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1、SpaceandTimeWarpsThislectureistheintellectualpropertyofProfessorS.W.Hawking.Youmaynotreproduce,editordistributethisdocumentinanywayformonetaryadvantage.Insciencefiction,spaceandtimewarpsareacommonplace.Theyareusedforrapidjourneysaroundthegalaxy,orfortravelthroughtime.Buttoday'ss
2、ciencefiction,isoftentomorrow'ssciencefact.Sowhatarethechancesforspaceandtimewarps.Theideathatspaceandtimecanbecurved,orwarped,isfairlyrecent.Formorethantwothousandyears,theaxiomsofEuclideangeometry,wereconsideredtobeselfevident.AsthoseofyouthatwereforcedtolearnEuclideangeometry
3、atschoolmayremember,oneoftheconsequencesoftheseaxiomsis,thattheanglesofatriangle,adduptoahundredand80degrees.However,inthelastcentury,peoplebegantorealizethatotherformsofgeometrywerepossible,inwhichtheanglesofatriangle,neednotadduptoahundredand80degrees.Consider,forexample,thesu
4、rfaceoftheEarth.ThenearestthingtoastraightlineonthesurfaceoftheEarth,iswhatiscalled,agreatcircle.Thesearetheshortestpathsbetweentwopoints,sotheyaretherootsthatairlinesuse.ConsidernowthetriangleonthesurfaceoftheEarth,madeupoftheequator,thelineof0degreeslongitudethroughLondon,andt
5、helineof90degreeslongtitudeeast,throughBangladesh.Thetwolinesoflongitude,meettheequatoratarightangle,90degrees.Thetwolinesoflongitudealsomeeteachotheratthenorthpole,atarightangle,or90degrees.Thusonehasatrianglewiththreerightangles.Theanglesofthistriangleadduptotwohundredandseven
6、tydegrees.Thisisgreaterthanthehundredandeightydegrees,foratriangleonaflatsurface.Ifonedrewatriangleonasaddleshapedsurface,onewouldfindthattheanglesaddeduptolessthanahundredandeightydegrees.ThesurfaceoftheEarth,iswhatiscalledatwodimensionalspace.Thatis,youcanmoveonthesurfaceofthe
7、Earth,intwodirectionsatrightanglestoeachother:youcanmovenorthsouth,oreastwest.Butofcourse,thereisathirddirectionatrightanglestothesetwo,andthatisupordown.Thatistosay,thesurfaceoftheEarthexistsinthree-dimensionalspace.Thethreedimensionalspaceisflat.Thatistosay,itobeysEuclideangeo
8、metry.Theanglesofatriangle,adduptoahundredandei
