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1、SpaceandTimeWarpsThislectureistheintellectualpropertyofProfessorS.W.Hawking.Youmaynotreproduce,editordistributethisdocumentinanywayformonetaryadvantage.Insciencefiction,spaceandtimewarpsareacommonplace.Theyareusedforrapidjourneysaroundthegalaxy,orfortravelthroughtime.Buttoday'ssciencefiction,
2、isoftentomorrow'ssciencefact.Sowhatarethechancesforspaceandtimewarps.Theideathatspaceandtimecanbecurved,orwarped,isfairlyrecent.Formorethantwothousandyears,theaxiomsofEuclideangeometry,wereconsideredtobeselfevident.AsthoseofyouthatwereforcedtolearnEuclideangeometryatschoolmayremember,oneofthe
3、consequencesoftheseaxiomsis,thattheanglesofatriangle,adduptoahundredand80degrees.However,inthelastcentury,peoplebegantorealizethatotherformsofgeometrywerepossible,inwhichtheanglesofatriangle,neednotadduptoahundredand80degrees.Consider,forexample,thesurfaceoftheEarth.Thenearestthingtoastraight
4、lineonthesurfaceoftheEarth,iswhatiscalled,agreatcircle.Thesearetheshortestpathsbetweentwopoints,sotheyaretherootsthatairlinesuse.ConsidernowthetriangleonthesurfaceoftheEarth,madeupoftheequator,thelineof0degreeslongitudethroughLondon,andthelineof90degreeslongtitudeeast,throughBangladesh.Thetwo
5、linesoflongitude,meettheequatoratarightangle,90degrees.Thetwolinesoflongitudealsomeeteachotheratthenorthpole,atarightangle,or90degrees.Thusonehasatrianglewiththreerightangles.Theanglesofthistriangleadduptotwohundredandseventydegrees.Thisisgreaterthanthehundredandeightydegrees,foratriangleonaf
6、latsurface.Ifonedrewatriangleonasaddleshapedsurface,onewouldfindthattheanglesaddeduptolessthanahundredandeightydegrees.ThesurfaceoftheEarth,iswhatiscalledatwodimensionalspace.Thatis,youcanmoveonthesurfaceoftheEarth,intwodirectionsatrightanglestoeachother:youcanmovenorthsouth,oreastwest.Butofc
7、ourse,thereisathirddirectionatrightanglestothesetwo,andthatisupordown.Thatistosay,thesurfaceoftheEarthexistsinthree-dimensionalspace.Thethreedimensionalspaceisflat.Thatistosay,itobeysEuclideangeometry.Theanglesofatriangle,adduptoahundredandei