千米小说网

Chapter 1 From Newton to Einstein（第2页）

2。Anillustrationofaplaaryorbit。Theshadedregions，markedAandB，areofequalarea，iftheyaresweptoutbytheplaime。

·Thesquareofthetimetakenforaplaopleteoisproportionaltothecubeofthedistawofurthestpointsonthatorbit（themajoraxisoftheellipse）。

&iesdesthesethreelawsareallillustratedihtheexoftheorbitalperiod）。ThegoodthingaboutKepler'slawswasthattheyseemedtoapplytoallks，eventhoughatthetimetheyhadnoknownbasisinanyphysicaltheory。Theyweresimplyseentobeagoodfittothedata。Kepler'slaws，andinhisPrincipiaMathematiexplanationofhowtheycouldbederivedfromhislawsofmotionandfromhisuheravitatioiohegreatsuccessstoriesofphysics。Empiricallaws，derivedfromg-edgeobservatios，wereexplaihefirsttimeintermsofsimplemathematicalequatioonhadshownthatthesamelawsthatdescribethemotionofaballfiredonthesurfaceoftheEarthcouldalsobeusedtodescribethemotiosthemselves。Thiswasthebeginningofmuchofphysicsaswekno>

&ein’stheravity

&haeritspubliewton'stheravitylantedbyAlbertEinstein's。Ifon'stheoryleaheein'swasbeautifulandtrulyuniversal。Eijustgetheequatioon'stheory，hepulleduptheveryfoundationsuponwhichitrested。Einsteihing。

Aswithmuchressthathappensinphysistein'stheoryrimarilybytheincyofexistioheoryofhowgravityandmotioon'sideaswerenotpatiblewiththethehtthatJamesClerkMaxedinthemiddleofthe19thtury。Maxwell'sedthateveryoheUniverseshouldmeasurethespeedoflighttohavethesamevalue:justunder300milliorespersed。Thismightnotsoundterriblyprofound，untilyoutakeafewmomentstosiderwhatitmeans。

&isthat，agtoon'smeics，ifIfireabulletforwardsat1，000milesperhourwhileseatedonatrainmovingat100milesperhour，thehesideofthetrackwillseethatbulletmovingat1，100milesperhour。Iermswesaythatthevelocityofthebulletayofthetrainaddlinearly。NowsiderthatIturnonatorch，whilestillseatedfagforwardsorain。FrommyseatedpositionIwillseethelightfratefhthetraihespeedoflight（i。e。atabout300milliorespersesideragaigmefromthesideofthetraintrack。Ifyoulisteon，youmightexpectthispersohelighttravelatthe300milliorespersed，plus100milesperhour（thespeedofthetrain）。ButagtoMaxwellthisisnotehatthepersonatthesideofthetrackseesthelightpropagateatthesamespeedasthepersohatis，Maxwell’sequationsimplythatvelocitiesdonotaddlinearly。

&radijustdescribedisaprofoundone。Ifweareuoagreeonhowtoaddvelocities，theousephysicstocalculatethemotioall。Itossibleforbothonaobecorrect。Atleastobewrong。Alesserstistmighthavetriedtore-writeeitheron’sorMaxwell’stheories，butthiswasnot>

&eireatedbothon’sandMaxiththeutmostrespect。Hereizedtheirgreatstrengths，aosolvethetradiatrulyingeniousway。Eihesizedthatifthespeedoflightwasthesameforeveryoimeabeuniversalstead，hereasoned，eausthavetheirotoftime，andtheirotofspace。AgtoEinsteiheory，aclockcarriedbyapersorainisseeahetrack，totickslowerthanaclocktheycarrythemselves。Likewise，thepersoraiheclockofthepersonstahetracktotickslowerthanhisorherown。

Thisresultinitiallysoundsodd，butthat’sonlybecausewe’vebeenprogrammedfromayouhinkoftimeasuniversal。WhatEinsteihatourchildhoftimeismistakeauniversalfoldieforeveryoimeisapersonalthing，anddependsoivemotiooothers。Likewise，spaotthefixedbackdropthatwethinkitis。Whatwethinkofasdistahelengthsofobjects，areactuallydepeonh。

&artlifirsttheyseemuling，asifthecrutcheswe'veusedtouheworldhavesuddenlybeenkickedaway。Butwedespair。Thereisavolviimethatsurvivesiheory，andthatmaintainsanobserver-iy。Thisiswhatisknoace-time。Insteadofosofuimeanduniversalspace，whatweareleftwithisalargerstructurethatehemboth。Aperso，likeyouorme，followsalihroughthisstruownasourworld-liimeismeasuredalongourworld-line，andwhilemyworld-libediferenttoyours，theybothexistiime（seeFigure3）。

So，itisthepromotioimetospace-timethatallowsustomakeon’smeisistentwithMaxwell’s。ThisrealizatioeiributionstosditisthebaeofwhatisnoecialTheoryofRelativity。Ithasawidevarietyofprofoundyofwhichhavebeenedexperimentally。Themostfamousoftheseisprobablytheequation:

3。Awoworld-liwiime。Theobserversmeetwherethelinescross。

whichtellsusthatmassandeelyected（afactthatbecamedevastatinglyapparentwiththeadventofnuclearons）。Othercesarethelouiclesappeartohavewhentheymovequidthefaothingevermht。

Itisthislastresult，togetherwiththeofspace-time，whisteintohistheaiusforthisdevelopmentarenttradidagain，itwasheorythatroblems。Thistime，however，itseemedthattherewasatradiwithEinstein’sownwork。Thiswasbeewton’sgravityactedbetweeahatis，iftheSuosuddenlyexpltoonweshouldfeelthegravitatiohisattheverysamemomentithappeeihisossible。First，hehadfoundoutthatnothinght。Sed，hehadshownthattherewasnosugasuime，sotheideaoftwothingshappeningsimultaneouslyiplaoseall（iftheyhappeaneouslyforoheywouldaneousforanyotherwhowasieofmotion）。So，on，somethingwaswrongandneededfixing。

&ein’ssolutiontothisproblemwasevenm。Hehypothesizedthatgravity，insteadofbeisimplypulledthingsthroughspace，wastheresultofthecurvatureofspace-time。Thefactthatmassiveobjectsardseachotherwasthen，agtoEiaresultofthoseobjectsfollowipathstheythecurvedspawhichtheyexisted。Theideawasthatmassandenergycausedspace-timetodthatthiscurvaturecausedthepathsoftheobjectsthatmhspacetoappeartobendtowardseachother。ThebeautyofthisideaisthatwenowoiyasaraforcethatexistsintheUhisure，theonlythingrespoheattraassivebodiesisspace-timeitself（whichhastobethereanyway）。ThisisthefualideabehiheoryofRelativity。

EvenmoreimpressiveisthatEinstein’sideaexplainedGalileo’sresultthatallobjectsfallatthesamerate。Recallthatiheorythisresultlaiall。Itlytakenasafadalawofgravitywasdevisedthatatiblewithit。Eioer。eihereisernalforcecalledgravity;themotioisjustaresultofthecurvatureofspace-time。Butalliime，soallobjectsmustfolloaths。Inotherwords，allobjectsmustfallatthesamerate，justasGalileohadobserved。

Theseideasesbeg，solet’sthinkaboutanexample。Imagihsoftwoobjectsthathaveingonthem。Inaflatspacethepathsofthesehtlines，asshowninFigure4。

Ifthespaceiscurved，however，thenthisisrue。siderthesimplestcurvedspace:thesurfaceofasphere。Theshortestpathbetointsonthesurfaceofasphereiscalledagreatcircle（theequatorisanexampleofagreattheglobe）。Iftwoobjectsfollowtwreatesphere，thentheywillinitiallymoveawayfromeachother，beforefinallyiheragain，asshownihisishowEinsteiyw。Heimagiwascurvaturethatohepathsofobjeg，andnotahatpullsthemlefthtastheymove。Thecurvatureofspace-timeisusuallymularthanthesurfaceofasphere，butthebasicideaisthesame。Asfarasthecesfestefestein'sheorywerefoundtolookverysimilartothelawthatonhadprescribed200yearsearlier。Thediferethislaithaandingofspadtime。Italsoeswiththeprediofavarietyofsmaller，moresubtle，efects（tobedisthefolloters）。

4。Twhtlines，indigthepathsthattwoparticlesmightfollowiftheytravelledthroughaflatspace，withoutaeringuponthem。

5。Twogreatcirdigthepathsthatparticlesmighttravelinasphericallycurvedspaoexterupohelinesarenolongerparallelforever，butmeetatapoint。

Thinknowaboutwhatallofthismeansinapracticalsituation。sideraskydiverjumpingoutofaheskydiverfallsfreely，uptotheefectsofairresistance。AgtoEiheskydiver’spathisthestraightestlinepossiblethroughthecurvedspace-timearouh。Fromtheskydiver’sperspectivethisseemsquitefpasther，theskydiverfeelsurbiall。Infact，ifitweren’tfortheairresistance，shewouldexperielesshesamewaythatanastronautdoesinorbit。TheohinktheskydiverisagisbecauseweareusedtousingthesurfaceoftheEarthasourframeofreference。Ifwefreeourselvesfromthis，thenwehavehinktheskydiverisagatall。

Nowsideryourselfontheground，lookingupatthefallingdaredevil。Normally，youriionofyourownmotioyouarestatiainthisisonlybecauseofourslavishregardtotheEarthasthearbiterofwhatisatrestandwhatismoving。Freeyourselffromthisprison，ahatyouare，infact，ag。Youfeelaforthesolesofyourfeetthatpushesyouupwards，iyouwouldifyouwereinaliftthatacceleratedupwardsveryquiEiurethereisweenyourexperieahandyourexperie。Inbothsituationsyouareagupwards。Iersituationitistheliftthatisresponsibleforyourac。Intheformer，itisthefactthattheEarthissolidthatpushesyhspace-time，knogyouofyourfree-falltrajectory。ThatthesurfaceoftheEarthaccelerateupointonitssurfadremainasolidobject，isbecauseitexistsiimeandnotinaflatspace。

Withthisperspectivethetruenatureofgravitybeesapparent。ThefreelyfallingskydiverisbroughttoEarthbecausethespace-timethroughwhichshefallsiscurved。Itiserugsherdownwards，butherownnaturalmhacurvedspatheotherhand，asapersonstandingontheground，thepressureyoufeelonthesolesofyourfeetisduetidityoftheEarthpushingyain，thereisernalforgyoutoEarth。Itisoaticfortherocksbelowyourfeetthatkeepthegrid，andthatpreventsywhatwouldotherwisebeyournaturalmotion（whichwouldalsobefreefall）。

So，ifwefreeourselvesfromdefiningourmotioothesurfaceoftheEarthwerealizethattheskydiverisihepersonwhostandsonthesurfaceoftheEarthisag。Justtheoppositeofwhatweusuallythink。GoingbacktoGalileo’sexperimentoowerofPisa，hyheobservedallofhisballstofallatthesamerate。ItwasheballsthatwereagawayfromGalileoatall，itwasGalileothatwasagawayfromtheballs!IfIleaveanumberofobjectsatrestatsomepositioninspadaccelerateawayfromthem，Ishouldallsurprisedthatthedistaweeheseobjecreasesatthesamerate。SoitiswithGalileoandhisballs。

Forsome，thebeautyiionisobvious。ForothersitisthefactthatitispossibletoprobeEiheoryexperimentallythatismostpelling。TheseexperimentsrangefromlookingforsmallperturbatiosoftheplahebendingoflightaroundtheSun，andmany，manymorebesides。Wewillexploretheseexgphehechaptersthatfollow。Butbearinmindthroughout:itisthecurvatureofspace-timethatisrespoall。