Relativity:AVeryShortIntroduction VERYSHORTINTRODUCTIONSareforanyonewantingastimulatingand accessiblewayintoanewsubject.Theyarewrittenbyexperts,andhavebeen publishedinmorethan25languagesworldwide. Theseriesbeganin1995,andnowrepresentsawidevarietyoftopicsin history,philosophy,religion,science,andthehumanities.Overthenext fewyearsitwillgrowtoalibraryofaround200volumes–aVeryShort IntroductiontoeverythingfromancientEgyptandIndianphilosophyto conceptualartandcosmology. VeryShortIntroductionsavailablenow: AFRICANHISTORY CHOICETHEORY MichaelAllingham JohnParkerandRichardRathbone CHRISTIANART BethWilliamson AMERICANPOLITICALPARTIES CHRISTIANITY LindaWoodhead ANDELECTIONS L.SandyMaisel CLASSICS THEAMERICANPRESIDENCY MaryBeardandJohnHenderson CharlesO.Jones CLASSICALMYTHOLOGY ANARCHISM ColinWard HelenMorales ANCIENTEGYPT IanShaw CLAUSEWITZ MichaelHoward ANCIENTPHILOSOPHY JuliaAnnas THECOLDWAR RobertMcMahon ANCIENTWARFARE CONSCIOUSNESS SusanBlackmore HarrySidebottom CONTEMPORARYART ANGLICANISM MarkChapman JulianStallabrass THEANGLO-SAXONAGE JohnBlair CONTINENTALPHILOSOPHY ANIMALRIGHTS DavidDeGrazia SimonCritchley Antisemitism StevenBeller COSMOLOGY PeterColes ARCHAEOLOGY PaulBahn THECRUSADES ChristopherTyerman ARCHITECTURE AndrewBallantyne CRYPTOGRAPHY ARISTOTLE JonathanBarnes FredPiperandSeanMurphy ARTHISTORY DanaArnold DADAANDSURREALISM ARTTHEORY CynthiaFreeland DavidHopkins THEHISTORYOFASTRONOMY DARWIN JonathanHoward MichaelHoskin THEDEADSEASCROLLS TimothyLim ATHEISM JulianBaggini DEMOCRACY BernardCrick AUGUSTINE HenryChadwick DESCARTES TomSorell BARTHES JonathanCuller DESIGN JohnHeskett BESTSELLERS JohnSutherland DINOSAURS DavidNorman THEBIBLE JohnRiches DOCUMENTARYFILM THEBRAIN MichaelO’Shea PatriciaAufderheide BRITISHPOLITICS AnthonyWright DREAMING J.AllanHobson BUDDHA MichaelCarrithers DRUGS LeslieIversen BUDDHISM DamienKeown THEEARTH MartinRedfern BUDDHISTETHICS DamienKeown ECONOMICS ParthaDasgupta CAPITALISM JamesFulcher EGYPTIANMYTH GeraldinePinch THECELTS BarryCunliffe EIGHTEENTH-CENTURYBRITAIN CHAOS LeonardSmith PaulLangford THEELEMENTS PhilipBall INTELLIGENCE IanJ.Deary EMOTION DylanEvans INTERNATIONALMIGRATION EMPIRE StephenHowe KhalidKoser ENGELS TerrellCarver INTERNATIONALRELATIONS ETHICS SimonBlackburn PaulWilkinson THEEUROPEANUNION JohnPinder ISLAM MaliseRuthven andSimonUsherwood JOURNALISM IanHargreaves EVOLUTION JUDAISM NormanSolomon BrianandDeborahCharlesworth JUNG AnthonyStevens EXISTENTIALISM ThomasFlynn KABBALAH JosephDan FASCISM KevinPassmore KAFKA RitchieRobertson FEMINISM MargaretWalters KANT RogerScruton THEFIRSTWORLDWAR KIERKEGAARD PatrickGardiner MichaelHoward THEKORAN MichaelCook FOSSILS KeithThomson LAW RaymondWacks FOUCAULT GaryGutting LINGUISTICS PeterMatthews FREEWILL ThomasPink LITERARYTHEORY JonathanCuller THEFRENCHREVOLUTION LOCKE JohnDunn WilliamDoyle LOGIC GrahamPriest FREUD AnthonyStorr MACHIAVELLI QuentinSkinner FUNDAMENTALISM MaliseRuthven THEMARQUISDESADE JohnPhillips GALAXIES JohnGribbin MARX PeterSinger GALILEO StillmanDrake MATHEMATICS TimothyGowers GameTheory KenBinmore THEMEANINGOFLIFE GANDHI BhikhuParekh TerryEagleton GEOGRAPHY JohnA.Matthewsand MEDICALETHICS TonyHope DavidT.Herbert MEDIEVALBRITAIN GEOPOLITICS KlausDodds JohnGillinghamandRalphA.Griffiths GERMANLITERATURE MEMORY JonathanFoster NicholasBoyle MODERNART DavidCottington GLOBALCATASTROPHES BillMcGuire MODERNCHINA RanaMitter GLOBALIZATION ManfredSteger MODERNIRELAND SeniaPašeta GLOBALWARMING MarkMaslin MOLECULES PhilipBall THEGREATDEPRESSIONAND MORMONISM THENEWDEAL EricRauchway RichardLymanBushman HABERMAS JamesGordonFinlayson MUSIC NicholasCook HEGEL PeterSinger MYTH RobertA.Segal HEIDEGGER MichaelInwood NATIONALISM StevenGrosby HIEROGLYPHS PenelopeWilson NELSONMANDELA EllekeBoehmer HINDUISM KimKnott THENEWTESTAMENTAS HISTORY JohnH.Arnold LITERATURE KyleKeefer HISTORYOFMEDICINE NEWTON RobertIliffe WilliamBynum NIETZSCHE MichaelTanner HIV/AIDS AlanWhiteside NINETEENTH-CENTURYBRITAIN HOBBES RichardTuck ChristopherHarvieand HUMANEVOLUTION BernardWood H.C.G.Matthew HUMANRIGHTS AndrewClapham NORTHERNIRELAND HUME A.J.Ayer MarcMulholland IDEOLOGY MichaelFreeden NUCLEARWEAPONS INDIANPHILOSOPHY SueHamilton JosephM.Siracusa THEOLDTESTAMENT RUSSIANLITERATURE MichaelD.Coogan CatrionaKelly PARTICLEPHYSICS FrankClose THERUSSIANREVOLUTION PAUL E.P.Sanders S.A.Smith PHILOSOPHY EdwardCraig SCHIZOPHRENIA PHILOSOPHYOFLAW ChrisFrithandEveJohnstone RaymondWacks SCHOPENHAUER PHILOSOPHYOFSCIENCE ChristopherJanaway SamirOkasha SCIENCEANDRELIGION PHOTOGRAPHY SteveEdwards ThomasDixon PLATO JuliaAnnas SEXUALITY VéroniqueMottier POLITICALPHILOSOPHY DavidMiller SHAKESPEARE GermaineGreer POLITICS KennethMinogue SIKHISM EleanorNesbitt POSTCOLONIALISM RobertYoung SOCIALANDCULTURAL POSTMODERNISM ChristopherButler ANTHROPOLOGY POSTSTRUCTURALISM JohnMonaghanandPeterJust CatherineBelsey SOCIALISM MichaelNewman PREHISTORY ChrisGosden SOCIOLOGY SteveBruce PRESOCRATICPHILOSOPHY SOCRATES C.C.W.Taylor CatherineOsborne THESPANISHCIVILWAR PSYCHIATRY TomBurns HelenGraham PSYCHOLOGY SPINOZA RogerScruton GillianButlerandFredaMcManus STUARTBRITAIN JohnMorrill THEQUAKERS PinkDandelion TERRORISM CharlesTownshend QUANTUMTHEORY THEOLOGY DavidF.Ford JohnPolkinghorne THEHISTORYOFTIME RACISM AliRattansi LeofrancHolford-Strevens Relativity RussellStannard TRAGEDY AdrianPoole THERENAISSANCE JerryBrotton THETUDORS JohnGuy RENAISSANCEART TWENTIETH-CENTURYBRITAIN GeraldineA.Johnson KennethO.Morgan ROMANBRITAIN PeterSalway THEVIKINGS JulianRichards THEROMANEMPIRE WITTGENSTEIN A.C.Grayling ChristopherKelly WORLDMUSIC PhilipBohlman ROUSSEAU RobertWokler THEWORLDTRADE RUSSELL A.C.Grayling ORGANIZATION AmritaNarlikar AvailableSoon: 1066 GeorgeGarnett Scotland RabHouston Autism UtaFrith Statistics DavidJ.Hand Expressionism TheUnitedNations KaterinaReed-Tsocha JussiM.Hanhimäki HistoryofLife MichaelBenton TheVietnamWar ReligioninAmerica TimothyBeal MarkAtwoodLawrence Formoreinformationvisitourwebsites www.oup.com/uk/vsi www.oup.com/us RussellStannard Relativity A Very Short Introduction 1 1 GreatClarendonStreet,OxfordOX26DP OxfordUniversityPressisadepartmentoftheUniversityofOxford. ItfurtherstheUniversity’sobjectiveofexcellenceinresearch,scholarship, andeducationbypublishingworldwidein Oxford NewYork Auckland CapeTown DaresSalaam HongKong Karachi KualaLumpur Madrid Melbourne MexicoCity Nairobi NewDelhi Shanghai Taipei Toronto Withofficesin Argentina Austria Brazil Chile CzechRepublic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore SouthKorea Switzerland Thailand Turkey Ukraine Vietnam OxfordisaregisteredtrademarkofOxfordUniversityPress intheUKandincertainothercountries PublishedintheUnitedStates byOxfordUniversityPressInc.,NewYork (cid:1)c RussellStannard2008 Themoralrightsoftheauthorhavebeenasserted DatabaserightOxfordUniversityPress(maker) FirstPublished2008 Allrightsreserved.Nopartofthispublicationmaybereproduced, storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans, withoutthepriorpermissioninwritingofOxfordUniversityPress, orasexpresslypermittedbylaw,orundertermsagreedwiththeappropriate reprographicsrightsorganization.Enquiriesconcerningreproduction outsidethescopeoftheaboveshouldbesenttotheRightsDepartment, OxfordUniversityPress,attheaddressabove Youmustnotcirculatethisbookinanyotherbindingorcover andyoumustimposethesameconditiononanyacquirer BritishLibraryCataloguinginPublicationData Dataavailable LibraryofCongressCataloginginPublicationData Dataavailable ISBN978–0–19–923622–0 1 3 5 7 9 10 8 6 4 2 TypesetbySPIPublisherServices,Pondicherry,India PrintedinGreatBritainby AshfordColourPressLtd,Gosport,Hampshire Contents Preface ix Listofillustrations xi 1 Specialrelativity 1 Theprincipleofrelativityandthespeedoflight 1 Timedilation 5 Thetwinparadox 10 Lengthcontraction 13 Lossofsimultaneity 16 Space–timediagrams 19 Four-dimensionalspacetime 24 Theultimatespeed 32 E=mc2 35 2 Generalrelativity 43 Theequivalenceprinciple 43 Theeffectsontimeofaccelerationandgravity 49 Thetwinparadoxrevisited 55 Thebendingoflight 60 Curvedspace 65 Blackholes 79 Gravitationalwaves 95 Theuniverse 99 Furtherreading 110 Index 112 Preface Allofusgrowupwithcertainbasicideasconcerningspace,time, andmatter.Theseinclude: * weallinhabitthesamethree-dimensionalspace; * timepassesequallyquicklyforeveryone; * twoeventsoccureithersimultaneously,oronebeforetheother; * givenenoughpower,thereisnolimittohowfastonecantravel; * mattercanbeneithercreatednordestroyed; * theanglesofatriangleaddupto180◦; * thecircumferenceofacircleis2×theradius; * inavacuum,lightalwaystravelsinstraightlines. Suchnotionsappeartobelittlemorethancommonsense.Butbe warned: Commonsenseconsistsofthoselayersofprejudicelaiddowninthe mindbeforetheageofeighteen. AlbertEinstein Infact,Einstein’stheoryofrelativitychallengesalltheabove statements.Therearecircumstancesinwhicheachofthemcanbe showntobefalse.Startlingassuchfindingsare,itisnotdifficult toretraceEinstein’sthinking.Inthisbookweshallseehow,
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