Conventions in Relativity Theory and Quantum Mecha

4790015-9018/02/0400-479/0©2002PlenumPublishingCorporationFoundationsofPhysics,Vol.32,No.4,April2002(©2002)ConventionsinRelativityTheoryandQuantumMechanicsKarlSvozil11InstitutfürTheoretischePhysik,UniversityofTechnologyVienna,WiednerHauptstraße8-10/136,A-1040Vienna,Austria;e-mail:[e-mail]24,2001;revisedJanuary18,2002Theconventionalisticaspectsofphysicalworldperceptionarereviewedwithanemphasisontheconstancyofthespeedoflightinrelativitytheoryandtheirreversibilityofmeasurementsinquantummechanics.AnappendixcontainsacompleteproofofAlexandrov’stheoremusingmainlymethodsofaffinegeometry.KEYWORDS:conventionality;theoryofrelativity;interpretationofquantumtheory.1.KNOWTHYSELFThisinscriptionontheOracleofApolloatDelphi,Greece,datesfrom6thcenturyB.C.,anditisstilloftremendousimportancetoday.Forwedonotandneverwillseetheworld‘‘asis,’’butratherasweperceiveit.Andhowweperceivetheworldismediatedbyoursenseswhichserveasinterfacestotheworld‘‘outthere’’(ifany);butnottoasmallextendalsobywhatweprojectontoit.Conventionsareprojectionswhichwehavetoadoptinordertobeabletocopewiththephenomena‘‘streamingin’’fromthesenses.Conventionsareanecessaryandindispensablepartofoperatio-nalizable2phenomenologyandtool-building.Thereisnoperceptionand2InwhatfollowsweshalladoptBridgman’sconceptof‘‘operational’’asoneofquitesimple-mindedexperimentaltestability,eveninviewofitsdifficultieswhichthisauthorapproachedlateron.(1–5)interveningwithoutconventions.Theylieattheveryfoundationsofourworldconceptions.Conventionsserveasasortof‘‘scaffolding’’fromFile:KAPP/825-foop/32-4371742-Page:1/24-Op:GC-Time:09:46-Date:05:04:2002whichweconstructourscientificworldview.Yet,theyaresosimpleandalmostself-evidentthattheyarehardlymentionedandgounreflected.Totheauthor,thisunreflectednessandunawarenessofconventio-nalityappearstobethebiggestproblemrelatedtoconventions,especiallyiftheyaremistakenlyconsideredasphysical‘‘facts’’whichareempiricallytestable.Thisconfusionbetweenassumptionandobservational,operationalfactseemstobeoneofthebiggestimpedimentsforprogressiveresearchpro-grams,inparticulariftheysuggestpostulateswhicharebasedonconven-tionsdifferentfromtheexistingones.Inwhatfollowsweshallmainlyreviewanddiscussconventionsinthetwodominatingtheoriesofthe20thcentury:quantummechanicsandrelativitytheory.2.CONVENTIONALITYOFTHECONSTANCYOFTHECHARACTERISTICSPEEDSupposetwoobserverscalledAliceandBobmeasurespaceandtimeintwocoordinateframes.Operationallytheiractivitiesamounttothefollowing.Theyhaveconstructed‘‘identical’’clocksandscalesof‘‘equal’’lengthwhichtheyhavecomparedinthedistantpast;whenBoblivedtogetherwithAlice.Thentheyhaveseparated.AlicehasdecidedtodepartfromBoband,sincethen,ismovingwithconstantspeedawayfromhim.HowdoBob’sandAlice’sscalesandclockscomparenow?Willtheybeidentical,orwilltheydephase?Thesearesomeofthequestionswhich‘‘relativity’’theorydealswith.ItderivesitsnamefromPoincaré’s1904‘‘principleofrelativity’’statingthat(see,forinstance,Ref.6,p.74)‘‘thelawsofphysicalphenomenamustbethesameforastationaryobserverasforanobservercarriedalonginauniformtranslation;sothatwehavenotandcannothaveanymeansofdis-cerningwhetherornotwearecarriedalonginsuchamotion.’’Formally,thisamountstotherequirementofforminvarianceorcovarianceofthephysi-calequationsofmotion.Oneoftheseeminglymindbogglingfeaturesofthetheoryofrelativityisthefactthatsimultaneityandeventhetimeorderoftwospatiallyseparatedeventsneedsnolongerbeconserved.ItmayindeedhappenthatAliceperceivesthefirsteventbeforethesecond,whileBobperceivesbotheventsashappeningatthesametime;oreventhesecondeventaheadofthefirst.Simultaneitycanonlybedefined‘‘relative’’toaparticularrefer-enceframe.Iftruethere,itisfalseinanydifferentframe.ThefirstpartofEinstein’sseminalpaper(7)isdedicatedtoadetailedstudyoftheintrinsicallyoperationalproceduresandmethodswhichare480SvozilFile:KAPP/825-foop/32-4371742-Page:2/24-Op:GC-Time:09:46-Date:05:04:2002necessarytoconceptualizethecomparisonofAlice’sandBob’sreferenceframes.Thispartcontainscertain‘‘reasonable’’conventionsfordefiningclocks,scales,velocitiesandinparticularsimultaneity,withoutwhichnosuchcomparisoncouldeverbeachieved.Theseconventionsappeartoberatherevidentandnatural,almosttrivial,andyieldaconvenientfor-malizationofspace-timetransformations,buttheyareneverthelessarbi-trary.Thesimultaneityissuehasbeenmuchdebatedinthecontemporarydiscussionsonconventionality.(8–10)Thereisanotherelementofconventionalitypresentinrelativitytheorywhichhasgottenlessattention.(11)Itistheassumptionoftheconstancyofthespeedoflight.Indeed,theInternationalSystemofunitsassumeslighttobeconstant.Itwasdecidedin1983bytheGeneralConferenceonWeightsandMeasuresthattheacceptedvalueforthespeedoflightwouldbeexactly299,792,458meterspersecond.Themeterisnowthusdefinedasthedistancetraveledbylightinavacuumin1/299,792,458second.Withthespeedoflightnolongerbeinganempiricalfactbutaconvention,theproperempiricalstatementisthatthelengthofarodneitherdependsontheorientationnorontheinertialframewherethatbodyisatrest.(12)Despitetheobviousconventionalityoft