Recent Experimental Tests of Special Relativity

arXiv:physics/0506168v1[physics.class-ph]21Jun2005RecentExperimentalTestsofSpecialRelativityPeterWolf1,2,S´ebastienBize1,MichaelE.Tobar3,Fr´edericChapelet1,Andr´eClairon1,Andr´eN.Luiten3,andGiorgioSantarelli11BNM-SYRTE,ObservatoiredeParis,61avenuedel’Observatoire,75014Paris,France2BureauInternationaldesPoidsetMesures,PavillondeBreteuil,92312S`evresCedex,France3UniversityofWesternAustralia,SchoolofPhysics,Nedlands6907WA,AustraliaSummary.WereviewourrecentMichelson-Morley(MM)andKennedy-Thorndike(KT)experiment,whichtestsLorentzinvarianceinthephotonsector,andreportfirstresultsofourongoingatomicclocktestofLorentzinvarianceinthemattersector.TheMM-KTexperimentcomparesacryogenicmicrowaveresonatortoahy-drogenmaser,andhassetthemoststringentlimitonanumberofparametersinalternativetheoriestospecialrelativity.IntheRobertson-Mansouri-Sexl(RMS)frameworkourexperimentconstrains1/2−βMS+δMS=(1.2±2.2)×10−9andβMS−αMS−1=(1.6±3.0)×10−7,whichisofthesameorderasthebestre-sultsfromotherexperimentsfortheformerandrepresentsa70foldimprovementforthelatter.InthephotonsectorofthegeneralLorentzviolatingstandardmodelextension(SME),ourexperimentlimits4componentsofthe˜κe−parametertoafewpartsin10−15andthethreecomponentsof˜κo+toafewpartsin10−11.Thiscorrespondstoanimprovementbyuptoafactor10onbestpreviouslimits.WealsoreportfirstresultsofatestofLorentzinvarianceintheSMEmattersector,usingZeemantransitionsinalasercooledCsatomicfountainclock.Wedescribetheexperimenttogetherwiththetheoreticalmodelandanalysis.Recentexperimentalresultsarepresentedandanalyzed,includingstatisticaluncertaintiesandabriefdiscussionofsystematiceffects.Basedontheseresults,wegiveafirstestimateofcomponentsofthe˜cpparametersoftheSMEmattersector.Afullanalysisofsystematiceffectsisstillinprogress,andwillbethesubjectofafuturepublicationtogetherwithourfinalresults.Ifconfirmed,thepresentlimitswouldcorrespondtofirstevermeasurementsofsome˜cpcomponents,andimprovementsby11and14ordersofmagnitudeonothers.1IntroductionOnehundredyearsafterEinstein’sfirstpaper[1]specialrelativityisstillstandinguptoallexperimentaltestsandverifications.Overthelastcentury2PeterWolfetal.alargenumberofsuchtestshaveprovidedwhatiscertainlyoneofthemostsolidexperimentalbasesofanypresentfundamentaltheoryofphysics.Asaconsequencespecialrelativityistodayunderpinningallofpresentdayphysics,rangingfromthestandardmodelofparticlephysics(includingnuclearandatomicphysics)togeneralrelativityandastronomy.Thatfactcontinuestopushexperimentaliststosearchfornewexperiments,orimproveonpreviousones,inordertouncoverapossibleviolationofspecialrelativity,asthatwouldmostcertainlyleadthewaytoanewconceptionofphysicsandoftheuniversesurroundingus.Additionalincentiveforsuchtestscomesfromunificationtheories(e.g.stringtheories,loopquantumgravity),someofwhich[2,3,4]suggestaviolationofspecialrelativityatsome,aprioriunknown,level.Giventhestrongtheoreticalmotivationforsuchtheories,butthelackofexperimentaldatathatwouldallowamorerigorousselectionamongthecandidatetheoriesandtheparameterspaceofeachclassofsuchtheories,anyexperimentalresultsthatcouldaidthetheoreticaleffortsarecertainlywelcome.ThefundamentalhypothesisofspecialrelativityiswhatEinsteintermedthe”principleofrelativity”[1],orinmoremoderntermsLocalLorentzInvari-ance(LLI)[5].Looselystated,LLIpostulatesthattheoutcomeofanylocaltestexperimentisindependentofthevelocityofthefreelyfallingapparatus.LLIcanbeviewedasaconstituentpartoftheEinsteinEquivalencePrinciplewhichisfundamentaltogeneralrelativityandallmetrictheoriesofgravita-tion[5].TheexperimentspresentedinthispapertestsomeaspectofLLI,ascharacterizedinLorentzviolatingtheoreticalframeworksliketheonesbrieflydescribedinsection2.Wereviewandpresenttwoofourrecentandongoingexperiments[7,8,9]thattestdifferentaspectsofLLI,analyzinganddescribingtheiroutcomeintwotheoreticalframeworks,thekinematicaltesttheoryofRobertson,Man-souriandSexl(RMS)[10,11]andtheLorentzviolatingextensionofthestan-dardmodel(SME)[12].Theseexperiments,aMichelson-MorleyandKennedy-Thorndiketest(section3),andanongoingatomicclocktestintheSMEmattersector(section4),areamongthemostpreciseLLItestsatpresent.ThevastmajorityofmodernexperimentsthattestLLIrelyessentiallyonthestabilityofatomicclocksandmacroscopicresonators,thereforeimprove-mentsinoscillatortechnologyhavegonehandinhandwithimprovedtestsofLLI.Theexperimentspresentedherearenoexception.Allofthememployclocksandresonatorsdevelopedandusedprimarilyforotherpurposes(na-tionalandinternationaltimescales,frequencycalibration,etc.)butadaptedfortestsofLLI.2TheoreticalframeworksNumeroustesttheoriesthatallowthemodelingandinterpretationofexper-imentsthattestLLIhavebeendeveloped.Kinematicalframeworks[10,11]RecentExperimentalTestsofSpecialRelativity3postulateasimpleparametrisationoftheLorentztransformationswithexper-imentssettinglimitsonthedeviationofthoseparametersfromtheirspecialrelativisticvalues.Amorefundamentalapproachisofferedbytheoriesthatparametrisethecouplingbetweengravitationalandnon-gravitationalfields(THǫμ[15,5,16]orχg[17]formalisms)whichallowthecomparisonofexper-iments