TheS tructaunrdeI nterpretoaft ion Quantum Mechanics R. I.H UGG.H ES HarvUanridv ePrrseistys CambridMgaes,s achuasnedLtt osn,d oEnn,g land 1989 Copyri©g 1h9t98b yt he PresainddFe enllto ws ofH arvardC ollege righrtsese rved All Printientd h Uen itSetda toesfA merica 109 8 7 6 5 4 3 2 1 This book printoenda cid-free apnadip tseb ri,n ding is materihaalvsbe e ecnh osenf osrtr engatnhdd urabliity. LiborCfao ryn gCraetsasli onPg uibnlgiD caattai on Hughes,I G.R. . The structuanrdei nterproeftq autiaonntumm echanics/ R. GI.H. u ghes p. cm. Bibolgriap:hp y. Incluidnesd. e x ISB0N- 64-78 4136-9 1Q.u antumt heo.r Py2h.y sics-Philoso.p ThIiyl.te . QC147.21.8H2 1998 88-15651 530.21-'dc19 CIP ToN ichaonlCdaa st harine (a.Nki.caakn.K d a te) Conettns Preafce xi IntrodtuicoTnh.eS trne-GelrachE xpeirment 1 ParIt Th eS trucotfQu uraen tThuemo ry VetcoSrp aces 1 11 Vectors 12 Operators 14 EigenvecatnodrsE igenvalues 21 2 IR InnePrr oducotsfV ectoirsn 26 CompleNxu mbers 28 2 C TheS pace 31 TheP aulSip iMna trices 36 MathematicGaeln eralization 38 VectoSrp aces 40 Linear Operators 42 InnePrr oducotsn t\f 43 SubspacaensdP rojection Operators 45 OrthonormBaals es 48 Operatowrsi tah Discrete Spe ctrum 49 Operatowrsi tha ContinuousS p ectrum 51 Hilbert Spaces 55 2 StataensdO bservalbesi nQ uantuMme chaincs 57 ClassiMceaclh anics: SyasntdeT mhse irS tates 57 ObservablaensdE xperimentaQlu estions 59 Stataensd O bservablienQs u antum Theory 63 ProbabiliatinedsE xpectatiVoanl ues 70 TheE volutioofnS tatiensC lassiMceaclh anics 72 Determinism 7 4 TheE volutioofnS tatiensQ uantum Mechanics 77 Theorieasn dM odels 79 Cnoetsn t vzzz PhyisclaT heorya ndH ibletr Spaces 3 83 Minimal Assumptionfso r PhysTihceaolry 85 TheR epresentoaftiO ount comeasn dE vents 86 TheR epresentoaftiS otna tes 88 Determinism, Indeterminism,a ndt heP rinciploef S uperposition 91 MixeSdt ates 93 ObservablaensdO perators 97 Relatiobnest ween Observables: Functionaanld C oDmeppaetinbdileintcye 99 IncompatiObblsee rvables 104 TheR epresentaCtiaopnaacilt oyfH ilbeSrpta ces 107 TheS chrodinEgqeura tion 113 4 Spiann dI tRse persetantion 119 Symmetry Conditioannsd SpSitna tes 120 2 IR A PartiaRle presentoaftiS opni inn 123 2 C TheR epresentoafti{ oSna i}n 127 Conclusion 131 5 DenistOyp erasta onrdT enso-rProdSupcatc es 136 Operatoorfts h e Trace Class 136 DensiOtpye rators 138 2 C Density Opeorna tors 139 Pure andM ixed States 141 TheD ynamicEavlo lutioofnS tates 145 GleasoTnh'eso rem 146 ComposiStyes temasn dT ensor-Product Spaces 148 TheR eductioonfS tatoefsC omposite Systems 149 ParIItTh eI nterproefQt uaatnitThouenmo ry 6 TheP roblemo fP roperties 155 PropertiEexsp,e rimenQtuaels tionansd, t heD ispersiPorinn ciple 155 TheE PRA rgument 158 Bohm'Vse rsioonf t heE PRE xperiment 159 TheS tatistiIcnatle rpretation 162 Kocheann dS peckeErx'asm ple 164 Generalizintgh eP roblem 168 TheB ell-WigneIrn equality 170 HiddeVna riables 172 InterpretiQnuga ntuTmh eoryS:t atistiSctaalt aensd V aluSet ates 175 7 QuantuLmo gic 178 TheA lgeborfaP ropertioefas S implCel assical System 178 BooleAalng ebras 182 Poseats ndLa ttices 186 TheS tructure of5 (11) 190 TheA lgeborfaE vents 194 A FormalA pproacthoQ uantumL ogic 201 Cotnetns zx UnexceptionIanbtleerp retaotifQo una ntuLmo gic Afl 207 Putnaomn Q uantuLmo gic 209 PropertiaensdD eviaLnotgi c 212 8 ProbalbitiyC,au sltaiy,a ndE xplanation 218 ProbabilGietnye ralized 219 TwoU niqueneRsess ults 220 TheT wo-SliEtx perimenWta:v esa ndP articles 226 TheT wo-Slit Experiment: Conditional Probabilities 232 TheB ell-WignIenre qualiatnydC lassical Probability 237 BellI nequaliatinedsE instein-Locality 238 BellI nequaliatinedsC ausality 245 Coupled SysatnedCm osn ditionParlo babilities 248 ProbabiliCtayu,s alitayn,dE xplanation 255 Meausrement 9 259 ThreeP rinciploefsLimi tation 259 IndetermiannadcM ye asurement 265 ProjectiPoons tulates 271 Measuremeanndt C onditionalization 275 TheM easuremePnrto bleamn dS chrodingCeart' s 278 JauchM'osd elof t heM easuremePnrto cess 281 A Problefmo rI nternAaclc ounotsf M easurement 284 ThreAec counotsf M easurement 288 AnI nterpraettioofnQ uantuTmhe ory 10 296 Abstractiaonn dI nterpretation 269 PropertiaensdLa tencieTsh:e Q uantum EvenItn terpretation 301 TheC openhagIennt erpretation 306 TheP rioritoyf t heC lassical World 310 QuantuTmh eorya ndt heC lassiHcoarilz on 312 AppendixA . GleasThoeno'rse m 321 AppendixB .Th e LuderRsul e 347 AppendixC . CouplSeysdt emsa ndC onditionalization 349 Refere3n5c1e s Index 363 Prfecae It akiet t ob ea nu nassailtarubtlhe that Twahoaits Cmo,n fucianismZ,e n Buddhisamn,d t he writinogfCs arloCsa stanehdaav ei nc ommont,h ey havei nc ommonw itqhu antumme chanics.t ruthgso ,h owevetrh,i osn e As isn'vte ryil luminating.Q uantumm echanicso,n eo ft het wogr eata nd revolutiotnhaeroyri oefsp hysitcosa ppeadru ringt hefir stt hiryteya rosf thicse ntuirsye ,s sentiaam laltyh ematitchaelo royn;ewil lg ainl itgtelneui ne insigihntti otw ithosuotm ea wareneosfts h em athematimcoadle liste m­ ploys. Thaits o neo ft het wob eliwehfisc hha veg uidedt hew ritingo ft hibso ok. Theo theirst hatth er equismiatteh ematikcnaolw ledigsen ota,f tearl l, In fearsomdifefilyc ulttoa cquiref.a cotn,e k indo fr eadeIhr a vei nm ind is ther eadwehro ,w hilneo ts eizbeydp aralyastti hses ighotfa m athematical formuldao,e sn oth appetno h avea workingk nowledogfev ector-space In theory.t hirse spetchteb ooki ss elf-conttainheemd a;t hematibcaaclk ­ groundi ta ssumeisst haotf h ighs choomla thematiacnsdt, h ea dditional mathematniecesd edt,h em athematoifcv se ctosrp aces,p reisse ntiend Chapte1ra sn d5 . Anothekrin do fr eadehra st akepnh ysiccosu rseasn,ds olvetde xtbook probleimnsq uantumme chanicbsu,t l,i kmeo sto fu sc,o ntinuteosfi ndt he theory demeypsltye riouPse.r haprsa shltyh,ir se adehro petsh aat p hilo­ sophical awilccloc ulnatr ify maBtettewrese.tn h estew oi deatly petsh eries , nota c ontinuous speacttl ruema,as c to nsiderable odfir veeardsetirots y if whom theb ookwil lp rovaec cessible. In presentitnhgem athematitchses, tr ateIgh ya veu sedi st otr eafitn itely dimensionsapla cepsa,r ticulartlwyo -dimensiosnpaalc eisn,s omed etail, andt hetno i ndiciantg ee nertaelrm sh owt hes amei deaasr ea ppliiendt he infinitedlimye nsioncaals eC.o rrespondintghleyq ,u antum-mechanical quantiItd ieeaswl i tahr eu sualslpyi cno mponenrtast,h tehra pno sitainodn