HOW DO WE LOOK AT GRAVITATION AND QED 2 HOW DO WE

sf89e,7/8/1996PROBABILITYINQUANTUMTHEORYyE.T.JaynesWaymanCrowProfessorofPhysicsWashingtonUniversity,St.LouisMO63130Abstract:Forsomesixtyyearsithasappearedtomanyphysiciststhatprobabilityplaysafundamentallydierentroleinquantumtheorythanitdoesinstatisticalmechanicsandanalysisofmeasurementerrors.Itisacommonlyheardstatementthatprobabilitiescalculatedwithinapurestatehaveadierentcharacterthantheprobabilitieswithwhichdierentpurestatesappearinamixture,ordensitymatrix.AsPauliputit,theformerrepresents\EineprinzipielleUnbestimmtheit,nichtnurUnbekanntheit.Butthisviewpointleadstosomanyparadoxesandmysteriesthatweexploretheconsequencesoftheuniedview,thatallprobabilitysigniesonlyincompletehumaninformation.Weexamineindetailonlyoneoftheissuesthisraises:therealityofzero{pointenergy.CONTENTSINTRODUCTION:HOWWELOOKATTHINGS1HOWDOWELOOKATGRAVITATIONANDQED?2HOWDOWELOOKATBASICQUANTUMTHEORY?4PROBABILITYTHEORYASTHELOGICOFSCIENCE7HOWWOULDQUANTUMTHEORYBEDIFFERENT?9ISZERO{POINTENERGYREAL?11THELAMBSHIFTINCLASSICALMECHANICS13CLASSICALSUBTRACTIONPHYSICS15CONCLUSION18REFERENCES19INTRODUCTION:HOWWELOOKATTHINGSInthisworkshopweareventuringintoasmokyareaofsciencewherenobodyknowswhattherealtruthis.Sucheldsarealwaysdominatedbythecompensationphenomenon:supremeself{condencetakestheplaceofrationalarguments.Thereforeweshalltrytoavoiddogmaticasser-tions,andonlypointoutsomeofthewaysinwhichquantumtheorywouldappeardierentifweweretoadoptadierentviewpointaboutthemeaningandfunctionaluseofprobabilitytheory.WethinkthattheoriginalviewpointofJamesBernoulliandLaplaceoerssomeadvantagestodayinbothconceptualclarityandtechnicalresultsforcurrentlymysteriousproblems.yArevisedandextendedversionofapaperpresentedattheWorkshoponComplexity,Entropy,andthePhysicsofInformation,SantaFe,NewMexico,May29{June2,1989.TheoriginalversionisintheProceedingsVolume,Complexity,EntropyandthePhysicsofInformation,W.H.Zurek,Editor,Addison{WesleyPublishingCo.,Reading,MA(1990).2Howwelookatatheoryaectsourjudgmentastowhetheritismysteriousorirrationalontheonehand;orwhetheritissatisfactoryandreasonableontheother.Thusitaectsthedirectionofourresearcheorts;andafortioritheirresults.Indeed,whetherwetheoristscaneveragainmanagetogetaheadofexperimentwilldependonhowwechoosetolookatthings,becausethatdeterminesthepossibleformsofthefuturetheoriesthatwillgrowoutofourpresentones.Oneviewpointmaysuggestnaturalextensionsofatheory,whichcannotevenbestatedintermsofanother.Whatseemsaparadoxononeviewpointmaybecomeaplatitudeonanother.Forexample,100yearsagoitwasamuchdiscussedproblemhowmaterialobjectscanmovethroughtheaetherwithoutresistance.Yetadierentwayoflookingatitwouldhavemadethemysterydisappearwithoutanyneedtodispensewiththeaether.Onecanregardmaterialobjects,notasimpedimentstothe\owofaether,butaspartsoftheaether(\knotsinitsstructure)whicharepropagatingthroughit.Onthiswayoflookingatit,thereisnomysterytobeexplained.AsastudentatPrincetonmanyyearsago,IwasfascinatedtolearnfromJohnWheelerhowmuchofphysicscanberegardedasreallyonlygeometry,inthisway.Todaywearebeginningtorealizehowmuchofallphysicalscienceisreallyonlyinformation,organizedinaparticularway.Butwearefarfromunravellingtheknottyquestion:\Towhatextentdoesthisinformationresideinus,andtowhatextentisitapropertyofNature?Surely,almosteveryconceivableopiniononthiswillbeexpressedatthisworkshop.Isthisvariabilityofviewpointsomethingtobedeplored?Well,eventuallyweshouldhopetopresentauniedpicturetotherestoftheworld.Butforthemomentthisisneitherpossiblenordesirable.Wearealllookingatthesamerealityandtryingtounderstandwhatitis.Butwecouldneverunderstandthestructureofamountainifwelookedatitonlyfromoneside.Therealitywearestudyingisfarmoresubtlethanamountain,andsoitisnotonlydesirable,butnecessarythatitbeexaminedfrommanydierentviewpoints,ifweareevertoresolvethemysteryofwhatitis.Herewepresentoneofthoseviewpoints,whichwethinkhasnotbeensucientlyrecognizedintherecentliterature.Firstwenoteamoreimmediateexampleoftheeectofhowwelookatthings,tosupportbyphysicalargumentswhatissuggestedlaterfromprobabilityconsiderations.HOWDOWELOOKATGRAVITATIONANDQED?Inteachingrelativitytheory,onemayencounterabrightstudentwhoraisesthisobjection:\Whyshouldsuchafundamentalthingasthemetricofspaceandtimebedeterminedonlybygravitationalelds|theweakestofallinteractions?Thisseemsirrational.Wepointouttohimadierentwayoflookingatit,whichmakestheirrationalitydisappear:\Oneshouldnotthinkofthegravitationaleldasakindofpreexistingforcewhich‘causes’themetric;rather,thegravitationaleldisthemainobservableconsequenceofthemetric.Thestronginteractionshavenotbeenignored,becausetheeldequationsshowthatthemetricisdeterminedbyalltheenergypresent.Accordingtotherstviewpoint,onemightthinkitapressingresearchproblemtoclearupthemysteryofwhythemetricdependsonlyongravitationalforces.Onthesecondviewpointthisproblemdoesnotexist.Butthenifthestudentisverybright,hewillbebackthenextdaywithanothercriticism:\Ifthegravitationaleldisonlyakindofbootstrapeectoftheotherforces,itraisesthequestionwhetherthegravitationaleldshouldbequantizeds