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LostinMath?J.Butterfield,TrinityCollege,CambridgeUK:jb56@cam.ac.uk

Saturday2February2019

ReviewforPhysicsinPerspectiveof:LostinMath:HowBeautyLeadsPhysicsAstray,bySabineHossenfelder.BasicBooks2018.ISBN:978-0-465-09425-7,304pages,$17.99(hardcover)Abstract:ThisisareviewofHossenfelder’sbook,LostinMath:HowBeautyLeadsPhysicsAstray.Thebookgivesabreezyexpositionofthepresentsituationinfundamentalphysics,andraisesimportantquestions:bothaboutthecontentofthephysics,andthewayphysicsresearchisorganized.Ifirststatemymaindisagreements.Then,Imostlypraisethebook:IconcentrateonHossenfelder’sdiscussionofsupersymmetry,naturalnessandthemultiverse.

1.IntroductionThisbook(Hossenfelder2018)isanengagingpopularaccountofthepresentsituationinfundamentalphysics.Itisalsoastrongcritiqueofthatsituation.AllcredittoSabineHossenfelderforwritingabookwhich---whilepersonal,indeedpassionate---isunpretentiousandhumorous.SheisatheoreticalphysicistinFrankfurt,whoalsowritesanexcellentblogaboutphysicsat:http://backreaction.blogspot.co.uk.Thusthebookiswritteninabreezystyle.Itisbothanessayonthepresentsituationinfundamentalphysics,andamemoirofhertravelsinrecentyears,conductingextendedinterviewswithaboutadozenphysicists,includingforexample:NimaArkani-Hamed,GeorgeEllis,GordyKane,GarrettLisi,KeithOlive,JoePolchinski,StevenWeinbergandFrankWilczek.Theirremarksarereproducedinextenso,interweavedwithHossenfelder’sthoughts.Theseareoftenappealinglyironicand-orself-deprecating.Forexample,whenPolchinskicomplimentsherbysaying:‘Ithinkyouhavetriedveryhardtoseparatebetweenideasthatsoundlikegoodideasandideasthatdonotseemlikegoodideas…It’sanimportantthingtodo.It’sreallythankless,though,becausethenumberofbadideasincreasesmuchmorerapidlythanthenumberofgoodideas...’;Hossenfelderadds:‘ThisispossiblythenicestwayI’veeverbeentoldI’mstupid’(p.177).Inshort,thebookisengaging,easytoread,andgivesvividexplanationsoftheissues:asIwilltrytoconveywithsomequotes.Andofcourse,theviewsoftheseintervieweesareboundtobeinteresting,especiallytoreadersofthisjournal.Hossenfelder’scriticismsofthepresentsituationinphysicsfallintotwomaingroups.Thefirstgroupconcernsthecontentofrecentproposalsinfundamentalphysics;thesecond,theprofessionalandinstitutionalorganizationofphysics.Hossenfelderdevotesmostofthebooktothefirstgroup.Here,sheemphasizessupersymmetry,naturalnessandthemultiverse.Sheseesallthreeaswrongturnsthatphysicshasmade;andashavingacommonmotivation---thepursuitofmathematicalbeauty.Hencehersub-title.Shediscussesthesecondgroupof

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criticismsattheendofthebook,alongwithrecommendationsabouthowwecould,andshould,changeourways.Iwillfollowsuit.Iwillemphasizethefirstgroup,especiallysupersymmetry,naturalnessandthemultiverse(Sections3to9).IwillturnonlyinthefinaltwoSections(10and11)totheorganizationofphysics.ButIbeginbyregisteringmymaindisagreementswithher(Section2).

2.DisagreementsIampersuadedbymuchofwhatHossenfeldersays.Insomeways,thisisunsurprising.Foronemainthemeofhersecondgroupofcriticismsisthatresearchinfundamentalphysicsconcentratesundulyonafewproblemsandresearchprogrammes,andshouldinsteadbemorediverse;anditiseasytoagreetothat.Also,onemainthemeofherfirstgroupofcriticismsisthatthepresentdifficulties,evendefects,offundamentalphysicsarepartlyduetoacavalierattitudetosomephilosophicalissues,suchasconfirmationandexplanation.Beingaphilosopher,Iofcoursefinditeasytoagreetothat.Butaseveryoneknows:youcannotexpectaphilosopher(orabook-reviewer)toagreecompletely.ThusIhavetwomainkindsofdisagreement:thefirstisgeneral,thesecondspecificallyaboutbeauty.Ingeneral,peopleareboundtodifferinhowtheyweighthemerits---theachievementshitherto,andthefutureprospects---ofagivenresearchprogramme;evenwhentheyareexpertswithmatchingknowledgeoftheprogramme’stechnicalities.Andsoalso,asregardscomparingthemeritsofdifferentresearchprogrammes.Similarly,forthemeritsofgeneral‘framework’ideaslikenaturalness,asagainstfully-fledgedresearchprogrammes.Andsimilarlyforopenproblems:peopleareboundtodifferabouttheirmerits,i.e.abouthowfruitfulitwouldbetonowaddresstheproblem.ThusforallthatHossenfeldersays:oneundoubtedlycouldmountarobustanddetaileddefenceofsome(perhapsall?)oftheprogrammesandideasshecriticizes.Forexample,considersupersymmetry.Aswewillsee,Hossenfelder’smaincriticismofsupersymmetryis,inshort,thatitisadvocatedbecauseofitsbeauty,butisunobserved.Butevenifsupersymmetryisnotrealizedinnature,onemightwelldefendstudyingitasaninvaluabletoolforgettingabetterunderstandingofquantumfieldtheories.Asimilardefencemightwellbegivenforstudyingstringtheory.Infact,Hossenfelderdoesnotgiveanextendeddiscussionofstringtheory.AsIsaid,shefocusesonsupersymmetry,naturalnessandthemultiverse;andforthefirstofthese,shestressessupersymmetryinextensionsofthestandardmodel,notinstringtheory.Agreed:shedoesintermittentlymentionstringtheory’slackofempiricalconfirmationandthebeautyofitsmathematics;andshebrieflyquotespractitionerssaying,sometwentyorthirtyyearsago,thatitsbeautysuggestsit‘hadtobepointingtosomethingdeep’(thusJohnSchwarz,onp.189).ButIthink

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manypractitioners,especiallynowadays,wouldnotmotivatestringtheorybyappealingtobeauty.Indeed,allagreethatitisaverycomplicatedframeworkwithmanydifferenttypesoffields,gaugegroups,symmetriesetc.(Seebelowonhowjudgmentsofbeautyarehistoricallyconditionedandfallible.)Rather,theywouldappealtomanytechnicalfeatures:suchashowitsvariousintellectualtechnologies(mostlyrootedinquantumfieldtheory)enableone(i)todomanycalculationsofobviousrelevancetoquantumgravity,e.g.aboutblackholes,and(ii)toaddresslong-standingissues,suchasimprovingtheultra-violetbehaviourofgravity.Orconsiderthecosmologicalmultiverse.Here,Hossenfelder’smaincriticismis,Ithink,notsimplythatthemultiverseisunobservable:thatis,theotherpocketuniverses(domains)apartfromourownareunobservable.Thatis,obviously,‘builtin’totheproposal;andsocanhardlycountasaknock-downobjection.Thecriticismis,rather,thatwehaveverylittleideahowtoconfirmatheorypostulatingsuchamultiverse.Towhichthereplywillbethat,agreed,itisfearfullydifficulttodoso:buttherearevariousideasintheliteratureabouthowtodoso,andsooneshouldjustdiveinandassess,andtrytoimprove,them.Inparticular,weshouldrecognizethatalthoughsomecosmologistsarecavalieraboutwhatconfirmationofamultiversewouldamountto:manyothersshowareflectiveandnuancedengagementwiththequestion,andrelatedphilosophicalissueslikeexplanation.Sophilosophers,andotherreadersofthisbook,shouldresistinferringthatthecosmologycommunityasawholeneeds,sotospeak,totakeacourseinphilosophyofscience.Thereisawealthofconceptual,indeedphilosophical,discussionbypractitionersthatisnotonlyclear-headedbutalsoinventive.Myspecificdisagreementisaboutbeauty:i.e.thecriticismstatedbythesub-title,thatthepursuitofmathematicalbeautyhasledphysicsastray.Butforclarity,Ishouldbeginwithanagreement.Hossenfelderisnotconcernedwithindividual,perhapsidiosyncratic,judgmentsofbeauty(orofrelatedideas,likeeleganceandsimplicity):butrather,withjudgmentscommontoascientificcommunity.Andrightlyso:itissuchcommunaljudgments,notindividualones,thatplayasignificantroleinchoosingwhichscientifictheorytoendorseortopursue.Thisisonereasonwhyitisnothelpfultolabelappealstobeautyas‘subjective’.RecallKuhn’swiseremarksabouttheperilsofthisword(1977,pp.333f.).Incidentally,hisessay’smainpointisthatthecriteriafortheorychoiceusuallyinvoked---Kuhnlistsfive:accuracy,broadscope,consistency(bothinternalandwithothertheories),simplicityandfruitfulness---cannotbeparlayedupintoaprecisealgorithmforchoosingtheories.Forscientistsareboundtodifferinhowtomakethempreciseinanysingleapplication,andinhowtoweighthemwhentheyconflict.Thatissurelytrue.Anditisofcoursethebasisofmyfirst,general,disagreementwithHossenfelder:sincepeopleareboundtodiffer,therecanbenodefinitivereasonstorejectresearchprogrammes,suchasstringtheory,orframeworkideas,suchassupersymmetry.ButIdisagreewithHossenfelderaboutwhatthephysicscommunitytakestheheuristicroleofjudgmentsofbeauty(andofrelatedideas,likeelegance)tobe.

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Aswewillsee(Section4),shearguesconvincinglythatsuchjudgments:(i)arestronglyinfluencedbyhistory,especiallybywhathasbeensuccessfulinpasttheories;and(ii)arethoroughlyfallible.SoIthinkthosewhoappealtobeautyinphysicaltheorizingmustadmittheselimitations;asmust,indeed,anyonewhoconsidersthetopic.Buthere’stherub---howIdisagreewithHossenfelder.Ialsothinkadvocatesofbeautyasaheuristicdoadmittheselimitations.Theyadvocatenomorethanahistoricallyconditioned,andfallible,heuristic.(Recallmycommentthatstringtheoristsagreetheirtheoryiscomplicated,anditsmeritslargelytechnical.)Inshort,IthinkHossenfelderinterpretsphysicistsasmoregung-ho,morenaïve,thatbeautyisaguidetotruththantheyreallyare.Butenoughofthesecavils.Thisisapopularbook,notanacademicone.Soitcanseemnit-pickingformetoemphasizethattheprogrammesandideascriticizedhaveplentytosayintheirdefence.Ofcoursetheydo.AndIdonotdoubtthatHossenfelder,inanacademicmodusoperandi,wouldconcedethatsuchdefenceshaveweight:thoughofcourse,howmuchweightisadelicate,detailedandinevitablycontroversial,affair.Sohavingregisteredmydisagreements,Iwillfromnowonenterthespiritofthebook---startingwithhowHossenfeldersketchesthepresentsituationinphysics.

3.Hasphysicslostitsway?ThebackgroundtoHossenfelder’saccusation,thatfundamentalphysicshaslostitsway,willbefamiliar.Inthelastfortyyearswehavesuccessfullyappliedthebasicframeworksofquantumfieldtheoryandgeneralrelativityinregimesfarbeyondthoseforwhichtheywereoriginallyconceived.Here‘farbeyond’meansseveralordersofmagnitudeinsomerelevantscalesuchasdistance,energyorfield-strength.Totakejustoneexamplefromsomethirtyyearsago:recallthe1993Nobelprize,awardedtoTaylorandHulse.Theiranalysisofdatafromabinarypulsartestedgeneralrelativityforgravitationalfields10,000timesstrongerthanthesolarsystemtests---andconfirmedittosometendecimalplaces.Theoverallresultofthisandmanysimilartriumphsisironic.Namely,thatnow,thesegreatframeworktheories,quantumfieldtheoryandgeneralrelativity,arevictimsoftheirownsuccess.Forweneedtogobeyondthem,sincetheyfacevarioustechnicalandconceptualproblems:suchasthehierarchyandcosmologicalconstantproblems.Butweareindireneedofcluesabouthowtodoso.Thusitisoftensaid(includinginthisbook)thatweneeddatathatshowssome‘chinkinthearmour’ofthesetheories:someempiricalmismatchthatenablesustogetabridgeheadformakingfurtherprogress.Andthesizeoftheparticleacceleratorsthatnowseemtobeneededtogatheranysuchdataissoenormousastomakethemastronomicallyexpensive.Indeed,‘astronomically’canherebeunderstoodliterally:Hossenfeldermentions(p.178)thattoreachPlanckian

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energiesdirectly(i.e.withthecurrentframeworkforacceleratordesign)wewouldneedanacceleratoraboutthesizeoftheMilkyWay.Andwearealsoindireneedofconceptualclues.ThestandardillustrationhereishowthenullresultoftheMichelson-Morleyexperimentpresagedspecialrelativity’sabandonmentofabsolutesimultaneity.Moreprecisely,toregisterthefactthattheresultseemsnottohaveinfluencedEinstein:thenullresultcouldhavebeenusedassuchaclue.Soperhapsthepresentsituationissimilar.Maybesomeempiricalfactscrucialtosolvingtoday’smainproblemsarealreadytohand,butourcurrentconceptualoutlookpreventsusrecognizingthem. Theseobstacles,bothempirical(financial!)andconceptual,tomakingprogressinfundamentalphysics,getrehearsedinthebook,bybothHossenfelderandherinterviewees.Ithinktheywouldbeacknowledgedbyanyoneconsideringthepresentstateofphysics.Soacasecanbemadethatinthelastfortyyears,fundamentalphysicshasgotstuck.Butevenifthatisright:itisonethingtobestuck,andanotherthingtobelost.Onecanbestuck---stationaryandunabletomove---withouthavingtakenawrongturn.YetHossenfelderarguesthatphysicshasindeedtakenawrongturn.AsIannouncedinSection1,shemakestwokindsofcriticism.First:thementionedobstacleshavepromptedamistakenappealtobeauty,andrelatedideaslikesimplicity,asacriterionforselectingphysicaltheories.Andsecond:theprofessionalandinstitutionalorganizationofphysicshasgoneawry.Hossenfeldermakesagood,thoughpolemical,case.Soitisgoodnewsthatthebookendswithsuggestionsabouthowweshouldmendourways.Althoughthebook’sinterviewsandChapterstendtominglethesetwogroupsofcriticisms,thefirstgetsmoredetailedattentionandmorepages.AndIshallemphasizethefirst:whichisanywaymuchclosertophilosophy,myhomeground.SoinSections4to9,Iwilldiscussthisfirstgroup,emphasizingthethreetopics:supersymmetry,naturalness,andthemultiverse.Thisgroupofcriticismsleadsintothesecond,aboutthesocialorganizationofphysics:whichIdiscussinSections10and11.Finally,Iwillendorsesomeofthebook’sclosingsuggestionsabouthowwecould,andshould,‘dobetter’.

4.ThedangersofbeautyItisofcoursesensible,evenmandatory,thatwhenwedonothaveenoughevidencetodecidebetweenrivaltheories,wemustuseothercriteria.Andthereisastrongtraditionthatphysicistsshouldseekbeautyand-orsimplicityintheirequations:adesideratumthatsome,suchasDirac(p.25),prizedveryhighly.Besides,inapproachinganintractablephysicsproblem,evenatamuchhumblerlevelthanthatofDiracandhisilk,itisoftenagoodideatoseeksomeelegantorsimpleformulation.Therearecountlesselementaryexamples,suchasusingasymmetrytoreducethenumberofvariablesinaproblem,andfindingnormalcoordinates.

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Ontheotherhand,whatcountsasbeautiful,simpleorelegantseemstobeintheeyeofthebeholder,inphysicsasmuchasineverydaylife.Atleast,thisseemstrueasregardsjudgmentsofthesefeaturesforgeneraltheoriesasagainstindividualphysicsproblems.Thatis:suchjudgmentsarestronglyinfluencedbyhistory,i.e.bywhathasbeensuccessfulinpasttheories---orpastattemptsattheories.Indeed,Hossenfelderbringsup(inherinterviewswithWeinbergandWilczek:pp.128and152)thatthephilosopherJamesMcAllister(1999)arguedthatscientificrevolutionsoverturnscientists’conceptionsofwhatcountsasbeautiful,elegantetc.intheirscience.WeinbergandWilczeksaytheyaresympathetictothisview---astheysurelyshouldbe.Acloselyrelatedpointisthatwhatfactscountasneedinganexplanationisstronglyinfluencedbyhistoricalcircumstances.AnexamplewhichWeinberghimselfrecalls(p.110)isKepler’sendeavourtoexplaintherelativesizesoftheplanets’orbitsbyinterpolatingPlatonicsolidsbetweenthem:sizesthatwenowacceptashistoricalaccidentsofhowthesolarsystemhappenstohaveevolved,withoutanyexplanationingeneraltheory.Exampleslikethisdrivehomethelessonthatalthoughwemightselectatheory(orsomethingmorepreliminary:anattemptatatheory)byitsbeautyorelegance—especiallyifwelackevidenceforit!---wemustinhonestyadmitthatanysuchjudgmentofbeautyetc.hasthreegreatlimitations.Namely:(i)itisverymuch‘byourlights’;(ii)itisfallible;and(iii)ithasnological,orinanywaysecure,connectionwiththetheorybeingtrue.TheselimitationswillrecurinthefollowingSections.Inshort,thelessonis:bewareoftheslogan‘toogoodnottobetrue’.Bewaretemptation.Accordingtothecurrentpopularimageoffundamentalphysics,theobviouschoiceofatargetforthiswarningisstringtheory,withitslackofempiricalconfirmationand(alleged!)beauty.Thusitwasthetargetofrecentbooks,whichwillbefamiliartoreadersofthisjournal:Smolin’sTheTroublewithPhysics(2006)andWoit’sNotEvenWrong(2006).ButasIreportedinSection2,Hossenfelderdiscussesstringtheoryonlybriefly.Sheandherintervieweesfocusonthreeothertargets---supersymmetry,naturalnessandthemultiverse:thoughtheyeachfeatureinstringtheory,theyalsofigureprominentlyoutsideit.Astosupersymmetry,whichisafamilyofsymmetriestransposingfermionsandbosons:themainpointisnotmerelythatitisunobserved.Rather,itisunobservedattheenergiesrecentlyattainedattheLHCatwhich---oneshouldnotsay:‘itwaspredictedtobeobserved’;butsotospeak---‘wewouldhavebeenpleasedtoseeit’.ThiscautiouschoiceofwordsreflectstheconnectiontoHossenfelder’ssecondtarget:naturalness,orinanotherjargon,fine-tuning.Moreprecisely,theselabelsareeachother’sopposites:naturalnessis,allegedly,avirtue:andfine-tuningistheviceofnotbeingnatural.Themainconnectionbetweensupersymmetryandnaturalness,expoundedbyHossenfelder,concernsthemassoftheHiggsboson.Thereisintricateadvancedphysicshere,whichHossenfelderexplainswellinvariouspassages.Butbefore

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turningtothatinSection7,Iwillconsidernaturalnessingeneralterms,inthenexttwoSections.

5.ThreekindsofnaturalnessNaturalnessis,Isubmit,aclusterofideas,ratherthanasingleone.Iwillarticulatethemasatrio:inorderofincreasingprecision---andperhapsplausibility.Ofcourse,Imakenospecialclaimformytrio:onemightwellexplicateanddisambiguate‘naturalness’differently.Fordetailedphilosophicaldiscussion,IrecommendWilliams(2015,especiallySections3,4;2018).Thesecondofthesepapersdevelopsmycontrastin(iii)belowbetweentypicalityashavingmoderateorhigherprobability,andasbeinginsensitivetothedetailsof(usuallyunknown)higher-energyphysics.Thesecondpaperalsorelatesnaturalnesstomythirdtheme,themultiverse.Inanycase:myconstrualofnaturalnessasatriorunsasfollows.(i)Againstcoincidence:Thereshouldbesomeexplanationofthevalueofafundamentalphysicalparameter.Examplesofsuchparametersarethechargeofanelectron,orrelatedlythefinestructureconstant.Thesearetraditionalexamples,owingnotleasttoEddington’sfamous---ornotorious---speculativeefforts(whichhecalled‘FundamentalTheory’)toprovidesuchexplanations.ThecontemporaryexamplethatHossenfelderconcentrateson(thankstoitsconnectionwithSUSY)isthemassoftheHiggsboson(cf.Section5).Butwhatevertheexample,theideahereis:thevalueshouldnotbea‘brutefact’,ora‘merematterofhappenstance’,ora‘numericalcoincidence’.(ii)Againstdifference:Thevalueofafundamentalphysicalparametershouldnotbeanarithmeticaldifferenceoftwootherphysicallysignificantnumbersthatarenearlyequalbutbothvastlylargerinmagnitudethantheparameteritself.

Forexample:imagineatheoreticalframeworkinwhichthechosenparameterpis10-6.Andimaginethisis‘because’(i.e.because,accordingtothisframework!)pisthedifferenceoftwoothernumbers,qandr,withsomephysicallysignificantinterpretations,thatarenearlyequalbutbothvastlylargerthanp:e.g.withvalues106+10-6and106.(Ofcourse,asHossenfelderexplains(pp.64-65):sincethevalueofaparameterusuallydependsonahumanchoiceofunits,thenumbers10-6etc.citedhereneedtobesuitablydimensionless.)

Sotheframeworkmakesthevalueofourchosenparameterpfine-tuned.Itisextremelysensitivetotheexactvaluesoftheseothernumbersqandr:inmyexample,sensitivetotheirthirteenthdigit.Hadqandrbeenslightlydifferent(intermsofproportionsoftheiractualvalues),thenp’svaluewouldhavebeenvastlydifferent(proportionately)fromitsactualvalue.

Thisidea,(ii),isclearlyaspecialcaseof(i).Forthevalueofpbeingsuchadifferenceisonewayforittobeanumericalcoincidence.Inotherwords:thepresumedtheoreticalframework,withitsequationp=q–r,givesonlyanunsatisfactorilyfragilederivationofp’svalue,notarobustexplanationofit.AndaswewillseeinSection7,contemporaryphysicsgivesadramaticexampleof

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thisuncomfortablesituation.ForthemassoftheHiggsbosonisjustsuchaparameterp:butwiththeexponent6replacedby14!Thatis:themassisadifferenceoftwonumbersthat,writtenindecimalnotation,matchintheirfirstfourteendigits,andthendifferinthefifteenthdigit.

Notefinallythatthisidea,(ii),isalsoaspecialcaseinanotherregard.Forarithmeticaldifferenceisofcoursejustonewayforourchosenparameterptobeasuspiciouslysensitive---afine-tuned---functionofsomeothernumbers.Thisleadstothemoregeneralideain(iii).(iii)Fortypicality:Thevalueofafundamentalphysicalparametershouldbetypical,insomeprecisesensedefinedbyanappropriatetheoreticalframework.

Physicsprovidestwooverallschemesforunderstandingthisideaoftypicality;Hossenfelderdiscussesboth.

Oneisgeneral,andhaslongbeenendemicinmanybranchesofphysics.Namely:thereshouldbeaprobabilitydistributionoverthepossiblevaluesoftheparameter,andtheactualvalueshouldnothavetoolowaprobability.Thisconnectsofcoursewithorthodoxstatisticalinference.There,itisstandardpracticetosaythatifaprobabilitydistributionforsomevariableishypothesized,thenobservingthevalueofavariabletolie‘inthetailofthedistribution’---tohave‘alowlikelihood’(i.e.lowprobability,conditionalonthehypothesisthatthedistributioniscorrect)---disconfirmsthehypothesisthatthedistributionisthecorrectone:i.e.thehypothesisthatthedistributiontrulygovernsthevariable.Thisschemeforunderstandingtypicalityseemstome,andsurelymostinterestedparties---betheyphysicistsorphilosophers---sensible,perhapsevenmandatory,aspartofscientificmethod.Agreed:questionsremainabout:

(a)howfarunderthetailofthedistribution---howmuchofanoutlier---anobservationcanbewithoutdisconfirmingthehypothesis,i.e.withoutbeing‘atypical’;

(b)howingeneralweshouldunderstand‘confirm’and‘disconfirm’,e.g.whetherinBayesianorintraditional(Neyman-Pearson)terms;andrelatedly

(c)whethertheprobabilitydistributionissubjectiveorobjective;ormoregenerally,whatprobabilityreallymeans.Butthesequestionsarenotspecifictofundamentalphysics.SoIwillnotpursuethemhere,andnordoesHossenfelder.Butthisisnottosuggestthattheyareeasy,orthatthey‘canbesafelylefttothephilosophers’.AttheendofthisSection,andagaininSection8(aboutthemultiverse),weshallseequestions(a)and(c)returntohauntus.

Thesecondschemeforunderstandingtypicalityisspecific,andofrecentvintage.Itdevelopedaspartoftheeffectivefieldtheory‘vision’thatcamefromKenWilson’sdeepre-thinkingofrenormalizationgroupflow.Itendeavourstounderstandaparameter’svaluebeingsensitiveorinsensitivetootherparameters’values,intermsofthevalues’functionaldependences---andsoapparentlywithoutregardtoprobability.AsHossenfelderexplains(pp.42-48):weenvisageaspaceoftheories,whereeachtheoryisidentifiedby,roughlyspeaking,thesetofparameterssuchascouplingconstantsthatoccurinitsLagrangian(orHamiltonian).Onethenimaginesproceedingalongacurveinthespaceoftheories,fromtheoriesdescribinghigh-energy,short-distance,physicstotheoriesdescribinglow-energy,long-distance,physics.Thisisdone,ineffect,

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byintegratingoutsuccessivelymorehigh-energymodesofthefields.Traversingsuchacurveiscalled‘followingtherenormalizationgroupflow’.Thequestionarises:dothecurves,alongwhichoneproceeds,divergeorconverge?

Iftheydiverge,thatmeansthatsmalldifferencesintheparametersofthehigh-energytheoryonestartedfromengenderlargedifferencesintheparametersofthelow-energytheoryonearrivesat.Thatis:divergencemeansthelow-energyphysics,i.e.thephysicswecannowobserve,isextremelysensitivetothevaluesofparametersdescribinghigh-energyphysics,i.e.thephysicswecannotnow,andmightnever,observe.Sodivergencemeansfine-tuning:badnews.Convergence,ontheotherhand,wouldmeanthatthevaluesofparametersdescribinglow-energyphysicsarerobusttovariationsinhigh-energyphysics.Thissuggeststhevaluesare‘notacoincidence’:goodnews.

Isaidthatmylist,(i)to(iii),wouldproceedinorderofincreasingprecision,andperhapsplausibility.Itisclearthat(i)isvague,andperhapsunpersuasive.Thepointhereisnotjustthat,afterall,explanationhastocometoanendsomewhere.Thereisalsoamorespecificpoint.Someone(likemyself)whofollowsDavidHumeintakinglawsofnaturetobewhatHumecalled‘constantconjunctions’---i.e.contingentglobalpatternsofco-instantiationofproperties---acceptsthatanyexplanation,evenwhenitappealstosomethingasfundamentalaslawsofnature,endsinwhatareultimately‘just’brutefacts,ormattersofhappenstance.Ofcoursepeopledifferinhoweasilytheyacceptthatexplanationmustterminateinthissortofway.Buttospeakformyself,asaHumean:Iamcontent. HereIcanmakecommoncausewithHossenfelder---inpart.ForthisHumeancognitivemodesty,thisacceptanceoflimitstoarationalistunderstandingofnature,mesheswellofcoursewithsomeofwhatshesaysinhercritiqueofpursuingbeauty.Namely,whensheurges(cf.Section4)thatrationalist,evenapriori,speculationslikeEddington’s‘FundamentalTheory’beingbeautiful(orelegantetc.)givesusnoreasontobelievethemtobetrue.ButthisreturnsustomyseconddisagreementinSection2.ForIthinkthegreatmajorityofphysicists---indeedallright-mindedfolk!---wouldconcur.Theyaremoremodest---lessgung-ho,andlessnaïve---aboutbeautyetc.asaguidetotruth,thanHossenfelderportraysthemasbeing.Indeed,oneseesthisinthebook.ForsometimesHossenfelder’sintervieweesavowscepticismaboutwhethernaturemustturnouttoberational,orcomprehensible,or‘nothappenstance’:forexample,Arkani-Hamed---thoughhesaysitwithexpletives,ratherthanphilosophicaljargon(p.75).Somuchfor(i).Butyoushouldalsohavemisgivingsaboutthemorepreciseproposals,(ii)and(iii).Andyoushoulddoso,evenifyouarenotaHumean;butinstead,fullofconfidenceandambitionaboutourabilitytorationallyunderstandnature.

ThusInotedthat(ii)’smainidea,ofasuspiciouslysmallvs.amoderateorlargedifferenceofrealnumbers(i.e.ashortvs.alongintervalofrealnumbers)leadsinto(iii).For(iii)triestomakethatideapreciseas,essentially:either

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smallvs.moderate-to-largeprobability,ordependenceonsmalldifferencesathighenergyvs.dependenceonlyonlargedifferencesathighenergy.

Butthecommonthemehere---asmallvs.largecontrast---isalltooliabletobeamatterofsubjectivejudgment:where(asIsaidinSection2)thesubjectivityatissueisusually,notofanindividual,butofascientificcommunity.Forjudgmentsofsmallvs.largemightwellbeinfluencedbyourbackgroundtheoreticalbeliefs(andthusbyourhistoricalcircumstances)..

Thusrecallquestions(a)and(c)inthefirst,probabilistic,schemein(iii);andsimilarlyinthesecondscheme,appealingtotherenormalizationgroupflow.Herealso,onecan---andshould---pressthepoint:whatcountsasasmallorlargedifferenceinaparameter’svalueinthehighenergyregimeisverylikelytobeinfluencedbytheoreticalbeliefs.

Andsimilarlyfornaturalnessproposalsthatcombinethetwoschemes(assomedo:p.47)byproposingaprobabilitydistributionoverparameters’valuesinthehighenergyregime,andanalyzingitsflowdowntolowenergy.Onecan---andshould---pressthequestion:whatjustifiesthemeasure?Tosumup:IendorseHossenfelder’ssummingupofthesemisgivings:‘theissueof…naturalnessshowsthatwedonotunderstandwhatitmeansforalawofnaturetobeprobable’(pp.208-209).Indeed:weshallseethemisgivingsabove,i.e.thedangerthatnaturalnessargumentsareinfectedbysubjectivity,inthenextSection’shistoricalexamples.

6.TychoBraheandAristotleIturntotwoexamplesofargumentsbasedonnaturalness,fromRenaissanceandancientscience.ThefirstisTychoBrahe’sargumentagainsttheheliocentricsystem:Hossenfelderexpoundsitonpp.75-77.ThesecondisAristotle’sargument,inDeAnima,thatlightcannotbeanysortofpropagation.Bothargumentsareplausible,evenimpressive:thoughthatishardlysurprising,giventheirauthors’supremebrilliance.

Butbothargumentsarewrong.Fortheyturnonrejectingasunimaginable,andsounacceptable,averylargevalueofaphysicalparameter:inBrahe’scase,adistance;andinAristotle’scase,aspeed.Butsomuchforhumanimagination!Forinfact,theparameterstakethoseverylargevalues.ThusBraherejectedtheheliocentricsystemonthegroundsthatthestarsappearfixed.IftheEarthgoesroundtheSun,thenthereshouldbestellarparallax:thatis,thestars’apparentpositionsshouldchangeinthecourseoftheyear.Indeedtheydo.Butthestarsaresodistantthattheeffectwastoosmallforastronomerstomeasure,untilthenineteenthcentury.Afterall,ourcloseststar,ProximaCentauri,is4.2light-yearsaway:whichisabout30,000timesmoredistantthantheplanets.However,theideathatthestarsareseveralordersofmagnitudefurtherfromusthanaretheplanetswas,inthesixteenthcentury,unacceptable.Besides,asHossenfelderexplains,thesituationhadanotherconfusingfeature.Namely:sixteenthcenturyastronomersover-estimatedstars’size,sothatsupposingthemtobeveryfarawayalsoimpliedthattheyweremuchlarger---

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unacceptablylarger---thantheSun.Thusshequotes(p.77)Brahewritingin1602:

‘itisnecessarytopreserveinthesematterssomedecentproportion,lestthingsreachouttoinfinityandthejustsymmetryofcreaturesandvisiblethingsconcerningsizeanddistancebeabandoned:itisnecessarytopreservethissymmetrybecauseGod,theauthoroftheuniverse,lovesappropriateorder,notconfusionanddisorder’.

Noblesentiments---butwrong.Similarlytwomillenniaearlier.AristotleintheDeAnimaarguesthatlightis---notapropagationofanythingatall(whetherraysorwavesorparticles),butrather---thetransparencyofthemedium(typicallyair,ofcourse).Hegivesashisreasonthefactthatatsunrisetheentirelandscapeisilluminatedatonce.Thusherejectsapropagationtravellingsofastoverthemiles-widelandscape,astolooktousasifitarriveseverywheresimultaneously.Suchapropagationwouldbe`unimaginablyfast'intheliteralsense:itisunimaginable,andaccordinglytoberejected.Thushewrites:

`Empedocles(andwithhimallotherswhousedthesameformsofexpression)waswronginspeakingoflightas'travelling'orbeingatagivenmomentbetweentheearthanditsenvelope,itsmovementbeingunobservablebyus;thatviewiscontrarybothtotheclearevidenceofargumentandtotheobservedfacts;ifthedistancetraversedwereshort,themovementmighthavebeenunobservable,butwherethedistanceisfromextremeEasttoextremeWest,thedraughtuponourpowersofbeliefistoogreat.'(DeAnima,Book2,Chapter7(418b21-26:translatedbyJ.A.Smith)

Soherewehavetwoargumentswhosegistis:‘itmustbeso,sinceotherwisesomephysicalparameterwouldhaveanunacceptablyvastvalue’.Theyarebothlogicallyvalid;andtheirpremiseswere,atthetime,plausibleandevencompelling.Butinfact:thestarsareimplausibly---‘unimaginably’---distant;andthespeedoflightisunimaginablyfast.

ThemoralisasHossenfelderstressedabove;andIthink,asallshouldagreewith;andaswealsosawinWeinberg’sexample(p.110)ofKepler’stryingtoexplaintherelativesizesoftheplanets’orbitsbyinterpolatingPlatonicsolids.Namely:whatwefindplausibleoracceptableisstronglyinfluencedbyourbackgroundtheoreticalbeliefs,andthusbyourhistoricalcircumstances.Andsowewoulddowelltointerrogatethosebackgroundbeliefs---adviceIwillreturntoinSection9.

7.ThetroubleabouttheHiggsmass

AsIsaidattheendofSection4:themainconnectionbetweensupersymmetryandnaturalness,expoundedbyHossenfelder,concernsthemassoftheHiggsboson.

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Ishallnotlingerontheadvancedphysicsofthis,whichisbeyondmyken.(Foraphilosophicalexposition,cf.Williams(2015,Section2,3;2018Section2.)IwillonlyquotetwopassagesshowinghowwellHossenfelderexplainstheissues.Namely:first,howtheHiggs’smassconnectssupersymmetryandnaturalness;andsecond,whattheimpliedscientific,indeedempirical,problemis.Aboutthefirsttopic,shewrites(pp.37-38):

‘TheHiggs…suffersfromapeculiarmathematicalproblemthattheotherelementaryparticlesareimmuneto:quantumfluctuationsmakeahugecontributiontotheHiggs’smass.Contributionslikethisarenormallysmall,butfortheHiggstheyleadtoamassmuchlargerthanwhatisobserved---toolarge,indeed,byafactorof10^{14}.Notalittlebitoff,butdramatically,inadmissibly,wrong.…Onecanamendthetheorybysubtractingatermsothattheremainingdifferencegivesthemassweobserve.Thisamendmentispossiblebecauseneitherofthetermsisseparatelymeasurable;onlytheirdifferenceis.Doingthis,however,requiresthatthesubtractedtermbedelicatelychosentoalmost,butnotexactly,cancelthecontributionfromthequantumfluctuations.Forthisdelicatecancellationoneneedsanumberidenticaltothatgeneratedbythequantumfluctuationsforfourteendigits,andthendifferentinthefifteenthdigit.Butthatsuchaclosepairofnumberswouldcomeaboutbychanceseemshighlyunlikely....

SupersymmetrymuchimprovesthesituationbecauseitpreventstheoverlylargecontributionsfromquantumfluctuationstotheHiggsmass.Itdoessobyenforcingtherequireddelicatecancellationsoflargecontributionswithouttheneedtofine-tune.Insteadthereareonlymoremoderatecontributionsfromthemassesofthesuperpartners.AssumingallmassesarenaturalthenimpliesthatthefirstsuperpartnersshouldappearnottoofarawayfromtheHiggsitself.That’sbecauseifthesuperpartnersaremuchheavierthantheHiggs,theircontributionmustbecancelledbyafine-tunedtermtogiveasmallerHiggsmass.Andwhilethatispossible,itseemsabsurdtofine-tuneSUSY,sinceoneofthemainmotivationsforSUSYisthatitavoidsfine-tuning.’

Inshort:SUSYhelpstheHiggs’masstobenatural.Sooneasks:whatisthescientificproblemabouttheHiggsmass?Theanswerliesinthelastpartofthequotationjustgiven.Namely:theHiggshasbeenobservedattheLHC,withamassof125GeV---butsupersymmetryhasnotbeenobservedat,orcloseto,thatenergy.Norhasitbeenobservedatanyenergy;(intheLHC’ssecondrun,fromearly2015tolate2018,theenergywas13TeV.)

AsHossenfeldersays:‘[if]allmassesarenaturalthen…thefirstsuperpartnersshouldappearnottoofarawayfromtheHiggsitself.’OrtoquoteGordyKane’sprediction,backin2001:‘thesuperpartnermassescannotbeverymuchlargerthantheZ-bosonmass,ifthiswholeapproachisvalid’(p.36).Thisandsimilarpredictions(p.39)haveprovenfalse.

Onecouldofcourseinterpretthissituationasillustratingthatnaturalness,asmadepreciseintherelevantsupersymmetricmodels,hasthemeritofbeingfalsifiable---indeedfalsified.ButHossenfelderrejectsanysuch

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Popperianorfalsificationistgleeatexperimenthavingkilledyetanothertheory.Insteadsheconcludes(p.39):‘weknownowthatifthesuperpartnersexist,theirmassesmustbefine-tuned.Naturalness,itseems,isjustnotcorrect.[This]hasleftparticlephysicistsatalossforhowtoproceed.Theirmosttrustedguideappearstohavefailedthem.’Later,sheagainsumsupthisscientific,indeedempirical,problem.Shewrites(pp.63-64):

‘TheLHCeventuallyconfirmedtheHiggswithamassof125GeV,justontheupperedgeoftherangethathadsofarnotbeenexcluded.AheavierHiggsallowsheaviersuperpartners,soasfarassupersymmetryisconcerned,theheaviertheHiggs,thebetter.ButthefactthatnosuperpartnerhasyetbeenfoundmeansthatsuchasuperpartnerwouldhavetobesoheavythatthemeasuredHiggsmasscouldonlybeachievedbyfine-tuningtheparametersofthesupersymmetricmodels.’

SoHossenfelderconstruesthefalsificationofthesespecificversionsofnaturalnessasillustratinghermaintheme.AsIsummarizeditinSection4(andendorsedit):judgmentsofbeauty,simplicityetc.areoflimitedvaluesincetheyare:(i)historicallyconditioned(ii)fallibleand(iii)withoutanysecureconnectiontothetheoryinquestionbeingtrue.Thussheadds,justafterthisquote,aremarkbyKeithOlive:‘Sonowweknowthereissomefine-tuning.Andthatitselfbecomesaverysubjectiveissue.Howbadisthefine-tuning?’

8.ThemultiverseSomuchbywayofdiscussingsupersymmetryandnaturalness.IturntothethirdmaintopicofHossenfelder’scritiqueofthecontentofcurrentfundamentalphysics:themultiverse.Hossenfelder’sdiscussionisintwoparts:thefirstpartofherinterviewwithWeinberg(pp.100-116),theendofwhichcovershisinfluentialanthropicpredictionofthevalueofthecosmologicalconstant;andherinterviewwithEllis(pp.209-218).

By‘multiverse’,Iprincipallymeanthemultiverseofmoderncosmology:notthemultiverseoftheEverett,ormanyworlds,interpretationofquantumtheory---thoughIwilltouchonthelatter,hereandinSection9.Aswewillsee,themultiverseisconnectedwiththetopicsofsupersymmetryandnaturalness.Moderncosmologypostulatesthattheveryearlyuniverseunderwentaverybriefepochofacceleratingexpansion:dubbed‘inflation’.ThisinflationaryepochprecededtheslowingexpansionsuccessfullydescribedbythestandardBigBangcosmologythatwasestablishedinthemid1970s.(RecallSection3’sdiscussionofmodernphysicsbeingavictimofownsuccess.)

Thisacceleratingepochisveryconjectural.Itis,however,supportedbythefactthatitimpliesfeaturesofthecosmicmicrowavebackgroundthatareconfirmedbyobservationslikethatoftheCOBEandPlancksatellites.Theepochismeanttohaveoccurredattimesthatare(logarithmically!)muchearlier---energiesmuchhigher,temperaturesmuchhotter---thanestablishedphysicscandescribe.Thusitissaidtohavebegunatabout5x10-35secondsaftertheBigBang,withacharacteristicexpansiontime(i.e.thetime-scaleonwhichthescale

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factor---theradiusoftheuniverse---ismultipliedbye)ofabout10-36seconds;andtohaveendedatabout10-34seconds.ThisisatimecorrespondingtoGUT-scaleenergies,viz.1015GeV;sothatthetemperaturewas1028K.Thesefiguresimplyexpansionbyafactorofaboute50:whichisabout1022!

Theputativemechanismdrivinginflationisyetmoreconjectural.Themainproposedingredientisaso-farunidentifiedfield,calledtheinflaton.Therearemanymodels,withdifferentdetails(e.g.potentialsfortheinflaton).Butmanysuchmodelsgiverisetoamultiverse.Thatis:toavastsetof(non-interacting)pocketorbubbleuniverses---ofwhichourownuniverseisthereforejustone.Besides,thesebubbleuniverseswillvary,notjustindetails,butalsointhevaluesoffundamentalphysicalparameterssuchasthecosmologicalconstant,andalsoperhapstheconstantsgoverningthestrengthsofthenon-gravitationalforces,suchasthefinestructureconstant.Thisisthecosmologicalmultiverse.

Here,thereisaconfluencewithdevelopmentsinthelasttwentyyearswithinstringtheory.Backinthe1980s,stringtheoristshopedtheconstraintsonconstructingaconsistentstringtheorywouldbesostrongthattherewouldbeauniqueconsistentstringtheory;oratleast,onlyafewsuch.Thishopewasambitious.Forthesenseof‘theory’atissuehereismorespecificthana‘frameworktheory’like,say,elementaryclassicalorquantummechanics,withtheir‘silence’or‘generality’aboutthesystem’sdegreesoffreedomandtheforcesimpressedonit(i.e.itsHamiltonianorLagrangian).Here,‘astringtheory’isnotsilentinthissense.Itistoencodetheforces,i.e.aHamiltonian;andtherebyagroundstate.

Butthishopehasbeendashed.Inthelasttwentyyears,ithasturnedoutthatstringtheoryadmitsavastnumberoflocalgroundstates(metastablevacua):statesthatareinalocalminimumofthepotential.Atrulyvastnumber:anestimateoftencitedis10500,whileTaylorandWang’s(2015)estimateis10272,000---daunting,indeeddepressing,numbers.The‘towers’ofexcitedstatesbuiltupfromeachsuchgroundstatewouldthencountasdifferentstringtheories.Thisisthestringtheorylandscape.Besides,theoverallschemeofstringtheorysuggeststhatthedifferenttheories---thetowersofexcitedstates---differinvaluesoffundamentalphysicalparameters,suchasthecosmologicalconstantandthefinestructureconstant.

Sohereistheconfluencewiththecosmologicalmultiverse.Forinbothcases,weareconfrontedwithavastpopulationofwhatonemight(tochooseaneutralword)call‘domains’:domainsthatvaryinfundamentalparameters.

Furthermore,thisconfluenceisstrengthenedbyawidespread,albeitusuallyimplicit,adoptionbystringtheoristsoftheEverettinterpretationofquantumtheory.Fortheideaofthecosmologicalmultiverseisthatthecountlessdomainsareallequallyreal.Ididnotstressthisabove.Foronetakesitinone’sstride,whenreadingthewords‘thereisasetofbubbleuniverses,ofwhichourownuniverseisjustone’.Buttheideaisclear:thedomainsare‘just’differentregions---different‘parishes’---ofavastactualitywithanintricatespatiotemporalandcausalstructure.

ButaccordingtotheEverettinterpretation,onecansaythesameaboutthevarioustowersofexcitedstatesbuiltupfromthevariousvacuainthestringtheorylandscape.Thatis:supposethatthequantumstateoftheentirecosmosissomesortofsum,orintegral,ofstatesinthevariousdifferenttowers(orasum

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oftensorproductsofsuch);orisamixture,i.e.densitymatrix,withtheseascomponents.Thenthereis,inEverettianparlance,anamplitudeforvariousbranchesassociatedwithvariousdifferentvacua:ormoreprecisely,associatedwithexcitationsabovevariousdifferentvacua.Sothereisanamplitudeforvariousdifferentvaluesoffundamentalparameters.AndaccordingtotheEverettian,thedifferentbranchesareequallyreal:justas,wesaw,thecountlessdomainsofthecosmologicalmultiversearemeanttobe.Somuchbywayofdescribingthedizzyingvisionofthemultiverse,cosmologicalandstring-theoretic.Thisbriefdescriptionraisesahostofquestions,bothtechnicalandphilosophical.Hossenfelder,withherintervieweesWeinbergandEllis(pp.100-116,209-218),exploresthelatter.AswillI,inthisSectionandthenext.

AsIseematters,therearetwomainphilosophicalquestionstoconsider,asfollows.(Formorediscussion,cf.e.g.AzharandButterfield(2018).)Iwilltaketheminturn.

(1):How,ifatall,canweconfirm(ordisconfirm)atheorypostulatingsuchamultiverse,sincewecanonlyobserveourowndomain---ourown‘parish’?Thisquestionisurgentsinceitisatreasuredhallmarkofsciencethatweshouldbeabletoconfirm(ordisconfirm)ourclaims:atreasureweareindangeroflosing.(Cf.EllisandSilk(2014),whoalsodiscussstringtheory.)Thisquestionwillalsoleadintothesecondquestion.

(2):Whatdoesittaketoexplainthevalueofafundamentalphysicalparameter,suchasthecosmologicalorfinestructureconstant?Indeed,whatdoesitevenmeantoexplainthis?Inamoment,wewillseetwomorepreciseversionsofthislatterquestion.Asto(1),theobviousapproachistosaythatacosmologicaltheorymayassigndifferingprobabilitiestovariousvaluesofanobservableparameter,ofwhicheachdomainexhibitsonevalue;andthatthisenablesustoassessthetheorybyorthodoxstatisticalinference.Namely:theobservedvalueshouldnotbetoomuchofanoutlier:nottoomuch‘inthetail’oftheprobabilitydistribution.Thatis:iftheobservedvalueisinthetail,wewillconcludethatthetheoryisdisconfirmed.

Admittedly,thisapproachraisesagaintheusualquestionsaboutmakingprecise,andjustifying,one’sproceduresofstatisticalinference.Recallquestions(a)to(c)abouttheprobabilisticconstrualofnaturalness,in(iii)ofSection5.

Butmoreimportant:inthepresentcosmologicalsetting,thisapproachfacestwobigproblems;(thesecondinthenextSection).Eachwillleadtoaversionofquestion(2)above.

Thefirstproblemis:Whencetheprobabilitydistributionwhichthisapproachinvokes?Itdoesnothelptosay‘fromourcosmologicaltheory’;oreventosay,apparentlymorespecifically,‘fromtheusualBorn-ruleprobabilitiesascribedbyaquantum(saystring-theoretic)stateofthecosmos’.Forwedonothavesuchatheory,orsuchastate,fromwhichwecaneveninprinciplecalculateadistribution.

Andevenifwecouldcalculateone,anaggingquestionofmeaningwouldremain.Forallourunderstandingofprobabilityderivesfromcaseswherethere

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aremanysystems(coins,dice…orlaboratorysystems)thatare,orarebelievedtobe,suitablysimilar.Andthisputsusatalosstosaywhat‘theprobabilityofacosmos’,orsimilarphraseslike‘theprobabilityofastateoftheuniverse’,or‘theprobabilityofavalueofafundamentalparameter’reallymean.Thisisineffectanaggravatedversionofquestion(c),abouttheprobabilisticconstrualofnaturalness,in(iii)ofSection5.Namely:‘Whatisthemeaningofprobability?’Tosumup:wemustrecognizethatHossenfelder’sSection-title,‘Cosmicpoker’(pp.107,112)isameremetaphor.

Ishouldaddanancillaryremark(whichisnotinHossenfelder’sdiscussion).Onemightsaythatsinceallthesedomainsofthemultiverse,allthesealternativeoutcomesofthecosmicdistribution,arepresumedtobeactual,weshouldunderstandprobabilityinthiscontextjustbycounting.Thatis:whynottakeprobabilitytoberelativeproportion,relativefrequency,inthevastactualpopulationofdomains?Agreed:inphilosophicaldiscussionsofprobability,identifyingprobabilitieswiththecorrespondingactualrelativefrequencies(called‘naïvefrequentism’)isalmostalwaysrejectedassimplistic.Andnodoubtrightly:onemustallowforstochasticvariation---forprobabilitiesnottobeexactlymatchedbythefrequenciesthathappentooccur.Butofcourse,thesediscussionsarenotconcernedwiththecosmosasawhole,norwithascenarioinwhichallalternativeoutcomesofthedistribution,actuallyoccur---anddosomultiply.Soperhaps,inthissortofcosmicscenario,‘justcounting’istherightwaytointerpretprobability.(ThisdiscussionofcoursebearsontheEverettinterpretationsince,asImentioned,itispopularamongstringtheoristsand,moregenerally,quantumcosmologists.)

Butunfortunately:evenif‘justcounting’isright,wearereallynofurtherahead.Forwestillhavenoideaatallhowtocalculateanysuchrelativefrequencies.Theproblemispartlythatoftenthesetstobecountedareinfinite,suggestingarelativefrequencyof‘infinity/infinity’.Andevenelementaryexamplesliketheproportionofoddnumbersamongthenaturalnumbers(Guth2007,p.6820)showtheambiguitiesofprescriptionsforgettingafiniteanswer.

9.BiasedsamplingThereisalsoasecondproblemwithwhatIcalled‘theobviousapproach’ofapplyingstatisticalinferencetotheobservedvalueofparameterslikethecosmologicalconstantorthefinestructureconstant.

Namely,thedangerofbiasedsampling;orinotherjargon,selectioneffects.Theissueisfamiliarineverydaylife,andisvividlyillustratedbyEddington’s(1939)metaphorofthefishingnet.Fishermenwhosenethasameshofsay10centimetresshouldnotinfer,fromobservingthatallthefishintheircatcharelongerthan10centimetres,thatthefishinthelakearealsolongerthan10centimetres.

Similarlyforthecosmologicalmultiverse.Weobserversarelikefishermen.Ourobservationsofaphysicalparameter(e.g.thecosmologicalconstant)arelikemeasurementsofthelengthoffishinthecatch.Andweshouldnotinferthatinunobserveddomains---indomainsotherthanours---the

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parametertakes,orislikelytotake,avalueclosetowhatweobserve.Formaybetheparameter’svalueiscorrelatedwithwhetherthedomainhasobserversinit.

ThepointhasbeenwellexpressedbyHartle,HertogandWilczek,asfollows.‘Whatismostprobabletooccurisnotnecessarilywhatismostprobabletobeobserved’(HartleandHertog2017,p.182);and:‘Observersarelocatedonlyinplaceswithspecialproperties.Asatrivialconsequence,probabilitiesconditionedonthepresenceofobserverswilldiffergrosslyfromprobabilitiesperunitvolume’(Wilczek2007,p.43). Inshort:Ourexpectationsaboutwhatweobserveshouldbeconditionedonwhatwebelieveaboutourprocessofobservation.

Agreed:withinphysics,biasedsamplingisusuallynotasignificantdanger.Iftheobservationalprocessisinfactbiased---i.e.thevalueoftheparameterwewishtoobserveiscorrelatedwiththeprocess---wecanusuallyrecognizethisandcompensateforthebias.Thatis:wecanquantifytheamountofcorrelation,andaccordinglyadjustourestimateofthevalueconcerned.Butfortheobservationoffundamentalparametersinthecontextofthemultiverse,biassedsamplingthreatenstobeasignificantdanger---andonethatitisveryhardtobequantitativelypreciseabout.

Thereasonliesinthefactthatparameterslikethecosmologicalconstantorthefinestructureconstantarecorrelatedwithvariousdifferentaspectsofourmakingobservations.Besides,thesecorrelationsareoftennumericallyverysensitive.Asmallchangeintheparameterwouldmakeanenormouschangetotheobservationalprocess,includingwhethertherewasanobservationatall.Hencethejargonoffine-tuning;(meaning,asinSections5and6,theoppositeofnaturalness).Andfurthermore,thesecorrelationsofteninvolvevariousdifferentmechanisms,whicharerelatedtooneanother.

Forexample,therearemanydifferentnecessaryconditions,eachscientificallydescribable,ofourobservingthevalueofthefinestructureconstant.Theobserverisalive;andliferequires---onemaywellargue---complexcarbonchemistry.Carbonrequiresstellarnucleosynthesis.Andthecomplexchemistryofliferequires---onemayargue---thataplanetorbitastaratasuitabledistance(neithertoohotnortoocold,likeGoldilocks’porridge!),andforalongenoughtime,thatlifecanevolve.

Allthesecorrelations,andthemechanismsunderpinningthem,andthesemechanisms’mutualrelations,areferociouslyhardtodisentangle.Andthisissoevenifwesomehowsettleonsomeexactdefinitionof‘observation’or‘life’;anditissoevenforasingleparametersuchthefinestructureconstant,letaloneallthephysicalparametersofinterest.

Agreed:thesearewell-establishedproblems.Thelocusclassicus(whichHossenfelderofcoursecites)isBarrowandTipler’ssuperbbook,TheAnthropicCosmologicalPrinciple(1986).Buttheyremainasimportanttodayastheywerethirtyyearsago,notleastbecausetheyaremadeacuteandvividbythecosmologicalmultiverseandthestring-theorylandscape.Besides,attemptstoaddressthemcontinue.

Oneinfluentialexample,perhapsthemostfamousexample,isWeinberg’sexplanationofthevalueofthecosmologicalconstantasanobservationselectioneffect.Despitethecomplexitiesjustmentioned,thisexampleiscomparativelystraightforwardtocalculate:asWeinbergrecognized.Fortherequirementthatlifeevolvesinanexpandinguniverseofthe(‘FRW’)typeusuallyconsideredin

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cosmologyseemstobecorrelatedwiththevalueofthecosmologicalconstantbyasingle,andcomparativelysimple,mechanism.ThusWeinbergwrites:

…inacontinuallyexpandinguniverse,thecosmologicalconstant(unlikecharges,masses,etc.)canaffecttheevolutionoflifeinonlyoneway.Withoutundueanthropocentrism,itseemssafetoassumethatinorderforanysortoflifetoariseinaninitiallyhomogeneousandisotropicuniverse,itisnecessaryforsufficientlylargegravitationallyboundsystemstoformfirst...However,onceasufficientlylargegravitationallyboundsystemhasformed,acosmologicalconstantwouldhavenofurthereffectonitsdynamics,orontheeventualevolutionoflife(1987,2607-2608;cf.also1989,p.7).

Thustheideaisthattheevolutionoflifeconstrainsthecosmologicalconstantinasimpleway,becausewecanthinkof(apositivevalueof)theconstantasalong-rangerepulsive(‘anti-gravity’)force.Thusoneassumesthat(i)lifecanonlyexistonplanets,and(ii)lifetakesalongtime,saybillionsofyears,toevolve.Since(i)requiresthatmatterhasthechancetoclumptogetherundergravitysoastoformplanets,theinitialexpansioncannotbetoopowerful.Thatis,thereisanupperboundonthecosmologicalconstant.Ontheotherhand,(ii)meansthattheuniversemustlastlongenoughforlifetoevolve.Sogravitycannotbesopowerful(theinitialexpansioncannotbesoweak)thatgravityovercomestheinitialexpansioninaBigCrunch,wellbeforelifehastimeenoughtoevolve.

Indeed,thecalculationalongtheselinesin1997,byWeinbergandhisco-authors,amountedtoapredictionthatthecosmologicalconstantwaspositive.(Cf.Marteletal.(1997),whichbuiltonpreviouswork,suchasWeinberg(1987,1989SectionV);Vilenkin(2007)isafinereviewoftheconceptualissues.)Thepositivevaluewasonlymeasuredinthefollowingyear:(thoughtherehadbeenearlierhints).

Weinberg,inhisinterviewwithHossenfelder,takesupthisexample.Hiscommentcanservetosummarizeourdiscussionofselectioneffects.Hesays(p.116):

‘Weassumedtheprobabilitydistributionwascompletelyflat,thatallvaluesoftheconstantareequallylikely.Thenwesaid,‘Whatweseeisbiasedbecauseithastohaveavaluethatallowsfortheevolutionoflife.Sowhatisthebiasedprobabilitydistribution?’Andwecalculatedthecurvefortheprobabilityandasked‘Whereisthemaximum?Whatisthemostlikelyvalue?’…[Hossenfelderadds:‘themostlikelyvalueturnedouttobequiteclosetothevalueofthecosmologicalconstantwhichwasmeasuredayearlater’.]…Soyoucouldsaythatifyouhadafundamentaltheorythatpredictedavastnumberofindividualbigbangswithvaryingvaluesofthedarkenergy[i.e.cosmologicalconstant]andanintrinsicprobabilitydistributionforthecosmologicalconstantthatisflat...thenwhatlivingbeingswouldexpecttoseeisexactlywhatwesee.’

Thelastwordsconveythelureofwhatisoftencalled‘anthropicexplanation’.Butofcourse,therelevantnotionintermsofwhichweshouldformulatetheprocessofobservationisnothumankind,butsomethingmoregeneral,suchas

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life,orevolvedlife.Soratherthanthelabel‘anthropicexplanation’,weshoulduseaphraselike‘parochialexplanation’,i.e.explanationthatinvokesthelocalcircumstancesofour‘cosmicparish’.

Whateverthelabel,wefacetoughquestions,aboutbothphysicsandphilosophy.Astophysics,Ishouldmentionthatsomerecentdiscussionssuggestthestringlandscapecontainsnouniverseswithapositivecosmologicalconstant.Cf.forexampleWoit’sbloghttp://www.math.columbia.edu/~woit/wordpress/?p=10486.Andthephilosophicalquestionaboutexplanationisalsotough.Canwebecontent,asWeinbergis,withaparochialexplanationofthevalueofafundamentalphysicalparameter?Ormustweseekanexplanationinvokingmoretraditionalconsiderations,especiallyprinciplesofdynamicsand-orsymmetry?

10.Topicswewoefullyneglect

Somuchbywayofexpoundingthemultiverse,anditsconnectionwithsupersymmetry,especiallystringtheory,andnaturalness.Together,theyformHossenfelder’sthreemaincharges:herthreemainaccusationsabouthowcontemporaryphysicshastakenawrongturn.

Hereweshouldagaindistinguish,asinSection3,betweenasubjectgettingstuckandittakingawrongturn.Ofcourse,wecanhardlyblamethephysicscommunityforthesubjectbeingstuckinthesenseoflackingdata.Forexample:whilewewouldhavebeenpleasedtoseeSUSYintheLHC,itisnoone’sfaultthatnature‘chosenottooblige’.Sucharethefortunes---oftentimes,misfortunes---ofenquiry.Noamountofhightalentandgenerousfundingguaranteessuccess.

Butaswehaveseen,Hossenfelderarguesthatthephysicscommunityhaserred,notmerelyfacedmisfortune:thatphysicshastakenawrongturn.ShesumsupthecritiqueofthepreviousSectionsasfollows(pp.107-108).

‘Themultiversehasgainedinpopularitywhilenaturalnesshascomeunderstress,andphysicistsnowpitchoneastheother’salternative.Ifwecan’tfindanaturalexplanationforanumber,sotheargumentgoes,thenthereisn’tany.Justchoosingaparameteristoougly.Therefore,iftheparameterisnotnatural,thenitcantakeonanyvalue,andforeverypossiblevaluethere’sauniverse.Thisleadstothebizarreconclusionthatifwedon’tseesupersymmetricparticlesattheLHC,thenweliveinamultiverse. Ican’tbelievewhatthisonce-venerableprofessionhasbecome.Theoreticalphysicistsusedtoexplainwhatwasobserved.Nowtheytrytoexplainwhytheycan’texplainwhatwasnotobserved.Andthey’renotevengoodatthat.Inamultiverse,youcan’texplainthevaluesofparameters;atbestyoucanestimatetheirlikelihood.Buttherearemanywaysnottoexplainsomething.’

Indeed,acridecoeur.Obviously,thedebatecontinuesaboutwhethertheoreticalphysicsisinfactinsuchaparlousstate:recallmydisagreementsinSection2.

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Foraringsideseatatthedebate,notethattheproceedingsofthe“WhyTrustaTheory?”conferenceatMunichin2015areonline:https://www.whytrustatheory2015.philosophie.uni-muenchen.de/program/index.html.)Ofcourse,thatconferencealsoaddressesseveralissuesIhavenotmentioned,includingphilosophicalones:inparticular,theimportantsuggestionbyDawid(inhisStringTheoryandtheScientificMethod(2013:especiallyChapter3)thatatheorysuchasstringtheorycangatherconfirmationveryindirectly,viz.onaccountofourfailure,despitemucheffort,tofindanalternativetheoreticalframework.ButevenifonethinksHossenfelder’scritiquesofaristoopessimistic,orunfair,itleadstoanother:aboutneglectedproblemsandresearchprogrammes.

Forinthecourseofherdiscussionsandinterviews,Hossenfelderalsodescribesproblemsthatareperfectlyvalid,evenpressing,butareneglected.Andcorrespondingly,forresearchprogrammes,ratherthanproblems.Thereareprogrammesthatareperfectlycoherent,evenpromising,butareunfashionable‘underdogs’.Thustheproblemsgounaddressed,andtheresearchprogrammesunfunded.

ThiscritiquereturnstoSection3’sremarkthat,aswellaslackingdataathighenergies,weareindireneedofconceptualcluesabouthowtogobeyondourpresenttheories.ThusrecalltheanalogywiththenullresultoftheMichelson-Morleyexperiment:maybesomeempiricalfactscrucialtoprogresstodayarealreadytohand,butourmindsetpreventsusrecognizingthem.

Ofcourse,peoplewilldifferaboutwhichsuchproblemsandresearchprogrammesshouldbepursued,andwhicharenotworththecandle.ButHossenfeldermakesagoodcasethatfundamentalphysicssuffersfromagooddealtoomuchconformism,andanunmeritedhegemonyofafewresearchprogrammes.Andcorrelatively,thereisfartoolittlecollegialandliberalencouragementofdiverseapproaches.

Thiscritique,thisaccusationofundueneglect,hastwoaspects:aboutthecontentsofthephysicsatissue,andaboutthesociologyandprofessionalorganizationofthediscipline.Iwilltaketheminturn,inthisSectionandthenext.

SeveralofHossenfelder’sinterviewsrevealaneglectedproblemoranunderdogresearchprogramme;andsomearemostlyaboutsuch.Theobviousexampleistheinterpretationofquantumtheory,especiallythemeasurementproblem.Isay‘obvious’,notjustbecauseIamaphilosopherofphysics;norjustbecauseHossenfelderdevotesherChapter6toit.Also:inthatChapter,Weinberg,oneofhermostdistinguishedinterviewees,isfrankandforthrightinadmittingtheproblem.Forexample,hesays:‘wedon’thaveanyreallysatisfactorytheoryofquantummechanics’(p.123);andthen,inamannerreminiscentofJohnBell’sfamousstrictures(e.g.1989)againstinvokingtheconceptofmeasurementinthepostulatesofabasicphysicaltheory,headds(p.124):

‘...it’saformalismforcalculatingprobabilitiesthathumanbeingsgetwhentheymakecertaininterventionsinnaturewecallexperiments.Andatheoryshouldnotrefertohumanbeingsinitspostulates.Youwould

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liketounderstandmacroscopicthingslikeexperimentalapparatusesandhumanbeingsintermsoftheunderlyingtheory.Youdon’twanttoseethembroughtinonthelevelofaxiomsofthetheory.’

(Weinberg’sfrankadmissionoftheproblemisdevelopedinhis2017articleinTheNewYorkReviewofBooks.)Buttheinterpretationofquantumtheory,especiallymeasurement,isbynomeansHossenfelder’sonlyneglectedissue.Forexample,shediscussestheresearchprogrammesofAlainConnes(pp.157-159)andXiao-GangWen(pp.190-194).Topickoutthelatter:theverybroadideaisthatthoughphysicistsareusedtotheinfinitiesthatbesetquantumfieldtheory(eventhefreetheory),theyareasickness---andquantumfieldtheory’ssuccesses,includingthestandardmodel,shouldberecoveredfromathoroughlyfinitisticbasisofqubits.Somuchbywayofexamples.Hossenfelder’sbroadpointaboutthemisthatalltoooften,physicistsneglecttheseproblemsandresearchprogrammesfornogoodreason.Theyjustfollowtheall-toofallibleguideofaestheticjudgment,orcurrentfashion,orhabit;ortoputitmoreneutrally:whatthecommunityjusthappenstogetinterestedin.Thustowardstheendofthebook,shesummarizeswiththreeexamplesamongthoseIhavediscussed:themeasurementproblem,Wen’sprogramme,andthemultiverse.Shewrites(pp.208-209):

‘Therejustisn’tany[justificationforrelyingonbeautyinselectingtheories].AsmuchasIwanttobelievethatthelawsofnaturearebeautiful,Idon’tthinkoursenseofbeautyisagoodguide;incontrastithasdistractedusfromother,morepressingquestions.LiketheonethatStevenWeinbergpointedout:thatwedonotunderstandtheemergenceofthemacroscopicworld.Or,asXiao-GangWenremindedme,thatwedonotunderstandquantumfieldtheory.Orhowtheissueofthemultiverseandnaturalnessshowsthatwedonotunderstandwhatitmeansforalawofnaturetobeprobable.’

11.HowtomendourwaysIturnnowtothesecondaspectofHossenfelder’saccusationofundueneglect.Thisisaboutthesociologyandprofessionalorganizationofphysicsasadiscipline.

Agreed:Hossenfelder’svariouscausesforconcernabouttheorganizationofphysicscannoteasilybeseparatedfromassessingthecontent,andconfirmation,ofphysicaltheories.Aseverystudentofscience---betheyscientist,philosopher,historianorsociologist---willagree:valuesandattitudesmingleindissolublywithcognition.Soonecouldwriteawholereviewofthebook,stressingtheseconcerns.Butalthoughtheycropupthroughoutthebook,Hossenfelderdevotesfewerpagestothem;andwithspacepressing,Iwillfollowsuit.

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Hossenfelderdescribesvariousincidentsorpatternsofcommunalbehavior,thatareundoubtedlypeculiar:andmostofuswouldsay,dysfunctional---thoughofcoursetheyhavetheiranalogues(perhapsworseones)outsidephysics,andoutsidescience.

Oneexampleisthestoryofthediphotonanomaly.LHCdatafromDecember2015suggestedadiscoveryof‘newphysics’,i.e.incompatibilitywiththestandardmodel.Thiswaspursuedforcefully,alsobytheorists.Forexample,tenpapersappearedonthearxivadayafterthefirstannouncement;andinthenexteightmonths,fivehundredpaperswerewritten,someofthemgettingthreehundredcitations.Buteighteenmonthslater,theanomalywasgoneforgood(pp.85,235).Agreed:inafieldstarvedofnewdata(Section3),itisperfectlyrationaltoscrutinizecloselyapossibleanomaly.Butgivenhowmanyproblemsandresearchprogrammesweneglect,itisworryingtoseehowmucheffortwentintoexplainingastatisticalfluctuation.

Anotherexampleisthedepressingincreaseinhype(p.195).A2015surveyfoundthatthefrequencyinscientificpapersofwordssuchas‘ground-breaking’and‘unprecedented’increasedinthefortyyearsfrom1974to2014byadepressing2500%.(Butthereissomeconsolationforphysicsfans.Thissurveywasofpapersinbiomedicalscience...soperhapsthatexplainswhynowadaysbiologistsseemtogetmuchmorefundingthanphysicists…)

ForHossenfelder,themainpointofsuchexamplesishowtheyrevealconsiderablecognitivebiasesintheoreticalphysicists’selection,orrejection,ofproblems,andcorrespondingly,intheirsupportfororscepticismaboutresearchprogrammes.ThesebiasesarethemainthemeofthefinalChapter(‘Knowledgeispower’):whichincludesausefulsummaryofsometenmaintypesofbias---usefulsincethebiasesdescribedaresadlyfamiliar(pp.229-231).

‘Thereisthesunkcostfallacy,morecommonlyknownasthrowinggoodmoneyafterbad…Thein–groupbiasmakesusthinkresearchersinourownfieldaremoreintelligentthanothers...thefalseconsensuseffect:wetendtooverestimatehowmanyotherpeopleagreewithusandhowmuchtheydoso...Thenthereisthemotherofallbiases,thebiasblindspot---theinsistencethatwecertainlyarenotbiased.’

So,finally,wefacethequestion:whatcanwe,whatshouldwe,doaboutit?AnAppendix,called‘Whatyoucandotohelp’(p.245f.),makessome

dozenrecommendations,aimedatthreetypesofreaderofthebook.Namely:(i)ascientist;(ii)anadministratorinhighereducation,orsciencepolicymaker,orrepresentativeofafundingagency;(iii)asciencewriterormemberofthepublic.Alltherecommendationsarereasonable,anddoable:andevenifyoudisagree,theyareallworththinkinghardabout.Here,toconclude,aresomethatIforoneendorse.

Forgroup(i)i.e.thescientists,therecommendationsinclude:‘Learnabout,andtrytoprevent,socialandcognitivebiases’.Forgroup(ii),theyinclude:‘Makecommitments:youhavetogetovertheideathatallsciencecanbedonebypostdocsontwo-yearFellowships...short-termfundingmeansshort-termthinking’.And:‘Encourageachangeoffield:ifthepromiseofaresearchareadeclines,scientistsneedawaytogetout...offerre-educationsupport,one-ortwo-yeargrantsthatallowscientiststolearnthebasicsofanewfield’.

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Andperhapsmostuncomfortableofall:Forgroup(iii),therecommendationis:‘Askquestions.You’reusedtoaskingaboutconflictsofinterestduetofundingfromindustry.Butyoushouldalsoaskaboutconflictsofinterestduetoshort-termgrantsoremployment.Doesthescientist’sfuturefundingdependonproducingtheresultstheyjusttoldyouabout?…’

Here,Isubmit,Hossenfelderhasdonephysicsandsciencemoregenerally---andourbetterselves---aservice.Thesearesalutarywarningsandwisecounsels.Weshouldalltakenotice,anddowhatwecan.

AcknowledgementsForcommentsandcorrectionstopreviousversions,Iamverygratefulto:FerazAzhar,GuidoBacciagaluppi,AlexChamolly,RichardDawid,GeorgeEllis,HenriqueGomes,SabineHossenfelder,JoeMartin,SebastienRivat,PorterWilliams,andespeciallySebastianDeHaro.

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UniversityPress,pp.181-205.Hossenfelder,S.(2018).LostinMath:HowBeautyLeadsPhysicsAstray,BasicBooks:ISBN:978-0-465-09425-7,304pages,$17.99(hardcover).Kuhn,T.(1977).Objectivity,valuejudgmentandtheorychoice,inhisTheEssentialTension,UniversityofChicagoPress,pp.320-339.MartelH.,ShapiroP.andWeinbergS.(1997),LikelyvaluesofthecosmologicalconstantAstrophysicalJournal492,pp.29–40.McAllister,J.(1999).BeautyandRevolutioninScience.CornellUniversityPress.Smolin,L.(2006).TheTroublewithPhysics,HoughtonMifflin(Penguin2007).Taylor,WandWangY-N(2015).TheF-theorygeometrywithmostfluxvacua,JournalofHighEnergyPhysics12,pp.1-21;arxiv.org/abs/1511.03209doi:10.1007/JHEP12(2015)164Vilenkin,A.(2007),Anthropicpredictions:thecaseofthecosmologicalconstant,inB.Carr(ed)UniverseorMultiverse?CambridgeUniversityPress,pp.163-180.astro-ph/0407586Weinberg,S.(1987).Anthropicboundonthecosmologicalconstant,PhysicalReviewLetters,59,2607–2610.Weinberg,S.(1989).Thecosmologicalconstantproblem,ReviewsofModernPhysics,61,1–23.S.Weinberg,(2017).Thetroublewithquantummechanics,NewYorkReviewofBooks,19January2017;availableat:https://www.nybooks.com/articles/2017/01/19/trouble-with-quantum-mechanics/Wilczek,F.(2007),Enlightenment,knowledge,ignorance,temptation,inB.Carr(ed)UniverseorMultiverse?CambridgeUniversityPress,pp.43-54.Williams,P.(2015).Naturalness,theautonomyofscalesandthe125GeVHiggs.StudiesintheHistoryandPhilosophyofModernPhysics51,pp.82-96

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