Introduction
OnSeptember14,1959,twelvedaysafterpassingthroughherpointofclosestapproach totheEarth,theplanetVenuswasbombardedbypulsesofradiowavessentfromEarth. AhandfulofanxiousscientistsatLincolnLaboratoriesinMassachusettswaitedtodetect theechoofthereflectedwaves.Totheirinitialdisappointment,neitherthedatafromthis day,norfromanyofthedaysduringthatmonth-longobservation,showedanydetectable echonearinferiorconjunctionofVenus.However,alater,improvedreanalysisofthedata showedabonafideechointhedatafromoneday:September14.Thusoccurredthefirst recordedradarechofromaplanet.
Exactlyfifty-sixyearslater,onSeptember14,2015,aratherdifferentsignalwas receivedbyscientists,thistimeinHanford,Washington,andLivingston,Louisiana.The signalwasnotelectromagneticbutinsteadwasawaveinthefabricofspacetimeitself. Itwasthefinalburstofgravitationalwavesfromtwoblackholesthatmergedtoforma singleblackholesomewhereinthesouthernskysome1.3billionyearsago.Thesignalwas recognizedwithinminutesbyautomateddataprocessingsoftware.Thistime,thescientists, numberingover1,000,wereanxiouslestthesignalbeanunluckyartifactofinstrumental noise.ButonFebruary11,2016,afteranintensiveandsecretivefivemonthsofdetailed analysis,checksandcross-checks,theyannouncedataWashington,DC,pressconference thattheLaserInterferometerGravitational-WaveObservatory(LIGO)hadmadethefirst directdetectionofgravitationalwaves.
Asifthe100thanniversaryofthegeneraltheoryofrelativityduring2015wasnot alreadysomethingtocelebrate,thedetectionofgravitationalwaveswasicingonthe cake.1 Itwasalsothecapstoneofahalf-centuryperiodduringwhichgeneralrelativity experiencedaremarkablerenaissance,fromasubjectrelegatedtothebackwatersof physicsandastronomy,toonethatisregardedascentraltothemajorscientificquestions oftheday,fromthenatureofthefundamentalparticlestothefateoftheuniverse.Itwas aperfectillustrationofhowthefieldwastransformedfromonethatwasoncecalled“a theorist’sparadiseandanexperimentalist’spurgatory,”tooneinwhichexperimentalists andtheoristsworkhandinhand.Ithighlightedthefield’sevolutionfromtheworldof “smallscience,”whereindividualsorsmallgroupsscratchedoutmathematicalformulas intheirtinyoffices,tothatof“bigscience,”whereworldwidecollaborationsofscientists conducttheiraffairsviateleconandSkype,spendbudgetsmeasuredinunitsofmegabucks ormegaeuros,andrequireprojectmanagerstokeepmattersontrack.
1 Andascoopoficecreamontopoftheicingwastheawardofthe2017NobelPrizeinPhysicstothreeof LIGOsfounders,RainerWeiss,BarryBarish,andKipThorne.Theotherpioneeroftheproject,RonDrever, hadalreadydiedinMarchofthatyear.
Theoriginsofthisremarkabletransformationofgeneralrelativityfromanobscureniche ofmathematicsandphysicstoamajorsubfieldofphysicsandastronomy,todaycalled “GravitationalPhysics,”canbefoundinasetofeventsoftheacademicyear1959–1960, beginningwiththatfirstradarechofromVenus.Fourkeyeventsfollowed.
OnMarch9,1960,theeditorialofficeof PhysicalReviewLetters receivedapaper byRobertPoundandGlenRebkaJr.,entitled“ApparentWeightofPhotons.”Thepaper reportedthefirstsuccessfullaboratorymeasurementofthegravitationalredshiftoflight. ThepaperwasacceptedandpublishedintheApril1issue.
InJune1960,thereappearedinvolume10ofthe AnnalsofPhysics apaperon“ASpinor ApproachtoGeneralRelativity”byRogerPenrose.Itoutlinedastreamlinedcalculusfor generalrelativitybasedupon“spinors”ratherthanupontensors.
Laterthatsummer,CarlBrans,ayoungPrincetongraduatestudentworkingwithRobert Dicke,beganputtingthefinishingtouchesonhisPhDthesis,entitled“Mach’sPrinciple andaVaryingGravitationalConstant.”Partofthatthesiswasdevotedtothedevelopment ofa“scalar-tensor”alternativetothegeneraltheoryofrelativity.Althoughitsauthorsnever referredtoitthisway,itcametobeknownastheBrans-Dicketheory.
OnSeptember26,1960,justoverayearaftertherecordedVenusradarecho, astronomersThomasMatthewsandAllanSandageandcoworkersatMountPalomarused the200-inchtelescopetomakeaphotographicplateofthestarfieldaroundthelocation oftheradiosource3C48.Althoughtheyexpectedtofindaclusterofgalaxies,whatthey sawatthepreciselocationoftheradiosourcewasanobjectthathadadecidedlystellar appearance,anunusualspectrum,andaluminositythatvariedonatimescaleasshortas fifteenminutes.Thenamequasistellarradiosourceor“quasar”wassoonappliedtothis objectandtootherslikeit.
Thesedisparateandseeminglyunrelatedeventsoftheacademicyear1959–1960,in fieldsrangingfromexperimentalphysicstoabstracttheorytoastronomy,signaledthe beginningofaneweraforgeneralrelativity.Thiserawastobeoneinwhichgeneral relativitynotonlywouldbecomeanimportanttheoreticaltooloftheastrophysicistbut alsowouldhaveitsvaliditychallengedasneverbefore.Yetitwasalsotobeatimein whichexperimentaltoolswouldbecomeavailabletotestthetheoryinunheard-ofways andtounheard-oflevelsofprecision.
Theopticalidentificationof3C48(MatthewsandSandage,1963)andthesubsequent discoveryofthelargeredshiftsinitsspectrallinesandinthoseof3C273(Greensteinand Matthews,1963;Schmidt,1963)presentedtheoristswiththeproblemofunderstanding theenormousoutputofenergyfromaregionofspacecompactenoughtopermitthe luminositytovarysystematicallyovertimescalesasshortasdaysorhours.Manytheorists turnedtogeneralrelativityandtothestrongrelativisticgravitationalfieldsitpredicts,to providethemechanismunderlyingsuchviolentevents.Thiswasthefirstuseofthetheory’s strong-fieldaspect,inanattempttointerpretandunderstandobservations.Thesubsequent discoveryofthecosmicmicrowavebackground(CMB)radiationin1964,ofpulsarsin 1967,andofthefirstblackholecandidatein1971showedthatitwouldnotbethelast. However,theuseofrelativisticgravitationinastrophysicalmodelbuildingforcedtheorists andexperimentaliststoaddressthequestion:Isgeneralrelativitythecorrectrelativistic theoryofgravitation?Itwouldbedifficulttoplacemuchconfidenceinmodelsforsuch
phenomenaasquasarsandpulsarsiftherewereseriousdoubtaboutoneofthebasic underlyingphysicaltheories.Thus,thegrowthof“relativisticastrophysics”intensifiedthe needtostrengthentheempiricalevidencefororagainstgeneralrelativity.
ThepublicationofPenrose’sspinorapproachtogeneralrelativity(Penrose,1960)was oneoftheproductsofanewschoolofrelativitytheoriststhatcametotheforeinthelate 1950s.Theserelativistsappliedtheelegant,abstracttechniquesofpuremathematicsto physicalproblemsingeneralrelativity,anddemonstratedthatthesetechniquescouldalso aidintheworkoftheirmoreastrophysicallyorientedcolleagues.Thebridgingofthegaps betweenmathematicsandphysicsandmathematicsandastrophysicsbysuchworkersas Bondi,Dicke,Sciama,Pirani,Penrose,Sachs,Ehlers,Misner,andotherschangedtheway thatresearch(andteaching)inrelativitywascarriedout,andhelpedmakeitanactiveand excitingfieldofphysics.Yetagainthequestionhadtobeaddressed:Isgeneralrelativity thecorrectbasisforthisresearch?
Theotherthreeeventsof1959–1960contributedtotherebirthofaprogramtoanswer thatquestion,aprogramofexperimentalgravitationthathadbeensemi-dormantforforty years.
ThePound-Rebka(1960)experiment,inadditiontoverifyingtheprincipleofequivalenceandthegravitationalredshift,demonstratedthepowerfuluseofquantumtechnology ingravitationalexperimentsofhighprecision.Thenexttwodecadeswouldseefurther usesofquantumtechnologyinsuchtoolsasatomicclocks,laserranging,superconducting gravimeters,andgravitational-wavedetectors,tonameonlyafew.Recordingradar echosfromVenus(Smith,1963)openedupthesolarsystemasalaboratoryfortesting relativisticgravity.Therapiddevelopmentoftheinterplanetaryspaceprogramduring theearly1960smaderadarrangingtobothplanetsandartificialsatellitesavitalnew toolforprobingrelativisticgravitationaleffects.Coupledwiththetheoreticaldiscovery in1964oftherelativistictime-delayeffect(Shapiro,1964),itprovidednewandaccurate testsofgeneralrelativity.Forthenextdecadeandahalf,untilthesummerof1974,the solarsystemwouldbetheprimaryarenaforhigh-precisiontestsofgeneralrelativity. Finally,thedevelopmentoftheBrans-Dicke(1961)theoryprovidedaviablealternative togeneralrelativity.Itsveryexistenceandagreementwiththeexperimentalresultsofthe daydemonstratedthatgeneralrelativitywasnotauniquetheoryofgravity.Someeven preferreditovergeneralrelativityonaestheticandtheoreticalgrounds.Attheveryleast,it showedthatdiscussionsofexperimentaltestsofrelativisticgravitationaleffectsshouldbe carriedonusingabroadertheoreticalframeworkthanthatprovidedbygeneralrelativity alone.Italsoheightenedtheneedforhigh-precisionexperimentsbecauseitshowedthatthe mere detection ofasmallgeneralrelativisticeffectwasnotenough.Whatwasnowrequired wasmeasurementsoftheseeffectstoaccuraciesof10percent,1percent,orfractionsofa percentandbetter,todistinguishamongcompetingtheoriesofgravitation.
Toappreciatemorefullytheregenerativeeffectthattheseeventshadongravitational theoryanditsexperimentaltests,itisusefultoreviewbrieflythehistoryofgeneral relativityintheforty-fiveyearsfollowingEinstein’spublicationofthetheory.
Inderivinggeneralrelativity,Einsteinwasnotparticularlymotivatedbyadesireto accountforunexplainedexperimentalorobservationalresults.Instead,hewasdriven bytheoreticalcriteriaofeleganceandsimplicity.Hisprimarygoalwastoproducea
gravitationtheorythatincorporatedtheprincipleofequivalenceandspecialrelativityin anaturalway.Intheend,however,hehadtoconfrontthetheorywithexperiment.This confrontationwasbasedonwhatcametobeknownasthe“threeclassicaltests.”
Oneofthesetestswasanimmediatesuccess–theabilityofthetheorytoaccount fortheanomalousperihelionshiftofMercury.Thishadbeenanunsolvedproblemin celestialmechanicsforoverhalfacentury,sincetheannouncementbyUrbainJeanJoseph LeVerrierin1859that,aftertheperturbingeffectsoftheplanetsonMercury’sorbithad beenaccountedfor,thereremainedinthedataanunexplainedadvanceintheperihelion ofMercury.Themodernvalueforthisdiscrepancyisaboutforty-threearcsecondsper century.Anumberofadhocproposalsweremadeinanattempttoaccountforthisexcess, includingtheexistenceofanewplanet,dubbed“Vulcan,”neartheSun,andadeviation fromtheinverse-squarelawofgravitation.Ahalfcenturyofastronomicalsearchesfor Vulcanyieldednumerousclaimedsightings,butintheend,nosolidevidencefortheplanet wasfound.AndwhileachangeintheNewtonianinverse-squarelawproposedbySimon Newcombe,fromthepower2tothepower2.000000157,couldaccountfortheperihelion advanceofMercury,itultimatelyconflictedwithdataonthemotionoftheMoon.
EinsteinwaswellawareoftheproblemofMercury,and,infact,heuseditasaway totesthisearlyattemptsatatheoryofgravity;forexample,hefinallyrejectedthe1912 “Entwurf”or“draft”theorythathehaddevelopedwithMarcelGrossmanninpartbecause itgavethewrongperihelionadvance.Butwhenhethoughthehadobtainedthefinaltheory inNovember1915,thefactthatitgavethecorrectadvanceconvincedhimthathehad succeeded.
Thenextclassicaltest,thedeflectionoflightbytheSun,wasnotonlyasuccess,itwas asensation.ShortlyaftertheendofWorldWarI,twoexpeditionsorganizedbyArthur StanleyEddingtonsetoutfromEngland:oneforSobral,inBrazil;andonefortheisland ofPrincipeoffthecoastofAfricatoobservethesolareclipseofMay29,1919.Theirgoal wastomeasurethedeflectionoflightaspredictedbygeneralrelativity:1.75arcseconds foraraythatgrazestheSun.Theobservationshadtobemadeinthepathoftotalityof asolareclipse,duringwhichtheMoonwouldblockthelightfromtheSunandreveal thefieldofstarsaroundit.Photographicplatestakenofthestarfieldduringtheeclipse werecomparedwithplatesofthesamefieldtakenwhentheSunwasnotpresent,andthe angulardisplacementofeachstarwasdetermined.Theresultswere1.13 ± 0.07timesthe EinsteinpredictionfortheSobralexpedition,and0.92 ± 0.17forthePrincipeexpedition (Dysonetal.,1920).TheNovember1919announcementoftheseresultsconfirmingthe theorycaughttheattentionofawar-wearypublicandhelpedmakeEinsteinacelebrity. Nevertheless,theexperimentswereplaguedbysystematicerrors,andsubsequenteclipse expeditionsdidlittletoimprovethesituation.
ThethirdclassicaltestwasactuallythefirstproposedbyEinstein(1908):thegravitationalredshiftoflight.Butbycontrastwiththeothertwotests,therewasnoreliable confirmationofituntilthe1960Pound-Rebkaexperiment.Onepossibletestinvolved theredshiftofspectrallinesfromthesun.A1917measurementbyastronomerCharles St.John(1917)failedtodetecttheeffect,sowingconsiderabledoubtaboutthevalidity ofthetheory.Thirtyyearsofsuchmeasurementsrevealedmainlythattheobservedshifts insolarspectrallinesaredominatedbyDopplershiftsduetoradialmassmotionsinthe
solarphotosphere,andbylineshiftsduetothehighpressuresinthesolaratmosphere, makingdetectionoftheEinsteinshiftverydifficult.Itwouldbe1962beforeareliablesolar redshiftmeasurementwouldbemade.Similarlyinconclusivewereattemptstomeasure thegravitationalredshiftofspectrallinesfromwhitedwarfs,primarilyfromSiriusB and40EridaniB,bothmembersofbinarysystems.Becauseofuncertaintiesinthe determinationofthemassesandradiiofthesestars,andbecauseofpossiblecomplications intheirspectraduetoscatteredlightfromtheircompanions,reliable,precisemeasurements werenotpossible.Furthermore,bythelate1950s,itwasbeingsuggestedthatthe gravitationalredshiftwasnotatruetestofgeneralrelativityafterall.AccordingtoLeonard SchiffandRobertDicke,thegravitationalredshiftwasaconsequencepurelyofthe principleofequivalence,anddidnottestthespecificfieldequationsofgravitationaltheory. Cosmologywasoneareawheregeneralrelativitycouldconceivablybeconfronted withobservation.Initiallythetheorymetwithsuccessinitsabilitytoaccountforthe observedexpansionoftheuniverse,yetbythe1940stherewasconsiderabledoubt aboutitsapplicability.Accordingtopuregeneralrelativity,theexpansionoftheuniverse originatedinadenseprimordialexplosioncalledthe“bigbang.”However,atthattime, themeasuredvalueoftheexpansionratewassohighthatworkingbackwardintimeusing thecosmologicalsolutionsofgeneralrelativityledtotheconclusionthattheageofthe universewaslessthanthatoftheEarth!Oneresultofthisdoubtwastheriseinpopularity duringthe1950softhesteady-statecosmologyofHermanBondi,ThomasGold,andFred Hoyle.Thismodelavoidedthebigbangaltogether,andallowedfortheexpansionofthe universebythecontinuouscreationofmatter.Butbythelate1950s,revisionsinthecosmic distancescalehadreducedtheexpansionratebyafactoroffive,andhadtherebyincreased theageoftheuniverseinthebigbangmodeltoamoreacceptablelevel.Nevertheless, cosmologywasstillinitsinfancy,hardlysuitableasanarenafortestingtheoriesof gravity.Theeraof“precisioncosmology”wouldnotbeginuntilthelaunchoftheCosmic BackgroundExplorer(COBE)satellitein1989followedbyitsprecisemeasurementsof thespectrumandfluctuationsofthecosmicbackgroundradiation.
Meanwhile,asmall“cottageindustry”hadsprungup,devotedtotheconstruction ofalternativetheoriesofgravitation.Someofthesetheorieswereproducedbysuch luminariesasHenriPoincar ´ e,AlfredNorthWhitehead,EdwardArthurMilne,George Birkhoff,NathanRosen,andFrederickBelinfante.Manyoftheseauthorsexpressedan uneasinesswiththenotionsofgeneralcovarianceandcurvedspacetime,whichwere builtintogeneralrelativity,andrespondedbyproducing“specialrelativistic”theories ofgravitation.Manyofthesetheoriesconsideredspacetimeitselftobegovernedby specialrelativity,andtreatedgravitationasafieldonthatbackground.Asof1960,itwas possibletoenumerateatleasttwenty-fivesuchalternativetheories,asfoundintheprimary researchliteraturebetween1905and1960;forapartiallist,seeWhitrowandMorduch (1965).
Thus,by1960,itcouldbearguedthatthevalidityofgeneralrelativityrestedon thefollowingempiricalfoundation:onetestofmoderateprecision(theperihelionshift, approximately10percent),onetestoflowprecision(thedeflectionoflight,approximately 25percent),oneinconclusivetestthatwasnotarealtestanyway(thegravitational redshift),andcosmologicalobservationsthatcouldnotdistinguishbetweengeneral
relativityandthesteady-statetheory.Furthermore,avarietyofalternativetheorieslaid claimtoviability.
Inaddition,theattitudetowardthetheoryseemedtobethat,whereasitwasundoubtedly importantasafundamentaltheoryofnature,itsobservationalcontactswerelimited.This viewwaspresentforexampleinthestandardtextbooksongeneralrelativityofthisperiod, suchasthosebyMøller(1952),Synge(1960),andLandauandLifshitz(1962).Asa consequence,generalrelativitywascutofffromthemainstreamofphysics.Itwasduring thisperiodthatonenewlymintedgraduateoftheCaliforniaInstituteofTechnologywas advisednottopursuethissubjectforhisgraduatework,becausegeneralrelativity“hadso littleconnectionwiththerestofphysicsandastronomy”(hisname:KipThorne).
However,theeventsof1959–1960changedallthat.Thepaceofresearchingeneral relativityandrelativisticastrophysicsbegantoquickenand,associatedwiththisrenewed effort,thesystematichigh-precisiontestingofgravitationaltheorybecameanactiveand challengingfield,withmanynewexperimentalandtheoreticalpossibilities.Theseincluded newversionsofoldtests,suchasthegravitationalredshiftanddeflectionoflight,with accuraciesthatwereunthinkablebefore1960.Theyalsoincludedbrandnewtestsof gravitationaltheory,suchasthegyroscopeprecession,thetimedelayoflight,andthe “Nordtvedteffect”inlunarmotion,alldiscoveredtheoreticallyafter1959.
Becausemanyoftheexperimentsinvolvedtheresourcesofprogramsforinterplanetary spaceexplorationandobservationalastronomy,theircostintermsofmoneyandmanpower washighandtheirdependenceuponincreasinglyconstrainedgovernmentfundingagencieswasstrong.Thus,itbecamecrucialtohaveasgoodatheoreticalframeworkaspossible forcomparingtherelativemeritsofvariousexperiments,andforproposingnewonesthat mighthavebeenoverlooked.Anotherreasonthatsuchatheoreticalframeworkwasnecessarywastomakesomesenseofthelarge(andstillgrowing)numberofalternativetheories ofgravitation.Suchaframeworkcouldbeusedtoclassifytheories,elucidatetheirsimilaritiesanddifferences,andcomparetheirpredictionswiththeresultsofexperimentsina systematicway.Itwouldhavetobepowerfulenoughtobeusedtodesignandassessexperimentaltestsindetail,yetgeneralenoughnottobebiasedinfavorofgeneralrelativity.
AleadingexponentofthisviewpointwasDicke(1964).Itledhimandotherstoperform severalhigh-precisionnullexperimentsthatgreatlystrengthenedtheempiricalsupportfor thefoundationsofgravitationtheory.Withinthisviewpointoneasksgeneralquestions aboutthenatureofgravityanddevisesexperimentstotestthem.Themostimportant dividendoftheDickeframeworkistheunderstandingthatgravitationalexperimentscan bedividedintotwoclasses.Thefirstconsistsofexperimentsthattestthefoundations ofgravitationtheory,oneofthesefoundationsbeingtheprincipleofequivalence. Theseexperiments(E ¨ otv ¨ osexperiment,Hughes-Dreverexperiment,gravitationalredshift experiment,andothers)accuratelyverifythatgravitationisaphenomenonofcurved spacetime,thatis,itmustbedescribedbya“metrictheory”ofgravity,atleasttoa highlevelofprecision.GeneralrelativityandBrans-Dicketheoryareexamplesofmetric theoriesofgravity.
Thesecondclassofexperimentsconsistsofthosethattestmetrictheoriesofgravity. HereanothertheoreticalframeworkwasdevelopedthattakesupwheretheDicke frameworkleavesoff.Knownasthe“Parametrizedpost-Newtonian”or PPN formalism,
itwaspioneeredbyKennethNordtvedtJr.(1968b),andlaterextendedandimproved byWill(1971c),WillandNordtvedt(1972),andWill(1973).The PPN frameworktakes theslowmotion,weakfield,orpost-Newtonianlimitofmetrictheoriesofgravity,and characterizesthatlimitbyasetoftenreal-valuedparameters.Eachmetrictheoryofgravity hasparticularvaluesforthe PPN parameters.The PPN frameworkwasideallysuitedto theanalysisofsolarsystemgravitationalexperiments,whosetaskthenbecameoneof measuringthevaluesofthe PPN parametersandtherebydelineatingwhichtheoryofgravity iscorrect.Asecondpowerfuluseofthe PPN frameworkwasinthediscoveryandanalysis ofnewtestsofgravitationtheory,examplesbeingtheNordtvedteffect(Nordtvedt,1968a), preferred-frameeffects(Will,1971b),andpreferred-locationeffects(Will,1971b,1973). TheNordtvedteffect,forinstance,isaviolationoftheequalityofaccelerationofmassive bodies,suchastheEarthandMoon,inanexternalfield;theeffectisabsentingeneral relativitybutpresentinmanyalternativetheories,includingtheBrans-Dicketheory.The thirduseofthe PPN formalismwasintheanalysisandclassificationofalternativemetric theoriesofgravitation.After1960,theinventionofalternativegravitationtheoriesdidnot abatebutchangedcharacter.ThecrudeattemptstoderiveLorentz-invariantfieldtheories describedpreviouslyweremostlyabandonedinfavorofmetrictheoriesofgravity,whose developmentandmotivationwereoftenpatternedafterthatoftheBrans-Dicketheory.
A“theoryofgravitationtheories”wasdevelopedaroundthe PPN formalismtoaidin theirsystematicstudy.The PPN formalismthusbecamethestandardtheoreticaltoolfor analyzingsolarsystemexperiments,lookingfornewtests,andstudyingalternativemetric theoriesofgravity.
Butbythemiddle1970sitbecameapparentthatthesolarsystemcouldnolongerbethe soletestinggroundforgravitationtheories.Thereasonwasthatmanyalternativetheories ofgravityagreedwithgeneralrelativityintheirweak-field,slow-motionlimitsclosely enoughtopassallsolarsystemtests.Buttheydidnotnecessarilyagreeinotherpredictions, suchasneutronstars,blackholes,gravitationalradiation,orcosmology,phenomenathat involvedstrongordynamicalgravity.
Thiswasconfirmedinthesummerof1974withthediscoverybyJosephTaylorand RussellHulseofthebinarypulsar(HulseandTaylor,1975).Herewasasystemthat featured,inadditiontosignificantpost-Newtoniangravitationaleffects,highlyrelativistic gravitationalfieldsassociatedwiththepulsar(andpossiblyitscompanion)andthe possibilityoftheemissionofgravitationalradiationbythebinarysystem.Theroleof thebinarypulsarasanewarenafortestingrelativisticgravitywasconfirmedfouryears laterwiththeannouncement(Tayloretal.,1979)thattherateofchangeoftheorbital periodofthesystemhadbeenmeasured.Theresultagreedwiththepredictionofgeneral relativityfortherateoforbitalenergylossduetotheemissionofgravitationalradiation. Butitdisagreedstronglywiththepredictionsofmanyalternativetheories,evensomewith post-Newtonianlimitsidenticaltothatofgeneralrelativity.
By1981,whenthefirsteditionofthisbookwaspublished,itwasnotuncommonto describetheperiod1960–1980asa“goldenera”forexperimentalgravity.Manyofthe eventsofthatperiodweredescribedforalayaudienceinmy1986book WasEinstein Right? (Will,1986).Butthephrase“goldenera”suggeststhatitwasdownhillfromthat timeforward.Quitetheoppositewastrue.
Solar-systemtestsofrelativisticgravitycontinued,withhighlightsincludingdramaticallyimprovedmeasurementsoflightdeflectionandtheShapirotimedelay,measurements of“frame-dragging”bytheGravityProbeBandtheLaserGeodynamicsSatellite (LAGEOS)experiments,andsteadilyimprovinglunarlaserranging.Binarypulsartests continued,aidedbyremarkablediscoveries,includingthefamous“doublepulsar”anda pulsarinatriplesystem.
Atthesametime,thecentralthrustoftestinggravitybegantoshiftawayfromtheweakfieldlimit.Twothemesbegantoemergeasthekeythemesforthefuture.
ThefirstthemeisDynamicalGravity.Thisinvolvesphenomenainwhichthevariation withtimeofthespacetimegeometryplaysanimportantrole.Inthesolarsystem,velocities aresmallcomparedtothespeedoflightandthemassesoftheplanetsaresmallcompared tothemassofthesun,sotheunderlyingspacetimegeometrycanbeviewedeitherasbeing stationaryorasevolvinginaquasistationarymanner.Butinthebinarypulsar,forexample, thetwobodieshavealmostthesamemassandareorbitingeachothertentimesfaster thanplanetsinthesolarsystem,andconsequentlythevaryingspacetimegeometrythat theybothgeneratedevolvesintogravitationalwavespropagatingawayfromthesystem, causingittoloseenergy.Amoredramaticexampleisthefinalinspiralofthetwoblack holeswhosegravitationalsignalwasdetectedbyLIGOin2015.Theblackholesaremade ofpurecurvedspacetime,andthemannerinwhichthatgeometryevolvedduringthe finalfractionsofasecondoftheinspiralandmergerleftitsimprintonthegravitational wavesthatweredetected.Thefinalblackholethatwasleftoverevenoscillatedafew times,emittingaspecifickindofgravitationalradiationcalledringdownwaves.Thisisthe regimeofdynamicalgravity.Dynamicalgravityoftengoeshandinhandwithgravitational radiation.
ThesecondthemeisStrongGravity.Muchlikemodernart,theterm“strong”means differentthingstodifferentpeople.Tosomeonesteepedingeneralrelativity,theprincipal figureofmeritthatdistinguishesstrongfromweakgravityisthequantity ∼ Gm/c2 r, where m isthecharacteristicmassscaleofthephenomenon, r isthecharacteristicdistance scale,and G and c aretheNewtoniangravitationalconstantandthespeedoflight, respectively.Neartheeventhorizonofanonrotatingblackhole,orfortheexpanding observableuniverse, ∼ 1;forneutronstars, ∼ 0.2.Thesearetheregimesofstrong gravity.Forthesolarsystem, < 10 5 ;thisistheregimeofweakgravity.
Analternativeviewof“strong”gravitycomesfromtheworldofparticlephysics.Here thefigureofmeritis Gm/c2 r3 ∼ 2 ,wherethecurvatureofspacetimeassociated withthephenomenon,representedbytheleft-handside,iscomparabletotheinverse squareofafavoritelengthscale .If isthePlancklength ( G/c3 )1/2 ∼ 10 35 m,this wouldcorrespondtotheregimewhereoneexpectsconventionalquantumgravityeffects tocomeintoplay.Anotherpossiblescalefor istheTeVscaleassociatedwithmany modelsforunificationoftheforces,ormodelswithextraspacetimedimensions.Fromthis viewpoint,stronggravityiswheretheradiusofcurvatureofspacetimeiscomparableto thefundamentallength.Weakgravityiswheretheradiusofcurvatureismuchlargerthan this.TheuniverseatthePlancktimeisstronggravity.Justoutsidetheeventhorizonofan astrophysicalblackholeisweakgravity.
Wewilladopttherelativist’sviewofstronggravity.
Theboundarybetweendynamicalgravityandstronggravityissomewhatfuzzy.Onecan explorestronggravityalonebystudyingthemotionofastararoundastaticsupermassive blackholeorofgasaroundaneutronstar.Gravitationalwavescanbeemittedbyabinary systemofwhitedwarfs,wellcharacterizedbyweakgravity.However,thestrongestwaves tendtocomefromsystemswithcompact,stronglygravitatingbodies,becauseonlysuch bodiescangetcloseenoughtogethertoreachtherelativisticspeedsrequiredtogenerate stronggravitationalwaves.Andtheuniverseasawholecanbethoughtofasboth“strong gravity”anddynamical,yetbecauseofthehighdegreeofsymmetry,gravitationalwaves donotplayamajorroleinitsevolution.Bycontrast,primordialgravitationalwavescould bedetectable,influctuationsofthecosmicbackgroundradiation,forexample.Regardless ofthespecificcontext,testinggeneralrelativityinthestrong-fieldanddynamicalregimes willdominatethisfieldforsometimetocome.
AsayoungstudentofseventeenatthePolytechnicalInstituteofZ¨urich,Einsteinstudied theworkofHelmholtz,Maxwell,andHertz,andultimatelyusedhisdeepunderstanding ofelectromagnetictheoryasafoundationforspecialandgeneralrelativity.Heappears tohavebeenespeciallyimpressedbyHertz’sconfirmationthatlightandelectromagnetic wavesareoneandthesame(Schilpp,1949).TheelectromagneticwavesthatHertzstudied wereintheradiopartofthespectrum,at30MHz.Itisamusingtonotethat,sixtyyears later,the“goldenage”fortestingrelativisticgravitybeganwithradiowaves,the440MHz wavesreflectedfromVenus,andendedwithradiowaves,thepulsedsignalsfromthebinary pulsar,observedat430MHz.Wearenowinanewerafortestinggeneralrelativity,anera inwhichwecanexploitandstudyanentirelynewkindofwave,awaveinthefabricof spacetimeitself.
Duringthehalf-centurythatclosedonthecentenaryofEinstein’sformulationofgeneral relativity,theempiricalfoundationsofhisgreattheorywerestrengthenedasneverbefore. Thequestionthenarises,whybothertocontinuetotestit?Onereasonisthatgravityisa fundamentalinteractionofnature,andassuchrequiresthemostsolidempiricalunderpinningwecanprovide.Anotheristhatallattemptstoquantizegravityandtounifyitwith theotherforcessuggestthatthestandardgeneralrelativityofEinsteinmaynotbethelast word.Furthermore,thepredictionsofgeneralrelativityarefixed;thepuretheorycontains noadjustableconstants,sonothingcanbechanged.Thuseverytestofthetheoryiseither apotentiallydeadlytestorapossibleprobefornewphysics.Althoughitisremarkable thatthistheory,born100yearsagooutofalmostpurethought,hasmanagedtosurvive everytest,thepossibilityoffindingadiscrepancywillcontinuetodriveexperimentsfor yearstocome.TheseexperimentswillsearchfornewphysicsbeyondEinsteininmany differentdirections:thelargedistancescalesofthecosmologicalrealm;scalesofvery shortdistancesorhighenergy;andtherealmsofstronganddynamicalgravity.
Throughoutthisbook,wewilladopttheunitsandconventionsofstandardtextbookssuchasMisner,Thorne, andWheeler(1973)(hereafterreferredtoasMTW)orSchutz(2009).Forapedagogicaldevelopmentofmany ofthetopicspresentedhere,suchasNewtoniangravity,post-Newtoniantheory,andgravitationalradiation, wewillreferreaderstoPoissonandWill(2014)(hereafterreferredtoasPW).Althoughwehaveattemptedto
Box1.1
produceareasonablyself-containedaccountofgravitationtheoryandgravitationalexperiments,thereader’s pathwillbegreatlysmoothedbyafamiliaritywithgeneralrelativityatthelevelofoneofthesetexts.
Wewilluse“geometrizedunits,”inwhich G = c = 1(exceptinChapter2)andinwhichmassandtimehave thesameunitsasdistance.Greekindicesonvectorsandtensorswillrunoverthefourspacetimedimensions, whileLatinindiceswillrunonlyoverspatialdimensions.WewillusetheEinsteinsummationconvention, inwhichonesumsrepeatedindicesovertheirrange.Multi-indexobjects,suchasproducts x j x k x l willbe denotedusingcapitalsuperscripts,e.g., x N ,where N isthenumberofindices.Partialderivativesandcovariant derivativeswillbedenotedbycommasandsemicolonsprecedingindices,respectively.Parenthesesenclosing indiceswilldenotesymmetrization,whilesquarebracketswilldenoteantisymmetrization.
TheEinsteinEquivalencePrinciple
ThePrincipleofEquivalencehasplayedacentralroleinthedevelopmentofgravitation theory.Newtonregardedthisprincipleassuchacornerstoneofmechanicsthathedevoted theopeningparagraphsofhismasterwork PhilosophiaeNaturalisPrincipiaMathematica (oftencalledthe“Principia”)toadetaileddiscussionofit(Newton,1686).Onpage1, Definition1,hedefinedthe“quantity”ofmattertobeitsmass,andalsodefinedthe “weight”ofabody.Heassertedthatthemass“isproportionaltheweight,asIhavefound byexperimentsonpendulums,veryaccuratelymade,whichshallbeshownhereafter.”To Newton,thePrincipleofEquivalencedemandedthatthe“mass”ofanybody,namelythat propertyofabody(inertia)thatregulatesitsresponsetoanappliedforce,beequaltoits “weight,”thatpropertythatregulatesitsresponsetogravitation.Bondi(1957)coinedthe terms“inertialmass” mI ,and“passivegravitationalmass” mP ,torefertothesequantities, sothatNewton’ssecondlawandthelawofgravitationtaketheforms
where g isthegravitationalfield.ThePrincipleofEquivalencecanthenbestated succinctly:foranybody,1
Analternativestatementofthisprincipleisthatallbodiesfallinagravitationalfieldwith thesameaccelerationregardlessoftheirmassorinternalstructure.Newton’sequivalence principleisnowgenerallyreferredtoasthe“WeakEquivalencePrinciple”(WEP).
ItwasEinsteinwhoaddedthekeyelementtoWEPthatrevealedthepathtogeneral relativity.Ifallbodiesfallwiththesameaccelerationinanexternalgravitationalfield, thentoanobserverinafreelyfallingelevatorinthesamegravitationalfield,thebodies shouldbeunaccelerated,exceptforpossibletidaleffectsduetoinhomogeneitiesin thegravitationalfield.Tidaleffectscanbemadeassmallasonepleasesbyconfining everythingasufficientlysmallelevator.Thus,insofarastheirmechanicalmotionsare concerned,thebodieswillbehaveasifgravitywereabsent.Einsteinwentonestepfurther. Heproposedthatnotonlyshouldmechanicallawsbehaveinsuchanelevatorasifgravity wereabsentbutalsososhouldallthelawsofphysics,including,forexample,thelawsof electrodynamics.ThisnewprincipleledEinsteintogeneralrelativity.Itisnowcalledthe “EinsteinEquivalencePrinciple”(EEP).
Yet,itwasonlyinthe1960sthatwegainedadeeperunderstandingofthesignificanceof theseprinciplesofequivalenceforgravitationandexperiment.Largelythroughthework
1 AlthoughNewtonassertedonlythat mP and mI beproportionaltoeachother,theycanbemadeequalby suitablechoiceofunitsfor a and g
ofRobertDicke,wehavecometoviewprinciplesofequivalence,alongwithexperiments suchastheEotvosexperimentandthegravitationalredshiftexperiment,asprobesmoreof thefoundationsofgravitationtheorythanofgeneralrelativityitself.Thisviewpointispart ofwhathascometobeknownastheDickeFramework,tobedescribedinSection2.1, allowingonetodiscussataveryfundamentallevelthenatureofspacetimeandgravity. Withinthisframeworkoneasksquestionssuchas:Doallbodiesrespondtogravitywiththe sameacceleration?Doesenergyconservationimplyanythingaboutgravitationaleffects? Whattypesoffields,ifany,areassociatedwithgravitation–scalarfields,vectorfields, tensorfields ?InSection2.2,wearguethattheEinsteinEquivalencePrincipleisthe foundationforallgravitationtheoriesthatdescribegravityasamanifestationofcurved spacetime,theso-calledmetrictheoriesofgravity.InSection2.3wedescribetheempirical supportforEEPfromavarietyofexperiments.
Einstein’sgeneralizationoftheWeakEquivalencePrinciplemaynothavebeena generalizationatall,accordingtoaconjecturebasedontheworkofLeonardSchiff. InSection2.4wediscussSchiff’sconjecture,whichstatesthatanycompleteandselfconsistenttheoryofgravitythatsatisfiesWEPnecessarilysatisfiesEEP.Schiff’sconjecture andtheDickeFrameworkhavespawnedanumberofconcretetheoreticalformalismsfor comparingandcontrastingmetrictheoriesofgravitywithnonmetrictheories,foranalyzing experimentsthattestEEP,andforprovingSchiff’sconjecture.Theseincludethe TH μ and c2 formalisms,presentedinSection2.5,andtheStandardModelExtension(SME), discussedinSection2.6.
Whatwouldhappenifaviolationofoneoftheseprincipleswereobserved?One possibilityisthattheentireedificeofmetrictheoriesofgravity,includinggeneralrelativity, wouldcometumblingdown.Anotherpossibilityisthattheapparentviolationwould actuallysignalthepresenceofsomefieldorinteractionthatliesoutsidethestandard modelofstrong,electromagneticandweakinteractions,plusgravity.Thislatterviewpoint hasproventobefruitful,exploitingtheultrahighprecisionapparatusdevelopedtotest equivalenceprinciplesinordertosearchforandultimatelyplacelimitsonnewphysics. WewilldescribeafewexamplesofthisapproachinSection2.7.
2.1TheDickeFramework
TheDickeFrameworkforanalyzingexperimentaltestsofgravitationwasspelledoutin appendix4ofDicke’sLesHoucheslectures(Dicke,1964).Itmakestwomainassumptions aboutthetypeofmathematicalformalismtobeusedindiscussinggravity:
1.Spacetimeisafour-dimensionaldifferentiablemanifold,witheachpointinthemanifold correspondingtoaphysicalevent.Themanifoldneednot apriori haveeitherametric oranaffineconnection.Thehopeisthatexperimentwillforceustoconcludethatit hasboth.
2.Theequationsofgravityandthemathematicalentitiesinthemaretobeexpressedina formthatisindependentoftheparticularcoordinatesused,i.e.,incovariantform.
Noticethatevenifthereissomephysicallypreferredcoordinatesystemorreference frameinspacetime,thetheorycanstillbeputintocovariantform.Forexample,ifa theoryhasapreferredcosmictimecoordinate,onecanintroduceascalarfield T(P ),whose numericalvaluesareequaltothevaluesofthepreferredtime t accordingto T(P )= t(P ), where P isapointinspacetime.Ifspacetimeisendowedwithametric,onemightalso demandthat ∇T beatimelikevectorfieldandbeconsistentlyorientedtowardthefuture (orthepast)throughoutspacetimebyimposingthecovariantconstraints ∇T · ∇T < 0 and ∇ ⊗ ∇T = 0.where ∇ isacovariantderivativewithrespecttothemetric.Other typesoftheorieshave“flatbackgroundmetrics” η ;thesecanalsobewrittencovariantly bydefining η tobeasecond-ranktensorfieldwhoseRiemanntensorvanisheseverywhere, thatis, Riem (η )= 0andbydefiningcovariantderivativesandcontractionswithrespect to η .Inmostcases,thiscovarianceisachievedatthepriceoftheintroductionintothe theoryof“absolute”or“priorgeometric”elements (T, η ),thatarenotdeterminedby thedynamicalequationsofthetheory.Someauthorsregardtheintroductionofabsolute elementsasafailureofgeneralcovariance(Einsteinwouldbeoneexample),howeverwe willadopttheweakerassumptionofcoordinateinvariancealone.(Forfurtherdiscussion ofpriorgeometry,seeSection3.3.)
Havinglaiddownthismathematicalviewpoint,Dickethenimposestwoconstraintson allacceptabletheoriesofgravity.Theyare:
1.Gravitymustbeassociatedwithoneormorefieldsoftensorialcharacter(scalars, vectors,andtensorsofvariousranks).
2.Thedynamicalequationsthatgoverngravitymustbederivablefromaninvariantaction principle.
Theseconstraintsstronglyconfineacceptabletheories.Forthisreasonweshouldaccept themonlyiftheyarefundamentaltooursubsequentarguments.Formostapplicationsof theDickeFrameworkonlythefirstconstraintisneeded.Itisafact,however,thatthemost successfulgravitationtheories,and all theoriesofcurrentinterest,arethosethatsatisfy bothconstraints.
TheDickeFrameworkisparticularlyusefulforaskingquestionssuchaswhattypesof fieldsareassociatedwithgravity,andhowdotheyinteractwiththefundamentalfieldsof thestandardmodelofelectromagnetic,weakandstronginteractions.Forexample,thereis strongevidencefromelementaryparticlephysicsforatleastonesymmetricsecond-rank tensorfieldthatisapproximatedbytheMinkowskimetric η whengravitationaleffectscan beignored.TheHughes-Dreverexperimentrulesoutorstronglyconstrainstheexistence ofmorethanonesecond-ranktensorfield,eachcouplingdirectlytomatter,andvarious laboratorytestsofLorentzinvarianceruleoutalong-rangevectorfieldcouplingdirectly tomatter.However,thisisnottheonlypowerfuluseoftheDickeFramework. ThegeneralunbiasedviewpointembodiedintheDickeFrameworkhasallowedtheorists toformulateasetoffundamentalcriteriathatanygravitationtheoryshouldsatisfyifitis tobeviable[herewedo not imposeconstraints(1)and(2)above].Twoofthesecriteria arepurelytheoretical,whereastwoarebasedonexperimentalevidence.
(i)Itmustbecomplete,thatis,itmustbecapableofanalyzingfrom“firstprinciples” theoutcomeofanyexperimentofinterest.Itisnotenoughforthetheorytopostulate
thatbodiesmadeofdifferentmaterialfallwiththesameacceleration.Thetheorymust incorporateacompletesetofelectrodynamicandquantummechanicallaws,whichcan beusedtocalculatethedetailedbehaviorofrealbodiescomposedofnucleonsand electronsingravitationalfields.Thisdemandshouldnotbeextendedtoofar,however. Inareassuchasquantumgravity,unificationwiththestandardmodelofparticlephysics, spacetimesingularities,andcosmicinitialconditions,evenspecialandgeneralrelativity arenotregardedasbeingcompleteorfullydeveloped.Wealsodonotregardthepresence of“absoluteelements”andarbitraryparametersingravitationaltheoriesasasignof incompleteness,eventhoughtheyaregenerallynotderivablefrom“firstprinciples,”rather weviewthemaspartoftheclassofcosmicboundaryconditions.Themostcommon andsuccessfulwayofformulatinga“complete”theoryistouseanactionprinciplethat combinesthestandardmodelaction(asitiscurrentlyknown)forthenongravitational sectorwithanactionforthegravitational“fields”(includingthespacetimemetric), togetherwithsomecouplingbetweenthem.
(ii)Itmustbeself-consistent,thatis,itspredictionfortheoutcomeofeveryexperiment mustbeunique.Whenonecalculatespredictionsbytwodifferent,thoughequivalent methods,onemustgetthesameresults.Anexampleisthebendingoflightcomputed eitherinthegeometricalopticslimitofMaxwell’sequationsorinthezero-rest-masslimit ofthemotionoftestparticles.
(iii)Itmustberelativistic,thatis,inthelimitasgravityis“turnedoff”comparedto otherphysicalinteractions,thenongravitationallawsofphysicsmustreducetothelaws ofspecialrelativity,eitherperfectlyortoahighdegreeofprecision.Theevidenceforthis comesfrommorethanacenturyofsuccessesofspecialrelativityinareasrangingfrom high-energyphysicstoatomicphysics(seeBox2.1).Thisdoesnotnecessarilyimplya blindorperfectacceptanceofLorentzinvarianceandspecialrelativity,andinfactvigorous experimentalsearchesforpotentialviolationsofLorentzinvariancearecontinuing,inpart tosearchforrelicsignaturesofquantumgravityorofweakcosmicfieldsthatcoupleto matter(seeSection2.6).
ThefundamentaltheoreticalobjectthatenterstheselawsistheMinkowskimetric η , whichhasorthonormaltetradsrelatedbyLorentztransformations,andwhichdetermines thetickingratesofatomicclocksandthelengthsoflaboratoryrods.Ifweview η asa field,thenweconcludethattheremustexistatleastonesecond-ranktensorfieldinthe Universe,asymmetrictensor ψ ,thatiswellapproximatedby η whengravitationaleffects canbeignored.
Letusexaminewhattheevidenceforspecialrelativitydoesanddoesnottellusaboutthe tensorfield ψ .First,itdoes not guaranteetheexistenceof global Lorentzframes,thatis, coordinatesystemsextendingthroughoutspacetimeinwhich ψ = η = diag( 1,1,1,1). Nordoesitdemandthatateachevent P ,thereexistlocalframesrelatedbyLorentz transformations,inwhichthelawsofnongravitationalphysicstakeontheirspecial relativisticforms.Specialrelativityonlydemandsthat,inthelimitasgravityis“turned off”thenongravitationallawsofphysicsreducetothelawsofspecialrelativity.
Wewillhenceforthassumetheexistenceofthetensorfield ψ . (iv)ItmusthavethecorrectNewtonianlimit,thatis,inthelimitofweakgravitational fieldsandslowmotions,itmustreproduceNewton’slaws.Theoverwhelmingmajorityof phenomenaintheuniversecanbeveryadequatelydescribedbythelawsofNewtonian
Box2.1
Testsofspecialrelativity
Specialrelativityhasbeensothoroughlyintegratedintothefabricofmodernphysicsthatitsvalidityisrarely challenged,exceptbycranksandcrackpots.Butweshouldrememberthatitdoesrestonastrongempirical foundation,includinganumberofclassictests.
TheMichelson-Morley(1887)experimentanditsmanydescendents(Shanklandetal.,1955;Champeney etal.,1963;Jasejaetal.,1964;BrilletandHall,1979;Riisetal.,1988;Krisheretal.,1990b)failedtofindevidence ofavariationofthespeedoflightwiththeEarth’svelocitythroughahypothetical“aether.”
Severalclassicexperimentswereperformedtoverifythatthespeedoflightisindependentofthespeed oftheemitter.Ifthespeedoflightweregivenby c + k v,where v isthevelocityoftheemitter,and k isa parametertobemeasured,thenorbitsofbinary-starsystemswouldappeartohaveananomalouseccentricity unexplainablebynormalNewtoniangravity.Thistestisnotunambiguousatopticalwavelengths,however, becauselightisabsorbedandreemittedbytheinterveninginterstellarmedium,therebylosingthememory ofthespeedofthesource,aphenomenonknowntoastronomersasextinction.ButatX-raywavelengths,the pathlengthofextinctionistensofkiloparsecs,soBrecher(1977)usedthreenearbyX-raybinarysystemsin ourgalaxytoobtainabound |k | < 2 × 10 9 ,fortypicalorbitalvelocities v /c ∼ 10 3 .
Attheotherextreme,a1964experimentatCERNusedneutralpionsmovingat v /c ≥ 0.99975asthe sourceoflight.Photonsproducedbythedecay π 0 → γ + γ werecollimatedandtimedoveraflightpath of30meters.Theagreementofthephotons’speedwiththelaboratoryvaluesetabound |k | < 10 4 for v ≈ c (Alvägeretal.,1964).
Theobservationalevidencefortimedilationisoverwhelming.IvesandStilwell(1938)measuredthe frequencyshiftsofradiationemittedintheforwardandbackwarddirectionbymovingionsofH2 andH3 molecules.Thefirst-orderDopplershiftcancelsoutfromthesumoftheforwardandbackwardshifts,revealing thesecond-ordertime-dilationeffect,whichwasfoundtoagreewiththeory.(Ironically,Iveswasadie-hard opponentofspecialrelativity.)
TheclassicRossi-Hall(1941)experimentshowedthatthelifetimeof μ-mesonswasprolongedbythe Lorentzfactor γ =(1 v 2 /c 2 ) 1/2 .Muonsarecreatedintheupperatmospherewhencosmic-ray protonscollidewithnucleiofair,producingpions,whichdecayquicklytomuons.Witharesthalf-lifeof 2.2 × 10 6 s,andwithnotimedilation,amuontravellingnearthespeedoflightshouldtravelonly2/3 ofakilometeronaveragebeforedecayingtoaharmlesselectronorpositronandtwoneutrinos.Yetmuons aretheprimarycomponentofcosmicraysdetectedatsealevel.RossiandHallmeasuredthedistributionof muonsasafunctionofaltitudeandalsomeasuredtheirenergies,andconfirmedthetime-dilationformula.
Inanexperimentperformedin1966atCERN,muonsinastorageringmovingat v /c = 0.997were observedtohavelifetimes12timeslargerthanmuonsatrest,inagreementwiththepredictionto2percent (Farleyetal.,1966).Also,sincethestorageringwas5metersindiameter,themuons’accelerationswere greaterthanthegravitationalaccelerationontheEarth’ssurfacebyafactorof1019 ;theseaccelerationshad noapparenteffectontheirdecayrates.
TheincorporationofLorentzinvarianceintoquantummechanicsprovidedfurthersupportforspecial relativity.Theachievementsincludethepredictionofanti-particlesandelementaryparticlespin,andthe manysuccessesofrelativisticquantumfieldtheory.
Forapedagogicalreviewwrittenontheoccasionofthe2005centenaryofspecialrelativity,seeWill(2006). Wewilldescribecontemporarytestsofwhatistodaycalled“LocalLorentzInvariance”inSection2.3.2.
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[Contents]
S
L L .
CHAPTER I.
R
A .—T H .
Aiohikupua1 was a very strong man, both in boxing and wrestling. When he set sail from Maui and landed at Kauhola, in Kohala, he found the people gathered at Hinakahua, where they were holding their customary games of boxing, wrestling and other manly exhibitions of strength. At this
N M K L .
MOKUNA I.
N A . N H .
He kanaka ikaika o Aiohikupua i ke kui a me ka mokomoko. Ia ia i holo ai mai Maui aku a pae ma Kauhola i Kohala, e mokomoko ana o Hinakahua. Kahi o na kanaka a pau e piha ana. Ilaila o Ihuanu, he kanaka ikaika no Kohala i ke kui.
place he met Ihuanu, a very expert and strong boxer who belonged to that district, Kohala.
When Aiohikupua and his companions came ashore in Kohala they proceeded up to see the wrestling. When they arrived at the grounds, Ihuanu came out and challenged: “Who is to come from that side and meet me, wrestling?” No one was seen to come and accept the challenge because they were all afraid of him. After this Ihuanu turned to Aiohikupua and said: “Say, stranger, you had better join in the fun.” When Aiohikupua heard the invitation he went up to Ihuanu and said: “Say, son of the soil, you have asked me to join you in the fun, and this is what I wish to say to you: Get two others beside yourself on your side, making three of you. With that number the stranger will feel it worth while to join you.” When Ihuanu heard this from Aiohikupua, he made reply: “You are a very conceited man. I am the best man among all the people of Kohala, and here you have asked that there must be
A pae o Aiohikupua ma Kohala, pii aku la lakou e ike i ka mokomoko. A hiki lakou, oili mai la o Ihuanu, a kahea mai la:
“Owai mai ma kela aoao e mokomoko mai me a’u,” aohe kanaka aa mai, ua makau ia o Ihuanu e na mea a pau loa. A pau ka olelo ana a Ihuanu, huli ae la ia a olelo mai ia
Aiohikupua: “E ka malihini, e pono paha ke lealea.” A lohe o Aiohikupua i keia leo o Ihuanu, hele aku la ia a kokoke, a olelo aku la: “E ke kamaaina! ua noi mai oe ia’u, e lealea kaua. A eia hoi ka’u ia oe. I elua ma kou aoao, hui pu me oe, akolu. Alaila, akolu oukou, e aho ia mikomiko iho ka malihini.” A lohe o Ihuanu i keia olelo a
Aiohikupua, olelo mai la ia: “He oi oe o ke kanaka olelo hookano. Owau no ka oi mamua o na mea a pau o Kohala nei, a ke olelo mai nei oe i ekolu aku makou ma kekahi aoao, a i hookahi oe. He keu oe o ke kanaka wahahee, heaha la oe i kuu manao.”
three of us on one side to meet you alone on your side. You are the most conceited2 man that I have ever seen. What are you to me?”
Aiohikupua then boasted, saying to Ihuanu: “I am not going to stand up and box with you unless you have three on your side. And what do I care for you and the people that have gathered here? I can turn this crowd into nothing with my left hand.” Because of these words of Aiohikupua, one of the strong men in Kohala who had come to witness the games came up behind Aiohikupua and said to him: “Say, don’t get Ihuanu angry, for he is the strongest man in Kohala; there is nothing kept away from him when he asks.” At this Aiohikupua pushed him to one side3 whereby the man was killed. Upon seeing this, one of the warriors came up behind Ihuanu and said to him: “Say, Ihuanu, we see that our side will not be victorious this day. I am sure the stranger will win out, because one of our companions is killed by just
I aku o Aiohikupua i kana olelo kaena i mua o Ihuanu: “Aole au e ku aku ana e kui me oe, ke ku ole mai oukou ekolu i mua o’u. A heaha la oe a me ka lehulehu ia’u? e hiki ia’u ke hoolilo i keia aha i mea ole, i loko o kuu lima hema.” A no keia olelo a Aiohikupua, hele mai la kekahi koa ikaika a ma ke kua o Aiohikupua. Olelo mai la: “E! mai olelo aku oe ia Ihuanu, o ko
Kohala oi no kela, aohe puko momona ia ia.” Ia wa, huli ae la o Aiohikupua a papale ae la. Ia wa no make loa ua kanaka ala. Hele mai la kekahi mau koa a ma ke kua o Ihuanu, a olelo mai la: “E Ihuanu, ke ike nei makou, aole e lanakila ana ko kakou aoao i keia la. Ma kuu manao paa, o ka malihini ke lanakila ana. No ka mea, ua make ko kakou kanaka, i pale wale ia mai nei no, o ka make ia. Nolaila, ke noi aku nei au e hui ka aha, e pau ka mokomoko ana, a me
receiving a mere push. Therefore I beg of you that the crowd be dispersed and the games brought to an end and you withdraw your challenge and meet the stranger in a kindly way and shake hands, and in that way save yourself.”4 By these words the hot anger in Ihuanu was [408]rekindled, and so he replied: “Say, my men, don’t be afraid because of the death of that man from the push he received. Did I not do the very same thing some few days ago? Then why should you all be afraid? But if you are afraid, then go and hide your faces in the sky; and if you should hear that Ihuanu is victorious, remember it was by the blow known as Kanikapihe,5 the blow the teacher has not instructed you of, for I see he will not be able to overcome me, for I hear the end of my loin cloth snap6 behind me.” His companions then said to him: “We have nothing more to say to you, we have done our part. Stand up then and face your opponent; perhaps you will be saved by means of the blow your teacher has not instructed
kou aa ana i ka malihini, a e aloha olua me ka lulu lima ana, alaila oe ola.” Ma keia olelo, ua hoaa ia ko [409]Ihuanu huhu wela loa. Nolaila, olelo aku o Ihuanu: “E ko’u poe kanaka, mai hopohopo, ma ka make ana o kela kanaka o kakou, ma ke pale ana o ka lima. Aole anei au i hana pela, mamua aku nei, a heaha la ko oukou mea i makau ai? Nolaila, ina hopo oukou, alaila, e huna aku i ko oukou mau maka i ke aouli. A i lohe aku oukou, ua lanakila o Ihuanu, e hoomanao oukou i kuu puupuu o Kanikapihe, ka ai a ke kumu i koe ia oukou, aole i ao ia. No ka mea, ke ike nei au aole e lanakila mai oia maluna o’u, no ka mea, ua kani ka pola o kuu malo i ka hope.” I aku na hoa mokomoko ia Ihuanu: “Ua pau ka makou olelo ia oe, aohe olelo i koe, ku ia i mua o ko hoa. Malama o pakele oe i ka ai a ko kumu i koe ia makou, a pela no hoi ka pola o ko malo.” Alaila, nee aku la na hoa ma waho o ka aha mokomoko.
us of, and perhaps the end of your loin cloth did tell you the truth.”7 With this the companions of Ihuanu retired to the outer edge of the crowd.
While Ihuanu was boasting before the people, Aiohikupua came out of the crowd and stood in the presence of Ihuanu, then clapped his arms around his body and said to Ihuanu: “Say, Ihuanu, strike sixteen blows at my middle.” When Ihuanu heard this from Aiohikupua he turned and surveyed the crowd that was around them and when he saw a small boy, who was being held in the arms of a certain person, he called out: “Let that small boy come and strike Aiohikupua.”
Continuing, Ihuanu said boastingly: “Let this small boy strike you.”8 When Aiohikupua heard this from Ihuanu, his anger welled up within him until his very hair stood on end; he then turned to the people and said: “What man is willing to face the boy from Kauai? I will therefore at this time say, that my god is able to give me the victory over your strong man this day and to
Ia Ihuanu e olelo kaena ana i mua o ka aha, oili mai la o Aiohikupua a ma ke alo o Ihuanu ku iho la, a upoipoi na lima, me ka olelo aku ia Ihuanu: “E Ihuanu, kui ia i kuu piko a pololei, i eha kauna kui.” (Ua like me umikumamaono puupuu.) A lohe o Ihuanu i keia olelo a Aiohikupua, huli ae la o Ihuanu a puni ka aha mokomoko. A ike aku la i kekahi keiki opiopio e hii ia mai ana, kahea aku la ia, e hele mai e kui ia Aiohikupua. Wahi a na olelo kaena a Ihuanu: “Na keia keiki opiopio oe e kui.” A lohe o Aiohikupua i keia olelo a Ihuanu. Pii ae la kona huhu a ke poo o kalakala. Huli aku la o Aiohikupua a olelo i ka aha kanaka. “Owai ke kanaka i aa mai i ko Kauai keiki nei, nolaila, ke olelo nei au. He hiki i kuu akua ke haawi mai ia’u e lanakila maluna o ko oukou kanaka ikaika i keia la. A e hoolilo hoi i ke poo i milimili na kuu poe
make his head a plaything for my canoe men.” After making the above remarks, he prayed to his god as follows: hoewaa.” A mahope o keia mau olelo a Aiohikupua, pule iho la ia i kona mau akua, penei:
Lanipipili, Lanioaka, Lanikahuliomealani.
Say, Hekilikaakaa, Say, Nakolowailani, Recognize your offspring, Look at your child And present me with the head of Ihuanu, That the multitude might see That I am the conqueror. It is ended, the kapu is released.9
At the close of the prayer, Aiohikupua asked his opponent: “Are you ready, Ihuanu, to strike at me?” Ihuanu replied: “I will not strike you. I want you to strike at me.” When the boxing teacher of Ihuanu heard what his pupil had answered he came up to his side and said to him: “If he should again ask you to strike him do it,10 because this is the proper time.” Shortly after this Aiohikupua again requested of Ihuanu to strike him. At this request, Ihuanu let drive at his
Lanipipili, Lanioaka, Lanikahuliomealani, E Hekilikaakaa, E Nakolowailani, E ike i ka oukou pulapula, E nana i ka oukou Kama, E haawi mai ke poo o Ihuanu I ike keia aha apau loa, Owau ka lanakila maluna, Amama, ua noa.
A pau ka pule, olelo aku o
Aiohikupua, ua makaukau anei oe e Ihuanu e kui mai ia’u? Olelo mai o Ihuanu: “Aole au e kui ia oe, nau e kui mai ia’u.” A lohe ke kumu kui a Ihuanu, hele mai la a ma ka aoao. I mai la: “E! i olelo hou mai e kui oe, kui ia, no ka mea, o ka manawa iho la no ia.”
Mahope o laila, ninau hou o
Aiohikupua ia Ihuanu, e waiho mai ana o Ihuanu i ka puupuu, hu ka makani, aole nae i ku o
Aiohikupua, [411]no ka mea, ua alo ia, a hala ae la ka Ihuanu
opponent but did not hit him, for [410]Aiohikupua was on his guard and dodged. After dodging this blow from Ihuanu, Aiohikupua struck at his opponent, hitting him just below the chest so strong that the fist of Aiohikupua went clear through and came out at the back. Aiohikupua then raised up his arm, with the body of Ihuanu on it, twirled the body around over his head and then threw it outside of the rows of people that were standing around. At sight of this great strength a mighty shout came from the people and after this they began to disperse. After this Aiohikupua went over to the place where the body of Ihuanu was lying and cut off his head and took it to his canoe men11 , and they all returned to their double canoe, which they boarded and set sail for Hamakua, landing at Paauhau.
.
Haunaka was the strongest man, in boxing and wrestling, in the whole of Paauhau and he was at
puupuu. A hala ka Ihuanu puupuu, e poho lalo ae ana o Aiohikupua i kana puupuu, komo i ka houpo, a hula ma ke kua. Ia wa kaikai o Aiohikupua ia Ihuanu me ke koali i ka lima, a kiola aku la ma waho o ka aha. Uwa ae la ka pihe, hui ka aha. Lalau iho la o Aiohikupua i ke poo o Ihuanu a lawe ae la na na hoewaa, a hoi aku la i na waa, a holo aku la a pae ma Paauhau i Hamakua.
.
O ko Paauhau kanaka oi ia i ke kui a me ka mokomoko, he kanaka ikaika loa ma ia hana. A
this time very famous. In fact his fame had traversed over the whole district of Hamakua.
When the canoe of Aiohikupua touched at the landing at Paauhau, he jumped ashore and asked of the people of the place, saying: “What is that shouting in the uplands?” One of the men said: “The people are gathered there to witness the champion wrestler, Haunaka, the strongest man in the district.” When Aiohikupua heard this he proceeded to the place where the games were being held. As soon as he arrived, Haunaka called out to him: “Come here.” When Aiohikupua came in the presence of Haunaka, he said: “You will never be able to hurt the boy from Kauai for he is like the branch of a tree that stands on the side of a cliff.” While Aiohikupua was saying this one of the men who had seen him in Kohala came up and said to Haunaka: “Say, Haunaka and the company gathered here, this is the very man who struck Ihuanu, in Kohala, and killed him. This man’s blow is sharp
ua laha ae kona kaulana a puni o Hamakua.
Ia lakou e piha ana ma Paauhau, lele aku la o Aiohikupua a pae i uka. Ninau aku la i ke kamaaina: “Heaha keia uwa o uka?” I mai la ke kamaaina: “He mokomoko na Haunaka, koonei mokomoko nui.” Pii aku la o Aiohikupua a hiki. Kahea mai la o Haunaka: “Hele mai.” A hiki o Aiohikupua i mua o Haunaka, olelo aku la o Aiohikupua. “Aole e eha ke keiki o Kauai ia oe. He lala kamahele no ka laau ku pali.” Ia Aiohikupua e kamailio ana, hele mai la kekahi kanaka i ike ia ia i Kohala nei, a kahea ae la ia Haunaka. “E Haunaka a me ka aha. O ke kanaka no nei nana i kui mai nei o Ihuanu, i Kohala, a make loa. O kai nei puupuu, ua like me ka pololu ka oi, nolaila, aole oukou e ola.” A lohe o Haunaka, hele mai la ia a aloha ia Aiohikupua, a pau ae la ka mokomoko, hoi mai la o Aiohikupua a holo i Hilo, e imi i ka wahine ia Laieikawai.
like the point of a spear; you people will therefore have no chance against him.” When Haunaka heard this he came up to Aiohikupua and extended his greetings.12 At the conclusion of the games Aiohikupua returned to his canoe and set sail for Hilo, on his way in search of his lover, Laieikawai.
CHAPTER II.
R
K .—
U A .
MOKUNA II.
N K .—
U A .
Kihanuilulumoku13 was the god of Kahalaomapuana and her sisters, who were living in Paliuli. This god had a very large and wide mouth. When opened the upper lip would touch the heaven while the lower lip touched the ground. This god was very powerful and nothing could overcome him. He was also very
O Kihanuilulumoku, he ’kua ia no Kahalaomapuana ma, i Paliuli kahi i noho ai. He oi kona waha i ka nui a me ke akea, e pa ka lehelehe luna i ka lani, a o ka lehelehe lalo i ka honua. A he ikaika loa ia mamua o na mea a pau loa, a he koa, a he kiai no Paliuli kahi o Laieikawai e noho ana. I ka wa e noho ana na
brave and he was placed as the watchman at Paliuli, where Laieikawai was residing.
While the sisters of Aiohikupua, Kahalaomapuana and her sisters, were acting as the guards of Laieikawai in Paliuli, Aiohikupua arrived in Puna and landed at Keaau.
kaikuahine o Aiohikupua i Paliuli, oia o Kahalaomapuana ma, e kiai ia. Hiki aku la o Aiohikupua a pae i kai o Keaau i Puna.
O ka nui o na waa o Aiohikupua ma keia holo ana, he iwakalua kaulua, elua kanaha [413]kaukahi, he kanaha waa peleleu nui, a he mau waa ohua ka nui. A he nui hoi na kanaka koa ma keia holo ana a Aiohikupua, a me na lii. Na mea kaua a pau loa, a me ka ilio aikanaka a Aiohikupua, o Kalahumoku ka inoa.
The number of canoes on this expedition under the command of Aiohikupua, was [412]twenty double canoes, eighty single canoes and forty large war canoes, besides several single ones carrying the servants.14 Aiohikupua had a large army with him on this expedition and with him were several chiefs. These warriors were all well armed and Aiohikupua had with him his man-eating dog, called Kalahumoku.
After the army had disembarked from the canoes at Keaau,
A mahope o ka pae ana o na waa o Aiohikupua ma Keaau, pii aku la ia me kona kuhina i Paliuli e nana ia Laieikawai. A hiki o Aiohikupua me kona kuhina i Paliuli, e noho ana na kaikuahine o Aiohikupua, he mau kiai no Laieikawai.
Olelo mai la lakou: “E Aiohikupua, e hoi oe ano, he
Aiohikupua with his chief adviser went up to Paliuli to see Laieikawai. When they arrived at Paliuli, they saw the sisters of Aiohikupua guarding Laieikawai. When the sisters saw their brother, they said to him: “Say, Aiohikupua, you must go back at once for a kapu has been placed over this place.” Aiohikupua would not listen to this order, but insisted on staying.
Kahalaomapuana15 then said to him: “If you insist on remaining here you will be killed.” When Aiohikupua heard this he turned and went back, filled with bitter anger. When he reached Keaau he ordered ten men to go up and put his sisters to death.16
While Aiohikupua was giving his orders to the men, Waka, the grandmother of Laieikawai, by her supernatural powers, was aware of what Aiohikupua was up to, so she told the facts to Kahalaomapuana, the chief adviser of Laieikawai. When she heard this she prayed to Kihanuilulumoku as follows:
kapu o uka nei.” Hoopaa aku o Aiohikupua. I mai o
Kahalaomapuana: “Ina oe e paa loa mai, make oe ano.” A lohe o
Aiohikupua, a hoi mai la me ka huhu wela loa. A hiki i Keaau, kena aku la he umi kanaka, e pii e pepehi i na kaikuahine a make.
Ia Aiohikupua e olelo ana i na kanaka e pii, ike mai la o Waka, ke kupunawahine o Laieikawai i keia hana a Aiohikupua. Hai aku la o Waka ia Kahalaomapuana, ko Laieikawai kuhina nui, a lohe ia, pule aku la ia ia
Kihanuilulumoku, penei:
Say, Kihanuilulumoku, E Kihanuilulumoku,
Our all powerful god; Watch for the enemy, The mischievous people of the land, And put them to death Sparing none. Be watchful however of Kalahumoku, The man-eating dog of Aiohikupua. If you are careless we are lost; Let all your strength be at your command. It is ended, the kapu is removed.
By early dawn of the next morning, the ten warriors, with the chief adviser of Aiohikupua, arrived at Paliuli. After their arrival the trees were heard to be rustling and the wind began to moan, caused by the tongue of Kihanuilulumoku. After they had advanced along the way they got further and further into the middle of the mouth of the lizard [god, Kihanuilulumoku], the upper jaw then came down and the men were shut up in the mouth and were swallowed; no one escaped to carry the tidings to Aiohikupua.
Ko makou akua mana, Nana ia ke kupu, Ka eu o ka aina nei la, Pepehi ia a make, A holo ke olohelohe, E ao nae oe ia Kalahumoku, I ka ilio aikanaka a Aiohikupua, Hemahema oe pau kakou, Kulia ko ikaika a pau i luna, Amama, ua noa, lele wale.
Ia po a wanaao, hiki na koa he umi i uka, me ke kuhina o Aiohikupua. Mahope o ko lakou hiki ana i Paliuli, nehe ana ka laau a me ka makani i ke alelo o Kihanuilulumoku. Ia lakou e hoomau ana i ka hele, kaa loa lakou i waena o ka waha o ua moo nei. Ia wa, maluna ke a luna, he poi ana iho na luna, pau loa lakou nei i loko, aohe ahailono i koe aku, e lohe ai o Aiohikupua.
After waiting for two days for the return of his men, Aiohikupua again sent up more men, twenty of the best of his warriors, and orders were given them to go and put his sisters to death. When the men reached Paliuli the lizard caught and ate them all.17
The chief waited until the expiration of one day, when he again sent up more men, forty warriors, and on their arrival at Paliuli, the lizard killed these also. Because [414]of the continued absence of his men the thought entered Aiohikupua to dispatch his fleetest messengers to find out the cause of the non-return of his men.
Elua la i hala o ke kali ana o Aiohikupua, aohe hoi mai o kela poe, nolaila, hoouna aku la ia he iwakalua poe koa loa ona, e pii e pepehi i na kaikuahine. Pii aku la, lakou a hiki, hamo mai la no ka moo pau i ka ai ia.
Kakali hou ke ’lii, a hala hou he la, hoouna hou i na koa he kanaha ka nui, a hiki no i uka, pau no i ka make i ka moo. Ma keia hoi ole mai o na koa, kupu ae la ko Aiohikupua [415]manao e hoouna i kana mau elele mama loa, i maopopo ke kumu o ka hoi ole ana mai i kai nei.
. .
Ulili and Aikeehiale were the fleetest of Aiohikupua’s messengers.18 While they were going along the road they met a man who inquired: “Where are you two going?” They replied: “We are going up to see about
O laua na elele mama a Aiohikupua. Ia laua e pii ana ma ke alanui, halawai mai la he kanaka, a ninau mai la: “E pii ana olua i hea?” “E pii ana maua e nana i ko makou poe, aohe hoi ae nei.” Olelo mai la kela: “Ua
our people, for they have not returned.” The man said: “They have been killed by the maneating lizard who lives up here, called Kihanuilulumoku.” At the conclusion of this conversation, the two messengers continued on their way up. Not very long after this they heard the rustling of the leaves and the low murmuring of the wind, which reminded them of the conversation they just had with the man. The two messengers then changed themselves into the form of birds and flew up. When they reached a good ways up they looked about them and saw that the rays of the sun were hidden, and in looking to see the cause of this they saw it was the upper jaw of the mouth of the lizard. At sight of this they continued flying until they reached a point above the jaw. From this position they looked down and saw the trees and earth uprooted as though a large oo19 was tearing up the ground, causing them to tremble because of its terribleness. By what they saw they made sure that all their men had been killed
make aku la i ka moo aikanaka o uka nei, oia o Kihanuilulumoku.”
A pau ke kamailio ana, pii aku la laua, nehe mai ana ka lau o ka laau, e hele ana ma o a ma o, e hu ana ka makani noonoo iho la laua i ka olelo a ke kanaka. Ia wa, lele laua i luna me ko laua kino manu. I nana ae ka hana, malu ana maluna. A ike laua o ke a luna, e oni ae ana laua i luna loa a pakele aku la i ka moo. A hala laua maluna o ke a luna, o ka moo, i nana iho ka hana, hele ana ka laau o lalo, me he oo palau la ka owe o ka honua, a he mea weliweli loa ia laua ke nana iho. Nolaila, mapopo ia laua ua pau na kanaka o lakou i ka make i ka moo, nolaila, hoi aku la laua a olelo ia Aiohikupua i ka laua mea i ike ai. Ia wa, kii o Kalahumoku, ka ilio ai kanaka a Aiohikupua.
by the lizard. The two then returned to Aiohikupua and related what they had seen. When Aiohikupua heard this he sent for Kalahumoku, his maneating dog.
CHAPTER III.
R
K .—B
B D L .
Kalahumoku20 was a man-eating dog from Kahiki. He had two natures, that of a god and that of a human being. As a dog he had supernatural powers and was possessed of very great strength in fighting.
When the dog came into his presence Aiohikupua said: “You go up and kill the lizard, and after that go and kill all my sisters.” After Aiohikupua had
MOKUNA III.
N K .—K K A I M .
He ilio ai kanaka o Kalahumoku no Kahiki mai. Elua ano, he ’kua, he kanaka. He ilio mana, he ilio ikaika loa ma ka hakaka ana.
I aku o Aiohikupua, e pii oe e pepehi i ka moo a make, alaila, luku oe i o’u mau kaikuahine a pau i ka make. A pau ka Aiohikupua olelo, hai aku ka ilio i
issued these orders the dog then turned and addressed the chiefs and all the men as follows:
You must all keep looking to the uplands,
And if you should see the fog go straight up
And then lean over toward the lee side,
Know that I have met Kihanuilulumoku,
And you can be assured that we have become friends.
But if the fog should lean toward the windward
Know that we are being engaged in battle;
Then you must pray to the god Lanipipili.21
After that look again and if you should see the fog lean toward the sea, here, [416]
Know that the lizard has won out.
But if, however, the fog should lean toward the mountain
Know that I have defeated the lizard,
And I have conquered over it. Therefore, you must continue praying for me.
kona manao, i na ’lii a me na kanaka a pau loa, penei:
E nana oukou i uka,
I pii ka ohu a pololei i luna, A hina ka ohu ma ka lulu, Ua halawai au me
Kihanuilulumoku, Manao ae oukou ua hoaikane maua,
A i hina ka ohu i ka makani, Ua hakaka maua, Alaila, pule oukou i ke ’kua ia Lanipipili.
Nana ae oukou a i hina ka ohu i kai nei, [417]
Ua lanakila ka moo,
Aka hoi i pii ka ohu a moe i ke kuahiwi, Ua hee ka moo ia’u,
A ua lanakila au maluna, Nolaila, e hoomau oukou i ka pule no’u.
.
When Kalahumoku arrived at Paliuli, he found the lizard sleeping, so he continued on up leaving the lizard behind him and after some time he came to the place where the guards were stationed.
Shortly after this the lizard, Kihanuilulumoku, smelt the dog and so it awoke from its sleep and followed on after Kalahumoku until they met. Kihanuilulumoku then opened wide its mouth to bite, when Kalahumoku showed its sharp teeth. The two then jumped at each other and a terrible battle was fought, biting one another. Not very long after this the lizard conquered over Kalahumoku; his ears were cut off and his tail was bitten off short.
While the two were engaged in this conflict, Aiohikupua and his men watched the fog. They saw it rise up straight, and after it had reached some distance in the sky, it leaned toward the sea,
.
A hiki o Kalahumoku i uka o Paliuli, e moe ana ka moo, nolaila, hala ka moo mahope nei, kaa loa ka ilio i kahi o na kiai e noho ana.
A no ka hohono o ka ilio puoho ae la o Kihanuilulumoku, a ala ae la, hanu aku la a loaa o Kalahumoku. Wehe ae la o Kihanuilulumoku i kona waha e nahu, ia wa, hoike o Kalahumoku i kona mau niho oi loa. Ia wa laua i lele ai me ka weliweli loa, e nahu ana kekahi i kekahi, aole i liuliu iho, lanakila ka moo maluna o Kalahumoku. Pau na pepeiao a mumuku, moku ka huelo.
Ia laua ala e kaua ana, he mea mau ia Aiohikupua ma, ka nana i ka ohu. Pii ae la ka ohu a pololei i luna, moe i kai, manao iho la no o Aiohikupua, ua pio o Kalahumoku.
which caused Aiohikupua to think that Kalahumoku was defeated.
Sometime after this the dog arrived and when they looked at it they saw that its ears were cut off and the tail was cut off short. This ended the desire of Aiohikupua to stay in Puna and he and his men boarded their canoes and returned to Kauai, without obtaining Laieikawai. Thus was the plan of Aiohikupua to kill his sisters defeated.22 [407]
Mahope o laila, hoi mai la ka ilio a hiki, i nana aku ka hana, ua mumuku na pepeiao, ua poomoku ka huelo. Pau ae la ka manao i ka noho, nolaila, hoi mai la lakou ma na waa i Kauai, me ka loaa ole o Laieikawai. Pela iho la ka make hewa o ko Aiohikupua manao pepehi i kona mau kaikuahine. [418]
This was the champion athlete of Kauai, known to some as Aiwohikupua, a high chief, who was on his way to Puna to win the affections of Laieikawai, at Paliuli. ↑
Kanaka wahahee, rendered literally would be “deceitful” man, but “conceited” is the truer term in its use here, i.e., representing himself other than his true self. ↑
A summary act for, possibly, an intended friendly caution. ↑
This is very Hawaiian-like, and at its repetition with his next antagonist the advice is followed ↑
Kani-ka-pihe, ringing the voice of sorrow Used also as an exultant term ↑
This expression, made use of in several stories, would seem to indicate it as an accepted premonition of sure victory ↑
Leaving the boaster, sarcastically, to his own conceit ↑
Belittling each other in taunting fashion. ↑
Petitioning his gods for the double purpose of strengthening his own side and intimidating his opponent. ↑
His teacher discerns signs of fear, or waning confidence, and bids him to seize his opportunity. ↑
In accordance with his prayer ↑
Aiohikupua’s skill has quicker recognition than at Kohala, seeing his fame had preceded him ↑
Kihanuilulumoku, the dragon-god defender of Paliuli and protector of Laieikawai. ↑
Quite a fleet for the enforcement of a lover’s suit. ↑
Kahalaomapuana was the youngest of the Aiohikupua sisters who had been appointed guards of Laieikawai, of which she was the chief superintendent, hence the authoritative one to deal with all intruders ↑
Chagrined at being thus thwarted in his plans he seeks to be avenged upon his sisters. ↑
This moo, or lizard-god, must have been of dragon character to have swallowed warriors by the score. The
question naturally arises where the idea of mammoth lizard of Hawaiian tradition originates, seeing the only varieties of lizard known to the islands are of the skink and gecko species, neither of which exceed six inches to the tip of the tail. ↑
These messengers had the supernatural power of changing to the form of birds. Ulili is the Wandering Tattler; the other is not identified. ↑
Oo, the Hawaiian gardening implement of spade character. ↑
Kalahumoku, Aiohikupua’s
supernatural dog-man defender ↑
Lanipipili, one of the gods appealed to in the Kohala contest ↑
22
Make hewa, rendered “defeated,” has in its use here the sense of uselessness of the attempt. ↑
