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1、PHYSICALREVIEW0VOLUME24,NUMBER215JULY1981SagnaceffectinrelativisticandnonrelativisticphysicsJ.AnandanDepartmentofMathematics,UniversityofCalifornia,Berkeley,California94720(Received13February1981)Asimplespecial-relativisticderivationoftheSagnaceffect,whichreconci
2、lestheearliergeneral-relativisticandnonrelativisticderivations,isgiven.Adistinctionismadebetweenthe"classicalSagnaceffect"andthequantum"Sagnaceffect.Anewgroup-theoreticderivationoftheseeffectsisalsogiven.Itispointedoutthattheremustexistaphaseshiftduetothej.homasp
3、recessionintheinterferenceofparticleswithintrinsicspin.Thegroup-theoretictreatmentalsoelucidatestheconnectionbetweenrelativisticandnonrelativisticphysics,onaclassicalandquantumlevel,withandwithoutgravity.Aformulationoftheprincipleofequivalence,whichisrelatedtothe
4、Sagnaceffect,isgiveninrelativisticandnonrelativisticphysicsintermsoftherespectiveinvariancegroups.NewexperimentsareproposedtotesttheSagnaceffectinsuperfluidhelium.Thepossibleuseofthegeneral-relativisticSagnaceffecttomeasurethecurvaturetensorandinparticulartodetec
5、tgravitationalwavesissuggested.I.INTRODUCTIONtivisticallytheformereffectiszerowhilethelatterisnonzero.Thephaseshiftintheinterferenceoftwoco-InSec.III,weexaminethegroup-theoreticalherentlightbeamsduetotherotationoftheap-meaningoftherelativisticandnonrelativisticpa
6、ratuswasfirstobservedbySagnacandMichel-Sagnaceffects.Thisthrowslightontheirrela-son.'Thesameeffectintheinterferenceofneu-tionship,bothonclassicalandqu3ntum-mecha-tronbeamsduetotheEarth'srotationhasbeennicallevels.'Thisconsideration,inourview,observedbyWernejt',St
7、audenmann,andColella'providesthedeepestreasonfortheexistencebymeansofanexperimentproposedbytheau-oftheSagnaceffectandalsoyieldsaphaseshiftthor.'Therehavebeentwoapparentlyunrelatedduetothe'Thomasprecessionintheinterferenceexplanationsforthiseffect.Oneisgeneralrela
8、-ofparticleswithintrinsicspin.'TheSagnaceffecttivistic''andtheotherisnonrelativistic.""'isgeneralizedtoarbitraryspace-timegroups.Unfortunately,therelativistict
