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1、SpaceandTimeWarpsThislectureistheintellectualpropertyofProfessorS.W.Hawking.Youmaynotreproduce,editordistributethisdocumentinanywayformonetaryadvantage.Insciencefiction,spaceandtimewarpsareacommonplace.Theyareusedforrapidjourneysaroundthegalaxy,orfortravelthroughtim
2、e.Buttoday'ssciencefiction,isoftentomorrow'ssciencefact.Sowhatarethechancesforspaceandtimewarps.Theideathatspaceandtimecanbecurved,orwarped,isfairlyrecent.Formorethantwothousandyears,theaxiomsofEuclideangeometry,wereconsideredtobeselfevident.Asthoseofyouthatwereforc
3、edtolearnEuclideangeometryatschoolmayremember,oneoftheconsequencesoftheseaxiomsis,thattheanglesofatriangle,adduptoahundredand80degrees.However,inthelastcentury,peoplebegantorealizethatotherformsofgeometrywerepossible,inwhichtheanglesofatriangle,neednotadduptoahundre
4、dand80degrees.Consider,forexample,thesurfaceoftheEarth.ThenearestthingtoastraightlineonthesurfaceoftheEarth,iswhatiscalled,agreatcircle.Thesearetheshortestpathsbetweentwopoints,sotheyaretherootsthatairlinesuse.ConsidernowthetriangleonthesurfaceoftheEarth,madeupofthe
5、equator,thelineof0degreeslongitudethroughLondon,andthelineof90degreeslongtitudeeast,throughBangladesh.Thetwolinesoflongitude,meettheequatoratarightangle,90degrees.Thetwolinesoflongitudealsomeeteachotheratthenorthpole,atarightangle,or90degrees.Thusonehasatrianglewith
6、threerightangles.Theanglesofthistriangleadduptotwohundredandseventydegrees.Thisisgreaterthanthehundredandeightydegrees,foratriangleonaflatsurface.Ifonedrewatriangleonasaddleshapedsurface,onewouldfindthattheanglesaddeduptolessthanahundredandeightydegrees.Thesurfaceof
7、theEarth,iswhatiscalledatwodimensionalspace.Thatis,youcanmoveonthesurfaceoftheEarth,intwodirectionsatrightanglestoeachother:youcanmovenorthsouth,oreastwest.Butofcourse,thereisathirddirectionatrightanglestothesetwo,andthatisupordown.Thatistosay,thesurfaceoftheEarthex
8、istsinthree-dimensionalspace.Thethreedimensionalspaceisflat.Thatistosay,itobeysEuclideangeometry.Theanglesofatriangle,adduptoahundredandei
