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Quantum Theory: A Two-Time Success Story Daniele C. Struppa (cid:2) Jeffrey M. Tollaksen Editors Quantum Theory: A Two-Time Success Story Yakir Aharonov Festschrift Editors DanieleC.Struppa JeffreyM.Tollaksen SchmidCollegeofScienceandTechnology SchmidCollegeofScienceandTechnology ChapmanUniversity ChapmanUniversity Orange,USA Orange,USA ISBN978-88-470-5216-1 ISBN978-88-470-5217-8(eBook) DOI10.1007/978-88-470-5217-8 SpringerMilanHeidelbergNewYorkDordrechtLondon LibraryofCongressControlNumber:2013939094 ©Springer-VerlagItalia2014 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’slocation,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer. PermissionsforusemaybeobtainedthroughRightsLinkattheCopyrightClearanceCenter.Violations areliabletoprosecutionundertherespectiveCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Whiletheadviceandinformationinthisbookarebelievedtobetrueandaccurateatthedateofpub- lication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityforany errorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,withrespect tothematerialcontainedherein. Coverillustration:MagneticFieldofaSolenoid(Aharonov-Bohmeffect),artworkbyPaulNylander (http://bugman123.com/) Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface Thisvolume,“QuantumTheory:ATwo-TimeSuccessStory,”ispartofanumberof newinitiatives,startedin2012,tohonorandadvancethevisionofYakirAharonov during the year of his 80th birthday. Starting with a conference held at Chapman UniversityfromAugust16–18,2012,theseinitiativesalsoincludedthelaunchofa newInstituteforQuantumStudies,1thededicationoftheAharonovalcoveinChap- man’slibrary,andtheintroductionofanewjournalcalledQuantumStudies:Math- ematics and Foundations, with Yakir as the chief-editor and administered through theInstitute.2 Weallknowthatquantummechanicsisthemostsuccessfulscientifictheoryin historyandresultedintechnologicaladvancesthatdriveoureconomy,suchasthe entirecomputerrevolution,electronics,andthenuclearpowerindustry.Inaddition, itimpactsmanyotherdisciplinessuchasgenetics,medicineandmathematics. However,thefoundationsofthetheoryaresonon-intuitivethatthereisnocon- sensusastothemeaningofthetheory.Thismaybeimpedingthedevelopmentof newformsofquantumtheoryrequiredforitsextensiontonewfrontierssuchascos- mology,gravity,andhighenergyparticlephysics.Itistotheadvancementofthose foundationalquestionstowhichthisvolumeisdedicated.AsNobelLaureateDavid Grossemphasizedinhischapter: “...thedeepconceptualmysteriesofquantummechanicsarestillwithus.Overmostof [Yakir’s]eightyyears(forwhichthisFestschriftisacelebration),Yakirsuccessfullystrug- gledtobetterunderstandtheseextraordinaryaspectsandtousethemtoconstructnewand surprisingresults.” Indeed,evenafteracareerspanning6decades,Yakir’sproductionofmajorsci- entific discoveries has continued to increase and deepen to this very day. Perhaps SirMichaelBerrysaiditbestatthebeginningofhiscontributiontothisFestschrift: “forYakirAharonovonhis80thbirthday:stillquick,stilldeep,stillsubtle” 1TheInstitute’swebsiteisquantum.chapman.edu. 2Thejournals’websiteiswww.birkhauser-science.com/QSMF. v vi Preface Sir Michael Berry was paraphrasing his own article which he offered 20 years agoforYakir’s60thbirthday,anarticlewhichallbutlaunchedanewfieldofmath- ematics. Yakir’scontributionstophysicsaretoomanytomention.Thecontributorstothis booktendedtofocusonafewofthemwhichdeservespecialattention.Originally discoveredand/orinspiredbyYakir,theycompriseaseriesofstudieswhichsetouta newinterpretationofquantumtheory.Elementsofthisinterpretationincludetopo- logical phases (the Aharonov-Bohm effect and its generalizations), “weak” mea- surementsand“weak”values,time-symmetricboundaryconditions,nonlocalmea- surementsandrelativisticcausality,“modular”variables,andnewaxiomsforquan- tumtheory,tonameafew. Webrieflyfocuson2oftheseitems: 1. Topological phases: In 1959, Aharonov and Bohm discovered the AB effect3 whichrevolutionizedourunderstandingof therole of potentialsinphysics and appearsinmostmoderntextsonquantummechanics.TheimpactoftheABef- fect has been huge and has continued to grow very rapidly. For the first time, theyshowedthataparticlemovinginafield-freeregioncouldbeaffectedbya fieldinadisjointregion.Suchaneffectisalientoclassicalphysics;indeed,itisa definingpropertyofthequantumworld.Numerousexperimentshaveverifiedthe effect, and recent novel techniques allow precise measurements of the shifts in electroninterferencepatternsthatdemonstratethephase(theABphase)picked upbyachargedparticlemovingaroundasolenoid.TheABphaseisubiquitous in modern physics—including cosmology, particle physics, non-abelian gauge theories,condensedmatterchemicalandmolecularphysics,andlaserdynamics. GeneralizationsoftheABphasetonon-abeliangaugetheories,suchastheWil- sonandt’Hooftloops,areimportanttoolsforstudyingtheissuesofconfinement and spontaneous symmetry breaking. The topological quantum phase explains chargequantization,thequantumHalleffect,theJosephsonjunctionandmany effectsinthenewfieldofmesoscopicphysicswheretinyelectroniccircuitsex- hibitquantumbehavior.TheABphaseplaysacrucialroleinelectronmicroscope holography. 2. Time-symmetry: Aharonov, Bergmann and Lebowitz4 suggested a two vector timesymmetricformulationofquantummechanics.Aharonov,Albert,andVaid- man5usedABLinconjunctionwithweakintermediatemeasurementsperformed onpre-andpost-selectedensemblestointroducethenotionofthe“weakvalues.” These values can be surprisingly large and have proven to be very useful tools foranalyzingvariousphysicalphenomena,forconstructingefficientdevicesfor highprecisionmeasurements,etc.Phenomenawhichwerethoughttobeunmea- sureable have now been seen using this new approach. As a new paradigm for 3Y. Aharonov, D. Bohm, “Significance of Electromagnetic Potentials in the Quantum Theory,” PhysicalReview,115,485(1959). 4Y.Aharonov,P.G.Bergmann,andJ.L.Lebowitz,Phys.Rev.134,B1410(1964). 5Y.Aharonov,D.Albert,L.Vaidman,Phys.Rev.Lett.60(1988). Preface vii thedesignofsensors,itisbeingbroadlyappliedtoprecisionDopplerfrequency measurements, gravitational detectors, etc.6 This also led to a new branch of mathematics, originally referred to as “Super-Fourier” by Sir Michael Berry, whichmanifestsinsuper-oscillationsandQuantumwalks.7 ThesecorethemesofYakir’slife-workalsoimpactperhapsthemostcontrover- sial—yet the most important—aspect of his research which concerns the issue of time in quantum mechanics. As Nobel Laureate Sir Anthony Leggett said at the dedicationoftheInstituteandlibraryalcoveatChapmanUniversity: “...throughoutall[previousscientific]revolutionsinhistory,Ithinkthere’soneassumption thathasnotreallybeenseriouslychallengedandthatispreciselythatthepastcanaffectthe presentandthepresentcanaffectthefutureandnotviceversa.Personally,Ibelieveifthere isareallyreallymajorrevolutioninphysicsinthenext50or100years,thenitwillinvolve theoverthrowofthatprinciple.Ifthathappens,IthinkYakirAharonovwillbeseentohave playedamajorroleinthepreparatoryworkleadingtothatrevolution.” Aquickreaders-note:wheneverpossible,we,theeditors,haveaddedfootnotes tothefirstpageofeachchapterinordertoreferthereadertorelevanton-linevideos oftalksgivenbytherespectivechapter’sauthorattheAharonov-80conferencein 2012atChapmanUniversity.Finally,wehaveorganizedthisbookintosixsections to allow the reader to more easily find particular subjects which were inspired by Yakir: PartI:QuantumMechanicsandReality PartII:BuildingBlocksofNature PartIII:TimeandCosmology PartIV:UniverseasaWavefunction PartV:Nonlocality PartVI:WeakValues PartVII:MathematicsofWeakMeasurements PartVIII:WeakMeasurementExperiments PartIX:YakirAharonov:ThinkingQuantum Acknowledgements TheeditorsaregratefultoSpringerforagreeingtopublishthisvolumeandtoChap- manUniversityforsponsoringtheconferenceandthisFestschrift.Also,wearemuch indebted to the Program Committee who played key roles in organizing the conference held at Chapman University in honor of Yakir Aharonov’s 80th birthday from August 16–18, 2012. In particular, we would like to thank Doug Dechow, ErikaCuriel,AshleyMelton,LevVaidman,SchmuelNussinov,KyleLee,Shannon Halverson,SheriLedbetter,SusannaBranch,EssraaNawar,andCaseyColemanfor avarietyofassistanceintheconferenceand/orthepublicationofthisbook.Finally, 6O.Hosten,P.Kwiat,Science,319,787(2008). 7Y.Aharonov,L.Davidovich,N.Zagury,Phys.Rev.A,48(1993)1687. viii Preface we wish to thank Yakir Aharonov for contributing two chapters to this Festschrift andforgenerallyinspiringthisentireprojectalongwiththenovelresearchreported hereandthecontributorsthemselves.Tothisday,hecontinuestodeepenandenrich hisprofoundimpactonthephysicsworld,asDavidAlbertsoeloquentlyputit: “...Icouldn’tthink ofanybody ...intheirtwenties—whowereeven remotelyas brave, orasopen,orascreative,orasexperimental,orasovercomewithwonder,orasbursting withlife,orasconstantlyandresolutelyexpectingtheimpossible,or(inbrief)asyoung,as Yakir.ButevenIcouldnothaveimaginedatthetimethatthirtyyearslaterhewouldturn outtobeyoungerstill.” Yakir, we dedicate this book to you with love and friendship and look forward to another80years. Orange,California DanieleC.Struppa April26,2013 JeffreyM.Tollaksen Contents PartI QuantumMechanicsandReality 1 ACenturyofQuantumMechanics . . . . . . . . . . . . . . . . . . 3 DavidGross 2 RealismandthePhysicalWorld . . . . . . . . . . . . . . . . . . . . 9 A.J.Leggett 3 EachInstantofTimeaNewUniverse . . . . . . . . . . . . . . . . . 21 YakirAharonov,SanduPopescu,andJeffTollaksen PartII BuildingBlocksofNature 4 TheBrout-Englert-HiggsMechanismandItsScalarBoson. . . . . 39 FrancoisEnglert 5 NET=T.O.E.? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 ShmuelNussinov PartIII TimeandCosmology 6 TheLimitsofBlackHoleComplementarity . . . . . . . . . . . . . 73 LeonardSusskind 7 QuantumWeakMeasurementsandCosmology . . . . . . . . . . . 101 P.C.W.Davies 8 TheQuantumMechanicalArrowsofTime. . . . . . . . . . . . . . 113 JamesB.Hartle PartIV UniverseasaWavefunction 9 CollapseMiscellany . . . . . . . . . . . . . . . . . . . . . . . . . . 131 PhilipPearle 10 ManyWorlds,theBornRule,andSelf-LocatingUncertainty . . . 157 SeanM.CarrollandCharlesT.Sebens ix