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1、SpaceandTimeWarpsThislectureistheintellectualpropertyofProfessorS.W.Hawking.Youmaynotreproduce,editordistributethisdocumentinanywayformonetaryadvantage.Insciencefiction,spaceandtimewarpsareacommonplace.Theyareusedforrapidjourneysaroundthegalaxy,orfortrav
2、elthroughtime.Buttoday'ssciencefiction,isoftentomorrow'ssciencefact.Sowhatarethechancesforspaceandtimewarps.Theideathatspaceandtimecanbecurved,orwarped,isfairlyrecent.Formorethantwothousandyears,theaxiomsofEuclideangeometry,wereconsideredtobeselfevident.
3、AsthoseofyouthatwereforcedtolearnEuclideangeometryatschoolmayremember,oneoftheconsequencesoftheseaxiomsis,thattheanglesofatriangle,adduptoahundredand80degrees.However,inthelastcentury,peoplebegantorealizethatotherformsofgeometrywerepossible,inwhichtheang
4、lesofatriangle,neednotadduptoahundredand80degrees.Consider,forexample,thesurfaceoftheEarth.ThenearestthingtoastraightlineonthesurfaceoftheEarth,iswhatiscalled,agreatcircle.Thesearetheshortestpathsbetweentwopoints,sotheyaretherootsthatairlinesuse.Consider
5、nowthetriangleonthesurfaceoftheEarth,madeupoftheequator,thelineof0degreeslongitudethroughLondon,andthelineof90degreeslongtitudeeast,throughBangladesh.Thetwolinesoflongitude,meettheequatoratarightangle,90degrees.Thetwolinesoflongitudealsomeeteachotheratth
6、enorthpole,atarightangle,or90degrees.Thusonehasatrianglewiththreerightangles.Theanglesofthistriangleadduptotwohundredandseventydegrees.Thisisgreaterthanthehundredandeightydegrees,foratriangleonaflatsurface.Ifonedrewatriangleonasaddleshapedsurface,onewoul
7、dfindthattheanglesaddeduptolessthanahundredandeightydegrees.ThesurfaceoftheEarth,iswhatiscalledatwodimensionalspace.Thatis,youcanmoveonthesurfaceoftheEarth,intwodirectionsatrightanglestoeachother:youcanmovenorthsouth,oreastwest.Butofcourse,thereisathirdd
8、irectionatrightanglestothesetwo,andthatisupordown.Thatistosay,thesurfaceoftheEarthexistsinthree-dimensionalspace.Thethreedimensionalspaceisflat.Thatistosay,itobeysEuclideangeometry.Theanglesofatriangle,adduptoahundredandei