Probability,Laws,andtheUltimateFine–TuningArgument

BarryLoewer(Rutgers)

PhilosophyandCosmology

•“Thereisnoideasoabsurdthatithasnotbeenseriouslytaughtbysomephilosopher”ReneDescartes

•“Cosmologistsareofteninerrorbutneverindoubt”LevLandau

TheUltimateFineTuningArgument

Theargumentthatifthelaws,constantsandinitialconditionsofatheorythatisproposedasafundamentalandcompletephysicaltheoryoftheuniverseareorhavevaluesthatarefine-tunedforasalientphenomena(e.g.complexity,life)thetheoryisincompleteandthatcompletingitmayinvolvehypothesesthatarenotusuallyconsideredpartsofsciencee.g.hypothesesthatinvokedesign,aselectorlaw,oramultiverse.Inotherwords,anadequatetheoryofrealitymustleavenofinetuningsunexplained.

PossibleUniverses

• BeginningwithLeibnizphilosophershaveemployedtheideaofpossibleuniversesorworldstoexplicatenotionsinmetaphysics,semantics,andscience.Theyalsoplayacentralroleindiscussionsoffine-tuningarguments.

• A possibleuniverseisdescribedbyacompletedistributionoffundamentalontology(e.g.particles,strings,fieldsetc.)andtheirproperties(e.g.mass,charge,fieldvaluesetc.)inann-dimensionalmanifold(thatmayhavethemetricalstructureofaspace-time)andlawsthatdescribeorgovernthedistributionoffundamentalentitiesandtheirpropertiesinthemanifold.Lawsimplytrueregularitiesinthedistributionoffundamentalontology.Allthenon-fundamentaltruthsthatholdatapossibleuniverseUareentailedbythedescriptionofthedistributionofthefundamentalontology,propertiesandthelawsatU(andthatitisthefullfundamentaldescription).

TwoAccountsofPossibleUniverses

• 1.Leibnizandthemajorityofcontemporaryphilosophersthinkofpossibleuniversesasabstractentities(eithercompletesetsofpropositionsormaximalproperties)oneofwhichdescribesorisinstantiatedbytheuniquelyexistingconcreteactualuniverse.Soasetofpropositionsthatspecifythelawsandforeachregioninthemanifoldwhatproperties/relations/entitiesareinstantiatedattheregionrepresentsapossibleuniverse.

• 2.AdifferentviewwasproposedbyDavidLewiswhoarguesthatthebestaccountofpossibleuniversesisthattheyarenotabstractbutconcretetotalities– themanifoldswiththeirlawsandontologiesthemselves- oneofwhichistheuniverseweoccupythatwecall“theactualuniverse”whiletheoccupantsofotheruniversesifanywouldbecorrecttocalltheuniversestheyoccupy“actual.”

• InmydiscussionIwillmostlyfollowthemajorityview.

NumberandVarietyofUniverses

• Thereisavastnumberofpossibleuniverses-atleastasmanyasthesetofrealnumbers- andplausiblyamuchhigherorderofinfinity.Andthereisanimmensevarietyofuniverses.Thelaws,themanifoldandtheontologyanditsdistributionmaydifferfromthoseoftheactualuniverseinanenormousnumberofwayssothereareuniversesthatgroundanypropositionsnotexcludedbylogicormetaphysics.Itisplausiblethatthereareuniverseswithanynumberofdimensions,withfieldsandparticlesunlikeanyoftheactualworld,universesthatcontainbeingsthatappeartobedragonsandtalkingdonkeys,universeswithobjectsthattravelsuperluminallyanduniversesthatcontainmindsbutnophysicalobjectsatall,universeswithnolaws,andsoonandonandon,….Aslongasadescriptionofadistributionoffundamentalontologyandlawsislogicallyandmetaphysicallyconsistentitcanbeembeddedinadescriptionofapossibleuniverse.Thevastvarietyofpossibleuniverseswillfigurecentrallyinmyreflectionsonfinetuning.

Whybelievetherearepossibleuniverses?

Philosopherspositpossibleworldsnot asapartofascientifictheoryintendedtoexplaincontingenteventsorfeaturesoftheactualuniverse(asforexample,thepocketuniversesofeternalinflation,theuniverseofthestringlandscape,andtheworldsofEverettianQM)butrathertocharacterizethelogic,semanticsandtruthmakersofmodalpropositions-e.g.propositionsaboutnecessity,possibility,counterfactuals,probabilityandsoon.Theyplayaroleinaccountsoflaws,causation,chance,fundamentalityand,aswewillsee,incharacterizingfine-tuning

Examples:a)necessity:Itismetaphysicallynecessarythatpiffpobtainsinallpossibleuniverses;b)counterfactuals:ifphadbeenqwouldhavebeeniffinallworldsthataremostsimilartotheactualworldatwhichpobtainsqalsoobtains.c)probability:P(A)=xiffacertainmeasureontheclassofuniversesatwhichAistrueisx

TheActualUniverse• Whilethecompleteandcorrectaccountofthephysicsoftheactualuniverseisnotknown(sincethereisnoagreedonquantumtheoryofgravity)andmayneverbeknowncurrentphysicspartlyandapproximatelycharacterizesitasfollows:

• 1.Fundamentalentitiesandproperties:quantummechanicalstatesthatdescribeentities(fermions,bosons)andfieldsofthestandardmodel.

• 2.space-time:describedbythemetricofgeneralrelativity• 3.laws:quantumfieldtheoryandgeneralrelativity(withaverysmallcosmologicalconstant)• 4.Distribution:14billionyearsinthepasttheparticles/fieldsinthecurrentlyobservableuniverseortheirprecursorswereconcentratedinaverysmallrapidlyexpandingpatchofspacewithaverylowentropydistributionthatevolvedinconformitywiththelawstothepresentstate.*

• *If,assomecosmologistsclaim,thereisamultiversethentheactualuniversecontainsmanypocketuniverses.

Whatarelaws?Twoviews:

• 1.non-Humean:Lawsareentities(differentfromphysicalentities)thatgovern theevolutionofstatesoastomakecertaingeneralizations(equations)true.(Maudlin,Armstrong)

• 2.Humean:Lawsareregularities(equations)entailedbyanideatruesystematization(asystematizationthatoptimizesscientificvirtues;simplicity,informativeness,naturalness,minimizingfinetuningsetc.)(Lewis,Hicks,Loewer).Thisaccountcanbeextendedtoincludeobjectiveprobabilities.Theideaisthatallowinglawstotaketheformofassignmentsofobjectiveprobabilityfacilitatesthesimplicityandinformativenessofasystematization.

Physicalism

• Physicalismistheviewthatthereisacompletecharacterizationofthefundamentalontologyandpropertiesoftheactualuniverseintermsofphysicsandthatthisgroundsallotherfactsabouttheuniverse.Somephilosophersthinkthereareaspectsoftheuniversethatareinevitablyleftoutbyphysics- inparticularaspectsinvolvingconsciousness.Ifsothentheactualuniversecontainsfundamentalmentalorproto-mentalontologyand/orpropertiesinadditionthoseofphysics.Butwhetherornotphysicalismistrueitisnaturaltowonderwhythephysicsoftheactualuniverse- theonethatexistsaccordingtoLeibniz- isthewayitis.Whydoesithavetheontology,properties,andlawsthatithas?Whydoesitsphysicallawsandontologysupportintelligentlife?

AFortunateUniverse?• Itmayseemthatgiventhevastnumberandvarietyofpossibleuniverses– manywithoutbeauty,intelligentlife,lifeofanykind,orevenwithoutstarsoranythingcomplex-itisveryfortunatethattheactualuniversehasthelaws,ontology,anddistributionofitsontologythatitdoestopermittheexistenceofbeauty,intelligentlifeandsoon.LukeBarnesinhisexcellentAFortunateUniverseshowsthatitiseasytodescribecounterfactualuniversesbyalteringtheactuallawsthatwouldprohibittheexistenceoflifeorevencomplexity.Suppose,forexample,thatthecosmologicalconstantwerenegative(theuniversewouldcollapse)ormuchlarger(theuniversewoulddilutebeforestarscouldform)orifthequarkmassesdifferedsotheproton’smassweregreaterthantheneutron’smass.Inthatcaseatomswouldnotform.

Heasks:• “ifauniversewerechosenatrandomfromthesetofuniverses,whatistheprobabilitythatitwouldsupportintelligentlife?Ifthatprobabilityissuitably(androbustly)small,thenweconcludethatthatregionofpossible-physics-spacecontributesnegligiblytothetotallife-permittingsubset.”(LukeBarnesp.18FT)

• SinceBarnesthinksthattheprobabilityofselectingauniversewithintelligentlifeissmallhethinksthattheactualuniverseisfine-tunedfortheexistenceofintelligentlifeandthisremarkableandfortunatefactcriesoutforanexplanation.

StructureofaFineTuningArgument

• TheclaimthattheprobabilityofasalientphenomenaE,e.g.theexistenceofintelligentlife,isverylowrelativetobackgroundassumptionsBandso“criesout”foranexplanationmotivatesthesearchforanhypothesisHwhichexplainsEandwhenaddedtoBrenderstheprobabilityofEmuchhigheri.e.P(E/B)<<P(E/B&H).ByordinaryBayesianreasoningitfollowsfromthisthatEconfirmsH.SoafinetuningargumentforHproceedsbyarguingfromthefactthatwithoutHtheallegedlyfinetunedEisimprobablebutwithHisprobabletotheconclusionthatHislikely.

• Butitdoesn’tfollowthatifonethinksthataphenomenacriesoutforanexplanationthatithasanexplanation.

Bayesianinference

P(H/E&B)= P(H/B)xP(E/H&B)_________P(H/B)xP(E/H&B)+P(-H)xP(E/-H&B)

TheprobabilitiesthatoccurinBayestheoremareepistemic(degreesofbelieforcredences).HoweverforittobeobjectivethatEconfirmsHthelikelihoodsP(E/H&B),P(E/-H&B)mustbeobjectivecredences.

TwoFacesofProbabilityepistemic/physicalsubjective/objective

Bayes’Theorem

• ThefinetuningargumentrequiresasaninputtoBayestheoremnotonlyprobabilitiesofthehypothesesH,-Hbutalsoanobjectiveprobabilitydistributionoverthesetofpossibleuniverses(oroverthesetofuniverseswiththeactuallawsandconstantssimilartotheactuallawsandconstantsdifferentfromtheiractualvalues)conditionalwhichassignsaverysmallprobabilitytoE(theactualuniversebeinghospitabletointelligentlife)givenHandgiven-H.Theseprobabilitiesaresupposedtorepresenttheobjectivecredencesofarationalinquirer notthesubjectivecredencesofanactualinquirersinceactualinquirersallassigncredence1totheexistenceoflife.

ScientificExplanations

• Sincethefundamentallawsandontologyoftheactualworldarenotyetcompletelyknownitmaybethatsomeoftheconstantsthatappearinthelawsandsomeofthelawsincurrentphysicsthatappeartobefinetunedareexplainedintermsofmorefundamentallawsandontology.Iftherearefewerconstantsandlawsintheexplanansthenthismayreducetheextentoffinetuning.Thisisaperfectlyacceptablescientificfine-tuningargument.Butunlessthereisonlyonemetaphysicallypossiblesetoflawsandontology—averyimplausibleprospect- therewillalwaysremainsomeconstants/lawsunexplainedi.e.someappearanceoffinetuning.Sowhilescientificdevelopmentsmayreducefinetuningitwillnotcompletelyeliminateit.

Lewis’AccountofPossibleUniversesandAnthropicExplanations• OnLewis’accountallpossibleuniversesexistasamatterofmetaphysicalnecessitysoanylivingbeingthatinquireswhysheinhabitsalifehospitableworldhasherquestionansweredby“itcouldn’tbeotherwise”.However,sincetherearelifehospitablepossibleuniverseswithverydifferentontologies,laws,constantsfromeachothertherewillbenoexplanationsoffinetuning,ifany,oftheseinvirtueoftherebeinglife.i.e.onecannotconcludeanythingaboutthelaws/constantsmerelyfromthefactthattheinquirerexistsexceptthattheyarecompatiblewithherexistence.

ScientificMultiverseandAnthropicExplanations• Thelawsandconditions(andinparticulareternalinflation)entailthattheuniverseisamultiverseconsistingofmany“pocketuniverses”whichvaryinthetheirinitialconditionsandvaluesoftheconstantsthatoccurinlaws.Thepocketuniversescorrespondtoasmallproportionofallmetaphysicallypossibleuniverses.Amongthese“pocketuniverses”aresomethatarelifehospitableanditisnotsurprisingthatwefindourselvesinoneofthese.

• Itisimplausiblethatmultiverse/anthropicexplanationscompletelyeliminatefine-tuningworriessincethetheoriesthatleadtoamultiversethemselveshavelaws,constants,andinitialconditions.Andthemultiversecreatestheproblemthatwithoutaprobabilitymeasureoverthepocketuniversestheaccountisdevoidofpredictiveandexplanatorypower.

Leibniz’sExplanation:Design:TheBestofallpossibleuniverses• “Godhaschosenthemostperfectworld,thatis,theonewhichisatthesametimethesimplestinhypothesesandtherichestinphenomena,asmightbealineingeometrywhoseconstructioniseasyandwhosepropertiesandeffectsareextremelyremarkableandwidespread”“…….insofarasitismadeupofminds,itisalsothebestrepublic,therepublicthroughwhichmindsderivethegreatestpossiblehappinessandjoy”

Parfit’s“selectorlaw”explanation.

• Theactualuniversesatisfiesa“non-scientific”selectorlaw.AccordingtoDerekParfitandJohnLeslietheremaylawsthatdeterminethenatureoftheactualuniverse.Forexample,aselectorlawmightdeclarethattheactualworldistheworldthatmaximizesthevarietyofkindsofphenomenaalongwiththesimplicityoflawsthatdescribethephenomena.

• ItisdifficulttotakeseriouslyeitherLeibniz’sdesignorParfit’sselectorexplanations.Theselawsseemtomakefalsepredictionsandversionsthatavoidrefutationarenon-predictive.

• Soneithermultiversenortheologicalexplanationslooklikepromisingwaysofaccountingforfine-tuningforlife.• Ratherthanpursuethemlet’slookatthepresuppositionsoftheargumentthattheactualuniverseisfine-tunedforlifeandthatthisfact“criesoutforexplanation.”

Presuppositionsoffinetuningandthedemandforittobeexplained• “howevermanywaysthereareofproducingalife-permittinguniverse,therearevastlymanymorewaysofmakingalife-prohibitingone.Bythetimewediscoverhowouruniversesolvesthecosmologicalconstantproblem,wewillhavecompiledaratherlonglistofwaystoblowauniversetosmithereens,orquicklycrushitintooblivion.Amidstthepossibleuniverses,life-permittingonesareexceedinglyrare.Thisisfine-tuningparexcellence.”• Barnesarguesthatmostcounterfactualuniversesthataredescribedbyalteringthefundamentalconstantsthatoccurinthelawsorthelawsthemselvesareinhospitabletointelligentlife(life,complexity,etc.)andconcludesthatlifesupportinguniversesarerareandsotheprobabilitythatarandomlyselectedworldsupportsintelligentlifeisverysmall.Butthislineofreasoningisdoublymistaken.

Mistake1

• 1.Itdoesn’tfollowfromtheclaimthatcounterfactualuniversesinwhichtheconstantsthatappearinthelawsoftheactualuniversehavevaluesdifferentfromtheiractualvaluesareinhospitabletolifethatmostpossibleuniversesareinhospitabletolife.Thereareinfinitelymany(atleastthesizeofthesetofreals)possibleuniversesandofthosetherearejustasmanyhospitabletolifeasinhospitabletolife.TakeanyuniverseWinhospitabletolifeandaddlivingcreatures(evenintelligentlivingcreatures)tomakeuniverseW*.ThistypicallywillinvolvealteringtheontologyandlawsofW(notmerelybyalteringthevaluesofconstantsintheactuallaws).ButthereisnologicaloranalyticcontradictioninthedescriptionofW*andIknowofnometaphysicalprinciplethatrulesoutW.*Barnesmightberightthatuniverseshospitabletolifearerareamongthosethatinwhichtheconstantsthatoccurintheactuallawsarealteredbutheiswrongthatamongallmetaphysicallypossibleuniversesthesetoflife-hospitableuniversesissmallerthanthesetoflife-inhospitableuniverses.

Comment

• Barnesnotesthathisexamplesoffinetuningmostlyinvolveworldsthataresimilartoours….i.e.theyconsideruniverseswiththesamelawsbutdifferentfreeparametersandwonderswhetherthisbiasesthesearch.Hesaysitdoesbutbiasesit“infavoroffindinglife.”Justasitsbettertosearchformushroomsnearothermushroomsitsbettertosearchforlifehospitableuniversesneartheactualuniverse.Butthisisn’tcorrect.Inthevastmegaverseofpossibleuniversesthecardinalityofthesetoflifehospitableuniversesisthesameasthecardinalityoflifeinhospitableuniverses.Aslongaslawsandontologycanbealteredalongwiththeparameterstherewillbelifehospitableworldswiththealteredparametervalues.

Mistake2

• ThesecondmistakeisthepresuppositionthatthereisanobjectiveprobabilitydistributionoverpossibleuniversesandspecificallythatP(E/B),P(E/B&H),P(E/B&-H)representobjectiverationalcredences.• Thereisnogoodreasontothinkthatthereisanobjectiveprobabilitydistributionoverallpossibleuniverses.i.e.overallpossiblelaws,valuesofconstantsetc.

Twoproposalsforhowaprobabilitydistributioncanrepresentobjectivelyrationalcredences• 1.Physicalprobability:IfthereisaknownphysicalprobabilityP(E/B)thenP(E/B)representsanobjectiverationalcredence.Thelinkbetweenaphysicalprobabilityandarationalcredencesiscalled“ThePrincipalPrinciple.”• e.g.iftheQMprobabilityofanx-spinmeasurementresulting“up”is.5thenyourcredenceshouldbe.5.

• 2.Logic:Thereisatradition(Keynes,Carnap,Jaynes)ofattemptingtocharacterizeepistemicallyobjectivecredences.Anexampleistheprincipleofindifferencee.g.ifyourcompleteinformationisthatoneof3peoplecommittedthemurderyoushouldassignequalcredencetoeach.

Thereisnoroutetoobjectiveprobabilitydistributionoverthesetofuniverses.• 1.TheprobabilitiesinvolvedintheFTAarenotphysicalprobabilitiesspecifiedbyathelawsofatruephysicaltheorye.g.quantummechanicsorstatisticalmechanicssincelawsvaryamongtheworlds.Thisisclearsincetherequiredprobabilitydistributionoverworldsassignsprobabilitiestoworldswhoselawsdifferfromtheactuallaws.

• TheFTAprobabilitiesarenotfrequenciessincethefrequencyofaninfinitesubsetofaninfinitesetisnotwelldefined.

ObjectiveBayesianism?

• 2. Theprincipleofindifferenceleadstocontradictionsand/ordoesn’tdetermineauniqueprobabilitydistributionwhenappliedtoinfinitesets.BarnesreferencesE.T.Jaynes’proposalofasophisticateddevelopmentoftheindifferenceprinciplewhichclaimsthatincertainsituationstheobjectivecredencedistributionistheonethatmaximizesentropyofaprobabilitydistributionsubjecttoobjectiveconstraints.ButitisnotclearhowJaynes’approachappliestothesetofallpossibleworldsandsetofworldswithintelligentlifeor,forthatmatter,whyitisrationaltoassignanyprobabilitydistributionatalloverthesesets.Therationalattitudeseemsrathertonotassignanyprobabilityatall…orasDavidAlbertputsit“Idon’thaveaclue!”

Whywemighthavecometobelieveinobjectivelyrationalprobabilitydistributions.• OneoftenreadsthattheBoltzmannprobabilitydistributionthatgroundsstatisticalmechanicalinferencesisderivedfromtheapplicationoftheprincipleofindifference.Butthisisamistake.ThestatisticalmechanicalprobabilitymeasureistheuniformmeasureonthephasespaceconditionalonthePastHypothesis(thepropositionthatthespecifiesthemacrostateoftheveryearlyuniverseashaving.averylowentropy).ItisbestunderstoodasanempiricalprobabilityalongthelinesofDavidLewis’HumeanAccountoflawsandprobabilities.

Statisticalmechanicalprobabilities

• Statisticalmechanicalprobabilitiesmatchthecredencesdeterminedbytheprincipleofindifferenceandthemaximumentropyprincipleinmanysituations.Forexample,itisplausiblethatthestatisticalmechanicalprobabilityofanordinarysymmetricaldielandingshowinganyoneofitssixfacesis1/6.Iconjecturethatwehavegrownsoaccustomed(byexperienceandbyevolution)tousingthestatisticalmechanicaldistributionthatwecometobelieveinobjectiveepistemicprobabilitiesderivedfromrationalityalone.Butuseoftheprincipletoproblemswherestatisticalmechanicsdoesn’tapplyleadsusastray.Thisiswhathappenswhenwethinkthatrationalityrecommendsauniformdistributionoverallmetaphysicallypossibleworlds.

Conclusion1

• Theultimatefine-tuningargumentbeginswiththepremisethatalterationsintheconstantsthatappearinthelawsorinthelawsthemselvesyieldmanymoremetaphysicallypossibleuniversesthatarelifeprohibitingthanarelifehospitable.Thisismistakenandbasedonamisunderstandingofmetaphysicallypossibility.Soitcannotbeusedtosupportaprobabilitydistributionoverpossibleuniverseswhichassignsahigherprobabilitytolifeprohibitinguniversesthantolifehospitableuniverses.Norcansuchaprobabilitydistributionbesupportedbyphysicalprobabilitiesderivedfromthelawsnoraretheysupportablebyaprincipleofindifferenceoranyotherprinciplesofrationality.ForthesereasonsP(E/B&H)andP(B&-H)thatoccurinBayestheoremarenotobjectiverationalcredences andtheultimatefinetuningargumentcollapses.

ConclusionII

• Whenaphysicistseeslaws,constants,initialconditionsasbeingfinetuneditisasifshehasanitch.Sometimesscratchingitrelievestheitch.Thisiswhathappenswhenascientifictheoryexplainstheapparentfinetuninge.g.theexplanationofwhyalltheplanetstravelonorbitsinthesamedirection.Sometimesscratchingtheitchjustcausesittoitchmore.Thisiswhatmayhappeninthecaseofinflationwhichwasproposedtosolvefine-tuningproblemsofflatnessandhomogeneitybutleadstofine-tuningproblemsoftheinflatonfield.Andsometimestheitchisjustinourminds.Thisisthesituationofthosewhoareseducedbytheultimatefinetuningargumentintolookingoutsideofscienceforrelief.

Areallfine-tuningargumentsbadarguments?• Notallfinetuningargumentsarebad

Thebestofallpossibleuniverses

Argumentsfromfinetuning

• AfinetuningargumentpointstoaproblemwithatheoryTbyclaimingthatThasanexplanatorydeficit;itleavessomethingunexplainedthatshouldbeexplained.ConsidersomephenomenonoreventEe.g.theexistenceofstars.SupposeitfollowsfromTthatforEtoobtainacertainrestrictedsmallrangeoflawsLorconstantsthatoccurinlawsQorinitialconditionsImustobtain.SohadthingsbeendifferentwithrespecttotheseEwouldnothaveoccurred.SomefinetuningargumentsgoontoclaimthatgivenTLorQorIareimprobable.EithertheoccurrenceofEmustberegardedasanunexplainedcoincidence,orelseTmustbemodifiedorreplacedbyT*whichrendersE likelytooccurratherthananunlikelycoincidence.