thetheoryofloopquantumgravity,orlooptheory,combinesgeneralrelativitywithquantummechanicsinaratherconservativeway,becauseitdoesnotemployanyotherhypothesisapartfromthoseofthetwotheoriesthemselves,suitablyrewrittentorenderthemcompatible.Buttheconsequencesareradical.
Generalrelativitytaughtusthatspaceissomethingdynamic,liketheelectromagneticfield:animmense,mobilemolluscinwhichweareimmersed,whichstretchesandbends.Quantummechanicsteachesusthateveryfieldofthissortismadeofquanta,thatistosay,ithasafine,granularstructure.Itfollowsthatphysicalspace,beingafield,ismadeofquantaaswell.Thesamegranularstructurecharacterizingtheotherquantumfieldsalsocharacterizesthequantumgravitationalfield,andthereforespace.Weexpectspacetobegranular.Weexpectquantaofgravity,justastherearequantaoflight,quantaoftheelectromagneticfield,andasparticlesarequantaofquantumfields.Butspaceisthegravitationalfield,andthequantaofthegravitationalfieldarequantaofspace:thegranularconstituentsofspace.
Thecentralpredictionoflooptheoryisthereforethatspaceisnotacontinuum,itisnotdivisibleadinfinitum,itisformedofâatomsofspaceâ.Abillionbilliontimessmallerthanthesmallestofatomicnuclei.
Looptheorydescribesthisatomicandgranularquantumstructureofspaceinaprecisemathematicalform.ItisobtainedbyapplyingthegeneralequationsofquantummechanicswrittenbyDiractoEinsteinâsgravitationalfield.
Inparticular,looptheoryspecifiesthatvolume(forexample,thevolumeofagivencube)cannotbearbitrarilysmall.Aminimumvolumeexists.Nospacesmallerthanthisminimumvolumeexists.Thereisaminimumquantumofvolume:anelementaryatomofspace.
AtomsofspaceRememberAchilleschasingafterthetortoise?ZenoobservedthatthereissomethingdifficulttoacceptintheideathatAchilleshastocoveraninfinitenumberofdistancesbeforereachingtheslow-movingcreature.Mathematicshadfoundapossibleanswertothisdifficulty,showinghowaninfinitenumberofprogressivelysmallerintervalscouldneverthelessamounttoafinitetotalinterval.
Butisthiswhattrulyhappensinnature?ArethereintervalsbetweenAchillesandthetortoisethatcanbearbitrarilyshort?Doesitreallymakesensetotalkofabillionthofabillionthofabillionthofamillimetre,andthentothinkofdividingitagainfurtherinnumerabletimes?
Thecalculationofthequantumspectraofgeometricquantitiesindicatesthattheanswerisnegative:arbitrarilysmallchunksofspacedonotexist.Thereisalowerlimittothedivisibilityofspace.Itisataverysmallscaleindeed,butitisthere.ThisiswhatMatveiBronĹĄtejnhadintuitedinthe1930s.ThecalculationofthespectraofvolumeandareaconfirmsBronĹĄtejnâsideaandframesitinamathematicallyprecisemanner.
Achillesdoesnotneedaninfinitenumberofstepstoreachthetortoisebecause,inaspacemadeofgrainsoffinitesize,infinitelysmallstepsdonotexist.Theherowillcomeeverclosertothecreatureuntil,intheend,hereachesitinasinglequantumleap.
But,onreflection,wasthisnotpreciselythesolutionproposedbyLeucippusandbyDemocritus?Theyspokeofthegranularstructureofmatter,andweareratherunsureastowhat,precisely,theysaidaboutspace.Unfortunately,wedonothavetheirtextsandmustmakedowiththesparsefragmentsinthecitationsofothers.ItisliketryingtoreconstructShakespeareâsplaysfromalistofShakespearequotes.fn36Democritusâsargumentontheincongruityofthecontinuumasacollectionofpoints,reportedbyAristotle,maybeappliedtospace.IimaginethatifwecouldaskDemocritus
![Page 69: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/69.jpg)
ifitmakessensetosplitaspaceintervaladinfinitum,hisreplycouldonlybetorepeatthatdivisibilitymusthavealimit.ForthephilosopherofAbdera,matterismadeofatomsthatcannotbedivided.Havingonceunderstoodthatspaceisverymuchlikematterâspace,ashehadsaidhimself,hasitsownnature,âacertainphysicsââIsuspecthewouldnothavehesitatedtodeducethatspace,too,canonlybemadeofelementarychunksthatcannotbedivided.WeareperhapsjustfollowinginthefootstepsofDemocritus.
Icertainlydonâtmeantoimplythatthephysicsoftwomillenniawasuseless,thatexperimentsandmathematicsarepointlessandthatDemocrituscouldbeasconvincingasmodernscience.Obviouslynot.Withoutexperimentsandmathematics,wewouldneverhaveunderstoodwhatwehaveunderstood.Yetwedevelopourconceptualschemaforunderstandingtheworldbyexploringnewideasbutalsobybuildingonthepowerfulintuitionsofgiantfiguresfromthepast.Democritusisoneofthem,andwediscoverthenewsittingonhistitanicshoulders.
Butletusreturntoquantumgravity.
SpinnetworksThegraphswhichdescribethequantumstatesofspacearecharacterizedbyavolumevforeverynodeandahalf-integerjforeveryline.Agraphwiththisadditionalinformationiscalledaspinnetwork(figure6.4).(Half-integersinphysicsarecalledâspinâbecausetheyappearinthequantummechanicsofspinningobjects.)Aspinnetworkrepresentsaquantumstateofthegravitationalfield:aquantumstateofspace;agranularspaceinwhichareaandvolumearediscrete.Fine-meshgridsareusedelsewhereinphysicstoapproximatecontinuousspace.Here,thereisnospacecontinuumtoapproximate:spaceisgenuinelygranular.
Thecrucialdifferencebetweenphotons(thequantaoftheelectromagneticfield)andthenodesofthegraph(thequantaofgravity)isthatphotonsexistinspace,whereasthequantaofgravityconstitutespacethemselves.Photonsarecharacterizedbyâwheretheyareâ.fn37Quantaofspacehavenoplacetobein,becausetheyarethemselvesthatplace.Theyhaveonlyonepieceofinformationwhichcharacterizesthemspatially:informationaboutwhichotherquantaofspacetheyareadjacentto,whichoneisnexttowhichother.Thisinformationisexpressedbythelinksinthegraph.Twonodesconnectedbyalinkaretwonodesinproximity.Theyaretwograinsofspaceincontactwitheachother:thisâtouchingâconstructsthestructureofspace.
Figure6.4Aspinnetwork
Thequantaofgravity,thatis,arenotinspace,theyarethemselvesspace.Thespinnetworkswhichdescribethequantumstructureofthegravitationalfieldarenotimmersedinspace;theydonotinhabitaspace.Thelocationofsinglequantaofspaceisnotdefinedwithregardtosomethingelsebutonlybythelinksandtherelationtheseexpress.
IfIstepfromgraintograinalongthelinksuntilIcompleteacircuitandreturntothegrainfromwhichIstarted,Iwillhavemadeaâloopâ.Thesearetheoriginalloopsofthelooptheory.InChapter4Ishowedthatthecurvatureofspacemaybemeasuredbylookingatwhetheranarrowtransportedacrossaclosedcircuitreturnspointinginthesamedirection,orturned.The
![Page 70: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/70.jpg)
mathematicsofthetheorydeterminesthiscurvatureforeveryclosedcircuitonaspinnetwork,andthismakesitpossibletoevaluatethecurvatureofspacetime,andhencetheforceofthegravitationalfield,fromthestructureofaspinnetwork.fn38
Now,quantummechanicsismorethangranularity.Thereisalsothefactthatevolutionisprobabilisticâthewayinwhichthespinnetworksevolveisrandom.Iâllspeakaboutthisinthenextchapter,devotedtotime.
Andthereisthefactthatwhatmattersisnothowthingsare,butratherhowtheyinteract.Spinnetworksarenotentities;theydescribetheeffectofspaceuponthings.Justasanelectronisinnoplacebutdiffusedinacloudofprobabilityinallplaces,spaceisnotactuallyformedbyasinglespecificspinnetworkbutratherbyacloudofprobabilitiesoverthewholerangeofallpossiblespinnetworks.
Atanextremelysmallscale,spaceisafluctuatingswarmofquantaofgravitywhichactuponeachother,andtogetheractuponthings,manifestingthemselvesintheseinteractionsasspinnetworks,grainsinterrelatedwitheachother(figure6.5).
Figure6.5Ataminutescale,spaceisnotcontinuous:itiswovenfrominterconnectedfiniteelements.
Physicalspaceisthefabricresultingfromtheceaselessswarmingofthiswebofrelations.Thelinesthemselvesarenowhere;theyarenotinaplacebutrathercreateplacesthroughtheirinteractions.Spaceiscreatedbytheinteractionofindividualquantaofgravity.
Thisisthefirststeptowardsunderstandingquantumgravity.Thesecondconcernstime.And,totime,thenextchapterisdevoted.
*Theresultofthecalculationissimple.IshowitheresoyoucanseehowDiracâsspectrawork.ThepossiblevaluesoftheareaAaregiveninthefollowingformula,wherejisaâhalf-integerâ,thatistosay,anumberwhichishalfofaninteger,suchas0,½,1,3â2,2,5â2,3âŚ
Aistheareathatasurfaceseparatingtwograinsofspacecanhave.8isthenumbereight,nothingspecialaboutit.ĎistheGreekpiwhichwestudiedatschool:theconstantwhichgivestherelationbetweenthecircumferenceandthediameterofanycircle,andwhichappearseverywhereinphysics,Idonâtknowwhy.LpisthePlancklength,theextremelysmallscaleatwhichthephenomenaofquantumgravitytakeplace.L2pisthesquareofLp,whichisthe(extremelysmall)areaofatinysquarewithsidesequaltothePlancklength.Therefore8ĎL2pissimplyaâsmallâarea:theareaofaminusculesquarewithasidewhichisaboutamillionthofabillionthofabillionthofabillionthofacentimetre(10-66cm²).Theinterestingaspectoftheformulaisthesquarerootandwhatiswithinit.Thekeypointisthatjisahalf-integer,thatistosay,itmayhaveonlyvalueswhicharemultiplesof½.Foreachoneofthese,theroothasacertainvalue,listedapproximatelyintable6.1.
![Page 71: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/71.jpg)
Table6.1Spin(half-integers)andcorrespondingvalueoftheareainunitsofminimalarea.
![Page 72: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/72.jpg)
Multiplyingthenumbersintheright-handcolumnbythearea8ĎL2p,weobtainthepossiblevaluesoftheareaofthesurface.Thesespecialvaluesareliketheoneswhichappearinthestudyoftheorbitsofelectronsinatoms,wherequantummechanicsallowsonlycertainorbits.Thepointisthatnootherareasapartfromthevaluesderivedbythisequationexist.Nosurfacecanhaveanareaonetenthof8ĎL2p.
![Page 73: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/73.jpg)
7.TimeDoesNotExist
Itmustnotbeclaimedthatanyonecansensetimebyitselfapartfromthemovementofthings.âLucretius,Dererumnatura1
Thealertreaderwillhaverealizedthatintheprecedingchapterlittleattentionwasgiventotime.AndyetEinsteinshowed,overacenturyago,thatwecannotseparatetimeandspace,thatwemustthinkofthemtogetherasasinglewhole:spacetime.Themomenthascometorectifythisandbringtimebackintothepicture.
Researchonquantumgravityhasrevolvedforyearsaroundspatialequations,beforehavingthecouragetoconfronttime.Inthelastfifteenyears,awayofthinkingabouttimehasbeguntoemerge.Iâlltrytoexplainit.
Spaceasanamorphouscontainerofthingsdisappearsfromphysicswithquantumgravity.Things(thequanta)donotinhabitspace,theydwelloneovertheother,andspaceisthefabricoftheirneighbouringrelations.Asweabandontheideaofspaceasaninertcontainer,similarly,wemustabandontheideaoftimeasaninertflowalongwhichrealityunfurls.Justastheideaofthespacecontinuumcontainingthingsdisappears,so,too,doestheideaofaflowingcontinuumâtimeâduringthecourseofwhichphenomenahappen.
Inacertainsense,spacenolongerexistsinfundamentaltheory;thequantaofthegravitationalfieldarenotinspace.Inthesamesense,timenolongerexistsinthefundamentaltheory:thequantaofgravitydonotevolveintime.Timejustcountstheirinteractions.AsevidencedwiththeWheelerâDeWittequation,thefundamentalequationsnolongercontainthetimevariable.Timeemerges,likespace,fromthequantumgravitationalfield.
Thiswasalreadypartiallytrueforclassicalgeneralrelativity,wheretimealreadyappearsasanaspectofthegravitationalfield.Butaslongasweneglectquantumtheory,wecanstillthinkofspacetimeinaratherconventionalmanner,likethetapestryinwhichthestoryoftherestofrealityunfolds,evenifitisadynamical,movingtapestry.Themomentwetakequantummechanicsintoaccount,werecognizethattime,too,musthavethoseaspectsofprobabilisticindeterminacy,granularityandrelationalitywhicharecommontoallofreality.Itbecomesaâtimeâmarkedlydifferentfromallthatwehavehithertomeantbytheword.
Thissecondconceptualconsequenceofthetheoryofquantumgravityismoreextremeeventhanthevanishingofspace.
Letâsattempttounderstandit.
TimeisnotwhatwethinkitisThatthenatureoftimeisdifferentfromthecommonideawhichwehaveofitwasalreadyclearoveracenturyago.Specialandgeneralrelativitymadethisexplicit.Today,theinadequacyofourcommon-senseviewoftimecanbeeasilyverifiedinalaboratory.
Letâsreconsider,forexample,thefirstconsequenceofgeneralrelativity,asillustratedinChapter3.Taketwowatches,ensurethattheymarkexactlythesametime,placeoneonthefloorandtheotheronapieceoffurniture.Waitforabouthalfanhourandthenbringthembacknexttoeachother.Willtheystilltellthesametime?
AsdescribedinChapter3,theanswerisno.Thewatcheswhichweusuallywearonourwrists,orhaveonourmobilephones,arenotsufficientlyprecisetoallowustoverifythisfact,butinphysicslaboratoriesallovertheworldtherearetimepiecespreciseenoughtodemonstratethediscrepancywhichoccurs:thewatchleftonthefloorisslowwhencomparedtotheonewhichhasbeenraisedaboveit.
Why?Becausetimedoesnotpassinthesamewayeverywhereintheworld.Insomeplaces,itflowsmorequickly;inothers,moreslowly.ThecloseryougettotheEarth,wheregravityfn39ismoreintense,theslowertimepasses.RememberthetwinsinChapter3,whoendedupwithdifferentagesasaresultofhavinglivedoneatsealevelandoneinthemountains?Theeffectisveryslight:thetimegainedduringalifespentbythesea,withrespecttoonepassedinthemountains,consistsoffractionsofasecondâbutthesmallnessoftheamountdoesnotalterthefactthatthereisarealdifference.Timedoesnotworkaswecustomarilyimagineitdoes.
Wemustnotthinkoftimeasiftherewereagreatcosmicclockthatmarksthelifeoftheuniverse.Wehaveknownformorethanacenturythatwemustthinkoftimeinsteadasalocalizedphenomenon:everyobjectintheuniversehasitsowntimerunning,atapacedeterminedbythelocalgravitationalfield.
![Page 74: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/74.jpg)
Buteventhisnotionofalocalizedtimenolongerworkswhenwetakethequantumnatureofthegravitationalfieldintoaccount.QuantumeventsarenolongerorderedbythepassageoftimeatthePlanckscale.Time,inasense,ceasestoexist.
Whatdoesitmeantosaythattimedoesnotexist?First,theabsenceofthevariabletimefromthefundamentalequationsdoesnotimplythat
everythingisimmobileandthatchangedoesnothappen.Onthecontrary,itmeansthatchangeisubiquitous.Only:elementaryprocessescannotbeorderedalongacommonsuccessionofinstants.Attheextremelysmallscaleofthequantaofspace,thedanceofnaturedoesnotdeveloptotherhythmkeptbythebatonofasingleorchestralconductor:everyprocessdancesindependentlywithitsneighbours,followingitsownrhythm.Thepassingoftimeisintrinsictotheworld,itisbornoftheworlditself,outoftherelationsbetweenquantumeventswhicharetheworldandwhichthemselvesgeneratetheirowntime.
Infact,thenonexistenceoftimedoesnotmeananythingparticularlycomplicated.Letâstrytounderstand.
ThecandlechandelierandthepulseTimeappearsinmostequationsofclassicphysics.Itisthevariableindicatedbythelettert.Theequationstellushowthingschangeintime.Ifweknowwhathashappenedinthepast,theyallowustopredictthefuture.Moreprecisely,wemeasuresomevariablesâforexample,thepositionAofanobject,theangleBofaswingingpendulum,thetemperatureCofanobjectâandtheequationsofphysicstellushowthesevariablesA,BandCwillchangewithtime.TheypredictthefunctionsA(t),B(t),C(t),andsoon,whichdescribethechangingofthesevariablesintimet.
GalileowasthefirsttounderstandthatthemovementofobjectsonEarthcouldbedescribedbyequationsforthefunctionsoftimeA(t),B(t),C(t)âandthefirsttowriteexplicitequationsforthesefunctions.ThefirstlawofterrestrialphysicsfoundbyGalileo,forexample,describeshowanobjectfalls,thatistosay,howitsaltitudexvarieswiththepassageoftimet.fn40
Todiscoverandverifythislaw,Galileoneededtwokindsofmeasurements.Hehadtomeasuretheheightxoftheobjectandthetimet.Therefore,heneeded,inparticular,aninstrumenttomeasuretime.Heneededaclock.
WhenGalileolivedtherewerenoaccurateclocks.Galileohimself,asayoungman,discoveredakeytomakingprecisetimepieces.Hediscoveredthattheoscillationsofapendulumallhavethesameduration(irrespectiveoftheamplitude).Thus,itispossibletomeasuretimebysimplycountingtheoscillationsofapendulum.Itseemssuchanobviousidea,butittookGalileotofindit;ithadnotoccurredtoanyonebeforehim.Soitgoes,withscience.
Butthingsarenotreallythisstraightforward.Accordingtolegend,GalileoalightedontheideainPisaâsmarvellouscathedralwhilewatching
theslowoscillationsofagiganticcandlechandelier,whichisstillthere.(Thelegendisfalse,sincethechandelierwasactuallyfirsthungthereyearsafterGalileoâsdeath,butitmakesforagoodstory.Perhapstherewasanotheronehangingthereatthetime.)Thescientistwasobservingtheoscillationsduringareligiousserviceinwhichhewasevidentlynotparticularlyabsorbed,andhewasmeasuringthedurationofeachoscillationofthechandelierbycountingthebeatsofhisownpulse.Withmountingexcitement,hediscoveredthatthenumberofbeatswasthesameforeachoscillation:itdidnotchangewhenthechandelierslowedandoscillatedwithdiminishedamplitude.Theoscillationsallhadthesameduration.
Itâsafinestorybut,onreflection,itleavesusperplexedâandthisperplexitygoestotheheartoftheproblemoftime.HowcouldGalileoknowthathisownindividualpulse-beatsalllastedforthesameamountoftime?fn41
NotmanyyearsafterGalileo,doctorsbegantomeasuretheirpatientsâpulsesbyusingawatchâwhichisnothing,afterall,butapendulum.Soweusethebeatstoassureourselvesthatthependulumisregular,andthenthependulumtoascertaintheregularityofthepulse-beats.Isthisnotsomewhatcircular?Whatdoesitmean?
Itmeansthatwe,inreality,nevermeasuretimeitself;wealwaysmeasurethephysicalvariablesA,B,CâŚ(oscillations,beats,andmanyotherthings)andcompareonevariablewithanother,thatistosay,wemeasurethefunctionsA(B),B(C),C(A),andsoon.Wecancounthowmanybeatsforeachoscillation;howmanyoscillationsforeverytickofmystopwatch;howmanyticksofmystopwatchbetweenintervalsoftheclockonthebell-towerâŚ
Thepointisthatitisusefultoimaginethatavariabletexistsâtheâtruetimeââwhichunderpinsallthosemovements,evenifwecannotmeasureitdirectly.Wewritetheequationsforthephysicalvariableswithregardtothisunobservablet,equationswhichtellushowthingschangeint;thatis,forinstance,howmuchtimeittakesforeachoscillation,andhowlongeachheart-beatlasts.Fromthis,wecanderivehowthevariableschangeinrelationtoeachotherâhowmanyheartbeatsthereareinoneoscillationâandcomparethispredictionwithwhatweobserveintheworld.Ifthepredictionsarecorrect,wetrustthatthiscomplicatedschemaisasoundoneand,inparticular,thatitisusefultoemploythevariableoftimet,evenifwecannotmeasureitdirectly.
![Page 75: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/75.jpg)
Inotherwords,theexistenceofthevariabletimeisausefulassumption,nottheresultofanobservation.
ItwasNewtonwhounderstoodallofthis:heunderstoodthatthiswasagoodwaytoproceed,andclarifiedanddevelopedthisschema.Newtonassertsexplicitlyinhisbookthatwecanâtevermeasurethetruetimetbut,ifweassumethatitexists,wecansetupanefficientframeworktodescribenature.
Havingclarifiedthis,wecanreturntoquantumgravityandthemeaningofthestatementthatâtimedoesnotexistâ.ItsimplymeansthattheNewtonianschemanolongerworkswhenwearedealingwithsmallthings.Itwasagoodone,butonlyforlargethings.
Ifwewanttounderstandtheworldwidely,ifwewanttounderstandhowitfunctionsinthelessfamiliarsituationswherequantumgravitymatters,weneedtoabandonthisschema.Theideaofatimetwhichflowsbyitself,andinrelationtowhichallthingsevolve,isnolongerausefulone.Theworldisnotdescribedbyequationsofevolutionintimet.WhatwemustdoissimplytoenumeratethevariablesA,B,CâŚwhichweactuallyobserve,andwriteequationsexpressingrelationsbetweenthesevariables,andnothingelse:thatis,equationsfortherelationsA(B),B(C),C(A)âŚwhichweobserve,andnotforthefunctionsA(t),B(t),C(t)âŚwhichwedonotobserve.
Intheexampleofthepulseandthecandlechandelier,wewillnothavethepulseandthecandelabrumevolvingintime,butonlyequationswhichtellushowthetwovariablesevolvewithrespecttoeachother.Thatistosay,equationswhichtellusdirectlyhowmanypulse-beatsthereareinanoscillation,withoutmentioningt.
âPhysicswithouttimeâisphysicsinwhichwespeakonlyofthepulseandthechandelier,withoutmentioningtime.
Itâsasimplechangeâbutfromaconceptualpointofview,itâsahugeleap.Wemustlearntothinkoftheworldnotassomethingwhichchangesintimebutinsomeotherway.Thingschangeonlyinrelationtooneanother.Atafundamentallevel,thereisnotime.Oursenseofthecommonpassageoftimeisonlyanapproximationwhichisvalidforourmacroscopicscale.Itderivesfromthefactthatweperceivetheworldinacoarse-grainedfashion.
Theworlddescribedbythetheoryisthusfarfromtheonewearefamiliarwith.Thereisnolongerspacewhichcontainstheworld,andnolongertimeduringthecourseofwhicheventsoccur.Thereareelementaryprocessesinwhichthequantaofspaceandmattercontinuouslyinteractwitheachother.JustasacalmandclearAlpinelakeismadeupofarapiddanceofamyriadofminusculewatermolecules,theillusionofbeingsurroundedbycontinuousspaceandtimeistheproductofalong-sightedvisionofadenseswarmingofelementaryprocesses.
SpacetimesushiHowdothesegeneralideasapplytoquantumgravity?Howcanwedescribechangewithouttheideasofspaceasacontainer,ortimealongwhichtheworldglides?
Consideraprocess:forexample,thecollisionoftwobilliardballsonatableâsgreenbaize.Imaginearedballplayedinthedirectionofayellowone;itgetsclose,collides,andthetwoballsmoveawayindifferentdirections.Thisprocess,likeallprocesses,takesplaceinafinitezoneofspaceâletâssayonatableapproximatelytwometreswideâandlastsforafiniteintervaloftimeâletâssaythreeseconds.Todealwiththisprocessinthecontextofquantumgravity,itisnecessarytoincludespaceandtimeintheprocessitself(figure7.1).
Wemustnot,inotherwords,describeonlythetwoballs,butalsoallthatisaroundthem:thetableandanyothermaterialobjectsâandthespaceinwhichtheyareimmersedduringthetimethatelapsesbetweenthestartoftheshotandtheendoftheprocess.Spaceandtimearethegravitationalfield,Einsteinâsâmolluscâ:wearealsoincludingthegravitationalfield,thatistosay,apieceofthemollusc,intheprocess.EverythingisimmersedinEinsteinâsgreatmollusc:here,imaginethatyouareslicingasmall,finiteportionofit,likeapieceofsushi,whichencompassesthecollisionandwhatsurroundsit.
![Page 76: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/76.jpg)
Figure7.1Aregionofspaceinwhichablackballhitsastationarywhiteball,propelsitandrebounds.Theboxistheregionofspacetime.Withinitaredrawnthetrajectoriesoftheballs.
Whatweobtainfromthisisaspacetimebox(asinfigure7.1):afiniteportionofspacetimeafewcubicmetresindimensionbyafewsecondsoftime.Thisprocessdoesnotoccurâinâtime.Theboxisnotinspacetime,itincludesspacetime.Itisnâtaprocessintime,inthesamewayinwhichgrainsofspacearenotinspace.Thepassageoftimeisonlythemeasureoftheprocessitself,justasquantaofgravityarenotinspace,astheythemselvesconstitutespace.
Thekeytounderstandinghowquantumgravityworksliesinconsideringnotsolelythephysicalprocessgivenbythetwoballsbutrathertheentireprocessdefinedbythewholeboxwithallthatitentails,includingthegravitationalfield.
NowletusreturntoHeisenbergâsoriginalinsight:quantummechanicsdoesnottelluswhathappensduringthecourseofaprocess,buttheprobabilitywhichtiestogetherthedifferentinitialandfinalstatesoftheprocess.Inourcase,theinitialandfinalstatesaregivenbyallthathappensattheborderofthespacetimebox.
Whattheequationsofloopquantumgravitygiveusistheprobabilityassociatedwithagivenpossibleboundaryoftheboxâtheprobabilitythattheballswillcomeoutoftheboxinoneparticularconfigurationoranother,iftheyhaveentereditinanother.
Howisthisprobabilitycomputed?RecallFeynmanâssumoverpaths,whichIdescribedwhenspeakingaboutquantummechanics.Probabilities,inquantumgravity,canbecalculatedinthesameway.Byconsideringallthepossibleâtrajectoriesâthathavethesameboundary.Sinceweareincludingthedynamicsofspacetime,thismeansconsideringallpossiblespacetimeswhichhavethesameboundaryasthebox.
Quantummechanicsassumesthatbetweentheinitialboundary,wherethetwoballsenter,andthefinalboundarywheretheyexit,thereisnodefinitespacetimenordefinitetrajectoryoftheballs.Thereisaquantumâcloudâinwhichallthepossiblespacetimesandallpossibletrajectoriesexisttogether.Theprobabilityofseeingtheballsgoingoutinonewayoranothercanbecomputedbysummingoverallpossiblespacetimes.
SpinfoamIfquantumspacehasthestructureofaspinnetwork,whatstructurewillspacetimehave?Whatwilloneofthespacetimespreviouslyalludedtointhecalculationbelike?
Itmustbeaâhistoryâofaspinnetwork.Imaginethatyoutakethegraphofthespinnetworkandmoveit:everynodeinthewebdrawsaline,liketheballsinfigure7.1,andeverylineofthegraph,moving,drawsasurface(forexample,amovingsegmentdrawsarectangle).Butthereismore:anodecanopenupintotwoormorenodes,justasaparticlecansplitintotwoormoreparticles.Conversely,twoormorenodescancombineintoasingleone.Inthisway,agraphwhichevolvesdrawsanimageliketheoneinfigure7.2.
![Page 77: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/77.jpg)
Figure7.2Anevolvingspin-network:threenodescombineintoasinglenode,andthenseparateagain.Ontheright,thespinfoamrepresentingthisprocess.
Theimageportrayedontherightoffigure7.2isaâspinfoamâ.âFoamâbecauseitismadeofsurfaceswhichmeetonlines,whichinturnmeetonvertices,resemblingafoamofsoapbubbles(figure7.3).âSpinfoamâbecausethefacesofthefoamcarryspins,asdothelinksofthegraphswhoseevolutiontheydescribe.
Figure7.3Thefoamofsoapbubbles.
Tocomputetheprobabilityofaprocess,onemustsumupoverallthepossiblespinfoamswithintheboxwhichhavethesameboundaryasthatprocess.Theboundaryofaspinfoamisaspinnetworkandthematteronit.
Theequationsofloopquantumgravityexpresstheprobabilityofaprocessintermsofsumsoverspinfoamswithgivenboundaries.Inthiswayitispossibletocompute,inprinciple,theprobabilityofanyphysicalevent.fn42
![Page 78: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/78.jpg)
Figure7.4Avertexofspinfoam.CourtesyofGregEgan.
Atfirstsight,thiswayformakingcalculationsinquantumgravity,basedonspinfoams,seemsverydifferentfromtheusualwaysinwhichthingsarecomputedintheoreticalphysics.Thereisnogivenspace,nogiventime,andspinfoamsseemobjectsquiteremotefrom,say,theparticlesofthestandardmodel.Butinfacttherearestrongsimilaritiesbetweenthespinfoamtechniqueandthecalculationtechniquesusedinthestandardmodel.Infact,evenmorethanthis,thespinfoamtechniqueisactuallyabeautifulmergingofthetwomaincalculationtechniquesusedinthecontextofthestandardmodel:Feynmandiagramsandthelatticeapproximation.
Feynmandiagramsareused,forinstance,tocomputeprocessesdominatedbyelectromagneticorweakforces.AFeynmandiagramrepresentsasequenceofelementaryinteractionsamongparticles.Anexampleisinfigure7.5,whichrepresentstwoparticles,ortwoquantaofthefield,interacting.Theparticleontheleftsplitsintotwoparticles,oneofwhichsplitsinturnintotwoparticles,whichthenreunite,convergingwiththeparticleontheright.Thegraphportraysahistoryofthefieldâsquanta.
![Page 79: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/79.jpg)
Figure7.5AFeynmandiagram.
Thelatticeapproximationisusedwhentheforcesarestrongandtheparticlepictureisnolongereffectivefordescribingphysics,forinstanceincomputingthestrongforcesbetweenquarksinsidethenucleusofanatom.Thelatticetechniqueentailsapproximatingacontinuousphysicalspacebymeansofalattice,oragrid,asinfigure7.6.Thisgridisnotassumedtobeafaithfuldescriptionofspace,butonlyanapproximation,aswhenengineerscalculatetheresistanceofabridgebyapproximatingtheconcretewithafinitenumberofelements.ThesetwomethodsofmakingcalculationsâFeynmandiagramsandthelatticeâarethetwomostefficienttechniquesofquantumfieldtheory.
Figure7.6Agridapproximatingphysicalspacetime.
Inquantumgravity,somethingbeautifuloccurs:thetwomethodsofmakingcalculationsbecomeoneandthesame.Thespacetimefoamrepresentedinfigure7.2,usedtocomputeaphysicalprocessinquantumgravity,maybeinterpretedeitherasaFeynmandiagramorasalatticecalculation.fn43Therefore,thetwocalculationtechniquesusedforthestandardmodelturnouttobeparticularcasesofacommontechnique:summingoverthespinfoamsofquantumgravity.
Earlier,IsetoutEinsteinâsequations.Again,Icanâtresistincludingherethecompletecollectionoftheequationsoflooptheory,evenifthereaderwillobviouslynotbeabletodecipherthemânot
![Page 80: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/80.jpg)
beforeundertakingthestudyofagooddealofmathematics.SomeoneonceclaimedthatatheoryisnâtcredibleifitsequationscannotbesummarizedonaT-shirt.HereisthatT-shirtforloopquantumgravity(figure7.7).
Figure7.7Theequationsofloopquantumgravity,summarizedonaT-shirt.
Theseequationsfn44arethemathematicalversionofthepictureoftheworldIhavegiveninthelasttwochapters.Wearenotatallsureiftheyarethecorrectequationsâbut,inmyopinion,theyarethebestaccountofquantumgravitywehaveatpresent.
Spaceisaspinnetworkwhosenodesrepresentitselementarygrains,andwhoselinksdescribetheirproximityrelations.Spacetimeisgeneratedbyprocessesinwhichthesespinnetworkstransformintooneanother,andtheseprocessesaredescribedbysumsoverspinfoams.Aspinfoamrepresentsahistoryofaspinnetwork,henceagranularspacetimewherethenodesofthegraphcombineandseparate.
Thismicroscopicswarmingofquanta,whichgeneratesspaceandtime,underliesthecalmappearanceofthemacroscopicrealitysurroundingus.Everycubiccentimetreofspace,andeverysecondthatpasses,istheresultofthisdancingfoamofextremelysmallquanta.
Whatistheworldmadeof?Thebackdropofspacehasdisappeared,timehasdisappeared,classicparticleshavedisappeared,alongwiththeclassicfields.Sowhatistheworldmadeof?
Theanswernowissimple:theparticlesarequantaofquantumfields;lightisformedbyquantaofafield;spaceisnothingmorethanafield,whichisalsomadeofquanta;andtimeemergesfromtheprocessesofthissamefield.Inotherwords,theworldismadeentirelyfromquantumfields(figure7.8).
Thesefieldsdonotliveinspacetime;theylive,sotospeak,oneontopoftheother:fieldsonfields.Thespaceandtimethatweperceiveinlargescaleareourblurredandapproximateimageofoneofthesequantumfields:thegravitationalfield.
Fieldsthatliveonthemselves,withouttheneedofaspacetimetoserveasasubstratum,asasupport,andwhicharecapablebythemselvesofgeneratingspacetime,arecalledâcovariantquantumfieldsâ.Thesubstanceofwhichtheworldismadehasbeenradicallysimplifiedinrecentyears.Theworld,particles,light,energy,spaceandtimeâallofthisisnothingbutthemanifestationofasingletypeofentity:covariantquantumfields.
![Page 81: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/81.jpg)
Figure7.8Whatistheworldmadeof?Ofonlyoneingredient:covariantquantumfields.
CovariantquantumfieldshavebecometodaythebestdescriptionthatwehaveoftheáźĎξΚĎον,theapeiron,theprimalsubstanceofwhicheverythingisformedhypothesizedbythemanthatcouldperhapsbecalledthefirstscientistandthefirstphilosopher,Anaximander.fn45
TheseparationbetweenthecurvedandcontinuousspaceofEinsteinâsgeneralrelativityandthediscretequantaofquantummechanicswhichdwellinaflatanduniformspacehasdissolved.Theapparentcontradictionisnolongerthere.Betweenthespacetimecontinuumandquantaofspace,thereisthesamerelationshipasbetweenelectromagneticwavesandphotons.Thewavesgiveanapproximatelarge-scalevisionofphotons.Photonsarethewayinwhichwavesinteract.Continuousspaceandtimeareanapproximatelarge-scalevisionofthedynamicofquantaofgravity.Thequantaofgravityarethewayinwhichspaceandtimeinteract.Thesamemathematicscoherentlydescribesthequantumgravitationalfieldasotherquantumfields.
Theconceptualpricepaidistherelinquishingoftheideaofspace,andoftime,asgeneralstructureswithinwhichtoframetheworld.Spaceandtimeareapproximationswhichemergeatalargescale.Kantwasperhapsrightwhenheaffirmedthatthesubjectofknowledgeanditsobjectareinseparable,buthewasdefinitelymistakenwhenheconsideredNewtonianspaceandtimeasaprioriformsofknowledge,partsofanindispensablegrammarforunderstandingtheworld.Thisgrammarhasevolved,andisstillintheprocessofevolving,withthegrowthofourknowledge.
Generalrelativityandquantummechanicsare,intheend,notasincompatibleastheyseemed.Oncloserinspection,theyshakehandsandengageinabeautifuldialogue.ThespatialrelationsthatweaveEinsteinâscurvedspacearetheveryinteractionsweavingtherelationsbetweenthesystemsofquantummechanics.Thetwobecomecompatibleandconjoined,twosidesofthesamecoin,assoonasitisrecognizedthatspaceandtimeareaspectsofaquantumfield,andquantumfieldscanexistevenwithoutbeinggroundedinanexternalspace.
Thisrarefiedpictureofthefundamentalstructureofthephysicalworldisthevisionofrealityofferedtodaybyquantumgravity.
Themainrewardofthiskindofphysicsisthat,asweshallseeinthenextchapter,infinitydisappears.Theinfinitelysmallnolongerexists.Theinfinitieswhichplagueconventionalquantumfieldtheory,predicatedonthenotionofacontinuousspace,nowvanish,becausetheyweregeneratedpreciselybytheassumption,physicallyincorrect,ofthecontinuityofspace.ThesingularitieswhichrenderEinsteinâsequationsabsurdwhenthegravitationalfieldbecomestoostrongalsodisappear:theyareonlytheresultofneglectingthequantizationofthefield.Littleby
![Page 82: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/82.jpg)
little,thepiecesofthepuzzlefindtheirplace.Inthefinalsectionsofthisbook,Idescribesomeofthephysicalconsequencesofthistheory.
Itmayappearstrangeanddifficulttothinkofdiscreteelementaryentitiesnotinspaceandtime,butweavingspaceandtimewiththeirrelations.ButhowstrangeitmusthaveseemedtolistentoAnaximander,whenheclaimedthatbeneathourfeettherewasonlythesameskythatwecanseeaboveourheads?OrtoAristarchus,whenhetriedtomeasurethedistancefromtheEarthtotheMoonandtheSun,discoveringthattheyareextremelydistant,andarethereforenotthesizeoflittleballs,butgiganticâandtheSunisimmensecomparedtotheEarth.OrtoHubble,whenherealizedthatthesmall,diaphanouscloudsbetweenstarsarevastseasofimmenselydistantstarsâŚ
Forcenturies,theworldhascontinuedtochangeandexpandaroundus.Weseefurther,understanditbetterandareastonishedbyitsvariety,bythelimitationsoftheimageswehadofit.Thedescriptionwemanagetoproducetoaccountforitbecomesincreasinglyrarefied,yetsimple.
Weareakintosmall,blindmolesundergroundwhoknowlittleornothingabouttheworld.ButwecontinuetolearnâŚButallthestoryofthenighttoldoverAndalltheirmindstransfiguredsotogetherMorewitnesseththanfancyâsimagesAndgrowstosomethingofgreatconstancy;But,howsoever,strangeandadmirable.2
![Page 83: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/83.jpg)
![Page 84: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/84.jpg)
PartFour
BEYOND SPACE AND TIME
Ihaveillustratedthebasisofquantumgravity,andtheimageoftheworldwhichemergesfromit.InthefinalchaptersIdescribesomeconsequencesofthetheory:whatthetheorytellsusaboutphenomenasuchastheBigBangandblackholes.Ialsodiscussthecurrentstateofpossibleexperimentstotestthetheory,andwhatitseemstomenatureistellingusâinparticularwiththefailureoftheexpectedobservationofsupersymmetricparticles.
Iconcludewithafewreflectionsonwhatisstillmissingfromourunderstandingoftheworld:especiallythermodynamics,theroleofinformationinatheorywithouttimeandspacesuchasquantumgravity,andthere-emergenceoftime.
Allofthistakesustotheedgeofwhatweknow,tothevantagepointfromwhichwelookuponwhatwedefinitelydonâtknow,theimmensemysterythatsurroundsus.
![Page 85: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/85.jpg)
8.BeyondtheBigBang
ThemasterIn1927ayoungBelgianscientist,aJesuit-educatedCatholicpriest,studiesEinsteinâsequationsandrealizesâjustasEinsteinhadâthattheypredicttheuniversemustexpandorcontract.Butinsteadoffoolishlyrejectingtheresultandstubbornlytryingtoavoidit,asEinsteindid,theBelgianpriestbelievesitandlooksforastronomicaldatatotestit.Atthetime,galaxieswerenotcalledgalaxies.Theywerecallednebulaebecause,seenthrougha
telescope,theylookedlikesmall,opalescentcloudsamongthestars.Itwasnotyetknownthattheyaredistant,immenseislandsofstarslikeourveryowngalaxy.ButtheyoungBelgianpriestunderstandsthatthescarceavailabledataonthegalaxieswereindeedcompatiblewiththepossibilitythattheuniverseisexpanding:nearbygalaxiesaremovingawayatgreatspeed,asiftheyhadbeenlaunchedintothesky;distantgalaxiesaremovingawayatevengreaterspeed.Theuniverseisswellinglikeaballoon.Twoyearslater,theinsightisconfirmed,thankstotwoAmericanastronomers,HenriettaLeavitt
andEdwinHubble.Leavittdiscoversagoodtechniqueformeasuringthedistanceofthenebulae,confirmingthattheyareveryfaraway,outsideofourowngalaxy.UsingthistechniqueandthegreattelescopeofthePalomarObservatory,Hubblecollectsprecisedatathatconfirmthatthegalaxiesaremovingaway,ataspeedproportionaltotheirdistance.
Figure8.1HenriettaLeavitt.
ButitistheyoungBelgianpriestwhounderstands,alreadyin1927,thecrucialconsequence:ifweseeastoneflyingup,itmeansthatthestonewaspreviouslylowerdownandsomethinghasthrownitupwards.Ifweseethegalaxiesmovingawayandtheuniverseexpanding,itmeansthatthegalaxieswerepreviouslymuchcloserandtheuniversewassmaller:andsomethingcausedittostartexpanding.TheyoungBelgianpriestsuggeststhattheuniversewasoriginallyextremelysmallandcompressed,andstarteditsexpansioninagiganticexplosion.Hecallsthisinitialstatetheprimordialatom.TodayitisknownastheBigBang.HisnamewasGeorgesLemaĂŽtre.InFrench,thisnamesoundslikelemaĂŽtremeaningâthemasterâ,
andfewnamesaremoreappropriateforthemanwhofirstunderstoodtheexistenceoftheBigBang.Butinspiteofthisname,LemaĂŽtreâscharacterwasreserved;heavoidedpolemics,andneverevenclaimedpriorityforthediscoveryoftheexpansionoftheuniverse,whichendedupbeingattributedtoHubble.Twoepisodesfromhislifeillustratehisprofoundintelligence.ThefirstinvolvesEinstein,thesecondapope.Asmentioned,Einsteinwasscepticalabouttheexpansionoftheuniverse.Hehadgrownup
thinkingthattheuniverseisfixed,andhadnotbeenabletoaccepttheideathatthiswasnotthecase.Eventhegreatestmakemistakesandarepreytopreconceivedideas.LemaĂŽtremetEinstein
![Page 86: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/86.jpg)
andtriedtodissuadehimfromhisprejudicialview.Einsteinresisted,goingsofarastoanswerLemaĂŽtre:âCorrectcalculations,abominablephysics.âLater,EinsteinwasobligedtorecognizethatLemaĂŽtrewastheonewhowasactuallyright.ItdoesnâtfalltoeveryonetodisproveEinstein.
Figure8.2GeorgesLemaĂŽtre.CopyrightArchivesGeorgesLemaĂŽtre,Louvain.
Thesamethinghappenedagain.Einsteinhadintroducedthecosmologicalconstant,thesmallbutimportantmodificationofhisequationsIdescribedinChapter3,inthe(mistaken)hopeofrenderingtheequationscompatiblewithastaticuniverse.Whenhehadtoacknowledgethattheuniverseisnotstatic,heturnedagainstthecosmologicalconstant.LemaĂŽtre,forthesecondtime,triedtopersuadehimtochangehismind:thecosmologicalconstantdoesnotrendertheuniversestatic,butitisneverthelessright,andthereisnoreasontotakeitout.Onthisoccasion,too,LemaĂŽtrewascorrect:thecosmologicalconstantproducesanaccelerationoftheexpansionoftheuniverse,andthisaccelerationhasrecentlybeenmeasured.Onceagain,EinsteinwaswrongandLemaĂŽtrewasright.WhentheideathattheuniversehademergedfromaBigBangbegantobeaccepted,PopePius
XIIdeclaredinapublicaddress(on22November1951)thatthetheoryconfirmedtheaccountofCreationgiveninGenesis.1LemaĂŽtrereactedtothispapalpositionwithgreatconcern.HegotintouchwiththescientificadvisortothepontiffandwenttogreatlengthstopersuadethePopetorefrainfrommakingreferencestolinksbetweendivinecreationandtheBigBang.LemaĂŽtrewasconvincedthatitwasfoolishtomixscienceandreligioninthisway:theBibleknowsnothingaboutphysics,andphysicsknowsnothingaboutGod.2PiusXIIallowedhimselftobepersuaded,andtheCatholicchurchneveragainmadepublicallusiontothesubject.ItisnotgiventoeveryonetodisprovethePope.Andofcourse,onthisalso,itwasLemaĂŽtrewhowasright:todaythereisagreatdealoftalk
concerningthepossibilitythattheBigBangisnotarealbeginning,thattherecouldhavebeenanotheruniversebeforeit.ImagineinwhatanembarrassingpositiontheCatholicChurchwouldfinditselftoday,ifLemaĂŽtrehadnotpreventedthePopefrommakingitofficialdoctrinethatthatBigBangandCreationwerethesamething.FiatluxwouldhavetobechangedtoâSwitchthelightbackon!âTocontestbothEinsteinandthePope,convincingboththattheyweremistaken,andtoberightin
bothcases,issurelysomethingofaresult.âThemasterâliveduptohisname.Todayconfirmationsareoverwhelming:theuniverse,inafar-distantpast,wasextremelyhotand
extremelycompact,andhasexpandedsince.Wecanreconstructindetailthehistoryoftheuniverse,startingwithitsinitialhot,compressedstate.Weknowhowatoms,elements,galaxiesandstarsformedandhowtheuniverseasweseeittodaydeveloped.RecentextendedobservationsoftheradiationthatfillstheuniversecarriedoutmainlybythePlancksatelliteonceagainconfirmedinfullthetheoryoftheBigBang.Weknowwithareasonabledegreeofcertaintywhathappenedonalargescaletoouruniverseinthelast14billionyears,fromthetimewhenitwasaballoffire.Andtothinkthat,initially,thephraseâtheoryoftheBigBangâwascoinedbyopponentsofthe
theory,tomockanideathatseemedoutlandishâŚInstead,intheend,wewereallpersuaded:14billionyearsagotheuniversewasacompressedballoffire.Butwhathappenedbeforethisinitialhotandcompressedstate?Regressingintime,temperatureincreases,asdoesthedensityofmatterandenergy.Thereisa
pointatwhichtheyreachthePlanckscale:14billionyearsago.Atthatpoint,theequationsof
![Page 87: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/87.jpg)
generalrelativityarenolongervalid,becauseitisnolongerpossibletoignorequantummechanics.Weenterintotherealmofquantumgravity.
QuantumcosmologyTounderstandwhathappened14billionyearsago,therefore,quantumgravityisrequired.Whatdotheloopstellusaboutthesubject?Considerananalogousbutsimplersituation.Accordingtoclassicalmechanics,anelectronfalling
straightintoanatomicnucleuswouldbeswallowedbythenucleusanddisappear.Butthisisnotwhathappensinreality.Classicmechanicsisincomplete,anditisnecessarytotakequantumeffectsintoaccount.Arealelectronisaquantumobjectanddoesnotfollowaprecisetrajectory:itisnâtpossibletokeepitinsidetoosmallaregion.Themoreitisconcentrated,themoreitslipsrapidlyaway.Ifwewanttostopitaroundthenucleus,themostwecandoistoforceitintoanorbitofthesizeofthesmallestatomicorbital:itcouldnotstayanyclosertothenucleus.Quantummechanicspreventsarealelectronfromfallingintoanucleus.Aquantumrepulsionpushesawaytheelectronwhenitgetstooclosetothecentre.Thus,thankstoquantummechanics,matterisstable.Withoutit,electronswouldfallintonuclei,therewouldbenoatomsandwewouldnotexist.Thesameappliestotheuniverse.Letusimagineauniversecontractingandbecomingextremely
small,squashedbyitsownweight.AccordingtoEinsteinâsequations,thisuniversewouldbesquashedadinfinitumandatacertainpointwoulddisappearaltogether,liketheelectronfallingintothenucleus.ThisistheBigBangpredictedbyEinsteinâsequations,ifweignorequantumtheory.Butifwetakequantummechanicsintoaccount,theuniversecannotbeindefinitelysquashed.A
quantumrepulsionmakesitrebound.Acontractinguniversedoesnotcollapsedowntoapoint:itbouncesbackandbeginstoexpand,asifitwereemergingfromacosmicexplosion(figure8.3).
Figure8.3TheBigBounceoftheuniverseinagraphicalrepresentationbyFrancescaVidotto,theItalianscientistwhofirstusedspinfoamstocomputetheprobabilityofthisprocess.
Thepastofouruniversemaythereforewellbetheresultofjustsucharebound.AgiganticreboundknownasaBigBounceinsteadofBigBang.Thisiswhatseemstoemergefromtheequationsofloopquantumgravitywhentheyareappliedtotheexpansionoftheuniverse.Theimageofthebouncemustnotbetakenliterally.Goingbacktotheexampleoftheelectron,
recallthatifwewanttoplaceanelectronascloseaspossibletoanatom,theelectronisnolongeraparticle;wecanthinkofit,instead,asopenedupinacloudofprobabilities.Anexactpositionnolongermakessensefortheelectron.Thesamefortheuniverse:inthecrucialpassagethroughtheBigBounce,wecannolongerthinkofasingle,althoughgranular,spaceandtime,butonlyofaspread-outcloudofprobabilitiesinwhichtimeandspacewildlyfluctuate.AttheBigBounce,theworldisdissolvedintoaswarmingcloudofprobabilities,whichtheequationsstillmanagetodescribe.Ouruniversecouldthusbetheresultofthecollapseofapreviouscontractinguniversepassing
acrossaquantumphase,wherespaceandtimearedissolvedintoprobabilities.Thewordâuniverseâbecomesambiguous.If,byâuniverseâ,wemeanâallthatthereisâ,then,by
definition,therecannotbeaseconduniverse.Butthewordâuniverseâhasassumedanothermeaningincosmology:itreferstothespacetimecontinuumthatweseedirectlyaroundus,filledwithgalaxiesthegeometryandhistoryofwhichweobserve.Thereisnoreasontobecertainthat,inthis
![Page 88: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/88.jpg)
sense,thisuniverseistheonlyoneinexistence.Wecanreconstructthepastuptothetimewhen,asintheimagebyJohnWheeler,thespatiotemporalcontinuumbreaksuplikeseafoamandfragmentsintoaquantumcloudofprobabilities,andthereisnoreasontodiscardthepossibilitythatbeyondthishotfoamtherecouldnotbeanotherspatiotemporalcontinuum,similartotheonewhichweperceivearoundus.TheprobabilityforauniversetocrossthephaseoftheBigBounce,passingfromcontractionto
expansion,canbecomputedusingthetechniquesdescribedintheprecedingchapter:thespacetimeboxes.Calculationsaremadeusingspinfoamsthatconnectthecontractinguniversewiththeexpandingone.Allofthisisstillatanexploratorystage,butwhatisremarkableinthisstoryisthattodaywehave
equationswithwhichtotrytodescribetheseevents.Wearebeginningtocastthefirstfewcautiousglances,forthemomentonlytheoretically,beyondtheBigBang.
![Page 89: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/89.jpg)
9.EmpiricalConfirmations?
TheappealofquantumcosmologygoesbeyondthefascinatingtheoreticalexplorationsofwhattheremightbebeyondtheBigBang.Thereisanotherreasonforstudyingtheapplicationofthetheorytocosmology:itmightprovidetheopportunitytofindoutwhetherornotthetheoryisactuallycorrect.Scienceworksbecause,afterhypothesesandreasoning,afterintuitionsandvisions,after
equationsandcalculations,wecancheckwhetherwehavedonewellornot:thetheorygivespredictionsaboutthingswehavenotyetobserved,andwecancheckwhetherthesearecorrect,ornot.Thisisthepowerofscience,thatwhichgroundsitsreliabilityandallowsustotrustinitwithconfidence:wecancheckwhetheratheoryisrightorwrong.Thisiswhatdistinguishessciencefromotherkindsofthinking,wheredecidingwhoisrightandwhoiswrongisusuallyamuchthornierquestion,sometimesevendevoidofmeaning.WhenLemaĂŽtredefendstheideathattheuniverseisexpanding,andEinsteindoesnotbelieveit,
oneofthetwoiswrong;theotherright.AllofEinsteinâsresults,hisfame,hisinfluenceonthescientificworld,hisimmenseauthority,countfornothing.Theobservationsprovehimwrong,anditâsgameover.AnobscureBelgianpriestisright.Itisforthisreasonthatscientificthinkinghaspower.Thesociologyofsciencehasshedlightonthecomplexityoftheprocessofscientific
understanding;likeanyotherhumanendeavour,thisprocessisbesetbyirrationality,intersectswiththegameofpowerandisaffectedbyeverysortofsocialandculturalinfluence.Nevertheless,despiteallofthis,andinoppositiontotheexaggerationsofafewpostmodernists,culturalrelativistsandthelike,noneofthisdiminishesthepracticalandtheoreticalefficacyofscientificthinking.Becauseintheend,inthemajorityofcases,itispossibletoestablishwithclaritywhoisrightandwhoiswrong.AndeventhegreatEinsteincouldgoontosay(andhedidso),âAhâŚImadeamistake!âScienceisthebeststrategyifwevaluereliability.Thisdoesnotmeanthatscienceisjusttheartofmakingmeasurablepredictions.Some
philosophersofscienceoverlycircumscribesciencebylimitingittoitsnumericalpredictions.Theymissthepoint,becausetheyconfusetheinstrumentswiththeobjectives.Verifiablequantitativepredictionsareinstrumentstovalidatehypotheses.Theobjectiveofscientificresearchisnotjusttoarriveatpredictions:itistounderstandhowtheworldfunctions;toconstructanddevelopanimageoftheworld,aconceptualstructuretoenableustothinkaboutit.Beforebeingtechnical,scienceisvisionary.Theverifiablepredictionsarethesharpenedtoolwhichallowsustofindoutwhenwehave
misunderstoodsomething.Atheorylackingempiricalconfirmationisatheorywhichhasnotyetpasseditsexams.Examsneverend,andatheoryisnotcompletelyconfirmedbyone,twoorthreeexperiments.Butitprogressivelyacquirescredibility,stagebystage,asitspredictionsarerevealedtobecorrect.Theoriessuchasgeneralrelativityandquantummechanics,whichinitiallyleftmanyperplexed,earnedtheircredibilitygradually,asalloftheirpredictionsâeventhemostbizarreâweregraduallyconfirmedbyexperimentsandobservations.Theimportanceofexperimentalproof,ontheotherhand,doesnotmeanthat,withoutnew
experimentaldata,wecannotmakeadvances.Itisoftensaidthatsciencetakesstepsforwardonlywhenthereisnewexperimentaldata.Ifthisweretrue,wewouldhavelittlehopeoffindingthetheoryofquantumgravitybeforemeasuringsomethingnew,butthisispatentlynotthecase.WhichnewdatawereavailabletoCopernicus?None.HehadthesamedataasPtolemy.WhichnewdatadidNewtonhave?Almostnone.HisrealingredientswereKeplerâslawsandGalileoâsresults.WhatnewdatadidEinsteinhavetodiscovergeneralrelativity?None.HisingredientswerespecialrelativityandNewtonâstheory.Itsimplyisnâttruethatphysicsadvancesonlywhenitisaffordednewdata.WhatCopernicus,Newton,Einsteinandmanyothersdidwastobuilduponpre-existingtheories
whichsynthesizedempiricalknowledgeacrossvastfieldsofnature,andtofindawayofcombiningandrethinkingthemtoimprovethegeneralpicture.Thisisthebasisonwhichthebestresearchonquantumgravityoperates.Theoriginof
knowledge,asalwaysinscience,isultimatelyempirical.Butthedataonwhichquantumgravityisbuiltisnotnewexperiments:itisthetheoreticaledificeswhichhavealreadystructuredourknowledgeoftheworld,informswhichareonlypartlycoherent.Theâexperimentaldataâforquantumgravityaregeneralrelativityandquantummechanics.Buildingonthese,tryingto
![Page 90: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/90.jpg)
understandhowaworldinwhichbothquantaandcurvedspaceexistmaybemadecoherent,weattempttolooktowardstheunknown.Theenormoussuccessofthegiantswhohaveprecededusinsimilarsituations,suchasNewton,
EinsteinandDirac,givesusencouragement.Wedonotpresumetobeoftheirstature.Butwehavetheadvantageofsittingontheirshoulders,andthisallowsustolookfurtherthantheydid.Onewayoranother,wecannotbuttry.Wemustdistinguishbetweencluesandstrongevidence.CluesarewhatsetSherlockHolmeson
therighttrack,allowinghimtosolveamysteriouscase.Strongevidenceiswhatthejudgeneedstosentencetheguilty.Cluesputusontherightpathtowardsacorrecttheory.Strongevidenceisthatwhichsubsequentlyallowsustotrustwhetherthetheorywehavebuiltisagoodoneornot.Withoutclues,wesearchinthewrongdirections.Withoutevidence,atheoryisnotreliable.Thesameappliestoquantumgravity.Thetheoryisinitsinfancy.Itstheoreticalapparatusis
gainingsolidity,andthefundamentalideasarebeingclarified:thecluesaregood,andconcreteâconfirmedpredictionsarestillmissing.Thetheoryhasnotyettakenitsexams.
SignalsfromnatureThemoststudiedalternativetotheresearchdirectionrecountedinthisbookisstringtheory.Themajorityofphysicistswhohaveworkedonstringtheory,orstring-relatedtheories,expectedthatassoonasthenewparticleacceleratoratCERNinGenevabegantofunction(theLHCorLargeHadronCollider),particlesofanewkindneverbeforeobserved,butanticipatedbythetheory,wouldimmediatelybecomeevident:supersymmetricparticles.Stringtheoryneedstheseparticlestobeconsistent:thatiswhythestringtheoristseagerlyexpectedthemtobefound.Loopquantumgravity,ontheotherhand,iswelldefinedevenwithoutsupersymmetricparticles.Thelooptheoristswereinclinedtothinkthattheseparticlesmightnotexist.Thesupersymmetricparticleswerenotobserved,tothegreatdisappointmentofmany.The
fanfarethatgreetedthediscoveryoftheHiggsbosonin2013alsomaskedthisdisappointment.Thesupersymmetricparticlesarenotthereattheenergywheremanystringtheoristsexpectedthemtobe.Thisisnotadefinitiveproofofanythingâfarfromit;butnaturehasgivenasmallclueinfavouroftheloops.Therehavebeenthreemajorexperimentalresultsinfundamentalphysicsinrecentyears.The
firstistherevelationoftheHiggsbosonatCERNinGeneva(figure9.1).ThesecondisthemeasurementsmadebythePlancksatellite(figure9.2),measurements,thedataofwhichwerealsomadepublicin2013,confirmingthestandardcosmologicalmodel.Thethirdisthefirstdetectionofgravitationalwavesannouncedinthefirstmonthsof2016.Thesearethethreesignalsthatnaturehasrecentlygivenus.
Figure9.1AneventatCERNwhichshowstheformationoftheHiggsparticle.
![Page 91: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/91.jpg)
Figure9.2ThePlancksatellite.
Thereissomethingincommonbetweenthesethreeresults:thecompleteabsenceofsurprise.Thisdoesnotdiminishtheirimportance:ifanything,itmakesthemevenmoremeaningful.ThediscoveryoftheHiggsbosonisarock-hardconfirmationofthevalidityoftheideasbehindthestandardmodelofelementaryparticles,basedonquantummechanics.Itistheverificationofapredictionmadethirtyyearspreviously.ThePlanckmeasurementsareasolidconfirmationofthestandardcosmologicalmodel,basedongeneralrelativitywiththecosmologicalconstant.Thedetectionofgravitationalwavesisaspectacularconfirmationofgeneralrelativity,atheoryahundredyearsold.Thethreeresults,obtainedwithstrenuoustechnologicaleffortsandextensivecollaborationsbetweenhundredsofscientists,donothingotherthanreinforcetheunderstandingthatwealreadyhadofthestructureoftheuniverse.Norealsurprises.Butsuchanabsenceofsurpriseswasinasenseitselfsurprising,becausemanyexpectedtobe
surprised,thatis,toseeânewphysicsâ,notyetdescribedbyestablishedtheories.TheyexpectedsupersymmetryatCERN,nottheHiggsboson.AndmanyexpectedthatPlanckwouldmeasurediscrepanciesfromthestandardcosmologicalmodel,discrepanciesthatwouldsupportalternativecosmologicaltheoriestogeneralrelativity.Butno.Whatnatureisconfirmingissimple:generalrelativity,quantummechanicsand,within
quantummechanics,thestandardmodel.Manytheoreticalphysicistsaretodaylookingfornewtheoriesbypickingarbitraryhypotheses.
âLetusimaginethatâŚâIdonâtthinkthatthiswayofdoingsciencehaseverproducedgoodresults.Ourfantasyistoolimitedtoâimagineâhowtheworldmaybemade,unlesswesearchforinspirationinthetraceswehaveatourdisposal.Thetracesthatwehaveâourcluesâareeitherthetheorieswhichhavebeensuccessful,ornewexperimentaldata,nothingelse.Itisinthisdataandinthesetheoriesthatwemusttrytouncoverwhatwehavebeenunableyettoimagine.ThisishowCopernicus,Newton,MaxwellandEinsteinproceeded.Theynevertriedtoâguessâanewtheoryâunlike,inmyopinion,thewayinwhichtoomanytheoreticalphysicistsaretryingtodotoday.ThethreerecentexperimentalresultsImentionedspeakwiththevoiceofNatureitself:âStop
dreamingofnewfieldsandstrangeparticles;supplementarydimensions,othersymmetries,paralleluniverses,strings,andwhateverelse.Thepiecesofthepuzzlearesimpler:generalrelativity,quantummechanicsandthestandardmodel.Thenextstepforwardmaybeâonlyâaquestionofcombiningtheminthecorrectmanner.âItâsreassuringadvicefortheloopquantumgravitycommunity,becausethesearethehypothesesofthetheory:generalrelativity,quantummechanicsandcompatibilitywiththestandardmodel,nothingelse.Theradicalconceptualconsequencesâthequantaofspace,thedisappearanceoftimeâarenotboldhypotheses:theyaretherationalconsequencesthatfollowfromtakingthebasicinsightsofourbesttheoriesseriously.Onceagain,thesearenotdefinitiveproofs.Supersymmetricparticlesmightfinallyexist,perhaps,
atascalestillnotreached,andcouldexisteveniflooptheoryiscorrect.Supersymmetryfailedto
![Page 92: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/92.jpg)
showupwhereexpected,andstringtheoristsarealittledowncast,looptheoristsarebuoyant,butitisstillamatterofclues;thereisnostrongevidenceatall.Tofindmoreconcreteconfirmationofthetheory,weneedtolookelsewhere.Theprimordial
universecouldopenthewindowtopredictionscapableofconfirmingthetheory.Inanottoodistantfuture,wehope.Ortheycouldprovethetheorywrong.
AwindowontoquantumgravityIfwehavetheequationsthatdescribethetransitionoftheuniverseacrossthequantumphase,wecancomputeeffectsofquantumphenomenaupontheuniversewhichweobservetoday.Theuniverseisfilledwithcosmicradiation:aseaofphotonsremainedinthecosmossincetheearlyhotphase,theresidualglareoftheearlyhightemperature.Theelectromagneticfieldintheimmensespacebetweengalaxiestrembleslikethesurfaceofthe
seaafterabigstorm.Thisquivering,disseminatedthroughouttheuniverse,iscalledthecosmicbackgroundradiation.IthasbeenstudiedinthepastfewyearsbysatellitessuchasCOBE,WMAPand,mostrecently,Planck.Animageoftheminutefluctuationsofthisradiationisgiveninfigure9.3.Thedetailsofthestructureofthisradiationtellusthehistoryoftheuniverseand,hiddeninthefoldsofthesedetails,therecouldbefootprintsofthequantumbeginningofouruniverse.Oneofthemostactivesectorsofresearchinloopquantumgravityisstudyinghowthequantum
dynamicoftheprimordialuniverseisreflectedinthisdata.Theresultsarepreliminary,butencouraging.Withmorecalculationsandmoreprecisemeasurements,itshouldbepossibletoarriveatatestofthetheory.In2013AbhayAshtekar,IvanAgulloandWilliamNelsonpublishedanarticleinwhichthey
calculatethat,undercertainhypotheses,thestatisticaldistributionofthefluctuationsofthissourceofcosmicradiationshouldrevealtheeffectoftheinitialbounce:thewide-anglefluctuationsshouldbedifferentfromthosepredictedbythetheorythatdoesnottakequantaintoaccount.Thecurrentstateofthemeasurementisdescribedinfigure9.4,wheretheblacklinerepresentsthepredictionbyAshtekar,AgulloandNelson,andthegreydotsthemeasureddata.Fornow,thesearenotsufficienttoevaluatewhethertheupwardbendoftheblacklinepredictedbythethreeauthorsiscorrectornot.Butmeasurementsaregettingmoreprecise.Thesituationisstillfluid.Butthosewho,likemyself,havespenttheirlivesseekingtounderstandthesecretsofquantumspacearefollowingwithcloseattention,anxietyandhopethecontinuoushoningofourcapacitytomakeobservations,tomeasureandtocalculateâandareawaitingthemomentinwhichnaturewilltelluswhetherwearerightornot.
Figure9.3Thefluctuationsofthecosmicbackgroundradiation.Thisistheimageoftheoldestobjectintheuniverseavailabletous.Thesefluctuationswereproduced14billionyearsago.Inthestatisticsofsuchfluctuationswehopetofindconfirmationofthe
predictionsofquantumgravity.
![Page 93: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/93.jpg)
Figure9.4Possiblepredictionofthespectrumofbackgroundradiation,ofloopquantumgravity(shownbythesolidline)comparedwiththecurrentexperimentalerrors(asrepresentedbythepoints).CourtesyofA.Ashtekar,I.AgulloandW.Nelson.
Tracesofthegreatprimordialheatmustalsobeinthegravitationalfielditself.Thegravitationalfield,too,thatistosay,spaceitself,mustbetremulouslikethesurfaceofthesea.Therefore,acosmicgravitationalbackgroundradiationmustalsoexistâoldereventhantheelectromagneticone,becausethegravitationalwavesaredisturbedlessbymatterthantheelectromagneticonesandwereabletotravelundisturbedevenwhentheuniversewastoodensetolettheelectromagneticwavespass.Wehavenowobservedgravitationalwavesdirectly,withtheLIGOdetector,formedbytwoarmsof
afewmilesinlength,atarightangletoeachother,inwhichlaserbeamsmeasurethedistancebetweenthreefixedpoints.Whenagravitationalwavepasses,thespacelengthensandshortensimperceptibly,andthelasersrevealthisminusculevariation.fn46Thegravitationalwavesobservedweregeneratedbyanastrophysicalevent:collidingblackholes.Thesearephenomenadescribedbygeneralrelativitywhichdonotinvolvequantumgravity.ButamoreambitiousexperimentcalledLISAisatthestageofbeingevaluatedandiscapableofdoingthesamethingbutonamuchlargerscale:byputtingintoorbitthreesatellites,notaroundtheEarthbutaroundtheSun,asiftheywereminiatureplanetstrackingtheEarthinitsorbit.Thethreesatellitesareconnectedbylaserbeamsmeasuringthedistancebetweenthemor,betterstill,thevariationsinthedistanceswhenagravitationalwavepasses.IfLISAislaunched,itshouldbeabletoseenotonlythegravitationalwavesproducedbystarsandblackholesbutalsothediffusebackgroundofprimordialgravitationalwavesgeneratedatatimeclosetotheBigBang.Thesewavesshouldtellusaboutthequantumbounce.Inthesubtleirregularitiesofspace,weshouldbeabletofindtracesofeventswhichtookplace14
billionyearsago,attheoriginofouruniverse,andconfirmourdeductionsonthenatureofspaceandtime.
![Page 94: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/94.jpg)
10.QuantumBlackHoles
Blackholespopulateouruniverseingreatnumber.Theyareregionsinwhichspaceissocurvedastocollapseinonitself,andwheretimecomestoastandstill.Asmentioned,theyform,forinstance,whenastarhasburnedupalloftheavailablehydrogenandcollapses.Frequently,thecollapsedstarformedpartofapairofneighbouringstarsand,inthiscase,the
blackholeandthesurvivingcounterpartcircleonearoundtheother;theblackholesucksmatterfromtheotherstarcontinuously(asinfigure10.1).Astronomershavefoundmanyblackholeswithasize(thatis,mass)oftheorderofourSun(abit
larger,infact).Buttherearealsogiganticbackholes.Thereisoneoftheseatthecentreofalmostallofthegalaxies,includingourown.
Figure10.1Representationofacouplestar/blackhole.Thestarlosesmatter,whichispartlyabsorbedbytheblackhole,partlyprojectedbyitinjetsinthedirectionofitspoles.
Theblackholeatthecentreofourowngalaxyiscurrentlybeingstudiedindetail.IthasamassamilliontimesgreaterthanourSun.Everysooften,astargetstooclosetothismonster,isdisintegratedbythegravitationaldistortionandswallowedbythecyclopeanblackhole,likeasmallfishswallowedbyawhale.ImagineamonsterthesizeofamillionSuns,whichswallowsinaninstantourownSunanditsminiatureplanetsâŚThereisawonderfulongoingprojecttoconstructanetworkofradioantennaedistributedacross
theEarthfrompoletopole,withwhichastronomerswillbeabletoachievearesolutionsufficienttoâseeâthegalacticblackhole.Whatweexpecttoseeisasmallblackdiscsurroundedbythelightproducedbytheradiationofthematterfallingin.Whatentersablackholedoesnotcomeoutagain,atleastifweneglectquantumtheory.The
surfaceofablackholeislikethepresent:itcanbecrossedonlyinonedirection.Fromthefuture,thereisnoreturn.Forablackhole,thepastistheoutside;thefutureistheinside.Seenfromoutside,ablackholeislikeaspherewhichcanbeenteredbutoutofwhichnothingcancome.Arocketcouldstaypositionedatafixeddistancefromthissphere,whichiscalledthehorizonoftheblackhole.Todosoitneedstokeepitsenginesfiringintensely,toresistthegravitationalpullofthehole.Thepowerfulgravityoftheholeimpliesthattimeslowsdownforthisrocket.Iftherocketstaysnearenoughtothehorizonforonehour,andthenmovesaway,itwouldthenfindthat,outside,inthemeantime,centurieshavepassed.Theclosertherocketstaystothehorizon,theslowerâwith
![Page 95: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/95.jpg)
respecttotheoutsideâtimerunsforit.Thus,travellingtothepastisdifficult,buttravellingtothefutureiseasy:weneedonlytogetclosetoablackholewithaspaceship,keepwithinitsvicinityforawhile,andthenmoveaway.Onthehorizonitself,timestops:ifwegetextremelyclosetoitandthenmoveawayafterafewof
ourminutes,amillionyearsmighthaveelapsedintherestoftheuniverse.Thereallysurprisingthingisthatthepropertiesofthesestrangeobjects,todaycommonly
observed,wereforeseenbyEinsteinâstheory.Now,astronomersstudytheseobjectsinspace,butuntilnotlongagoblackholeswereconsideredascarcelycredibleandbizarreconsequenceofanoutlandishtheory.IremembermyuniversityprofessorintroducingthemassolutionstoEinsteinâsequations,towhichârealobjectswereunlikelyevertocorrespondâ.Thisisthestupendouscapacityoftheoreticalphysicstodiscoverthingsbeforetheyareobserved.TheblackholesweobservearewelldescribedbyEinsteinâstheory,andquantummechanicsisnot
neededtounderstandthem.Buttherearetwomysteriesofblackholesthatdorequirequantummechanicsinordertobeunravelledand,foreachofthese,looptheoryoffersapossiblesolution.Oneofthesecouldalsoofferanopportunitytotestthetheory.Thefirstapplicationofquantumgravitytoblackholesconcernsacuriousfactdiscoveredby
StephenHawking.Earlyinthe1970shetheoreticallydeducedthatblackholesareâhotâ.Theybehavelikehotbodies:theyemitheat.Indoingso,theyloseenergyandhencemass(sinceenergyandmassarethesamething),becomingprogressivelysmaller.Theyâevaporateâ.ThisâevaporationofblackholesâisthemostimportantdiscoverymadebyHawking.Objectsarehotbecausetheirmicroscopicconstituentsmove.Ahotpieceofiron,forexample,isa
pieceofironwheretheatomsvibrateveryrapidlyaroundtheirequilibriumposition.Hotairisairinwhichmoleculesmovefasterthanincoldair.
Figure10.2Thesurfaceofablackholecrossedbyloops,thatistosay,bylinksofthespinnetworkthatdescribethestateofthegravitationalfield.Eachloopcorrespondstoaquantumareaoftheblackholeâssurface.ŠJohnBaez.
Whataretheelementaryâatomsâthatvibrate,makingablackholehot?Hawkingleftthisproblemunanswered.Looptheoryprovidesapossibleanswer.Theelementaryatomsofablackholethatvibrate,andarethusresponsibleforitstemperature,aretheindividualquantaofspaceonitssurface.Thus,itispossibletounderstandthepeculiarheatofblackholespredictedbyHawkingusingloop
theory:theheatistheresultofthemicroscopicvibrationsoftheindividualatomsofspace.Thesevibratebecauseintheworldofquantummechanicseverythingvibrates;nothingstaysstill.Theimpossibilityofanythingbeingentirelyandcontinuouslystillinaplaceisattheheartofquantummechanics.Black-holeheatisdirectlyconnectedtoloopquantumgravityâsfluctuationsoftheatomsofspace.Theprecisepositionoftheblackholeâshorizonisdeterminedonlyinrelationtothesemicroscopicfluctuationsofthegravitationalfield.Hence,inacertainsense,thehorizonfluctuateslikeahotbody.Thereisanotherwayofunderstandingtheoriginoftheheatofblackholes.Thequantum
fluctuationsgenerateacorrelationbetweentheinteriorandtheexteriorofahole.(IwillspeakatlengthaboutcorrelationsandtemperatureinChapter12).Quantumuncertaintyacrossthehorizonoftheblackholegeneratesfluctuationsofthehorizonâsgeometry.Butfluctuationsimplyprobability,andprobabilityimpliesthermodynamics,andthereforetemperature.Concealingfromusapartoftheuniverse,ablackholemakesitsquantumfluctuationsdetectableintheformofheat.
![Page 96: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/96.jpg)
Figure10.3StephenHawkingandEugenioBianchi.Ontheblackboardaretheprincipalequationsofloopquantumgravitywhichdescribeblackholes.
ItwasayoungItalianscientist,EugenioBianchi,todayaprofessorintheUnitedStates,whocompletedanelegantcalculationwhichshowshow,startingfromtheseideasandfromthebasicequationsofloopquantumgravity,itispossibletoderivetheformulafortheheatofblackholesforeseenbyHawking(figure10.3).Thesecondapplicationofloopquantumgravitytoblack-holephysicsismorespectacular.Once
collapsed,astarvanishesfromexternalview:itisinsidetheblackhole.But,insidethehole,whathappenstoit?Whatwouldyouseeifyouletyourselffallintothehole?Atfirst,nothinginparticular:youwouldcrossthesurfaceoftheblackholewithoutmajorinjuries
âthenyouwouldplummettowardsthecentre,atevergreaterspeed.Andthen?Generalrelativitypredictsthateverythingissquashedatthecentreintoaninfinitelysmallpointofinfinitedensity.Butthisis,onceagain,ifweignorequantumtheory.Ifwetakequantumgravityintoaccount,thispredictionisnolongercorrectâthereisquantum
repulsionâthesamerepulsionthatmakestheuniversebounceattheBigBang.Whatweexpectisthat,ongettingclosertothecentre,thefallingmatterissloweddownbythisquantumpressure,uptoaveryhighbutfinitedensity.Mattergetssquashed,butnotallthewaytoaninfinitelysmallpoint,becausethereisalimittohowsmallthingscanbe.Quantumgravitygeneratesahugepressurethatmakesmatterbounceout,preciselyasacollapsinguniversecanbounceoutintoanexpandinguniverse.Thebounceofacollapsingstarcanbeveryfast,ifwatchedfromdownthere.Butârememberâ
timepassesmuchmoreslowlytherethanoutside.Seenfromtheoutside,theprocessofthebouncecantakebillionsofyears.Afterthistime,wecanseetheblackholeexplode.Intheend,basically,thisiswhatablackholeis:ashortcuttothedistantfuture.Thus,quantumgravitymightimplythatblackholesarenoteternallystableobjects,asclassical
generalrelativitypredicted,afterall.Theyare,ultimately,unstable.Seeingtheseblack-holeexplosionswouldbeaspectacularconfirmationforthetheory.Veryold
blackholes,suchasthoseformedintheearlyuniverse,couldbeexplodingtoday.Somerecentcalculationssuggestthatthesignalsoftheirexplosioncouldbeintherangeofradiotelescopes.Ithasevenbeensuggestedthatcertainmysteriousradiopulseswhichradioastronomershavealreadymeasured,calledFastRadioBursts,couldbe,precisely,signalsgeneratedbytheexplosionofprimordialblackholes.Ifthiswasconfirmed,itwouldbefantastic:wewouldhaveadirectsignofaquantumgravitationalphenomenon.LetâswaitandseeâŚ
![Page 97: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/97.jpg)
11.TheEndofInfinity
Whenwetakequantumgravityintoaccount,theinfinitecompressionoftheuniverseintoasingle,infinitelysmallpointpredictedbygeneralrelativityattheBigBangdisappears.Quantumgravityisthediscoverythatnoinfinitelysmallpointexists.Thereisalowerlimittothedivisibilityofspace.TheuniversecannotbesmallerthanthePlanckscale,becausenothingexistswhichissmallerthanthePlanckscale.Ifweignorequantummechanics,weignoretheexistenceofthislowerlimit.Thepathological
situationspredictedbygeneralrelativity,wherethetheorygivesinfinitequantities,arecalledsingularities.Quantumgravityplacesalimittoinfinity,andâcuresâthepathologicalsingularitiesofgeneralrelativity.Thesamehappensatthecentreofblackholes:thesingularitythatclassicgeneralrelativity
anticipateddisappearsassoonaswetakequantumgravityintoaccount.Thereisanothercase,ofadifferentkind,inwhichquantumgravityplacesalimittotheinfinite,
anditregardsforcessuchaselectromagnetism.Quantumfieldtheory,startedbyDiracandcompletedinthe1950sbyFeynmanandhiscolleagues,describestheseforceswellbutisfullofmathematicalabsurdities.Whenweuseittocomputephysicalprocesses,weoftenobtainresultswhichareinfinite,andmeannothing.Theyarecalleddivergences.Thedivergencesaretheneliminatedwithcalculations,usingabaroquetechnicalprocedurewhichleadstofinitefinalresults.Inpractice,itworks,andthenumbers,intheend,comeoutright;theyreproducetheexperimentalmeasurements.Butwhymustthetheorygoviatheinfinitetoarriveatreasonablenumbers?Inthelastyearsofhislife,Diracwasveryunhappywiththeinfinitiesinhistheoryandfeltthat,
allthingsconsidered,hisobjectiveoftrulyunderstandinghowthingsworkedwasnotachieved.Diraclovedconceptualclarity,evenifwhatwasclaritytohimwasnotalwaysclaritytoothers.Butinfinitiesdonotmakeforclarity.Buttheinfinitiesofquantumfieldtheoryfollowfromanassumptionatthebasisofthetheory:the
infinitedivisibilityofspace.Forexample,tocalculatetheprobabilitiesofaprocess,wesumupâasFeynmanhastaughtusâallofthewaysinwhichtheprocesscouldunfold,andtheseareinfinite,becausetheycanhappeninanyoneoftheinfinitepointsofaspatialcontinuum.Thisiswhytheresultcanbeinfinite.Whenquantumgravityistakenintoaccount,theseinfinitiesalsodisappear.Thereasonisclear:
spaceisnotinfinitelydivisible,therearenoinfinitepoints;therearenoinfinitethingstoaddup.Thegranulardiscretestructureofspaceresolvesthedifficultiesofthequantumtheoryoffields,eliminatingtheinfinitiesbywhichitisafflicted.Thisisatremendousresult:ontheonehand,takingquantummechanicsintoaccountresolvesthe
problemsgeneratedbytheinfinitiesofEinsteinâstheoryofgravity,thatistosay,thesingularities.Ontheother,takinggravityintoaccountsolvestheproblemsgeneratedbyquantumfieldtheory,thatistosay,thedivergences.Farfrombeingcontradictory,astheyatfirstseemed,thetwotheorieseachofferthesolutiontotheproblemsposedbytheother!Puttingalimittoinfinityisarecurrentthemeinmodernphysics.Specialrelativitymaybe
summarizedasthediscoverythatthereexistsamaximumvelocityforallphysicalsystems.Quantummechanicscanbesummarizedasthediscoverythatthereexistsamaximumofinformationforeachphysicalsystem.TheminimumlengthisthePlancklengthLP,themaximumvelocityisthespeedoflightc,andthetotalinformationisdeterminedbythePlanckconstanth.Thisissummarizedintable11.1.Theexistenceoftheseminimumandmaximumvaluesforlength,velocityandactionfixesa
naturalsystemofunits.Insteadofmeasuringspeedinkilometresperhour,orinmetrespersecond,wecanmeasureitinfractionsofthespeedoflight.Wecanfixthevalue1forthevelocitycandwrite,forexample,v=½,forabodywhichismovingathalfthespeedoflight.Inthesameway,wecanpositbydefinitionandmeasurelengthinmultiplesofPlanckâslength.Andwecanposith=1andmeasureactionsinmultiplesofPlanckâsconstant.Inthisway,wehaveanaturalsystemoffundamentalunitiesfromwhichtheothersfollow.TheunityoftimeisthetimethatlighttakestocoverthePlancklength,andsoon.Thenaturalunitiesarecommonlyusedinresearchonquantumgravity.Theidentificationofthesethreefundamentalconstantsplacesalimittowhatseemedtobethe
infinitepossibilitiesofnature.Itsuggeststhatwhatwecallinfiniteoftenisnothingmorethansomethingwhichwehavenotyetcounted,orunderstood.Ithinkthisistrueingeneral.âInfiniteâ,
![Page 98: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/98.jpg)
ultimately,isthenamethatwegivetowhatwedonotyetknow.Natureappearstobetellingusthatthereisnothingtrulyinfinite.Table11.1Fundamentallimitationsdiscoveredbytheoreticalphysics.
PhysicalQuantity Fundamentalconstant Theory Discovery
Velocity c Specialrelativity Amaximumvelocityexists
Information(actions) â Quantummechanics Aminimumofinformationexists
Length Lp Quantumgravity Aminimumlengthexists
Thereisanotherinfinitywhichdisorientatesourthinking:theinfinitespatialextensionofthecosmos.ButasIillustratedinChapter3,Einsteinhasfoundthewayofthinkingofafinitecosmoswithoutborders.Currentmeasurementsindicatethatthesizeofthecosmosmustbelargerthan100billionlightyears.Thisistheorderofmagnitudeoftheuniversewehaveindirectaccessto.Itisaround10120timesgreaterthanthePlancklength,anumberoftimeswhichisgivenbya1followedby120zeroes.BetweenthePlanckscaleandthecosmologicalone,then,thereisthemind-blowingseparationof120ordersofmagnitude.Huge.Extraordinarilyhuge.Butfinite.Inthisspaceâbetweenthesizeoftheminutequantaofspace,uptoquarks,protons,atoms,
chemicalstructures,mountains,stars,galaxies(eachformedbyonehundredbillionstars),clustersofgalaxies,andrightupuntiltheseeminglyboundlessvisibleuniverseofmorethan100billiongalaxiesâunfoldstheswarmingcomplexityofouruniverse;auniverseweknowonlyinafewaspects.Immense.Finite.ThecosmologicalscaleisreflectedinthevalueofthecosmologicalconstantÎ,whichentersinto
thebasicequationsofourtheories.Thefundamentaltheorycontains,therefore,averylargenumber:theratiobetweenthecosmologicalconstantandthePlancklength.Itisthislargenumberthatopensthewaytothevastcomplexityoftheworld.Butwhatweseeandunderstandoftheuniverseisnotaninfinitytodrownin.Itisawidesea,butafiniteone.ThebookofEcclesiasticus,orSirach,fn47openswithastupendousquestion:Whocannumberthesandofthesea,andthedropsofrain,andthedaysofeternity?Whocanfindouttheheightofheaven,andthebreadthoftheearth,andthedeep,andwisdom?
Notmuchlongeraftertheselineswerecomposed,anothergreattextwaswritten,withanopeningwhichstillresounds:Somethink,OKingHiero,thatthegrainsofsandcannotbecounted.
ThisistheopeningofPsammites(TheSandReckoner)byArchimedes,inwhichthegreatestscientistofantiquityâŚcountsthegrainsofsandintheuniverse!Hedoessoinordertodemonstratethattheirnumberislargebutfinite,andcanbedetermined.
Thenumericalsystemofantiquitydidnotallowfordealingwithverylargenumberseasily.InTheSandReckoner,Archimedesdevelopsanewsystemofnumbering,similartoourexponentials,thatmakesitpossibletodealwithverylargenumbers,andshowsitspowerbycounting(certainlyplayfully)howmanygrainsofsandthereare,notjustontheseashoresbutintheentireuniverse.TheSandReckonerisplayful,butprofound.Withaflightoffancythatseemstoanticipatethe
Enlightenmentbymillennia,Archimedesrebelsagainsttheformofknowledgethatinsistsontherebeingmysterieswhichareintrinsicallyinaccessibletohumanthought.Hedoesnotclaimtoknowtheexactdimensionsoftheuniverse,ortheprecisenumberofgrainsofsand.Itisnâtthecompletenessofhisknowledgethatheisasserting.Onthecontrary,heisexplicitabouttheapproximateandprovisionalnatureofhisestimates.Hespeaksaboutpossiblealternativesregardingthetruesizeoftheuniverseâbetweenwhichhedoesnotmakeadefinitechoice.Thepointatstakehereisnotthepresumptionofknowingeverything.Itistheopposite:anawarenessthatyesterdayâsignorancemayhavelightshedonittoday,andthattodayâsmightbeilluminatedtomorrow.Thecentralpointisrebellionagainsttherenunciationofthedesiretoknow:adeclarationoffaith
inthecomprehensibilityoftheworld,aproudretaliationtothosewhoremainsatisfiedwiththeirownignorance,whocallinfinitethatwhichwedonâtunderstandanddelegateknowledgetoelsewhere.Centurieshavepassed,andthetextofEcclesiasticus,alongwiththerestoftheBiblecanbefound
incountlesshomes,whileArchimedesâtextisreadonlybythefew.ArchimedeswasslaughteredbytheRomansduringthesackingofSyracuse,thelastproudremnantofMagnaGreciatofallundertheRomanyoke,duringtheexpansionofthatfutureempirewhichwouldsoonadoptEcclesiasticusasoneofthefoundationaltextsofitsofficialreligion,apositionwhichitwastooccupythereformorethanathousandyears.Duringthatmillennium,thecalculationsmadebyArchimedeslanguishedinastateofincomprehensibility:noonewasabletouse,oreventounderstandthem.
![Page 99: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/99.jpg)
NearArchimedesâSyracusethereisoneofthemostbeautifulsitesinItaly,thetheatreofTaormina,whichlooksoutattheMediterraneananduponMountEtna,thesmokingvolcano.InArchimedesâtime,thetheatrewasusedtostageplaysbySophoclesandEuripides.TheRomansadapteditforgladiatorialcombat,forthepleasureofwatchinggladiatorsdie.ThesophisticatedplayfulnessofTheSandReckonerisperhapsnotonlyaboutanaudacious
mathematicalconstruction,orthevirtuosityofoneofthemostextraordinarymindsofantiquity.Itisalsoadefiantcryofreason,whichrecognizesitsownignorancebutrefusestodelegatetoothersthesourceofknowledge.Itisasmall,reservedandpowerfullyintelligentmanifestoagainstinfinityâagainstobscurantism.QuantumgravityisoneofthemanylinesthatcontinuethequestofTheSandReckoner.Weare
countingthegrainsofspaceofwhichthecosmosismade.Avastcosmos,butafiniteone.Theonlytrulyinfinitethingisourignorance.
![Page 100: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/100.jpg)
12.Information
Weareapproachingtheconclusionofourjourney.Inthepreviousfewchapters,Ispokeabouttheconcreteapplicationsofquantumgravity:thedescriptionofwhathappenedtotheuniversearoundthetimeoftheBigBang;thedescriptionofthepropertiesoftheheatofblackholesandthesuppressionofinfinity.Beforeconcluding,Iwouldliketoreturntothetheory,butlookingatitsfuture,andtospeak
aboutinformation:aspectrethatishauntingtheoreticalphysics,arousingenthusiasmandconfusion.Thischapterisdifferentfromtheprecedingones,whereIspokeofideasandtheoriesnotyet
testedbutwelldefined;here,Iâmspeakingofideasstillconfused,badlyinneedoforganization.If,dearreader,youhavefoundthejourneysofaralittlerough,thenholdontighter,becauseweârenowflyingbetweenvoidsofair.Ifthischapterseemsparticularlyopaque,itâsnotbecauseyourideasareconfused.Itâsbecausetheonewiththeconfusedideasisme.Manyscientistssuspecttodaythattheconceptofâinformationâmayturnouttobeakeyfornew
advancesinphysics.Informationismentionedinthefoundationsofthermodynamics,thescienceofheat,thefoundationofquantummechanicsandinotherareasbesides,withthewordquiteoftenusedveryimprecisely.Ibelievethereissomethingimportantinthisidea.Iâlltrytoexplainwhy,andtoshowwhatinformationhastodowithquantumgravity.Beforeanythingelse,whatisinformation?Thewordâinformationâisusedincommonparlanceto
meanavarietyofdifferentthings,andthisimprecisionisasourceofconfusioninscienceaswell.Thescientificnotionofinformation,however,wasdefinedwithclarityin1948,bytheAmericanmathematicianandengineerClaudeShannon,andissomethingverysimple:informationisthemeasureofthenumberofpossiblealternativesforsomething.Forexample,ifIthrowadie,itcanlandononeofsixfaces.Whenweâveseenitfallonaparticularoneofthese,wehaveanamountofinformationN=6,becausethepossiblealternativesaresixinnumber.IfIdonâtknowwhichdayoftheyearisyourbirthday;thereare365distinctpossibilities.Ifyoutellmethedate,IhavetheinformationN=365.Andsoon.InsteadofthenumberofalternativesN,scientistsmeasureinformationintermsofaquantity
calledS,forâShannoninformationâ.Sisdefinedasthelogarithminbase2ofN:S=log2N.TheadvantageofusingthelogarithmisthattheunitofmeasurementS=1correspondstoN=2(because1=log22),makingtheunitofinformationtheminimumnumberofalternatives:thechoicebetweentwopossibilities.Thisunitofmeasurementiscalledâbitâ.WhenIknowatroulettethatarednumberhascomeupratherthanablack,Ihaveonebitofinformation;whenIknowthatared,evennumberhaswon,Ihavetwobitsofinformation;whenanevenrednumberâmanqueâ(eighteenorless,inrouletteparlance)wins,Ihavethreebits.Twobitsofinformationcorrespondtofouralternatives(redeven,reduneven,blackeven,blackuneven).Threebitsofinformationcorrespondtoeightalternatives.Andsoon.fn48Akeypointisthatinformationcanbelocatedsomewhere.Imagine,forinstance,thatyouhavein
yourhandaballwhichcanbeeitherblackorwhite.ImaginethatIalsohaveaballwhichcanbeeitherblackorwhite.Therearetwopossibilitiesonmypart,andtwoonyours.Thetotalnumberofpossibilitiesisfour(2x2):white-white;white-black;black-whiteandblack-black.Now,supposethatforsomereasonwearecertainthatthetwoballsareoppositeincolour(forinstance,becausewehavetakentheballsfromaboxthatcontainedonlyonewhiteandoneblackball).Thetotalnumberofalternativesisthenonly2(white-blackorblack-white),evenifthealternativesarestilltwoonmypartandtwoonyours.Notethat,inthissituation,somethingpeculiarhappens:ifyoulookatyourball,thenyouknowthecolourofmine.Inthiscase,wesaythatthecoloursofthetwoballsarecorrelated,thatistosay,linkedtooneanother.Wesaythatmyballâhasinformationâaboutyours(aswellasviceversa).Ifyouthinkaboutit,thisispreciselywhathappensinlifewhenwecommunicate:forexample,
whenIphoneyou,Iknowthatthephonecausesthesoundsonyoursidetobedependentonthesoundsonmine.Thesoundsonbothsidesarelinked,likethecolouroftheballs.Theexampleisnotchosenatrandom:Shannon,whoinventedthetheoryofinformation,worked
foratelephonecompany,andwaslookingforawaytomeasureaccuratelyhowmuchatelephonelinecouldâcarryâ.Butwhatdoesatelephonelinecarry?Itcarriesinformation.Itcarriesthecapacitytodistinguishbetweenalternatives.Forthisreason,Shannondefinedinformation.Whyisthenotionofinformationuseful,perhapsevenfundamental,tounderstandingtheworld?
Forasubtlereason:becauseitmeasurestheabilityofonephysicalsystemtocommunicatewith
![Page 101: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/101.jpg)
anotherphysicalsystem.LetâsreturnforafinaltimetotheatomsofDemocritus.Letâsimagineaworldformedofan
interminableseaofatomswhichbounce,attractandclingtogether,andofnothingelse.Arenâtwemissingsomething?PlatoandAristotleinsistedonthefactthatsomethingwasindeedmissing;theythoughtthatthe
formofthingswasthissomethingextrathathadtobeaddedtothesubstanceofwhichthingsweremadeinordertounderstandtheworld.ForPlato,formsexistbythemselves,inanetherealidealworldofforms,aworldofâideasâ.Theideaofahorseexistspriortoandindependentlyofanyactualhorse.ForPlato,arealhorseisnothingbutapalereflectionoftheideaofahorse.Theatomswhichmakeupthehorsecountforlittle:whatcountsistheâhorsenessâ,theabstractform.Aristotleisabitmorerealistic,butforhim,too,theformcannotbereducedtothesubstance.Inastatue,thereismorethanthestoneofwhichitismade.Thismore,forAristotle,istheform.ThisisthebasisofthecritiqueofDemocritusâsmaterialisminantiquity.Itstillremainsacommoncritiqueofmaterialism.ButwasDemocritusreallyproposingthateverythingcanbereducedtoatoms?Letâslookatit
moreclosely.Democritussaysthatwhenatomscombinewhatcountsistheirform,theirarrangementinthestructure,aswellasthewayinwhichtheycombine.Hegivestheexampleofthelettersofthealphabet:thereareonlytwentyorsolettersbut,asheputsit,âItispossibleforthemtocombineindiversemodes,inordertoproducecomediesortragedies,ridiculousstoriesorepicpoems.âTherearemorethanjustatomsinthisidea:whatcountsisthewayinwhichtheyarecombined,
oneinrelationtoanother.Butwhatrelevancecanthewayinwhichtheyarecombinedhave,inaworldinwhichthereisnothingbutotheratoms?Iftheatomsarealsoanalphabet,whoisabletoreadthephraseswrittenwiththisalphabet?Theanswerissubtle:thewayinwhichtheatomsarrangethemselvesiscorrelatedwiththeway
otheratomsarrangethemselves.Therefore,asetofatomscanhaveinformation,inthetechnical,precisesensedescribedabove,aboutanothersetofatoms.This,inthephysicalworld,happenscontinuouslyandthroughout,ineverymomentandinevery
place:thelightwhicharrivesatoureyescarriesinformationabouttheobjectswhichithasplayedacross;thecolouroftheseahasinformationonthecolouroftheskyaboveit;acellhasinformationaboutthevirusthatisattackingit;anewlivingbeinghasplentyofinformationbecauseitiscorrelatedwithitsparents,andwithitsspecies;andyou,dearreader,whenreadingtheselines,receiveinformationaboutwhatIamthinkingwhilewritingthem,thatistosay,aboutwhatishappeninginmymindatthemomentinwhichIwritethistext.Whatoccursintheatomsofyourbrainisnotanymoreindependentfromwhatishappeningintheatomsofmine:wecommunicate.Theworldisnât,then,justanetworkofcollidingatoms:itisalsoanetworkofcorrelations
betweensetsofatoms,anetworkofrealreciprocalinformationbetweenphysicalsystems.Inallofthis,thereisnothingidealisticorspiritual;itâsnothingbutanapplicationofShannonâs
ideathatalternativescanbecounted.AllthisisasmuchapartoftheworldasthestonesoftheDolomites,thebuzzingofbeesandthewavesofthesea.Oncewehaveunderstoodthatthisnetworkofreciprocalinformationexistsintheuniverse,itis
naturaltoseektousethistreasuretodescribetheworld.Letâsstartwithanaspectofnaturewellunderstoodsincetheendofthenineteenthcentury:heat.Whatisheat?Whatdoesitmeantosaythatsomethingishot?Whydoesacupofscalding-hotteacoolitselfdown,ratherthanheatingitselfupfurther?ItwastheAustrianscientistLudwigBoltzmann,thefounderofstatisticalmechanics,whofirst
understoodwhy.fn49Heatistherandommicroscopicmovementofmolecules:whentheteaishotter,themovementofthemoleculesismoreagitated.Whydoesitcooldown?Boltzmannhazardedasplendidhypothesis:becausethenumberofpossiblestatesofthemoleculesinhotteaandcoldairissmallerthanthenumberincoolteaandslightlywarmerair.Thecombinedstateevolvesfromasituationwheretherearelesspossiblestatestoasituationwheretherearemorepossiblestates.Theteacanâtwarmitselfup,becauseinformationcannotincreasebyitself.Iâllelaborate.Themoleculesofteaareextremelynumerousandextremelysmall,andwedonât
knowtheirprecisemovements.Therefore,welackinformation.Thislackofinformationâormissinginformationâcanbecomputed.(Boltzmanndidit:hecomputedthenumberofdistinctstatesthemoleculescanbein.Thisnumberdependsonthetemperature.)Iftheteacools,alittleofitsenergypassesintothesurroundingair;therefore,themoleculesofteamovemoreslowlyandthemoleculesofairmovemorequickly.Ifyoucomputeyourmissinginformation,youdiscoverthatithasincreased.If,instead,teaabsorbedheatfromthecolderair,thenthemissinginformationwouldbedecreased.Thatis,wewouldknowmore.Butinformationcannotfallfromthesky.Itcannotincreasebyitself,becausewhatwedonâtknow,wejustdonâtknow.Therefore,theteacannotwarmupbyitselfincontactwithcoldair.Itsoundsabitmagical,butitworks:wecanpredicthowheatbehavesjustonthebasisoftheobservationthatourinformationcannotincreaseforfree!Boltzmannwasnottakenseriously.Attheageoffifty-six,inDuino,nearTrieste,hecommitted
suicide.Today,heisconsideredoneofthegeniusesofphysics.Histombisincisedwithhisformula
S=klogW
![Page 102: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/102.jpg)
whichexpresses(missing)informationasthelogarithmofthenumberofalternatives,Shannonâskeyidea.Boltzmannpointedoutthatthisquantitycoincideswiththeentropyusedinthermodynamics.Entropyisâmissinginformationâ,thatis,informationwithaminussign.Thetotalamountofentropycanonlyincrease,becauseinformationcanonlydiminish.fn50Today,physicistscommonlyaccepttheideathatinformationcanbeusedasaconceptualtoolto
throwlightonthenatureofheat.Moreaudacious,butdefendedtodaybyanincreasingnumberoftheorists,istheideathattheconceptofinformationcanbeusefulalsotothemysteriousaspectsofquantummechanicsillustratedinChapter5.Rememberthatakeyresultofquantummechanicsispreciselythefactthatinformationisfinite.
Thenumberofalternativeresultsthatwecanobtainmeasuringaphysicalsystemfn51isinfiniteinclassicalmechanics;but,thankstoquantumtheory,wehaveunderstoodthat,inreality,itisfinite.Quantummechanicscanbeunderstoodasthediscoverythatinformationinnatureisalwaysfinite.Infact,theentirestructureofquantummechanicscanbereadandunderstoodintermsof
information,asfollows.Aphysicalsystemmanifestsitselfonlybyinteractingwithanother.Thedescriptionofaphysicalsystem,then,isalwaysgiveninrelationtoanotherphysicalsystem,theonewithwhichitinteracts.Anydescriptionofasystemisthereforealwaysadescriptionoftheinformationwhichasystemhasaboutanothersystem,thatistosay,thecorrelationbetweenthetwosystems.Themysteriesofquantummechanicsbecomelessdenseifinterpretedinthisway,asthedescriptionoftheinformationthatphysicalsystemshaveaboutoneanother.Thedescriptionofasystem,intheend,isnothingotherthanawayofsummarizingallthepast
interactionswithit,andusingthemtopredicttheeffectoffutureinteractions.Theentireformalstructureofquantummechanicscaninlargemeasurebeexpressedintwo
simplepostulates:1
1. Therelevantinformationinanyphysicalsystemisfinite.2. Youcanalwaysobtainnewinformationonaphysicalsystem.
Here,theârelevantinformationâistheinformationthatwehaveaboutagivensystemasaconsequenceofourpastinteractionswithit:informationallowingustopredictwhatwillbetheresultforusoffutureinteractionswiththissystem.Thefirstpostulatecharacterizesthegranularityofquantummechanics:thefactthatafinitenumberofpossibilitiesexists.Thesecondcharacterizesitsindeterminacy:thefactthatthereisalwayssomethingunpredictablewhichallowsustoobtainnewinformation.Whenweacquirenewinformationaboutasystem,thetotalrelevantinformationcannotgrowindefinitely(becauseofthefirstpostulate),andpartofthepreviousinformationbecomesirrelevant,thatistosay,itnolongerhasanyeffectuponpredictionsofthefuture.Inquantummechanicswhenweinteractwithasystem,wedonâtonlylearnsomething,wealsoâcancelâapartoftherelevantinformationaboutthesystem.fn52Theentireformalstructureofquantummechanicsfollowsinlargemeasurefromthesetwosimple
postulates.Therefore,thetheorylendsitselfinasurprisingwaytobeingexpressedintermsofinformation.Thefirsttorealizethatthenotionofinformationwasfundamentaltotheunderstandingof
quantumrealitywasJohnWheeler,thefatherofquantumgravity.WheelercoinedthephraseâItfrombitâtoexpressthisidea,meaningthatâeverythingisinformationâ.Informationreappears,then,inthecontextofquantumgravity.Remember:theareaofany
surfaceisdeterminedbythespinsoftheloopwhichintersectthissurface.Thesespinsarediscretequantities,andeachonecontributestothearea.Asurfacewithafixedareamaybeformedfromtheseelementaryquantaofareainmanydifferent
ways,say,inanumberofwaysN.Ifyouknowtheareaofasurfacebutdonâtknowexactlyhowitsquantaofareaaredistributed,youhavemissinginformationaboutthesurface.Thisisoneofthewaysofcomputingtheheatofblackholes:thequantaofareaofablackholeenclosedinasurfaceofacertainareacanbeinNdifferentpossibledistributions.Itislikeforthecupoftea,inwhichthemoleculescanmoveinNdifferentpossibleways.Thuswecanassociateaquantityofmissinginformation,thatistosay,entropy,withablackhole.TheamountofinformationassociatedthuswithablackholedependsdirectlyupontheareaAof
thehole:thelargerthehole,thegreatertheamountofmissinginformation.Wheninformationentersintoablackhole,itisnolongerrecoverablefromoutside.Butthe
informationwhichenterstheblackholecarrieswithittheenergybywhichtheblackholebecomeslargerandincreasesitsarea.Viewedfromoutside,theinformationlostintheblackholenowappearsasentropyassociatedwiththeareaofthehole.ThefirsttosuspectsomethingsimilarwastheIsraeliphysicistJacobBekenstein.Butthesituationisanythingbutclearbecause,aswehaveseeninthelastchapter,blackholes
emitthermalradiationandveryslowlyevaporate,becomingsmallerandsmalleruntiltheyprobablydisappear,subsumedinthatoceanofmicroscopicblackholeswhichconstitutesspaceatthePlanckscale.Wheredoestheinformationthathasfallenintotheblackholeastheblackholeshrinksendup?Theoreticalphysicistsaredebatingthequestion,andnoonehasacompletelyclearanswer.
![Page 103: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/103.jpg)
Allofthis,Ibelieve,indicatesthatinordertograspthebasicgrammaroftheworld,weneedtomergethreebasicingredients,notjusttwo:notjustgeneralrelativityandquantummechanics,butalsothetheoryofheat,thatis,statisticalmechanicsandthermodynamics,whichwecanalsodescribeasinformationtheory.Butthethermodynamicsofgeneralrelativity,thatistosay,thestatisticalmechanicsofquantaofspace,isasyetonlyinitsfirstinfancy.Everythingisstillconfused,andthereisaverygreatdealwhichremainstobeunderstood.AllofthisbringsustothelastideaIdescribeinthisbook:thermaltime.
ThermaltimeTheproblemattherootoftheideaofthermaltimeissimple.InChapter7,Ishowedthatitisnotnecessarytousethenotionoftimetodescribephysics.Itisbettertoforgettimealtogether.Timeplaysnoroleatthefundamentallevelofphysics.Oncewehaveunderstoodthis,itiseasiertowritetheequationsofquantumgravity.Therearemanyeverydaynotionswhichnolongerhaveanyroleinthefundamentalequationsof
theuniverse;forexample,thenotionsofâupâandâdownâ,orâhotâandâcoldâ,soitisnotparticularlystrangethatsharedquotidiannotionsdisappearfromfundamentalphysics.However,oncewehaveacceptedthisidea,weobviouslyopenupasecondproblem.Howcanwerecoverthenotionsofoureverydayexperience?Howdotheyemerge,inourspecificcontext?Forexample,thenotionsofâupâandâdownâdonâtenterintoNewtonâsequations,butweknow
whattheymeaninaschemawithoutabsoluteupanddown.âUpâandâdownâaremeaningfulnearalargemass,likeaplanet.âDownâindicatesthedirectiontowardswhichthelarge,nearmassexertsgravitationalpull;âupâindicatestheoppositedirection.Thesamegoesforâhotâandâcoldâ:therearenoâhotâorâcoldâthingsatamicroscopiclevelbut,whenweputtogetheralargenumberofmicroscopicconstituentsanddescribethemintermsofaverages,thenthenotionofâheatâappears:ahotbodyisabodywheretheaveragespeedofsingleconstituentsisraised.Weareabletounderstandthemeaningofâupâorâhotâincertainsituations:thepresenceofanearbymass,orthefactthatwearedealingonlywithaveragevaluesofmanymolecules,andsoon.Somethingsimilarmustapplytoâtimeâ.Ifthenotionoftimehasnoroletoplayatanelementary
level,itcertainlyplaysasignificantroleinourlives,justasâupâandâhotâdo.Whatdoesâthepassageoftimeâmean,iftimeplaysnopartinthefundamentaldescriptionoftheworld?Theanswerissimple.Theoriginoftimemaybesimilartothatofheat:itcomesfromaveragesof
manymicroscopicvariables.Letâslookatthisindetail.Thatthereisalinkbetweentimeandtemperatureisanancientandrecurrentidea.Ifyouthink
aboutit,allphenomenawherewedetectthepassageoftimeareco-involvedwithtemperature.Thesalientcharacteristicoftimeisthatitmovesforwardsandnotbackwards,thatistosay,thereareirreversiblephenomena.Mechanicalphenomenaâonesthatdonâtinvolveheatâarereversible.Ifwefilmthemandthenrunthefilmbackwards,weseesomethingrealistic.Ifwefilmaswingingpendulum,orastonethrownupwardsthenfalling,andthenwatchthefilminreverse,westillseeaplausiblependulumswinging,orastonerisinganddroppingtotheground.Whenthestonereachestheground,itstops,youmightobject:ifyouwatchthefilmreversed,you
seeastoneleapingupfromthegroundbyitself,andthisisimplausible.Butwhenthestonereachesthegroundandstops,wheredoesitsenergygo?Itheatstheground!Attheprecisemomentwhenheatisproduced,theprocessisirreversible:thepastdiffersfromthefuture.Itisalwaysheatandonlyheatthatdistinguishesthepastfromthefuture.Thisisuniversal.Aburningcandleistransformedintosmokeâthesmokecannottransformintoa
candleâandacandleproducesheat.Aboiling-hotcupofteacoolsdownanddoesnotheatup:itdiffusesheat.Weliveandgetold:producingheat.Ouroldbicyclewearsoutwithtime:producingheatthroughfriction.Thinkofthesolarsystem.Atfirstapproximation,itcontinuestoturnlikeanimmensemechanismalwaysequaltoitself.Itdoesnâtproduceheatand,infact,ifyouwatcheditinreverseyouwouldnâtnoticeanythingstrangeaboutit.Butlookedatmoreclosely,therearealsoirreversiblephenomena:theSunisusingupitscombustiblehydrogenandwilleventuallyexhaustitandextinguish:theSun,too,isgettingolderand,infact,producesheat.TheMoonalsoappearstoorbittheEarthunchanginglyandbealwaysequaltoitself,whereasinrealityitisslowlymovingaway.Thisisbecauseitraisestides,andthetidesheattheseaalittle,thusexchangingenergywiththeMoon.Wheneveryouconsideraphenomenoncertifyingthepassageoftime,itisthroughtheproductionofheatthatitdoesso.Thereisnopreferreddirectionoftimewithoutheat.Butheatisourwaytonameaveragesovermanyvariables.Theideaofthermaltimereversesthisobservation.Thatistosay,insteadofenquiringhowtime
producesdissipationinheat,itaskshowheatproducestime.ThankstoBoltzmann,weknowthatthenotionofheatcomesfromthefactthatweinteractwith
averages.Theideaofthermaltimeisthatthenotionoftime,too,comesfromthefactthatweinteractonlywithaveragesofmanyvariables.fn53Aslongaswehaveacompletedescriptionofasystem,allthevariablesofthesystemareonthe
samefooting;noneofthemactsasatimevariable.Thatistosay:noneiscorrelatedtoirreversiblephenomena.Butassoonaswedescribethesystembymeansofaveragesofmanyvariables,we
![Page 104: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/104.jpg)
haveapreferredvariablethatfunctionslikecommontime.Atimealongwhichheatisdissipated.Thetimeofoureverydayexperience.Hencetimeisnotafundamentalconstituentoftheworld,butitappearsbecausetheworldis
immense,andwearesmallsystemswithintheworld,interactingonlywithmacroscopicvariablesthataverageamonginnumerablesmall,microscopicvariables.We,inoureverydaylives,neverseeasingleelementaryparticle,orasinglequantumofspace.Weseestones,mountains,thefacesofourfriendsâandeachofthesethingsweseeisformedbymyriadsofelementarycomponents.Wearealwayscorrelatedwithaverages.Averagesbehavelikeaverages:theydisperseheatand,intrinsically,generatetime.Thedifficultyofgraspingthisideacomesfromthefactthatitishardforustothinkofaworld
withouttime,andoftimeemerginginanapproximatemanner.Wearetoousedtothinkingofrealityasexistingintime.Wearebeingswholiveintime:wedwellintime,andarenourishedbyit.Weareaneffectofthistemporality,producedbyaveragevaluesofmicroscopicvariables.Butthelimitationsofourintuitionsshouldnotmisleadus.Understandingtheworldbetteroftenentailsgoingagainstintuition.Ifthiswerenotthecase,understandingwouldbeeasy.Timeisaneffectofouroverlookingofthephysicalmicrostatesofthings.Timeisinformationwe
donâthave.Timeisourignorance.
RealityandinformationWhydoesinformationplaysuchacentralroleasthis?Perhapsbecausewemustnotconfusewhatweknowaboutasystemwiththeabsolutestateofthesamesystem.Whatweknowissomethingconcerningtherelationbetweenthesystemandourselves.Knowledgeisintrinsicallyrelational;itdependsjustasmuchonitsobjectasuponitssubject.Thenotionoftheâstateâofasystemrefers,explicitlyorimplicitly,toanothersystem.Classicalmechanicsmisledusintothinkingthatwecoulddowithouttakingaccountofthissimpletruth,andthatwecouldaccess,atleastintheory,avisionofrealityentirelyindependentoftheobserver.Butthedevelopmentofphysicshasshownthat,attheendoftheday,thisisimpossible.Careful:whenIsaythatweâhaveinformationâaboutthetemperatureofcupoftea,orweâdonât
haveinformationâaboutthevelocityofeverysinglemolecule,Iamnotsayingsomethingaboutmentalstates,orabstractideas.Iamonlysayingthatthelawsofphysicsdetermineacorrelationbetweenourselvesandthetemperature(forinstance,Iâvelookedatathermometer),butnotbetweenourselvesandthevelocityoftheindividualmolecules.ItisthesamenotionofinformationastheoneIstartedfrominthischapter:thewhiteballinyourhandâhasinformationâaboutthefactthattheballinmyhandisblack.Weâredealingwithphysicalfacts,notmentalnotions.Aballhasinformation,inthissense,eveniftheballdoesnothavementalstates,justasaUSBstoragedevicecontainsinformation(thenumberofgigabytesprintedonthedevicetellsushowmuchinformationitcancontain),evenifaUSBstoragedevicedoesnotthink.Informationinthissenseâcorrelationbetweenstatesofsystemsâisubiquitousthroughouttheuniverse.Ibelievethatinordertounderstandrealitywehavetokeepinmindthatrealityisthisnetworkof
relations,ofreciprocalinformation,whichweavestheworld.Wesliceuptherealitysurroundingusintoobjects.Butrealityisnotmadeupofdiscreteobjects.Itisavariableflux.Thinkofanoceanwave.Wheredoesawavefinish?Wheredoesitbegin?Thinkofmountains.Wheredoesamountainstart?Wheredoesitend?HowfardoesitcontinuebeneaththeEarthâssurface?Thesearequestionswithoutmuchsense,becauseawaveandamountainarenotobjectsinthemselves;theyarewayswhichwehaveofslicinguptheworldtoapprehendit,tospeakaboutitmoreeasily.Theselimitsarearbitrary,conventional,comfortable:theydependonus(asphysicalsystems)morethanonthewavesorthemountains.Theyarewaysoforganizingtheinformationwhichwehaveor,better,formsofinformationwhichwehave.Itâsthesameforeveryobject,properlyconsidered,includinglivingorganisms.Thisiswhyit
makeslittlesensetoaskwhetherahalf-cutfingernailisstillâmeâorhasbecomeânot-meâ;orifthehairsleftonmysofabythecatarestillpartofthecat,ornot;orpreciselywhenachildâslifebegins.Achildbeginstoliveonthedaywhenapersondreamsofherforthefirsttime,longbeforeherconception,orwhensheformsherfirstself-image,orwhenshebreathesforthefirsttime,orwhensherecognizeshername,orwhenweapplyanynumberofotherconventions:theyarealluseful,butarbitrary.Theyarewaystothink,andtoorientateourselveswithinthecomplexityofreality.Alivingorganismisasystemwhichcontinuallyre-formsitselfinordertoremainitself,interacting
ceaselesslywiththeexternalworld.Ofsuchorganisms,onlythosecontinuetoexistwhicharemoreefficientatdoingsoand,therefore,livingorganismsmanifestpropertieswhichhavesuitedthemforsurvival.Forthisreason,theyareinterpretable,andweinterpretthem,intermsofintentionality,ofpurpose.Thefinalisticaspectsofthebiologicalworld(thisisDarwinâsmomentousdiscovery)arethereforetheresultoftheselectionofcomplexformseffectiveinpersisting.Buttheeffectivewayofcontinuingtoexistinachangingenvironmentistomanagecorrelationswiththeexternalworldbetter,thatistosay,information;tocollect,store,transmitandelaborateinformation.Forthisreason,DNAexists,togetherwithimmunesystems,senseorgans,nervoussystems,complexbrains,
![Page 105: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/105.jpg)
languages,books,thelibraryofAlexandria,computersandWikipedia:theymaximizetheefficiencyofinformationmanagementâthemanagementofcorrelationsfavouringsurvival.ThestatuethatAristotleseesinablockofmarbleismorethantheblockofmarble:butitisnotan
abstractformthatresidesjustinthestatue.ItissomethingresidinginthecorrelationsbetweenthemindofAristotle,orours,andthemarble;somethingthatpertainstotheinformationwhichthemarbleprovidesregardingsomethingthatissignificantforAristotle,orforus.Itissomethingregardingadiscusthrower,Phidias,Aristotleandthemarble,andresidesinthecorrelateddispositionsoftheatomsofthestatue,andthecorrelationsbetweentheseandathousandothers,inourmindsorinAristotleâs.Thesespeakofadiscusthrower,justasthewhiteballinyourhandtellsyouthattheballinmineisblack.Wearestructuredtomanagepreciselythisâinformationâandremaininexistencethankstothis.Evenfromthisbriefoverviewitshouldbeclearthatthenotionofinformationplaysacentralrole
inourattemptstounderstandtheworld.Fromcommunicationtothebasisofgenetics,fromthermodynamicstoquantummechanicsanduptoquantumgravity,thenotionofinformationisgaininggroundasatoolforunderstanding.Theworldshouldnotbeunderstoodasanamorphousensembleofatomsâbutratherasagameofmirrors,foundedonthecorrelationsbetweenthestructuresformedbycombinationsoftheseatoms.AsDemocritussaid,itisnotjustaquestionoftheseatomsbutalsooftheorderinwhichtheyare
arranged.Atomsarelikethelettersinanalphabet:anextraordinaryalphabet,sorichastobeabletoread,reflectandeventhinkaboutitself.Wearenotatoms;weareordersinwhichatomsarearranged,capableofmirroringotheratomsandmirroringourselves.Democritusgaveastrangedefinitionofâmanâ:âManiswhatweallknow.â2Atfirstsight,this
seemsrathersillyandempty,butitisnotso.SalomonLuria,themajorscholarofDemocritus,observesthatitisnotabanalitythatDemocritus
isgivingus.Thenatureofamanisnothisinternalstructurebutthenetworkofpersonal,familialandsocialinteractionswithinwhichheexists.Itisthesewhichâmakeâus,thesewhichguardus.Ashumans,wearethatwhichothersknowofus,thatwhichweknowofourselves,andthatwhichothersknowaboutourknowledge.Wearecomplexnodesinarichwebofreciprocalinformation.Allofthisisnotyetatheory.Thesearetrackswearefollowing,Ibelieve,inseekingtounderstand
theworldaroundusbetter.Therestillremainsagreatdealtounderstand.Iâllspeakofthisinthefinalchapter.
![Page 106: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/106.jpg)
13.Mystery
Thetruthisinthedepths.âDemocritus1
IâvedescribedwhatIthinkisthenatureofthingsinthelightofwhatwehavelearnedtodate.Iâvesummarizedthedevelopmentofsomekeyideasoffundamentalphysics,andIhaveillustratedthegreatdiscoveriesmadebyphysicsinthetwentiethcenturyandtheimageoftheworldemergingfromtheresearchintoaquantumtheoryofgravity.
AmIsureaboutallthis?Iamnot.OneoftheveryfirstandmostbeautifulpagesinthehistoryofscienceisthepassageinPlatoâs
PhaedoinwhichSocratesexplainstheshapeoftheEarth.SocratessaysheâbelievesâtheEarthisasphere,withgreatvalleyswheremenlive.Heâsbasically
right,ifabitconfused.Headds,âIâmnotsure.âThispageisworthmuchmorethanallofthenonsenseontheimmortalityofthesoulwhichfillstherestofthedialogue.ItisnotjusttheoldesttexttocomedowntouswhichspeaksexplicitlyofthefactthattheEarthmustbespherical.Moreimportantly,itshineswiththecrystallineclaritywithwhichPlatoacknowledgesthelimitsoftheknowledgeofhistime.âIâmnotsure,âsaysSocrates.
Thisacuteawarenessofourignoranceistheheartofscientificthinking.Itisthankstothisawarenessofthelimitsofourknowledgethatwehavelearnedsomuch.Wearenotcertainofallwhichwesuspect,justasSocrateswasnotsureofthesphericalnatureoftheEarth.Weareexploringatthebordersofourknowledge.
Awarenessofthelimitsofourknowledgeisalsoawarenessofthefactthatwhatweknowmayturnouttobewrong,orinexact.Onlybykeepinginmindthatourbeliefsmayturnouttobewrongisitpossibletofreeourselvesfromwrongideas,andtolearn.Tolearnsomething,itisnecessarytohavethecouragetoacceptthatwhatwethinkweknow,includingourmostrootedconvictions,maybewrong,oratleastnaĂŻve:shadowsonthewallsofPlatoâscave.
Scienceisbornfromthisactofhumility:nottrustingblindlyinourpastknowledgeandourintuition.Notbelievingwhateveryonesays.Nothavingfaithintheaccumulatedknowledgeofourfathersandgrandfathers.Welearnnothingifwethinkthatwealreadyknowtheessentials,ifweassumethattheywerewritteninabookorknownbytheeldersofthetribe.Thecenturiesinwhichpeoplehadfaithinwhattheybelievedwerethecenturiesinwhichlittlenewwaslearned.Hadtheytrustedtheknowledgeoftheirfathers,Einstein,NewtonandCopernicuswouldneverhavecalledthingsintoquestionandwouldhaveneverbeenabletomoveourknowledgeforwards.Ifnoonehadraiseddoubts,wewouldbestillworshippingpharaohsandthinkingthattheEarthissupportedonthebackofagiantturtle.Evenourmostefficaciousknowledge,suchasthatfoundbyNewton,mayeventuallyturnout,asEinsteinshowed,tobesimplistic.
Scienceissometimescriticizedforpretendingtoexplaineverything,forthinkingthatithasananswertoeveryquestion.Itâsacuriousaccusation.Aseveryresearcherworkingineverylaboratorythroughouttheworldknows,doingsciencemeanscominguphardagainstthelimitsofyourignoranceonadailybasisâtheinnumerablethingswhichyoudonâtknow,andcanâtdo.Thisisquitedifferentfromclaimingtoknoweverything.WedonâtknowwhichparticleswemightseenextyearatCERN,orwhatournexttelescopeswillreveal,orwhichequationstrulydescribetheworld;wedonâtknowhowtosolvetheequationswehave,andsometimeswedonâtunderstandwhattheysignify;wedonâtknowifthebeautifultheoryonwhichweareworkingisright.WedonâtknowwhatthereisbeyondtheBigBang;wedonâtknowhowastormworks,orabacterium,oraneyeâorthecellsinourownbodies,orourthoughtprocesses.Ascientistissomeonewholivesimmersedintheawarenessofourdeepignorance,indirectcontactwithourowninnumerablelimits,withthelimitsofourunderstanding.
Butifwearecertainofnothing,howcanwepossiblyrelyonwhatsciencetellsus?Theanswerissimple.Scienceisnotreliablebecauseitprovidescertainty.Itisreliablebecauseitprovidesuswiththebestanswerswehaveatpresent.Scienceisthemostweknowsofarabouttheproblemsconfrontingus.Itispreciselyitsopenness,thefactthatitconstantlycallscurrentknowledgeintoquestion,whichguaranteesthattheanswersitoffersarethebestsofaravailable:ifyoufindbetteranswers,thesenewanswersbecomescience.WhenEinsteinfoundbetteranswersthanNewton,hedidnâtquestionthecapacityofsciencetogivethebestpossibleanswersâonthecontrary,heconfirmedit.
Theanswersgivenbyscience,then,arenotreliablebecausetheyaredefinitive.Theyarereliablebecausetheyarenotdefinitive.Theyarereliablebecausetheyarethebestavailabletoday.Andthey
![Page 107: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/107.jpg)
arethebestwehavebecausewedonâtconsiderthemtobedefinitive,butseethemasopentoimprovement.Itâstheawarenessofourignorancethatgivesscienceitsreliability.
Anditisreliabilitythatweneed,notcertainty.Wedonâthaveabsolutecertainty,andneverwillhaveitâunlessweacceptblindbelief.Themostcredibleanswersaretheonesgivenbyscience,becausescienceisthesearchforthemostcredibleanswersavailable,notforanswerspretendingtocertainty.
Thoughrootedinpreviousknowledge,scienceisanadventurebasedoncontinuouschange.ThestoryIhavetoldreachesbackovermillennia,tracinganarrativeofsciencethathastreasuredgoodideasbuthasnâthesitatedtothrowideasawaywhensomethingwhichworksbetterwasfound.Thenatureofscientificthinkingiscritical,rebelliousanddissatisfiedwithaprioriconceptions,withreverenceandsacredoruntouchabletruth.Thesearchforknowledgeisnotnourishedbycertainty:itisnourishedbyaradicaldistrustincertainty.
Thismeansnotgivingcredencetothosewhosaytheyareinpossessionofthetruth.Forthisreason,scienceandreligionfrequentlyfindthemselvesonacollisioncourse.Notbecausesciencepretendstoknowultimateanswersbutpreciselyfortheoppositereason:becausethescientificspiritdistrustswhoeverclaimstobetheonehavingultimateanswers,orprivilegedaccesstoTruth.Thisdistrustisfoundtobedisturbinginsomereligiousquarters.Itisnotsciencewhichisdisturbedbyreligion:therearecertainreligionsthataredisturbedbyscientificthinking.
Toacceptthesubstantialuncertaintyofourknowledgeistoacceptlivingimmersedinignoranceand,therefore,inmystery,toacceptlivingwithquestionstowhichwedonotknowtheanswers.Perhapswedonâtknowthemyetorâwhoknows?âweneverwill.
Tolivewithuncertaintymaybedifficult.Therearethosewhopreferanycertainty,evenifunfounded,totheuncertaintywhichcomesfromrecognizingourownlimits.Therearesomewhoprefertobelieveinastoryjustbecauseitwasbelievedbythetribeâsancestorsratherthanbravelytoacceptuncertainty.
Ignorancecanbescary.Outoffear,wecantellourselvescalmingstories:uptherebeyondthestars,thereisanenchantedgarden,withagentlefatherwhowillwelcomeusintohisarms.Itdoesnâtmatterifthisistrue,itisreassuring.
Thereisalways,inthisworld,someonewhopretendstotellustheultimateanswers.TheworldisfullofpeoplewhosaythattheyhaveTheTruth.Becausetheyhavegotitfromthefathers;theyhavereaditinaGreatBook;theyhavereceiveditdirectlyfromagod;theyhavefounditinthedepthsofthemselves.ThereisalwayssomeonewhohasthepresumptiontobethedepositoryofTruth,neglectingtonoticethattheworldisfullofotherdepositoriesofTruth,eachonewithhisownrealTruth,differentfromthatoftheothers.Thereisalwayssomeprophetdressedinwhite,utteringthewords,âFollowme,Iamthetrueway.â
Idonâtcriticizethosewhoprefertobelieveinthis:weareallfreetobelieveinwhateverwewant.Maybe,afterall,thereisagrainoftruthinthejokereportedbyStAugustine:WhatwasGoddoingbeforecreatingtheworld?HewaspreparingHellforthosewhoseektoscrutinizedeepmysteries.2ButthesedeepmysteriesarepreciselytheâdepthsâinwhichDemocritus,inthequotethatopensthischapter,invitesustoseekthetruth.
Formypart,Iprefertolookourignoranceintheface,acceptitandseektolookjustabitfurther:totrytounderstandthatwhichweareabletounderstand.Notjustbecauseacceptingthisignoranceisthewaytoavoidbeingentangledinsuperstitionsandprejudicesâbutbecausetoacceptourignoranceinthefirstplaceseemstometobethetruest,themostbeautifuland,aboveall,themosthonestway.
Toseektolookfurther,togofurther,seemstometobeoneofthesplendidthingswhichgivessensetolife.Likeloving,orlookingatthesky.Thecuriositytolearn,todiscover,tolookoverthenexthill,thedesiretotastetheapple:thesearethethingswhichmakeushuman.AsDanteâsUlyssesremindshiscompanions,wearenotmadeâtolivelikebrutes,buttoseekvirtueandknowledgeâ.
Theworldismoreextraordinaryandprofoundthananyofthefablestoldbyourforefathers.Iwanttogoandseeit.Toacceptuncertaintydoesnâtdetractfromoursenseofmystery.Onthecontrary:weareimmersedinthemysteryandthebeautyoftheworld.Theworldrevealedbyquantumgravityisanewandstrangeoneâstillfullofmystery,butcoherentwithitssimpleandclearbeauty.
Itisaworldwhichdoesnotexistinspaceanddoesnotdevelopintime.Aworldmadeupsolelyofinteractingquantumfieldstheswarmingofwhichgeneratesâthroughadensenetworkofreciprocalinteractionsâspace,time,particles,wavesandlight(figure13.1)
Itcontinues,itcontinues,teeminglife,anddeathTenderandhostile,clearandunknowable.
Andthepoetgoeson:Somuchtheeyecansee,fromthiswatchingtower.3
Aworldwithoutinfinity,wheretheinfinitelysmalldoesnotexist,becausethereisaminimumscaletothisteeming,beneathwhichthereisnothing.Quantaofspaceminglewiththefoamofspacetime,andthestructureofthingsisbornfromreciprocalinformationwhichweavesthe
![Page 108: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/108.jpg)
correlationsbetweentheregionsoftheworld.Aworldwhichweknowhowtodescribewithasetofequations.Perhaps,tobecorrected.
Figure13.1Anintuitiverepresentationofquantumgravity.
Itâsavastworld,withmuchstilltoclarifyandexplore.Itâsmyfondestdreamthatsomeoneâoneoftheyoungerreadersofthisbook,Ihopeâwillbeabletovoyageacrossitandilluminateitbetter.Beyondthenexthillthereareworldsstillmorevast,stilltobediscovered.
![Page 109: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/109.jpg)
Notes
1.Grains1OnAnaximanderandtheMilesians,seeCarloRovelli,TheFirstScientist:AnaximanderandHisLegacy,trans.MarionLignanaRosenberg(Yardley,Westholme,2007).
2TheMilesianoriginofLeucippusisgiven,forinstance,bySimplicius(seeM.Andolfo,Atomistiantichi.Frammentietestimonianze(AncientAtomism.FragmentsandTestimonies),(Milan,Rusconi,1999),p.103.Butitisnotcertain.ThereferencetoMiletusandtoEleaissignificantinrelationtohisculturalroots;thedebtLeucippusowedtoZenoofEleaisdiscussedinthefollowingpages.
3Seneca,Naturalesquestiones,VII,3,2d.4Cicero,Academicapriora,II,23,73.5SextusEmpiricus,Adversusmathematicos,VIII,135(trans.R.G.BuryAgainsttheProfessors),(LoebClassicalLibrary,1989).
6SeeAristotle,OnGenerationandCorruption,A1,315b6,inTheCompleteWorksofAristotle,Vol.I,ed.JonathanBarnes(Princeton,PrincetonUniversityPress,1984).
7AcollectionofancientfragmentsandtestimonieswhichspeakofatomismisgiveninM.AndolfoâsAncientAtomists.AcompleteanthologyoffragmentsandtestimoniesconcerningDemocritushasbeenpublishedbySolomonLuria.(SeeentryâDemocritusâinthebibliographyforanEnglishalternative.)
8ForabriefandinterestingrecentworkonthethoughtofDemocritus,placingitinthecontextofhumanism,seeS.Martini,Democrito:filosofodellanaturaofilosofodellâuomo?(Democritus:PhilosopherofNatureorPhilosopherofMan?),(Rome,Armando,2002.)
9Plato,Phaedo,ed.DavidGallup(Oxford,OxfordUniversityPress,2009),XLVI.10RichardFeynman,TheFeynmanLecturesonPhysics,Vol.1,eds.RobertLeightonandMatthewSands(London,BasicBooks,2011).
11SeeAristotle,OnGenerationandDecay,A2,316a,inTheCompleteWorksofAristotle,Vol.I,ed.JonathanBarnes(Princeton,PrincetonUniversityPress,1984).
12AgoodrecentaccountofZenoâsparadoxes,andoftheirphilosophicalandmathematicalrelevance,isgivenbyVincenzoFanoinIparadossidiZenone(ZenoâsParadoxes),(Rome,Carocci,2012).
13Amores(LovePoems),I,15,23â4.14Lucretius,OntheNatureoftheUniverse,trans.E.A.Latham,(Harmondsworth,Penguin,1951),p.173
15Ibid.,p.89.16Ibid.,p.2717Ibid.,p.60.18GuidoCavalcanti,Rime.,trans.LeonardCottrell.19ForanaccountoftherediscoveryofLucretiusâstextanditsimpactuponEuropeanculture,seeStephenGreenblatt,TheSwerve:HowtheWorldBecameModern(NewYork,Norton,2011).
20SeeM.Camarota,âGalileo,LucretiusandAtomismâ,inF.CittiandM.Beretta(eds.),Lucrezio,lanaturaelascienza(Lucretius,NatureandScience),(Florence,LeoS.Olshki,2008),pp.141â75.
21SeeR.Kargon,AtomisminEnglandfromHariottoNewton(Oxford,OxfordUniversityPress,1966).
22WilliamShakespeare,RomeoandJuliet,1.4,55â60,CompleteWorks,eds.JonathanBateandEricRassmussen(London,Macmillan/TheRoyalShakespeareCompany,2007),p.1690.
23OnTheNatureoftheUniverse,pp.63â4.24PiergiorgioOdifreddihaspublishedafinetranslationofandcommentaryonLucretiusâstext,designedforuseinschools.(Comestannolecose.IlmioLucrezio,lamiaVenere(TheNatureofThings.MyLucretius,MyVenus),(Milan,Rizzoli,2013).Itwouldbewonderfulifschoolsadoptedthisbookandifthisextraordinarytextwasmorewidelyknown.Areadingofthetext,andofitsauthor,diametricallyopposedtoOdifreddiâsisgivenbyV.E.AlfieriinLucrezio(Lucretius),(Florence,LeMonnier,1929)andemphasizesthepoignant,poeticqualitiesofthework,derivingfromthemanoblebutbitterinterpretationofthecharacterofLucretius.
25H.DielsandW.Kranz,eds.,DieFragmentederVorsokratiker(ThePresocratics:Fragments),(Berlin,Weidmann,1903),68b247.
![Page 110: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/110.jpg)
2.TheClassics1OnthevalueofAristotleâsphysics,seeC.Rovelli,âAristotleâsPhysics:APhysicistâsLookâ,inJournaloftheAmericanPhilosophicalAssociation,1(2015),pp.23â40.
2IamblichusofChalchis,Summapitagorica(Milan,Bompiani,2006).ForanEnglishtranslation,seeIamblichus,LifeofPythagoras,trans.ThomasTaylor(Vermont,InnerTraditionsInternational,1986).
3IsaacNewton,Opticks(1704),(NewYork,Dover,1979),p.400.4GiacomoLeopardi,TheCanti,withaSelectionofHisProse,trans.J.G.Nichols(NewYork,Routledge,2003),p.53.
5IsaacNewton,LetterstoBentley(Montana,Kessinger,2010).CitedinH.S.Thayer,NewtonâsPhilosophyofNature(NewYork,Hafener,1953),p.54.
6Ibid.7MichaelFaraday,ExperimentalResearchesinElectricity(London,BernardQuaritch,1839â55),3vols.,pp.436â7.
3.Albert1Simplicius,AristotelisPhysica(AristotleâsPhysics),28,15.2A.Calaprice,DearProfessorEinstein.AlbertEinsteinâsLetterstoandfromChildren(NewYork,PrometheusBooks,2002),p.140.
3TheletterisquotedinA.FĂślsing,Einstein:ABiography(London,Penguin,1998),p.337.4F.P.DeCeglia(ed.)ScienziatidiPuglia:secoliVaC.-XXI,dC,Parte3(ScientistsofPuglia:FromtheFifthCenturyBCtotheTwentiethCenturies,Part3)(Bari,Adda,2007),p.18.
5A.Calaprice,DearProfessorEinstein.AlbertEinsteinâsLetterstoandfromChildren(NewYork,PrometheusBooks,2002),p.208.
4.Quanta1AlbertEinstein,âĂbereinendieErzeugungundVerwandlungdesLichtesbetreffendenGesichtspunktâ,AnnalenderPhysik,17,pp.132â48.
2ForabiographyofDiracwhichillustrateshisdisconcertingpersonality,seeGrahamFarmelo,TheStrangestMan:TheHiddenLifeofPaulDirac,QuantumGenius(London,Faber,2009).
3Lucretius,OntheNatureoftheUniverse,trans.E.A.Latham,(Harmondsworth,Penguin,1951),II,218.
4Foradiscussionofthisrelationalinterpretationofquantummechanics,seeâRelationalQuantumMechanicsâintheonlineStanfordEncyclopediaofPhilosophy,http://plato.stanford.edu/archives/win2003/entries/rovelli,orCarloRovelli,âRelationalQuantumMechanicsâ,inInternationalJournalofTheoreticalPhysics,35,1637,1996,http://arxiv.org/abs/quant-ph/9609002.
5BasvanFrassen,âRovelliâsWorldâ,inFoundationsofPhysics,40,2010,390â417;MichelBitbol,PhysicalRelationsorFunctionalRelations?ANon-metaphysicalConstrualofRovelliâsRelationalQuantumMechanics,PhilosophyofScienceArchives,2007,http://philsci-archive.pitt.edu/3506/;MauroDorato,RovelliâsRelationalQuantumMechanics,MonismandQuantumBecoming,PhilosophyofScienceArchives,2013,http://philsci-archive.pitt.edu/9964/,andChecosâèiltempo?Einstein,GĂśdelelâesperienzacommune(WhatisTime?Einstein,GĂśdelandSharedExperience),(Rome,Carocci,2013).
5.SpacetimeisQuantum1TheworkonthemeasurabilityoffieldsbyNielsBohrandLeonRosenfeldisâDetKongelikeDanskeVidenskabernesSelskabsâ,inMathematiks-fysikeMeddelelser,12,1933.
2SeeMatveiBronĹĄtejn,âQuantentheorieschwacherGravitationsfelderâ,inPhysikalischeZeitschriftderSowjetunion,9,1936,140â57;andâKvantovaniegravitatsionnykhvolnâ,inPiâsmavZhurnalEksperimentalânoiITeoreticheskoiFiziki,6,1936,195â236.
3SeeF.GorelikandV.Frenkel,MatveiPetrovichBronsteinandSovietTheoreticalPhysics(Boston,BirkhauserVerlag,1994).âBronsteinâwasalsotherealsurnameofTrotsky.
4TheepisodeisrecalledbyBryceDeWitt,http://www.aip.org/history/ohilist/23199.html.
7.TimeDoesNotExist1Lucretius,OntheNatureoftheUniverse,trans.E.A.Latham,(Harmondsworth,Penguin,1951),p.41.
2WilliamShakespeare,AMidsummerNightâsDream,5.1,23â7,RSCedition,p.403.
8.BeyondtheBigBang
![Page 111: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/111.jpg)
1ThespeechcanbefoundontheVaticanwebsite:http://www.vatican.va/holy_father/pius_xii/speeches/1951/documents/hf_p-xii_spe_19511122_di-serena_it.html#top.
2SeeS.Singh,BigBang(London,HarperCollins,2010),p.362.
12.Information1AdetaileddiscussionofthesetwopostulatescanbefoundinCarloRovelli,âRelationalQuantumMechanicsâ,inInternationalJournalofTheoreticalPhysics,35,1637,1996,http://arxiv.org/abs/quant-ph/9609002.
2Cicero,Academicapriora,II,23,73.
13.Mystery1CitedinDiogenesLaertius,LivesofEminentPhilosophers,2vols.,(NewYork,Loeb,1989).2StAugustine,Confessions,XI,12(Harmondsworth,Penguin,2002).3MarioLuzi,Dallatorre,inDalfondodellecampagne(Turin,Einaudi)p.214.
![Page 112: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/112.jpg)
AnnotatedBibliography
Andolfo,Matteo,Atomistiantichi.Frammentietestimonianze(AncientAtomism.FragmentsandTestominies),Milan,Rusconi,1999.
Aristotle,OnGenerationandCorruption,inTheCompleteWorksofAristotle,Vol.I.Ed.JonathanBarnes,Princeton,PrincetonUniversityPress,1984.TheprincipalworkbyAristotlewhichprovidesinformationonthethoughtofDemocritus.
Bitbol,Michel,PhysicalRelationsorFunctionalRelations?ANon-metaphysicalConstrualofRovelliâsQuantumMechanics.PhilosophyofScienceArchives,2007,http://philsci-archive.pitt.edu/3506/.CommentaryonandKantianinterpretationofrelationalquantummechanics.
Baggott,Jim,TheQuantumStory:AHistoryinFortyMoments.NewYork,OxfordUniversityPress,2011.Agoodandcompletereconstructionofthemainstagesinthedevelopmentofquantummechanics,fromitsorigintothepresentday.
Bojowald,Martin,OnceBeforeTime:AWholeStoryoftheUniverse.NewYork,AlfredA.Knopf,2010.Anexplanatorydescriptionoftheapplicationofloopquantumgravitytotheoriginoftheuniverseâbyoneofthefirstscientiststouseitinthisway.Includesanaccountoftheso-calledâBigBounceâoftheuniverse,whichmayhavehappenedbeforetheBigBang.
Calaprice,Alice(ed.),DearProfessorEinstein.AlbertEinsteinâsLetterstoandfromChildren.NewYork,PrometheusBooks,2002.AdelightfulcollectionoflettersexchangedbetweenEinsteinandseveralchildren.
Democritus,Raccoltadeiframmenti(CollectedFragments).InterpretationandCommentarybyS.Luria.Trans.It.Milan,Bompiani,2007.ThereisnoEnglishtranslationofthisclassicedition.
Democritus,TheAtomists:LeucippusandDemocritus.Fragments.AtextandtranslationwithcommentarybyC.C.W.Taylor.Toronto,TorontoUniversityPress,1999.Diehls,H.andKranz,W.(eds),DieFragmentederVorsokratiker.Berlin,Weidmann,1903.Theclassiccollection,inthreevolumes,oftheâfragmentsâofthePresocratics.
Dorato,Mauro,Checosâèiltempo?Einstein,GĂśdelelâesperienzacommune.Rome,Carocci,2013.Preciseandcompletediscussion,centredaroundspecialrelativity,oftheEinsteinianmodificationoftheconceptoftime.
â,RovelliâsRelationalQuantumMechanics,MonismandQuantumBecoming.PhilosophyofScienceArchives,2013,http://philsci-archive.pitt.edu/9964/.DiscussionbyanItalianphilosopherofinterpretationsofquantummechanics.
Fano,Vincenzo,IparadossidiZenone.Trans.It.Rome,Carocci,2012.AnexcellentstudywhichhighlightsthetopicalityoftheproblemsposedbyZenoâsparadoxes.
Farmelo,Graham,TheStrangestMan:TheHiddenLifeofPaulDirac,QuantumGenius.London,Faber,2009.AnextensivebuthighlyreadableaccountofthelifeandbafflingcharacterofthegreatestphysicistafterEinstein.
Feynman,Richard,TheFeynmanLecturesonPhysics,eds.RichardB.LeightonandMatthewSands(3vols.).London,BasicBooks,2011.EssentialphysicstextbookdrawnfromthelecturesofthegreatestAmericanphysicist.Theyarebrilliant,original,lively,theproductofanoutstandingintelligence.Nostudentofphysicswhoistrulyinterestedinscienceshouldfailtoreadthem.
FĂślsing,Albrecht,AlbertEinstein:ABiography.NewYork,Penguin,1998.ExtensiveandcompletebiographyofEinstein.
Gorelik,GennalyE.andFrenkel,Victor,MatveiPetrovichBronsteinandSovietTheoreticalPhysicsintheThirties.Boston,BirkhauserVerlag,1994.HistoricalstudyofBronĹĄtejn,theyoungRussianwhoinitiatedresearchinquantumgravityandwasexecutedbyStalin.
Greenblatt,Stephen,TheSwerve:HowtheWorldbecameModern.NewYork,W.W.Norton,2011.AbookwhichreconstructstheinfluenceoftherediscoveryofLucretiusuponthebirthofthemodernworld.
Heisenberg,Werner,PhysicsandPhilosophy:TheRevolutioninModernScience.NewYork,Harper&Row,1962.Thetrueoriginatorofquantummechanicsreflectsongeneralproblemsofphilosophyandscience.
Kumar,Manjit,Quantum:Einstein,BohrandtheGreatDebateabouttheNatureofReality.London,IconBooks,2009.Afineexplanatory,detailedreconstructionofthebirthofquantummechanicsand,aboveall,ofthelongdialoguebetweenBohrandEinsteinonthemeaningofthenewtheory.
![Page 113: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/113.jpg)
Lucretius,OnTheNatureoftheUniverse(Dererumnatura),trans.R.E.Latham.Harmondsworth,Penguin,1951.Thewonderfulpoemfromwhichweknowtheideasandspiritofancientatomism.
Newton,Isaac,ATreatiseoftheSystemoftheWorld.London,F.Fayram,1731.Alittle-knownworkbyNewtoninwhichhegiveshistheoryofuniversalgravityinamuchlesstechnicalformthaninhisgreattreatise(Principia).
Odifreddi,P.,Comestannolecose.IlmioLucrezio,lamiaVenere.Milan,Rizzoli,2013.TranslationwithextensivecommentaryofLucretiusâspoem.Anidealschooltextbook.
Plato,Phaedo,ed.DavidGallop.Oxford,OxfordUniversityPress,2009.Theoldestextanttexttospeakexplicitlyaboutthesphericalnatureoftheearth.
Rovelli,Carlo,âAristotleâsPhysics:APhysicistâsLookâinJournaloftheAmericanPhilosophicalAssociation,1(2015)23â40.
â,SevenBriefLessonsonPhysics,trans.SimonCarnellandEricaSegre.London,AllenLane,2015.Aconciseguidethroughthescientificrevolutionthatshookphysicsinthetwentiethcenturyandstillcontinuestoshakeustoday.
â,TheFirstScientist:AnaximanderandHisLegacy,trans.MarionLignanaRosenberg.Yardley,Westholme,2007.AreconstructionoftheideasofAnaximanderâoneofthegreatestscientistsofalltimeâandtheirinfluenceonthedevelopmentofscience.Thebookisalsoareflectiononthebirthandnatureofscientificthinking:itsdistinctivecharacter,itsdifferencefrommythicalthinking,itslimitationsandstrength.
â,âQuantumGravityâ,inButterfield,J.andEarman,J.(eds.),HandbookofThePhilosophyofScience,PhilosophyofPhysics.Amsterdam,Elsevier/North-Holland,2007,pp.1287â330.Alongarticleaimedatphilosophers,withadetaileddiscussionofthecurrentstateofquantumgravity,ofitsunresolvedproblemsandthevariousapproachestothem.
â,QuantumGravity.Cambridge,CambridgeUniversityPress,2004.Technicalmanualonquantumgravity.Definitelynotrecommendedforanyonewithoutabackgroundinphysics.
â,âRelationalQuantumMechanicsâinTheStanfordEncyclopaediaofPhilosophy,http://plato.stanford.edu/archives/win2003/entries/rovelli/.Synthesisoftherelationalinterpretationofquantummechanics.
â,âRelationalQuantumMechanicsâinInternationalJournalofTheoreticalPhysics,35(1996),1637,http://arxiv.org/abs/quant-ph/9609002.Thearticlewhichfirstintroducesthetheoryofrelationalquantummechanics.
Smolin,Lee,ThreeRoadstoQuantumGravity.NewYork,BasicBooks,2002.Anintroductiontoquantumgravityanditsopenquestions.
VanFraassen,Bas.âRovelliâsWorldâinFoundationsofPhysics,40(2010),390â417.Adiscussionofrelationalquantummechanics,byanimportantanalyticphilosopher.
![Page 114: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/114.jpg)
![Page 115: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/115.jpg)
THEBEGINNINGLettheconversationbeginâŚ
FollowthePenguinTwitter.com@penguinUKbooks
Keepup-to-datewithallourstoriesYouTube.com/penguinbooks
PinâPenguinBooksâtoyourPinterest
LikeâPenguinBooksâonFacebook.com/penguinbooks
ListentoPenguinatSoundCloud.com/penguin-books
FindoutmoreabouttheauthoranddiscovermorestorieslikethisatPenguin.co.uk
![Page 116: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/116.jpg)
ALLENLANEUK|USA|Canada|Ireland|AustraliaIndia|NewZealand|SouthAfricaAllenLaneispartofthePenguinRandomHousegroupofcompanieswhoseaddressescanbefoundatglobal.penguinrandomhouse.com
FirstpublishedinItalianunderthetitleLarealtà nonècomeciapparebyRaffaelloCortinaEditoreSpA2014ThistranslationfirstpublishedinGreatBritainbyAllenLane2016CopyrightŠRaffaelloCortinaEditoreSpA,2014TranslationcopyrightŠSimonCarnellandEricaSegre,2016ThemoralrightoftheauthorandtranslatorshasbeenassertedCovercredit:CoralieBickford-SmithISBN:978-0-241-25797-5
![Page 117: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/117.jpg)
fn1Intechnicalterms,thereareconverginginfinitesums.Fortheexampleofthestring,theinfinitesum½+Âź+1â8+1â16âŚconvergesto1.InfiniteconvergentsumswerenotunderstoodinZenoâstime.Archimedesunderstoodthemafewcenturieslater,andusedthemtocalculateareas.Newtonusedthemheavily,butnotuntilthenineteenthcentury,withBolzanoandWeierstrass,wasconceptualclarityonthesemathematicalobjectsachieved.Aristotle,however,hadalreadyunderstoodthatthiswasapossiblewaytoanswerZeno;theAristoteliandistinctionbetweenactualinfinityandpotentialinfinityalreadycontainsthekeyidea:thedifferencebetweentheabsenceofalimittodivisibility,andthepossibilityofhavingalreadydividedsomethinganinfinitenumberoftimes.
![Page 118: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/118.jpg)
fn2HereisthelistofalloftheworksofDemocritus,withtheirtitlesasgivenbyDiogenesLaertius:GreatCosmology;LittleCosmology;Cosmography;OnthePlanets;OnNature;OnHumanNature;OnIntelligence;OntheSenses;OntheSoul;OnFlavours;OnColour;OnDiverseMovementsoftheAtoms;OfChangesinShape;TheCausesofCelestialPhenomena;TheCausesofAtmosphericPhenomena;OnFireandOnThingsinFire;TheCausesofAcousticPhenomena;ConcerningtheMagnet;TheCausesofSeeds,PlantsandFruits;OnAnimals;ADescriptionoftheSky;Geography;ADescriptionofthePole;OnGeometry;GeometricalReality;OntheTangentsoftheCircleandtheSphere;Numbers;OnIrrationalLinesandSolids;Projections;Astronomy;AstronomicalTable;OnRaysofLight;OnReflectedImages;OnRhythmandHarmony;OnPoetry;OntheBeautyofSong;OnEuphonyandCacophony;ConcerningHomer,oronCorrectEpicDiction;TheScienceofMedicine;OnAgriculture;OnWords;OnNames;OnValues,orOnVirtue;OntheDispositionwhichCharacterizestheWise;OnPainting;ATreatiseonTactics;CircumnavigationoftheOcean;OnHistory;TheThoughtofChaldea;TheThoughtofthePhrygians;OntheSacredWritingsofBabylon;OntheSacredWritingsofMeroe;OnFeversandtheCoughsDerivingfromIllness;OnAporiae;LegalQuestions;Pythagoras;OnLogic,orCriterionofThought;Confirmations;PointsofEthics;OnWell-being.AlllostâŚ
![Page 119: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/119.jpg)
fn3ThebadreputationofAristotelianphysicsdatesbacktothepolemicsofGalileo.Galileohadtomoveforwardandthereforeneededtobecritical.HeattackedAristotleviciously,withscornandsarcasm.ButhetookAristotleâsphysicsveryseriously.fn4(x=½at²).fn5Thesquareoftheperiodofrevolutionisproportionaltothecubeoftheradiusoftheorbit.Thislawwasshowntobecorrectnotonlyfortheplanetsorbitingthesun(Kepler),butalsoforthemoonsofJupiter(Huygens).Newtonassumes,byinduction,thatitshouldalsoholdforthehypotheticallittlemoonorbitingtheEarth.Theconstantofproportionalitydependsonthebodyaroundwhichtheorbitismade:thisiswhydataonthelunarorbitallowustocomputetheperiodofthelittlemoon.fn6a=v²/r,wherevisthespeedandrtheradiusoftheorbit.fn7Theenergyreleasedbycombustionenginesischemicalandtherefore,ultimately,electromagnetic.fn8TheequationsfillapageinMaxwellâsoriginaltreatise.Todaythesameequationscanbewritteninhalfaline:dF=0,d*F=J.Weâllsoonseewhy.fn9Ifyouvisualizethefieldasavector(anarrow)ateachpointofspace,thepointofthearrowindicatesthedirectionoftheFaradaylines,thatistosay,thetangentoftheFaradaylines,andthelengthofthearrowisproportionaltothedensityoftheFaradaylines.
![Page 120: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/120.jpg)
fn10Thesetofeventsataspace-likedistancefromareferenceevent.fn11Theastutereaderwillobjectthatthehalfwaymomentofmyquarterofanhourcanbeconsideredsimultaneoustoyourreply.ThereaderwhohasstudiedphysicswillrecognizethatthisisâEinsteinâsconventionâfordefiningsimultaneity.ThisdefinitionofsimultaneitydependsonhowImove,andconsequentlydoesnotdefinesimultaneitybetweentwoeventsbutonlyasimultaneityrelativetothestateofmovementofparticularbodies.Infigure3.3adotishalfwaybetweenaandb,thepointsatwhichIexitfromthepastoftheobserverandenterhisfuture.Theotherdotishalfwaybetweeneandd,thepointsatwhichIexitfromthepastoftheobserverandenterintohisfutureifImovealongadifferenttrajectory.Bothdotsaresimultaneousasregardsthereader,accordingtothisdefinitionofâsimultaneityâ,buttheyoccurinsuccessivetimes.Thetwodotsareeachsimultaneoustothereader,butrelativetotwodifferentmotionsofmine.Hencethetermârelativityâ.fn12Airplaneandballfollowageodesicinacurvedspace.Inthecaseoftheball,thegeometryisapproximatelygivenbythemetricds²=(1â2ÎŚ(x))dt²âdx²,whereÎŚ(x)istheNewtonianpotential.Theeffectofthegravitationalfieldisreducedtothedilationoftimewithaltitude.(Thereaderfamiliarwiththetheorywillnoticethecurioussigninversion:thephysicaltrajectorymaximizespropertime.)fn13ObservationsofthebinarysystemPSRB193+16showthatthetwostarswhichrevolvearoundoneanotherradiategravitationalwaves.TheseobservationsbroughtaNobelPrizeforRussellHulseandJosephTaylorin1993.fn14Plutarch,Adversuscolotem,4,1108.ThewordĎĎĎΚνmeansânatureâ,andincludesthesenseâthenatureofsomethingâ.fn15Thistermiscalledâcosmologicalâbecauseitseffectsoccuronlyatanextremelylarge,orâcosmologicalâdistances.TheconstantÎiscalledtheâcosmologicalconstantâ,anditsvaluewasmeasuredattheendofthe1990s,bringingaNobelPrizein2011fortheastronomersSaulPerlmutter,BrianP.SchmidtandAdamG.Riess.fn16GĂśttingen,whereHilbertworked,wasatthistimetheseatofthemostimportantschoolofgeometry.fn17AsphereisthesetofpointsinR3determinedbytheequationx2+y2+z2=1.The3-sphereisthesetofpointsinR4determinedbytheequationx2+y2+z2+u2=1.fn18IthasbeenobjectedthatDantespeaksofâcirclesâandnotofâspheresâ.Buttheobjectionisinvalid.BrunettoLatiniwritesofâacircle,liketheshellofaneggâ.Thewordâcircleâ,forDante,asforhisteacherandmentor,designateseverythingwhichiscircular,includingspheres.fn19OnthesurfaceoftheEarth,forinstance,theNorthPoleandtwopointsontheequatorcanmakeatrianglewiththreesidesofequallengthandthreerightanglesâsomethingwhichclearlycannotbedoneonaplane.
![Page 121: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/121.jpg)
fn20AHilbertspace.fn21Thesearetheeigenvaluesoftheoperatorassociatedwiththephysicalvariableinquestion.Thekeyequationistheeigenvalueequation.fn22Thiscloudisdescribedbyamathematicalobjectcalledwavefunction.TheAustrianphysicistErwinSchrĂśdingerhaswrittenanequationdescribingitsevolutionintime.Quantummechanicsisoftenmistakenlyidentifiedwiththisequation.SchrĂśdingerhadhopesthattheâwaveâcouldbeusedtoexplaintheodditiesofquantumtheory:fromthoseoftheseatoelectromagneticones,wavesaresomethingweunderstandwell.Eventoday,somephysiciststrytounderstandquantummechanicsbythinkingthatrealityistheSchrĂśdingerwave.ButHeisenbergandDiracunderstoodatoncethatthiswouldnotdo.ToviewSchrĂśdingerâswaveassomethingrealistogiveittoomuchweightâitdoesnâthelpustounderstandthetheory;onthecontrary,itleadstogreaterconfusion.Exceptforspecialcases,theSchrĂśdingerwaveisnotinphysicalspace,andthisdivestsitofallitsintuitivecharacter.ButthemainreasonwhySchrĂśdingerâswaveisabadimageofrealityisthefactthat,whenaparticlecollideswithsomethingelse,itisalwaysatapoint:itisneverspreadoutinspacelikeawave.Ifweconceiveanelectronasawave,wegetintroubleexplaininghowthiswaveinstantlyconcentratestoapointateachcollision.SchrĂśdingerâswaveisnotausefulrepresentationofreality:itisanaidtocalculationwhichpermitsustopredictwithsomedegreeofprecisionwheretheelectronwillreappear.Therealityoftheelectronisnotawave:itishowitmanifestsitselfininteractions,likethemanwhoappearedinthepoolsoflamplightwhiletheyoungHeisenbergwanderedpensivelyintheCopenhagennight.fn23Diracâsequation.fn24Thereisaphenomenonwhichseemsnottobereducibletothestandardmodel:âdarkmatterâ.Astrophysicistsandcosmologistsobserveintheuniverseeffectsofmatterwhichseemsnottobethetypeofmatterdescribedbythestandardmodel.Outthere,therearestillmanythingsthatwedonâtknow.fn25IfindtheclaimthattheHiggsbosonâexplainsmassâexaggerated.TheHiggsbosondoesnotâexplainâanythingabouttheoriginofmass.WhatwouldâexplainâthemassoftheHiggs?Thepointistechnical:thestandardmodelreliesoncertainsymmetries,andthesesymmetriesseemedtopermitonlyparticlesdevoidofmass.ButHiggsandothersrealizedthatitispossibletohavebothsymmetriesandmass,aslongasthelatterentersindirectlyviatheinteractionwiththefieldknowntodayastheHiggsfield.fn26Afiniteregionofthephasespaceâthespaceofthepossiblestatesofasystemâcontainsaninfinitenumberofdistinguishableclassicstates,butalwaysonlyafinitenumberoforthogonalquantumstates.Thisnumberisgivenbythevolumeoftheregion,dividedbythePlanckconstant,raisedtothenumberofdegreesoffreedom.Thisresultisgeneral.fn27OrFeynmanâsintegral.TheprobabilityofgoingfromAtoBisthesquaremoduleoftheintegraloverallthepathsoftheexponentialoftheclassicalactionofthetrajectory,multipliedbytheimaginaryunitanddividedbyPlanckâsconstant.fn28Amechanismintheboxopensthesmallwindowontherightforaninstant,allowingaphotontoescapeatsomeprecisetime.Byweighingthebox,itispossibletodeducetheenergyofthereleasedphoton.Einsteinhopedthatthiswouldcreatedifficultiesforquantummechanics,whichpredictsthattimeandenergycannotbebothpreciselydetermined.Bohrreplied,mistakenly,thatthewayoutofthedifficultyrequiredEinsteinâsgeneralrelativity,andEinstein,mistakenly,acceptedBohrâsreply.ThecorrectresponsetoEinstein,whichBohrwasunabletofindbutthatiscleartoday,isthatthepositionoftheescapingphotonandtheweightoftheboxremaintiedtoeachother(âcorrelatedâ),evenifthephotonisalreadyfaraway.
![Page 122: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/122.jpg)
fn29ThemarkonthehofPlanckâsconstantservesonlytoindicatethatPlanckâsconstantisinthisequationdividedby2Ď,aratheruselessandidiosyncraticadditionbytheoreticalphysicists:placingthesmall,hard,angularmarkonthehâmakesitelegantâ.fn30Tohearthismetaphordirectlyinhisownvoice,gotothesitehttp://www.webofstories.com/play/9542?o=MS.fn31DeWittreplacesderivativeswithderivativeoperatorsintheHamiltonâJacobiequationforgeneralrelativity(writtenalittlewhileearlierbyPeres).Thatis,hedoeswhatSchrĂśdingerhaddonetowritehisequation,inhisfirstwork:replacingderivativeswithderivativeoperatorsintheHamiltonâJacobiequationofaparticle.fn32OrtheâEinsteinâSchrĂśdingerâequation.fn33Thebestknownalternativetoloopquantumgravityisstringtheory,whosemainconcernisnotsomuchstudyingthequantumpropertiesofspaceandtime,butratherwritingaunifiedtheoryofallknownfields,anobjectivethatmightbeprematuregivencurrentknowledge.
![Page 123: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/123.jpg)
fn34Theeigenvalueequationforthevolumeoperator.fn35Hencethequantumstatesofgravityareindicatedwith|jl,vn>,wherenindicatesthenodesandlthelinksofthegraph.fn36ImaginewhatanonsensicalhotchpotchtheideasofAristotleandPlatowouldseemifweonlyhadthecommentariesonthemwrittenbyothersandwereunabletoaccessthelucidityandcomplexityoftheoriginaltexts!fn37ThequantumnumberofthestatesofphotonsinFockâsspaceisthemomentum,Fourierâstransformationofposition.fn38Theoperatorassociatedwiththegeometryofgranularspaceistheholonomyofthegravitationalconnections,orrather,inphysicalterms,aâWilsonloopâofgeneralrelativity.
![Page 124: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/124.jpg)
fn39Thegravitationalpotential.fn40x(t)=½at².fn41EspeciallysincehehadbecomeexcitedâŚfn42Theactualstructureoftheverticesofthespinfoamisabitmorecomplexthantheoneinfigure7.2,andresemblesmorecloselytheoneshowninfigure7.4.fn43ItâsaFeynmandiagrambecauseitisahistoryofquanta,asintheFeynmandiagrams.Exceptthatnow,thequantaarenotquantamovinginspace,butratherquantaofspace.Thegraphtheydrawintheirinteractionsisnotarepresentationofthemovementofparticlesinspace,butrepresentstheplotofspaceitself.Buttheresultingpictureisalsopreciselyalatticeliketheoneusedinthelatticeapproximation,becauseitrepresentsadiscretizedspacetime.Withthedifferencethatitisnolongeranapproximation,buttherealdiscretestructureofspaceatasmallscale.fn44ThefirstdefinestheHilbertspaceofthetheory.Theseconddescribesthealgebraoftheoperators.Thethirddescribesthesizeoftransitionofeachvertex,suchastheoneshowninfigure7.4.fn45â[âŚ]allthedifferentelementaryparticlescouldbereducedtooneuniversalsubstancewhichcouldequallybecalledenergyormatter,andnoneoftheparticlesshouldbeprivilegedandconsideredmorefundamental.ThispointofviewcorrespondstoAnaximanderâsdoctrine,andIamconvincedthatinmodernphysicsthisisthecorrectpointofview.âWernerHeisenberg,PhysicsandPhilosophy:TheRevolutioninModernScience(NewYork,Harper&Row,1962).
![Page 125: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/125.jpg)
fn46Thisisaninterferometer:itusestheinterferencebetweenthelaserswhichrunalongthetwoarmstorevealtheminutevariationsinlengthofthesearms.
![Page 126: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/126.jpg)
fn47TheEcclesiasticusisconsideredpartoftheBiblebyCatholics,mostoftheOrientalOrthodoxChurchandsomeJews.TheLutheranchurchesincludeitintheirlectionaries,andasabookproperforreading,devotionandprayer,butnotintheBible.FormostJewsand.theAnglicanChurchthesituationissimilar.
![Page 127: Carlo Rovelli - Web Education](https://reader035.fdocuments.net/reader035/viewer/2022062301/62a5202d9405ff44931b43e7/html5/thumbnails/127.jpg)
fn48Asubtlepoint:informationdoesnâtmeasurewhatIknowbutthenumberofpossiblealternatives.TheinformationIamgivenwhenthenumber3comesupinrouletteisN=37,becausethereare37numbers;buttheinformationIhavewhennumber3winsonredisN=18,becausethereare18rednumbers.HowmuchinformationdowehaveifwelearnwhichofthebrothersKaramazovmurderedtheirfather?TheanswerdependsonhowmanyKaramazovbrothersthereare.fn49Boltzmanndidnotusetheconceptofinformation,buthisworkcanbereadinthisway.fn50Entropyisproportionaltothelogarithmofthevolumeofthephasespace.Theconstantofproportionality,k,isBoltzmannâsconstant,whichtransformstheunitsofmeasurementforinformation(bits)intotheunitsofmeasurementforentropy(Kelvinâsjoules).fn51Inafiniteregionofitsphasespace.fn52Thisiswhatcametobecalled,inappropriately,theâcollapseâofthewavefunction.fn53Hereishowitworkstechnically:aBoltzmannstatisticalstateisdescribedbyafunctiononphasespacegivenbytheexponentialoftheHamiltonian.TheHamiltonianisthegeneratoroftimeevolution.Inasysteminwhichtimeisnotdefined,thereisnoHamiltonian.Butifwehaveastatisticalstate,wejusttakeitslogarithmandthisdefinesaHamiltonian,andhenceanotionoftime.