2013学年春季学期《课外阅读》

期末论文

题 目： A Reading Report On The 作 者： 罗瑶

系 别： 英语

班 级： 一班

学 号： 20113568

20xx年 6 月 20 日

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Abstract

With the continuous development and progress of human civilization, the relationship between scientific development and humanity has become one of the important factors affecting the peaceful coexistence of mankind and the earth. This paper is just one of the classics most filled with humanistic care and guiding significance. By scientific fantasy,——take the time machine to a singular journey of the future world，the author told us ——Only with humanity progress, the scientific development will become the gospel. Otherwise it will be a huge disaster and even become the crowning calamity.

Key words: scientific development; future world; humanity; disaster

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摘要

随着人类文明的不断发展与进步，科学发展与人性的相互关系成为影响人类与地球和平共存的一个重要因素，而本文正是这样一部最具人文关怀与指导性意义的成长名著。作者通过科学幻想——乘坐时间机器来到未来世界的奇异旅程告诫我们——只有伴随人性的进步，科学发展才会成为人类的福音，否则将会是巨大的灾难甚至成为灭顶之灾。

关键词：科技发展；未来世界；人性；灾难

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Contents

Abstract………………………………………………………………………….2

摘要……………………………………………………………………………….3

Ⅰ、Introduction…………………………………………………………………5

Ⅱ、A Critical and Negative Perspective on the Progress of Science…………………………………………………………………………….6

2.1 In Terms of the Plots and Ideas………………………………………………6

2.2 In Terms of the Author’s Original Words ………………………………………6

Ⅲ、Conclusion……………………………………………………………………8

Bibliography……………………………………………………………………….8

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Ⅰ、Introduction

The Time Machine is a science fiction by H. G. Wells, first published in 1895. The novel soon became popular because of the appealing plot and the future world he described in the story. It describes a time traveler to travel by inventing a time machine to the year AD 802701. There are two kinds of people. One kind of people called Eloi. They are well-dressed, doing no work, and pursue an easy life. And the other kind of strange white ape-like creatures called Morlocks. This group of creatures lives underground. They are very cruel. When they come out of the underground in the night, they begin to kill and eat Eloi as their food. The time traveler helps Eloi and fights against Morlocks. Morlocks hide his time machine into a statue, but He finally gets it, and use the machine into the future. But he makes some mistakes, and travels thirty million years into the future. He finds the life is almost extinct at that time. However, he returns to the present time in the end.

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Ⅱ、A Critical and Negative Perspective on the Progress of Science

2.1 In Terms of the Plots and Ideas

From the whole novel of well’s, a disastrous and fading future world was expressed in front of us. There is a polarization between two groups of people. One group called Eloi can do nothing except for consuming; another called Morlocks did every work mechanically and they feed on Eloi people. It is very sorrowful for us to see this situation in the future.

The author held a critical and negative perspective on the progress of science. Well’s creation purpose was not on foreseeing the possibilities of the development of science in the future times but the mutual relationship between the development of science and the human nature——if there were no progress of human nature, the development of science would only be disaster for human beings. Well’s perspective is a warning as well as a reminder to the people nowadays.

2.2 in terms of the author’s original words

“I understood now what all the beauty of the over-world people covered. Very pleasant was their day, as pleasant as the day of the cattle in the field. Like the cattle, they knew of no enemies and provided against no needs. And their end was the same.”

“But clearly, the old order was already in part reversed. The Nemesis of the delicate ones was creeping on apace. Ages ago, thousands of generations ago, man had thrust his brother man out of the ease and the sunshine. And now that brother was coming back——changed! Already the Eloi had begun to learn one old lesson anew. they were becoming reacquainted with fear.”

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“I cannot convey the sense of abominable desolation that hung over the world. The red eastern sky, the northward blackness, the salt dead sea, the stony beach crawling with these foul, slow-stirring monsters, the uniform poisonous-looking green of the lichenous plants, the thin air that hurts one’s lungs: all contributed to an appalling effect.”

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Ⅲ、Conclusion

Like all of Well’s futurist fiction, The Time Machine has a tingle of negative, making the readers to consider the possibility of the darker side, not only humanity, but also the nature. Wells justifies the monstrous behavior of the creatures in his novel not only just by his great imagination but also the theory of natural selection and Darwin’s theory of evolution. What I like about this novel is not just the world that Wells creates, but the great differences between modern human and the future human. This point gives us a warm in some degree. By making the central character of his story a time traveler who can transport himself back and forth in time with the help of a machine he invented, Wells attempted to fathom what will become of human beings in the distant future. The novel's enduring popularity is the best evident of Well’s belief he illustrates. Of course the fate of the humanity can only be known when the future becomes reality. The future is still black and blank.

Bibliography

1. Wagar. W. Warren. Indiana University Press. 1982.

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第二篇：The Loss of Unitarity in the Vicinity of a Time Machine

TheLossofUnitarityintheVicinityofaTimeMachine

DaliaS.Goldwirth

CenterforAstrophysics,60GardenStreet,Cambridge,MA02138,USA

MalcolmJ.Perry

arXiv:gr-qc/9209005v1 14 Sep 1992DAMTP,UniversityofCambridge,SilverStreet,Cambridge,CB39EW,EnglandTsviPiranCenterforAstrophysics,60GardenStreet,Cambridge,MA02138,USAWeconstructthepropagatorofanon-relativisticnon-interactingparticleina?atspacetimeinwhichtworegionshavebeenidenti?ed.Thiscorrespondstothesimplest“timemachine”.Weshowthatwhilecompletenessislostinthevicinityofthetimemachineitholdsbeforethetimemachineappearsanditisrecoveredafterwards.Unitarity,however,isnotsatis?edanywhere.Wediscusstheimplicationsoftheseresultsandtheirrelationshiptothelossofunitarityinblackholeevaporation.MsnumberLV4936.PACSnumbers:04.20.Cv,04.20.Jb,04.60.tn

TypesetUsingREVTEX

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Spacetime,andthephenomenonofgravitation,aredescribedverywellataclassicallevelbythetheoryofGeneralRelativity.Locally,spacetimeisisomorphictoMinkowskiandthereisawellde?nedlightconeandmicroscopicCausality.Globallyhowever,thingsmaybequitedi?erent.Thereisnothinginthelawsofclassicalgeneralrelativitythatpreventsspacetimesfromhavingclosedcausal(timelikeornull)curves,thatisfuturedirectedcurvesthroughapointpsuchthatifonetravelsalongthemtowardsthefuture,onereturnstothesamespacetimepoint.Itiseasyto?ndexamplesofspacetimesinwhichclosedtimelikecurveshavealwaysexisted[1].Noneoftheseexamples,generallyreferredtoaseternaltimemachines,lookverymuchlikeourUniverse.Ineachofthesecases,itisnotpossibletoposetheCauchyproblemformatter?eldspropagatinginthesespacetimes[2],andonecanthereforebelievethatthesespacetimesareratherpathological.

Anothertypeofcausalityviolationisoneinwhichclosedtimelikecurvesdevelopduringtheevolutionofaspacetimefromsomereasonableinitialconditions.AnexampleofsuchbehaviorisfoundintheKerrsolutionwhichisbelievedtobetheendpointofgravitationalcollapsewithrotation.Theregioninwhichcausalityviolationoccursisclosetothesingu-larityandinteriortotheinnerhorizon.ItmightbethecasethattheKerrexampleisgenericundercertaincircumstances,asTipler[3]hasshownthatifmatterobeystheweakenergycondition,andclosedtimelikelinesdeveloptothefutureofsomeCauchysurface,thenthespacetimemustbegeodesicallyincomplete.Ifonebelievesinthecosmiccensorshiphy-pothesis[4],thenundersuchcircumstances,thesingularityisalwaysenclosedbyahorizon,andweconjecturethatiftheweakenergyconditionissatis?edtheclosedtimelikelineswillalsoonlyoccurintheinteriorofthehorizonandthephysicsexteriortoanyhorizonwouldalwaysbeuna?ectedbytheparadoxesanddi?cultiesassociateswithclosedtimelikecurves.Hawking[5]hasproposedtheChronologyProtectionConjecture,presentlystillunproven,thatwouldpreventcausalityviolationunderawiderangeofcircumstances.

Systemsthatobeytheweakenergyconditionsclassically,forexampleafreescalar?eld,donotnecessarilyobeyitafterquantization[6,7].Underthesecircumstances,itappearstobepossibletocreatearegionofspacetimethatincludesclosedtimelikecurveswithout

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theoccurrenceofspacetimesingularities,otherthanthatassociatedwiththechronologyhorizon.Similarly,sincethelawsofphysicsaretimereversalinvariant,weexpectthatsuchregionscoulddisappear.Thistypeofspacetimewerefertoasa“timemachine.”Morris,ThorneandYurtsever[8]haveshownonewaythatsuchspacetimescanarise,whenawormholeconnectstwospacelikeseparatedpointsinMinkowskispace.Therearenumberofundesirableparadoxesthatariseinsuchaspacetime.Recentlyseveralauthors[9,10],discussedtheresolutionoftheseparadoxeswithintherealmofclassicalphysics.However,inthepresenceoftimemachinestheCauchyproblemfailstobewell-posedinaveryexplicitway[9].Foreachclassicalinitialvalueproblem,thereexistanin?nitenumberofconsistent(i.e.nonparadoxical)classicalevolutions.Inotherwords,althoughtheparadoxescanbeavoided,predictabilitywillstillbeviolated.

Ouraimistoexplorethenatureofthesequantummechanicalprocessesinthepresenceoftimemachines.Intheabsenceofanymicroscopicquantumtheoryofgravity,wecanonlystudyquantummechanicalprocessesona?xedspacetimebackground.ConceptuallyitiseasiesttoworkintheSchr¨odingerpicture.Thenthestateattimet,|ψ(t)?,isdeterminedintermsoftheHamiltonianoperator,H(t)andaninitialstate|ψ(0)?.WecannotusethismethodherebecausetheHamiltonianonlyexistsinspacetimesthataregloballyhyperbolic.Anyspacetimethathasclosedtimelikecurvesfailstobegloballyhyperbolic.

AnalternativeapproachistousetheFeynmanpathintegralto?ndthetransitionam-plitude?ψ(t)|ψ(0)?.ThepathintegralcanbederivedfromtheSchr¨odingerformulationforcertainclassesofHamiltonian,providedthattheHamiltonianexists[11].However,intheabsenceofaHamiltonian,thepathintegralistheonlytoolthatthereis,andweregardsitasthefundamentalde?nition.

Westudyafreenon-relativisticparticle.Atatimeti,theparticleisinaneigenstateofpositionatxi,soitisinthestate|i,ti?.ThepropagatoristheamplitudeGjigivenby:

Gji=?j,tj|i,ti?=?exp[iSji/h?](1)

wherethesummationisoverallpathsfrom(xi,ti)to(xj,tj)andSjiistheclassicalaction

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evaluatedalongthepathinquestion.

Accordingtothepostulatesofquantummechanicsthepropagatormustobeythegrouppropertiesofcompleteness:

Gji=

andunitarity:

?k?kGjkGkitj≥tk≥ti(2)?GkiGkj=?δij,?????

ijifti=tj<tkti<tj<tktj<ti<tk.(3)

CompletenessassertsthatifoneexaminesGik,thentheparticlewillhavebeenatsomepositionatanyintermediatetimetj.Unitarityisthestatementthatitispossibletoreversethetimeevolutionofasystemsoastoreconstructanearlierstateofthesystemgiventhestateatalaterinstantoftime.Unitaritycanbeviewedasbeingequivalenttoconservationofprobability.Itshouldbenotedthatcompletenessandunitarityensurethatthetimeevolutionofasystemisdescribedbyelementsofagroup,sincetheadditionalaxiomofassociativityisclearlysatis?edasaconsequenceof(2).IftheHamiltonianexists,anditisHermitian,thencompletenessandunitarityaretriviallysatis?ed,asHisageneratoroftheLiealgebraassociatedwiththegroupoftimeevolution.

AsanexplicitexampleconsiderthepropagatorKjiofafreenonrelativisticparticleofmassmpropagatingina?atspacetime[11].

??????????????m2?????G?,Gji,ififexpKji=?im(xj?xi)2

Nowwewishtostudywhathappensquantummechanicallytoparticlestravelinginaspacetimethathasclosedtimelikelines.Firstly,weneedto?ndamodelspacetimeinwhichcalculationsarestraightforwardbutneverthelesshasthepropertiesofarealistictimemachine.Wethereforeconsidera?atspacetimeinwhichweidentifytwoselectedspatialregionsV?andV+insuchawaythatforeachpoint(x?,t?)∈V?wematchanotherpoint(x+,t+)∈V+witht+>t?.Thisidenti?cationmimics,inasimplewaythee?ectofconnect-ingtwotimelikeseparatedregionsbyawormholeandhence,byconventionwerefertotheconnectionbetween(x+,t+)and(x?,t?)asthe“wormhole.”Theidenti?cationissothatafuture-directedtimelikelinearrivingat(x+,t+)emergesat(x?,t?)againtravelingtowardthefutureandafuture-directedtimelikelinearrivingat(x?,t?)willemergeat(x+,t+).Wecallthisatwosidedwormhole[12].WedenotebyW?+andW+?thepropagators“inside”thewormhole.SincewejustidentifythepointsinV+andV?,W?+andW+?degeneratetoanidentityfunction.

Hadtherebeennowormholethenthepropagatorinthetime-machinespacetime,Gji,wouldsimplybecomeKjigivenbyequation(4).However,itisnottoohardtoevaluate

(1)explicitlyinthetime-machinespacetimewhichweareconsidering,becauseitissimpleto?ndallpossiblepathsbywhichaparticlecanpropagatefrom(xi,ti)to(xj,tj).WewillexplicitlycalculateGjiforthecasethatti<t?<t+<tj.Thepossiblepathsarethenlabeledbythenumberoftimesnthattheparticletraversesthewormhole,andthecontributiontoGjifromallpathswith?xednisGji.Forn=0wehave:

(0)Gji(n)=Kji??+d3xKj+K+i?

??+d3x?+d3x′Kj+′K+′?K?i

?+??d3xKj?K?i(5)(?)denotes?whereKjiistheordinarypropagatorinthe?atspacetimegivenby(4)and

integrationoverthevolumeV+(V?).The?rsttermcomesfromallpathsthatgofrom(xi,ti)to(xj,tj).Howeverthesecondandthirdterms,whichrepresentthecontributionofallpathsfrom(xi,ti)to(xj,tj)viaV+,andallpathsfrom(xi,ti)to(xj,tj)viaV?respectively,mustbesubtractedo?sinceanyparticlethatarrivesat(x+.t+)hastraveledviathewormholeand

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emergedat(x?,t?)(andsimilarlyforparticlesarrivingat(x?,t?)).Inthesesubtractionswehavedoublecountedthepathsthatinordinaryspacewouldhavegonefrom(xi,ti)viaV?toV+andthento(xj,tj)andthoseareaddedinthelastterm.

Forn=1thecalculationcanbedoneinmuchthesameway:

(1)Gji=?+dx3??dxKj?′?

??3′?W?′+K+i+dx3??+dxKj+′′K+′′?′3′′?

+d3x′Kj+′W+′?K?i

(6)=Kj?W?+K+i?Kj+′K+′?W?+K+i+Kj+W+?K?i

whereinthesecondequalityweadoptthenotation,likethesummationconvention,thatrepeatedadjacentindicesareintegratedover(thustheindicesbehavelikematrixindices).The?rsttermin(6)isthecontributionfromaparticletravelingthroughthewormholeonce.Thesecondrepresentspathsthattraversethewormholeonceandthenwouldhavetraveledto(xj,tj)via(x+.t+).SuchpathsaredoomedtotravelthroughthewormholeoncemoreandthosewillcontributetoGjiwithn≥2.Thelasttermrepresentsthecontributionofpathsthatreached(x?,t?)andhavetraveledthroughthewormholeto(x+.t+)andfromthereto(xj,tj).

SimilarlyonecanconstructthegeneralGjiforpathstraversingthewormholentimes.Unliketheprevioustwocasesforn≥2wehavecontributionsonlyfrompathsthatbeganbyreaching(x+.t+):

Gji=Kj?W?+K+?′W?′+K+′?′′W?′′+′′....K+′′?′′′W?′′′+′′′K+′′′i

?Kj+K+?′W?′+K+′?′′W?′′+′′....K+′′?′′′W?′′′+′′′K+′′′i

ThecompletepropagatorcannowbeevaluatedintermsofKjiby:

Gji=∞?(n)(n)(n)?(n?1)times???(7)ntimesGji=Kji+(Kj?W?+?Kj+)(δ++′?K+?′W?′+′)?1K+i

+(Kj+W?+?Kj?+Kj+K+?)K?i.(8)(n)n=0

Notethatδ++′hasthedimensionofL?3.(δ++′?K+?′W?′+′)?1istoberegardedasamatrixinverse.ThepropagatorGjiwasderivedassumingthatti<t?andthattj>t+.However,

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(8)holdsforallpossibletimeorderingsprovidedonerecallsfrom(4)thatKji=0iftj<ti,ascanreadilybeseembyconsideringallofpossibletimeorderingofti,t?,t+andtj.Thelasttermdoesnotappearifwechooseaonesidedwormhole,insteadofthetwosidedonethatweareconsidering[12].

TosimplifythecalculationsweconsidernowV+andV?ofspatialextent?x?h?T/mXwhereTandXareanyofthetimeorlengthscalesintheproblem(e.g.t+?t?...).Then,eachofthepropagatorscanbetakentobeconstantoverV+andV?.IfvisthevolumeofV+(andV?),thenwe?ndthat[13]:

G(Kj??Kj+)K

ji≈Kji+v+i

1?vK+??K?i

+v?Kj?(2?vK+?)?Kj+

intersectingtheinteriorofthewormholewewouldhavediscoverednoviolationofcomplete-ness.

IfwetrytocheckunitarityeitherbyusingtheunitarityofKji,orbytheexplicitfunctionalformofKji,(4),wediscoverthattheunitarityconditionisviolated,unlessallti,tjandtkaretoeitherthepastortothefutureofthetimemachine,inwhichcaseGij=Kij.Asanexampleofviolationofunitarityweconsiderthespecialcaseof:ti=tj<t?<t+<tk,i.e.theinitialand?nalpointsaretothepastofthetimemachineandtheintermediatepointistothefutureofit(itwillbetoolengthytowriteouthereallpossibleorderingsofti,tj,tk,t?andt+).Then

?k?GkjGki=δji+v?K+i

??K?j?1?vK+?

+v2??K+?K?j??vK+?K?i+1?2???K+i+K+i?K?i+??K?i+v22K+?K?i

??vK+?K?i+?K+i?+v2K+jK+?K?i?(11)

andunitarityisbroken[13].ThephysicalreasonforunitarityviolationisthatthepathintegralforthereverseprocessisnotgivensimplybythecomplexconjugateofGjiasisusuallythecase.InfactitisnotpossibletoconstructaninversetoGijascanbeseenbyattemptingtoconstructtheinverseofGijorderbyorderinn.

Wehaveshownthatinthissimpli?edmodelforatimemachineunitarityisviolated,althoughcompletenessisnot.Thismeansthatthereisnolongeraunitarytimeevolutionoperatorforthissystem,andsothecanonicalformulationofquantummechanicsisinap-plicable.However,itshouldbenotedthatdespitethefactthatthegrouppropertyoftimeevolutionisviolated,thefactthatcompletenessispreservedmeansthattimeevolutioncanbedescribedbyasemigroup[15].Thismeansthatonecanpredictthefuturefromagivenmicroscopictheorygivendataspeci?edbeforethetimemachinewasformed,butitisim-possibletoreconstructthepastonthebasisofwhatonecandescribetothefutureofatimemachine.ThisisthequantumanalogoftheresultsofEcheverria,ThorneandKlinkhammer

[9].

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Fromthissimplepicture,itisclearthatquantummechanics(asusuallyformulated)breaksdowninsuchspacetimesessentiallybecauseoftheexistenceofaclosedtimelikecurves.Ifwetrytoextendourcalculationstomorecomplicatedorrealisticcases-forexamplebyhavingrelativisticparticles-exactlythesamephenomenonwilloccurbecausethepathologiesareassociatedwiththenon-existenceofaHamiltonianduetotheappearanceofclosetimelikelines.However,inthesecases,itwillbemorecomplicatedtoseeexplicitlyhowthedi?cultiesarise.

Thebreakdownofquantummechanicsdiscusseshereisveryreminiscentofthephe-nomenonofblackholeevaporation[7].Ifblackholesevaporatecompletely,thenitseemslikelythatinformationaboutthecollapsingmatterisannihilated,asaconsequenceoflackofaunitarytimeevolutionwhichmanifestitselfasapurestatedevelopingintoamixedstate.

Wewouldliketoconcludewithsomespeculations.StandardHamiltonianquantummechanicsisviolatedbyclosedtimelikecurves,sowecansupposethatifthelawsofnaturearetrulyquantummechanicalthenitwillbeimpossibletoconstructtimemachines.Ifhowever,ashasbeensuggestedonthebasisofblackholephysics,quantummechanicsbreaksdownwhengravitationistakenintoaccount[16](i.e.blackholeevaporationwhennon-unitaryevolutionofsimilarnaturealsoappearstotakeplace)thenweseenoreasonwhyitshouldnotbepossibletoconstructsuchmachines[17].

ACKNOWLEDGMENTS

ItisapleasuretoacknowledgeS.Coleman,J.Hartle,A.StromingerandK.S.Thorneforenlighteningconversations.WethanktheAspenCenterforPhysicsforhospitalitywhilethisresearchwasdone.ThisresearchwaspartiallysupportedbyaCenterforAstrophysicsfellowship(DSG),andbytheRoyalSocietyandTrinityCollege(MJP).

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REFERENCES

[1]K.G¨odel,Rev.Mod.Phys.21,447,1949;W.J.vanStockum,Proc.Roy.Soc.Edinburgh57,135,1937;F.J.Tipler,Phys.Rev.D9,2203,1973;A.H.Taub,Ann.Math.53,472,1951;E.T.Newman,L.TamburinoandT.J.Unti,J.Math.Phys.4,915,1962;J.R.GottIII,Phys.Rev.Lett.66,1126,1991.

[2]S.W.HawkingandG.F.R.Ellis,“TheLargeScaleStructureofSpacetime”,Chapter.

6.,CambridgeUniversityPress,CambridgeEngland,1973.

[3]F.J.Tipler,Phys.Rev.Lett.37,879,1976;F.J.Tipler,Ann.Phys.108,1,1977.

[4]R.Penrose,RivistadelNuovoCimento1,252,1969.

[5]S.W.Hawking,“TheChronologyProtectionConjecture”,DAMTPCambridgepreprint,1992.

[6]H.B.G.Casimir,Konink.Nederl.Akad.Weten.,Proc.Ser.Sci.51,793,1948.

[7]S.W.Hawking,Comm.Math.Phys.43,199,1976.

[8]M.S.Morris,K.S.ThorneandU.Yurtsever,Phys.Rev.Lett.61,1446,1988.

[9]F.Echeverria,K.S.ThorneandG.Klinkhammer,Phys.Rev.D44,1077,1991;

[10]K.S.Thorne,DotheLawsofPhysicsPermitClosedTimelikeCurves”,CaltechPreprint

GRP-251,1991.I.NovikovPhys.Rev.D,inpress,1992.

[11]R.FeynmanandA.R.Hibbs,“ThePathIntegralformulationofQuantumMechanics,”

McGraw-Hill,NewYork,1965.

[12]Notethat“inside”this(two-way)wormhole,inwhichparticlestravelinbothdirections,

timeorientabilityislost.ThiscanbeavoidedbyconsideringtwinwormholesconnectionstheregionsV+andV?orbychoosingaonesidedwormhole,i.e.oneinwhichaparticlethatistravelingtowardsthefuturethatarrivesat(x+.t+)istransportedto(x?,t?)and

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placedbackinthespacetimethere,butaparticlethatreaches(x?,t?)isnottransportedinsidethewormholeto(x+.t+).Ourmainresultholdsalsofortheone-waywormhole.

[13]D.S.Goldwirth,M.PerryandT.Piran,GRG,inpress,1992.

[14]NotethatourresultdoesnotcontradictthatofJ.L.FriedmanandM.S.Morris,Phys.

Rev.Lett.66,401,1991,whoconsideredonlyeternaltimemachinesandwereforcedtouseboundaryconditionsatpasttimelikein?nity.

[15]Asemigroup,S,obeysalltheaxiomsofagroupexceptthatelementsofSnolonger

arerequiredtohaveaninverse.

[16]S.W.Hawking,Phys.Rev.D14,2460,1976;S.W.Hawking,Comm.Math.Phys.87,

395,1982.

[17]D.Deutsch,Phys.Rev.D44,3197,1991.

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