ContentsPreface

Acknowledgements

Introduction

ChapterOne:Nineteenth-CenturyBoyAntecedentsEarlyyearsAnempire’slasthurrahScientificstirringsFromschoolboytoundergraduate

ChapterTwo:PhysicsbeforeSchrödingerNewtonandtheworldofparticlesMaxwellandtheworldofwavesBoltzmannandtheworldofstatistics

ChapterThree:Twentieth-CenturyManStudentlifeLifebeyondthelabWarserviceontheItalianFrontBacktoViennaTheaftermathTheperipateticprofessor

ChapterFour:TheFirstQuantumRevolutionWhenblackbodiesarebright

EnterthequantumThequantumbecomesrealInsidetheatomTrippingthelightfantasticEinsteinagain

ChapterFive:SolidSwissRespectabilityTheuniversityandtheETHPersonalproblemsandscientificprogressPhysicsandphilosophyLifeandlove“Myworldview”Quantumstatistics

ChapterSix:MatrixMechanicsHalf-truthsWhatyouseeiswhatyougetMatricesdon’tcommuteJusticeisn’talwaysdone

ChapterSeven:SchrödingerandtheSecondQuantumRevolution

ScienceandsensualityRidingthewaveAquantumofuncertaintyTheCopenhagenconsensus

ChapterEight:TheBigTimeinBerlinMakingwavesinAmericaBerlinandBrussels

ThegoldenyearsBacktothefuturePeopleandpolitics

ChapterNine:TheComingoftheQuantumCatBackintheUSAOxfordandbeyondFasterthanlight?ThecatintheboxFromOxfordwithlove

ChapterTen:There,andBackAgainWhistlinginthedarkRealitybitesTheunhappyreturnBelgianinterlude

ChapterEleven:“TheHappiestYearsofMyLife”“Dev”SettlinginEarlydaysattheDIAS“Family”lifeinDublinThepost-waryearsManyworlds

ChapterTwelve:WhatIsLife?LifeitselfQuantumchemistryThegreenpamphletSchrödinger’svariationonthetheme

Thedoublehelix

ChapterThirteen:BacktoViennaFarewelltoDublinHomeistheheroDecliningyearsThetriumphofentropy

ChapterFourteen:Schrödinger’sScientificLegacyHiddenrealityandamathematician’smistakeTheBelltestandtheAspectexperimentQuantumcryptographyandthe“nocloning”theoremQuantumteleportationandclassicalinformationThequantumcomputerandtheMultiverseQuantumphysicsandreality

Postscript

SourcesandFurtherReading

Index

Copyright©2013byMaryandJohnGribbin.AllrightsreservedCoverDesign:TomPoland

CoverImage:ProfessorErwinSchrödinger©Bettmann/CORBISPublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJersey

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visitusatwww.wiley.com.

LibraryofCongressCataloging-in-PublicationDataGribbin,John,date.

ErwinSchrödingerandthequantumrevolution/JohnGribbin.pagescm

Includesbibliographicalreferencesandindex.ISBN978-1-118-29926-5(hardback);ISBN978-1-118-33411-9(ebk);

ISBN978-1-118-33188-0(ebk);ISBN978-1-118-33519-2(ebk)1.Schrödinger,Erwin,1887-1961.2.Physicists—Austria—Biography.3.

Physics—Philosophy.4.Quantumtheory.I.Title.QC16.S265G752013

530.092—dc23[B]

2013025742

ForTerryRudolph,eventhoughhewon’treadit

Wemust not forget that pictures andmodels finally have no other purposethan to serve as a framework for all the observations that are in principlepossible.

ErwinSchrödinger,Frankfurt,December1928Hisprivatelifeseemedstrangetobourgeoispeoplelikeourselves.Butallthisdoes not matter. He was a most lovable person, independent, amusing,temperamental, kind and generous, and he had amost perfect and efficientbrain.

MaxBorn,MyLife(1978)

Preface

WhilewritingmybookInSearchoftheMultiverse,Icameacrossaprescientbutlittle-known piece ofwork by the quantum pioneer Erwin Schrödinger,whichpointed the way, had anyone taken notice of it at the time, towards the verymodernideaofapluralityofworlds,separatedfromoneanothernotinspacebutin some other sense—“parallel universes,” in the language of science fiction.Therewasnosuitablewaytosqueezethishistoricaldeadendintothatbook,butit remindedme that Schrödinger was aman of many talents, and well worthbeingthesubjectofapopularbiography—abiographywhichwouldgivemeachance todustdownthat forgottenpieceofworkandgive it therecognition itdeserves,set in thecontextofSchrödinger’s lifeandwork.ThemoreI lookedintohis life, themore remarkable it seemed; Ihopeyouagree thathis isverymuchastoryworthtelling.

AcknowledgementsAlthough her name does not appear on the cover of this book,MaryGribbinplayedaninvaluableroleasaresearcher,diggingupdetailsofSchrödinger’slifeand liaising with libraries and research institutions. As ever, we are bothindebtedtotheAlfredC.MungerFoundationforfinancialsupport.Ourspecialthanksgotothefollowingpeoplewhoandplacesthathelpedus,overtheyears,in our search for Schrödinger: Michel Bitbol; Dominic Byrne; John Cramer;Dublin Institute for Advanced Studies; Einstein Archive, Princeton; JohnsHopkinsUniversityArchive;SirWilliamMcCrea;OxfordUniversityArchive;Rudolf Peierls; Terry Rudolph; Schrödinger Archive, Alpbach; SchrödingerArchive,Vienna;ChristineSutton;UniversityofBerlinArchive;UniversityofWisconsinArchive;ViennaUniversityArchive.

Introduction

It’sNotRocketScience

Rocket science is the purest expression of the laws of physics spelled out byIsaacNewtonmorethanthreehundredyearsago,oftenreferredtoas“classical”science.Newtonexplainedthatanyobjectstaysstillormovesinastraightlineat constant speedunless it is affectedby anoutside force, such as gravity.Hetaught us that if you push something it pushes back—action and reaction areequalandopposite,aswhena riflekicksbackagainstyourshoulderwhile thebulletfliesoffintheoppositedirection.Healsogaveusasimplelawofgravity,explaininghowtheforceofgravitydependsonmassanddistance.The“actionand reaction” bit is at the heart of rocket science. A rocket throws out stuff(usuallyhotgas,althoughinprinciplemachine-gunbulletswoulddothetrick)inone direction, and the reaction makes the rocket accelerate in the oppositedirection.Whenthemotorsarenotrunning,thespaceprobedriftsinwhatwouldbe a straight line except for the influence of gravity. All sound Newtonianphysics,andnotreallyverydifficulttounderstand.Classical science describes an utterly predictable world. It is possible, for

example,toworkoutexactlyhowmuchrocketthrustinwhatdirectionisneededto set a spaceprobewith a certainmass on a trajectory, falling through spaceundertheinfluenceofgravity,thatwilltakeit tointercepttheplanetMarsataprecise date months in the future. Assuming their engines work properly,spaceprobesonlymisstheirtargetwhensomebodygetsthesumswrong—whenthereishumanerror.ForcenturiesafterthetimeofNewtonclassicalscienceposedarealproblem

foranyonewhobelievesinfreewill.Inprinciple,ifyouknewthepositionandspeedofeveryparticleintheUniverse,includingtheatomswearemadeof,atanychosenmomentof time, itwouldbepossiblenotonlytopredict theentirefuture of theUniverse, but to reconstruct its entire history in exquisite detail.Leavingaside thepracticalproblemsofactuallydoing this, itseemedto implythat everything, including human behaviour,was pre-ordained.But then camequantumphysics.Quantum physics is not like classical physics. It is definitely not rocket

science; it’smuch harder to understand than that. It tookmany top scientists,workingover the first threedecadesof the twentieth century, toworkout justwhatquantumphysics is, andwhen theydid findout someof them, includingthesubjectofthisbook,didn’tlikewhattheyhadfound.Quantum physics mostly describes the world of the very small—roughly

speaking, things the size of atoms and smaller.What physicists painstakingly(and painfully) discovered during those first three decades of the twentiethcentury is that particles can behave like waves and waves like particles; thatquantumentitiescanbeinatleasttwoplacesatonce;thattheycangetfromoneplacetoanotherwithoutpassingthroughanyofthespaceinbetween;andthatthere is no certainty in the quantum world, where everything depends onprobabilities. It’sas ifyousentaspaceprobeon itsway in theknowledge thattherewas a50per cent chance that itwould arrive atMars anda50per centchance that it would arrive at Venus, but no way to tell in advance where itwouldendup.Greatforrestoringabeliefinfreewill,butscarcelyreassuringinanyotherway.Andyetallthisbafflingbehaviourofthequantumworldhasbeentestedandconfirmedincountlessexperiments.ErwinSchrödinger’smasterpiece, thework forwhichhe received theNobel

Prize, tried to restore the common sense of classical physics to the quantumworld.Itisn’tgivingawaytoomuchofourstorytosaythathefailed,andthathisworkbecameanintegralpartoftherevolutionarynewphysics.But therewasmuchmore toSchrödinger than the reluctant revolutionaryof

quantum physics. One of the most intriguing aspects of Schrödinger thephysicist, and one that lies at the heart of his antipathy to the revolution heparticipatedin,isthatalthoughhemadeamajorcontributiontothenewscienceof the twentieth century, he was brought up in the scientific tradition of thenineteenth.Hegraduatedfromhighschoolandstartedatuniversityin1906,theyear afterAlbertEinsteinpublishedhis classicpaperson the special theoryofrelativity and quantumphysics.ButEinstein, of course,was an exception; hisideas on quantum physics, in particular, were not taken seriously for at leastanother ten years, and the real quantum revolution took place at the hands ofYoungTurkssuchasWernerHeisenberg(bornin1901)andPaulDirac(bornin1902),who,alongwiththelikesofNielsBohr,LouisdeBroglie,andEinstein,allcomeintothestoryofSchrödinger’slifeandwork.Schrödingerwasn’tjustaphysicist.HewasadiscipleofArthurSchopenhauer,

with a profound interest in philosophy and Eastern religion, particularlyespousing the Hindu Vedanta and subscribing to the idea of a single cosmic

consciousness ofwhichwe are all part.He studied colour vision, andwrote abook,WhatIsLife?,whichFrancisCrickandJamesWatsoneachindependentlycitedasamajor influenceon theworkwhich led them to thediscoveryof theDNAdoublehelix.Schrödingeralsoaddressedquestionssuchas“Whatisalawofnature?”andwhetherornottheworldisinprinciplecompletelydeterministicand predictable. He wrote poetry (badly) and a book about the science andphilosophyofancientGreece.Schrödinger’sprivatelifewasnolessinteresting.Broughtupincomfortinthe

lastdaysoftheAustro-HungarianEmpire,heservedasanartilleryofficerintheFirst World War and suffered the consequences of the post-war blockade ofAustria(along-forgottenAlliedatrocitywhichcausedmassstarvation)andtherunaway inflationof theearly1920s.After theseexperiences,oneofhismainconcernswastosecurehisownandhiswife’sfinancialfuture;heworriedaboutpensions until his death. His first attempt to get away from Nazi-influencedEuropecametonothingwhenheturnedupinOxfordwithbothhiswifeandhismistress, offending the academic establishment there bymaking no attempt toconcealtheirlivingarrangements,withwhichhiswife,whohadherownlovers,wasquitehappy.ThepossibilityofapostinPrincetonalongsideAlbertEinsteinfell through for the same reason. Schrödinger eventually landed up in moretolerantDublin,where at the behest of Éamon deValera, theTaoiseach (IrishPrimeMinister),theDublinInstituteforAdvancedStudieswassetuptoprovidehimwithabase.Schrödingerwasalsounconventionalinotherrespects.Asauniversitylecturer

inthelastdaysofPrussianformality,heneglectedtowearatie,anddressedsocasuallythathewasoftenmistakenforastudentandsometimesforatramp.Onatleastoneoccasionhehaddifficultygainingaccesstoanimportantscientificmeeting because he had hiked to the venue, rather than going by train, andpresented himself straight off the road, dressed for rambling and carrying arucksack.When he retired in 1956, Schrödinger returned to Vienna and served as

Austria’s representative at the InternationalAtomicEnergyAgency before hisdeath in 1961. Like other elderly physicists, including Einstein, he had triedunsuccessfully to find a unified theory of physics. But generations of physicsstudentsknowhimfromtheequationwhichbearshisname,andcountlessnon-physicistsknowhimfromtheparableofSchrödinger’scat.Thewholepointofthatparablewastodemonstrate theabsurdityofquantumphysics,anditcouldonlyhavebeendreamedupbyaphysiciststeepedintheclassical tradition.So

thesearchforSchrödingerbeginswithclassicalphysics.

ChapterOne

Nineteenth-CenturyBoy

ErwinSchrödingerwas theonlychildofawealthyViennesefamily in the lastdecadesoftheAustro-HungarianEmpire.Thisupbringingnaturallyaffectedthekind of person he grew up to be; it also affected the way he thought aboutscienceandinfluencedthedevelopmentofhisgreatestscientificidea,forwhichhereceivedtheNobelPrize.

AntecedentsErwinwasthesonofRudolfandGeorgine(Georgie)Schrödinger,whomarriedin1886.Rudolf’sparentswereprofoundlyaffectedbythealmostcasualwayinwhichdeathcouldstrikeeveninthemostaffluentpartsofthecivilizedworldinthenineteenthcentury.At the timeofhermarriage in1853hismother,Maria,wasanineteen-year-oldorphan.Justfiveyearslater,shediedfollowingthebirthofastillbornbaby.Shehadalreadyproducedason,Erwin,whodiedasachild,a daughter, Marie, and another son, Rudolf, born on 27 January 1857. Herhusband, Josef, whose family came originally from Bavaria but had lived inVienna for several generations, brought up the surviving children on his own,without(aswouldhavebeenmoreusualat the time)remarrying.Butalthoughthechildrenmayhave lackedamother, theirmaterialneedswerewell cateredfor. Josef owned a modest but profitable business, a factory manufacturinglinoleumandoilcloth;thisfamilybusinesswouldinduecoursebepassedontohissurvivingson,Erwin’sfather,Rudolf.Socially,Georgie’sfamilywereacutabovetheSchrödingers;indeed,theyhad

aristocratic pretensions. Theywere descended from aminor nobleman,AntonWittmann-Denglass,who had been born into aCatholic family in 1771. Suchwere the religious stricturesof the time thatwhenhisdaughter Josepha fell inlovewithaProtestant,shewasforcedtoabandonherlove-matchandmarrythefamily doctor, a goodCatholic. She had three children before, perhaps to her

relief,shewaswidowedandable tomarryagain.This timeshechose—orhadchosenforher—AlexanderBauer,themanagerofherfather’sestates.Theeldestson of this secondmarriage, another Alexander Bauer, was born in 1836. HewouldbecomeErwinSchrödinger’smaternalgrandfather.AlexanderBauerwasthefirst inthefamilytoshowaninterestinscience,studyingmathematicsandchemistryinViennaandParis,andmovingontobecomearesearchchemist.Erwin’s maternal grandmother, Emily, was English and also came from a

family with upper-class connections. They claimed descent from the NormanForestièrefamily,althoughthenamehadlongsincebeenanglicizedtoForster,andhadbeenassociatedwithBamburghCastle innorth-eastEngland.ThomasForster,bornin1772,wasthesonofthegovernorofPortsmouth,andhiseldestdaughter,Ann, born in 1816 and one of five children,would becomeErwin’sgreat-grandmother. He had met her when visiting England as a child. Annmarried a solicitor, William Russell, and they had three children—William,Emily,andAnn(knownasFanny).TheyoungerWilliamRussellbecameananalyticalchemist.In1859–60,while

studying chemistry in Paris, hemet fellow studentAlexander Bauer. The twobecame friends, and when Emily (nicknamedMinnie) and her mother visitedWilliaminFrance,AlexmetMinnie,thenjustnineteenyearsold,andthecouplefell in love. OnceAlexander had completed his studies and obtained his first(very junior) academic post, they were able to marry. After their wedding inLeamingtonSpa,on21December1862, theylivedinVienna,wheretheirfirstdaughter,Rhoda,wasbornin1864,followedbyGeorgiein1867;soonafterthebirth of a third daughter, another Emily/Minnie, in 1874, Emily died ofpneumonia.AlexanderBauer’scareercontinuedtoflourishuntil1866,whenhelostaneye

inanexplosionatthelaboratory.Fromthenonheconcentratedonteaching,hisstudies in the history of chemistry, and the inevitable administrative dutiesassociatedwithhisrisetobecomeProfessorofGeneralChemistryattheViennaPolytechnic (later theTechnicalUniversityofVienna),aposthehelduntilhisretirementin1904.HewasalsoacuratoroftheMuseumofArtandIndustryandamemberof theTheatreCommission forLowerAustria,and tookpleasure inintroducinghisgrandsonErwintothetheatricalartsatanearlyage.Alexanderwasdevoted tohisdaughters, all ofwhommarriedmen theyhad

metthroughtheirfather’sconnections.Rhoda,theeldest,marriedtheDirectoroftheViennesePharmaceuticalCommission,HansArzberger,buthadnochildren.Minnie,theyoungest,marriedMaxBamberger,wholatersucceededAlexander

asProfessorofGeneralChemistry,andhadadaughter,Helga.GeorgiemarriedRudolfSchrödinger.Rudolfwas a frustrated scientistwho had studied underAlexanderBauer at

theTechnicalUniversity,butwasobligedtotakeoverthefamilybusinessratherthanpursueacareerinchemistry.HemarriedGeorgieon16August1886,whenhewastwenty-nineandshewasnineteen.AlthoughRudolf,likemostAustrians,wasatleastnominallyaCatholic,theweddingtookplaceataLutheranchurch(Georgie and her sisters had been brought up in the Lutheran tradition, thenearest thing inAustria to theAnglicanreligionof theirmother),making theirsonErwinnominallyaProtestant, althoughaswe shall see thismeant little inpractice. The family was essentially irreligious, attending church only forweddings and funerals. Indeed, when Erwin Rudolf Josef AlexanderSchrödinger, named after his father’s dead brother, his father, and his twograndfathers, was born in Vienna on 12 August 1887 and baptized five dayslater, even the naming ceremony took place at theSchrödingers’ home, not inchurch.

EarlyyearsAlthough Erwin’s English grandmother had died thirteen years before hewasborn,her influenceon theSchrödinger familywasstrong.HisauntRhodahadgrownuphearingonlyEnglish spoken at home, andhad spent yearswith herowngrandparentsinLeamingtonSpa.Hismother’syoungersister,Minnie,whowassimilarly fluent inEnglish,wasonly fourteenyearsolder thanErwin,andplayedwithhimasachild.SoErwingrewuphearingbothEnglishandGermanspokenathome;accordingtosomeaccounts,hespokegoodEnglishbeforehelearnedtospeak“proper”German.Erwinwasanonlychildwithtwodotingaunts,afemalefirstcousin(Dora,the

daughterofhis father’ssister),andasuccessionofnursesandmaidsattendingalmost to his everywhim. It is tempting to see here the origin of patterns inErwin’sadultrelationshipswithwomen.Hegrewuptoexpectwomentodanceattendanceonhim,whilebeingsomewhatinsensitivetotheirneeds.AccordingtothepsychiatristDennisFriedman,aboybroughtupwithbothhismotherandanannytolookafterhimispredisposedtobecomeaphilandererinlaterlife:theexperiencecreatesadivisioninhismindbetweenthewomanheknowstobehisnatural

motherandthewomanwithwhomhehasarealhands-onrelationship: thewomanwhobatheshimandtakeshimtotheparkandwithwhomhefeelscompletelyatone . . .hegrowsupwith the idea thatalthoughhewillonedaygothroughallthesocialandsexualformalitiesofmarriage,hewillhaveatthebackofhismindthenotionofthisotherwoman,whonotonlyknows,butcatersfor,allhisneeds.1

Although this suggestion has been challenged (for example, by childpsychologist Linda Blair), Friedman could have used Schrödinger as a casestudy in support of his hypothesis. But any such consequences lay far in thefuturewhentheboyErwinwasgrowingupinVienna.At the time Erwinwas born, his grandfather Alexander owned a new town

house in the centre of Vienna. The five-storey buildingwas divided into fiveseparateapartments,andin1890“our”Schrödingerandhisparentsmovedintothe spacious fifth-floor accommodation, with views overlooking St. Stephan’sCathedral.MostofwhatweknowaboutErwin’searlylifecomesfromtherecollections

ofhisauntMinnie,whichshouldbetakenwiththesamepinchofproverbialsaltassimilarrecollectionsmade(muchlaterinlife)byrelativesofAlbertEinsteinabout his precocious childhood. But in both cases the reminiscences surelycontainseedsoftruth.Fromanearlyage,Erwinwasinterestedinastronomy:hewouldpersuadeMinnietostandrepresentingtheEarthwhileheranroundhertobetheMoon,andthenmakeherwalkinacirclearoundalightrepresentingtheSunwhilehecontinuedtorunroundher.Healsokeptakindofdailydiaryevenbeforehecouldwrite,dictatinghis insights toMinnie.Asurvivingentry from1891 reads: “In the eveningAunt Emmy [Minnie] cooked a good supper andthen we spoke all about the world.” Recording his thoughts and activities onpaperwastobecomealifetimehabit.2

Erwindidnothavetoleavehiscosyfamilycircleeventogotoschooluntilhewasten,sinceuptothattimehewastutoredprivatelyathomefortwomorningsaweek.AccordingtoMinnie,hebegantoreadalmostassoonashecouldtalk,thankstoamaidwhoexplainedthenamesonstreetsignstohim;butapartfromsuchbasics,thepurposeofhisearlytuitionwastopreparehimfortheentranceexamination for the Gymnasium (equivalent to an English grammar school),wherehis realeducationwouldbegin.Butwhile theSchrödingersenjoyed thestereotypicallifeoftheuppermiddleclassesinVienna,theempirearoundthemwasshowingsignsofthestrainsthatwouldsoonalteralloftheirlives,notleasttheyoungErwin’s,fortheworse.

Anempire’slasthurrahViennahadbeenthecapitalofagreatempireforcenturies,ruledsince1276bytheHabsburgfamily.Thegeographicalextentofthisempirevariedconsiderablyovertime.Duringthesixteenthandseventeenthcenturiesitsfortunesebbedandflowed, and in 1683 the expandingOttomanEmpire reached as far asViennabeforebeingrepulsed.ButevenaftertheincursionsoftheNapoleonicWarstheEmperor(thenFranz)rulednotonlyovermuchoftheGerman-speakingworldbutalsooverHungary,muchofPoland,andwhatbecameCzechoslovakia,partsofItaly,and,cruciallyforEuropeanhistory,theSlavicstatesinBalkanDalmatia.TowardstheendoftheeighteenthcenturytheFrenchRevolutionhadstarteda

firethatwouldslowlyspreadacrossEuropetoendtheageofthegreatEuropeanempires.In1848theContinentwasrockedbyaseriesofpoliticalupheavalssowidespreadandsignificantthatitbecameknownas“theyearofrevolutions.”IntheAustrianEmpire,risingsinItaly,Bohemia,Hungary,andViennaitselfwereput down by force, but concessions had to be made; the Emperor, Ferdinand(whohadsucceededFranzin1835),wasforcedtoabdicate.ThenewEmperorwasFerdinand’snephew,FranzJosef,whohadbeenbornin

1830 but, in spite of his youth, at first looked backward rather than forward,dreamingof re-creating an absolutemonarchy rulingover a strong, expandingAustrianEmpire.The harsh reality ofmilitary and political failures, includingtheCrimeanWarandthelossofLombardyandVenice,forcedhimtochangehisapproach, and from themid-1860s onwardFranz Josef became less autocraticandgrantedhispeopleagreaterdegreeoffreedom.In1867Hungaryachieved(atleastnominally)equalstatuswithAustriainwhatbecamecalledtheAustro-HungarianDualMonarchyormore succinctlyAustria-Hungary.Butwhile theempire lost some territory, it gained elsewhere. In 1878 it took over theadministration of the Balkan states Bosnia and Herzegovina, although theseremainednominallypartof theTurkishEmpireuntilAustria-Hungaryannexedthemin1908.So theVienna inwhichErwinSchrödingerwas raisedwas the capital of an

empire that was visibly fraying at the edges. It contained people of manydifferent nationalities and political allegiances,many of them dreaming of, orworking for, independence. This was also, of course, a time of great socialchange, with industrialization, improved communications, and the consequentmovementofpeopleintothecities.Increasingly,asFranzJosefagedhebecamea relic of times long gone, losing his power and influence to a bureaucratic

systemwhichrumbledonasmuchthroughinertiaasanythingelse.Vienna, to some extent insulated from these realities, remained a glamorous

city famous for the arts. The Viennese loved opera and music, and in thenineteenth century the traditionofHaydn,Mozart, andBeethovenwas carriedforward here by Schubert, Liszt, Brahms, and Bruckner. And, of course, theStrauss family. But the people who now enjoyed these cultural delights wereincreasingly, likeRudolfSchrödinger, thenewbourgeoisie, rather than theoldaristocratic class.Among themost importantof theseupwardlymobilegroupswere the Jews.Like all non-Catholics inAustria, they had had few rights (letaloneprivileges)before1848,butasthegripoftheauthoritieseased,Jewsfromallovertheempirewereamongthepeopleattractedtothecapital.Theymadeaneconomicandartisticimpactoutofallproportiontotheirnumbers,inasocietywherecasualanti-Semitismwascommonand“theJews”oftengottheblameforanythingwrongwithsociety.ButthiswasnotaprejudicethatErwinwouldgrowuptoshare.

ScientificstirringsAlready famous for the arts, Austria, and Vienna in particular, also had aburgeoning scientific reputation in the second half of the nineteenth century.Among the changes that took place after 1848 was the establishment of aPhysics Institute at the University of Vienna; its Director, Johann ChristianDoppler, also became the first Professor of Experimental Physics at theuniversity. Born in Salzburg and educated in Vienna, Doppler served inacademicpostsaroundtheAustrianEmpirebeforebeingappointedtoheadthenewinstitute.Althoughhealsodidimportantworkinmathematicsandthestudyofelectricity,heisrememberedtodayforhisinvestigationofthewayinwhichthepitchofasoundorthecolourofalightisaffectedbytherelativemovementof the source and the person observing it. His calculations were famouslyconfirmed in 1845 by the Dutch meteorologist Christoph Buys Ballot, whoarrangedfor trumpetersstandingonanopencarblowingasinglenotewithalltheirmighttobetowedbyatrainpastmusicianswithperfectpitchstandingatthesideof the tracklisteningto thechangein thenote theyheardas the train,and the trumpeters, passed them. It is this “Doppler effect” that explains thechange in pitchof the sirenof an emergencyvehicle as it rushes past, and itsoptical equivalent is used to measure the speed with which stars are moving

towardsorawayfromus.Doppler died in 1853 at the age of only forty-nine, and was succeeded as

Director of the Physics Institute by Andreas von Ettinghausen. When vonEttinghausen,anundistinguishedscientist,becameillin1862anactingdirectorhadtobeappointed;andthemanchosenwastherisingstarofViennesephysics,twenty-seven-year-old Josef Stefan, then a juniormember of the university (aPrivatdozent, the first rung on the academic ladder). Stefan became a fullprofessor a year later, and in 1866 was officially appointed Director of theInstitute. A pioneer in the study of thermodynamics (discussed in Chapter 2),Stefan investigated thewayelectromagnetic energy (heat and light) is radiatedfrom a hot object. His findings, refined by his student Ludwig Boltzmann(himselfViennese),becameknownastheStefan–BoltzmannLawofblackbodyradiation, a key step on the road towhat became the first version of quantumphysics.Aswellasbeingafirst-ratescientist,Stefanwasalsoafirst-rateteacher,and

oneofhisstudents,FritzHasenöhrl,wouldhaveaprofoundinfluenceonErwinSchrödinger, so that in an academic sense Stefan was Schrödinger’s“grandfather.”Schrödinger’sotheracademicgrandfatherwasStefan’scolleagueJosef Loschmidt, whose particular claim to fame lay in calculating howmolecules bouncing off the walls of a container produce pressure, therebyconvincing his contemporaries of the reality of molecules, although he did agreat deal more work in the young science of thermodynamics. His studentFranzExner,whowas to succeedhimasprofessor at theuniversity (andwas,incidentally, instrumental in persuading theViennese authorities to giveMarieand Pierre Curie the pitchblende in which they discovered radium), wasSchrödinger’smentorinexperimentalphysics,whileHasenöhrlwashismentorintheoreticalmatters.By the end of the nineteenth century, physics was thriving in Vienna. But

whiletheAustrianphysicistswerehonouredintheirowncountry,theirrenownwasmuch less abroad—not least becauseStefan andLoschmidt, in particular,never travelled to spread the word about their achievements. As Boltzmanncommentedin1905:NeitherStefannorLoschmidtwent,accordingtomyknowledge,onatravelbeyond the borders of [their] Austrian homeland. At any rate, they nevervisited a [scientific conference] and did not establish closer personalrelationshipswith foreign scientists. I cannotapproveof that, for Ibelievethat they couldhave achieved stillmore if theyhad closed themselves off

less.Atleasttheywouldhavemadetheirachievementsknownfaster.3

This was not a mistake that Boltzmann himself made. He led the way inpromoting Austrian—or at least, his own—achievements among the widerscientific community.Boltzmannappreciated thatby the endof thenineteenthcentury science was an international endeavour in which it was essential tomaintaincontactwithcolleaguesindifferentcountries.Nobodywouldepitomizethe international nature of physics in the twentieth century better than ErwinSchrödinger, who arrived at the university just a year after Boltzmann madethoseremarks.

FromschoolboytoundergraduateHemight have entered university in 1905, but Erwin’s formal education wasdelayedbyayearbecausehesat theentranceexamination for theGymnasiumlater thanusual,having takena longholiday inEnglandwithGeorgieandhersisterMinnieinthespringof1898,whenhewasten.Itwasonthistripthathemet his great-grandmotherAnn,who had been born the year afterNapoleon’sfinaldefeatattheBattleofWaterloo.Minnietellsusthathealsolearnedtorideabicycle, rodeadonkeyon the sandybeachatRamsgate, andvisitedagreat-auntwhokeptsixAngoracats.TheholidaydidnotendwhenthepartyleftEnglandfromDoverbysteamer.

FromOstendetheytravelledtoBrugesandCologne,andthenuptheRhinebyboatasfarasFrankfurt-am-Mainbeforecompletingthejourneyhomebytrain.Inordertopreparehimfortheexamination(whichhepassedwithease),ErwinbrieflyattendedSt.NiklausSchool,hisfirstexperienceofformaleducation.Heentered theGymnasium in theautumnof1898,a fewweeksafterhiseleventhbirthday. The school was the most secular one of its kind in Vienna, andnumbered Boltzmann among its former pupils. But probably neither factorplayedapartintheSchrödingers’choice;morerelevantwasthefactthatitwasjust tenminutes’ walk from the family home, on the Beethoven Platz. Erwinwouldbeapupilthereforthenexteightyears.TheGymnasiumofferedaclassicaleducationdominatedbythestudyofLatin

and Greek language and civilization. Lessons took place from 8 a.m. until 1p.m.,sixdaysaweek,withanadditionaltwoafternoonsaweekforthestudyofLutheranism. “From this,” says Schrödinger, “I learned many things, but notreligion.”Hisfavouritequestionwas,“Sir,doyoureallybelievethat?”

In the first three years of school, there were eight hours of Latin a week,reducedtofivehourswhenthepupilsstartedGreek.TherewerealsocoursesinGerman languageand literature,geography,music, andhistory.Allof this leftjust three hours aweek formathematics and science. Hardly surprisingly, themathsnevergotas farascalculus,butcovered themathematicalequivalentofthe classics: geometry and algebra. Much of the physics would have beenfamiliartoNewton,andalthoughtherewereclassesinbiology(mostlybotany),theonlymentionmadeofDarwin’stheoryofevolutionbynaturalselectionwasinthereligiousclass,whereitwasdenounced.TheyoungSchrödinger learnedmore about the natural world from his father, a keen amateur botanist whopublishedarticles in learned journals (andwhoalways regrettedhavinghad togiveupanacademiccareer for the familybusiness);buthe, too,wascautiousaboutacceptingallofDarwin’sideas.OneofRudolf’sfriends,however,wasazoologist at the Natural History Museum, and much more enthusiastic aboutnatural selection.Underhis influence,ErwinsoonalsobecameanenthusiasticDarwinian.It was while he was at the Gymnasium that the first signs of Erwin’s

remarkable intelligence became evident outside his family. He was a goodstudentwhotellsusthathelovedmathematicsandphysics,butalsoenjoyedthelogic of grammar and philology; he loved poetry but hated “the pedanticdissection”ofliterature.Hewasalwaystopoftheclass,ineverysubject,andaschoolmate later recalled the deep impressionmade on the pupils by the onlyoccasiononwhichErwinfailed toansweraquestionfromthe teacher—itwas“What is thecapitalofMontenegro?”4 In theafternoons (whennot required toattendreligiousinstruction),ErwinstudiedEnglishandFrench.Perhapsbecauseofhisupbringinginabilingualhousehold,hebecameanexcellentlinguistwhocouldlectureinGerman,French,English,andSpanish,switchingbetweenthemto answer questions from polyglot audiences; as an adult he also translatedHomerintoEnglishandOldProvençalpoetryintomodernGerman.The student who had the frustrating experience of being second in class to

ErwinthroughouthiseightyearsattheGymnasiumwasTonioRella.Inspite(orperhapsbecause)ofthis,theybecamefirmfriends.TheRellafamilyownedaninn in the mountainous countryside, and Erwin often spent holidays there,developing, with Tonio, his love of hiking and the outdoor life. He alsodeveloped his first adolescent crush, on Tonio’s sister Lotte, although in thecircumstancesof the time this couldnotdevelopmuchbeyondholdinghands.Toniowenton tobecomeProfessorofMathematics at theVienneseTechnical

University, and remained friends with Erwin; he was killed by the shellingduringtheRussianadvanceonViennaattheendoftheSecondWorldWar.Erwin’sothergreatloveasanadolescentwasthetheatre,oneofthehighlights

ofViennese life at the beginning of the twentieth century.He usuallywent atleastonceaweek,oftentakingadvantageofthespecialmatineesheldonSundayafternoonsforstudentsandworkers.ThemaintheatrewasthesplendidHofburg,on theRingstrasse,oneof themost importantGerman-language theatres in theworld; but even the lesserVolkstheater could seat 1,900people,while smallertheatres offered operetta, farce, and even Hungarian vaudeville. Always anobsessivenote-taker,Erwinevenkeptarecord,withmini-reviews,ofhisvisitstothetheatre.Ofoneleadingactor,hewrote:“MuchbetterthanIhadexpected,notsomuchbywhathedoesasbywhathehasleftundone.”Thevisualartswerealsoatapeakinturn-of-the-centuryVienna,althoughnot

always appreciated.GustavKlimt, at the height of his powers,was creating astorm of controversy with what were perceived as his overly sexual, evenpornographic,paintings.In1906,theyearthatErwinSchrödingerandhisfriendTonioRellaentereduniversity,EgonSchiele,oneofKlimt’sfriends,wasgaoledfor twenty-four days for painting a “lewd” picture. But if Vienna was at thecuttingedgeoftheatreandartin1906,itwascertainlynotatthecuttingedgeofphysics. While Stefan and Boltzmann were beginning to make interestingadvances in their own research, the teaching of physics was lagging sorelybehind. Most of what Schrödinger would learn at the university as anundergraduatehadadistinctlyold-fashionedflavour,evenin1906.

Notes

1Friedman,AnUnsolicitedGift.2Unlessotherwiseindicated,commentsaboutSchrödinger’searlylifecomefromunpublishedmanuscriptsbyMinnieandbyErwinhimself,intheSchrödingerArchiveatAlpbach;seealsoMoore,Schrödinger:LifeandThought.3QuotedbyMehraandRechenberg,TheHistoricalDevelopmentofQuantumTheory.4QuotedbyMoore,Schrödinger:LifeandThought.

ChapterTwo

PhysicsbeforeSchrödinger

Thephysics thatSchrödinger learnedasanundergraduate rested, likea tripod,on three legs: theunderstandingofmechanicsdevelopedbyIsaacNewton; theunderstandingofelectromagnetismdevelopedbyJamesClerkMaxwell;andtheunderstanding of thermodynamics to which Ludwig Boltzmann was a majorcontributor. He was taught nothing about the new ideas of Albert Einstein,whose special theory of relativitywas only published in 1905, and very littleabout Max Planck’s investigation of electromagnetic radiation, published in1900,whichcametobeseenasthebirthofquantumtheory.Forourpurposes,physicsbeforeSchrödingermeansphysicsbefore1900.AnditbeginswithIsaacNewton.

NewtonandtheworldofparticlesIsaacNewton(1642–1727)iswidelyregardedasthefounderofmodernscience.Thisistrueinthesensethathespelledoutthemathematicallawswhichdescribethe motion of objects, and realized that the same laws which govern thebehaviourofobjectshereonEarth—inparticular,thelawofgravity—governthebehaviour of the Universe at large. This realization of the universality of thelaws of physics was far more important than the discovery of the lawsthemselves. It meant that scientists could expect, eventually, to explaineverythingintheUniverseonthebasisoflawsthatcouldbeinvestigatedintheirownlaboratories.ButevenNewtondidnotdoeverythingonhisown.Rightatthebeginningof

the seventeenth century, the English physician and scientist1 William Gilbert(1544–1603) published a treatise onmagnetism,Demagnete, inwhich he notonly gave a description ofmagnetic phenomena thatwas unsurpassed for twohundred years, but extended the understanding derived from his laboratorystudies to explain the Earth’s magnetic field—a significant step out into the

cosmos at that time. Gilbert also spelled out the basis of what became thescientific method: testing hypotheses by experiment and observation, andrejectinganyideaswhichdonotstanduptothosetests.Bizarrethoughitmayseemtous,eveninGilbert’sdayitwasstillcommonforphilosopherstotrytosettle arguments about what we would regard as scientific matters—such aswhetheraheavyobjectfallsfasterthanalighterobject—literallybyargument,ratherthanbydoingexperiments.Gilbertwasscathingaboutsuchpeople:Everyday,inourexperiments,novel,unheard-ofpropertiescametolight...Butwhy should I, in sovast anoceanofbookswhereby themindsof thestudious are bemuddled and vexed—of books of the more stupid sortwhereby the commonherd and fellowswithout a sparkof talent aremadeintoxicated, crazy, puffed up; and are led towrite numerous books and toprofess themselves philosophers, physicians, mathematicians, andastrologers,thewhileignoringandcontemningmenoflearning—why,Isay,shouldIaddaughtfurthertothisconfusedworldofwritings,orwhyshouldIsubmitthisnobleand(ascomprisingmanythingsbeforeunheardof)thisnewand inadmissible philosophy to the judgment ofmenwhohave takenoathtofollowtheopinionsofothers,tothemostsenselesscorruptersofthearts, to lettered clowns, grammatists, sophists, spouters, and the wrong-headedrabble, tobedenounced,torntotattersandheapedwithcontumely.Toyoualone,truephilosophers,ingenuousminds,whonotonlyinbooksbutinthingsthemselveslookforknowledge,haveIdedicatedthesefoundationsofmagneticscience—anewstyleofphilosophizing.

Andhesummedupthe“newstyleofphilosophizing”thus:Inthediscoveryofhiddenthingsandintheinvestigationofhiddencauses,stronger reasons are obtained from sure experiments and demonstratedargumentsthanfromprobableconjecturesandtheopinionsofphilosophicalspeculatorsofthecommonsort.

That notionof “sure experiments anddemonstrated arguments” is thebasis ofscience.Of course, the personwho is usually creditedwith developing the scientific

method,andinparticularwithdoingexperimentswithfallingbodies,isGalileoGalilei (1564–1642)—although as it happens Galileo himself did not dropobjects fromtheLeaningTowerofPisa.Hedidexperimentswithballs rollingdown inclined planes, and also interpreted the famous Leaning Towerexperiment,actuallycarriedoutbyarivaltryingtodisproveGalileo’sclaimthat

alightobjectandaheavyobjectdroppedatthesametimewouldhitthegroundtogether. Where, though, did Galileo learn the scientific method? He wascertainlycapableofworkingitoutforhimself;butifheneededanyproddingintherightdirection,hedefinitelygotit.WeknowthathereadDemagnete fromapproving comments hemade aboutGilbert’s book in a letter; and, of course,Newtonwas thoroughly familiar with thework ofGalileo and others such asRenéDescartes(1596–1650).AsNewtonhimselfputit,“IfIhaveseenfarther,itisbystandingontheshouldersofGiants.”Buthecertainlydidseefarther.Newton studied at the University of Cambridge, and became a Fellow of

TrinityCollegein1667.JusttwoyearslaterhewasappointedasonlythesecondLucasianProfessorofMathematics.Thisgavehimsecurityforlife,andinthosedays therewasnoobligationorevenpressure topublishscientificdiscoveries.Newtonmostly preferred to keephis ideas to himself, rather thanbebotheredwiththeattentionandtime-consumingcorrespondencethatwouldresultiftheybecamewidelyknown.Oneideahedidannounce,however,washisinventionofa new kind of telescope, which resulted in his being elected a Fellow of theRoyal Society (founded in 1660, with the epithet “Royal” bestowed thefollowingyear)in1672.ThisledtoNewtonpresentinghisideasaboutlightandcolours to the Society, and in turn to a virulent argumentwith Robert Hooke(1635–1703), themanwho asCurator of Experiments and later Secretary didmore than anyone to make the Society a success. The experience confirmedNewton’s view that publicizing his ideas only led to trouble, and he retreatedintohisshellinCambridge.Therehecontinuedthinkingdeeplyaboutthenatureofthephysicalworld,butstoppedtellinganyoneabouthisthoughts.Thatchanged in1684,whenEdmondHalley(1656–1742)visitedNewton in

Cambridge. The purpose of his visit was to ask if Newton could help with aproblemthathadbeenpuzzlingHalley,Hooke,andanotherFellowoftheRoyalSociety, ChristopherWren (1632–1723). The three scientists had realized thattheorbitsoftheplanetsaroundtheSuncouldbeexplainedbyaforcewhichfallsoff in proportion to the square of the distance of a planet from the Sun (aninverse-square law), but they could not prove that all of the lawsof planetarymotion,describedbyJohannesKepler(1571–1630),mustresultfromsuchalaw.Newton,neveroneforfalsemodesty,toldHalleythathehadsolvedthatpuzzlelongago,butclaimedhecouldnotfindtherelevantdocumentamonghispapers,andpromisedtosendacopytoHalleylater.ItisclearfromNewton’ssurvivingpapersthatthisclaimwasalieintendedtobuytimewhileNewton,confidentinhisownabilities,actuallydidsolvetheproblem.

In fact, in1684mostofNewton’s ideaswere incomplete,andvery littlehadbeenfullyworkedout.Halley’svisitwasthecatalystwhichencouragedhimtopulleverythingtogetherintoacoherentwhole.Inordertoexplainhowgravityaffected planets, Newton had to produce a mathematical explanation of howforcesaffectthemotionofobjectsingeneral,includinganunderstandingofthenatureofmassitself,andthewayinwhichanobjectresistsbeingpushedaround—its inertia. In November 1684, Halley received from Newton a nine-pagedocumentwiththetitleDemotucorporumingyrum(“Onthemotionofbodiesinanorbit”);butthiswasscarcelymorethanathroat-clearingexercise,becauseNewtonhadbecomegrippedbytheideaofpreparingacompletedescriptionofthe workings of the physical world. For about eighteen months beginning inAugust 1684 heworked obsessively on the project,which becamehis famousbookPhilosophiae naturalis principia mathematica, usually known simply asthePrincipia,publishedin1687.Newton’sdescriptionofthephysicalworldrestedonthreelawsofmotion,but

equally importantlyonhisconceptof inertiaand its relation to themassofanobject.Hisfirstlawsimplystatesthatanobjectstaysatrestorkeepsmovinginastraightlineunlessitisacteduponbyanoutsideforce.Itsoundssimple—butcontainedwithin this law is the significant scientific idea of an “ideal” objectmovinginsomeidealforce-freespace.OnEarth,nothingkeepsmovingunlessitispushed.Objectsfalltotheground,orstopmovingalongtheground.Newton,like Galileo before him, realized that this is because objects are experiencingexternalforcessuchasfrictionorgravity.Inanidealsituation,anobjectmovingfreely through spacewithout any external forceswould indeedkeepgoing foreverinastraightline.Buthowwouldsuchanobjectknowifitweremovingornot?Newtonhimselfthoughtthattheremustbesomefundamentalor“absolute”space against which all motion could be measured, and some fundamentalabsolutetimetickingawaythehistoryoftheUniverse;but,asweshallsee,thoseideashavesincebeenchallenged.Newton’ssecondlawexplainshowaforcealtersthemotionofanobject.The

accelerationproducedbytheforceisequaltotheforcedividedbythemassoftheobject.Thechangeinmotionisproportionaltotheforce,andtheresistanceto change (inertia) is measured in terms of the mass of the object. BeforeNewton,therewasnoclearideaofwhatmassis.ItwasNewtonwhodefinedtheconcept. In his own words: “The quantity of matter is that which arisesconjointlyfromitsdensityandmagnitude.Abodytwiceasdenseindoublethespaceisquadrupleinquantity.ThisquantityIdesignatebythenameofbodyor

ofmass.”SinceNewton’s lawofgravity tells us that the force exertedon anobject is

proportional to its mass, while his second law of motion tells us that theacceleration of an object is proportional to the force divided by the mass,together they explainwhy all objects fall at the same rate, regardless of theirmass—themasscancelsoutofthecalculation.Ifanobjectistwiceasmassive,itneedstwiceasmuchforcetoproducethesameacceleration—butitfeelstwiceasmuchforce!Newton’sthirdlawtellsusthatwhenoneobjectexertsaforceonanother, it

experiences an equal and opposite force in return.When the Sun pulls on theEarth,theEarthalsopullsontheSun;whenanappleispulledbythegravityoftheEarth,theEarthfeelsanequalforcepullingittowardstheapple;andsoon.The force of gravity acting between two objects, Newton explained, isproportionaltotheirtwomassesmultipliedtogetheranddividedbythesquareofthedistancebetweenthem.AnotherkeyfeatureofNewton’swork is thatherecognized thatgravity isa

universalforce—thateveryobjectintheUniverseattractseveryotherobjectinthe Universe in accordance with the same inverse-square law. This was thebeginningoftherealizationthatthelawsofphysicsderivedfromstudieshereonEarth could be applied anywhere in theUniverse: a generalization on a scaleundreamedofbypreviousphilosophers.Newtonwasclaimingnotonlythatthelawsofphysicswereuniversal,butthattheycouldaccountfordifferences,evenminor differences, between the behaviour of real objects and the behaviour ofidealobjects—forexample,thewayinwhichfrictionpreventsanobjectmovingin a straight line at a constant speed for ever. It was the beginning of trulyquantitativescience,anditledtoaprofound,ifpuzzling,implication.Whentwomovingobjectscollidewithoneanother,Newton’slawsenableyou

toworkoutexactlyhowtheywillbounceapart—inwhichdirectioneachobjectwillmove,andatwhatspeed.Thekeytothiscalculationisknowingthespeed,direction ofmotion, andmass of each object at themoment of impact. Thesethree entities are bound up in a single property, themomentum of the object.Speedjusttellsyouhowfastanobjectismoving,notitsdirection;thevelocityisthespeedanobjecthasinacertaindirection.Soifanaircraftistravellingat500km/hour,thatisitsspeed;butifIsayitisflyingduenorthat500km/hour,thatisitsvelocity.Themomentumofanobjectisitsmassmultipliedbyitsvelocity.Itisworthrepeatingatthisjunctureapointmadeearlier:thatacombinationof

Newton’s laws ofmotion and the inverse-square law of gravitymeans that in

principle, if you knew the position and themomentum of every object in theUniverse—every particle, in scientific language—at a certain moment ofabsolute time,youcouldnotonlypredict theentirefutureof theUniverse,butalsoreconstructitsentirehistory.2Itdoesn’tmatterthatitisimpossibleforustodo this in practice, since theUniverse itself “knows”where everything is andwhere it is going. The implication is that free will is an illusion, and thateverythingispredetermined.ThisleadstotheideaoftheUniverseasakindofcosmicclockworktrain,woundupbyGodinthebeginningandsettickingalongits already laid railway track for eternity. Although seldom openlyacknowledged, thisdisturbing implication remainedembedded inphysicsuntilthequantumrevolutionofthe1920s.Newtondidvery little scientificworkafter1687,buthecertainlykeptbusy.

Hecarriedoutexperimentsinalchemyandstudiedtheology,devotingmoretimeto these activities than he ever spent on science. He served asMaster of theRoyal Mint and as an MP, receiving a knighthood for his political activitiesratherthanforhisscience;andhewasPresidentoftheRoyalSocietyfrom1703onwards, following the death of his bitter rival Robert Hooke. Significantly,Newton’slastgreatscientificwork,hisbookOpticks,waspublishedjustayearlater, although the work it described had been completed many years before.NewtonhaddeliberatelywaiteduntilHookewasdeadsothathecouldpublishhistheoryoflightwithoutanychanceofHookereplying.One key feature of Newton’s work on light is relevant to our story. It was

basedontheideathatlightiscarriedbyastreamofparticles,liketinybullets.The theoryworkedquitewell at explainingphenomena such as reflection andrefraction, although therewas a no less successful rival theory,3 developed byChristiaanHuygens(1629–95)intheNetherlands, thatdescribedlight intermsofwaves, like ripplesonapond.Newton’sversionheld sway formore thanahundredyears, until thebeginningof thenineteenth century,partlybecauseofthestatusofNewtonhimselfas theacknowledged“greatest scientistwhoeverlived”andpartlybecauseHuygens,likeHooke,wasdeadby1704andNewtonhadthelastword.Butthen,everythingchanged.

MaxwellandtheworldofwavesIntheearlynineteenthcentury,thereceivedwisdomaboutthenatureoflightasa streamof particleswas overturned as a result of thework of twomen.The

first, Thomas Young (1773–1829), was an English polymath from a wealthyfamily.Althoughhetrainedandpractisedasadoctor,hehadtheluxuryofnotneeding to relyonmedicineforan income,sowasable todevotemuchofhistime to science, especially the nature of vision, howwe perceive colours, andmostnotablythewavetheoryoflight.ThesecondwastheFrenchmanAugustinFresnel(1788–1827),anengineerwhoworkeddiligentlyunder theNapoleonicregime, but cameout as a royalistwhenNapoleonwasdefeated and exiled toElba. As a result, when Napoleon returned briefly to power (during the“HundredDays” of 1815), Fresnelwas sacked and placed under house arrest.There he developed his ideas about light before Napoleon was beaten atWaterlooandFresnelreturnedtohisjobasanengineer.Historically, the work of both men is of equal importance; but I shall

concentrateononekeyexperiment,carriedoutbyYoung,becauseitlaterplayedacrucialpartinthedevelopmentofanunderstandingofquantumphysics.Itiscalled, for reasons that will become obvious, the “double slit experiment” or,more colloquially, “the experiment with two holes.” Much later, the greatAmericanphysicistRichardFeynman (1918–88) said that the experimentwithtwoholes encapsulates the “centralmystery”ofquantumphysics.Wewill seewhylater.InYoung’sexperiment,abeamoflight(ideally,asinglepurecolour)isshone

throughanarrowslitinathinsheetofcardinadarkroom,toproduceanarrowbeam.Thelightspreadsoutfromtheslitontheotherside,andthenencountersasecond sheet of card, this time with two parallel slits in it. Finally, lightspreadingoutfromeachofthosetwoslitsfallsonasheetofwhitecard,whichactsasascreenonthefarsideoftheexperiment.ThequestionYoungsoughttoanswerwas:“Whatpatterndoesthelightmakeonthefinalscreen?”Our everyday experience tells us that if light travels like a stream of tiny

particles,theyshouldpassthroughtheslitsinstraightlinesandgoontohitthefinalscreen.Thereshouldbeapile-upofparticlesarrivingjustbehindeachofthe slits, corresponding to two stripes of light on the far screen, with thebrightnessfadingawayeithersideofeachstripe.Ontheotherhand,asanyonewhohaswatchedripplesspreadingoutfromtwostonesdroppedsimultaneouslyintoapoolofstillwaterknows,wavesspreadingout fromthe twoslitswouldoverlapandinterferewithoneanother,makingamuchmorecomplicatedpatternof light and shade on the far screen. That is exactly what Young found—theinterferencepatterncorrespondingtowaves.Therewasno traceof thesimplerpatternthatwouldbeproducedbyparticles.

AlthoughYoungcarriedouttheseexperimentsandpublishedhisresultsinthefirstdecadeofthenineteenthcentury,itwasnotuntilthe1820s,andeventheninnosmallmeasure thanks to thecomplementaryworkofFresnel, that thewavetheoryoflightbegantobeaccepted,andittookevenlongerforthetheorytobefullyworkedout.WhatseemedthefinalsolutiontothepuzzleofthenatureoflightcamefromtheinvestigationofsomethingthatseemedcompletelyunrelatedatthetimeofYoungandFresnel—electromagnetism.Indeed,inthe1820stherewasnosinglesubjectofelectromagnetism,buttwo

seemingly separate fieldsof study, electricityandmagnetism.Thepersonwhobrought the two together was Michael Faraday (1791–1867), an archetypalexample of the kind of self-made man who became a symbol of success inVictorianBritain.UnlikeYoung,Faradaywasnotbornwithasilverspooninhismouth.Theson

ofablacksmith,heworkedasabookbinder’sapprenticeandthenaslaboratoryassistant (among other things, literally a bottle-washer) at the then newRoyalInstitution inLondon,becomingaprotégéofHumphryDavy(1778–1829).Hewas such a success that in 1825 he took over from Davy as Director of theLaboratory at theRI, andwent on to becomeProfessor ofChemistry there. Itwas Faraday who showed, in 1821, how an electric current could produce amagneticfield,andthen,tenyearslater,howamovingmagnetcouldproduceanelectriccurrent.Thesediscoveriesledtotheinventionoftheelectricmotorandthegenerator,aswellastotherealizationthatelectricityandmagnetismaretwofacets of a single phenomenon, electromagnetism. But Faraday lacked themathematicalskilltodevelopacompletetheoryofelectromagnetism,atriumphthatwasachieved in the1860sby theScottishphysicist JamesClerkMaxwell(1831–79).Maxwellcamefromamoderatelywell-offScottish family.His fatherowned

farmlandinGalloway,inthesouth-westcornerofScotland,whereyoungJameswasbroughtup.Hismotherwas fortywhen Jameswasborn, andhadalreadyhad a daughter, Elizabeth, who had died without reaching her first birthday;Jamesremainedanonlychild,andhismotherdiedwhenhewasjusteightyearsold.Fromtheageoften,hewaseducatedinEdinburgh:firstatschool,stayingwith an aunt in the city during termtime, then from the age of sixteen at theuniversity.Hedidn’tcompleteadegreethere,butmovedontoCambridgewhenhewasnineteen,graduatingfromTrinity(IsaacNewton’soldcollege)in1854.It’sasignofhowwellhehaddoneasanundergraduatethathewasabletostayon at the college as a “bachelor scholar”with the intention of applying for a

fellowship;however,thethoughtofstayingatTrinityindefinitelydidnotappealto him, since even in themid-1850s Fellows of Trinity were still required toremainunmarriedand(eventually)totakeHolyOrders.OverthenextcoupleofyearsMaxwellrefinedYoung’sworkoncolourvision,

showing how different mixtures of three basic colours (red, green, and blue)could fool the eye into seeingmanycolours (thebasis ofmodern colourTV),andwrotean important reviewofFaraday’sworkonelectromagnetism.But in1856,notlongafterhisfatherhaddied,MaxwelltookupapostasProfessorofNaturalPhilosophyatMarischalCollegeinAberdeen—where,attwenty-five,hewasfifteenyearsyoungerthantheyoungestofhisfellowprofessors.ThemostimportantworkhecarriedouttherewashisproofthattheringsofSaturncouldnotbesolidobjectsbutmustbemadeupfrommanytiny“moonlets,”eachinitsownorbit.ThemostimportantdevelopmentinhisprivatelifewashismarriagetoKatherineMaryDewar,thedaughteroftheCollegePrincipal.Butinspiteofthefamilyconnection,whenMarischalCollegemergedwithKing’sCollege inAberdeenhelosthisjobinthereorganizationandtemporarilymovedbacktothefamily home in Galloway before becoming, in 1860, Professor of NaturalPhilosophyandAstronomyatKing’sCollegeinLondon.ItwaswhilehewasatKing’s thatMaxwell’s ideas about electromagnetism,

whichhehadbeenpuzzlingoverforyears,cametofruition.In1861and1862hepublishedasetoffourscientificpaperspresentingamathematicaldescriptionofhowelectromagneticwaves couldbe transmitted.These equationsnaturallycontained a number corresponding to the speed with which electromagneticwavesmove,andtoMaxwell’ssurpriseanddelightthisnumberturnedouttobeexactlythespeedoflight,whichhadbeenmeasuredaccuratelybyexperimentsjust over ten years earlier. This meant that light must be a form ofelectromagnetic wave—or, as Maxwell put it, “we can scarcely avoid theinference that light consists in the transverse undulations of the samemediumwhich is the cause of electric andmagnetic phenomena” (his emphasis).Boththeory and experiment had proved, by themiddle of the 1860s, that light is awave. But the particle theory of lightwouldmake an astonishing revival lessthanfiftyyearslater.In1864,Maxwellmadeacommentthatisequallyprofound,butinadifferent

way. He said that “scientific truth should be presented in different forms andshould be regarded as equally scientificwhether it appears in the robust formandvividcolouringofaphysicalillustrationorinthetenuityandpalenessofasymbolic representation.” This prescient proposal accurately foreshadows the

wayphysicsdevelopedinthe1920s.Then,asweshallsee,thereweretwowaystodescribethequantumworld.Oneapproach,pioneeredbyWernerHeisenberg,dependedonabstractmathematical symbolism; theother,ErwinSchrödinger’sbrainchild, drew on the robust (and comfortingly familiar) imagery of waves.Butbothgaveexactlythesameanswerstoquantumpuzzles;bothwereequallyvalid.Itwasalsoin1864thatMaxwellpublishedhislastwordonelectromagnetism,

a paperwhich presented four equations that between them contain everythingthere is to know about electricity and magnetism, except for a few quantumphenomena. This was the greatest achievement of theoretical physics sinceNewton’sPrincipia, and effectivelymarked the end of the “classical” (that is,pre-quantum and pre-relativity) period of physics.Maxwell had also achievedsomethingelse—completingthejobbegunbyFaraday,hehadshownhowwhathadbeen regardedas twoseparate forcesofnature,electricityandmagnetism,couldbecombinedintoonepackage,electromagnetism.Thiswasthefirststeptowardsunifyingalltheforcesofnatureinonemathematicalpackage,adreamthatdrovemuchofSchrödinger’slatework.ButitwasnotMaxwell’sownlastwordonphysics.In1866,Maxwell had to resignhis post atKing’sbecauseof ill-health, and

although still only thirty-five retired to Galloway, where he wrote a book,TreatiseonElectricityandMagnetism,published in twovolumes in1873.Butbythenhishealthhadgreatlyimproved,andin1871hehadbeentemptedoutofretirement tobecome the firstCavendishProfessorofExperimentalPhysicsatCambridgeUniversityand toestablishand run thenewCavendishLaboratory,whichopenedin1874.Thisbecamethemostimportantcentreforexperimentalphysicsintheworldduringthedecadesthatfollowed;butMaxwellbarelylivedlongenoughtoseeitupandrunning,dyingin1879—likehismother,attheageofforty-eight.TheicingonthecakeofMaxwell’stheorycameinthefollowingdecade, when the German physicist Heinrich Hertz (1857–94) confirmedexperimentallytheexistenceofwhatwenowcallradiowaves—electromagneticwaves with wavelengths much longer than those of light—which Maxwellhimselfhadpredicted.EvenhissuccessatestablishingtheCavendishLaboratory,however,doesnot

exhaust the list ofMaxwell’s contributions to physics.Alongside hiswork onelectromagetism, he had pioneered the application of statistical techniques towork out the way in which the behaviour of large numbers of atoms andmolecules,speedingaboutandbouncingoffoneanotherandoffthesidesofany

container they were in, explains the properties of gases, such as the way thepressure, temperature, and volume of a gas are related. The resulting kinetictheoryofgasesestablished thatheat isa formofmotion,andfinallykilledoffthe earlier idea that it is a kind of fluid, dubbed “caloric.” As early as 1859,while still in Aberdeen, Maxwell calculated that molecules of air at atemperatureof16°Cundergomorethan8billioncollisionspersecond,andthatthe average distance they travel between collisions is (in the units he used)1/447,000 of an inch. But far more important for our story than the specificnumbersthatheusedwastheideabehindhiscalculations.Hefoundastatisticallaw,nowknownastheMaxwelldistribution,whichdidnotspecifythespeedsofindividualmolecules, but specified theproportionofmoleculeswith speeds inanyparticularrange—therelativenumberswithspeedsbetween14and15milesperminute,between15and16milesperminute,andsoon.Thiswas thefirstapplicationofastatisticallawtophysics—thebeginningofanapproachwhichwould lead to the birth of quantum theory, and would profoundly influenceSchrödinger.Maxwelldevelopedtheseideasfurtherinthe1860s,partlythroughhiscorrespondencewiththeAustrianphysicistLudwigBoltzmann(1844–1906),whothendevelopedthemfurtherstill.

BoltzmannandtheworldofstatisticsBoltzmann was born in Vienna, where his father was a tax official, and likeSchrödinger received his early education at home, before moving on to highschoolinLinz,wherehisfatherhadbeenposted.HisfatherdiedwhenLudwigwasfifteen,butthisdidnotaffecthiseducation,andin1863hebeganhisstudiesattheUniversityofVienna,wherehisteachersincludedJosefLoschmidt(1821–95) and Josef Stefan (1835–93). In this environment, Boltzmann became anearlyenthusiastforthekinetictheory(itwasStefanwhointroducedhimtotheworkofMaxwell),andafirmbelieverintherealityofatomsatatimewhentheconcept was still controversial. With Stefan as his supervisor, Boltzmanncompleted his studies for a PhD in 1866, with a dissertation on the kinetictheory.Althoughhewasstillonlytwenty-two,thiswasnotquitetheprecociousachievement itmight seem today, since in theGerman-speakingworld at thattime a PhDwas a first degree, although it did involve some originalwork.Ayear later,BoltzmannbecameaPrivatdozent,workingasStefan’sassistant fortwoyearsbeforemovingtoGrazasProfessorofMathematicalPhysicsin1869.

Although based in Graz, over the next few years Boltzmann took theopportunity to visit the universities of Heidelberg and Berlin for extendedperiods, keeping up to datewith the latest ideas in physics. The first of thesevisitstoBerlin,in1870,coincidedwiththeFranco-PrussianWar,whichsawthebirthofmodernGermany;althoughAustriakeptoutoftheconflict,Boltzmanncutshorthisvisit,butreturnedforalongerstaywhenthewarwasover.In1873hereturnedtoViennaasProfessorofMathematics,butremainedforonlythreeyearsbeforegoingbacktoGraztotakeupthepostofProfessorofExperimentalPhysics,stillagedonlythirty-two.Thesameyear,1876,hemarriedtwenty-two-year-old Henriette von Aigentler, one of the first women to be permitted toattendsciencelecturesatanAustrianuniversity,althoughshewasnotallowedtotakeadegree.Themarriageproducedthreedaughtersandtwosons,althoughtheolder boy, another Ludwig, would die of appendicitis when he was ten. Thefourteenyears followinghismarriage seem,apart from this loss, tohavebeenthe happiest, and certainly the most productive, period of Boltzmann’s life.Unfortunately,though,heseemstohavesufferedfrombipolardisorder,andthehappinesswouldnotlast.Thedepressionmayhavebeentriggeredbythedeathin1885,at theageof seventy-four,ofhismother, towhomhehadbeenclosesincehisfather’sdeathsomuchearlier.Boltzmann’s interest in atoms and the kinetic theory led him to develop an

explanation of the laws of thermodynamics, which had been derived byempirical studies, based on the statistical behaviour of very large numbers ofparticles. This became known as statistical mechanics; it was also derived,completelyindependently,bytheAmericanWillardGibbs(1839–1903),buthisideas didnot cross theAtlantic at that time.4The statistical approachprovidesinsight not only into the behaviour of particles, but also into the behaviour ofradiation, with important implications for quantum theory that I will describelater. But for now the implications for particles will give a good idea of thesignificanceofBoltzmann’swork.The simplestway to get a handle on statisticalmechanics is in termsof the

famoussecondlawofthermodynamics,whichsaysthattheamountofdisorderinasystemthatislefttoitsowndevices(aclosedsystem)alwaysincreases.Ineverydaylanguage,thingswearout—ifIdropawineglassitbreaks,butshardsneverspontaneouslycombine tomakeaglass.Theactofmakingawineglassdoesnotviolatethesecondlawbecauseitdoesnothappeninaclosedsystem—itinvolvesaninputofenergyfromoutside.But is it literally true thatshardsofglasscannever re-assemble themselves?

This is one of the puzzles that Boltzmann addressed. The problem can beexpressedinevensimplertermsbyimaginingasealedboxfullofgas.Everydayexperiencetellsusthatthegasfillstheboxuniformly;itdoesn’tallgatheratoneend.Indeed,ifwehaveaboxwithaslidingpartition,andputgasinonehalfoftheboxwiththepartitionclosed,wecanbesurethatwhenthepartitionisslidawaythegaswillspreadouttofillthebox.Itwillnevermovebackintoonehalfofthebox,givingusachancetoslidethepartitionbackandkeepitthere.Orwillit?Thepuzzleisthat,accordingtoNewton’slawsofmechanics,every

collision between atoms is reversible. If we made a movie showing the gasspreading out to fill the box, then ran the movie backwards, it might lookbizarre, but there would be nothing going on in the time-reversed version ofevents thatconflictedwithNewton’s laws. In1890, theFrenchphysicistHenriPoincaré (1854–1912)established that inaboxofgas like this, everypossiblearrangementoftheatomsintheboxmustoccursoonerorlater.Boltzmann’s resolution to the puzzlewas to point out that although there is

nothinginNewton’slawstopreventallthegasgatheringinonehalfofthebox,thestatistical likelihoodof thishappening isvery,verysmall. Ifyouwait longenoughthegaswillallgatherinoneendofthebox;ifyouwaitlongerstill,thewineglasswillreconstructitself.Butthetimerequiredforthesekindsofeventsto have a high probability of occurring aremind-bogglingly large—far longerthanwhatwenowestimatetobetheageoftheUniverse.Intheeverydayworldthings behave the way they do, in thermodynamic terms, because they areoverwhelmingly the most likely things to happen, statistically speaking; notbecause it is literally impossible for things to be otherwise. As Boltzmannemphasized in a paper published in the science journal Nature in 1894, thesecond“law”ofthermodynamicsisactuallyonlyastatementofprobability.Inaworldgovernedbystatisticalrules,neversaynever.Bythetimethatpaperwaspublished,though,Boltzmannhadmovedonagain,

and his life was heading for an unhappy ending. In 1890 he had becomeProfessorofTheoreticalPhysics inMunich,but in1893hehad the irresistibleopportunitytomovebacktoViennaasStefan’ssuccessorintheequivalentpostthere.Unfortunately, thiswouldbringhimintodirectconflictwithErnstMach(1838–1916), who had returned to Vienna from Prague (where he had beenProfessorofExperimentalPhysicssince1867) tobecomeProfessorofHistoryandTheory of the Inductive Sciences in 1895.Machwas a fine experimentalphysicist who studied air flow over moving objects, and whose name isimmortalized in the “Mach number” used to indicate the speed of an aircraft

relativetothespeedofsound.Buthisphilosophywasmorecontentious,anditwasonthisgroundthatMachandBoltzmannwouldclash.Machsubscribedtothepositivist view that only thingswe experiencedirectlywithour senses arereal(indeed,heisknownasthe“fatheroflogicalpositivism”).Thismadehimtheleadingopponentoftheideaofatoms,whichheregardedasmerelyheuristicdevices, rather in theway that in the seventeenth century theCatholicChurchsaidthatitwasacceptableforGalileotousetheideaofplanetsorbitingtheSunas a heuristic device tomake calculations easier, but itwasnot acceptable forhimtoteachthatplanetsreallydoorbittheSun.It was unfortunate that at a time when the idea of atoms had already been

accepted by almost all chemists and by the great majority of physicists,Boltzmannwasbasedinwhatwaseffectivelythelaststrongholdofoppositiontothe idea. Itwasalsounfortunate thatBoltzmannandMachdidnotgetonwellpersonally.Findingthesetensionsparticularlyhardtotakeinviewofhismentalhealthproblems,in1900BoltzmannmovedtotheUniversityofLeipzig.Theretooheencounteredprofessionaldisagreement, this timewithWilhelmOstwald(1853–1932),a leadingpositivistwhostronglydenied the realityofatomsandmaintainedthispositionuntil1908.EventhoughBoltzmannwasongoodtermswith Ostwald personally, as he had not been withMach, he was unhappy inLeipzig, troubled by failing eyesight and a developing fear of lecturing,worrying that his mind was losing its sharp edge and he might start talkingnonsense.Healsosufferedbadlyfromasthma.Fortunately,in1902,afterMachhadretiredbecauseofill-health,BoltzmannwasabletoreturntoViennaasanordinaryprofessorwithfewduties.HemadeasecondvisittotheUnitedStatesin1904,accompaniedbyhissonArthur,andyetanothertripacrosstheAtlanticin 1905, this time alone, to give lectures at the Berkeley campus of theUniversityofCalifornia.Even though Mach was no longer on the scene, in his darker moments

Boltzmann still felt, entirely erroneously, that his ideas had fallen on stonygroundandwerenotbeingtakenseriously.In1898,inthemiddleofhisdifficulttimealongsideMach inVienna,Boltzmannhadwritten inoneofhisscientificpapersthathewaspublishinghiscalculationsinthehope“that,whenthetheoryofgasesisagainrevived,nottoomuchwillhavetoberediscovered,”seeminglyunawareofhowwellhisideashadbeenreceivedintheEnglish-speakingworld.Thismisperceptionwasundoubtedlyafactorinwhathappenednext.Colleaguesknew of Boltzmann’s mood swings, although bipolar disorder was notunderstood at the time, and somewere aware that in his blackestmoments he

had previously attempted suicide.As he entered his sixties, he had to give upmuchofhisteachingbecauseoftheseproblems.Soitcannothavecomeastoomuchofashocktothemwhen,in1906,hehangedhimselfwhileonholidayinItaly. But the news did come as a shock to Erwin Schrödinger, then a youngstudentwhowasabouttobeginhisstudiesattheUniversityofVienna,andwhohadhopedtolearndirectlyfromoneofhisscientificheroes.

Notes

1Theterm“scientist”hadnotbeeninventedthen,butitisthemostapt.2Inprinciple,youneedtoincludeelectromagnetismaswell,buttheessenceoftheargumentisstillthesame.3Rival“theories”likethisaresometimescalled“models”;Ishallusethetermsinterchangeablyinthisbook.4AlthoughBoltzmannhimselfdidcrosstheAtlanticattheendofthenineteenthcentury,togiveaseriesoflectures,hedidnotmeetGibbsandremainedunawareofthefullsignificanceofhiswork.

ChapterThree

Twentieth-CenturyMan

WhenErwinSchrödinger began his studies at theUniversity ofVienna in theautumn of 1906, Boltzmann had just died, and the new professor, Friedrich(Fritz)Hasenöhrl(1874–1915),wouldnotbeappointeduntilthefollowingyear,leaving physics teaching at the university in limbo for eighteen months. ButHasenöhrlwastheidealmanforthejob,havingstudiedunderbothStefanandBoltzmann,and taughtat theTechnicalHighSchool inVienna.In1904,whilestudying the theoretical relationship between mass and energy, he had comeclosetoproducingthespecial theoryofrelativityayearbeforeAlbertEinsteinmadehisfamousbreakthrough.WhenhewasfinallyappointedtoBoltzmann’soldchair,HasenöhrlhitthegroundrunningwithatourdeforceinaugurallecturesummingupBoltzmann’sworkonstatisticalmechanics;Schrödinger,starvedofrealphysics foroverayear,washooked,and immediately resolved tomake ithis life’s work to follow where Boltzmann had led. Young and energetic, abrilliant lecturer and up to date on the latest ideas in at least some areas ofphysics, Hasenöhrl was a far better inspiration for Schrödinger than thedisillusionedoldmanBoltzmannhadbecomewouldhavebeen.

StudentlifeBythetimeheheardHasenöhrllecture,Schrödingeralreadyhadareputationasanoutstanding student—indeed, hehadbrought that reputationwithhim fromthe Gymnasium, where he graduated first in his class, and was sometimesreferred to by his fellow undergraduates as “the” Schrödinger. AlthoughSchrödingerhadfewclosefriendsamonghiscontemporariesatthetime,hewaswellliked,andcouldalwaysbereliedontohelpoutweakerstudentswiththeirmathsandphysics.Hisclosestfriendwasabotanist,FranzFrimmel,inspiteofthe fact that Frimmel had deep religious convictions. He also became firmfriends with one of the slightly older members of the university, Fritz

Kohlrausch, who completed his first degree while Schrödinger was halfwaythrough his own course, and stayed on as an experimental physicist. Thisfriendshiplastedforlife,andgrewtoincludethetwoscientists’families.But the major influence on Schrödinger’s life from 1907 to 1910 was

Hasenöhrl,wholecturedtothestudentsfivedaysaweek.Schrödingerlatersaidthattheonlypersonwhohadabiggerinfluenceonhislifewashisownfather.Andtheinfluenceextendedoutsidethelectureroom:Hasenöhrl,awintersportsenthusiast,organizedgroupexpeditionswithstudentsand,alongwithhisyoungwife,welcomedthemintohishome.ItwasjustaswellthatHasenöhrlwassuchanenthusiastic,friendly,andable

lecturer,sincetheteachingfacilitiesprovidedforhimwereadisgrace.Althoughthe impressive main university building had been completed in 1884, thephysicists were still stuck in “temporary” accommodation acquired in 1875.Studentshadtositonordinarychairsinthelectureroom,withtheirnotebooksontheirlaps;thefloorwascrackedandpollutedwithmercuryfromtheroom’stime as a laboratory; and the buildingwas so badly constructed, according toSchrödinger’s contemporaries, that thewallswould shake in a strongwind. IntheseconditionsSchrödingersatthroughnotonlytheinspiringlecturesgivenbyHasenöhrl, but also a lot more routine material, ranging from chemistry tocalculus—andincludingonecoursewhich,althoughseemingnothingspecialatthetime,mayliterallyhavesavedhislife:meteorology.Inthewiderworld, therewerestirringsofchange.Followingdemonstrations

andmarchesinsupportoftherighttovote,alladultmalesubjectswereallowedtocasttheirballotsintheAustrianelectionheldinMay1907.Butthiswaslittlemore than window-dressing; although the body they elected was sometimesreferredtoasthe“people’sparliament,”inpracticepowerremainedinthehandsof the Emperor and his advisers, and the Empire continued on its corrupt,ramshackle, and bureaucratic way. The following year Schrödinger’s personallifewasstirred,whenhehadabriefbutpassionateaffairwithagirlcalledEllaKolbe.AlthoughErwinwasstilllivinginthefamilyapartmentinthecentreofVienna,hewasabletomeetEllaatanapartmentneartheuniversitywhereoneofhis fellowstudents, JakobSalpeter, lived.Hesawa lotofSalpeterover thenext few years while they worked in the same laboratory on experiments tocompletetheresearchrequirementfortheirdegrees.ThetitleofSchrödinger’sdissertationwas“OntheConductionofElectricity

ontheSurfaceofInsulatorsinMoistAir,”anditisjustaboutasdullasthetitlesuggests.Schrödingerdidlittlemorethanthebareminimumthatwasrequiredin

ordertoobtainhisdegree,andtheonlygoodthingtobesaidabouttheprojectisthat it gave him experience of practical laboratory work that would come inuseful later.The rest of hiswork, though,wasofhisusual high standard, andhavingpassedoutfirstinhisclassSchrödingerwasdulyawardedhisDoctorofPhilosophydegree(aboutequivalenttoamodernMSc)inJune1910.Thenextstep,afterasummerbreak,wasmilitarytraining.

LifebeyondthelabIn theAustro-HungarianEmpire at that time, all able-bodiedyoungmenwererequired todo threeyearsofmilitary training.At least,hoipolloihad toserveforthreeyears.Theeducatedupperclasseswereallowedinsteadto“volunteer”forofficer training,whichtookonlyoneyear.If theychose, thisexperienceofmilitarylifecouldbeprettyeasy,sincethecadetswerenotevenrequiredtopassthe final examination which would qualify them to be commissioned in thereserve.ThestratificationofAustriansocietywas reflected in thearmy,wherethecavalrywereregardedastheélite,theartillerywereoflowersocialstanding(although the fortress artillery held themselves to be superior to the fieldartillery),andeverybody lookeddownon thepoorbloody infantry. InOctober1908,Schrödingerenrolledinthefortressartillery,whichaccuratelyreflectsthepositionofhisfamilyinViennesesociety.Thankstohisservicerecord,weknowthatSchrödingerwas167.5centimetres

(5 feet 6 inches) tall, with blue/green eyes and fair hair. Unlike many of hisfellow volunteers, he took his duties seriously, although in fact theywere notonerous. After the first two months living in barracks, the young men wereallowedtofindtheirownlodgingsnearby,wheretheywereresponsiblefortheirown expenses. Leave came as early asChristmas, atwhich point Schrödingerwentskiingwithafellowphysicist,HansThirring(1888–1976),whowasthenin his final year at the university. This casually taken holiday had an almostimmediateeffectonSchrödinger’scareer.Thirringbrokehisfoot,andasaresultwasexcusedmilitaryservice,sohewasavailabletobecomeHasenöhrlassistantwhen the post became vacant; other things being equal, the jobwould surelyhavegonetoSchrödinger,thebeststudentinhisyear.Thirringwent on to become a leading physicist and a pacifist, active in the

SocialistPartyofAustria.Heisbestknownforhisworkonthegeneraltheoryofrelativity;butsomeofourknowledgeofSchrödinger’sstudentdayscomesfrom

Thirring’sreminiscences.Schrödingerwentontocompletehismilitarytrainingwithout further incident, and was duly commissioned in the reserve with thecadet rank of Fähnrich, just below that of lieutenant. Free to return to theUniversity of Vienna, instead of working on theory as he would have donealongside Hasenöhrl, in 1912 he became an assistant to Franz Exner (1849–1926),asanexperimenterwithresponsibilityforthepracticalclassesofthefirst-yearphysicsstudents.In order to become a Privatdozent, the first step on the ladder towards a

professorship, Schrödinger had to carry out original scientific research.Significantly,hechoseproblems in theoreticalphysics,notexperimentalwork,althoughhedidworkontopicsrelevanttoExner’sstudies.Competitionforthefew places available for Privatdozenten was fierce, but Schrödinger neverunderestimated his own ability, and as usual his confidence was justified. Heearned his promotionwith a study of the nature ofmagnetismwhich, thoughcorrectly worked out, started (we now know) from a false assumption, and astudyofthewaysolidsmeltwhichwasgropingtowardsanunderstandingoftheway atoms andmolecules interact in solids and liquids.He could hardly haveachievedmoreatthetime,sincetheworkwascarriedoutin1912,exactlywhenWilliamBragg(1862–1942)andhissonLawrence(1890–1971)inEngland,andMaxvonLaue(1879–1960)inGermany,werebeginningtostudythecrystallinestructureofsolidsusingX-rays.Hasenöhrl,onbehalfoftheexaminingcommittee,gaveSchrödingeraglowing

report—“In the opinion of the committee, all the works of Schrödingerdemonstrateaverywellfoundedandbroadscholarshipandasignificantoriginaltalent”—and in spite of the opinion of one committee member that theappointmentwasprematureonthegroundsofSchrödinger’syouth,aftermonthsof further formalities including an oral examination and the need to have theappointmentconfirmedbytheMinistryforCultureandInstruction,SchrödingerwasappointedasaPrivatdozentintheUniversityofViennainJanuary1914,attheageoftwenty-six.Butwhileallthishadbeengoingon,Schrödingerhadbeendistractedbylove,

andupuntil themiddleof1913hadbeenseriouslyconsideringabandoninganill-paidacademiccareerinordertojoinhisfather’sbusinessandmakeenoughmoneytosupportawifeandfamily.ThenotionhorrifiedRudolf,whohadhadtogive up his own academic ambitions for business, and delighted in Erwin’sprogress;butintheenditcametonothing.TheobjectofErwin’saffectionsatthistimewastypicalofthegirlshewould

laterbe involvedwith,and in the futurehisamorousadventureswouldhaveaprofoundinfluenceonhisacademiccareer.ShewasFelicieKrauss,thedaughterofKarlandJohannaKrauss,familyfriendswhohappenedtobewealthy,strictCatholics, and socially a step above the Schrödingers, with pretensions to(minor)aristocracy(theywereentitledtotheprefix“von”beforetheirsurname).Feliciewasnineyearsyounger thanErwin,andasachildhehadoften, tohisdisgust,hadtolookafterthelittlegirlwhenthetwofamiliesgottogether.Whenherfatherdiedin1911,Feliciewasnotquitefifteen,andErwin’sfeelingswerenowquitethereverse—hewashappytobewithheroneverypossibleoccasion,although what was possible was strictly limited by the conventions of politesociety. Johanna Krauss was alarmed by the developing relationship betweenFelicieandErwin,whoasanimpoverished,free-thinking(perhapsevenatheist)academic was in her eyes quite unsuitable husband material. She forbad thecouple to meet more than once a month—which, of course, increased theirardouruntiltheybecameinformallyengaged.ItwasatthispointthatErwinaskedhisfatheraboutgivingupphysicstojoin

thelinoleumbusiness.RudolfwasadamantthatErwinshouldnotmakethesamesacrifices that he had had tomake, and JohannaKrausswas adamant that themarriagewouldnevertakeplace.Athermother’sbehest,FelicietoldErwinthatitwasalloverinthesummerof1913,whenhewashalfwaythroughtheprocessofbecomingaPrivatdozent.ButFelicie,who latermarried a lieutenant in theAustrian army from a similar social background to her own, remained friendswithErwin, and laterwith hiswife,Anny.Schrödinger threwhimself into hiswork, and inMarch 1914 produced his first really significant scientific paper,developing some of Boltzmann’s ideas and improving the mathematicaldescriptionoftheinteractionsbetweenatomsinmolecules.HisrelationshipwithFeliciemayhavebeenshort-livedbut,inoneway,itwasformative.Erwinneverlosthisfascinationwithyounggirlsonthebrinkofadolescence.Despitehispersonaldilemmas,in1912and1913Schrödingerdidnotneglect

hisexperimentaldutiesasExner’sassistant.AndthosedutiesbroughthimintocontactwiththegirlwhowouldreplaceFelicieinhisaffectionsandeventuallybecomehiswife.Oneof the research interestsofExner’sgroupwas the studyof atmospheric

electricity. This involved measuring the electrical conductivity of the air atvarious locations and different times, andmeasuring the background radiationwhichmadeelectricallychargedinstruments(electroscopes)graduallylosetheircharge.The radiation turnedout tocomefromtwosources.Onewasnaturally

occurring radioactive material, such as radium in the rocks; the other wasradiation penetrating the Earth’s atmosphere from outer space. This latterradiation, now known as cosmic rays, was first discovered by Victor Hess(1883–1964),whoworkedat theInstituteofRadiumResearchof theVienneseAcademy of Sciences. He made the discovery on high-altitude (and highlydangerous) balloon flights in 1912; it earned him theNobel Prize in Physics,thoughnotuntil1936,nearlytwenty-fiveyearslater.Schrödinger’scontributionwasmoredowntoEarth.In1910,FritzKohlrausch

hadmadesomemeasurementsofatmosphericelectricityatthelakesideresortofSeeham,ontheMattsee.In1913,Exnerdecidedthatitwouldbeagoodideatorepeat the measurements to see if there had been any change, and gaveSchrödingerthefarfromoneroustaskofspendingthesummer,fromlateJulytoearlySeptember,onthejob.ThiswasjustafterthesplitwithFelicie.Theworkwas dull rather than demanding, and produced no great scientific

discoveries.Schrödingerwasabletotakefulladvantageoftheopportunitiesforhiking and swimming, even though it was a wet summer, and to enjoy thecompanyofhisfriendstheKohlrauscheswhentheybroughttheirchildrenforaholidayat the lake.Theyalsobroughtwith themateenagegirl fromSalzburg,Annemarie(Anny)Bertel, to lookafter thechildren.Shehadbeenbornonthelast day of 1896, so in the summer of 1913 shewas only sixteen, and still inpigtails. Fifty years later, in an interview for the Archives for the History ofQuantum Physics, she recalled being impressed by the “very good looking”young scientist, and he clearly noticed her, but nothing significant passedbetweenthematthetime.Much more significant was the event that hastened Schrödinger’s return to

ViennafromSeehamearlyinSeptember.Asplendidnewphysicsbuildinghadatlastbeenopenedinthespringof1913,andthatautumnitwasthesettingforamajorscientificconference,knownas theCongressofVienna, involvingmorethan seven thousand scientists, including the rising star Albert Einstein, andendowedwithallthepompandglamourofthelastdaysoftheEmpire,uptoandincludinganImperialReception.ApartfromEinstein,whodiscussedtheneedtomodify Isaac Newton’s theory of gravity, the speaker who made the biggestimpressiononSchrödingerwasMaxvonLaue,whodescribedhisworkonX-raycrystallography.In1914,thefirstcourseSchrödingergaveafterhebecameaPrivatdozentwasentitled“InterferencePhenomenaofX-rays”;itwasonlylaterthathegothisteethintotheproblemofgravitation.Buthehadbarelygotintohis stride as a lecturer when the First World War intervened. Vienna—and

Schrödinger—wouldneverbethesameagain.

WarserviceontheItalianFrontWhen Archduke Franz Ferdinand, the heir to the imperial throne of Austria-Hungary,wasassassinatedinSarajevoon28June1914,theoldEmperor,FranzJosef,shedonlycrocodiletears.TheassassinationwastreatedequallycalmlybymostofViennesesociety.FranzFerdinandwaswidelyregarded(notleastbyhisuncle, theEmperor)asunsuitableforthetopjob,asindicatedby,amongotherthings, his decision to marry for love. His wife, Sophie, a former lady-in-waiting, was so much his social inferior that the marriage had only beenpermittedonamorganaticbasis—that is,with thestipulation thatanychildrenwouldnot inheritFranzFerdinand’s titlesandrightofsuccession.Withsuchadangerousfree-thinkeroutoftheway,theheirapparentwasFranzJosef’sgreat-nephew Charles, who was much more of a traditionalist and would probablyhavemadeanexcellentnineteenth-centuryEmperor.The troublewas, itwasno longer thenineteenthcentury,andCharleswould

nevergetarealchancetoprovehismettle.TheassassinationofFranzFerdinandprovokedAustria into attacking Serbia (after all, even the assassination of anunpopularheircouldnotgounpunished),andtheobligationsthistriggeredinacomplex web of international treaties—where A promised to attack B if Battacked C, but D had promised to defend B from attack by A, and so on—resulted in the First World War. When all the treaty obligations had beeninvoked,theCentralPowersofGermanyandAustria-Hungarywereleftfacing(and more or less surrounded by) the Triple Entente of Britain, France, andRussia, soon joined by Italy, and lesser allies—including, of course, Serbia.Reserve artillery officer Erwin Schrödinger received his call-up papers on thelastdayofJulyandwentwithhisfathertobuytwopistols,neitherofwhichheeverhadtouse.HealsofoundtimebeforeleavingViennatosendagifttoAnnyBertel—abookofessaysbytheAustrianwriterandcritic(andauthorofBambi)FelixSalten.Schrödingerwas sent to a fortified artillery position near the Italian border,

highinthemountainsoverlookingtheVenetianplain.Thiswasasgoodaplaceasanytobepostedinthesummerof1914,farremovedfromthefiercefightingon theRussianFront,where theAustrians lost aquarter of amillionkilledorwoundedandahundredthousandprisonersinthefirstthreeweeks.Bycontrast,

withItalynotyetinvolvedinthewar,thingsweresoquietinthemountainsthatSchrödinger was even able to carry out some scientific work, completingcalculations based on experiments he had carried out in Vienna. After all, heneedednothing for thiswork except paper, a pencil, and a fewbooks—unlikemanymathematicalphysiciststoday,whowouldbelostwithoutacomputer.Soon27October1914SchrödingerwasabletosendashortpaperonthepressureexertedbygasbubblestothejournalAnnalenderPhysik.Before the winter, Schrödinger was posted to a fortress in the South Tyrol,

dominating the entrance to theBrenner Pass.He spent thewinter of 1914–15there,enjoyingthebeautifulmountainscenerywhiletheconflictontheWesternFrontsettledintothegrimtrenchwarfareforwhichtheFirstWorldWarisbestrememberedbyBritainandtheotherWesternparticipants.Hisnextpostingwasto the equally peaceful, but less scenic, garrison town of Komárom, betweenViennaandBudapest.There,Schrödingerwroteapaperaboutthebehaviourofsmallparticlesbeingjostledinafluid(gasorliquid)bytheimpactofmoleculesof the fluid. This is known as Brownian motion, after the Scottish physicistRobert Brown (1773–1858), who studied it in the 1820s. In 1905, AlbertEinstein had proved that this erratic jittering can be explained statistically ascaused by the constant but uneven bombardment that particles such as pollengrains receive from atoms and molecules, and thereby provided compellingevidence for the realityof atoms—just too late for this tobemuchcomfort toBoltzmann.1

In a quite separate investigation, culminating in 1912, theAmerican RobertAndrews Millikan (1868–1953)—who also, incidentally, coined the term“cosmic rays”—had managed to measure the charge on the electron bymonitoringthewaytinyelectricallychargeddropletsofwateroroildrift inanelectric field. These droplets are small enough to be affected by Brownianmotion,andSchrödingeranalysedstatisticallytheimportanceoftheseeffectsinMillikan-type experiments. Nothing dramatic came out of the study, but it isimportant in the context of Schrödinger’s career because it was his firstpublishedforayintostatistics,whichwouldlaterloomlargeinhiswork.By the time this paper was published, the war, and Schrödinger, had both

movedon.ItalywaspersuadedtojointheTripleEntentewithpromisesoflargechunksofAustria, anddeclaredwaron23May1915.Aspartof theAustrianresponse, Schrödinger’s unit was moved to Oreia Drega, near Görz (laterGorizia), north-west of Trieste. This would be the scene of fierce fighting atvariousstagesinthewar(immortalizedbyErnestHemingwayinAFarewellto

Arms), but the artillery were well back from the front line and engaged theenemyatlongrange,sometimescomingunderheavyfirebutsufferingrelativelyfewcasualties.SchrödingerwasevenabletovisitGörzwhenoffduty,relaxinginoneoranotherofthecity’scoffeehouses.Judgingfromhisdiaries,theworstproblem he had to face during the summer of 1915 was boredom; but inSeptember he received some books and copies of scientific journals, and thediaryentriesstopas,presumably,hebeganaboutofworkandstudy.Soon,healso began the most active phase of his military career, for in October andNovember 1915 Schrödinger was acting commander of the battery, in chargeduring several fierce engagements and behaving with sufficient distinction toreceiveamilitarycitation.Thefightingeasedupforthewinter,butinMay1916,justafterSchrödinger

hadbeenpromoted toOberleutnant, it flaredupagain in theGörzsector,withlosses amounting to more than a hundred thousand on the Austrian side andmorethanaquarterofamillionontheItalian.ButbythenSchrödingerhadbeenpostedtocommandabatteryinthemountainsnorthofTriesteinwhathelatercalled“anextremelyboringbutbeautifulspot.”Ifyouhadtobeasoldier,itwasbetter tobe in the artillery than in the trenches—apoint broughthomeby thedeathofFritzHasenöhrlleadinganinfantrychargeintheTyroleansectorofthefront.Thingsbegantochangeagainattheendof1916.On21NovemberFranzJosef

died;hissuccessor,Charles,madestrenuouseffortstoconcludeapeacewiththeEntente,butmetstiffresistancefromtheItalians,whoinsistedonhavingalltheterritory they had been promised by their allies.Also, andmore crucially, themilitaryrulersofGermany,bynowverymuchtheseniorpartneroftheCentralPowers,refusedtolettheAustriansnegotiateanindependentpeace.Meanwhilethewarcontinuedquietly forSchrödinger.Heevenenjoyedavisit fromAnnyBertel,whohad turned twentyat theendof1916.According toSchrödinger’snotebooks,whichratherungallantlyindicateallhislovers(albeitincode),theydidnotbecomeintimateatthistime,butclearlysomethingwasintheair.Annywas the only one of his female friendswho visited Schrödingerwhile hewasservingon the ItalianFront.But soonhis friends inViennawouldnothave totravelfartoseehim.

BacktoVienna

The weather—or rather, meteorology—came to Schrödinger’s rescue in thespringof1917.HewaspostedbacktoViennatoteachacourseinmeteorologyfor antiaircraft gunnery officers, combining thiswith teaching an introductorypracticalphysicscourseattheuniversity.Itispossiblethat,followingthedeathofHasenöhrlandthesuccessionofCharles,theauthoritiesinViennawantedtoensurethattherewasatleastonegoodphysicistaroundtopickupthethreadsattheuniversityafterthewar.Orhemayjusthavebeenlucky.Whatever the reasons for the posting, it gave Schrödinger the chance to

recommenceresearch,andtobeginpublishingscientificpapersagain.Themostsignificant of his 1917papers, in the light of later developments,washis firstapplication of quantum theory (ofwhichmuchmore in the next chapter) to ascientific problem.Theproblemhad to dowith theheat capacity of solids—ameasureofhowmuchenergyisrequiredtoincreasethetemperatureofacertainamountofmaterial by a certainnumberofdegrees.This is related to thewaymolecules vibrate, which in turn depends on their quantum properties.Schrödinger’s contribution followed a line of enquiry, rooted inthermodynamics, which had also been pursued by Max Planck and AlbertEinstein. In one study he investigated the random fluctuations in the rate atwhichsamplesofradioactivematerialdecay(relatedtotheconceptofthehalf-life,thetimeinwhichexactlyhalfoftheatomicnucleiinasamplewilldecay).Schrödinger alsobecame interested in thegeneral theoryof relativity,which

Einsteinpublishedin1916;newsofthebreakthroughreachedSchrödingerwhilehewasstillservingontheItalianFront.Einstein’sdescriptionofgravity,andtherelationship between gravity and matter, in terms of curved spacetimecompletely changed the way many physicists thought about the fundamentalproperties of theUniverse, Schrödinger among them.Hewrote two papers in1917 on the implications of the general theory: the first investigated thedescriptionofenergyprovidedbyEinstein’sequations;thesecondaddressedthenatureoftheUniverseitself.HefoundasolutiontoEinstein’sequationswhichdescribesauniversecompletelydevoidofmatterbutinwhichemptyspacehastension,likeastretchedspring;thisisclearlynotadescriptionofourUniverse,butitshowsboththepowerofEinstein’stheoryandthebreadthofSchrödinger’sinterests.Exciting as these investigations were, they were carried out against a

background of increasing hardship as the war ground towards its close. TheentryoftheUnitedStatesintotheconflictagainstGermanyinApril1917madethe ultimate outcome inevitable, although the USA did not declare war on

Austria-Hungaryuntiltheendoftheyear.Longbeforethen,theAlliedblockadeoftheCentralPowershadbroughtbothAustria’seconomyanditsarmytotheirknees.When the bread rationwas cut from200 grams a day to 160 grams inJanuary 1918,munitionsworkerswent on strike, and seven divisions of half-starvedsoldiers(thoseinthefrontlinereceivedonly200gramsofmeataweek,others half that)were brought back from the front to restore order. InVienna,thosewhocouldaffordtheblackmarketdidnotgohungry,buthadtosacrificetheirpossessions inorder to eat.Closer tohome, thingswere alsogoing frombad toworse. Schrödinger’smother underwent an operation for cancer of thebreastin1917andErwinhimselfwasillin1918withwhatseemstohavebeentuberculosis. The family business was ruined by the lack of raw materials.Schrödingerstayedonthearmypayrolluntiltheendof1918,butjustwhenhelost that income, and in spite of—in fact, becauseof—the endof thewar, thesituationinViennabecameevenworse.

TheaftermathEven after the Armistice of 11 November 1918, the victorious powersmaintained theirblockadeofAustria-Hungary,andwatched through thewinterof1918–19while theEmpire fell apart.This constitutedoneof theworstwarcrimesofthetwentieth(orindeedany)century,butremainslittleknowntoday,because, of course, history is usuallywritten by the victors. Food supplies nolonger came in from Hungary, coal no longer came in from Czechoslovakia,Italian troops (themselves reasonably but not generously well fed) occupiedVienna;sodesperatedidthesituationbecomethatGermany,eventhoughitselfblockaded, sent some food. Italy andSwitzerland also provided some aid; thecriminalswere the intransigentBritishandFrench.TheEmperorwasdeposed,althoughhardlyanyonenoticed,andAustriabecamearepublic.Asalastresort,with the empire now lost, the government tried to make the country part ofGermany, but theFrenchvetoed any suchnotion.On the rare occasionswhenfoodwasavailable,mobsofwomenwouldrushthesupplies,andwouldhavetobecontrolledbymountedpolice;inonewidelyreportedincident,whenapolicehorsefellinthecrushitwasslicedupandthemeatcarriedawayinamatterofminutes.Schrödingerwastrappedinthismess.Hehadbeenofferedajobasaphysics

lecturer in Czernowitz—but Czernowitz was now part of Romania, and the

Romaniangovernmentforbadtheappointmentofaforeignertosuchapost.Inthemidstofallthisturmoil,hefoundconsolationinphilosophy,flinginghimselfintoastudyofWittgenstein,Schopenhauer,andthroughSchopenhauerEastern,and in particular Indian, philosophy. He was particularly fascinated by theVedanta, a school of Hindu philosophy which teaches that there is only onereality.These philosophical ideaswould strongly influenceSchrödinger’s laterthinkingaboutquantumphysics.ThesituationinViennabegantoimproveafterHerbertHoover, thenheadof

theAmericanReliefAdministration and later to becomeUSPresident, visitedthe city in January1919.Alarmedby theprospectof aCommunist revolutionbeing triggeredby theappallingconditions,hearranged for the firstAmericanaid to be sent toVienna, and the blockade ofAustriawas lifted at last on 22March—although it continued to be applied to Germany, where the kind ofrevolution Hoover feared very nearly did happen. As the threat of starvationreceded,otherproblemsaccumulated.Schrödinger’sincomefromtheuniversitywasmodest(fartoosmalltosupportafamily),buthespentasmuchtimeashecouldthere,escapingfromthemountingtroublesinthefamilyapartment,wherehisfatherwasincreasinglyillwithhypertensionandatherosclerosis,andwherelimited gas supplies meant that the rooms were cold and dark. The familydependedonincomefromRudolfSchrödinger’sinvestments,butasthecostoflivingbegantoincreasethisbecamelessandlessadequate.Themetaphorical light in thisgloomcamefromAnny.Schrödingerwasable

tovisither inSalzburg,andintheautumnof1919theybecameengaged; theyalso, according to his notebooks, became lovers in the physical sense at thistime.Annymoved toVienna, and obtained awell-paid job as a secretary—toErwin’sembarrassment,hermonthlyincomewasmorethanheearnedinayear.Anny’s employer was a Bauer, Friedrich (known as Fritz), but not a closerelativeofSchrödinger’smaternalgrandfather.FritzBauerwas theDirectorofthePhoenix InsuranceCompany, and lived in agrandhouse in the suburbsofVienna.Ononeoccasionin1920AnnytookErwin,asherfiancé,toteaheretomeet the Bauer family. Fritz’s thirteen-year-old daughter Johanna, known asHansi,laterrememberedSchrödingerasverystiffanduncomfortable,nodoubtbecausethesurroundingsemphasizedhisownlimitedprospects.2The lightandthegloomcollidedevenmoredramaticallyonChristmasEve1919,whenAnnywas staying with her family in Salzburg. That evening, a basket of presentsarrivedfromAnny;barelyanhourearlierRudolfSchrödinger,sittingpeacefullyinhischair,haddied.

Schrödingerwould latercome to think that itwas justaswellhis fatherhadnotlivedtosee1920,whenrunawayinflationwipedoutallthefamily’ssavings.ButdevelopmentsinSchrödinger’slifemovedalmostasfastastheinflationthatcrippled the city. In January 1920 he was offered a promotion to assistantprofessor inVienna,but thesalarywouldnothavebeensufficient tosupportawife, and, although eager tomarry, Schrödinger had no intention of living offAnny’sincome.ButhewasalsoofferedasimilarpostinJena,inGermany,withasalarysufficienttoallowthemarriagetotakeplace.Hedulyaccepted,andthecouple were married. In fact they were married twice—first in a Catholicceremonyon24March1920,theninanEvangelicalchurchon6April.Shewastwenty-three, and hewas thirty-two.An earlier biographer,WalterMoore, hasdescribedtheunionintermswhicharehardtobeat:“Sheenteredthemarriagewiththehopeandexpectationthatitwouldbeatrueunionofmindsandbodies,in which she would achieve happiness through boundless submission to herbrilliantandbeautifullover.Theseillusionsmayhavelastedforatleastayear.”Nevertheless, the marriage lasted for life. As Anny herself later told HansThirring,“Itwouldbeeasiertolivewithacanarybirdthanwitharacehorse,butIprefertheracehorse.”The racehorse had not been scientifically idle in the three difficult years

leadingup tohismarriage.Onepieceofworkwasparticularly relevant to thelater development of his career, and was also his last significant piece ofexperimentalresearch.Intheseconddecadeofthetwentiethcentury,therewasagreatdealofpuzzlementaboutthenatureoflight.Bytheendofthenineteenthcentury,theworkofphysicistssuchasThomasYoungandJamesClerkMaxwellseemedtohaveestablishedthatlightwasawave.Butwithinthefirstfiveyearsof thenewcentury, theworkofMaxPlanckand, inparticular,AlbertEinsteinhadrevived the ideaof lightasastreamofparticles. (Moreof this in thenextchapter.) Schrödinger decided to carry out an experimental test to decidebetweentherivalwaveandparticlemodelsofthebehaviouroflight.Hisworkwas essentially a refinement of the double slit experiment, using a very fineelectricallyheatedwireasthelightsourceandstudyingtinyinterferencefringeswithamicroscope.Theresultswereexactly in linewithwhatwasexpectedofthewavemodel, reinforcingSchrödinger’s faith in theworldviewof classicalphysics.ButthemostimportantworkthatSchrödingercarriedoutinthelastyearsof

the century’s second decade concerned a quite different topic—the theory ofcolourvision.Thefruitsofhis laboursappearedinaseriesofscientificpapers

publishedin1920,describingandquantifyingtheperceptionofhue,brightness,andsaturationofcolours,andhowachangeinoneofthesepropertiescanaffecttheperceptionoftheothertwo.ThisledtoSchrödingerbeingaskedtowritethearticle “The Visual Sensations” for a major encyclopedia, the Lehrbuch derPhysik;this104-pageessay,publishedin1926,becamethestandardreferenceonthesubject.Hereturnedbrieflytocolourtheoryinthemid-1920s,applyinghisideastothepracticalproblemofcomparingthecoloursofstarswithoneanother,animportanttaskindeterminingtheirtemperatures.ButbythenhismainlineofresearchwasleadinghimnotoutintotheUniversebutinanddown,totheworldofatoms.Hehadalsomovedon—fromJenatoZürich,viaStuttgartandBreslau.

TheperipateticprofessorSchrödingersettledinwell inJena,wherehearrivedwithAnnyinApril1920,but the post there was only a temporary one, and when he was offered apermanent associate professorship in Stuttgart he had no hesitation inmovingthereinOctoberofthesameyear.Whilethere,hehadtimetodosomeworkonthetheoryofelectronorbits.Butbythistime,financialsecuritywasbecomingaparamount concern.Roaring inflation inGermanymeant thatSchrödingerwasbarelyabletosupporthimselfandAnny,andhadnoreserveswithwhichtohelphisailingmotherwhenherownfatherbecamesodesperatefor incomethathehad to turnheroutof the largeapartment inViennaand rent it out.Georgie’sfamilyhelpedher to settle,as faras shecould, in smallerpremises,andAnnyhelpedduringherfinalillness.Shediedthere,ofcancer,inSeptember1921.Theimageofhiswidowedmotherdyinginsuchreducedcircumstances,andthefearthatsomethingsimilarmighthappentoAnny,hauntedSchrödingerfor therestofhis life,andstrongly influencedhisdecisionsaboutcareermoves.Financialsecuritywouldalwayscomefirst.In these circumstances it is no surprise that Schrödinger accepted an

appointmentasProfessorofTheoreticalPhysicsinBreslauinthespringof1921,even though Breslau (now Wrocław) was uncomfortably close to the PolishborderandahotbedofCommunistsympathizers—arealconcerngiventhecivilwar then raging in Russia. But after some eighteen months as a peripateticprofessor, and less than six months in Breslau, Schrödinger was saved by anofferhecouldn’trefusefromasaferhaveninSwitzerland.TheUniversityofZürich,havingmanagedwithoutaprofessorof theoretical

physicsduringthewaryears,waslooking,slowly,foranewone.Thelaboriousprocessof finding the rightmanfor the job, involving interminablecommitteemeetings,beganat theendof1919anddraggedon formore thanayear.Onereasonfor the lackofurgencywas thatwith thehelpof junior lecturers thingswere ticking overmore or lessOK, and the university (or rather, the cantonalgovernment)wassavingmoneybynotappointingaprofessor.Then, inMarch1921,PaulEpstein,whohadbeenoneofthelecturershelpingtofillthegapinZürich, left to take up a post in Leiden. This concentrated the minds of thecommittee, and, finding that they could not afford their first choice,Max vonLaue(whohadalreadyheldthepostonce,briefly,beforethewar),theyofferedthe post to Schrödinger on the basis of his all-round ability and publicationsacross a wide range of topics. The appointment would be for six years,commencinginOctober1921,atanannualsalaryof14,000Swissfrancs—thetopendof therangeforsuchapost.AlthoughSwitzerlandhadsuffered in theEuropeanpost-wardepression,ithadnotexperiencedrunawayinflationandthesalarywasmorethanadequate(norwasthereanyriskofCommunistrevolutionin Switzerland). Schrödinger wrote to accept the offer on 16 September, andmovedtoZürichsoonafterhismother’sfuneral,makingonlyabriefdetourtowinduphisaffairsinBreslau.ItwouldbeinZürichthatSchrödingerwouldmakehismajorcontributionto

physics, duringwhat becameknown as the secondquantum revolution; but toput that work in perspective, we need to take a step back to look at the firstquantum revolution, triggered by the work of Max Planck at the end of the1890s.

Notes

1Theneedtoprovethisaslateas1905isclearfromEinstein’sAutobiographicalNotes,wherehetellsusthatatthattimehedeliberatelysetouttofindevidence“whichwouldguaranteeasmuchaspossibletheexistenceofatoms.”2InformationaboutHansiBauerandherrelationshipwithSchrödingercomesfromaninterviewshegavetoWalterMoorequotedinSchrödinger:LifeandThought.

ChapterFour

TheFirstQuantumRevolution

The quantum revolution began just as the nineteenth century gaveway to thetwentieth. InDecember 1900, theGerman physicistMax Planck (1858–1947)announcedthathehadsolvedafundamentalpuzzleaboutthenatureoflightandotherelectromagneticradiation,usingstatisticaltechniquesthatMaxwellwouldhave appreciated. But the breakthrough came at a price—it involved treatinglightasifitcameindiscretepackets,whatlatercametobeknownasquanta.Tosay thatPlanckwas uncomfortablewith the ideawould be anunderstatement.He believed that light must be a wave, but that it could only be absorbed orradiatedbyatomsindefiniteamounts.Nevertheless, theequationswere tellingthetruth.ItwouldbelefttoAlbertEinstein(1879–1955)toestablishtherealityof light quanta (also known as photons)—thework forwhich he received hisNobelPrize.ThepuzzlePlancksolvedconcernedthenatureofwhatisusuallyknowntoday

asblackbodyradiation,butwhichin theGerman-speakingworldof the1890swentbythemoreaccurate,butlessdramatic,termofcavityradiation.

WhenblackbodiesarebrightTo a physicist, a black body is an object that absorbs all the electromagneticradiation that falls on it, including light. Black body radiation is the kind ofradiationthatwouldbeemittedbysuchanobjectif itwerehot.Cavitiescomeintothestorybecausethebestwaytosimulateablackbodyinthelaboratoryistohaveahollowcontainer,likealargeinsulatedbox,withatinyholeinoneofitswalls. Ifyoushineradiation into thehole, itgoes into theboxandbouncesaroundinside,withverylittleescaping.Butastheradiationfillsthebox,itwillget hotter, and now if you stop shining anything into the hole radiation willescapefromthecavitythroughthathole:thisiscavityradiation.Itturnsoutthattheexactnatureoftheradiationbeingemitted(itsspectrum)dependsonlyonthe

temperature inside the cavity, and not on what the box is made of. This hasimportantpracticalapplications—forexample,weknowthe temperatureat thesurfaceoftheSunbecausetheradiationwereceivefromtheSuncorrespondstocavity(blackbody)radiationwithatemperatureofjustunder6,000°C,andweknewthisbeforeweknewthecompositionoftheSun.Asthisexampleshows,ablackbodycanbebright—anditcanbeyellow,orred,oranyothercolour.ButwhatpuzzledPlanckandhiscolleagues in the latenineteenthcenturywas thataccordingtothelawsofphysicstheyknewatthattime,itshouldhavebeenevenbrighter—indeed,infinitelybright.Cavity radiationwas first studiedby theGermanphysicistRobertKirchhoff

(1824–87)inthe1850s.Thekeyfeatureofthisradiationisthatforanyspecifictemperature its spectrum has a peak, corresponding to the maximum energybeingradiated,ataspecificwavelength,withlessenergybeingradiatedatbothshorterwavelengthsand longerwavelengths.Agraphof theamountofenergyradiated by a black body at different wavelengths rises smoothly from lowerenergiesatshorterwavelengthstoapeakatsomeintermediatewavelength,thenslidesdownsmoothlyagaintowardslowerenergiesatlongerwavelengths.Thewavelengthof this peakdependsonlyon the temperatureof theobject. In thevisible spectrum, wavelength corresponds to colour, and the peak shifts toshorterwavelengths as the temperature of the object increases. This is why alump of iron, which radiates almost like a black body, glows red when it isrelatively cool, yellowwhen it is hotter, andblue-whitewhen it is hotter still.But that isnotwhatclassicalelectromagnetic theory—the theoryofMaxwell’swaveequations—predictedinthesecondhalfofthenineteenthcentury.Ifelectromagneticwavesaretreatedmathematicallyinthesamewayasother

kinds of wave, such as the waves corresponding to notes played on a violinstring, the equations tell us that it is easier to radiate energy at shorterwavelengths. Indeed, the amount of energy radiated ought to be inverselyproportional to the wavelength. A black body—any black body made of anymaterial—ought, according to the calculations, to radiate huge amounts ofenergyattheshortestwavelengths.Sincevioletlighthastheshortestwavelengthof any light in the visible spectrum, and radiation with an even shorterwavelength is known as ultraviolet, this came to be known as the “ultravioletcatastrophe.” Something had to be wrong with the ideas behind thosecalculations.Butwhat?Theanswercamefromanunexpectedquarter.

EnterthequantumMaxPlanckwas among the first generation of physicists to growupwith thestatistical interpretation of thermodynamics developed by Maxwell andBoltzmann. He didn’t like the idea at first; but at least he was familiar withBoltzmann’s work when the opportunity came to apply it in a new andunexpectedcontext.PlanckenteredtheUniversityofMunichin1874,andreceivedhisPhD,fora

thesis on the second law of thermodynamics, in 1879. After a spell as aPrivatdozentthere,hemovedtoKielin1885andontoBerlinin1888,becomingafullprofessortherein1892andstayinginthepostuntilheretiredin1926,tobesucceededby—ErwinSchrödinger.Planckdidsolidbutunspectacularwork,mostlyinthermodynamics,andgavebeautifullyclear,preciselecturesthatwerealmostalwaysstandingroomonlyevents.Heturnedhisattentiontothepuzzleof black body radiation in 1894—not, initially, in the abstract quest forunderstanding, but because a consortium of electricity companies hadcommissionedhimtofindouthowtoproducelightbulbsthatwouldprovidethemaximumamountoflightfromtheminimumamountofenergy.Butoncehegothis teeth into the problem of black body radiation he became hooked, andworried away at it for years until he found an answer, publishing severalimportant papers on the relationship between thermodynamics andelectrodynamicsalongtheway.Itwas,indeed,Planck’sgraspofstatisticalthermodynamicsthatledhimtothe

resolutionoftheultravioletcatastrophe—althoughhewasnotmotivatedtodosobythecatastropheassuch.WhatPlanckwantedtoachievewasanunderstandingof the physical processes responsible for the exact shape of the spectrum ofcavityradiation—theblackbodycurve.Hehadtwocluestohelphim.In1896,WilhelmWien(1864–1928),workinginBerlin,putforwardanempiricalrule—an equation derived more or less by trial and error—which gave an accuraterepresentation of the short-wavelength side of the black body curve, andspecified the wavelength of the peak for a given temperature. What becameknownasWien’sLawsaysthatthetemperatureofablackbody(inKelvin,theabsoluteunitsoftemperature)isgivensimplybydividingthenumber2,900bythewavelengthofthepeak(inmicrometres).Soifthepeakisatawavelengthof5micrometres (0.005mm), the temperatureof theobject is580K(307°C).Buttherewasnoexplanation forwhyWien’sLawworked,and itonlyworkedfortheshort-wavelengthsideofthepeak—theequationwashopelesslyinaccurateat

longer wavelengths. Intriguingly, though, there was another equation whichworkedforthelong-wavelengthsideofthepeak,butwashopelesslyinaccurateat shorter wavelengths, where it “predicted” the non-existent ultravioletcatastrophe. This second equation was the fruit of the work of two men, theBritish physicists Lord Rayleigh (1842–1919) and James Jeans (1877–1946),and became known as the Rayleigh–Jeans Law. Rayleigh came up with theoriginalequation,whichwaslaterrefinedbyJeans,attheendofthenineteenthcentury;itessentiallytreatslightasaclassicalwave,withallthatthatimplies.Planck’s achievement was to find a single law, based on sound physical

principles combinedwith statistical techniques familiar from thermodynamics,toproduceasinglerulewhichnotonlybridgedthegapbetweenWien’sLawandthe Rayleigh–Jeans Law but explained thewhole black body curve. But, as Ihavementioned,theachievementcameataprice.Planck’sstartingpointwastoassumethat theradiationfromablackbodyis

beingproducedbyanarrayof“electromagneticoscillators.”Hewascarefulnottospecify thenatureof theseoscillators.By the1890s itwaswellknown thatmovingelectricchargescouldproduceelectromagneticradiation,andthat lightwasaformofelectromagneticradiation;soitwasnaturaltoassumethatelectricchargesoscillatingtoandfroproducedtheradiationemittedbyblackbodies.Inthe summer of 1900, Planck found thatwith a littlemathematical juggling hecouldcomeupwithanequationthatsmoothlyjoinedthegoodbitofthecurvedescribedbyWien’sLawtothegoodbitofthecurvedescribedbytheRayleigh–JeansLaw,providingasingleequationtodescribetheentireblackbodycurve;but at that stage he still had no physical basis for the equation. Then, havingexhausted all other attempts at finding such a basis, in October that year herealized thatwhat he neededwasBoltzmann’s statistical interpretation appliednotjusttotheelectromagneticoscillators,buttoenergy—totheelectromagneticradiationitself.Boltzmann’s statistical approach to thermodynamics involves cutting energy

up into little pieces mathematically (using the techniques of calculus),manipulatingthepiecesasrequiredbythelawsofstatistics,andthenaddingthemodifiedpiecestogether(integration)atalaterstageofthecalculation.Planckhad never been a fan of this approach, but almost in desperation he tried itanyway, treating the electromagnetic radiation as made up of little pieces ofenergyinsteadofasmoothwave.Theastoundingresultwasthattheequationhehad already discovered empirically, which provided a complete description ofthe black body curve, fell out of the calculation at the stage before the pieces

wereintegratedbacktogether—beforethecalculationhadbeencompleted.SincePlanckknewtheanswerhewaslookingfor,hestoppedthere,andannouncedhisdiscovery at a meeting of the Berlin Academy of Sciences on 14 December1900, when thirteen-year-old Erwin Schrödinger was still in high school. Hecalled the little chunks of energy “energy elements,” and found that they arerelated to the frequencyof radiation (frequency is essentially1dividedby thewavelength, so high frequency corresponds to short wavelength) by a verysimpleequation—E=hν

—whereE is the energy of an “element”; theGreek letter ν (nu) denotes thefrequency of the wave; and h is a simple number, now known as Planck’sConstant.AsPlanckputittothemeeting:“Wethereforeregard—andthisisthemostessentialpointoftheentirecalculation—energytobecomposedofaverydefinitenumberofequalfinitepackages.”Butjusthowdoesthisresolvetheultravioletcatastropheandexplaintheshape

of the black body curve? There is no need to go intomathematical details tounderstand what is going on. At low frequencies (long wavelengths), it isrelativelyeasytoproduceenergyquanta,sinceeachcarriesonlyalittleenergy,andlotsoftheoscillators(wemightaswellcallthematomsfromnowon)haveenoughenergytodothejob.Therearemanyquanta,butbecauseeachhasonlyasmallamountofenergy,overalltheamountofenergycarriedbytheradiationislow. At high frequencies (short wavelengths), each quantum carries a lot ofenergy(relativelyspeaking),butitishardtomakesuchquantaandonlyafewoftheatomshaveenoughenergytodothejob.Soalthougheachquantumcarriesalotofenergytherearefewquanta,andonceagaintheoverallenergyradiatedislow.Itisonlyinthemiddleground,correspondingtothepeakintheblackbodycurve,thatitispossibletomakealotofquanta,eachwithamoderateamountofenergy,sothattheoverallamountofenergyradiatedishigh.And,naturally,forhotterobjectsthereismoreenergyavailable,soitiseasierfortheatomstomakehigher-energyquanta,andthepeakshiftstowardshigherfrequencies—intermsofcolour,fromredthroughorangetowardsblue.In spite of this success, Planck’s announcement did not change physics

overnight.Nobodyknewquitewhattomakeofit,andtomanypeople,atfirst,itdid not seem to domuchmore than tidy up the work ofWien and Rayleigh(Jeans’srefinementcamealittlelater).Planckhimselfdidn’tquiteknowwhattomake of it either; many years later he wrote: “I can characterise the wholeprocedureasanactofdespair...atheoreticalinterpretationhadtobefoundat

anyprice.”1But thepricePlanckwaswillingtopaystoppedshortofacceptingtherealityofhisenergyelementsasphysicalentities.Hebelievedthatwhattheequationswere telling himwas that the packages of electromagnetic radiationcouldonlybeemittedorabsorbedinamountsofhν,butthattheradiationitselfwasaclassicalwave.Aroughanalogymightbewiththerelationshipbetweenacash machine and money. The cash machine can only dispense money inmultiplesof£10—whatyoumightcall“moneyelements.”Butotheramountsofmoney,suchas£55.76,existintheworldoutsidethecashmachine.Planckwasforty-twowhenhemadehisunexpecteddiscovery,andtoosetin

his ways to make the next leap. It took a much younger man, with a freshapproach to physics, to look at the implications of accepting that energyelements—what we now call quanta—are real, physical entities; at thepossibilitythat,asitwere,weliveinaworldwheremoneyonlyexistsinunitsof£10,insideoroutsidethecashmachine.ThatyoungermanwasAlbertEinstein,whomadehisbreakthroughin1905,whenhewastwenty-six.

ThequantumbecomesrealEinstein graduated from the Swiss technical university, theETH, in 1900, theyear of Planck’s breakthrough. But he had not covered himself in glory as astudent, partlybecausehedidn’t bother to attend lectures and studiedmoreorlesswhatheliked.Graduatingbottomofhisclassasaresult,hewasunabletopursue his ambition of working at the ETH for a PhD and becoming aPrivatdozent,buteventuallymanagedtogetthenow-famousjobasaTechnicalExpertThirdClassatthepatentofficeinBern.Itwaswhileworkingtherethatin1905,ayearbeforeSchrödingerenteredtheUniversityofVienna,heproducedanastonishingsetofscientificpapers,includingaPhDthesis,thespecialtheoryofrelativity,andonethathedescribedthatyearinalettertohisfriendConradHabicht as “very revolutionary”—a term he did not apply even to the specialtheory.Itdealtwiththerelationshipbetweenradiationandatoms,anditprovedthatlightquanta—photons—arereal.Einstein’s jumping-offpointwas theworkofPhilippLenard (1862–1947), a

Germanphysicistwhohadcarriedoutaseriesofexperiments,startingin1899,to investigate the way ultraviolet light shining on the surface of ametal in avacuumcouldmakethemetalemitwhatwerethenstillcalledcathoderays,butwhicharenowknownaselectrons.

Lenardhaddiscoveredthattheenergyoftheindividualelectronsproducedbythisso-calledphotoelectriceffectdoesnotdependonthebrightnessofthelightshiningon thesurface.But itdoesdependon thewavelength,or frequency,ofthe light. Thiswasweird.A faint light has less energy than a bright light, sosurely a fainter beam of light should produce electronswith less energy.Andwhathadthefrequencyofthelightgottodowithit?Einsteinhadtheanswer—or rather,he realized thatPlanckhadgivenhim theanswer. Ifelectromagneticradiationwithaparticularfrequencyνreallyismadeupofastreamofparticleseachwithenergyhν,theneverytimeoneoftheseparticles(quanta,nowknownasphotons)knocksanelectronoutofthemetalitdoessowiththesameamountof energy. Turning the brightness of the radiation down reduces the overallenergyof thebeam,butonlybecause it reduces thenumberofphotons.Foraparticular frequency, eachphoton still has the sameenergy.Soalthough fewerelectronsareknockedoutofthemetal,eachonestillgetsakickwiththesameamountofenergy,hν.AsEinsteinputit,“thesimplestconceptionisthatalightquantumtransfersitsentireenergytoasingleelectron.”Theonlywaytochangetheamountofenergycarriedbyeachphotonis tochangethefrequencyof thelight,notitsintensity.Einsteinagain:“Accordingtotheassumptionconsideredhere, in the propagation of a light ray from a point source, the energy is notdistributedcontinuouslyoverever-increasingvolumesofspace,butconsistsofafinite number of energy quanta localised at points of space thatmovewithoutdividing and can be absorbed or generated only as complete units.” In otherwords, ifyouhadinfinitelysensitiveeyesandlookedatasourceof lightfromveryfaraway,youwouldnotseeafaint,continuousoverallglow,butindividualflashesoflight,withcompletedarknessinbetween,asindividualquantaarrivedatyoureyes.AcenturyafterEinsteinmadethisclaim,thisisexactlywhatastronomersdo

“see,”usingsensitiveelectronicdetectorstostudythelightfromdistantobjects.Theyliterallyobservethearrivalofindividualphotons,oneafteranother.Butin1905,therewerenoexperimentssensitiveenoughtosupportthisclaim.Indeed,even Lenard’s experiments, although suggestive, were not really accurateenough to justify Einstein’s far-reaching interpretation of the data, and it waswidelyfeltthathehadgonetoofarindrawingsuchaconclusionfromimperfectevidence—notleastsincetherewasstillthecompellingevidence,fromYoung’sexperimentandothers,thatlighttravelsasawave.Howcoulditbebothwaveandparticle?Onepersonwas so infuriatedbywhathe sawasEinstein’snonsensical idea

that he set out to prove him wrong. Robert Millikan was an AmericanexperimenterworkingattheUniversityofChicago.Hewassuperblyskilfulandamong other thingsmade the first accuratemeasurement of the charge on anelectron. He was also, like all good scientists, willing to admit when he waswrong, and after an investigation lasting several years he concluded that therelationshipbetweentheenergyofanejectedelectronandthefrequencyoftheradiation involved exactly matched Einstein’s prediction. But he had no ideawhy.In1916hewrote:“TheEinsteinequationaccuratelyrepresentstheenergyofelectronemissionunder irradiationwithlight[but] thephysical theoryuponwhichtheequationisbased[is]totallyunreasonable.”Andagainin1949,inanarticleintheReviewsofModernPhysics,hewrote:“Ispenttenyearsofmylifetesting that 1905 equation of Einstein’s and contrary to allmy expectations, Iwas compelled to assert its unambiguous verification in spite of itsunreasonableness.”Nevertheless, the experiments provoked byEinstein’s “unreasonable” theory

provided Millikan with an accurate measurement of Planck’s Constant,demonstrating that it had real significance.After all, if you canmeasure it, itmustbereal. It isnocoincidencethat itwasafterMillikanreportedhisresultsthat theNobel Committee gave the physics prize for 1918 to Planck, and theprize for 1921 (the year Schrödinger took up his appointment in Zürich) toEinstein;Millikanreceivedhisprizein1923.Bythen,theimportanceofquantaand quantum physics was no longer in doubt, and the understanding of therelationship between electrons, light, and atoms had been transformed by theapplicationofquantumideas.Themanchieflyresponsibleforthebreakthroughwas the Dane Niels Bohr (1885–1962) whose own Nobel Prize, awarded in1922,slottedinbetweenthoseofEinsteinandMillikan.

InsidetheatomEvenwhile some physicistswere still questioning the reality of atoms, othershadbeenstarting theprocessofbreakingatomsapart todiscoverevensmallercomponents of thematerialworld.Theprocess really began in 1896,with thediscovery of radioactivity byHenri Becquerel (1852–1908),working in Paris.Hefoundthatsomepreviouslyunknownemissionfromuraniumcouldproducefoggingofaphotographicplateeventhoughtheplatewaswrappedinadoublelayer of black paper to prevent light getting to it. This spontaneous emission

cametobeknownasradioactivity,andotherradioactivesubstancesweresoondiscovered. Just a year after Becquerel’s breakthrough, J. J. Thomsonannounced,inalectureattheRoyalInstitutioninLondon,thediscoverythattheradiation from a wire that is carrying an electric current in a vacuum tube ismade up of a stream of electrically charged particles—what we now callelectrons.TheexperimentalstudyofradioactivitywasswiftlycarriedforwardbytheCuries,Marie(1867–1934)andPierre(1859–1906),attheSorbonne;buttheperson who first appreciated what radioactivity involved, and then usedradioactivity to probe the structure of atoms, was Ernest Rutherford (1871–1937),aNewZealanderwhoworkedinCanadaandEngland.RutherfordarrivedinEnglandin1895andworkedforatimeunderThomson

at the Cavendish Laboratory in Cambridge. Under Thomson’s influence, hebecame interested in atomic physics, and soon discovered that there are twokinds of radioactivity, one producing positively charged particles which hedubbed alpha radiation, and the other producing negatively charged particleswhichhecalledbetaradiation.Itsoonbecameclearthatbetaparticlesareinfactfast-moving electrons, but the name stuck.WhenRutherford identified a thirdkindofradiation,in1900,itseemednaturaltocallitgammaradiation;gammarays carry no charge and are a form of electromagnetic radiation—essentially,veryenergeticX-rays.By the time he discovered gamma radiation, Rutherford had moved on to

McGill University in Montreal, where he worked with the English chemistFrederick Soddy (1877–1956). Together, they discovered that the process ofradioactivityinvolvesthetransformationofatomsofoneelementintoatomsofanother element, and that this process (known as decay) takes place on acharacteristic timescale, different for each radioactive substance, measured bywhatiscalleditshalf-life.Foranyquantityofaparticularradioactiveelement,inonehalf-lifehalfofthesample(halftheatoms)decaysintoanotherelementbyemittingalphaorbetaradiation.Forexample,radium,oneoftheradioactiveelements discovered by the Curies, decayswith a half-life of 1,600 years, byemittinganalphaparticle fromeachatom thatdecays, toproduceagascalledradon.Alphaparticlesthemselvesturnedouttobeidenticaltoatomsofhelium,the second-lightest element, from which two electrons have been removed,leaving themwith two units of positive charge. Each alpha particle hasmorethanseventhousandtimesasmuchmassasanelectron,roughlythesameasthemassoffourhydrogenatoms.Butevenbeforeheknewwhatanalphaparticlewas,orhowsuchparticlescouldbeejectedathighspeedfromradioactiveatoms

suchasthoseofuraniumorradium,Rutherfordwasabletousethemtostudythestructureofatoms.BackinEngland,in1907hebecameProfessorofPhysicsattheUniversityof

Manchester, and in 1908 received the Nobel Prize for his work on thetransmutationof theelements.TheNobelCommitteeregardedthisasabranchof chemistry, so hewas awarded the chemistry prize, even thoughRutherfordregardedhimselfasaphysicistandoncefamouslysaid:“Allofscienceiseitherphysics or stamp collecting.” The year after he received the Nobel Prize,Rutherford suggested an experiment, actually carried out by two of his juniorcolleaguesinManchester,HansGeiger(1882–1945)andErnestMarsden(1889–1970),thatprovidedthefirstinsightintothestructureoftheatom.GeigerandMarsdenusedalphaparticlesfromaradioactivesourcetobombard

thinsheetsofmetal foil,andadetectordevisedbyGeigerandRutherford(theprecursor of the famousGeiger counter) tomonitor where the alpha particleswent after they hit themetal. To their astonishment, they found that althoughmostoftheparticleswentrightthroughthefoilasifitwerenotthere,someweredeflectedatlargeanglesandoccasionallyonebouncedrightbackfromit,likeaballbeinghitagainstabrickwall.Rutherfordexplainedthisbysuggestingthatanatomconsistsofatinycentralkernel(soontobedubbedthenucleus),whichispositivelycharged(soitrepelspositivelychargedalphaparticles)andcontainsmostofthemassoftheatom,surroundedbyacloudofelectrons,whichtakeupmostofthespacebuthaveverylittlemass.Analphaparticlecanbrushpasttheelectronswithhardlyanyeffect,butifitjusthappenstohit,orpasscloseby,anucleusitwillbedeflectedviolently.Bycarefulstudyofthestatisticsofwhichproportionsofthealphaparticlesweredeflectedatdifferentangles,Rutherfordwasevenabletocalculatetherelativesizeofthenucleus.Anatomistypicallyabout10−8 centimetres (one hundred-millionth of a centimetre) across, and thenucleusistypicallyabout10−13cmacross(onehundred-thousandththediameteroftheatom).Rutherford announced this nuclear model of the atom in 1911, although he

only introduced the term “nucleus” in this context a year later. It neatlyexplainedthewayalphaparticles(nowregardedasthenucleiofheliumatoms)are deflected by atoms. But it posed one big problem—since electrons havenegative charge, and thenucleusof an atomhaspositive charge, andoppositechargesattract,whydon’talltheelectronsfallintothenucleus?Bygreatgoodfortune,someonewhowasabletoseetheanswertothispuzzlejusthappenedtobe visiting Manchester from Denmark for a few months, at exactly the time

Rutherford’steamwasmakingthisbreakthrough.NielsBohrwastobecomeoneofthemostinfluentialofthefoundingfathersofquantumtheory.

TrippingthelightfantasticTherewasanotherpuzzleabouttherelationshipbetweenlightandmatter,whichdatedbacktotheearlynineteenthcentury,whenThomasYoungwaspromotingthe wave model of light. One of Young’s friends, WilliamWollaston (1766–1828), having made a fortune by inventing a technique for producing pureplatinum, was able to indulge his passion for science as an independentinvestigator.Hewasastrongsupporterofthewavemodeloflight,andwasthefirstpersontonoticethatthelightfromtheSun,whenspreadoutintoaspectrumusing a prism and studied through amicroscope, ismarked by amultitude ofdarklines.TheselineswerestudiedinmoredetailbytheGermanphysicistJosefvon Fraunhofer (1787–1826), who developed the “prism spectrometer” into arefined scientific instrument, later known as the spectroscope. He used thisinstrument to study the spectrum of the Sun in the second decade of thenineteenth century; these dark lines within the spectrum are now known asFraunhoferlines.Butwhatcausesthem?Inthedecadesthatfollowed,researchersincludingFraunhoferhimself,Robert

Bunsen(1811–99),andRobertKirchhoff,establishedfromexperimentsintheirlaboratoriesthateachelementproducesitsownsetoflinesinthespectrum.Eachlinecorrespondstoaparticularfrequency,orcolour,oflight,andeachelementradiates at its characteristic frequencies when hot, but absorbs light at thosefrequencies when cold. The pattern of lines associated with each element isunique, and as distinctive as a fingerprint or a bar code. For example, whensodiumishotitradiatesatparticularfrequenciesintheyellow-orangepartofthespectrum.Somestreet lightscontainagaswhich includes sodiumcompounds,which is why their light is orange. But if light passes through a cool gascontainingthesamesodiumcompounds,thesodiumabsorbslightintheyellow-orangepartofthespectrum.Spectroscopy—theanalysisofthesepatterns—turnedouttobeahighlyuseful

tool for chemists in analysing the composition of different substances, eventhoughnobodyknewhowthelineswereproduced.AnditmeantthattheremustbeamultitudeofdifferentelementsintherelativelycoolatmosphereoftheSun,absorbinglightpassingthroughitfromthemuchhottersurfacebelow,eachset

ofblack linescorresponding toanelement.Thecrowning triumphof thisnewbranch of science came when the British astronomer Joseph Lockyer (1836–1920) used the discovery of a set of lines in the solar spectrum that did notcorrespond to anyknownelement to infer that theymust be associatedwith a“new”element,whichhecalledhelium;itwasonlyin1895,nearlythirtyyearsafterLockyerreachedthisconclusion,thatheliumwasidentifiedonEarth.Bohr’sgeniuswas to solve themysteryof spectroscopy, locate theoriginof

Planck’s (or Einstein’s) quanta, and explain why atoms don’t collapse—all inoneneatpackage.Physicswouldneverbethesameagain.Bohr began to developwhat became known as theBohrmodel of the atom

during his first visit toManchester (he came back for a longer visit between1914 and 1916), but completed it back inCopenhagen in 1912.The ideawaspublished a year later, around the time Schrödingerwas seriously thinking ofgivingupphysics inorder tomarryFelicieKrauss. Itcontained theessenceofBohr’sapproachtoanyproblem—awillingnesstocombinedifferentideasfromdifferentareasofphysicsinapatchworktomakeaworkingmodel,evenifthedifferentpatchesdidn’t, at first sight, seem tobelong together.Once thisgavehim a rough idea of amodel, he (or someone else) could adjust the pieces tomakeasnuggerfitand(hopefully)comeupwithsomethingbetter.The first piece of Bohr’s patchwork came from classical physics. It

“explained” Rutherford’s discoveries about the structure of the atom bypostulating that electrons are “in orbit” around the central nucleus, in a wayreminiscent of the way planets orbit the Sun. According to classical physics(Maxwell’sequations),electricallychargedparticlesmovinginsuchorbitsoughttoradiateelectromagneticenergycontinuously,andspiraldownintothenucleusas a result.Bohr ignored this dogma, and for his next piece of the patchworkturned instead to quantumphysics.He suggested that the electrons could onlyemit or absorb energy in definite lumps—Planck’s quanta. So they could notspiral steadily inward. Instead, they could only jump, outward or inward, bydefinite amounts, corresponding to hν. Only certain orbits, corresponding tocertain amounts of energy, were allowed, and electrons could move betweenthoseorbits,jumpinginwardiftheyreleasedaquantumofenergyandoutwardiftheyabsorbedaquantumofenergy.(Therulesaboutwhichenergylevelswereallowedwereinitiallyworkedoutempirically,andlabelledbyasetofnumberssimply known as “quantum numbers.”) It would be as if the Earth suddenlyjumped either inward to the orbit of Venus, or outward to the orbit ofMars,without—andthisisacrucialpointthatwouldlaterstickinSchrödinger’sthroat

—passingthroughthespaceinbetween.Butstill,whydidn’talltheelectronsinanatomjumpdownintothelowestorbit?Because,saidBohr,pluckinganotherrabbitoutofthehat,theinnerorbitswerealreadyfull!Theremustbealimittohowmanyelectrons couldoccupyeachorbit, andonce that limitwas reachedanymoreelectronshadtooccupyorbitsfartheroutfromthenucleus.Theideawassooutrageousthatitmighthavebeenlaughedoutofcourt.But

Bohr had an ace up his sleeve—or rather, a pair of aces. The first is onlytangentiallyrelevanttothestoryofSchrödingerasareluctantquantumpioneer,soIwillnotgointodetailshere(IhavedescribeditfullyinmybookInSearchofSchrödinger’sCat).Briefly,itisthatBohr’smodeloftheatomgavethefirstplausibleexplanationofwhyatomscanonlyjointogethertomakemoleculesincertain ways, by forming so-called “bonds”—why, for example, a watermoleculealwaysconsistsofasingleoxygenatomjoinedtotwohydrogenatoms,andweneverfindamoleculecomposedofasinglehydrogenatomjoinedtotwooxygen atoms. It made chemistry a branch of physics. The fact that Bohr’smodelwas later supersededbyabettermodelofchemistrydoesn’tmatteranymorethanthefactthatNewton’stheoryofgravitywassupersededbyEinstein’sgeneraltheoryofrelativity.The second ace, however, is directly relevant to my story. When the

appropriatenumberswereputin,inparticularfromPlanck’sradiationequation,the Bohr model predicted the lines in the spectrum, produced by electronsjumping between energy levels, known to correspond to the simplest element,hydrogen(thecalculationsweretoocomplicatedtoworkouttheoreticalspectraforheavier elements). It alsopredicted some lines thatwerenot seen,but thatwasarelativelyminorproblemthatcouldbe(andwas)tidieduplater.Forallitspatchwork nature, Bohr’s model of the atomwas the first to explain spectrallines,aswellasthefirsttoexplaintheobservationsmadebyRutherford’steam.EventhoughprogressintheoreticalphysicswasslowedbytheFirstWorldWar,Bohr’sideaswererefinedandimprovedbyothers,notleastbyAlbertEinsteinoncehehadcompletedhismasterwork,thegeneraltheoryofrelativity,in1916.

EinsteinagainIn its original form, like Planck’s equation for black body radiation, Bohr’satomicmodeldidnotsaywhetherelectromagneticradiationcouldonlyexistinthe form of discrete chunks (quanta), or whether it could only be emitted or

absorbed in discrete chunks, like money from the cash machine. And what,exactly, was the relationship between Bohr’smodel and Planck’s equation? ItwasEinsteinwhoprovidedtheanswers—andmore.Thecalculationsforthehydrogenatomhadbeensimpleenoughtoworkwith

becauseeachhydrogenatomhasasinglepositivelychargedparticle(aproton)in its nucleus, and a single negatively chargedparticle (an electron) “in orbit”around it, jumping between the permitted energy levels in a way crudelyanalogous to a ball bouncing up and down a flight of steps. Einstein’scontribution was to find a way to describe mathematically what is going onwhenmanyelectronsarejumpingaroundtheenergylevelsinlargenumbersofmuchmorecomplicatedatoms,asifaboxofballshadbeenemptiedontothestaircase and theywere all bouncing around at once.Naturally, as the leadingproponent of the idea that photons are real, he argued that when an electronjumps down an energy level it emits a photon with the same energy as thedifference between the two levels, which in turn corresponds to a precisefrequency of light (given by Planck’s formula), and when an atom absorbs aphotononeofitselectronsjumpsupanenergylevel;butthisisonlypossibleifthe atompossesses two energy levels separated by a gap just the right size toabsorbradiationwiththatfrequency.Einstein’soveralldescriptionofwhatwasgoingonwasbasedonstatistics.Heusedstandardstatisticaltechniquestoworkouttheprobabilitythatanatomwithaparticularsetofquantumnumberswould“decay” into a state with lower energy and a correspondingly different set ofquantumnumbers,emittingaphotonintheprocess.Addingupthecontributionsofthesephotonemissions,hewasabletocalculatetheoverallradiationfromalargenumberofatomsinahotobject.TheresultwasPlanck’sequationfortheblackbodycurve.Itwas this discovery that established the acceptance ofBohr’smodel of the

atom, and finally completed the first quantum revolution. But it contained aticking time bomb. The whole edifice rested upon probabilities. Einstein hadintroduced into quantum physics the idea that you could never calculate withcertainty just what a particular atom (or any other quantum object) would donext.Youmightsaythattherewasa1in3chance,forexample,thataparticularkindofatomwithaparticularsetofquantumnumberswouldemitaphotonwithaparticularfrequencyinthenexttenminutes.Butitmightnotdecayfordays,oryears.Thecalculationsworkedbecauselargenumbersofatomswereinvolved.If you had a million atoms like this you could be sure that almost exactly333,333ofthemwoulddecayinthenexttenminutes—butyoucouldnevertell

inadvancewhichatomswoulddecayandwhichoneswouldnot.Inthe1920s,probability and uncertainty became integral parts of the second quantumrevolution,leadingSchrödingerand(ironically)Einsteintohaveseriousdoubtsabout the whole enterprise. Even when he introduced the idea in his paperdescribing his breakthrough in understanding the quantum theory of radiation,Einstein had described this as “aweakness of the theory,” expressing concernthat“itleavestimeanddirectionofelementaryprocessestochance.”Buttheoldquantumphysics,asitcametobeknown,stillhadacoupleofcontributionstomakebeforeitwasblownaway.AndEinsteinhimselfwasstillonthecase.Oneoftheotherideasinhisquantumtheoryofradiationpaper,publishedin

1917,wasawayinwhichatomsmightbeencouragedtoemitradiation.Ifmanyatoms,perhapsinacrystal,werepreparedinahigh-energystate—ineffect,withan electron in each atom sitting on a particular high step of the staircase—itoughttobepossibletotriggerthemintodecayingintothelower-energystatebygiving them a nudge. And the most efficient way to provide such a stimuluswouldbetonudgetheatomwithaphotonthathadexactlythesameenergyasthe jumpyouwanted to trigger, causingakindof resonance. If enoughatomswere available to be jostled in this way, a single photon could trigger one ofthem todecaywithout being altered itself, so that therewouldnowbe twoofthemtotriggerthenextpairofatoms,thenfour,eight,sixteen,andsooninanexponentially growing cascade. The result would be an intense beam of pureradiation, allwith exactly the same frequency (colour), amplified up from theoriginal stimulus.Decades later, this ideaof “light amplificationby stimulatedemissionofradiation”becameapracticality,andgaveustheterm“laser.”Lasersarepurequantumphysicsputtopracticaluse.But there was still more in Einstein’s paper. Any moving particle in the

everydayworldcarriesbothenergyandmomentum—momentumisameasureofhowmuch impact amoving object has on anythingwithwhich it comes intocontact, anddependsonboth themassof theobject and itsvelocity, so that alightobjecttravellingveryfastcanhitwithanimpactasgreatasthatofaheavyobjectmovingmore slowly. If photonswere real particles that carried energy,theymusthavemomentum.Einsteinshowedthat,althoughphotonsareaspecialcase because they always travel at the speed of light, usually denoted by theletterc,themathematicsofPlanck’sdescriptionoftheblackbodycurveandhisown description of the interaction between atoms and radiation were onlyconsistentwithoneanotherifeachphotonwithenergyEhasamomentumgivenbydividingEbyc.

This was a dramatic claim, and encouraged experimenters to test Einstein’sprediction.TheonewhosucceededwastheAmericanphysicistArthurCompton(1892–1962),whomeasured the transferofmomentum fromX-rayphotons toelectrons in so-called “scattering” experiments late in 1922 (the results werepublishedin1923).HereceivedtheNobelPrizeforwhatbecameknownastheComptoneffectin1927.Itwaswelldeserved,sincetheComptoneffectprovidesdefinitiveproofof the realityofphotonsand theaccuracyofquantumphysics(eventheoldquantumphysics!)asadescriptionofthesubatomicworld.Butburiedwithinall thiswasamysterythatwouldbeoneof the triggersof

the second quantum revolution, and would inspire Schrödinger’s masterwork.PlanckhadshownthattheenergyofaphotonisrelatedtoitsfrequencybytheequationE =hν.Einsteinhad shown that themomentumof a photon, usuallydenotedbytheletterp,isrelatedtoitsenergybytheequationp=E/c.Inotherwords, p = hν/c. The momentum of a photon, which had previously beenregardedaspurelyaparticleproperty,isdirectlyrelatedtoitsfrequency,whichhadpreviouslybeenregardedaspurelyawaveproperty.Whatwasgoingon?Itwas against this background that Schrödinger arrived in Zürich, and at firstconsolidatedhispositionasasoundbutunspectacularscientist.

Notes

1SeeMehraandRechenberg,TheHistoricalDevelopmentofQuantumTheory,vol.1.

ChapterFive

SolidSwissRespectability

Schrödingerarrived inZürich in theautumnof1921,andsoonsettled into therhythm of life as a respectable professor in a respectable university in arespectablecountry.Itwouldbefiveyearsbeforehemadethebreakthroughthatsealedthesuccessofthesecondquantumrevolution—yearsinwhichhegavenohintofwhatwastocome.Zürichwasnotquiteabackwaterofscienceinthe1920s,butitcertainlywas

not a centre of excellence in research, in spite of having two respectableinstitutes of higher learning.The town’s location on a lake and a river,wherenorth–south and east–west trade routes crossed, meant that there had been asettlementtheresincepre-Romantimes,andbytheendofthefirstmillenniumA.D.ithadbecomeanimportantcentreoftrade,politics,andreligion.In1218Zürich acquired the status of a free city, and in 1351 it joined the SwissConfederationandwasinvolvedinthewarsandtribulationsthateventually(in1648)ledtoSwissindependencefromtheHabsburgEmpire.Acenturyearlier,ZürichhadbecomeacentreoftheProtestantReformationandasafehavenforProtestants fleeing persecution in other countries, boosting its cultural andintellectual diversity andmaking the city one of the intellectual centres of theGerman-speakingworldintheeighteenthcentury.ThemodernSwissstatedatesfromthetimeoftheFrenchinvasionof1798,itsconstitutionevolvingthroughvariousmodificationsinthenineteenthcentury.

TheuniversityandtheETHTheUniversityofZürichwasestablishedin1833,butalthoughtheteachingofphysics got started on a good footing, very little research in the subject wascarriedout thereuntil thearrivalofRudolfClausius (1822–88)asprofessor in1857.Hedidn’thave tocome far to takeup theposition, sincehehadbeenaprofessor at the new Zürich polytechnical institute, or Polytechnikum, since

1855—indeed,heretainedthatpostalongsidehisroleattheuniversity.Thiswastypicalofthecloselinksbetweenthetwoinstitutions.ThePolytechnikumhadacuriousbackground.Theoriginalplan,datingback

to the1790s,hadbeen toestablisha technical institutealong theFrench lines,like the École Polytechnique in Paris; but by the time the scheme came tofruition, in 1855, the model that emerged was more like that of a GermantechnischeHochschule,reflectedinitsfullname,theEidgenössicheTechnischeHochschule,orSwissFederalInstituteofTechnology.ThepresenceofbothETHand university in the same city is a result of the structure of the SwissFederation.TheETHisafederalinstitution,anditsnaturalhomeisthelargestcityinSwitzerland,whichhappenstobeZürich;buttheuniversityisacantonalinstitutiongovernedbythelocalcommunity.SotheETHis—orcertainlywasatthattime—themoreimportantofthetwo,eventhoughtomodernearsthename“university”hasmoreprestigiousovertones.For thenext fiftyyears, theETH,rather than theuniversity,was the leadingcentreofphysics inZürich,and theuniversity’s only period of excellence in the field came during the tenure ofClausius,from1857to1867,whenheheldtheETHpostaswell.Clausius had studied and worked in Berlin beforemoving to the ETH. His

greatclaimtofameishisrecognitionofthefundamentallawofnaturethatheatcannotflowofitsownvolitionfromacolderobjecttoahotterobject;or,asheput it in a paper published in 1850, “it is impossible by a cyclic process totransferheat fromacolder toawarmer reservoirwithoutnetchanges inotherbodies.”Thisisthesimplestformulationofthesecondlawofthermodynamics.AnditwasClausiuswho, in1865whilehewasworkinginZürich, introducedinto physics the term and mathematical concept of “entropy” as a precisemeasureofdisorder.Butin1867Clausiusmovedon,firsttoWürzburgandthentoBonn,andphysicsinZürichlanguished.Butmathematicsflourished,atleastattheETH,whereitsmostfamouspupil,

Albert Einstein, arrived in 1896 to take the course intended to produce high-school teachersof science.Amonghisown teacherswasHermannMinkowski(1864–1909),who famously once described youngAlbert as “a lazy dogwhonever bothered about mathematics at all,” but soon came to appreciate theachievementsofhisformerstudentandin1908cameupwiththebrilliantideaof explaining Einstein’s special theory of relativity, published just three yearsearlier,intermsofthegeometryoffour-dimensional“spacetime.”Minkowski’sgeometrizationofthespecial theorywasamajorfactorinitsrapidacceptance,andwouldlaterbecomeapowerful toolinunderstandingthegeneral theoryof

relativity.JustayearafterMinkowskipresented the idea,Einsteinreceivedhisfirstacademicappointment,attheUniversityofZürich.Buttheresultingsecondfloweringofphysicsattheuniversitywastobeevenmoreshort-livedthanthefirst.Einstein’sgrowingreputationbroughtastreamofeminentvisitorstoZürichto

discussphysicswithhim,andoneofhisresearchinterestsatthetime,applyingquantumtheorytotheunderstandingofspecificheats,ledtohisbeinginvitedtopresentapaperonthesubjecttoaconferenceinBrusselsintheautumnof1911.By the time he presented that paper, however, Einstein had moved on fromZürichtoPrague,andhissuccessor,PeterDebye(1884–1966),hadrecentlybeeninstalled.Debyewasanexcellentphysicistwhowouldcarryoutimportantworkonatomicandquantumtheory,buthelastedonlyayearinZürichbeforemovingon toUtrechtandbeing replacedbyMaxvonLaue,1whowasby thenawell-establishedscientist;hisideaofinvestigatingcrystalstructureusingX-rayshadbeen suggested in the spring of 1912 and confirmed by experiments later thesame year. But vonLauewas too big a fish for Zürich to hold on to, and hemoved toFrankfurt-am-Main in the summerof 1914, a fewmonthsbefore hereceivedtheNobelPrize.Meanwhile, in 1912 Einstein had returned to Zürich to take up a special

professorship at the ETH, free from any general lecturing duties, although hewas required to give lectures and seminars for advanced students. Aswell asother work, including research in statistical mechanics, during his time as aprofessorat theETHEinsteinwasdeeplyinvolvedindevelopinghis theoryofgravity—what would become the general theory of relativity. But he too waslured away in 1914, this time to a prestigious and well-paid post in Berlin,where, free fromany teachingdutiesatall,hewasable tocomplete thisworkoverthenexttwoyears.All this left Zürich distinctly light in theoretical physics expertisewhen the

First World War began, and, partly because of the restrictions on movementbetweencountriescausedbythewar,eventhoughSwitzerlandwasneutral,thesituation did not improve for the rest of the decade. As far as teaching wasconcerned, two young Privatdozenten, Simon Ratnowsky (1884–1945) at theuniversityandMieczyslawWolfke(1883–1947)at theETH,didasterlingjob,updatingthelecturestoincludethelatestadvancesinquantumtheory.Buttheirresearch was solid second-division stuff, not material likely to attract theattentionoftheNobelCommittee.Towardstheendofthedecadetheybegantobeovershadowedbytheworkof theircolleagues,notablyPaulEpstein(1883–

1966), aquantum theoristwhoarrivedat theuniversity fromMunich in1919,and Hermann Weyl (1885–1955), who had been at the ETH since 1913 andwhosegrowingreputationhadreachedapeakwithamasterfulbookonrelativitytheory,Space–Time–Matter,publishedin1918.In1920PeterDebyereturnedtoZürichasDirectorof thePhysics Instituteat theETH,andwhenWolfkewentbacktohisnativePolandthefollowingyeartotakeupapostinWarsaw,thewayseemed clear for either Ratnowsky or Epstein to be promoted to the chair oftheoretical physics at the university, which had been vacant since von Laue’sdeparture nearly a decade earlier. But to the surprise of many at both Zürichinstitutions, itwas a relativelyunknownoutsider,ErwinSchrödinger,whogotthejob.Infact,theappointmentmadesense.AsIhavementionedinanearlierchapter,

thecommissioninchargeofmakingtheappointmenthadtriedtogetvonLaueback, but were unable to meet his financial expectations, and Epstein ruledhimselfoutinMarch1921byacceptingthepostinLeiden.Thephysicsfacultythen recommended Schrödinger on the grounds of his excellence as a teacherand his versatility, covering “the fields of mechanics, optics, capillarity,electrical conductivity, magnetism, radioactivity, gravitation theory, andacoustics”—alistinwhichquantumtheoryisconspicuoustomoderneyesbyitsabsence. One reference also mentioned that “he has a nice wife.” WhenSchrödingerarrivedinZürich,though,theymusthavewonderedifhewasuptothejob.

Personalproblemsandscientificprogress

The cause for concern was Schrödinger’s health. Mentally and physicallyexhausted by the events of the years since 1918,which included the death ofboth parents and a grandfather, as well as the economic difficulties and theproblemofsimplygettingenoughtoeat,hewasforcedtoabandonhislectureslessthanhalfwaythroughhisfirstterminZürichbyasevereboutofbronchitis.Respiratoryproblemspersistedthroughthewinter,culminatinginthediagnosisofamildcaseoftuberculosis.Inthe1920s,theonlytreatmentforTBwastorest,preferablyathighaltitude,

and hope for the best. The idea behind this “cure” was that high altitude

encouragesthebodytoproduceredbloodcells,whichwerethoughttofighttheinfection; in fact, in so far as the cure did any good at all, it was probablybecause,aswenowknow, theTBbacterianeedplentyofoxygen,which is inshort supply at high altitude, in order to thrive. Whatever the reason,Schrödinger’sstayat theAlpineresortofArosa,nearDavos,provedeffective.Hewas there—withAnny and a splendid cookwhoprepared all his favouritemeals—for nine months, returning to the university only in November 1922,wellafter thestartof theacademicyear.Suntannedbutweakand liable to tireeasily,hewas ready topickuphis teachingduties,although lackinganydrivefor his own research.Over the next few years, Schrödinger returned toArosaseveral times, including during the summer of 1925 and the followingChristmas,forholidaysandforthebenefitofhishealth.Remarkably, though, Schrödinger had completed two scientific paperswhile

convalescing inArosa in1922.Onewasamundanepieceofworkonspecificheats. But the other contained a nugget thatwould not be appreciated for thepuregolditwasuntil1926,afterSchrödingermadethebreakthroughforwhichhereceivedtheNobelPrize.TheproblemSchrödingeraddressedinthissecondpaperof1922wastheway

inwhich theorbits allowed for anelectron in theBohrmodelof theatomarequantized.HestartedfromanapproachdevelopedbyWeyl inhisbook,whichhadalreadybecomeastandardtext,andfoundthatforthenthorbitoutfromthenucleus a property known as the “unit ofmeasure” peaks n times around theorbit,withtroughsinbetween.AsSchrödingerputit:“Iftheelectroninitsorbitcarried along with it a ‘distance,’ which is transferred unchanged during themotion,thenthemeasureofthisdistancewould—ifonestartedfromanarbitrarypointontheorbit—alwaysbemultipliedbyanintegralmultipleofeν,exp(h/γ)whenevertheelectronreturnsapproximatelytoitsinitialposition.”Schrödinger did not attempt to find a physical explanation for this

mathematicalresult,althoughhedidsaythatitwas“hardtobelieve”thattherewasno“deeperphysicalmeaning” to it.But this is,ofcourse,exactly like thepictureofastandingwavesurroundingthenucleus.IfSchrödingerhadnotbeensodebilitatedbyhis illnessandexhaustedbyhis teaching,hemightwellhavecomeupwithhisBigIdeabytheendof1922,insteadofin1926.Therewasalsoamoresubtle,butnolessimportant, ideatuckedawayat the

end of the paper. Schrödinger pointed out that the equation he had foundcontained a number which could have either of two values. One of thesesolutionswasanordinarynumber—whatmathematicianscalla“real”number.

Buttheotherwaswhattheycallan“imaginary”number,meaningthatitisarealnumbermultiplied by the square root of −1,which is denoted by the letter i.Numberssuchas1,2,3...arereal;numberssuchasi,2i,3i...areimaginary.Such“imaginarynumbers”canbemanipulatedmathematicallyinjustthesameway as real numbers, and sometimes crop up in situations where they areregarded as physically meaningless and ignored. One place where imaginarynumbers cannot be ignored, though, is in the equations that describe thebehaviourofwaves.Butwhatweseeclearlywithhindsightwasnomorethanavaguehintofwhatwastocometoeventhesharpestmindsof1922.Schrödinger’steachingloadwasenoughtoslowthehoningofhisownsharp

mindashegraduallyrecoveredfromhisillness—inareversalofthesituationinmost universities today, in the 1920s the senior professors did most of theteaching,andinSchrödinger’scasethisamountedtoelevenhoursperweek.Hewas also distracted by the need to prepare and present his formal inaugurallecture as a professor,more than a year after his arrival at the university.Thesubjectofthetalk,givenon9December1922,wasoneclosetohisheart,ifnotquitewhattheaudiencemighthaveanticipated.

PhysicsandphilosophyThe title of the inaugural lecturewas “What Is aPhysicalLaw?”SchrödingertookashisstartingpointBoltzmann’sideasaboutthermodynamics,accordingtowhich the second law is merely a statistical rule that applies to very largenumbers of atoms and molecules, but individual atoms and molecules areunawareofit(sothatthereisno“arrowoftime”foracollisionbetweenasinglepairofatoms).SchrödingerwasinfluencedbyFranzExner,withwhomhehadworkedbefore thewar,whohad taken theextremepositionofarguing thatallnaturaleventsareanaccumulationofchanceoccurrences,andthatatthelevelofindividualatomsthereareno“lawsofnature.”Schrödinger’s ownpositionwas also influenced byEinstein’s discovery that

lightcarriesmomentum.Ifanatomejectedaparticlewhichcarriedmomentum,the atomought to experience a recoil, just as agun“kicks”backwardwhenabullet is fired from it. This obeys a rule known as the law of conservation ofmomentum, verified in countless experiments,which says that themomentumcarriedbythebulletinonedirectionisexactlyequaltothemomentumcarriedintheoppositedirectionbytherecoilinggun.Asmallbulletmovingathighspeed

hasthesameamountofmomentumasalargegunrecoilingmoreslowly.Butifanatomradiatesasphericalwaveoflightequallyinalldirections,asphysiciststhoughtitdidin1922,howcantherebeanyrecoil?In a letter to Weyl written while he was preparing his inaugural lecture,

Schrödinger said thathewasdriven toconclude that at the levelof individualatoms the lawofconservationofmomentumdidnothold.And if that lawdidnot hold, why should any of the other laws of physics? Schrödinger wasdoubtingtheveryideaofcausality,seeminglyabedrockofscience.Inhisownwords: “Physical research has clearly and definitely shown that chance is thecommonrootofallrigidconformitytoLawthathasbeenobserved,at least intheoverwhelmingmajorityofnaturalprocesses,theregularityandinvariabilityofwhichhaveledtotheestablishmentofthepostulateofuniversalcausality.”2

Thiswas completely counter to the viewofmost physicists, then and since,althoughSchrödinger’sclosestfriendinZürich,HermannWeyl,sharedsomeofhisideas.Themainstreamremainedfullyconvincedthatthebasiclawssuchasthe conservation of momentum apply with full force to collisions betweenindividual pairs of atoms or molecules (and, indeed, to subatomic particles).Evenin1922,Schrödingerwasskatingonthinicewiththeseideas.Ithadbeenknown fordecades that the lawsofconservationofenergyandmomentum, inparticular,areintimatelyboundupwithourunderstandingofthenatureofspaceand time. Specifically, if the laws are invariant, in the sense that they applyanywhereinspaceandatanymomentintime,theyhavetobeabsolutetruths,not statistical half-truths. And Schrödinger knew this! In the same lecture inwhich he suggested that physical laws might be only statistical in nature, headmittedthat“theEinsteintheory[thatis,thespecialtheoryofrelativity]innouncertain terms makes plain the absolute validity of the energy-momentumprinciples.” For once, in that lecture Schrödinger the philosopher clouded thejudgement of Schrödinger the physicist. But within a few years he hadcompletely reversed his position, and after the second quantum revolution hebecame,alongwithEinstein,oneof themostoutspokenopponentsof the ideathat chanceplayedapart indetermining theoutcomeof events at the levelofatomsandsubatomicparticles.Withtheinaugurallectureoutoftheway,Schrödingersettledintoaquietbut

steadylifeasauniversityprofessor.Hemaintainedanddevelopedhis interestsincolourvision,culminatingintheencyclopediaarticlecompletedin1925andpublished in 1926, and in statistical mechanics; and alongside this work hebegan to make minor, but significant, contributions to atomic and quantum

theory, moving on from the paper completed during his “cure” at Arosa. Hisoutput increased as his health improved, although for a long time he wastroubledbyapersistentcough.Eventhoughhepublishednothingatallin1923,between 1922 and his breakthrough work in 1926 Schrödinger published sixpapers on statistical mechanics, five (including the encyclopedia article) oncolour vision, four on specific heats, four on atomic structure, and one onrelativitytheory.It’sasignofSchrödinger’sstatusinthephysicscommunityatthistimethatin1924hewasinvitedtoattendaprestigiousscientificgatheringinBrussels,theSolvayCongress,butnottopresentapaperthere;hewashighlyregarded,butnotoneoftheélite.Schrödingerseemstohavehadaknackofbelievingtwocontradictorythings

atonce(oratleast,inturn),whichwasaninvaluableabilityforanyonetryingtoget to grips with the quantum world in the 1920s. Although in his inaugurallecturehefirmlyespousedtheideaoflighttravellingasawave,earlierin1922hehadpublishedapaperwhich tidiedupa looseend inquantumphysics (theterm “quantummechanics”was not introduced until 1924, in a paper byMaxBorn).ThisgaveafullmathematicaldescriptionoftheDopplereffect(thewaythe wavelength of radiation is affected by motion) within the context of thespecial theory of relativity, but based entirely on the idea of light quanta(photons) carrying momentum. This was before Compton’s experimentalconfirmation of the physical reality of Einstein’s light quanta. But he stillaccepted theevidencefromexperimentssuchasYoung’s that light travelsasawave.InthelettertoPeterDebyementionedearlier,hereferredtothisasa“fataldilemma”whichledhimtoconcludethatmomentumisnotconservedinatomicprocesses.Theideathatthelawsofphysicsmightonlybestatisticalrulesfittedinwith

Schrödinger’slongstandinginterestinstatisticalmechanics.Thiscontinuedtobepartofhisresearch,aswellashisteaching,inthefirsthalfofthe1920s.Aswellashispublishedworkonspecificheats,heplanned,butnevercompleted,abookon “molecular statistics.” In 1924, when the Indian physicist Satyendra NathBose(1894–1974)cameupwithanewwayofapplyingstatisticstolightquanta,and Einstein found other applications of the new idea, it was inevitable thatSchrödingerwould seize upon it anddelve into the implications.That delvingwouldleadhimtohismasterwork—drivenbyinspirationnotjustfromphysics,butalsofromhisprivatelife.

LifeandloveLifeinZürichwasprettygood.TheSchrödingersmovedinacircleofacademicsandintellectuals.Therewasalivelynightlife,whichdidn’tparticularlyappealtoErwin,butalsotheatreandtheopera,whichcertainlydid.WhenAnnywantedtogotooneofthefineballsinthecity,shewentwithoneoranotherofErwin’sfriends,whilehestayedathome. Insummer,groupsof friendswould take thesteamertotheislandofUfenauforpicnickingandswimmingexcursions,givingErwin a chance to admire the pretty girls and engage in somemild flirtation.SomethingmorethanmildflirtationsoondevelopedbetweenAnnySchrödingerandWeyl.InanechooffindesiècleVienna,liaisonsbetweenmarriedmembersof the academic set and others who were not their spouses were regarded asnormal, and nothing tomakemuch fuss about. In this particular circle, AnnySchrödinger and Hermann Weyl (known as Peter among his friends) soonbecame an item, as did Weyl’s wife, Hella, and the physicist Paul Scherrer(1890–1969),oneofDebye’sprotégés,wholaterbecameheadofphysicsattheETH.Erwinenjoyedseveralbriefaffairs,buttherelationshipbetweenAnnyandWeylwentdeeper,andtherewaseventalkofdivorce,partlyfuelledbyErwin’sdisappointmentthathismarriagewithAnnywaschildless.But,asweshallsee,theyfoundotherwaystoresolvethesituation.Schrödinger also toyed with the idea of getting a “divorce” from the

UniversityofZürich.TheseedwassownwhenheattendedameetingofGermanscientistsinInnsbruck,inSeptember1924.WithGermanythenattheforefrontofresearchinphysics,manyofthebignamesinvolvedinwhatwasnowcomingto be known as quantum mechanics were there. Once again Schrödinger,althoughactively involved in the scientificdiscussions,didnotmakea formalcontributiontotheproceedings;buthewashappytobebackinAustria,where,asinGermany,thingsseemedtobesettlingdownatlastaftertheturmoiloftheFirstWorldWar, inspiteofsomerecentunrest—itwasnowfivemonthssinceAdolfHitler (a fellowAustrian) had been sent to gaol,where hewaswritingMeinKampf,forhispartintheMunich“beer-hallputsch.”Oblivioustohowthiswouldaffecthis life,whenSchrödingerwas invited in the summerof1925 totakeupaprofessorshipinInnsbruckhewasverytempted,notleastbywhathereferred to as the “gilded” memory of his visit the previous autumn. “TheSwiss,”hewrotetofellowphysicistArnoldSommerfeld(1868–1951),“arefartoocheerless.”HiscorrespondencerevealsthatinhisownmindSchrödingerhaddecidedby

January1926 to turndown theoffer,but thathestrungout thenegotiations inordertoobtainleverageforanimprovementintheconditionsinZürich—anewblackboardandalargerbudgetforthephysicslibrary.HeofficiallydeclinedtheinvitationtoInnsbruckonlyinMarch1926,afterthefirstofhisground-breakingpapersonquantummechanicshadbeenpublished.While thiswasgoingon,Schrödingerbecame involved inacontroversy that

couldhavehadseriousrepercussions,andcastapermanentslightpalloverhisreputation.Einstein’sspecialtheoryofrelativityisbaseduponthepostulatethatthemeasuredspeedoflightisthesameforallobservers,nomatterwheretheyareorhowtheyaremoving,andthis isborneoutbyavarietyofexperiments.Thekeypracticalevidence,asofthe1920s,camefromaseriesofexperimentscarriedoutbyAlbertMichelson(1852–1931)andEdwardMorley(1838–1923),datingbacktothe1880s.In1921,asimilarexperimentwascarriedoutatthetopof Mount Wilson, the site of an astronomical observatory in California, andseemedtoshowaslightlydifferentresultfrommeasurementsmadeatsealevel.Itwas thisclaimthatpromptedEinstein toexpresshisdisbeliefbymakinghisfamouscomment“TheGoodLordissubtle,butheisnotmalicious.”But others were malicious. Anti-Semites in Germany had long rejected

Einstein’s“Jewish”theory,andtheyseizeduponthis“evidence”ofhisfallibility.OneoftheleadingphysicistsinGermany,PhilippLenard,wasanotherAustrianwhosharedsomeoftheseunsavouryviews.In1922,whentheGermanforeignminister, the Jewish Walther Rathenau, had been assassinated, Lenard, asDirector of the Physics Institute inHeidelberg—which became notorious as acentreofright-wingactivism—hadrefusedtohavetheflagloweredtohalf-mast,andhadtobetakenintoprotectivecustodytosavehimfromtheresultingwrathof themob.Theextentof theundercurrentofunthinkinganti-Semitism rifeatthetimecanbegleanedfromSchrödinger’sowncommentontheMountWilsonexperiment, that it “is very important, but it has been played down in Jewishcirclesofphysicists.”HeurgedthattheexperimentberepeatedontheJungfrau,andwasquiteunfazedwhenitwassuggestedthatamemberoftheHeidelbergInstitutewouldbetherightmanforthejob.Others doubted whether any of Lenard’s protégés would give an honest

appraisal;butSchrödingerfuriously insisted that thescientific truthwouldout,whateverthepoliticsoftheexperimenter.Intheevent,aHeidelbergteamdiddothe experiment and it proved that Einstein was correct. So, in a sense, wasSchrödinger;butalthoughheseemstohaveactedfromanapoliticalstandpoint,the incident established a perceived connection between him and the political

right.Butattheendof1925Schrödinger’smindwasfocusedonphilosophy,rather

thanpolitics.Hewasnowinhis late thirties, farpast theagewhenmostgreattheoristsmake theircontribution toscience,andsettled inwhatcouldbea jobforlifeinasafe,secure,butdullsetting.Itwasagainstthisbackgroundthathesatdownandwroteasummaryofhisphilosophicalviewsonthenatureof theworld, which was published much later asMeineWeltansicht (translated intoEnglishasMyViewoftheWorld).

“Myworldview”TheopeningpartofSchrödinger’s1925essayshowsthathewaswellawareofwhatwashappeninginEuropeatthetime,andstilldeeplytroubledbyhisownexperiences.Hewrote:“Asortofgeneralatavismhassetin;westernmanisindanger of relapsing to an earlier level of development which he has neverproperlyovercome:crass,unfetteredegoismisraisingitsgrinninghead,anditsfist, drawing irresistible strength from primitive habits, is reaching for theabandonedhelmofourship.”It is hardly surprising that Schrödinger, appalled by this vision, should be

drawntotheVedanticviewoftheworld.InMeineWeltansicht,hedescribestheidea of “a soul dwelling in the body as in a house, quitting it at death, andcapable of existing without it” as “naively puerile,” and asks four questionswhich,he says, cannotbeanswered“yes”or“no”but“leadone inanendlesscircle”:

DoesthereexistaSelf?DoesthereexistaworldoutsideSelf?DoesthisSelfceasewithbodilydeath?Doestheworldceasewithmybodilydeath?

TheheartoftheessayisSchrödinger’sversionof“TheVedanticVision,”whichresolvesthesequestionsbyarguingthatthereisonlyoneconsciousness,andthatwe(and,indeed,therestof“nature”)arepartofit,likethedifferentfacetsofamany-facetedjewel:Itisnotpossiblethatthisunityofknowledge,feelingandchoicewhichyoucall your own should have sprung into being from nothingness at a givenmoment not so long ago; rather this knowledge, feeling and choice are

essentiallyeternalandunchangeableandnumericallyoneinallmen,nayinallsensitivebeings...you—andallotherconsciousbeingsassuch—areallinall.

ThisoneuniversalbeingiswhatisknownasBrahman.“Itisthevisionofthistruth,”saysSchrödinger,“whichunderliesallmorallyvaluableactivity.”Intherestofhisessay,Schrödingerturnshisattentiontoevolutionarybiology,

consciousness, and the process of heredity.Although he strikingly asserts thatwhathiscontemporariesdelight incalling theageof technology“will insomelater time” be described “as the age of the evolutionary idea,” the only realinterest in this part of his essay today is that it showshis fascinationwith theprocess of inheritance, whichwould reach fruition two decades later with hisbook What Is Life?. But the essay was not published until 1961,3 whenSchrödingeraddedasecondessay,“WhatIsReal?,”totheslimvolume.Writtenin 1960, this essay contains the dramatic statement: “I have therefore nohesitation in declaring quite bluntly that the acceptance of a really existingmaterialworld,astheexplanationofthefactthatweallfindintheendthatweareempiricallyinthesameenvironment,ismysticalandmetaphysical.”Inotherwords, nothing is real. Although Schrödinger reached this conclusion onmetaphysicalgrounds,itresonatedstronglywithastandardinterpretationoftheimplicationsofthesecondquantumrevolution,inwhichheparticipatedin1926.SchrödingerwaspulledbackfromhisphilosophicalmusingsandthequietlifeinZürich to become one of the leading participants in this revolution by thediscoveryofanewway—therightway—tocountphotons.

QuantumstatisticsThediscoverycamefromtheIndianphysicistSatyendraNathBose,viaAlbertEinstein.WorkinginDacca,farawayfromtheEuropeancentreswherequantumphysics was being developed, but keeping in touch by reading the scientificpapersbeingpublishedbythequantumpioneers,Bosecameupwithhisbigideain1924,at theageof thirty.Hefoundthatbyusinganewkindofstatistics tocount photons he could derive the Planck black body law entirely from thedescriptionoftheradiationinacavityasaquantum“gas”ofparticles,withoutinvokingwavesat all.After theEnglish-languageversionof apaper reportinghisdiscoverywasrejectedbythePhilosophicalMagazine,herealizedthatsuchaclaimmightnotbetakenseriouslycomingfromanunknownIndianresearcher,

andsentittoEinstein,requestinghimtopassitonforpublicationifhelikedit.EinsteinwassoimpressedthathetranslatedthepaperintoGermanhimselfandsent it to the prestigious journal Zeitschrift für Physik, where it appeared inAugustthatyear.Itisnocoincidencethatthename“photon”wascoinedtorefertoaparticleoflightjusttwoyearslater.Einstein himself then developed the idea further, applying it to describe the

behaviourofanyhypotheticalcollectionofatoms—gasor liquid—obeying thesame rules. Those rules became known as Bose-Einstein statistics, and theyapply to all the quantum entities, such as photons, which are associated withforces (in this case, the electromagnetic force). Such particles are known asbosons. The rules that apply to what we think of as material particles in theeverydaysense (things likeelectrons)becameknownasFermi-Diracstatistics,aftertwooftheotherquantumpioneers,andtheparticlesareknownasfermions.Thekeydistinctionisthatanynumberofidenticalbosonscanexistinthesamequantumstate,butnotwoidenticalfermionscanexistinthesamequantumstate—that is,with identical quantumproperties.Fermions are also “conserved” ininteractions—youcannotincreasethenumberofelectronsintheUniverse—butbosonscanbemanufacturedindefinitelyifthereisasourceofenergy,whichiswhathappenswhenyouswitchalighton.ThediscoveryofBose-Einsteinstatistics,andtheimplications,werehottopics

among the cognoscenti at the Innsbruck meeting Schrödinger attended inSeptember1924.ThecontactSchrödingerhadwithEinsteinandPlanckat thatmeeting set him thinking about a new line ofwork on quantum statistics, gastheory, entropy, and statistical mechanics. He developed this thinking during1925, corresponding with Einstein on the subject throughout that year. ThecorrespondenceshowsthatatfirstSchrödingerthoughtthatBosehadmadeonlya minor tweak to Planck’s calculation, and it was only through Einstein’sexplanationthatherealizedthefundamentalnatureofBose’scontribution.TheEinsteinconnectionthenpointedSchrödingertowardshismasterwork.In1924,theFrenchphysicistLouisdeBroglie(1892–1987)hadsuggestedin

his PhD thesis that just as light, traditionally regarded as awave, behaved insomecircumstanceslikeastreamofparticles,soelectrons,previouslyregardedas particles, could in some circumstances behave as waves. De Broglie’ssupervisor, Paul Langevin, was so nonplussed by this that he asked Einsteinwhether or not to approve the thesis; Einstein said the idea was sound,4 deBrogliegothisdoctorate,andthework(ofwhichmoreinChapter7)wasalsopublished in the journal Annales de physique at the beginning of 1925.

Somehow, Schrödinger remained blissfully ignorant of all this until he saw inoneofEinstein’spapersareferencetodeBroglie’sideawiththecommentthat“onewasdealingwithmore thana formalanalogy”—inotherwords,Einsteinthought the waveswere real. Schrödinger still didn’t realize that de Broglie’sworkhadbeenpublishedintheAnnalesdephysique,whichhecouldhavefoundinthelibraryattheuniversity,butheobtainedacopyofthethesisalmostexactlya year after de Broglie had presented it in Paris. On 3 November 1925,SchrödingerwrotetoEinstein:“AfewdaysagoIreadwiththegreatestinteresttheingeniousthesisofLouisdeBroglie,whichIfinallygotholdof.Becauseofit,[your]workhasalsobecomecompletelycleartomeforthefirsttime.”AftermentioningthattherewassomeconnectionbetweendeBroglie’sideasandtheshortpaperhehadhimselfpublishedin1922,Schrödingerwenton:“Naturally,de Broglie’s consideration within his grand theory is altogether of far greatervaluethanmysinglestatementwhich,atfirst,Ididnotknowwhattomakeof.”Within a fewweeksof readingdeBroglie’s thesis,Schrödingerdeveloped a

complete, self-consistent theory of the quantum world, based on the idea ofwaves.Butafewmonthsearlier,theGermanWernerHeisenberg(1901–76)haddevelopedacomplete,self-consistenttheoryofthequantumworld,basedontheideaofparticles.Whatwasgoingon?Thetwindiscoverieswouldsparkdebatethatcontinuestothepresentday,andwouldprofoundlyaffectSchrödinger;butbefore I pick up the thread of his story, I need to digress to tell the story ofHeisenberg’s discovery of what became known as matrix mechanics. If youalreadyknowthatstory,andinparticularifyouhavereadmybookInSearchofSchrödinger’sCat,feelfreetoskipstraightontoChapter7.Ifnot,justturnthepage.

Notes

1Strictlyspeaking,heonlybecamea“von”in1913,whenaminortitlewasbestowedonhisfather.2Fromtheversionofhislecturepublishedin1929,asquotedbyMehraandRechenberg,TheHistoricalDevelopmentofQuantumTheory.3AndnotpublishedinEnglishuntil1964.4HeactuallycommentedtoLangevinthatdeBrogliehad“liftedacornerofthegreatveil.”

ChapterSix

MatrixMechanics

WhenWernerHeisenbergmadethediscoveryofmatrixmechanics,hewasevenyounger than the year of his birth might suggest. As he had been born on 5December 1901, he was still only twenty-three in the spring and summer of1925,atthebeginningofhiscareerinresearch.Buthehadalreadyshownsignsofaprecocioustalent.Heisenbergwasamong thefirstgenerationofphysicists tobebroughtupon

quantum ideas. Between 1920 and 1923 he studied physics andmathematics,first with Arnold Sommerfeld andWilhelmWien in Munich, then with MaxBorn(1882–1970)inGöttingen.HewaskeenlyinterestedinNielsBohr’sideasabout the behaviour of atoms, and in 1922, although still a student, thanks toSommerfeld’s recommendation hewas allowed to attend amajor gathering inGöttingenknownasthe“BohrFestival.”1HerehemetBohrhimselfandheardhim give a series of lectures on quantum physics. In his book Physics andBeyond,Heisenberglaterdescribedthesituationinquantumphysicsatthattimeas a “peculiar mixture of incomprehensible mumbo jumbo and empiricalsuccess.” But this “naturally exerted a great fascination.” Although he wasappointedasaPrivatdozentinGöttingenin1924,betweenEasterthatyearandspring1925Heisenberghad thebenefit ofworkingwithBohr inCopenhagen,thankstoaRockefellerfellowship.

Half-truthsTheworkthatfirstmadeSommerfeldtakenoticeofHeisenbergwascarriedoutwhentheyoungmanwasstillastudent.By1920,physicistshadbecomeusedtotheideaofdescribingthequantumstateofasystem(suchasanatom)intermsofquantumnumbers,anditwasalmostanitemofHolyWritthatthesealwayshadtobewholenumbers—integerssuchas1,2,3...ButHeisenbergrealizedthat certain puzzling features of atomic spectra could be explained if the

calculations included half-integer quantum numbers, such as 1/2, 3/2, 5/2 . . .Sommerfeldwasnotimpressed,andHeisenberg’sfriendWolfgangPauli(1900–58)“suggestedthatIwouldsoonhavetointroducequartersandeighthsaswell,until finally the whole quantum theory would crumble to dust in my capablehands.”SoHeisenbergdidnotpursuetheidea.Butafewmonthslateranolder,established physicist, Alfred Landé (1888–1976), hit upon the same idea andpublishedit.Itturnedoutthat,farfrommarkingthecrumblingawayofquantumtheory,the

concept of half-integer quantum numbers was a key to understanding thequantumworld,andalso that therewouldbenoneedfor thequarters,eighths,andsoonthatPaulihadfeared.This isbestunderstoodin termsofaquantumpropertyknownasspin.Thespinofanentitysuchasanelectroncanbethoughtof as an arrow which has a certain size but can only point in one of twodirections, up or down. Electrons which have opposite spin do not count asidentical particles, but electrons with the same spin do count as identicalparticles,andthisaffects thewaytheybehaveinatoms.But it isbest to try toavoidtheautomaticimagethattheterm“spin”conjuresup;thingslikeelectronsdonotbehave likespinning topsor twirling ice-skaters,andquantumspin isapurely quantum property that has no analogy in the everyday world. It is anunfortunatechoiceofterminologythatwearestuckwith.Whatevernameitgoesby, though,quantumspinis thekeytounderstanding

quantumstatistics.Objectsthathaveintegerorzerospin,suchasphotons,obeytherulesofBose-Einsteinstatistics.Objectsthathavehalf-integerspin,suchaselectrons,obeytherulesofFermi-Diracstatistics.ButthisrealizationstilllayinthefuturewhenHeisenbergreturned toGöttingen inApril1925 to takeuphisdutiesforthesummerterm.

WhatyouseeiswhatyougetLikemany physicists at the time,Heisenbergwas puzzling over the nature ofelectronorbits,thewayelectrons“jump”betweenorbits,andhowthisjumpingproducesthelinesseeninatomicspectra.Hewasboggeddowninamorassofmathematicswhen,lateinMay1925,hewasstruckbyanattackofhayfeversosevere that he had to ask his professor, Max Born, for leave of absence torecover.Hewasgranteda two-weekbreak,andon7Junewent straight to therockyislandofHeligoland,farfromanysourcesofpollen.

Heligoland is a tiny island, less than a square mile in area and rising onlyabout60metresabovethesea,locatedinthecorneroftheNorthSeaknownasthe German Bight. Because of its location, ownership of the island changedmanytimesuntil1714,whenitwastakenoverbyDenmark.In1807,HeligolandwascapturedbytheBritishduringtheNapoleonicWars,andtheyheldontoituntil 1890, when it was swapped with Germany for the African island ofZanzibar. When Heisenberg arrived there, after a three-hour journey by shipfromCuxhaven,atthemouthoftheElbe,itwasafadingseasidesparesort.“Imusthavelookedquiteasight,”hetellsus,“withmyswollenface;inanycase,my landlady took one look at me, concluded that I had been in a fight andpromisedtonursemethroughtheaftereffects.”2Butnonursingwasrequired,asthecleanairquicklyrestoredhimtofullfitness,andinbetweenlongwalksandlong swims,with no distractions “Imademuch swifter progress than IwouldhavedoneinGöttingen.”Apart from the lack of any distractions on the island, the reason why

Heisenbergmadesuchswiftprogresswasthathetriedanewwayoftacklingtheproblemofquantumjumps.SomebodyinthegroupinGöttingen—nobodycouldlater recall exactlywhich of them came upwith the idea, but themost likelycandidateisPauli—hadpointedoutthattherewasnowayofknowingwhatwashappening to an atom, or any other quantum entity, when it was not beingmeasured.You couldmake ameasurementwhich showed the atom to be in acertainquantumstate,thenmakeanothermeasurementwhichshowedittobeinanotherquantumstate,butyouhadnowayoftellingwhathadactuallyhappenedtotheatominbetweenthosemeasurements.Theideagrewupamongthegroupthat theonlyreality thatcouldbedescribedbyscientificmeasurementwas therealityof themeasurements themselves,andthataphysical theoryshouldonlybeconcernedwiththingsthatcanactuallybeobservedbyexperiments.Inotherwords,whatyouseeiswhatyouget;neithermorenorless.Heisenberghadbeenabitdubiousaboutthisideaatfirst—itsmackedtoomuchofthephilosophicaldebateaboutwhetheratreefallinginaforestmakesasoundifthereisnobodythere tohear it—buthedecided toseehowsucha theorymightbedeveloped,andthepiecesquicklyfellintoplace.The crucial thing about observations of quantum systems is that each

observationdealswithtwostatesatatime.Measuringtheenergyofaparticularlineinanatomicspectrum,forexample,tellsusabouttherelationshipbetweenthe two quantum states involved in the process of absorbing or emitting aphoton. SoHeisenberg beganworkingwith amathematical description of the

relationshipbetweenpairsofobservablequantumstates.Intheprocess,hefoundthat he had toworkwith a particular kind ofmathematical entity, a bit like atableofnumbers,thatdescribedeachquantumstate.I’vebeenwritingaboutquantumphysicsformorethanthirtyyears,andinall

that time I’ve never been able to come up with a better analogy for thesemathematical entities than that of a chess boardwith pieces arranged on it.Achess board is a two-dimensional array of sixty-four squares, and each squarecan be identified by a letter-number combination, starting with a1 andproceedingthrougha2,a3,andsoonallthewayuptoh8.The“state”ofachessgame can be described by an additional letter to tell you which squares areoccupiedbywhichpieces—forexample,Qc7wouldmeanthatthereisaqueenon the square c7 (for simplicity, I’ll ignore the difference between black andwhitepieces).Heisenbergusedarraysofnumbersnotunlikethistodescribethequantum state of a system, and worked out the rules for describing the wayquantumsystemsinteracttochangetheirstates—ineffect,multiplyingthearraysofnumbers together,andperformingothermathematicalmanipulations.As themathematicaldescriptionbegantofall intoplace,hedecidedtoapplyacrucialtestbycalculatingwhether the lawofconservationofenergywaspreserved inhiscalculations:Whenthefirst termsseemedtoaccordwiththeenergyprinciple,Ibecameratherexcited,andIbegantomakecountlessarithmeticalerrors.Asaresult,it was almost three o’clock in the morning before the final result of mycomputationlaybeforeme.Theenergyprinciplehadheldforalltheterms,andIcouldnolongerdoubtthemathematicalconsistencyandcoherenceofthekindofquantummechanicstowhichmycalculationspointed.AtfirstIwas deeply alarmed. I had the feeling that, through the surface of atomicphenomena, Iwas looking at a strangelybeautiful interior, and felt almostgiddy at the thought that I now had to probe thiswealth ofmathematicalstructuresnaturehadsogenerouslyspreadoutbeforeme.Buthewouldnothave tocarryout theprobingalone.WhenHeisenberggot

back toGöttingenandshowedhisworking toBorn,Bornsoon recognized thetables of numbers as examples of a kind of mathematical entity known tomathematicians (but to very few physicists in 1925) as matrices. A paper byHeisenbergannouncinghisdiscoverywassentoffforpublicationinZeitschriftfür Physik, and Heisenberg himself went off in the summer of 1925 to givelectures in Leiden and Cambridge. Although he did not mention his

breakthroughinthelectures,hediddiscussitprivately;andwhilehewasaway,Born and his junior colleague Pascual Jordan (1902–80) developed the theoryfurther using the language of matrices, establishing what became known asmatrix mechanics. As Heisenberg commented to Pauli, “It seems as if theelectronswillnomoremoveonorbits.”

Matricesdon’tcommuteThe task of theGöttingen teamwasmademuch easier by the stroke of goodfortunethatBornwasoneofthefewphysicistsofthetimealreadyfamiliarwithmatrices. He had had an unusually broad education, having first studied atBreslau, where his father was Professor of Anatomy, and also at Heidelberg,Zürich, and Göttingen, where he concentrated initially on mathematics ratherthan physics.He had learned aboutmatrices inBreslau.Apaper byBorn andJordanextendingHeisenberg’sworkwassentoffforpublicationjusttwomonthsafter Heisenberg’s breakthrough paper, and before the end of 1925—beforeSchrödinger had completed his first paper on what would become known aswavemechanics—Heisenberg,Born,andJordanhadtogethercompletedathirdpaperonmatrixmechanics.ThekeycontributionmadebyBornandJordanwasto stress the central importance of the fact that when you multiply matricestogether the answer you get depends on the order in which you do themultiplication. In otherwords,a ×b is not the same asb ×a. This had beenimplicit,butnotspelledout,inHeisenberg’soriginalpaper.In the language of mathematics, matrices do not commute. And using bold

letterstodenotematrices,withpandqrepresentingthequantumequivalentsofmomentumandposition,respectively,BornandJordanfoundthat

wherehisPlanck’sConstantandiisthesquarerootof−1.Thisrelationshipisso important that it has becomeknown as the fundamental equation ofmatrixmechanics, and it is engraved on Born’s tombstone. It is an important point,valid throughoutquantummechanics, that if thevalueofhwereactuallyzero,the equations would boil down to the equations of classical (Newtonian)mechanics;inthisparticularcase,wewouldhavepq=qp.But the Göttingen team were not the only ones who had been busy in the

secondhalfof1925.InJulythatyear,whenhewasinCambridge,HeisenberghaddiscussedhisworkwiththephysicistRalphFowler(1889–1944),andonhis

return to Göttingen he sent Fowler a copy of his paper, which arrived inCambridge inAugust.Fowlerpassed thepaperon tohis researchstudentPaulDirac (1902–84), who was just eight months younger than Heisenberg. LikeBorn and Jordan, Dirac realized the fundamental importance of the non-commutativityofthevariablesinquantummechanics—thefactthatmatricesdonot commute—andworking entirely independently,with no knowledge of thework underway inGöttingen, he reworked the entire theory using an elegantbranch of mathematics developed in the nineteenth century by the IrishmathematicianWilliamHamilton(1805–65).Acopyoftheresultingpaperwassent to theGöttingen team, andBorn later described it as “oneof thegreatestsurprisesofmyscientific life.For thenameDiracwascompletelyunknowntome,theauthorappearedtobeayoungster,yeteverythingwasperfectinitswayandadmirable.”Theauthor, indeed,wasstillastudent!Dirac’sPhD,whichhegained in 1926 for a thesis simply titled “QuantumMechanics,”was the firsteverawardedforquantummechanics.Diracwas undoubtedly the greatest genius of all the people involved in the

discoveryofquantummechanics,andalso“thestrangestman,”inthewordsofhis biographer Graham Farmelo, almost certainly because he suffered from aformofautism.Dirac’spaper,whichalsotookfullaccountoftheneedforhalf-integerquantumnumbers,waspublishedintheProceedingsoftheRoyalSocietyinDecember1925.HeisenbergwrotetoDirac:“Ihavereadyourextraordinarilybeautifulpaperonquantummechanicswith thegreatest interest,and therecanbenodoubtthatallyourresultsarecorrect...[thepaperis]reallybetterwrittenandmoreconcentratedthanourattemptshere.”SoSchrödingerwasactuallythethirdpersontocomeupwithacomplete,self-

consistenttheoryofquantummechanics.Beforelong,theirachievementswouldberecognizedbytheNobelCommittee—butwithonescandalousexception.

Justiceisn’talwaysdoneIt soon became clear, as I shall explain in the next chapter, how thework ofHeisenberg, Born, Jordan, Dirac, and Schrödinger could be combined tocomplete the quantum revolution. Armed with the new equations, physicistsfound that problems that had seemed intractable fell like toppling dominoes.Muchlater,inhisbookDirectionsinPhysics,Diracwrote:Itwasagame,averyinterestinggameonecouldplay.Wheneveronesolved

oneofthelittleproblems,onecouldwriteapaperaboutit.Itwasveryeasyin thosedaysforanysecond-ratephysicist todofirst-ratework.Therehasnotbeensuchaglorioustimesincethen.Itisverydifficultnowforafirst-ratephysicisttodosecond-ratework.

By1928,thevariouspeoplewhohaddiscoveredtherulesofthisnewgamewerealreadybeingnominatedforNobelPrizes.IntheirwisdomtheNobelCommitteefoundonecunningwaytosharetheglory,butalsomadeoneglaringomission.ThereisarulethatasingleNobelPrizecannotbesharedbymorethanthree

people,soamoresubtlewayhadtobefoundtohonouralltheparticipantsinthesecond quantum revolution. The solution the committee came upwithwas toholdthe1932physicsprizeoveruntil1933,andthentoawardthe1932prizetoHeisenberg, and the 1933 prize jointly to Schrödinger andDirac, so that theycouldallbehonoured togetherat the sameceremony.This raises twopuzzles.Whyweren’tBornandJordanhonoured?AndifthehonourswereonlygoingtoHeisenberg,Schrödinger,andDirac,whynotletthemshareasingleprize?Wemay never know for sure, but themost likely explanation is that by the

beginning of 1933 the committee had decided to award the 1932 prize toHeisenberg,Born,andJordan,andthe1933prizetoSchrödingerandDirac.ButatthebeginningofMay1933JordanjoinedtheNaziParty,justatthetimeHitlerwascomingtopowerinGermany.Unwillingtobeseentoendorseanavowedsupporter of Hitler’s activities, the committee removed both Born and Jordanfromconsideration,sinceitwouldbeimpossibletodisentangletheirjointworkandawardaprizetoeitherofthemalone.TheresultwasembarrassmentforHeisenberg,andwhatBornperceivedasa

humiliation for himself; hewas, after all, the seniormember of theGöttingenteam.HeisenbergwrotetoBornexpressinghisbadfeelingsatreceivingtheprizeonhisownfor“workdone inGöttingen incollaboration—you,JordanandI.”Bornwasbitterabouthisomissionfordecades.In1953hewrotetoEinstein:“Inthose days [Heisenberg] actually had no idea what a matrix was [until I toldhim]. Itwas hewho reaped all the rewards of ourwork together, such as theNobel Prize.”He also commented: “The fact that I did not receive theNobelPrizein1932togetherwithHeisenberghurtmeverymuchatthetime,inspiteofakindletterfromHeisenberg.”WhenBornfinallydidreceiveaNobelPrizein1954attheageofseventy-one,nobodywasmorerelievedthanHeisenberg.Buteventhisawardhadastinginitstail.The award came for Born’s second major contribution to the quantum

revolution,which involved the idea that theoutcomeofevents in thequantumworld depends on chance and probability—in effect, on the roll of dice. Thisidea,asIshallexplain,wasanathematoafewphysicists,notablyEinsteinandSchrödinger;itwasthetriggerforSchrödinger’sfamouscat“experiment.”Butitbecamethestandardwaythatmostphysiciststhoughtaboutthequantumworldfromthelate1920sonward.BecausemanyoftheassociatedideaswerethrashedoutduringscientificgatheringsatNielsBohr’sInstituteinCopenhagen,thiswayof looking at the quantum world became known as the CopenhagenInterpretation—or,asBorngrumbledtoEinstein,the“Copenhagenschoolwhichtoday lends its name almost everywhere to the line of thinking I originated.”Born exaggerates slightly, but his ideaswere seen as the key to incorporatingSchrödinger’s wave mechanics into the broader picture—even thoughSchrödingerhimselfdidn’tlikethatpicture.TimetogetbacktoSchrödinger’sworkinZürichattheendof1925.

Notes

1Oneofthedreadfulsemi-punsthatdelightsomescientists;Bohr=Beer.2ThisandthefollowingquotationsinthissectionarefromHeisenberg’sPhysicsandBeyond.

ChapterSeven

SchrödingerandtheSecondQuantumRevolution

EarlyinNovember1925,PeterDebye,attheETH,askedSchrödingertopreparea talk for theZürichphysicists aboutdeBroglie’swork,whichhehad read inAnnales de physique. This was part of a regular series of informal colloquiahostedalternatelybytheETHandtheuniversity,eachattractinganaudienceofmaybe a dozen or two dozen people. The date on which this particularcolloquium took place has not been recorded, but it must have been in lateNovemberorearlyDecember,beforetheendoftheacademicterm.InatalkhegavetotheAmericanPhysicalSocietyin1976,1theSwissphysicistFelixBloch(1905–83),whowasastudentattheETHin1925,recalledthatSchrödingergaveabeautifullyclearaccountofhowdeBroglieassociatedawavewithaparticleandhowhecouldobtainthequantizationrulesofNielsBohr and [Arnold] Sommerfeld by demanding that an integer number ofwavesshouldbefittedalongastationaryorbit.Whenhehadfinished,Debyecasuallyremarkedthathethoughtthiswayoftalkingwasratherchildish.Asa studentofSommerfeldhehad learned that, todealproperlywithwaves,onehadtohaveawaveequation.Itsoundedquitetrivialanddidnotseemtomakeagreatimpression[onthegroup],butSchrödingerevidentlythoughtabitmoreabouttheideaafterwards.Schrödinger’sfirstthoughtwastoattempttofindawaveequation,movingon

fromdeBroglie’swork,thatwoulddescribethebehaviourofanelectroninthesimplestatom,hydrogen.Henaturallyincludedinhiscalculationsallowancefortheeffectsdescribedbythespecialtheoryofrelativity,deriving,probablyearlyinDecember 1925,what became known as the relativistic hydrogen equation.Unfortunately,itdidn’twork.Thepredictionsoftherelativisticequationdidnotmatch upwith observations of real atoms.We now know that this is becauseSchrödingerdidnotallowforthequantumspinoftheelectron,whichishardlysurprising, since the idea of spin had not been introduced into quantum

mechanicsatthattime.Butitisparticularlyworthtakingnoteofthisfalsestart,since ithighlights thedeepandmuddywaters inwhichquantumphysicistsgoswimming—foryouneedtotakeaccountofspin,apropertyusuallyassociatedwithparticles,inordertoderiveawaveequationfortheelectron!But Schrödingerwasn’t stymied for long.With theChristmas break coming

up,hehadanopportunitytogetawayfromZürichandthinkthingsoverinthecleanairofArosa.Inspirationdidnot,however,comesolelyfromthefreshairandmountainviews.

ScienceandsensualityAlthoughSchrödingerhadmanyaffairswithwomen,thesewereseldom,ifever,casual relationships. Judging fromhisdiaries, lovewasmore important tohimthansex,althoughoftensexnaturallyhaditsplaceinalovingrelationship.Hewasofteninlove—orconvincedhimselfthathewasinlove—andwhenhewasinlove,byandlargelifewasgoodandhisscientificcreativitybenefited.Whichis one reasonwhy this aspect of Schrödinger’s private life cannot be ignored,eveninascientificbiography(thereisanotherreason,too,whichIshallcometoshortly). Even the science historian Abraham Pais, hardly known for hisprurience,feltitnecessary,whentryingtoexplaininhisbookInwardBoundthebafflingsuccessofthirty-eight-year-oldSchrödingerinDecember1925,toreferto“theremarkoncemadetomebyHermannWeylthatSchrödingerdidhisgreatwork during a late erotic outburst in his life.” Weyl, of course, was AnnySchrödinger’slover,sopresumablyknewwhathewastalkingabout.The point is that Schrödingerwas not alone inArosa. For the previous two

ChristmaseshehadbeentherewithAnny;butthistimehewasaccompaniedbyanoldgirlfriend fromVienna.Wedon’tknowwhoshewas,becausealthoughSchrödinger’s diaries are usually quite explicit on such matters, the relevantvolume is missing.Whoever she was, though, she seems to have triggered aburst of creative activity which carried Schrödinger right through 1926,producing six major scientific papers on what became known as wavemechanics.Butitallbeganwithwhatlooksatfirstlikeabackwardstep.Toputit in context,weneed to take a quick look atwhat itwas that deBroglie hadactuallydone.LouisdeBroglieverynearlydidn’tbecomeaphysicist.Astheyoungersonof

aFrenchnoblefamily(helaterinheritedthetitle“Prince”fromhiselderbrother,

Maurice), he initially studiedhistoryandwasexpected to enter thediplomaticservice.ButMaurice,whowasseventeenyearsolderthanLouis,hadbecomearespectedexperimentalphysicistbythetimeLouisenteredtheSorbonnein1910—just at the time theworld of sciencewas becoming excited about quantumphysics.EncouragedbyMaurice,Louis switched tophysics, buthis educationwas interruptedbymilitaryservice in theFirstWorldWar,whenheworked inradio communications at the Eiffel Tower. So it was not until 1923 that hepublishedhisfirstpapersonthenatureoflightquantaanddevelopedtheworkthatformedthebasisofhisdoctoral thesis,andnotuntil late1924thathewasawardedhisPhD(afterEinstein’sintervention!),bywhichtimehewasalreadythirty-two years old. Hardly surprisingly, de Broglie made no further greatcontributions tophysics; the surprise is that the evenolderErwinSchrödingerwasthepersonwhopickeduptheballandranwithit.DeBrogliehadstartedoutfromthetwoequationsthatEinsteinhadderivedfor

lightquanta:E=hν

andp=hν/c

Sincethewavelength(λ)ofawaveisrelatedtoitsfrequency(ν)bytheequationλ=c/ν

averysimplesubstitutionthentoldhimthatpλ=h

—or,inplainEnglish,thatthemomentumofaquantumentitymultipliedbyitswavelengthisequaltoPlanck’sConstant.Andthisapplies,inprinciple,toanyobject—ittellsusthatthereisamomentumassociatedwithlightwaves,butalsothat there isawaveassociatedwithelectronsandotherparticles.Theequationalsomakes it clearwhy such effects are not observed in the everydayworld:becausethemomentumofanythingwecanseeor touchsobigcomparedwithPlanck’sConstant,thewavinessassociatedwithsuchanobjectisfartoosmalltobenoticed.After his failure with the relativistic hydrogen equation, Schrödinger went

backtobasics.Startingwiththestandardwaveequationofclassicalmechanics,heusedtherelationshipdiscoveredbydeBroglietoconvertthewavelengthstomomenta, and came up with a very simple wave equation for the electron,similar to the wave equation for light and other electromagnetic wavesdiscoveredbyMaxwellinthenineteenthcentury.Thederivationisoneofthose

ideasthat,likedeBroglie’sdiscovery,seemsalmostembarrassinglysimpleoncesomeonehasthoughtofit,provokingthereaction“Whyonearthdidn’tIthinkofthat?,”butwasfarfromobviousuntilitwaspointedout.PerhapsSchrödingeralso thought it was embarrassingly simple, because before he published hisbreakthroughhecameupwithtwoother,morecomplicated(andthereforemoreimpressive)waysofderivinghisfamouswaveequationtosharewiththeworldof science. And, unlike Schrödinger’s relativistic equation from a few weeksearlier,thisonepredictedtherightvaluesforthequantumnumbersdeterminedby experiment. Einstein had been right to say that de Broglie’s equationrepresented“morethanaformalanalogy.”The bizarre thing was that this treatment, ignoring the implications of the

special theory of relativity, worked, when it had no right to do so. Withhindsight, we can see that the consequences of ignoring the special theory ineffectcancelledouttheconsequencesofignoringspin.The“right”equationfordescribingquantumwavescanindeedbederivedproperlybyincorporatingbothrelativityandspin,butbyluckitcanalsobederivedbyignoringbothofthem.Onsuchluck,NobelPrizessometimesdepend.ThingsmovedswiftlyafterChristmas1925.Atthebeginningofthenextterm

in Zürich, Schrödinger gave another colloquium, in which, Bloch recalled in1976,hebeganwiththewords:“MycolleagueDebyesuggestedthatoneshouldhaveawaveequation[fortheelectroninthehydrogenatom];well,Ihavefoundone.”Thiswasonlytrueuptoapoint;agreatdealofhardworkwasneededtoproduceacompletemathematicaldescriptionofthehydrogenatomintermsofthe“nonrelativistichydrogenequation.”Butwith thehelpofhis colleagues inZürich,SchrödingercompletedhisfirstpaperonwavemechanicsandsentitofftoAnnalenderPhysik,where itarrivedon27January, less thanamonthafterthebreakthrough inArosa,andwaspublishedon13March1926.By then thesamejournalhadalreadyreceivedasecondpaperfromSchrödinger,developingtheideafurther,whichwaspublishedon6April,followedinswiftsuccessionbyfourmorepapers,thelastpublishedon5September.Asifthatwerenotenough,Schrödingeralsowroteacomprehensiveoverviewtitled“AnUndulatoryTheoryoftheMechanicsofAtomsandMolecules,”whichwasfinishedon6Septemberand published in English in the journal Physical Review in December 1926.Wavemechanicswasessentiallycomplete,lessthanayearafterthefailurewiththe relativistic hydrogen equation. The key papers were collected in a singlevolumepublishedthefollowingyearinGerman,andin1928inEnglish.Itwasan astonishing creative outburst, unequalled in science by anyone of a

comparable age to Schrödinger in 1926, and arguably surpassed only by theyoungAlbert Einstein’s productivity in hisannusmirabilis of 1905, when hemade key contributions to several different areas of science. Einstein himselfwasimpressed;inMay1926hewrotetohisfriendMicheleBesso,“Schrödingerhascomeoutwithapairofwonderfulpapersonthequantumrules.”2

EvenSchrödinger,though,wassurprisedbytheoutcomeofhisinvestigations.Intheintroductiontothecollectededitionofhispapersonwavemechanics,hewrote:Ayoungladyfriendrecentlyremarkedtotheauthor:“Whenyoubeganthiswork you had no idea that anything so clever would come out of it, hadyou?” This remark, with which I wholeheartedly agreed (with duequalification of the flattering adjective),may serve to call attention to thefactthatthepapersnowcombinedinonevolumewereoriginallywrittenoneby one at different times. The results of the later sections were largelyunknown to the writer of the earlier ones. Consequently, thematerial hasunfortunatelynot alwaysbeen set forth in asorderly andas systematic [a]way as might be desired, and further, the papers exhibit a gradualdevelopmentofideas.

Thereferencetoa“youngladyfriend”highlightsthecontinuingimportanceofboth eroticism and science in the year of Schrödinger’s “late erotic outburst,”althoughwhich (if either)came first it is impossible to say.Shewas fourteen-year-oldIthaJunger,whomSchrödingerwascoachinginmathematics—amongotherthings.Itha was one of a pair of non-identical twin sisters whose mother was an

acquaintance of Anny Schrödinger. Formuch of July 1926, at the end of theacademicyear,Erwinhadbeenaway fromZürich, travelling toother researchcentres, includingMunich andBerlin, spreading the news of his breakthroughandraisinghisprofileconsiderablyintheGerman-speakingscientificworld.Inhisabsence,Annylearnedfromtheirmotherthatthetwins(christenedIthaandRoswitha, but known as Ithi and Withi) had failed to achieve the requiredstandard in mathematics at their convent school; Itha had done particularlybadly,andmighthavetobeheldbackforayear,eithersplittingthetwinsuporforcingRoswithatobeheldbackwithher.AnnysuggestedthatErwinwouldbetheidealpersontogivethemsomespecialtuition.Hereturnedshortlybeforethetwins’ fourteenth birthday in August, and eagerly took up the challenge. TheconsequencesweredescribedtoWalterMoorebyIthainaseriesofinterviewsin

1985.Themaths lessonswere a great success,withmost of their tutor’s attention

naturallybeingdevotedtoItha,andbothgirlsachievedthestandardrequiredtomoveonwiththeirclassmateswhenthenextschooltermbegan.Butaswellasthe maths, the lessons included “a fair amount of petting and cuddling,” andSchrödinger soon convinced himself that hewas in lovewith Ithi (“whateverloveis,”asPrinceCharlesoncesaid).Hetalkedtoherabouthisscientificworkandabouthisreligiousbeliefs,wrotepoetryforher,spentaskiingholidaywiththe two girls and their mother over Christmas 1927, and set out on a longcampaignofwhatwouldnowbedescribedasgrooming.Ofcourse,theheadoftheyoungconvent-schoolgirlwasturnedbyalltheattention,andinduecourseshefellinlovewithhim.Buthewaspatient.Itwasn’tuntilshewassixteenthathe went into Ithi’s room in the middle of the night (during another skiingholiday) and told her how much he loved her; and not until just after herseventeenth birthday, inAugust 1929, that the relationshipwas consummated.The affair continued into the 1930s, with Schrödinger at one point seriouslyconsideringdivorcingAnny tomarry Ithi,and formsabackdropwhichcannotbeignoredtoSchrödinger’sscientificlifeintheyearsfollowinghisdiscoveryofwavemechanics.Butthescientificworldknewnothingofthiswhenitbegantotakewavemechanicsseriouslyanddeveloped it intoacompletedescriptionofthequantumworld.UnfortunatelyforSchrödinger,though,thewayhisideawasdevelopedwasnotatalltohistaste.

RidingthewaveSchrödinger’s waves were a classic example of a continuous process;Heisenberg’smatricesprovidedaclassicdescriptionofadiscontinuousprocess,which Schrödinger found repugnant. In his paper “On the Relation of theHeisenberg–Born–JordanQuantumMechanics toMine,” published inAnnalenderPhysikinMay1926,henoted:My theory was inspired by L. de Broglie and by brief but infinitely far-seeingremarksofA.Einstein . . . IwasabsolutelyunawareofanygeneticrelationshipwithHeisenberg.Inaturallyknewabouthistheory,butbecauseofthetomeverydifficultseemingmethods...Ifeltdeterredbyit,ifnottosayrepelled.

Soitcameassomethingofasurprise,nottosayashock,whenhefoundthatnot

onlydid the two theoriesgive the same (correct) answerswhenapplied to thesameproblemsinatomicphysics,butthattheyweremathematicallyequivalent.Matrixmechanicscouldbederivedfromwavemechanicsbytakingthevariablescorresponding to position andmomentum inSchrödinger’swave equation andreplacing them with two of the expressions, known as operators, fromHeisenberg’s theory. This is a process the mathematicians call “substitution,”anditworksequallywellgoingtheotherway,frommatrixmechanicstowavemechanics.Schrödingerwasn’ttheonlypersontospotthelinksbetweenthetwotheories.

Paulihadalsonoticed theconnection,andmentionedit ina letter toJordan inApril 1926, before he had seen Schrödinger’s paper. And the American CarlEckart(1902–73),basedinPasadena,wrotetwopapersonthetopicinMayandJune1926,beforecopiesof the issueof theAnnalen containingSchrödinger’spaperhadreachedCalifornia.Eckart’sachievement,inthewordsheusedinthefirstof those twopapers,was“the inclusionof the resultsofSchrödinger inasingle calculuswith those of [Heisenberg,Born, and Jordan]. . . . Thiswouldseemtobethegreatestsupportwhicheitherofthetwodissimilartheorieshavethusfarreceived.”Butthedefinitivelastwordonthesubjectcamefromtheboywonder,PaulDirac.Schrödinger, Pauli, and Eckart had each shown empirically that matrix

mechanics andwavemechanicswere equivalent toone another at the level ofmakingsubstitutions.Butnoneofthemhadbeenabletosaywhythisshouldbethe case. Dirac developed yet another way of looking at the quantum world,which he called transformation theory, and proved (using some hairymathematics)thatallversionsofquantummechanicswerecontainedwithinthisoverarching theory. His paper describing the new theory was received by theRoyalSociety, forpublication in theirProceedings, inDecember1926; Jordandid some similar work at the same time, although without quite scaling theheightsDiracreached.Withoutgoingintothehairymathematics,thebestwaytounderstandDirac’s

achievementiswiththeaidofananalogywhichHeinzPagelsusedinhisbookTheCosmicCode.Hepointsoutthatatreemaybedescribedintwo(ormore)different languages, say, English and Arabic. The two descriptions may lookutterlydifferent—inthisexample,theydonotevenusethesamealphabet.Buttheybothdescribethesamething,andonedescriptioncanbetransformedintothe other using a dictionary and the rules of grammar. “That differentrepresentations are subject to laws of transformation is a profound idea,” says

Pagels.“Invariantsestablishthetruestructureofanobject.”Transformationtheoryisthecompletetheoryofquantummechanics.Butfew

ordinaryphysicistsinthe1920s(andfewsince,forthatmatter)botheredaboutthat.Theydidn’tlikethehairymathematics,andmostofthem,likeHeisenberg,hadn’tevenknownwhatamatrixwasbefore1926.Whattheyseizedonwasthefactthatifmatrixmechanicsandwavemechanicswereequivalent,whenitcametosolvingpracticalproblems,thenyoucouldusewhicheveroneyoulikedwhenconfrontedby thoseproblems.And theonepeople likedwaswavemechanics,since they all knew (or thought they knew) how waves behaved.Which wasgreatnewsforSchrödinger—atfirst.The problem for Schrödinger was that even if the maths said that matrix

mechanicsandwavemechanicswereequivalent,thatdidn’tgivehimaphysicalpictureofwhatwasgoingon insideatoms.Howcoulddiscontinuousquantumjumping be reconciledwith a continuouswave function?He puzzled over theproblemduringthesummerof1926(withlightrelieffromthisworkintheformof tutoring the twins), butwas getting nowhere, as a letter toWilhelmWien,writtenon25AugustandnowintheWienArchiveinMunich,testifies:The photoelectric effect [see Chapter 4 above] . . . offers the greatestconceptualdifficultyfortheachievementofaclassicaltheory...Inolongerlike to assume with Born that an individual process of this kind is“absolutely random” . . . I no longer believe today that this conception(whichIchampionedsoenthusiasticallyfouryearsago)accomplishesmuch.Schrödingerwas particularly concerned about the statistical interpretation at

this time because in June 1926 Max Born had come up with a new way ofinterpreting thewave function. He suggested that thewave function could beusedtocalculatetheprobabilityofaquantumentitysuchasanelectronbeingataparticularpointinspace.Adefiningfeatureofawaveisthatithasasize,oramplitude,whichvariesfromplacetoplace,andBornfoundthatthesquareofthe amplitude of Schrödinger’s wave function could be used as ameasure ofprobability.3He suggested that particles such as electrons are real entities, butthatwhereyoufindthemdependsontheprobabilityamplitudesassociatedwitha ghostlywave.The snag, as far as Schrödingerwas concerned,was that thismeantthatanentitysuchasanelectrondidnothaveadefinitepath,ortrajectory,through space, but might be found anywhere in a certain region of spacedetermined by the probabilities. Instead, Schrödinger favoured the idea that aparticleissomehowguidedbyafieldwhichobeysthewaveequation,sothatthe

particlerides thewave, likeasurfer.But:“Itwoulddependon the tasteof theobserver which he now wishes to regard as real, the particle or the guidingfield.”Muddywaters,indeed!AndaclearbreakwithSchrödinger’searlierideasabout the importance of statistical processes in even the most fundamentalsituationsinphysics.TheironyisthatwhereasSchrödingerhadpreviouslybeenin a minority when suggesting that the fundamental laws of physics arestatistical, from now on he would be in a minority in rejecting the idea thatstatisticsplayavitalroleinthebehaviourofthequantumworld.Withtheseideasbuzzinginhishead,SchrödingerwentonholidaywithAnny

in theSouthTyrol, thenon toCopenhagenat theendofSeptember todiscussquantumphysicswithBohrandhiscolleagues,includingHeisenberg,whowasworking at Bohr’s institute at the time. Schrödinger gave a lecture on wavemechanicsthereon4October,butthemostimportantfeatureofthevisitwastheopportunity to discuss his ideas, especially his concern about quantum jumps,withBohr.Hehadplentyof opportunity todo so, sincehewas staying at theBohrs’house.Eachmanheldfirmlytohisposition—justhowfirmlywecantellfromHeisenberg’sdetailedaccountof thedebateand itsaftermath inhisbookPhysicsandBeyond,wherehetellsusthat:AlthoughBohrwasnormallymostconsiderateand friendly inhisdealingswith people, he now struckme as an almost remorseless fanatic, onewhowasnotpreparedtomaketheleastconcessionorgrantthathecouldeverbemistaken.Schrödingerwasequallystubborn.Itishardlypossibletoconveyjusthowpassionatethediscussionswere,justhow deeply rooted the convictions of each, a fact thatmarked their everyutterance.Schrödinger’sentrenchedviewwasthatiftherewerenolawstodescribethe

motionofanelectronduringaquantumjumpthen“thewholeideaofquantumjumpsissheerfantasy”;Bohr’sfirmlyheldconvictionwasthatthisdoes not prove that there are no quantum jumps. It only proves that wecannot imagine them, that the representational concepts with which wedescribe events in daily life and experiments in classical physics areinadequatewhenitcomes todescribingquantumjumps.Norshouldwebesurprisedtofinditso,seeingthattheprocessesinvolvedarenottheobjectsofdirectexperience.

Itwasin thecourseof thisdebate thatSchrödingermadehisfamouscomment

“ifallthisdamnedquantumjumpingwerereallyheretostay,IshouldbesorryIevergotinvolvedwithquantumtheory.”Although the debate was inconclusive, it left Schrödinger, Bohr, and

Heisenberg(stillgoodfriendsinspiteoftheirintellectualdifferences)alldeeplypuzzledaboutwherequantumtheorywastakingthem.ItwaspuzzlingoverthequestionsraisedduringSchrödinger’svisittoCopenhagenthatledHeisenbergtothe next great discovery, essentially the last piece in the jigsaw puzzle ofquantum mechanics. It came to him on a winter’s night in an attic inCopenhagen;Schrödinger,onanextendedvisittotheUnitedStates(describedinthe next chapter), would learn nothing of this new idea until he returned toEuropeinApril1927.

AquantumofuncertaintyAlthough convinced that they were right, the Copenhagen scientists had nowrealized“howdifficultitwouldbetoconvinceevenleadingphysiciststhattheymustabandonallattemptstoconstructperceptualmodelsofatomicprocesses.”In the months following Schrödinger’s visit to Copenhagen, the physicalinterpretation of quantum physics was the central theme of the discussionsbetweenBohrandHeisenberg,withtheotherpieceofthepuzzlethathadbeenfoundbyMaxBorninthebackground.OneofthekeyproblemsthatoccupiedthemovertheweeksuptoChristmaswashowtoreconcileeitherversionofthenew quantum mechanics with “so simple a problem as the trajectory of anelectroninacloudchamber.”A cloud chamber is a relatively simple device: essentially, a sealed box

containingairsaturatedwithwatervapour,withaglasswindowthroughwhichtowatch,andphotograph,whatisgoingon.Whenaparticlesuchasanelectronzips through thechamber, it leavesa trailofcondensationbehind it, similar tothewayahigh-flyingaircraftproducesacondensationtrailacrossthesky.Thecloudchamberhadbeeninventedinthe1890sbyCharlesWilson(1869–1959),who received aNobel Prize for hiswork in 1927; but the technique had onlybeen fully developed after 1910, by Patrick Blackett (1897–1974), who alsoreceivedaNobelPrize,in1948.Theawardsindicatetheimportanceofthecloudchamber to the new physics. This was the nearest anyone could come in the1920s toseeingan individualelectron,and the tracksproducedreallydid lookliketheeffectsoffast-movingparticles.

BohrandHeisenbergwerepuzzledbecausetheveryconceptofatrajectorydidnotfitinwiththeideasofmatrixmechanics(whichHeisenberghimselfalwaysreferred to as quantum mechanics, although today that term embraces wavemechanicsaswell).Although it ispossible inwave theory tohavea localizedbunchofwavesmovingtogetherasaso-calledwavepacket,thiswouldrequireabeamofmatter spread out over awidthmuch greater than the diameter of anelectron.Notwhatwasseeninthecloudchamber.Earlyinthenewyear,withtheirdiscussionscontinuinglongaftermidnightfor

weeksonend,bothBohrandHeisenberg“becameutterlyexhaustedandrathertense.”SoHeisenbergwasmorethanhappywhenBohrdecidedtogoskiinginNorway in February 1927, leaving him to “think about these hopelesslycomplicatedproblemsundisturbed.”Hedidsoinhiscosyflatat thetopof thebuildingwhichhousedBohr’s institute, lookingoutoverCopenhagen.Back inthe spring of 1926, Heisenberg had been asked to give a talk on matrixmechanicsattheUniversityofBerlin,andafterwardshadhadalongdiscussionwithEinsteinaboutthenatureofrealityandtheimplicationsofthenewtheory.At one point, Einstein had commented: “It is quite wrong to try founding atheoryonobservablemagnitudesalone.Inrealitytheveryoppositehappens.Itisthe theorywhich decideswhatwe can observe.”At the time,HeisenbergwascompletelytakenabackbyEinstein’sargument.Butnow,nearlyayearlater,thewords suddenly came back to him one night after midnight, when he waswrestlingwiththepuzzleoftrajectories.Itisthetheorywhichdecideswhatwecan observe.Could this be the key?Too excited to sit at his desk any longer,Heisenberg went for a walk through the nearby Faelled Park. It was on thatnocturnalwalkthathecameupwiththeideaforeverassociatedwithhisname—quantumuncertainty.Heisenberghadrealizedthatwhatisactuallyobservedinacloudchamberisa

trailofwaterdropletstriggeredintocondensationbytheelectron.Thisisnotthecontinuouspathofanelectronthroughthechamber,butaseries“ofdiscreteandill-defined spots through which the electron has passed,” like a line of dotswhichwejoinuptocreateatrajectory.Wedon’tknowwhattheelectronisdoinginbetweenthosedots,anymorethanweknowwhatitisdoingwhenit“jumps”betweenenergylevelsinanatom.SoHeisenbergreasonedthattherightquestionto askwas: “Can quantummechanics represent the fact that an electron findsitself approximately in a given place and that it moves approximately with agivenvelocity,andcanwemaketheseapproximationssoclosethattheydonotcauseexperimentaldifficulties?”4

Hurryingbacktotheinstitute,armedwiththisinsightHeisenbergwasquicklyable to provemathematically that everythingwas consistent provided that thesystemobeyedasimplerule—whatbecameknownasHeisenberg’sUncertaintyPrinciple. Inhisownwords:“Theproductof theuncertainties in themeasuredvalues of the position and momentum . . . cannot be smaller than Planck’sConstant.”Oneslightadjustmenthasbeenmadesubsequently—wenowknowthattheproductoftheuncertaintieshastobelessthanPlanck’sConstantdividedby 4π. On 23 February, Heisenberg wrote a long letter to Pauli outlining hisdiscovery—essentially,adraftversionofthepaperthathewaspreparingfortheZeitschrift fürPhysik. “Thepath,”hesaid,“onlycomes intoexistence throughthis,thatweobserveit.”But what does this mean physically? The first key point is that the word

“measured”canberemovedfromHeisenberg’sstatement.Quantumuncertaintyhasnothingtodowithourability,orinability,tomakeprecisemeasurements.Itis something that is built into thequantumworld, so that an entity suchas anelectrondoesnothavebothapreciselydeterminedmomentum(whichineffectmeansvelocity)andapreciselydeterminedposition.AsHeisenbergputitwhenhe published the news of his discovery in the Zeitschrift later in 1927, “Wecannotknow,asamatterofprinciple,thepresentinallitsdetails.”Theelectronitselfdoesnot“know”bothexactlywhereitisandexactlywhere

it is going at the same time. But because the constraint (Planck’s Constantdividedby4π) isaproductof the twouncertainties,eitheroneof themcanbespecified as precisely as you like, provided there is correspondingly largeruncertainty for the other. The more accurately the velocity of an electron isspecified, the less accurately is its position specified; the more accurately itsposition is specified, the less accurately is its velocity specified. In the cloudchamber,thetrajectoryoftheelectronspecifiesitsvelocityfairlyprecisely,butitspositioncouldbeanywherealongthetrajectory.Inprinciple,thesamerulesapplyintheeverydayworld.Butquantumuncertaintydoesnotnoticeablyaffectobjects more massive than molecules, because Planck’s Constant is so small.TheamountofuncertaintyinthepositionofanobjectisproportionaltoPlanck’sConstant divided by the mass of the object, and for everyday objects theuncertainty is absolutely tiny. If we were the size of an electron, though,quantumuncertaintywouldbecommonsense.And this brings probability and statistics back to centre stage. In the

Zeitschrift,Heisenbergwrote:“Whenweknowthepresentprecisely,wecanpredictthefuture,”isnotthe

conclusion but the assumption. Even in principle we cannot know thepresentinalldetail.Forthatreasoneverythingobservedisaselectionfromaplenumofpossibilitiesandalimitationonwhatispossibleinthefuture.Asthe statistical character of quantum theory is so closely linked to theinexactness of all perceptions, one might be led to the presumption thatbehind the perceived statistical world there still hides a “real” world inwhichcausalityholds.Butsuchspeculationsseemtous,tosayitexplicitly,fruitlessandsenseless.Many disagreed, not least Schrödinger.Bohr, on his return fromNorway, at

firstthoughtHeisenbergwasbarkingupthewrongtree,andthathisconceptofuncertainty was incompatible with Bohr’s own developing ideas about thequantumworld.Butwithinafewmonthsoffiercedebateamongtheexperts,anewperceptionofthequantumworldemerged,andbecamethereceivedwisdom(though not without dissenters) for more than half a century. It was theconsensus known, to Born’s intense annoyance, as the “CopenhagenInterpretation.”

TheCopenhagenconsensusWhenBohrgotback toCopenhagenfromhisskiing trip,hebroughtwithhimanother new idea about the quantum world. It later became known ascomplementarity,anditliesattheheartoftheCopenhagenInterpretation.Itisadisarminglysimpleideaatfirstsight,butwithdeepramifications.Bohrsuggestedthatboththewaveandtheparticledescriptionsofthequantum

world are correct, and that they are complementary aspects of some greaterwhole.The simplest analogy—no lessgood forbeing simple—iswith the twosidesofacoin.Youcanseeeithertheheadorthetail,butnotbothatonce;theyarecomplementaryaspectsof thecoin.Similarly, ifwedoanexperimentwithelectronsdesignedtofindwaves,wewillseewaves;butifwedoanexperimentwithelectronsdesignedtofindparticles,wewillseeparticles.Whattheelectron“reallyis”isirrelevant,andperhapsbeyondhumanunderstanding.Whatmattersiswhatitislike,orhowitbehavesinparticularcircumstances.ThisledBohrandHeisenbergintoconflictinMarch1927,becauseHeisenberg

wantedtodoawaywiththeideaofwavesaltogether.SoatfirsthewaslessthanenthusiasticwhenBohr found a simpleway to derive the uncertainty relationusingwavemechanics.Thisprovedtobeveryeasy,becausealthoughalocalized

groupofwaves(awavepacket)canindeedbehaveinsomewayslikeaparticle,this can only be achieved if the packet contains many waves with differentwavelengths.Asinglewavehasawell-determinedmomentum,but,ofcourse,itdoesnothaveawell-determinedposition.Awavepackethasawell-determinedposition,butitdoesnothaveawell-determinedmomentum.Whenthenumbersareputin,Heisenberg’suncertaintyrelationcomesout.HeisenbergfinallyhadtoadmitthatBohrwasright,andincludedapostscriptreferringtoBohr’sworkinhisuncertaintypaper,whichwaspublishedattheendofMay.Onthestrengthofhiswork,provingthathewasnoone-hitwonder,HeisenbergmovedtoLeipzigasafullprofessor(theyoungestinGermany)attheendofJune.Meanwhile, Bohr struggled to get his own ideas down on paper. He had

notoriousdifficultywiththisthroughouthiscareer,goingthroughendlessdraftsandre-draftsinanattempttofindthepreciseformofwordsheneeded.Hewasusuallyhelpedinthetaskbyanassistant,andinthiscasethatfarfromeasyrolefelltoOskarKlein(1894–1977),aSwedishphysicistworkingatBohr’sinstitute.Draft followed draft, with the term “complementarity” appearing for the firsttime inaversiondated10July1927.Bohrwasworkingagainstadeadline, tocompletehispaperintimetopresentitataconferencetobeheldinComothatSeptembertomarkthecentenaryofthedeathofAlessandroVolta(1745–1827),but in typical Bohr fashion he failed to finish on time, and had to make apresentationbasedonthelatestworkingcopy.TheComomeetingwas the firstopportunity topresent thepackageof ideas

thatbecameknownastheCopenhagenInterpretationtotheleadingphysicistsofthe day.But these did not includeSchrödinger,who, as I describe in the nextchapter,was settling in aftermoving toBerlin andwas too busy to attend, orEinstein,whorefusedtovisitFascistItaly.TheessentialelementsofthepackageBohr described included Schrödinger’s wave equation, now interpreted as a“probability wave,” Born’s statistics, Heisenberg’s Uncertainty Principle,complementarity,and—something thatwould troubleSchrödingerandEinsteindeeply—anotioncalled“thecollapseofthewavefunction.”Bohralsostressedthat the only reality lay in the observations—that it was meaningless to askwhereaquantumentitysuchasanelectronwas,orwhatitwasdoing,whenitwas not being observed. The best way to understand how the interpretationworksisbylookingat theclassicpuzzleof thequantumworld, thedoubleslitexperiment. I’ll describe this in termsof electrons, but the same interpretationappliestoanyquantumentity.AccordingtotheCopenhagenInterpretation,whenanelectronisejectedfrom

anelectron“gun”ononesideoftheexperimentitleavesasaparticle,andcanbedetectedasaparticle.But it immediatelydissolves intoaprobabilitywave,which travels through both of the holes and interferes with itself to make apatternofprobabilityontheothersideoftheholes.Atthedetectorscreen,theelectroncanappear as aparticle at anypoint allowedby theprobabilities, butwith someplacesmore likely thanothers, and, crucially, some locationsbeingabsolutely forbidden. There is a “collapse of the wave function” at the pointwhere the electron is observed, or measured. It arrives as a particle. But themoment that it is no longer being observed, the probabilities spread out againfromthatpoint,sothatnexttimewelookfortheelectronwefinditsomewhereelse, thatsomewherebeinganywhereallowedby theprobabilitiesbut,asever,withsomelocationsmorelikelythanothers.Do not imagine, though, that the probability wave is in some sense a

“smeared-out” version of the electron. The electron is only ever seen as aparticle—wedonot,forexample,seehalfoftheelectricchargeoftheelectronpassingthrougheachofthetwoholes—buttheplacewheretheparticleisseenordetecteddependson the statistical rulesdeterminedby thebehaviourof thewave.AnddonotimaginethatbecausetherulesarestatisticaltheCopenhagenInterpretationappliesonlytothebehaviourofthousands,orbillions,ofseparateelectrons(orotherquantumentities)addedtogether.Itappliestoeachindividualelectron,justasIhavedescribed—and,unlikeBohrandhiscontemporaries,wehavethebenefitofmodernversionsofthedoubleslitexperimentcarriedoutbyfiring electrons literally one at a time through single slit and then double slit,whichhaveconfirmedeverypredictionofhisdescriptionofquantumreality.TheaudienceinComowereasbaffledbyBohr’spresentationofthisnewidea

asmostpeoplearewhentheyfirstencounterit.Few,ifany,wereconvinced.Butthefollowingmonth,inthelastweekofOctober1927,hehadasecondchancetomakehiscase,andthistimehegraspeditwithbothhands.Theoccasionwasthe fifth Solvay Congress, one of a series of scientific conferences held inBrussels, established in 1911 under the sponsorship of a wealthy Belgianindustrial chemist, Ernest Solvay. It turned out to be the greatest gathering ofquantumphysicists ever.Thegrandoldmenof the firstquantumrevolution—Planck,Einstein,andBohr—wereall there;but so toowere theyoungmenofthe second quantum revolution, including de Broglie, Dirac, Heisenberg, andPauli.There, too,wasSchrödinger,whowasatoncebothagrandoldman(asphysicists judge age) and a key player in the second quantum revolution.Theofficial titleof theconferencewas“ElectronsandPhotons,”and the invitation

sentouttoprospectiveparticipantsstressedthatitwouldbe“devotedtothenewquantummechanicsandtoquestionsconnectedwithit.”Whathappenedatthemeetingisbestsummedupbythecommentofphysicist

Paul Ehrenfest (1880–1933) in a letter he wrote just after the conference:“BOHRtoweringcompletelyovereverybody.Atfirstnotunderstoodatall . . .thenstepbystepdefeatingeverybody.”5Aslightlymore thoughtfulassessmentof the outcome of the conference came fromHeisenberg in 1963: “ThemostimportantsuccessoftheBrusselsmeetingwasthatwecouldseethatagainstanyobjections,againstanyattemptstodisprovethetheory,wecouldgetalongwithit.Wecouldgetanythingclearbyusingtheoldwordsandlimitingthembytheuncertaintyrelationsandstillgetacompletelyconsistentpicture.”6Eitherway,thesecondquantumrevolutionwascompleteandtheCopenhagenInterpretationheldcentrestage.AsSchrödingerbeganhisnewlifeasaprofessorinBerlin,thiswasnotatalltohisliking.

Notes

1PublishedinPhysicsToday,1976,vol.29,no.12.2QuotedinNielsBohr’sTimes,wheretheauthor,AbrahamPais,comments:“TothebestofmyknowledgethatwasthelasttimeEinsteinwroteapprovinglyonquantummechanics.”3Thiswastheworkforwhichhewould(eventually!)receivetheNobelPrize.4Myemphasis.5QuotedbyPais,NielsBohr’sTimes(Ehrenfest’semphasis).6QuotedbyPais,NielsBohr’sTimes.

ChapterEight

TheBigTimeinBerlin

Schrödinger’s discovery of wave mechanics came at the perfect time for hiscareer.Max Planck, who had been Professor of Theoretical Physics in Berlinsince1892,wasapproachinghisseventiethbirthday,theageatwhichhewouldberequired toretire. In thesummerof1926,exactlyat the timeSchrödinger’sideaswere being published towidespread acclaim, a committeewas set up toconsidertheappointmentofPlanck’ssuccessor.TheBerlinchairwasthetopjobin theoretical physics in mainland Europe, and the committee could pick andchoose from the best people; therewas noquestionof having to advertise thepost.Einsteinwasoutofconsideration,though.HewasalreadyinBerlin,wherehehadaspecialprofessorshipwhichcarriednoteachingdutiesatall.Heisenbergwasacontender,but in the summerof1926hewas stillonly twenty-four, tenyearsyoungerthanevenPlanckhadbeenatthetimeofhisappointment;itwasfeltthattheopportunityhadcometoosoonforhim,inspiteofhisprovenability.Thecommitteefinallycameupwithashortlistoftwo—MaxBornandErwin

Schrödinger.ByDecember1926,wherewepickup thestoryofSchrödinger’slife following his own annus mirabilis, Erwin knew that he was beingconsideredforthepost;butnothingwasdecidedwhenhesetoutwithAnnyonaworkingtriptotheUnitedStates.

MakingwavesinAmericaThe trip stemmed from an invitation made by the University of Wisconsin,which offered Schrödinger $2,500 (including expenses) to give a series oflecturesonwavemechanics.Hewasinitiallyreluctant totakeuptheoffer,notleastbecauseitwouldmeanbeingawayfromZürichfortheChristmasvacation(washethinkingofIthi?),butwaspersuadedbyAnnythat itwas toogoodanopportunitytomiss.Thecouplelefton18December,travellingbytrainandship(spendingChristmasonboard), andarriving inNewYork for thenewyear.A

memoirwrittenbyAnny,nowintheSchrödingerArchiveinVienna,givesusatasteoftheirexperiencesintheUnitedStates,andaninsightintoSchrödinger’scharacter.Alwaysaloverofthegreatoutdoors,hehatedNewYorksomuchthathethreatenedtogohomeonthenextship.AfterasinglenightinthecitytheymovedonbytraintoMadison,viaChicago(wherehewasterrifiedofbeingshotatbygangsters),andhere thingscalmeddown:Schrödinger regardedMadisonasapropercityintheEuropeanmould.Hislectureswentdownsowellthathewasofferedachairattheuniversity;hehadnointentionofmovingtoAmerica,a country so uncivilized that alcohol was prohibited, but was able to declinetactfullybylettingitbeknownthathewasintherunningfortheBerlinpost.HavinggotoverhisinitialimpressionsofNewYork,Schrödingerwaseagerto

spread the word about wave mechanics, and gave lectures at the midwesternuniversitiesofChicago,Iowa,andMinnesota,makingdowithgingeraleasanaccompanimenttothefinemealshewasofferedasguestofhonour.Thenitwason to California, which the Schrödingers loved (regretting only that it waspopulatedbyAmericansratherthanbyItaliansorSpanish),andanotherlecture,attheCaliforniaInstituteofTechnologyinPasadena.ThereturntripeasttookinAnnArbor,lecturesatbothHarvardandMIT,thenBaltimoreandWashington.Trailingcloudsofglory,SchrödingerwasnowofferedaprofessorshipatJohnsHopkinsUniversity on a salary of $10,000 a year; but nothing (especially notanything in America) would tempt him to miss out on the possibility of theBerlinchair.Fitting in onemore lecture at ColumbiaUniversity,making a total ofmore

thanfiftyinjustunderthreemonths,ErwinfinallylefttheNewWorldforhome,leavingwavemechanicsfirmlyestablishedinthemindsofphysicistsacrosstheUnited States as the leading version of quantum mechanics. He and Annyarrivedback inZürichon10April1927, justas thecommittee inBerlinweremakinguptheirminds.

BerlinandBrusselsThechoicebetweenBornandSchrödingerhadproveddifficult,butthereportofthecommittee,nowin theBerlinarchive,showsthat theywereswayedby thebreadth of Schrödinger’s research, by his “deep and original ideas,” and inparticular by his “especially daring design through his ingenious idea for thesolutionoftheformerparticlemechanicsbymeansofawavemechanics.”They

alsocommentedonhis“superb”styleasa lecturer,“markedbysimplicityandprecision,” andmentioned that he had “the charming temperament of a SouthGerman.”Had he been aware of it, Schrödinger would surely have loved thereference to particle mechanics as a thing of the past; but as an Austrian hemightnothavethoughtsohighlyofbeingdescribedasaSouthGerman.So the offer went out to Schrödinger at the beginning of the summer term.

AlthoughhehadkeenlywantedthehonourofbeinginvitedtoBerlin,nowtheballwasinhiscourtSchrödingerhesitatedbeforeacceptingtheoffer.Hehadbynow settled happily in Switzerland, valuing the peace and stability whichcontrasted with much of the rest of Europe at that time, and enjoying theproximityofthemountains.Asaplacetolive,itwasalmostasgoodasAustria.TheuniversityinZürichmadeeveryefforttokeephim;althoughtheycouldnotmatch the salary offered by Berlin, they proposed giving Schrödinger a jointprofessorshipattheuniversityandtheETH,providingtwiceasmuchmoney,butunfortunatelyrequiringtwiceasmuchlecturing.Itwasn’t only theuniversity authoritieswhowanted to keephim.When the

students heard the news that hemight be leaving, they organized a torchlightprocession through the streets to Schrödinger’s house—a traditional, but veryrare, way for the student body to honour favourite teachers. But whileSchrödingerhesitated,thebalancewastippedbyaremarkfromPlanckhimself:“Itwouldmakemehappy.”SotheSchrödingersmovedtoBerlinat theendofthesummerterm,shortlybeforeErwin’sfortiethbirthday,althoughhewouldnottakeuphisformaldutiesuntil1October1927.Hislecturesdidnotbeginuntil1November,afterhehadreturnedfromtheSolvayCongressinBrussels,whichhesawinaratherdifferentperspectivefromHeisenberg’s.Schrödinger must have enjoyed one aspect of Louis de Broglie’s early

contributiontotheproceedings,sincedeBroglietriedtodoawaywiththeideaofinterpretingSchrödinger’swavefunctionintermsofprobabilities.Butotheraspectsofhispresentationwerelessappealingtohim.DeBroglieofferedwhatbecameknownasthepilotwavemodel,whichsaysthatanelectronconsistsoftwo linkedandphysically realentities,awaveandaparticle,with theparticleridingthewavelikeasurfer—inmarkedcontrasttoBohr’sideathattheelectronbehaveseitherasawaveorasaparticle,butneverasbothtogether.DeBroglie’sidea received little attention from the delegates, although a version of it wastakenuplaterbysomephysicistsandplayedakeypart,asweshallsee,insomeofthemostexcitingdevelopments inphysicsduringthelate twentiethcentury.In1927,thephysicistsattheSolvayCongresssawthedebatelargelyintermsof

thediscussionsbetweenBohrandHeisenbergononesideandSchrödingerandEinsteinontheother,withtheCopenhagenapproachwinningoutandthemorediffidentdeBrogliebeingignored.OnereasonwhySchrödingerlostthedebatewasthathisideasaboutthenature

ofelectronsweretooabstractforsimplephysiciststofeelcomfortablewith.Forexample, the equation for a single electron involves a wave moving in threedimensions; if a second electron interactswith the first electron, that requiresanotherwavemovinginthreedifferentdimensions.Mathematiciansareusedtosuch ideas, and call the fictitious space in which the waves interact “phasespace.” But the idea of an extra three dimensions of phase space for everyparticleseemed,in1927,farlessattractivethantheCopenhagenInterpretation.AlthoughSchrödingerexpressedthehopethatfuturedevelopmentsofthetheorywould lead to a more conventional version involving the four ordinarydimensionsofspacetime,Heisenbergstoodupandreplied:“IseenothinginMr.Schrödinger’scalculationsthatwouldjustifythishope.”Schrödinger’s presentation, though, also included a remark which passed

largelyunnoticedat the time,but todayseems remarkablyprescient:“The realsystem is a composite imageof the classical system in all its possible states.”More of this later; but hold on to that idea of “the classical system in all itspossiblestates.”Einstein was not one of the main speakers at the conference, but made a

commentonBohr’scontributionwhichraisedasubjectthatwouldconcernthosequantumphysicistswhoworriedaboutsuchthingsfordecades.Hepointedoutthat in thedoubleslitexperiment,whenBohr’sprobabilitywavearrivesat thedetectorscreenthereisaparticularprobabilityoffindingtheelectronassociatedwith each point on the screen. But as soon as the electron is detected at onepoint, the probability everywhere else becomes zero—instantly. It is as if asignal of some kind has travelled across the detector screen in an instant—crucially,fasterthanthespeedoflight.Butaccordingtothetheoryofrelativity,nothingcantravelfasterthanlight.Thecollapseofthewavefunctionseemedtorequire faster-than-light signalling: what Einstein called “a peculiarinstantaneous action at a distance.” The puzzle persisted into the 1980s (seeChapter14).But very few quantum physicists did worry about such things. The

CopenhagenInterpretationgavethemapackagewhichworked,andwaseasytouse in calculations. They didn’t care about the philosophical interpretation ofwhatwasgoingonanymorethantheaveragecardrivercareshowaninternal

combustion engine works. At the other extreme, Dirac wasn’t interested ininterpretationbecausehebelievedthatthetruthlayintheequations,anditwaspointlesstoaskabouttheirphysicalmeaning.In the months following the Brussels conference, Heisenberg took up a

professorialpost inLeipzig,Paulibecameaprofessorat theETH,andPascualJordansucceededPauliinHamburg.BornwasalreadyestablishedinGöttingen,whileBohrcontinuedtoruletheroostinCopenhagen.Undertheirinfluence,theCopenhagenInterpretationthrived,andwasputtomanypracticaluses,notleastinexplaininghowatomsjointogether tomakemolecules.By1929,Diracwasable to write in one of his scientific papers, completely accurately, that “theunderlyingphysicallawsnecessaryforthemathematicaltheoryofalargepartofphysicsand thewholeofchemistryare thuscompletelyknown.” Itwashalf acentury later thathewrote abouthow“Itwasvery easy in thosedays for anysecond-ratephysicisttodofirst-ratework.”1

So itwaswithmixed feelings thatSchrödinger returned toBerlin to takeuphis lecturingduties inNovember1927.Wavemechanicswasthriving—butnotinaformheapprovedof.TheconsolationwasthepresenceinBerlinofEinstein,who shared his doubts about the Copenhagen Interpretation. The two becamefirmfriends,bouncingideasoffeachother,andinspiteofhisdoubtsabouttheroad quantum physics was taking, the next few years were a golden time forSchrödinger.

ThegoldenyearsTheUniversityofBerlinhadbeeninexistencesince1809.ItwasthebrainchildoftheexplorerandnaturalistAlexandervonHumboldt(1769–1859),thesonofa Prussian officer and statesman, and a member of the higher echelons ofPrussiansociety (hebecameBaronvonHumboldt)aswellasagreat scientist.Withthehelpofhiselderbrother,alawyeranddiplomat,hemadeaproposaltotheking,FriedrichWilhelmIII,fortheestablishmentofanewuniversity,whichthekingendowedwithbothfundsandahomeinaformerpalaceonUnterdenLinden.Bythesecondhalfofthe1920s,theGermaneconomyhadrecoveredfromits

post-war collapseandwasenjoyingaperiodof relative calmbefore the stormthatwastoengulfthecountryinthe1930s.Althoughthecountrywasgovernedby a variety of short-lived coalitions, from 1925 the President, providing an

image of stability, was the popular war leader Field Marshal Hindenburg, asymbol of many Germans’ belief in an army that had not, according to theirmythology,beendefeatedonthebattlefieldsoftheGreatWar.TheBerlinofthelate 1920s was a curious mixture of the artistic and the pornographic, a citywhere“anythinggoes”—thecityofBertoltBrechtandKurtWeil’sThreepennyOpera.Andscienceflourishedtherealongsidethearts.At the end of the 1920s, the physics faculty in Berlin was second to none.

Planck,although retired,continued togive lecturesasemeritusprofessor;LiseMeitner(1878–1968),whowasthefirstwomaninGermanytobeappointedasafull professor of physics and played a key part in the discovery of nuclearfission, lectured on nuclear physics; Walther Nernst (1864–1941), a leadingthermodynamicist,taughtexperimentalphysics;MaxvonLauewasthere;FritzLondon (1900–54), who helped develop the quantum theory of the chemicalbond,gavelecturesonthesubject,hotoffthepress.Inthisgalaxyofteachers,Schrödingerwastopdog.AndalthoughEinsteinhadnolecturingduties,hewastheretotalkthingsoverwith.Itwas generally agreed by the students that Schrödinger’s lectureswere the

clearestandthebest,givenwithoutnotesfromamasterathiscraft.Hewasalsopopularwiththestudentsforhisinformality,bothinhisstyleofteachingandinthe way he dressed. His informality in the matter of clothing had beencommented on at the Solvay Congress (not least by Dirac, who was always“correct”).With the confidencebornofhis successwithwavemechanics, andsecureinhisappointmentinBerlin—notjustajobforlifebutthejobforlife—hefeltnoneedtodresstoimpress,andturnedupatthesmarthotelinBrusselswhere the participantswere staying clad for hiking, with his knapsack on hisback.Intheofficialconferencephotograph,amongtheserriedranksofseriousscientists indarksobersuits,Schrödingerstandsout (even thoughhehasbeencarefullyplacedat theback tohidehimasmuchaspossible) ina lightcasualjacket.Thewonderisthathebotheredwiththejacketatall.InBerlin,whichwasstill steeped in the formal Prussian traditionwhich prescribed a dark suit andwhiteshirtwithcollarandtieasderigueurforlecturers,Schrödingeraddressedhis students wearing a sweater and a jaunty bow tie in winter, and an open-neckedshort-sleevedshirtinsummer.Ononefamousoccasion,whenhefailedto turnupontimefora lecture thestudentssentoutasearchparty to lookforhim, and found that the security guard had refused to admit the scruffy“imposter”; only with some difficulty was the gatekeeper persuaded that thisreallywasHerrProfessorSchrödinger,andthatthestudentswerewaitingtohear

himtalk.TheSchrödingerswerenolesspopularwiththeirpeers,andthrewlargeparties

which became a feature of the academic social scene. But they seem to havebeenlesspopularwitheachother,andSchrödinger’scolleagueswhovisitedhimathomeindividuallynoticedthatthecouplebarelyspoketooneanother.Erwinhad several romantic affairs while in Berlin (hewas always romantic, alwaysconvincedthathewasinlove),andalsosawIthaJungerwheneverpossibleonhistravelsoutsidethecity.In1929,anewpossibilityappearedonhisromantichorizonwhenhevisitedInnsbrucktogivealectureandstayedwiththerecentlymarriedphysicistArthurMarch(1891–1957).ErwinwasstruckbythecharmsofMarch’sbride,Hilde.Nothinghappenedatthetime,butyearslaterHildewouldhaveasignificanteffectnotjustonSchrödinger’sprivatelifebutonhiscareer.Meanwhile,therelationshipwithIthadevelopedtothepointwhereshecame

tostaywithSchrödingerinBerlininthesummerof1932,whileAnnywasaway.Theresultwaspregnancy,andanabortion.Probablyasaresultofthis,Itha,whowould latermarryanEnglishman,sufferedseveralmiscarriagesandwasneverable tohavechildren.After she leftBerlin,Erwinmetheronlyoncemore, inLondon in 1934.By then, theSchrödingerswerebased inOxford, having leftGermanybecauseofpoliticsandbeenwelcomedinEnglandbecauseofscience.Schrödinger’spositioninthescientificworldwascementedinFebruary1929,

whenhewaselectedamemberofthePrussianAcademyofSciences.Thiswasan honour that conferred membership of the élite, since membership wasrestrictedtothirty-fivepeopleineachoftwoclasses,thePhysical-MathematicalClass and the Philosophical-Historical Class. In nominating Schrödinger, whobecame theyoungestmemberof theAcademyat the ageof forty-two,Planckreferredtothewayinwhich“thehithertosomewhatmysteriouswavemechanics[ofdeBroglie]inonestrokewasplaceduponafirmfoundation.”TheAcademyregistered another, lesswelcome, sign of Schrödinger’s eminence a few yearslater,whentheNaziscametopowerinGermany.TheonlytwonamesexpungedfromthemembershiprecordsoftheAcademy,asiftheyhadneverexisted,werethoseofEinsteinandSchrödinger.Thediscoveryofwavemechanicswas, of course, an impossible feat to top,

andnobodyexpectedSchrödingertohitthoseheightsagain.Butduringhistimein Berlin Schrödinger’s idea received a boost from Dirac, and Schrödingerhimself made a suggestion which, although few people at the time took itseriously, was later revived, or rather rediscovered, in a big way. It wasconnectedtothe“DiracEquation.”

Dirac’sbreakthroughcamelatein1927.Bythentheconceptofelectronspinhadbeenaround for severalyears,andphysicistswerebecomingaware that itwasapurelyquantumpropertywhichhadnothingtodowithspin,orrotation,inthe everyday sense. The big drawback of the Schrödingerwave equationwasthat it did not include spin.Tweaking the equationsof quantummechanics bydroppingspininbyhandhelpedtomakepredictionsthatmatchedtheresultsofexperiments, but nobody had yet been able to come upwith an equation thatincorporatedspinasanintegralpartofthetheory.ThiswaswhatDiracnowdid.Hefoundanequationwhichdescribedthebehaviouroftheelectron,takingfullaccount of the requirements of relativity theory, and producing the propertyknownaselectronspin.Thisfullyrelativisticelectronequation,nowknownastheDiracEquation,didnotpredictanythingnew,butitexplainedeverythinginonemathematicalpackagewithnoneedforaddedextras.Ordiditpredictsomethingnew?Thepuzzlewasthattheequationseemedto

have two solutions, one positive and one negative, in the same way that anumber such as 4 has two square roots—in this case, 2 and −2. The DiracEquationseemed tobepredicting theexistenceofbotheverydayelectronsandnegativeelectrons—andsinceanelectronhasnegativeelectriccharge,andtwonegatives make a positive, a negative electron would have positive charge.Nobodyknewquitewhat tomakeof thisuntil 1932,when theAmericanCarlAnderson(1905–91)discoveredacounterpart to theelectron,butwithpositivecharge instead of negative charge, while studying cosmic rays. It was soondubbed the positron, or anti-electron. We now know that for every kind ofparticle there isakindofanti-particle—ananti-proton,ananti-neutron,andsoon. But while particles (such as electrons) are common in our world, anti-particles(suchaspositrons)arerare.Tohis contemporaries, themost interestingworkSchrödingerdidduringhis

timeinBerlinstemmedfromDirac’snewwork.Heinvestigated thepropertiesoftheelectronasdescribedbytheDiracEquation,andpublishedtwopapersonthetheme,in1930and1931,throughthePrussianAcademy.Hisresultsaretooesoterictogointohere;butinMarch1931SchrödingerofferedtheAcademyaremarkable paper which contains a breathtakingly simple, but almostunbelievable,idea,inthesameveinasDirac’snegativeelectrons.

Backtothefuture

This new speculation stemmed from Schrödinger’s early fascination withthermodynamics and the way the world is governed by statistical laws. Henoticed that hiswave equation had a similar structure to the equation used todescribe diffusion processes, such as the way molecules of perfume from anopenbottlespreadthroughtheair.Thankstohisworkinstatisticalmechanics,he was also aware of a curious property of the diffusion equation. Such anequation can be run in reverse, to describe a world in which molecules ofperfume come together out of the air and congregate in an open bottle, eventhoughwedonotseeeventslikethatgoingonintheeverydayworld.Thiskindof reversibility lies at the heart of the statistical understanding ofthermodynamicsdevelopedbyBoltzmannandothers.Now,youmightthinkthatifyouhadalltheinformationaboutthedistributionofscentmoleculesthroughthe air at a certain time, and the equivalent information for a later time, youcouldcalculatethedistributionofthemoleculesforanytimeinbetweeneitherbyworkingforwardfromtheearliertimeorbackwardfromthelatertime.But,asSchrödingerrealized,youwouldbewrong.Thewaytofind thedistributionforintermediatetimesistocombinethesolutionfortheequationgoingforwardin timewith the solution to the equation going backwards in time—in effect,multiplyingthetwoequations,ortheirsolutions,together.Theconnectionwithquantummechanics—whatSchrödingerdescribedinhis

paperas“themostinterestingthingaboutourresult”—comesfromthewaythesquare of Schrödinger’swave function is used to calculate probabilities in theCopenhagenInterpretation.ThewavefunctionisusuallydenotedbytheGreekletterpsi (ψ), but the square involved in the calculations is not simplyψ×ψ.Becausetheequations,likeallgoodwaveequations,involvethesquarerootofminusone(i),andaretherefore“complex”inthemathematicalmeaningoftheterm,thewavefunctionhastobemultipliedbysomethingknownasitscomplexconjugate,whichcanbedenotedbyψ*.Sotheprobabilityoffindinganelectronataparticularplacedependsonψ×ψ*.Butthecomplexconjugateis,ineffect,thesameas thewavefunctionrunningbackwardsin time.Likethesolutiontothediffusionproblem,theprobabilitiesintheCopenhagenInterpretationdependon combining two equations, one describing processes proceeding forward intimeandonedescribingprocessesproceedingbackwardsintime.AtthispointSchrödingerranintoabrickwall,andratherlamelyconcluded:“I

cannot foresee whether the analogy will prove useful for the explanation ofquantum mechanical concepts.” Nor could anyone else in the 1930s, andSchrödinger’spaper stirred so little interest that,half acentury later,when the

American physicist John Cramer (b. 1934) did find a way to interpret thecomplexconjugatetoprovideanewunderstandingofquantummechanicshedidsoincompleteignoranceofSchrödinger’s1931paper.IhavedescribedCramer’s“transactionalinterpretation”ofquantummechanics

fullyinmybookSchrödinger’sKittens,but it isworthgoingintoalittledetailheresinceitshowsjusthowdeepSchrödinger’sinsightwas.AlthoughCramerwasunawareofthisparticularinsight,oneoftheideasthathadsethimthinkingaboutwaves travellingbackwards in timewasnearly asold. In1940,RichardFeynman was a graduate student at Princeton University, working under thesupervisionof JohnWheeler (1911–2008).Hebecame interested in aproblemknownasradiationresistance,whichinsimplelanguagemeansthatitishardtopush charged particles like electrons around—they resist, more strongly thanuncharged particles resist, and at the same time they radiate electromagneticwaves. But Feynman knew that Maxwell’s equations, which describe allelectromagnetic radiation, are symmetrical in time (essentially for the samereasonthatSchrödinger’swavefunctionissymmetricalintime,althoughhedidnotmakethatconnectionin1940).Hesuggested,backingupthesuggestionwithcalculations, thatwhenanelectron(oranychargedparticle) is jiggledabout, itradiateselectromagneticwavesbothintothefutureandintothepast.Wherever,andwhenever,thisradiationmeetsanotherelectron(orotherchargedparticle),itmakes that particle jiggle about, and spread waves into the past and into thefuture.Theoverlappingwavesinteractwithoneanotherandmostlycancelout,like the probability waves in the Copenhagen Interpretation; but some of thewaves,frombothpastandfuture,returntotheoriginalelectronandprovidetheresistance needed to explain the reluctance of charged particles to be pushedaround.Wheeler was sufficiently impressed that he told the twenty-two-year-old

Feynman to give a talk explaining his ideas to the physics department atPrinceton.Thiswasadauntingtask,not leastsincetheaudienceincludedbothEinstein andPauli. Pauliwasunimpressed, and said that the ideawasnothingmorethanamathematicaltautology;butEinsteinreplied:“No.Thetheoryseemspossible.”Thework,tidiedupwiththehelpofWheeler,waspublishedin1941,and became known, though never universally accepted, as the “Wheeler-Feynman” theory of radiation resistance. A mere forty-five years later, JohnCramerincorporatedtheseideasintoquantummechanics.Mostquantummechanicsof the1980s ignored thephysical interpretationof

theSchrödingerequationandsimplyusedtheprobabilitieswithoutbotheringtoo

muchaboutwheretheycamefrom.ButCramerwentbacktothefullrelativisticversionoftheequationwithtwosetsofsolutions,onecorrespondingtoawavetravellingforwardintimeandonetoawaverunningbackwardsintime.Theseareknown,respectively,as“retarded”wavesand“advanced”waves.Withinthisframework, Cramer described a typical quantum “transaction” (such as aninteractionbetweentwoelectrons)intermsoftheparticles“shakinghands”witheachotheracrossspaceandtime.Inordertogetafeelforwhatisgoingon,youhave to stand outside of time, in a sense, and look at the interaction, ortransaction, from the perspective of some kind of supertime. There is nosuggestion,though,thatthissupertimeisreal;itisjustadevicetohelpusgetthepicturestraightinourminds.Imagineaquantumentity thatmakesa transition fromonequantumstate to

another—anelectron,perhaps,whichstartsinastatecorrespondingtoapositionon one side of the experiment with two holes, and ends up in a statecorresponding to a point on the detector screen on the other side of theexperiment. The electron is described by a wave which spreads out into thefuture.Itisalsodescribedbyawavetravellingintothepast,butignorethatforthemoment.Theretardedwavearrivesat thedetectorscreen,whereit triggersthe emission of further sets of advanced and retarded waves. The advancedwaves from the detector travel back in time to the original position of theelectron,whereonesetofwaves isselectedat random, inaccordancewith therulesofprobability, and“chosen” to combinewith theoriginal retardedwave.Thistriggerstheproductionofa“new”advancedwavetravellingbackwardsintime which cancels out the original advanced wave (which is why we couldignore it), anda“new” retardedwave travelling into the future,whichcancelsout the original retardedwave everywhere except where the “handshake” hasoccurred.Sotheelectronmakesatransitionfromitsstartingpointtoonepointonthedetectorscreen.Butitismeaninglesstoaskwhatitisdoing“inbetween”;thereisnoinbetween.AsCramerputit:“Theemittercanbeconsideredtoproducean‘offer’wave

whichtravelstotheabsorber.Theabsorberthenreturnsa‘confirmation’wavetothe emitter, and the transaction is completed with a ‘handshake’ acrossspacetime.” But in reality, there is no toing and froing; it all happensinstantaneously,producingtheeffectofwhatissometimesknownasactionatadistance. This “transactional interpretation” of quantum mechanics makesexactlythesame(correct)predictionsabouttheoutcomesofexperimentsastheCopenhagen Interpretation, andmakesnopredictions that differ from thoseof

theCopenhagenInterpretationorotherinterpretationsofquantummechanics;soultimatelythechoiceofwhichoneyoupreferisamatterofpersonaltaste.Butitdoesshowthatitispossibletounderstandquantummechanicswithoutinvokingthe “collapse of the wave function”—and that in itself is a thoroughly goodthing,since there isnothing in theequations thatdescribes,or requires,suchacollapse; it ismerelyaheuristicdevice introducedbyBohron thebasisofnoevidencewhatsoever.AndSchrödingerhatedit.As I discuss in the next chapter, Schrödinger’s antipathy to the idea of

collapsingwavefunctionsledhimtohismostfamousthoughtexperiment.Butby the time he came up with the idea he had left Berlin, as a result of thepoliticalturmoilthatsweptthroughGermanyintheearly1930s.

PeopleandpoliticsThe immediate trigger for that turmoil was the global economic crisis thatfollowed the Wall Street crash of October 1929. The recession and resultingmassunemploymentinGermanygainedtheNazipartymanyrecruits,andledtoviolentstreetbattlesbetweentheirsupportersandtheCommunists.Theirshareofthevotegraduallyroseduringsuccessiveelections,peakingat37percentinJuly 1932, when they became the largest party in the Reichstag, althoughwithoutanoverallmajority.Although tenured university professors were in many ways insulated from

theseproblems,andactuallybenefitedfromfallingpricesastheirsalariesweremaintained, research fundingwas slashed. Students and junior university staffsuffered with the general population, and many reacted the same way. Therewereriotswithinuniversityprecincts(wherethepolicewerenotallowed),anddemonstrationsinsupportof theideaofaquotalimitingthenumberofJewishstudents. Schrödinger made no secret of his dislike of the Nazis, but he wasneveractivelyinvolvedinopposingthem.Hecarriedonwithhis teaching,butdidlittleresearchasthingscametoahead.Inanotherelection,inNovember1932,theNazis’shareofthevotefellback

from37percentto32percent.Butanunholyallianceofoldgenerals,leadersofthearistocraticfamiliesknownastheJunkers,andindustrialistshaddecidedthatthekindofstrongleadershipandnationalpridethatthepartyofferedwouldbetherightthingforGermany,andpressuredHindenburg,whowasstillPresidenteventhoughhewasnowsenileandnotreallyawareofwhatwasgoingon,into

appointingAdolfHitlerasChancelloron30January1933.Thediewascast,andifthegeneralsandtheJunkersthoughtthatHitlerwouldbetheirgratefulpuppetthey were sadly mistaken. In March 1933 Hitler called new elections, andachievedamajority in theReichstagby the simple expedientof excluding theCommunists.He used thatmajority to pass an actwhich gave him dictatorialpower,andmadetheassemblyredundant.The troubles now began to have an impact closer to home for Schrödinger.

EinsteinwasinAmericaatthetimeHitlerwasappointedChancellor,andvowedthathewouldnotreturntoGermanyaslongastheNaziswereinpower;healsoresigned his membership of the Prussian Academy. The Academy replied, ineffect,“goodriddance,”andSchrödinger,withoutmakinganypubliccommentonthesituation,stoppedattendingitsmeetings.LawsexcludingJewsandother“undesirables”fromholdinggovernmentpositions,includingacademicpostsatuniversities, were passed, and within a year nearly two thousand facultymembersacrossGermanyweresacked—includingMaxBorn.Manyscientistsaroundtheworldwatchedinhorror,butfelttherewasnothing

they could do to help. Oneman in particular, though, decided hemust try toassist the expelled Jewish scientists. He was Frederick Alexander Lindemann(1886–1957),thenheadoftheClarendonLaboratoryinOxfordanduniversallyknownas“theProf.”LindemannseemsanunlikelyfiguretoleaptotheaidofGerman Jews.Hewas extremelywealthy, having inherited a fortune from hisfather, unmarried, and with an unpleasant streak that manifested itself insarcastic remarks about those he considered his inferiors (including mostwomen).HehadnoJewishconnections,andlikemostofhisclassinEnglandatthetimewasifanythingmildlyanti-Semitic.Hisinitialideaseemstohavebeensimply to get hold of some top scientists to enhance the physics faculty atOxford University. But his scheme grew like Topsy. In spite of the difficulteconomic situation, Lindemann managed to get funding from the Britishcompany Imperial Chemical Industries (ICI) to provide new posts for Jewishscientists with established reputations, so that British scientists would not beadverselyaffectedandnopublicmoneywouldberequired.Theschemebecameagreatsuccess,andprobablysavedmanylives;buthereIamonlyinterestedinthewayitaffectedSchrödinger.InApril1933,LindemannvisitedGermanytoassessthesituationanddrawup

ashortlistofscientistswhomhemightbeabletohelp.Hehadthoughtthattheproblemwouldbeatemporaryone,andthatGermanywouldsoonrecoverfromwhat he called “the Nazi madness”; but what he saw persuaded him that the

Naziswouldbeinpowerforalongtime.Duringhisvisit,hemetSchrödingerathis home in Berlin, and listened while he spoke of his distaste for the newregime. Lindemann offered one of the new ICI fellowships to Schrödinger’sassistantFritzLondon,thenaPrivatdozentat theuniversity,buttothesurpriseofbothLindemannandSchrödingerheaskedfortimetothinkthingsover.2SoSchrödinger said: “Offer it to me.” Lindemannwas taken aback. SchrödingerwasnotJewish,andatthattimeundernothreatfromtheregime;buthewassoopposedtowhatwasgoingoninGermanythatat theageofforty-fivehewaswilling togiveuphis job for lifeand faceanuncertain futureasanémigré inEnglandonashort-termappointment.ItwouldbeagreatcoupforOxford,andLindemannpromisedtocheckoutthepossibilitiesonhisreturntoEngland.Buttherewasonecatch(althoughLindemanndidnotknowitatthetime),involvingSchrödinger’s private life. He asked for additional funding for a post for hisfriendArthurMarch,onthegroundsthatheandMarchwantedtowriteabooktogether. The real reasonwas that Schrödingerwas by now,with Itha off thescene,inhotpursuitofMarch’swife,Hilde.The pursuit continued through the summer, and across Europe, while

Lindemann was, among other things, sorting out the funding situation inEngland.Schrödinger’sdeterminationtoleaveGermanywasreinforcedinMay,whentheGermangovernmentintroducedavisafeeof1,000marksforGermans,orstateemployeessuchasSchrödinger,wantingtovisitAustria.Thismeantthathe andAnny could not afford to visit their homeland, even for the seventiethbirthdaycelebrationsofAnny’smother.Withhardenedresolve,theSchrödingerspacked up many of their belongings and sent most to England and some toSwitzerland.Soonaftermakingthesearrangements,thecouplesetoffonholidayin their new BMW, heading for the Tyrol. They started out with a hiredchauffeur/instructor,whotaughtthemtodriveastheywentalong,andleftthemat the Swiss border. Schrödinger wrote a formal letter to the authoritiesrequesting“studyleave,”butdidnotresignhispost;healsosentapostcardtotheportersatthephysicsdepartmentinformingthemthathewouldnotbegivinghislecturesintheautumn.Hissalarywasstoppedon1September,butbythenhewassafelyoutofreach.Sofar,Schrödinger’spursuitofHildehadbeenunsuccessful,eventhoughhe

hadoffered todivorceAnnyandmarryher.Buthewasconfident. InMay,hewroteinhisdiary:“Ithasneverhappenedthatawomanhassleptwithmeanddidnotwish,inconsequence,tolivewithmeforallherlife.IswearinthenameofthegoodGodthatitwillbethesamethingwithher.”Andthesituationwas

abouttochange.With Anny doing most of the driving, the Schrödingers visited Zürich and

wentonthroughthemountainstoItaly,tothetownofBressanone,whereArthurMarch had been born when, under the name of Brixen, it was part of theAustrianEmpire.There, theymetupwith theMarches.TheBorn familywerestayingnearby,andAnnywentofftovisitthemwithherloverHermann(Peter)Weyl.Hilde’sresistancecrumbled,and,apparentlywithArthur’sacquiescence,shewentoffonacyclingtourwithErwin.Bythetimetheycameback,shewaspregnant, having been childless for four years ofmarriage. Thismay bewhyArthur condoned the arrangement and remained friendly with Erwin; as forAnny,shewashardlyinapositiontoobjectandremainedfriendlywithHilde.ItsayssomethingaboutSchrödinger’spropensityforflirtationthatevenwhile

fresh from his successful conquest of Hilde, he was not blind to otheropportunities. In September, Erwin moved on to Malcesine, on Lake Garda,havingwrittentoLindemann,whoheknewwouldbevisitingItaly,tosuggestameeting there. In Malcesine, he bumped into Hansi Bauer, the daughter ofAnny’soldemployer,nowtwenty-sixandonherhoneymoon.ShehadmarriedFranz Bohm, ten years her senior, who had studied engineering and politicalscienceinViennaandhadserved,likeSchrödinger,asanartilleryofficerintheFirstWorldWar.HewasnowworkingfortheIngersollcompany.Accordingtoheraccount inan interviewwithWalterMoore, thehoneymoonwasnotgoingwell,andshewasalreadydisillusionedbyhermarriagewhenshechanceduponErwininagroceryshopandtherewas“aspark”betweenthem.Butitwouldbesometimebeforethatsparklitaflame.LindemannsoonarrivedatLakeGardawithgoodnews.Hewasabletooffer

Schrödinger an appointment for twoyears, funded largelyby ICIbutbased inOxfordandcarryingoutresearchthere,withapackageofremunerationroughlyequivalenttothesalaryofaprofessor.On3October,SchrödingerwaselectedaFellow ofMagdalen College in his absence. Soon afterwards he set out withAnnyintheBMWforParisandBrussels,whereheattendedtheseventhSolvayCongress but took no active part. The couple finally arrived in Oxford on 4November1933.Thetimingwasperfect—onthedayofhisformalwelcomeasaFellowofMagdalen, news came thatSchrödinger hadbeen awarded the 1933NobelPrizeinphysics,jointlywithPaulDirac.Soinmorewaysthanone,itwasthebeginningofanewphaseofhislife.

Notes

1Dirac,DirectionsinPhysics.2Hardlysurprisingly,itdidn’ttakemuchthoughtforLondontodecidetotakeuptheoffer,andhetoobecameoneoftheProf’sprotégés.

ChapterNine

TheComingoftheQuantumCat

TheSchrödingersbarelyhadtimetosettleinOxfordbeforeitwastimetoleavefor the Nobel award ceremony; the awards are always presented on 10December, the anniversary of the death of Alfred Nobel, the inventor ofdynamite, who had left his fortune to establish the prizes. They arrived inStockholm on 8 December, and Erwin duly received his share of the physicsprize,100,000kroner(about$27,000attheprevailingexchangerate);wisely,hedecidedtokeepthebulkofthemoneyinSweden.On12DecemberhegavehisformalNobelLecture,on“TheFundamentalIdeaofWaveMechanics,”avoidinganydeepmathematics,andthenitwastimeforthecoupletoreturntoOxford.They eventually settled in a large rented house at 24 Northmoor Road; theMarchessettlednearby,at86VictoriaRoad.ButoneofthefirstdecisionsErwinhadtomakewaswhentotakeanextendedleaveofabsencefromOxford.

BackintheUSAWhen he had arrived in Oxford—before learning about the Nobel Prize—Schrödinger had found a letter from Princeton University waiting for him. Itcontained an invitation to give a series of lectures at Princeton for either one,two,orthreemonths,athischoice.Forthishewouldbepaidasalaryof$1,000per month; and there would be a contribution of $500 towards his travelexpensesthrownin.Inresponsetoanofferlikethat,roughlyequivalenttoayearofhisOxfordsalaryforthreemonths’work,theonlyquestionwaswhentoleaveandhowlongtogofor.There was an ulterior motive behind such a generous offer. The Physics

Department at Princeton was looking for someone to fill the vacantprofessorship ofmathematical physics, andSchrödingerwas on a short list oftwo (himself and Heisenberg). The lecture tour would give them a chance tolookathim,and,iftheylikedwhattheysaw,achancetopersuadehimtotake

up the full-time post. But it turned out that theywould have to exercise theirpowersofpersuasionratherswiftly,sinceSchrödingertookuptheofferofaone-month appointment, leaving England on 8 March 1934 and returning on 13April.InhisabsenceAnnyvisitedtheBorns,nowinCambridge.WhileinPrinceton,Schrödingerstayedat theGraduateCollege,animitation

of anOxbridge college housed in amock-Gothic building.He gave his usualimmaculate lectures, and was duly offered the professorship, a post which,ironically in view of the success of his lectures, had no teaching duties. HeimmediatelywrotetoLindemanntoinformhimofthesituation,explainingthathehadtoconsidertheofferseriously,“forafterallandinspiteofallso-calledreputationIamactuallywithoutwhatamanofmyageandmétierconsidersa[permanentposition].Andif,e.g.,Iweredrownedonthepassage[home],Iamafraid that my wife could neither live upon the German pension nor on the[Schrödingerequation].”ThisletterhighlightsSchrödinger’sincreasingconcernwithestablishinglong-

termsecurity,notsomuchforhimselfbutforhiswifeafterhisdeath,aconcernbasedonwhathehadseenhappentohisownmother.Gettingajobwithagoodpensionbecamealmostanobsessionwithhim,andwouldsoonleadhimintoanunwise move. But even for a pension Schrödinger was reluctant to live inAmerica,andstalledaslongaspossiblebeforefinallyturningtheofferdowninJune(Princetondidn’tgetHeisenberg,either).Significantly,althoughthesalaryon offer at Princetonwas excellent ($10,000, roughly twicewhat Schrödingerearned inOxford), thewidow’spension associatedwith thepostwasnotverygood,amountingtoonly$200ayear.Andtherewasanothersnag.WhattodoaboutthepregnantHildeMarch?In

hisprivatejournal,Schrödingerwrotethathewouldbesadto“leavethemotherand child,” and therewas certainlynoprospect of arranging apost forArthurMarch inPrinceton. It iswidelybelieved inPrinceton (as amatter of folklorerather than proven fact) that Schrödinger discussed the problem with JohnHibben,thePrincetonUniversityPresident,whowashorrifiedatthethoughtofSchrödinger bringing a wife, a mistress, and an illegitimate child to theconservative campus. TheOxford establishmentwas scarcely less horrified atwhattheyhadletintotheirmidst.

Oxfordandbeyond

In the male-dominated environment of Oxford colleges in the 1930s, it wasconsidered a bit odd to have onewife, let alone two.But Schrödinger treatedHildeexactlyasasecondwife,goingaroundwithherinOxfordinthemonthsleadinguptothebirthoftheirchild,andmakingnosecretoftheirrelationship.Their one concession to conventional morality was that when the baby, RuthGeorgeErica,wasborn,on30May1934, thenameofherfathergivenon thebirth certificate was Arthur March. Hilde, suffering perhaps from post-nataldepression,ormaybethestrainoflivingintheSchrödingerménage,orboth,hadlittleinterestinthebabyinitially,andshewaslargelylookedafterbyAnny(and,ofcourse,anurse)forthefirstfewmonths.Allof thisput a severe strainonSchrödinger’s relationshipwithLindemann

and ICI, who felt (correctly!) that they had been hoodwinked into appointingMarch. The antipathy between Schrödinger and Oxford was mutual. As heexplainedtoMaxBorn,1“Thesecollegesareacademiesofhomosexuality.Whatqueer types ofmen they produce.” And he was baffled by the informality ofcollegedinners.“Youneverknowwhoyourneighbourmightbe.Youtalktohimin your natural manner, and then it turns out that he is an archbishop or ageneral.” Nor was he mollified by his teaching duties—or rather, the lack ofthem. He only had to give one lecture a week, on “Elementary WaveMechanics,”andgrumbledtoAnnythattherewassolittleworktodothathefelthewas being treated as a charity case. But in the summer of 1934, he had achancetogetawayfromitall.Schrödingerwas invited to give lectures inSpain, at Santander andMadrid,

andseized theopportunity,whileAnnyseizedherownopportunity tomeetupwithWeyl inSwitzerland.TheSantander lectureswere translated intoSpanishand published as a book; even more significantly, Schrödinger struck up arapportwith thephilosopherJoséOrtega,whohadorganized themeeting.ThewholeexperiencewassuchadelightfulcontrastwithOxfordthatinthespringof1935hereturned,withAnnyandtheBMW,tomakeapropertourofthecountry,stoppingoff togiveanother seriesof lectures inMadrid.There seems tohavebeenarealpossibilityofapermanentmovetotheUniversityofMadrid,butanysuchprospectswerequashedbytheoutbreakoftheSpanishCivilWarin1936;Schrödinger’sfriendOrtega,astaunchRepublican,wasamongthoseeventuallyforcedintoexile.It may have been with the possibility of a move to Spain in mind that

Schrödinger tidiedupa looseendwhilehewas inMadrid.Hewrote toBerlinformally resigning his professorship there. The resignation was formally

accepted on 31 March; on 20 June, Hitler sent a formal letter of thanks toSchrödingerforhisservices,andinJuly1935hewasgiventhehonorarytitleofprofessoremeritus.All seemed tobe sweetnessand lightbetweenSchrödingerandtheauthoritiesinBerlin.BackinEngland,Schrödingerwasinvitedtogiveatalkinaseriesonfreedom,

ahottopicwiththeriseoffascisminEurope,broadcastonBBCradio.Thisisthesortof thingNobel laureatesareaskedtodo,whatever theirspeciality.Histitlewas“EqualityandRelativityofFreedom,”andthetalkwaspublished,alongwithothersintheseries,inTheListener.Hismainpoint,thatfreedomisrelative,hardlyseemsworld-shatteringnews,butthetalkissignificantinthecontextofSchrödinger’s life for one omission and one inclusion. The omission is anymentionofthesituationinNaziGermanyatthetime;theinclusionshowshowdeeply Schrödinger was affected by Itha’s abortion, although (ironicallyrevealing the suppressionof another freedom) inorder to refer to it in aBBCbroadcastofthe1930shehastousecircumlocutions:“Theindividual,thistimeafemale,inordertoavoidcontemptandrejectionbyallthe‘respectablepeople,’is compelled to commit an action, which is threatened by the law of mostcountrieswithpenalservitude.MostofyouwillknowwhatImean.”Justafterhemadethisbroadcast,Schrödinger’sattentionwasfocusedbackon

theinterpretationofquantummechanicsbythelatestcontributionfromEinstein.

Fasterthanlight?By1935,EinsteinwassettledinPrinceton,attheInstituteforAdvancedStudy.Hehadbeenworkingwithtwoyoungercolleagues,BorisPodolsky(1896–1966)andNathanRosen (1909–95),and together (ledbyPodolskyon thisoccasion)they had come upwith what seemed to them an unarguable refutation of thenonsense(astheysawit)inherentintheideaofcollapsingwavefunctionsandtheCopenhagen Interpretation.Their paper describingwhat became known asthe“EPRParadox,”even though it isnot reallyaparadox,appearedunder thetitle“CanQuantumMechanicalDescriptionofPhysicalRealityBeConsideredComplete?” in the journalPhysical Review inMay 1935.2 They described thepuzzleintermsofmeasurementofpositionandmomentum,butIshallusewhatseemstomeasimplerexampleinvolvingelectronspin.Imagineasituationinwhichtwoelectronsareejectedfromaquantumsystem

(suchasanatomicnucleus)indifferentdirections,butarerequiredbythelaws

ofsymmetrytohaveoppositespin.AccordingtotheCopenhagenInterpretation,neitheroftheelectronspossessesadefinitespinuntilitismeasured;eachexistsina50:50“superposition”ofspinupandspindownstates,untilitismeasured.Then,andonlythen,thewavefunctioncollapsesintooneortheotherstate.Butin this example the laws of symmetry require the other electron to have theoppositespin.Thisisfinewhenbothelectronsareinthesuperpositionofstates,but it means that at the instant one electron is measured, the other electron,whichmightbynowbefaraway(inprinciple,ontheothersideoftheUniverse),collapses into the opposite state at the same instant. How does it know to dothis?ItseemsthatwhatEinsteincalleda“spookyactionatadistance”linksthetwo particles, which communicate with one another faster than light. And allquantumentities(whichmeanseverything)mustbelinkedinthesameway.It is akey tenetof the theoryof relativity,whichhaspassedevery test ever

appliedtoit,thatnosignalcantravelfasterthanlight;soEinstein,inparticular,saw this argument as a complete refutation of Bohr’s ideas. The EPR paperconcludedthattheCopenhagenInterpretationmakestherealityofpropertiesofthesecondsystem“dependupontheprocessofmeasurementcarriedoutonthefirst system, which does not disturb the second system in any way. Noreasonabledefinitionofrealitycouldbeexpectedtopermitthis.”ThealternativethatEinsteinfavouredisthatthereissomekindofunderlying

reality,aninvisibleclockworkwhichcontrolstheworkingsoftheUniverseandgivestheappearanceofuncertainty,collapsingwavefunctions,andsoon,eventhough “in reality” each of the electrons, in this example, always has a well-definedspin. Inotherwords, thingsare“real,”not inasuperpositionofstates,evenwhenwearenotlookingatthem.TheideathattheUniverseiscomposed,even at thequantum level, of real things that existwhetheror notweobservethem,andthatnocommunicationcantravelfasterthanlight,isknownas“localreality.”It is, perhaps, just as well Einstein did not live to see a series of beautiful

experimentscarriedoutinthe1980swhichprovedthatlocalrealityisnotagooddescription of the Universe. I’ll go into these in more detail later, but theirimplication is that we are forced to abandon either the local bit (allowingcommunication faster than light) or reality (invoking instead collapsing wavefunctions)—or, as I shall explain, go for something else entirely. But nobodyknewthisin1935,andSchrödingerinparticularwasdelightedwhenhesawtheEPRpaper.HewroteatoncetoEinstein,commentingthat“myinterpretationisthatwedonothaveaq.m. that is consistentwith relativity theory, i.e.,witha

finite transmission speed of all influences,” and in a paper published in theProceedingsof theCambridgePhilosophicalSociety later thatyear said: “It israther discomforting that the theory should allow a system to be steered orpilotedintooneortheothertypeofstateattheexperimenter’smercyinspiteofhishavingnoaccesstoit.”3ThiswasthegenesisofSchrödinger’sfamouscat.

ThecatintheboxThe ideas encapsulated in the famous “thought experiment” involvingSchrödinger’s cat actually came in no small measure from Einstein, in theextended correspondence between the two triggered by the EPR paper andpreserved in the EinsteinArchive at PrincetonUniversity. Einstein introducedtheideaoftwoclosedboxesandasingleball,“whichcanbefoundinoneortheotherofthetwoboxeswhenanobservationismade”bylookinginsidethebox.Commonsensesaysthattheballisalwaysinoneoftheboxesbutnottheother;the Copenhagen Interpretation says that before either box is opened a 50:50wavefunctionfillsbothoftheboxes(butnotthespaceinbetween!),andwhenoneoftheboxesisopenedthewavefunctioncollapsessothatnowtheballisinoneboxortheother.Einsteincontinued:“Ibringintheseparationprinciple.Thesecondboxisindependentofanythingthathappenstothefirstbox.”In a later letter, Einstein came up with another reductio ad absurdum. He

suggestedtoSchrödingertheideaofaheapofgunpowderthatwould“probably”explodesometimeinthecourseofayear.Duringthatyear,thewavefunctionofthegunpowderwouldconsistofamixtureofstates,asuperpositionofthewavefunction for unexploded gunpowder and the wave function for explodedgunpowder:In the beginning the ψ-function characterises a reasonably well-definedmacroscopicstate.But,accordingtoyourequation,afterthecourseofayearthisisnolongerthecaseatall.Rather,theψ-functionthendescribesasortof blend of not-yet and of already-exploded systems. Through no art ofinterpretationcanthisψ-functionbeturnedintoanadequatedescriptionofareal state of affairs . . . in reality there is just no intermediary betweenexplodedandnot-exploded.Stimulated by the EPR paper and his correspondence with Einstein,

Schrödinger wrote a long paper, published in three parts in the journal DieNaturwissenschaftenlaterin1935,summinguphisunderstandingofthetheory

he had helped to invent. It was titled “The Present Situation in QuantumMechanics,”anditintroducedtotheworldboththeterm“entanglement”andthecat“paradox,”which(liketheEPR“paradox”)isnotreallyaparadoxatall.Anexcellent English translation of the paper, by John Trimmer, appeared in theProceedings of the American Philosophical Society in 1980, and can also befound in the volume edited by Wheeler and Zurek, Quantum Theory andMeasurement.Manygarbledaccountsofthe“catinthebox”“experiment”haveappearedovertheyears,butitisbesttogobacktothissourceandSchrödinger’sownwords(asinterpretedbyTrimmer)togetthepuzzleclear:One can even set up quite ridiculous cases. A cat is penned up in a steelchamber,alongwiththefollowingdiabolicaldevice(whichmustbesecuredagainstdirectinterferencebythecat):inaGeigercounterthereisatinybitofradioactivesubstance,sosmall,thatperhapsinthecourseofonehouroneof the atoms decays, but also, with equal probability, perhaps none; if ithappens,thecountertubedischargesandthrougharelayreleasesahammerwhichshattersa small flaskofhydrocyanicacid. Ifonehas left thisentiresystem to itself for an hour, one would say that the cat still lives ifmeanwhile no atom has decayed. The first atomic decay would havepoisoned it. The ψ-function of the entire system would express this byhaving in it the living and the dead cat (pardon the expression)mixed orsmearedoutinequalparts.It is typicalof thesecases thatanindeterminacyoriginallyrestrictedto theatomicdomainbecomestransformedintomacroscopicindeterminacy,whichcanthenberesolvedbydirectobservation.

In other words, according to the version of quantum mechanics that wasgenerally taught and widely (but not universally) accepted for the rest of thetwentiethcentury, thecat isbothdeadandalive (or ifyouprefer,neitherdeadnoralive)untilsomebodylooksinsidethechamberandbytheactofobservation“collapses the wave function.” But there is nothing in the equations aboutcollapsingwavefunctions.Remember,thisisanentirelyadhocideaintroducedbyBohr,withnobasis in reality.That is thesinglemost importantmessage totakeawayfromSchrödinger’sthoughtexperiment(which,Istress,isindeed“allinthemind”;nobodyhaseverdoneanythinglikethistoarealcat).Althoughthe“cat in thebox” ideadidnotgeneratewidespread interest in1935,Einstein atleast fully appreciated the importance of Schrödinger’s puzzle; Schrödingerdescribedtheideatohiminaletter,beforehispaperwaspublished,andEinstein

replied: “Your cat shows that we are in complete agreement concerning ourassessmentofthecharacterofthecurrenttheory.Aψ-functionthatcontainsthelivingaswellasthedeadcatjustcannotbetakenasadescriptionofarealstateofaffairs.”Schrödingerwasrighttopointoutthenonsensicalnatureoftheconceptofthe

collapseofthewavefunction,andtherearemuchbetterwaystounderstandtheworkings of the quantum world—the most intriguing of which Schrödingerhimself later came close to developing. But in the months following thepublicationofhisthree-partpaper,Erwinhadotherthingsonhismind.

FromOxfordwithloveICIhadoriginallyofferedfundingfortherefugeescientistsfortwoyearsonly,asanemergencymeasure,ontheassumptionthatthiswouldgivethemtimetofindpermanentposts.Somedid,butmanydidnot.Whentheirtwoyearsranout,ArthurMarch,Hilde, and babyRuth had to return to Innsbruck,whereHildestayed ina sanatoriumfor severalmonths, recovering from the strainofbeingSchrödinger’ssecond“wife”andthemotherofhischildindisapprovingOxford.Schrödingersoonfoundconsolation.FranzBohmandHansihadbeenlivinginBerlin,buttheycamefromawealthyJewishbackground,andhadgotoutfromundertheNazithreattoliveinLondon.Thiswasparticularlyconvenient,sinceAnnySchrödingerhadobtainedtheuseofaflatinLondon,whereshecouldgotogetawayfromErwinandleavehimmoretimewithHilde;sohenowhadthefreedom to “bewith”Hansi,who became a frequent visitor toOxford. In thesummerof1935,HansiandErwinevenwentonholidaytogether,totheChannelIslands.Professionally, though, thingswere less satisfactory. Although ICI had been

persuadedtomakeSchrödingeraspecialcase,andofferedhimtwomoreyears’funding,theproblemofapensionloomedlarge,andhehadneverfeltathomeamongOxford’scollegiatecommunity.ThebestofferhehadreceivedwasofaprofessorshipinMadrid,andhewouldprobablyhaveaccepteditiftheSpanishCivilWarhadnotbrokenoutinJuly1936.Buttherewasanotherprospectonthebackburner.AvacancywasknowntobecomingupattheUniversityofGraz,inAustria—

Schrödinger’s homeland.Hewas seriously tempted, provided that he couldbeallowed to have a few practical privileges, in particular keeping hismoney in

Sweden.InMay1935,hehadwrittentoEinstein:ItisnotthatIcan’tstanditinoneplaceforlong.UptillnowI’vegenerallybeencontentedwhereverIwasexcept inNaziGermany.Alsoit isnot thatthey haven’t been very nice and friendly tome here. But nonetheless thefeeling grows stronger of having no employment and living on thegenerosity of others.When I came here I thought I would be able to dosomething for the teaching, but no value is placed on that here . . . I amsittingherewaitingforthedemiseorthecompletedecrepitudeofaverydearold gentleman [the incumbent inGraz] and the possibility that theymightmakemehissuccessor.InDecember,SchrödingermadeavisittoAustria,partlytotestthewaters.He

stayedinGraz,gavelecturesinVienna,andvisitedtheMinistryofEducationtotalk about the possibilities and his special requirements. Over the Christmasperiod, he combined skiing with a chance to see Hilde and Ruth, and thenmanagedtosqueezeinavisittoMaxvonLaueinBerlinbeforeheadingbacktoEngland.Butthere,hisdevelopingplansforareturntoAustriaweretemporarilythrownintoconfusionbyanotheroffer.CharlesDarwin,aneminentphysicistandgrandsonof“the”CharlesDarwin,

resigned his professorship at the University of Edinburgh towards the end of1935, tobecome theMasterofChrist’sCollege,Cambridge.Acommitteewassetuptoseekhissuccessor,andinMay1936itreportedtotheUniversityCourtthat Schrödinger was the best available candidate. As part of the process offindingtherightmanforthejob,thecommitteehadinvitedSchrödingertovisitEdinburgh,wherehewasshownaroundbyDarwin,whohadnotyetlefttotakeuphisnewposition.Someof theseniormembersof theuniversityraisedtheirproverbial eyebrows at Schrödinger’s clothing: he came, as was his habit,dressed for a hiking tour of the Alps—not the conventional attire for whatamountedtoajobinterviewataBritishuniversity.Buttheylikedwhattheysawsufficientlyforaformaloffertobemade,subjecttoaguaranteefromtheHomeOffice that Schrödinger would be allowed to take up permanent residence inBritain.Thesalaryofferedwasamodest£1,200ayear;buthewouldnothavetoretirebeforereachingtheageofseventy,andtherewasagoodpensionattachedtothepost.Schrödinger was initially enthusiastic about the prospect of a move to

Scotland, andhe toldHansi that hewould accept theoffer if shewould comewithhim.Buthemusthaveknowntherewasnorealchanceofheracceptinghis

invitation, sincebynow shewaspregnantwithher first child (his orFranz’s?Nobodyknows)andabouttoreturntoVienna.Perhapsthatwasafactorinnowmaking Graz look more attractive than Edinburgh. Whatever the reasons,SchrödingercooledtowardstheEdinburghpost,whiletheHomeOfficetookaninterminable time tomake up itsmind. Before it did so, a formal offer camefromAustria—theprofessorshipatGraz,combinedwithanhonorary(butpaid)professorshipattheUniversityofVienna.Tactfully,SchrödingertoldEdinburghthat the chance to return to his homeland was too good to miss; he did notmention that thechance tobenearHilde,babyRuth,andHansiwouldalsobetoogoodtomiss.ButEdinburgh,althougheffectivelyjiltedatthealtar,didn’tdotoo badly: Darwin’s professorship went to Max Born, who stayed with theuniversity (with the Home Office’s approval) in a mutually satisfactoryrelationshipuntilheretiredin1953.SchrödingermusthaveleftEnglandinthesummerof1936,readytotakeuphisteachingdutiesinGrazon1October,withahappyheart.Buthewouldreturn,muchlesshappy,exactlytwoyearslater.

Notes

1SeeBorn,MyLife.A.J.Ayer’sautobiography,PartofmyLife,givesadeeperinsightintotheOxfordsocietyofthetime.2Thepaper,alongwithmanyotherrelevantpapers,canbefoundinthevolumeeditedbyJohnWheelerandWojciechZurek,QuantumTheoryandMeasurement;anextendeddiscussionoftheEPRParadoxcanbefoundinthevolumeeditedbyFrancoSelleri,QuantumMechanicsversusLocalRealism.Einsteinactuallyhadverylittletodowithwritingthepaper,butallowedhisnametogoonitasco-author.3Inanotherpaper,publishedthesameyearinNaturwissenschaften,hecoinedtheterm“entanglement”todescribethewaythetwoquantumentitiesarelinked.Inhisownwords,“Thecharacteristicofquantummechanics,theonethatenforcesitsentiredeparturefromclassicallinesofthought[isthat]bytheinteractionthetworepresentatives(orψ-functions)havebecomeentangled.”

ChapterTen

There,andBackAgain

Withhindsight,Schrödinger’sdecisiontoreturntoAustriain1936was, tosaytheleast,ill-judged.1Evenwithout thebenefitofhindsight,Schrödingershouldhaveknownwhathewaslettinghimselfinfor,andhelaterdescribedhisactionas“anunprecedentedstupidity.”2Ofcoursehewantedtoreturntohishomeland,andhewantedthesecurityofapension;butevenbythestandardsofAustriain1936,GrazingeneralandtheuniversityespeciallywerehotbedsofNazism.TheProfessorofPhysicalChemistrytherewasalsotheleaderofthelocalNaziparty;morethanhalfofthestudentswereactiveintheparty;andthelocalnewspaperswere hardline supporters of Nazism. Anti-Semitism was rife, and manyAustrianswelcomedtheattentionsofAdolfHitler,himselfanAustrianbybirth,whomadenosecretofhisdesiretoabsorbAustriaintoagreaterGermany.AlltoomanypeoplesawthisastheclosestthingtoarebirthoftheAustrianEmpirethattheycouldhopefor.From 1932, the Chancellor of Austria had been Engelbert Dollfuss, of the

ChristianSocialistparty.Asin“NationalSocialist,”theformalnameoftheNaziparty, the term “socialist” in the name is somewhat misleading: the ChristianSocialists were violently opposed to the main opposition party, the left-wingSocialDemocrats,butalso to theAustrianNazis,perceivedasa threat to theirownholdonpower.InMarch1933Dollfusssuspendedparliament,andAustriabecameafasciststatemoreorlessalongthelinesofItalyunderMussolini.Atthattime,Mussolini,asthefirstofthefascistdictators,stillhadagreatdealofinfluence,andsupportedDollfussagainstboththeNazisandtherealsocialists.Britain and France, however, were committed to appeasement, and advisedDollfussnottopickafightwithHitler.Instead,withMussolini’sencouragement,theAustrianarmyandpolicecrackeddownonthesocialistsinFebruary1934,killingmanyhundredsofactivistsandimprisoningmanyothers.Withthethreatfrom the left neutralized, the Austrian Nazis stepped into the vacuum,assassinating Dollfuss on 25 July 1934 and attempting a coup, which failedbecause Hitler was still too weak to intervene in the face of Mussolini’s

threatenedopposition.ThenewChancellor,KurtSchuschnigg,ruledthanksonlytoMussolini’ssupport;asHitler’spowerincreasedandItalybecameentangledinitsfoolhardyconquestofAbyssinia,Schuschnigg’spositionweakened.BythetimetheSchrödingersarrivedinGrazin1936,thewritingwasonthewall.

WhistlinginthedarkItwasn’t just the Schrödingerswhomoved toGraz.Having settled in a largerentedhousewhileErwintookuphislecturingdutiesinOctober,earlyin1937theywerejoinedbyHildeandRuth,whoweregiventhethirdfloorofthehouseas their own.ArthurMarchwas left behind in Innsbruck, andAnny,whohadturnedfortyonNewYear’sEve,nowstayedwithhermotherinViennamuchofthetime.Anny,though,seemstohavehadamuchmore“maternal”andlovingrelationshipwithRuththanthebaby’sbiologicalmotherdid.Schrödinger’s inaugural lecture as professor was not the tour de force that

mighthavebeenanticipated,butbasicallyarepriseofhisNobellecture,thesortof thingthatmightbeexpectedfromaGrandOldManofsciencesettlingintosemi-retirement. TheGrandOldMan statuswas confirmed by a new honour,when Schrödinger was inaugurated into the new Pontifical Academy ofSciences,asafoundermember,ataceremonyintheVaticanon1January1937.The other physicists honoured alongside Schrödinger included Bohr, Debye,Millikan,Planck,andRutherford—notexactlythe“YoungTurks”ofphysicsatthetime.Schrödinger’sresearchinGrazwasalsothekindofthingthatGrandOldMen

withestablishedreputations,tenuredposts,andguaranteedpensionsindulgein.He became fascinated by the cosmological ideas of Arthur Eddington (1882–1944),aBritishGrandOldManwhoseillustriouscareerhadincludedexplainingthe general theory of relativity to the English-speaking world and testingEinstein’s theorybymakingobservationsof the stars during a solar eclipse in1919.Hewasagreatpopularizerofscience,andintriguedbythepuzzleofhowto reconcile the general theorywith quantummechanics.But by the 1930s hewas in his scientific dotage. He had recently come up with a complicatedhypothesisclaimingtolinkcosmologywithquantumtheoryandcontainingasacrucialingredient(inwhathecalledthe“fundamentalrelation”)acalculationofthenumberof particles in theUniverse,N.Nobodyhas ever understood quitehowhearrivedatthis.Surprisingly,Schrödingertooktheideaseriously,atleast

for a time, and gave a talk about Eddington’s “theory” to a conference inBologna in October 1937. In a long correspondence with Eddington,Schrödinger nevermanaged to fathomwhy the numberN actually appears inEddington’s fundamental relation as the square root ofN, and his attempts tofindaquantumtheoryoftheUniverseoverthenextfewyearswereessentiallyawasteoftime.Teachingwasmoreproductive.Aswell as his lectures inGraz,Schrödinger

gave lecturesandseminars inViennaonedayaweek in termtime,andhadanapartmenttheresothathecouldstayovernight.Thisgavehimanopportunitytomeetupwithfriends,andtodiscussbothphysicsandthepoliticalsituation.Oneof those friends, Hermann Mark, later described these get-togethers in aninterviewwithWalterMoore.HeexplainedthatSchrödinger,whomheregardedthenasasocialist,stronglydislikedthepoliticalsituationinGraz,andspentasmuch time as he could in Vienna, where the Nazis had less influence.Schuschniggtheyregardedasa“moderate”but“nomatchforHitler.”Inthesummerof1937,withnoteachingduties,Schrödingerspentmoretime

inVienna,joiningswimmingpartiesontheDanubeandgoingtolivelyparties.AsMark toldMoore,“thosewerehappydays—butmostpeopledidnotknowtheywere dancing on a volcano.”Ormaybe it was that they did notwant toknow; either way, the parallels with the last days of the Austrian Empire areclear.HildeusuallystayedinGrazwhileErwinwasinVienna—butHansiwasthere,adding toSchrödinger’senjoymentof thecityand its surroundings.Theenjoymentwastobeshort-lived.

RealitybitesHitler’sfirstmovecameinFebruary1938,whenhedemandedthatSchuschniggvisit him in the “Eagle’s Lair” at Berchtesgaden. In these intimidatingsurroundings Schuschniggwas forced to agree to handing over control of theAustrian police and foreign policy to the Nazis, in exchange for a promise(which proved as reliable as all Hitler’s promises) that Germany would notinvadeAustria.Whenhegothome,however,Schuschniggmadeadefiantlyanti-Nazi speech in parliament, which triggered pro-Nazi riots in Graz. As a lastthrow of the dice, Schuschnigg then called, on 6March, for a referendum onAustrian independence, to be held just a week later. Hitler’s response was toorder his army to invadeAustria on 12March.When Schuschnigg turned for

help toBritain, hewas told byLordHalifax, the ForeignSecretary, that nonewould be forthcoming. So on 11 March Schuschnigg resigned, and to avoidbloodshedtoldhispeoplenottoresisttheinvasion,orAnschluss,thatdulytookplacethefollowingday,withoutashotbeingfired.On14MarchHitlerhimselfwaswelcomedinViennabydelightedcrowdsliningthestreets.What followed was a brutal assault on Jews and intellectuals worse than

anythingthathadhappenedundertheNaziregimeinGermanyuptothen.ApartfromthephysicalassaultsonJewsandthelootingoftheirbusinesses,inthefirstfewdaysof the takeover therewere some76,000arrests inVienna,andabout6,000peoplewere fired fromcivil service and teachingpositions at all levels.While thiswasgoingon, theheadof theCatholicChurch inAustria,CardinalInnitzer, ordered his churches to fly swastika flags and ring their bells incelebration.Hewasnotalone—theLutheransheldservicesofthanksgivingfortheAnschluss.IntheNazistrongholdofGrazthingswerecalmerthaninVienna,becausethe

Anschlussmerelyconsolidatedthestatusquo.Buttheuniversitywasclosed;itsRectoranddozensof facultymembersweredismissed,with someof theJewsbeingsenttoprisonandafewmanagingtoescapetoothercountries,leavingalltheir possessions andmoney behind.At first, Schrödinger did not seem to bedirectlythreatened,butwithtravelrestrictionsinplacehewasforcedtoabandonplansforavisittoOxfordintheautumnof1938.WhenhisEnglishcolleaguesheardthistheyfearedtheworst;earlyinAprilGeorgeGordon,thePresidentofMagdalen (where Schrödinger was still a Fellow), initiated enquiries aboutSchrödinger’swelfarethroughHalifaxandtheBritishambassadorinBerlin.Butwhilehisfriendsweretryingtohelp,Schrödingerwasmuddyingthewaters.Ifhewanted to stay inAustria,Schrödingerwouldhave toplayby thenew

rules.TheNazishadappointedoneoftheirown,HansReichelt,asRectorofthere-opened University of Graz, and his first task was to decide which of theremaining members of faculty could stay and which should be “cleansed.”Schrödinger’sabruptand(totheNazis)insultingdeparturefromBerlinhadnotbeenforgotten,andReicheltadvisedSchrödingerthatheshouldwriteapenitentlettertotheUniversitySenatespellingouthischangeofheart.Hedidso,andtheNazis made sure that the letter was published in full in both German andAustriannewspaperson30March.Thiswasaconsiderablepropagandacoupforthem,anditisworthquotingtheletterinfull:In themidstof theexultant joywhich ispervadingour country, therealsostandtodaythosewhoindeedpartakefullyofthisjoy,butnotwithoutdeep

shame, because until the end they had not understood the right course.Thankfullywehear the trueGermanwordof peace: thehand to everyonewilling,youwishtogladlyclaspthegenerouslyoutstretchedhandwhileyoupledgethatyouwillbeveryhappy,ifintruecooperationandinaccordwiththewilloftheFühreryoumaybeallowedtosupportthedecisionofhisnowunitedpeoplewithallyourstrength.It really goes without saying, that for an old Austrian who loves hishomeland, no other standpoint can come into question; that—to express itquite crudely—every “no” in the ballot box is equivalent to a nationalsuicide.There ought no longer—we ask all to agree—to be as before in this landvictors and vanquished, but a united people, that puts forth its entireundividedstrengthforthecommongoalofallGermans.Well meaning friends, who overestimate the importance of my person,consideritrightthattherepentantconfessionthatImadetothemshouldbemade public: I also belong to those who grasp the outstretched hand ofpeace,because,atmywritingdesk, Ihadmisjudgedup to the last the truewillandthetruedestinyofmycountry.Imakethisconfessionwillinglyandjoyfully.Ibelieveitisspokenfromtheheartsofmany,andIhopetherebytoservemyhomeland.

The reference to a ballot box concerned a referendum tobeheldon10April.Thevotethatday(supervisedbytheNazis)was99.73percentinfavouroftheAnschluss; just 11,929 people had the courage to vote “no.” Schrödinger nowavoidedseeingHansi,whocamefromaJewishfamily,andaskedhertoburnthelovelettershehadsenther.When reports of Schrödinger’s letter reached England, his friends assumed

that it must have been written literally at the point of a gun, or under worseduress.Gordonwasastonishedwhenoneof theFellowsofMagdalenreturnedfromaskiingholidayin theTyrolwithnewsthathehadmet theSchrödingersthere, enjoying a similar spring break, and had had a long conversation withErwin.HereportedthatSchrödingerwasquitehappytomakehispeacewiththeNaziregimeandsawnoneedtofleethecountry,thoughheexpressedastrongdislike of the anti-Jewish policy. He would nevertheless be grateful to meetanyone fromOxfordwhowas inAustria, and said that anything that couldbedone to stress his international position in science would be helpful. Perhapsmostsurprisingly,Schrödingerseemstohavehintedthathehopedforpromotion

to an important professorship in Vienna, made vacant by the dismissal of aJewishincumbent.HeseemsnottohaverealizedthatallsuchpostswouldnowbefilledbyactiveNazis.Atleasthisnaïvetédidnotextendtofinancialmatters,andhetookcaretoavoidhavinghisSwedishfundstransferredtoAustria.Thefacadeofnormalitywasmaintained throughoutmostofApril1938,and

onthetwenty-thirdSchrödingerattendedacelebratorymeetingheldinBerlintomarktheeightiethbirthdayofMaxPlanck.ButonhisreturntoGrazhefoundthat on the very day he had been celebrating Planck’s birthday with hiscolleaguesinBerlinhehadbeendismissedfromhishonorarypostinVienna.Hestill had his professorship in Graz, which was rapidly becoming a Naziuniversity devoted to “relevant” courses in things like the application ofchemistry for thewarmachine and trainingof theSSmedical corps.But as adirect result of Schrödinger’s dismissal from hisViennese postwheels startedturningtohisfutureadvantage.ÉamondeValera,PrimeMinisterofIreland,hada passion for mathematics and a pet project to establish an Institute forAdvanced Studies in Dublin. When he heard of Schrödinger’s situation, andrealized that hemight soon have to leaveAustria, deValera decided to try tomake contactwith him through intermediaries to offer him a post in the Irishcapital.Early in May, the German foreign minister, Joachim von Ribbentrop, had

confirmed to the British ambassador in Berlin that Schrödinger would not beallowed to travel to Oxford, since this might offer him an opportunity of“resuminghisanti-Germanactivities.”Oxford, for itspart,wasno longer surethatitwantedSchrödinger,inthelightofhis“confession”letter.ButdeValerahad managed to get a message to Anny’s mother in Vienna, via a chain ofintermediaries, including Max Born and an old friend of the Schrödingers,RichardBär,basedinSwitzerland,offeringtheSchrödingerswhatamountedtosanctuaryinDublin.OnthepretextofmakingacasualvisittomeetupwiththeBärs, Anny travelled to Konstanz, on the border between Germany andSwitzerland,andpassedontheirreply.TheSchrödingerswouldcometoDublin,butnobodymustbetoldanythinguntiltheyhadgotoutofAustria.Still Erwin didn’t act. Blind to the way events were unfolding, he took a

summerholidaywithHildeintheDolomites,anditwasonlyafterhereturnedtoGraz, at the end of August, that he was forced into action. First, he wasdismissedfromhispostinGraz.Eventhen,itwasonlywhenhewenttoViennatodiscuss alternativeswith someone identified simplyas “ahighofficial” andwas casually told, “Well, theywon’t let yougo to a foreign country,” that the

penny dropped. Within three days the Schrödingers—still, through someoversight,inpossessionoftheirpassports—werepackedandreadytoleave.Allvaluables, including money and Schrödinger’s Nobel medal, had to be leftbehind;soon14SeptembertheycaughtthetraintoRomewiththeirclothesinthreesuitcasesandtenmarksinErwin’spocket.

TheunhappyreturnAnny’s account of the Schrödingers’ flight from theNazis is preserved in theDublin archive; after Iwrote In Search of Schrödinger’s Cat, I heard anotheraccount from William McCrea, then (in the mid-1980s) a professor at theUniversity of Sussex, but from 1936 to 1944 Professor of Mathematics atQueen’s University of Belfast, and a frequent visitor to Dublin.3 When theSchrödingersarrivedinRome,Erwinhadtoaskthetaxidrivertotiptheporterwhocarriedtheirbagsfromthetrain,thengotthecommissionaireatthehoteltopaythetaxioff,havingconvincedhimthathereallywasafamousscientistanda friend of thewell-known Italian physicist Enrico Fermi (1901–54).He thenannouncedat thereceptiondeskthatProfessorFermiwouldpaytheirbill.Thestory, saidMcCrea, rings true, and “is entirely in character” for Schrödinger.Being a member of the Pontifical Academy clearly had its benefits, even ifErwin’ssplendidchainofofficehadhadtobeleftinGrazwithhisNobelmedal.Fermi,summonedbytelephone,cametothehotelandgavethemsomemoney,butwarnedthattheywerescarcelyoutofdangerinFascistItaly(beforetheendoftheyearhewouldbeforcedtofleehimself)andthatletterswerelikelytobecensored.Therewas,however,aloophole.FromthepremisesofthePontificalAcademy,

insidetheVatican,SchrödingerwasabletowritetoLindemann,tohisfriendBärinZürich,andtodeValera, informingthemthathewasinRome.LettersfromtheVatican,recognizedbyMussoliniasasovereignstate,escapedtheattentionsof the Italianauthorities. Itwaseasy tocontactdeValera, sinceat the timehewasPresidentof theLeagueofNations,andinGenevaonLeaguebusiness.Acouple of days later, while at theAcademy, Schrödinger received a telephonecallfromtheIrishEmbassy,advisingthemtogetoutofItalyassoonaspossible.ErwinspoketodeValerahimself(forthefirsttime)thatafternoon;thepoliticalsituationwashottingup,withGermany’s takeoverof theCzechSudetenlandarealthreat,anddeValeraurgedSchrödingertogettoEnglandorIrelandbefore

thelikelyoutbreakofwar.The IrishEmbassyprovided theSchrödingerswith first-class train tickets to

Geneva,butas itwas illegal to takecurrencyoutof Italyat that timethey leftwithonlyapoundinmoney.This led toanunanticipatedcomplication.At theborder, the trainwasstoppedand theSchrödingersseparatedfromoneanotherand interrogated while their luggage was searched; Anny described it as “thefright of my life.” But the problem was not, this time, political. TheSchrödingers’passportshadvisasfortravelrightacrossEurope,andthecustomsauthoritiescouldnotbelievethatpeoplewithfirst-classticketsandEurope-widevisaswere travellingwith only a single pound in currency.Their not illogicalconclusionwas that the couplemust be smuggling valuables in their luggage.Whennothingwasfound,theywereallowedtoleave,onthesametrain,whichhadbeenheldduringthesearch.DeValeramet theSchrödingers inGeneva,where they stayed for just three

days before moving on to England through France. The immediate politicalcrisis hadblownover,withBritain andFrance acceptingGermandemandsonCzechterritoryinthenotoriousMunichAgreement,supposedtobring“peaceinour time.” But it would take deValeramanymonths of domestic politicking,alongsidehisotherpoliticalactivities,togettheInstituteforAdvancedStudiesestablished in Dublin, and meanwhile the Schrödingers were once againhomeless.AtthebeginningofOctober1938theyturnedupinOxford,whereitwasmadequiteclear to themhowbadlyErwinhaddamagedhis relationshipstherewithhis confession letter.EvenMaxBorn, nowbased inEdinburghandwritingtoacolleagueinOxford,commented:“Howareyousupposedtobelieveamanwhohaspublished thatpretty letter?”4Wewillneverknow if therewasanythingmore to the “pretty letter” than naïveté, but it is consistent with theimagewehaveofamanwhoseprimaryaiminlifewastoprovidesecurityforhimselfandhisfamily.TheSchrödingersspentacoupleofuncomfortablemonthsinOxford,staying

with friends; Erwin also visited Hansi, who had escaped from Austria, inLondon.Itwascleartheywerenotwelcomeandtherewasnoprospectofevenatemporarypostthere.Buthelpcamefromanunexpectedquarter.Inthemiddleof November, Erwin visited Dublin to discuss the arrangements for the newInstituteandhisroleinit,andonhisreturntoOxfordhewasrelievedtofindaletterfromBelgiumofferinghimapostasvisitingprofessorattheUniversityofGhent for the academic year that had just started. He took up the offer, andarrived,withAnny,inmid-December1938.

BelgianinterludeAs well as giving lectures at the university, during his time in BelgiumSchrödinger attracted visitors from other universities to discuss physics, andtravelledtoBrussels,Louvain,andLiègetogivetalks.ThemostsignificantnewcontacthemadewaswithGeorgesLemaître(1894–1966)inLouvain.Lemaîtrewasapioneeringcosmologistwhoalsohappenedtobeanordainedpriest,andisoftenreferredtoasthe“fatheroftheBigBang,”sincehewasanearlyproponentoftheideathattheUniverseasweknowithasexpandedfromahot,densestate.Firsthintsoftheexpansion,thefamouscosmologicalredshiftwhichrevealshowrapidlygalaxiesarerecedingfromoneanother,hadbeendiscoveredjustovertenyearsearlier,andinapaperinNaturein1939Schrödingeraddedhisweighttothe discussion of what the redshift meant, concluding that it must indeed becaused by the expansion of the Universe.5 Having become interested incosmology,Schrödingermadeoneof the first attempts to integrate cosmologyandquantumphysics inonepackage.Hedidnot achieveanynotable success,but in a paper published in the journal Physica in October 1939 he made areferenceto“theproductionorannihilationofmatter,merelybyexpansion”ofthe Universe. The effect he discovered does not apply if the Universe isexpandingatasteadyrate,butisimportantiftheexpansionisaccelerating.Itisintriguingthatthepresent“bestbuy”ideaabouttheveryearlyUniverseisthatitwentthroughaphaseofrapidlyacceleratingexpansion,calledinflation,duringwhichallofthemass-energywasproduced;andithasrecentlybeendiscoveredthat after a long interval of steady expansion the Universe is now starting toaccelerateonceagain.Thingswerealsogoingwell,ifonlybriefly,atapersonallevel.ArthurMarch

brought Hilde and Ruth to Belgium, leaving them there when he returned toInnsbruck.AndtheUniversityofGhentawardedSchrödingerhisfirsthonorarydegree. But all of this was taking place against a background of increasingpoliticaltension,andSchrödingerandhisextendedfamilywerestillinBelgiumwhen Germany invaded Poland on 1 September 1939, prompting Britain andFrance to declare war two days later. “Schrödinger,” said McCrea, “had asingular talent for taking risks.” Although Schrödinger’s time in Ghent wascomingtoanend,asfarastheBritishwereconcernedhewasnowan“enemyalien,”andstringshadtobepulledbybothLindemann(inspiteofhisangeratthe confession letter and distaste for Schrödinger’s private life) and deValerabeforethewholeofSchrödinger’s“family”weregranted24-hourvisastotravel

throughBritaintoDublin,wheretheyarrivedon6October1939.

Notes

1ThischapterdrawsonSchrödinger:LifeandThoughtbyWalterMoore,whohadtheopportunitytointerviewseveralofSchrödinger’scontemporariesintheseyearsofcrisiswhohavesincedied,includingHermannMarkandHansiBauer-Bohm.2QuotedbyMoore,Schrödinger:LifeandThought.3Atthetimewehadthisconversation,McCreawaspreparinghiscontributiontothevolumeSchrödinger,editedbyCliveKilmister.4QuotedbyMoore,Schrödinger:LifeandThought.5Manypopular,andevenacademic,accountsimplythatafterEdwinHubblediscoveredtheredshift–distancerelationattheendofthe1920sthiswasimmediatelyacceptedasanindicationthattheUniverseisexpanding.Infact,ittookwellovertenyearsfortheideaoftheBigBangtocatchon.

ChapterEleven

“TheHappiestYearsofMyLife”

SchrödingerspentthenextseventeenyearsbasedinDublin—thelongesttimehehad spent living in the same city since his Viennese childhood. He laterdescribed these years as “the happiest of my life.” He made no more majorcontributions to physics—hardly surprising, since he was already fifty-two in1939—but he did make a surprisingly significant contribution to thedevelopment of biology, enhanced his reputation as a lecturer, enjoyed a fullprivate life,andmade theInstitute forAdvancedStudiesat least temporarilyamajorcentreofworldphysics.ButneitherhenortheInstitutewouldhavebeenthereifithadnotbeenforthetoweringfigureofIrishpoliticsinthefirsthalfofthetwentiethcentury,ÉamondeValera.

“Dev”DeValera,whowasuniversallyknownas“Dev,”hadbeenborninNewYorkin1882,thesonofanIrishmotherandaSpanishfather.Hisfatherdiedwhentheboywas three, and hewas taken to Ireland,where hewas raised as a devoutCatholic by his maternal grandmother, in a cottage in County Limerick. Hestudied mathematics in Dublin, became a passionate enthusiast for the Irishlanguage,andmarriedSinéadFlanagan,whohadtaughthimGaelic.Butinsteadof becoming an academic, Dev became involved in the active opposition toBritish rule, and in 1916 he took part in the Easter Rising in Dublin. Thismilitarilyfutileandviolent“rebellion”wasnotsupportedbythemajorityoftheIrish people, and resulted in the destruction of the centre of the city. But thebrutal response of the British military authorities, who executed many of theleadersof the rising,createdmartyrsandagroundswellofanti-British feeling.DeValerawasamongthosesentencedtodeath;butbeforethesentencecouldbecarried out orders came from an alarmed government in London to halt theexecutions.Hadhenotbeenthelastoftheleadersoftheuprisingtosurrender,

de Valera would have been shot before the new orders from London arrived.Instead,hewasimprisonedinBritain,butreleasedduringanamnestywhentheUnited States entered the FirstWorldWar; part of his sentencewas served inLewesgaol,wherehepassedthetimebywritinganoriginalmathematicalpaper,althoughthiswasneverpublished.Continuinghispoliticalactivities,nowasleaderoftherepublicanpartySinn

Féin,deValerawasarrestedand imprisonedonceagain,butescapedand tookpartintheIrishcivilwaroftheearly1920sthatfollowedtheAnglo-IrishTreatyof1921,whenthoseseekingfullindependenceclashedwiththoseseekingonlyhome rulewithin theBritishEmpire (Irelanddidhave its ownparliament, butwithlimitedpowers).Likeothercivilwars,thisonesetbrotheragainstbrotherand produced bitterness which persists to the present day; de Valera’srepublicanslostandhespentanotherspellinprison.Afterhisreleasein1924hefoundedanewparty,FiannaFáil,dedicatedtoestablishinganindependentIrishrepublic through politics rather than violence, and was elected to the Dublinparliament,theDáil,in1927.In1932,FiannaFáilanditsLabourpartnerformedacoalitiongovernment inDublin,andby1937deValera,asTaoiseach (PrimeMinister), was able to establish the Irish Republic as an independent entity,althoughstillwith some links to theBritishCommonwealth.Those linkswerenotfinallysevereduntil1948,which,asweshallsee,ledtoacuriousdelayinSchrödinger’sbeinghonouredbyelectiontotheRoyalSociety.Evenwithallofthisgoingon,Devnursedtwodreams.Onewastoestablisha

world-classcentre for theoreticalphysics in Ireland; theother, to revitalize theIrishlanguage.In1930,whentheInstituteofAdvancedStudieswasestablishedinPrinceton,notleasttoprovideahomeforAlbertEinstein,deValeratooknote.Whenhewasat last inaposition todosomethingabout it,he looked into thepossibility of founding such an institute inDublin, initiallywith two schools,Celticstudiesandtheoreticalphysics.Thekeytoestablishingthenewinstituteasacentreofexcellencewouldbeattractingatopphysicist—someoneasnearaspossible instatus toEinstein.Which iswhy,whenDevheardofSchrödinger’sproblemsinAustria,heactedimmediately.By 1938, Fianna Fáil had a clear majority in the Dáil, and Dev was in a

positiontopushthroughlegislationforwhatmanypeopleregardedassomethingofavanityproject.TheappropriatebillwasputbeforetheDáilon6July1939,spellingoutthat“theschoolswillbedevotedsolelytotheadvanceoflearning...whichwillbringstudentsofthepostgraduatetypefromabroad.”Inaspeechtothe Senate, the Taoiseach said that although thismight seem an inappropriate

timeforsuchabill,itshouldberegardedasagesture“toindicatethatthereisabetterwaythanwarforadvancingthewelfareofmankind.”ButevenDevwasshakenbythewindofchangeblowingacrossEurope;withothermatterstakingprioritythebilldidnotbecomelawuntil19June1940,andSchrödinger,thefirstProfessorintheSchoolofTheoreticalPhysics,wasnotabletotakeuphispostuntilthatOctober.ThisgavehimalmostayeartogetsettledinDublin,makingcontactsandbecomingawell-knownfigurethere.

SettlinginErwin,his two“wives,”andfive-year-oldRuthsettled in theDublinsuburbofClontarf, near the sea, in a typicalmiddle-class semi-detachedhousewithbaywindows.Until1943, thehousewas rented;but thenErwinwasable tobuy it(for £1,000), andhe sold it (for £2,150)when the family leftDublin in 1956.AnnyandHildetookturns,oneweekonandoneweekoff,atdoingthedomesticchores.YoumightexpectErwin’sunusualdomesticarrangements tohavebeeneven

moreofaprobleminCatholicIrelandthaninOxford;butinDublinatleasttherewasamarkedcontrastbetweenwhatwasofficially approvedandwhatpeopleactually did. The situation ismemorably summed up in thewords of an IrishCatholicfriendofmine,whoreferredto“sowingherwildoatsonweekdaysandprayingforacropfailureonSunday.”AccordingtoMcCrea,“SchrödingerandhishouseholdwereapparentlymadetofeelathomeinClontarf”inspiteofhis“irregular”arrangements.AnditwasentirelyinkeepingwiththeIrishattitudeoflaissez-faire thatoneof thefirst friendsErwinmade inDublinwasMonsignorPaddy Browne, a priest who taught mathematics to would-be priests at St.Patrick’sCollege.Msgr.Browne’s brotherwas a cardinal, but that didn’t stopPaddybecomingErwin’sbestfriendinIreland.LifeinDublinduringwhatwasknown in Ireland as “theEmergency”was safe and comfortable, apart from ashortageofteathroughoutthewar,andagrowingshortageofcoalandoil,whichled toprivate cars disappearing from the streets after 1942.SinceSchrödingerwasakeencyclistandhiker,thisneverbotheredhim.Schrödinger began lecturing in Dublin in November 1939, on an informal

basisatUniversityCollege.ThiswasthefirstopportunityforDublinerstolearnabout quantum mechanics from one of its founders, and the lectures werepacked. He also continued his research into aspects of quantum theory, and

began to publish a series of technical papers in theProceedings of the RoyalIrishAcademy (RIA). InApril1940hewasmadea temporaryprofessorat theRIA, an appointment which helped his financial situation by coming with anannualsalaryof£1,000,andherehegaveanotherseriesoflecturesonquantummechanics, this time at a more advanced level, again attracting sell-outaudiences.Then,inMay,hesetoffonasolitarycyclingtrip,catchingthetraintoGalwaybeforeheadingoff intoConnemara.Itwasthere, justacoupleofdaysintohisholiday,thathelearnedfromanewspaperthaton10Maythe“phoneywar”hadendedwiththeGermaninvasionoftheLowCountries,thediscoverysendinghimhurrying(ratherpointlessly)backtoDublin.The fallofFrancehad little effecton life in the Irishcapital, apart from the

naturalfeelingsofgloomengenderedbyHitler’ssuccess,andtherewasnothingtostoptheSchrödingers(justErwinandAnny;someproprietiesstillhadtobeobserved)acceptinganinvitationtoasummerholidaywithPaddyBrowneandhissister’sfamilyatahouseheownedontheDinglePeninsulainCountyKerry,with nothing except the wild Atlantic Ocean between them and America.Paddy’ssisterMargarethadthreechildren.Hereldest,Máire(eighteenin1940),later married the prominent Irish politician and writer Conor Cruise O’Brien.Themiddlechild,Seámus,wassixteenatthetime.Andheryoungest,adaughtercalledBarbara,wasjusttwelveandmadeabigenoughimpactonErwinthathehadtobewarnedoffbyPaddy.Eventhis,though,didnotaffecttheirfriendship.ShortlyaftertheirreturntoDublin,Schrödingerwasatlastabletotakeuphis

appointment at the Dublin Institute for Advanced Studies, with a salary of£1,200ayear.ThiswasnearlyhalfwhattheTaoiseachwaspaid,butonceagainSchrödingerwas in apostwhichdidnotprovideawidow’spension, althoughsecurity was assured as long as he lived. He wrote toMax Born that “to bereinstated to absolute security (at least as regards yourself) at 53 by a foreigngovernment,inmycasefillsyouwith—well,infinitegratitude.”The institutewashoused inMerrionSquare, a ten-minutewalk fromTrinity

CollegeDublin (TCD),whichhadawardedSchrödingeranhonorarydoctorateon3July;asimilarhonourwasconferredbytheNationalUniversityofIrelandon11July.1HewasalsomadeamemberofTCD’sSeniorCommonRoom,arareprivilege for outsiders which Schrödinger treasured, often lunching at thecollege. The institute formally came into being on 5October, under a councilwith Paddy Browne as chairman, and a governing board which includedSchrödingerandMcCrea.“ThefirstIknewofit,”McCreatoldme,“waswhenIreceived a telephone call from Éamon de Valera in October 1940.” Rather

tickledbyreceivingsuchacallfromtheheadofstateofaneutralcountrywhileBritainwasatwar,heaccepteddeValera’s invitation to join theboard,whichhad its firstmeeting on 21November.AsMcCrea put it, Irish neutralitywasvery flexible, and therewerenoproblems travellingbetweenNorthern Irelandand theSouth.Oneof thefirstactsof theboardwas toappointWalterHeitler(1904–81),arefugeeGermanphysicistwhohadmadeakeycontributiontothedevelopment of quantum chemistry, as an assistant professor. What McCreadescribed as “this splendid idea”must, he said, have come from Schrödingerhimself.SothestagewassetfortheearlysuccessofdeValera’sbrainchild.

EarlydaysattheDIASSchrödinger’s “infinite gratitude” to the Irish encouraged him towork hard atmaking the institute a success, and because of his awareness that his securitycameatacosttotheIrishtaxpayershemadeapointofansweringeveryletterhereceived fromthem,even theonesexpoundingcrazyscientific“theories.”TheinfluenceoftheDIAS,whichattractedeminentscientistsfromBritaintoattendmeetings(includingvisitorswhohadsettledintheUKafterfleeingtheNazis),extendedtoboththeuniversitiesinDublin,wheremembersoftheinstitutegavepublic lectures. The first scientific gathering at the institute (this one just forscholarsbasedinIreland)tookplaceinthesummerof1941,atthetimeHeitlertookuphispost.AsinBerlinintheolddays,though,fortheSchrödingersitwasasimportanttoplayhardastoworkhard.Theygaveteapartiesandlunchesattheir house, especially for the youngermembers of the institute and students,whom Erwin always liked to encourage. By the end of 1940, there was asignificant Austrian community in Dublin, and among these refugees was ayoung man, Alfred Schulhof, whose mother had been at school with Hilde.Schrödinger took Alfred under his wing, and paid for him to study electricalengineering. Erwin also “went native” sufficiently to attend the occasionalcricketmatch.The theatre was still one of Schrödinger’s passions, and he attended plays

accompaniedbybothhisladies.Movingintheatricalcircles,theymetthepoetPatrick Kavanagh, the actress SheilaMay, and her husband, David Greene, aCelticscholarthenworkingattheNationalLibraryinDublinbutlatertojointheCeltic studies school at the institute. Thewar came a little closer on 31May1941, when German bombs accidentally fell on Dublin, killing about thirty

people;but threeweeks laterHitlersealedhisownfateby invading theSovietUnion. Schrödingerwrote in his diary: “It is really a great joy to see the twowretches [Hitler and Stalin] in battle against each other,” but he clearlyrecognizedthattherecouldnowbeonlyoneoutcometotheconflict.Thefollowingyear,Schrödinger’sowntolerantviewoftheworldwasshown

duringastormina teacup thatsurroundedanewspapercolumnwrittenby theIrishhumoristBrianO’Nolan,whousedthepseudonym“Myles”(underwhichhewroteoneofthegreathumorousnovels,TheThirdPoliceman).Schrödingeralready knewMyles, through his circle of intellectual contacts, but that didn’tpersuadethecolumnisttopullanypunches.ReferringtoadebateheldatTrinityCollegeinwhichSchrödingerhadparticipated,MyleswroteintheIrishTimes:I understand also that Professor Schroedinger has been proving lately thatyoucannotestablisha first cause.The first fruitof the Institute, therefore,has been to show that there [is] no God. The propagation of heresy andunbeliefhasnothingtodowithpolitelearning,andunlesswearecarefulthisInstituteofourswillmakeusthelaughingstockoftheworld.This provoked a furious response from the council of the institute, which

demanded an apology. But Schrödinger distanced himself from the argument,writing to the council: “I beg to decline emphatically the inclusion of anystatementaboutmyhavingbeengrievedbythatarticle,orofanyapologytome. . . or of anything that gives the wrong impression that I have asked for anapology.” Although Schrödinger clearly was unconcerned, even amused, thecouncilwent aheadwithout him, and extracted a promise from the paper thatMyleswouldnevermentiontheinstituteagain.ButMylesandErwinremainedfriends.Shortlyafter thisbrouhaha, in thesummerof1942,amuchmoresignificant

event in thehistoryof theDIAStookplace—its first internationalcolloquium.Todescribethemeetingas“international”isaslightexaggeration,sincemostofthe fifty or so people present came from Ireland,North and South. ThemosteminentoftheIrishcontributorswasErnestWalton(1903–95),borninCountyWaterford, who had carried out pioneering “atom-smashing” experiments inCambridgewithJohnCockcroft(1897–1967)andwasnowaFellowofTCD.HebecametheonlyIrishscientisttoreceiveaNobelPrizeforhiswork(sharedwithCockcroftin1951).ButthemainspeakerswereDiracandEddington,whoeachgaveshort lecturecourses;McCrea,whowaspresent,described theeventasa“rareintellectualrefreshment”inatimeofwar.Eddingtonwasalmostasshyan

individual as Dirac, and McCrea recalled his surprise at seeing them bothbecomeunusuallyrelaxedandsociableinthefriendlyenvironmentprovidedbySchrödinger and his colleagues. McCrea always suspected that Schrödingerhimself, who spoke perfect English when he wanted to, deliberately droppednon-standard idioms into his talks to help to get his meaning across and cutthrough formality, rather likeAgathaChristie’sHerculePoirot (whomMcCreasomewhatresembled).Hethoughtitwasagreatshamethat“orthodox”EnglishwasalwaysusedinthepublishedversionsofSchrödinger’slectures.Soonafterthecolloquiumended,theSchrödingerhouseholdwasincreasedas

aresultofaholidayErwinandAnnytookinKillarney.Theretheymetateenagegirl,LenaLean,whomtheyinvitedtojointheminDublintohelplookingafterRuth;foronce,thisseemstohavebeenastraightforwardarrangementwhichcanbetakenatfacevalue.Schrödinger’sownscientificworkinthefirstcoupleofyearsoftheinstitute’s

existencehadconcentratedmainlyondevelopingtheimplicationsofMaxwell’selectromagnetic theory, and this fed into his growing interest (almost anobsession)from1943onwardsinthesearchforasingletheorytounitegravityandelectromagnetism.Although thisquestwasultimately fruitless,hebecamean expert on the general theory of relativity. But something that started outalmostasa relaxation fromhismain lineof researchwouldprovemuchmoreimportantandinfluential.Theinstitutewasrequiredbyitsstatutestogivepubliclectureseveryyear,alternatelyatTCDandUniversityCollege,andinFebruary1943Schrödingerchosetogiveaseriesofthreelectureshimself,atTCD,onthewaychangesatamolecularlevel(inthegenes)causemutationsexpressedinthebodyplansoflivingorganisms.Theselectures,towhichhegavethedeliberatelyprovocativetitle“WhatIsLife?,”attractedanaudiencethatincludeddeValera,senior members of the Irish Catholic Church, politicians, diplomats, and theintellectualéliteofDublin,aswellasmanyordinaryfolk.TheyweregivenonFridays, starting on 5 February, but were so popular that Schrödinger had torepeatthemonthefollowingMondaysforthebenefitofthoseunabletogetintothehall,whichcouldholdfourhundredpeople,ontheFridays.Thelectures,andthebookwhichresultedfromthem,provedsoimportantand

influential that I shall tell the full story in the following chapter. But the keyinsightwhichheoffered toawidepublic is thatchromosomescarrymessageswritten in code, not unlikeMorse code or, indeed, the alphabet in which thewords you are reading are written. Not long after Schrödinger gave thoselectures, his own life developed somemore of its usual complications: before

long,Ruthwouldhavetwohalf-sisters.

“Family”lifeinDublinDuring1943,themarriageofDavidGreeneandSheilaMayranintodifficulties,andSheilaturnedincreasinglytoherfriendErwinSchrödingerforconsolation.Sheilawasafeistywoman,activelyinvolvedinIrishpoliticsasamemberoftheLabourParty,andengagedinalong-runningbattlewiththeauthoritiesaboutthestateof the slums inDublin,where tuberculosis, rickets, andotherdiseasesofmalnutrition were rife. She bitterly pointed out that the only change that hadbeenmadetotheslumssinceIrelandbecameindependentwasthatthenamesofthe narrow streets had been changed from English to Irish. AlthoughSchrödinger was sympathetic to such views, theirs was an attraction ofopposites,betweenSheilatheactivistandErwinthethinker.Theirsexualaffairbegan in the springof 1944,whenErwinwrote in his diary: “What isLife? Iasked in1943. In1944,SheilaMay toldme.Glorybe toGod!”As everwithSchrödinger,itwasn’tjustaphysicalthing,butlove.Astreamofpoetryflowedfrom his pen, and in July he rented a flat in the centre ofDublinwhere theycouldmeet.Buttheliaisonwaslargelykeptsecret.AlthoughSheilaandDavidhadbynowbeenmarriedformorethanfiveyears,

they had no children because David did not want any. But soon, Sheila waspregnant,toErwin’sinitialdelight.Hewrote:“IamthehappiestmaninDublin,probably in Ireland,probably inEurope.”But,asWalterMoorehasput it inamemorable turnofphrase,“themysticunionofsexual lovedidnotendureforlong—with Erwin it was never able to survive tidings of pregnancy.” ByOctober,hewaswritingtoSheilatotellhertoconfessalltoDavidandsaythattheaffairwasover.AndDavidbecametheonlypersontoemergefromthemesswithanyrealcredit:henotonlyacceptedthechild,agirlbornon9June1945andchristenedBlathnaidNicolette,butwhenhe laterseparatedfromSheilahehadcustodyofherandbroughtherupashisowndaughter.Inthespringof1945,whileSheilawaspregnant,Erwinmetayoungwoman

whoworkedwithHildeasaRedCrossvolunteer,sendingparcelstoAustriavianeutralSweden.SheisknowntousasKateNolan—notherrealname,becauseherfamilyhavealwayswantedtopreservetheirprivacy.KatewasinmanywaystheoppositeofSheila.Althoughtwenty-sixwhenshemetSchrödinger,shecamefrom a strict Catholic background, had no intellectual pretensions, and was

sexually inexperienced. It tookErwinsome time tobreakdownher resistance;he did so in the summer of 1945, and when the inevitable happened KateconfessedtoLenaLean,theSchrödingers’residentchildminder,thatshewasnotquitesurehowshehadbecomepregnant.OfallSchrödinger’s“conquests,”thisisthehardesttojustifyonthegroundsof“truelove.”Thebaby,anothergirl,wasbornon3June1946,andchristenedLindaMary

Therese;shewasgiventhesurnameRussellinhonourofSchrödinger’sEnglishantecedents. Kate’s traditionally Catholic family were happy for her to bedistanced from the child:Lindawas unofficially adopted by theSchrödingers,andbroughtupintheirhousehold,withLena’shelp.Therewastalkofmakingthe adoption formal, andwith the returnofHilde andRuth toArthurMarch’shomeinInnsbruckthehouseholdtookonanalmostregularappearance.Butin1948KatefoundLenaoutwalkingwiththebabyinitspram,andtooktheinfantaway.ShequicklyputasmuchdistanceasshecouldbetweenherselfandErwin,moving tosouthernAfrica,andheneversawLindaagain,althoughhealwayscontributedtohermaintenance,andgave£1,000(thebestpartofayear’ssalary)tobe invested for her forwhen shegrewup. (There is another chapter to thisstory,whichItellinthePostscripttothisbook.)Whileallthiswasgoingon,andSchrödingerwasengagedinhisunsuccessful

pursuit of a unified field theory, Nazi Germany had been defeated on 7May1945,andthedroppingoftwonuclearbombshadbroughtanendtothewarwithJapanon15August.Schrödinger shared thedistressofmanyphysicists at thedestructionwroughtonHiroshimaandNagasakibytheapplicationoftheircraft—indeed,thisreactionwouldbeamajorfactorintheimpactofhisbookWhatIsLife?Aroundthetimethewarended,HeitlertookoverforaspellasDirectoroftheDublinInstitute,withSchrödingerreturningtotheroleonceagainin1949,atwhichpointHeitlerlefttofollowinhisfootstepsasaprofessorattheUniversityof Zürich. Thus Schrödinger had freedom to travel abroad as science acrossEuropeandAmericareturnedtoapeacetimefooting.

Thepost-waryearsThe first benefit to Schrödinger’s scientific life of the easing of travel camewhenPauli visitedDublin from thePrinceton Institute forAdvancedStudy inMarch 1946, bringing news of the latest developments in particle theory andnuclearphysics(atleast,thosedevelopmentsthatwerenotstillclassified).More

visitorsfollowed,andthen,inJuly,ErwinandAnnywereabletogotoEngland,visitingCambridgetorenewcontactwithDirac,and(inErwin’scase)Londontorenew contact with Hansi. After five days with Hansi, Erwin linked up withAnnyandtheytravelledontoSwitzerland—firsttoZürich,whereErwingaveaphysics lecture, and then to Ascona to participate in a philosophical meetingdevoted to “The Spirit of Nature,” where Erwin spoke about “The Spirit ofScience” toanaudience that includedCarl Jung. It seemsa longway togo topreachthemessagethat“thespirit,strictlyspeaking,canneverbetheobjectofscientificenquiry.”ThereactionofJung,whospenthiscareertryingtostudythespiritscientifically,hasnotbeenrecorded.In1946,CambridgeUniversityPresspublisheda shortbookbySchrödinger

on statistical thermodynamics, based on a lecture course he had given at theDublinInstitute;buthismainresearchinterestinthenextfewyearscontinuedtobe thesearch foraunified field theory.Somegooddidcomeof this—in1950CUPpublishedanotherofhismonographs,Space-TimeStructure,whichbecameastandardtextforgenerationsofstudentsbeingintroducedtothegeneraltheoryofrelativity.BackinIreland,duringthecampaigningfortheIrishgeneralelectionof1947

(which de Valera’s party lost), the institute came under criticism from somequartersasanexpensive luxury that thecountrycouldnotafford inwhatwerethenhard times;but its fundingwassecure,aswasSchrödinger’s future there,andon17February1948heandAnnybecameIrishcitizens.Thesamemonth,hegaveanotherseriesofpubliclectures,thistimeon“NatureandtheGreeks,”repeating them inLondon threemonths later, atUniversityCollege.While hewas inLondon,Schrödingerwas introducedbyHansi to thepotterLucieRay,whooverthenextfewyearswouldlargelyreplaceherinErwin’saffections.Intheshorterterm,hisreturntoIrelandwastobefollowedbyaseriesofpersonalproblemsthatdisturbedthecalmoftheSchrödingers’Dublinhome.Anny had always treated Ruth like her own daughter, and had become

depressed in themonths followingher return to Innsbruck.Erwin’sbehaviour,and his infatuation with his new daughter, Linda, cannot have helped, and inJuneAnnymadewhatwaseitheracryforhelporagenuinesuicideattemptbyslashingherwrists.ShespentseveralweeksinSt.Patrick’sHospital,whereshewas given electric shock therapy, then a routine treatment for psychologicaldisturbance, which seemed to help. But she suffered from recurrent bouts ofdepression through the rest of the Schrödingers’ time inDublin, and admittedherself tohospital for treatmentseveral times.Thesituationwasnothelpedby

herneed to takesteroids tocontrolherasthma,whichmadeherputonweightandfeelunattractive.Erwin’sproblemwasmoreeasilytreated.Hehadbeendevelopingcataractsin

botheyes,andon29June(whileAnnywasinhospital)hadanoperationonhisright eye. The cataract in his left eye was removed the following year. Bothoperationswerecompletelysuccessful.ButitwasnotlongafterthefirstoftheseoperationsandAnny’sdischarge fromhospital thatLindawassnatchedbyhermother.Noneof thisseemedtodisturbErwin’sequanimity,whatever itseffectonAnny.InAugusthewentonholidaytoNorthWaleswithHansi,stayingforawhileinPortmeirion,wheretheybumpedintoBertrandRussell;inSeptemberheattended the eighth Solvay Congress in Brussels, devoted to the subject of“ElementaryParticles”;andbackinDublinhestillspentmostSaturdayshikingwithsomeofhiscolleaguesintheWicklowMountains.InMay1949,Schrödinger receivedanoverduehonour—hewaselectedasa

foreignmember of theRoyal Society.Why had it been so long coming? In aword:“politics.”Between1938and1948noGermanorAustriancitizenswereelected to theRoyal. Inaddition,before1948onlyforeignnationalswhowerenot resident in one of the British Dominions were eligible for election.Technically,IrelandwasstillaBritishDominionuntil1948,whenthenewIrishgovernment formally severed this last link with the past. Although the newFellowof theRoyalSocietydidnotpublishany scientificpapers in1949 (hisfirst “fallow” year since 1923), he did issue a slim volume of poetry, whichwould surely not have appeared were it not for his fame as a physicist.Schrödinger’spoetry, infact,readsalmost likeapasticheofthekindofpoetryyou would expect a physicist to write—it is technically correct, in terms ofmetre, rhyme,andsoon,but lacks theemotional impactof theworkofa truepoet.Muchmore interestingwashis recording, the sameyear, of a talk at theBBCinLondonforaserieson“FrontiersofScience”;therecordingstillexists,andconfirmstheaccuracyofMcCrea’scommentthatSchrödingercouldspeakperfect English when he chose to. Two more talks, recorded in 1950, werebroadcastonlyontheEuropeanServiceoftheBBC.In the first quarter of 1951, at the recommendation of Arthur March,

Schrödinger spent a term at the University of Innsbruck. With Austria stilloccupiedbythevictoriouswartimeAllies,thesituationwas(asIshallexplaininChapter 13) politically complicated, but Innsbruck was in the French zone,where things were relatively calm. The trip did more than just rekindle oldmemories; itprovidedErwinwithanopportunity tomeetupwithhisdaughter

Ruth, who was now sixteen (although it was another year or so before shelearnedthathewasherfather).HegaveashortseriesoflecturesinViennaonthegeneral theoryof relativity,andwassoundedoutabout thepossibilityofapermanentpost inInnsbruck.Althoughin theend theuniversitywasunable tofind room for him, in the years that followed Schrödinger often returned toAustria, attending summer conferences at Alpbach and extending these intoholidays.DuringSchrödinger’s remaining years inDublin, after he largely abandoned

thesearchforaunifiedfield theoryasadeadend,hedid littlescientificworkthat received recognition at the time, but gavemany lectures, andwrote somepapers,onthefundamentalproblemoftheinterpretationofquantummechanics.These have largely been ignored, regarded as minor works of his scientificdotage, looking backward rather than forward and tidying up loose ends. Butthey actually contain profound insights, very relevant today, both into histhinkingandintothenatureoftheworld.Thesedeserveproperattention.Ishallcome on to this shortly, after briefly summarizing the key events inSchrödinger’slifeupuntilhisreturntoVienna.InAugust1952Erwinreachedhissixty-fifthbirthday.Afteraholiday in the

Tyrol the followingmonth hewas feeling full of vigour, and looking forwardboth to the new academic year in Dublin and to a conference on theinterpretationof quantummechanics to be held inLondon thatDecember.AlltheoldprotagonistswouldbethereforarerunofthedebatebetweenBohrandhisfellow“Copenhagers”andtherest.Schrödingerwroteapapertocontributeattheconference,buthenevergottopresentitinperson.AttheendofOctoberhe was struck down with appendicitis. The appendix burst, and he neededemergency surgery;his lifewasprobablyonly savedby theavailabilityof theantibioticsthatwerejustcomingintogeneraluse.Butheneverfullyrecoveredthe physical well-being he had felt just a month before, and the attacks ofbronchitishesufferedeverywinterbecamemoresevere—notthattheystoppedhim fromsmokinghispipe asmuchas ever.By1954,onhis regular summervisittotheTyrolhehadsomuchdifficultykeepingupwithhiscompanionsonlong walks that he was persuaded to see a doctor, who diagnosed severeemphysema and high blood pressure. It later became clear that he was alsosuffering from arteriosclerosis. From then on, alcoholwas forbidden, smokingwas restricted, his bedtimewas9p.m., andhiking in themountainsbecameathingofthepast.InDecember1952SchrödingerwasaskedtospendasemesteratHarvard,and

initially accepted the offer, making arrangements with the institute for anabsence from October to December 1954. But when the Harvard authoritieschangedthedatestorunfrom25SeptemberuntiltheendofJanuary1955,andsaidhisdutieswouldincludemarkingexaminationpapers,hechangedhismind.TherewasonlyoneplacethatSchrödingerwasreallywillingtoleaveDublinfor—Austria.Theopportunityarose,asIdescribeinChapter13,in1956.Butfirst,it is time to look at Schrödinger’s lasting scientific legacy from his time inDublin,startingwiththeinterpretationofquantummechanics.

ManyworldsSchrödinger’s lecture notes for his seminars, and other unpublished materialfromhislateryearsinDublin,wereeventuallygatheredtogetherandeditedbyMichelBitbol,oftheCentreNationaldelaTechercheScientifiqueinParis;theyappeared in book form in 1995. Bitbol explored the underlying philosophybehind this work in another book, published a year later, Schrödinger’sPhilosophyofQuantumMechanics.Hemakesaconvincingcasethat thisbodyofworkistheculminationofSchrödinger’sthinkingaboutquantummechanics,andpresentsaviewverydifferentfromtheCopenhagenInterpretation,butveryclosetoamodernunderstanding.The basis for Schrödinger’s thinking is actually summed up in one of his

published papers,which appeared in 1952with the title “Are ThereQuantumJumps?”Hesaid that there isnothing inexperimentalphysicswhichhas tobeinterpreted in termsofdiscreteparticles (remember theexampleof the trailofdots left by an electron in a cloud chamber). We may not be sure what a“particle”is,saidSchrödinger,but“wehavenowgained[insight]intowhatitisnot; it is not a durable little thing with individuality.” All we have fromexperimentsare therecordsofevents,whichweexamine longafter theeventshave happened—an observation that is, if anything, even more true today ofexperimentsinvolvingmachinesliketheLargeHadronColliderthanitwasforthesimplerexperimentsofSchrödinger’sday.IfweseeanelectroninpositionA, and later (even a split second later) see an electron in nearby (even verynearby)positionB,wehavenowayofknowingwhetheritis,infact,thesameelectron. And particles which have neither well-defined trajectories nor well-definedindividualitysimplyarenotparticles.“Itisbettertoregardaparticlenotas a permanent entity but as an instantaneous event,” said Schrödinger.2

“Sometimes these events form chains that give the illusion of permanentbeings.”Thisalsoremoves,atastroke,thepuzzleofactionatadistancethatsoworried

Einstein. Instead of thinking of two separate particles, with two separate butentangledwavefunctionsthatinteractwithoneanotherinsomespookyfashion,weshouldthinkofasinglewavefunctionwhichdescribesthewholesystem.Intermsof“localreality,”wecankeeprealityifweabandonlocality.Ihavealreadymentionedthenext,key,stepintheargument.Thereisnothing

intheequationsthatrequiresthecollapseofthewavefunction.Inthe“catinthebox” thoughtexperiment, theCopenhagenInterpretation tellsus that there isasuperposition of wave functions, or states, until the box is opened. Then, thesystem collapses and just one state becomes “real.”Why? asked Schrödinger.Thereisnoreasonforthesuperpositiontobedisturbedjustbyourlookingatit—andrememberthatin1935hehadsaidthatthesuperpositionofstatesis“thecharacteristic [trait] of quantum mechanics” (see note 3 to Chapter 9). Somefifteen years later, he said: “It is patently absurd to let the wave function becontrolled in two entirely different ways, at times by the wave equation, butoccasionallybydirect interferenceof theobserver, not controlledby thewaveequation.”Now, there is in any case something odd about the superposition of wave

functions in quantum mechanics. In the realm of classical waves, twosuperimposed waves add together to produce a composite wave; they do notretain their separate identities. Sowavemechanics is a radical departure fromclassical wave theory, and not, as was originally hoped and is still oftensupposed,lessradicalthanmatrixmechanics.Bytheearly1950s,Schrödingeristellingusthatinthecatexperimentbothstatesarereal,andtheyeachstayrealaftertheboxisopened.Themind-bogglingimplicationisthatallquantumstatesare real. This is the foundation of what later became known as the “ManyWorlds” interpretation of quantum mechanics, although nobody before Bitbolseems to have noticed that Schrödinger thought of it first. The key passagecomesfromatalkSchrödingergaveinDublinin1952:Nearly every result [the quantum theorist] pronounces is about theprobabilityofthisorthatorthat...happening—withusuallyagreatmanyalternatives.Theideathattheymaynotbealternativesbutallreallyhappensimultaneously seems lunatic tohim, just impossible.He thinks that if thelawsofnaturetookthisformfor,letmesay,aquarterofanhour,weshouldfindoursurroundingsrapidlyturningintoaquagmire,orsortofafeatureless

jelly or plasma, all contours becoming blurred, we ourselves probablybecomingjellyfish.Itisstrangethatheshouldbelievethis.ForIunderstandhegrants thatunobservednaturedoesbehave thisway—namelyaccordingto thewaveequation.Theaforesaidalternativescome intoplayonlywhenwe make an observation—which need, of course, not be a scientificobservation. Still it would seem that, according to the quantum theorist,nature is prevented from rapid jellification only by our perceiving orobservingit...itisastrangedecision.

Rather than undergoing “jellification,” though, with no collapse of the wavefunction the cat in the box becomes two cats in two boxes, in two separatebranchesoftheworld(ortwoseparateworlds);onecatdies,theotherlives.Andhere is a multitude of branches of reality—many worlds—corresponding toeverypossiblequantumstateof theUniverse.This removes thepuzzleofwhohastoobservetheUniverseitselftomakeitcollapseintoadefinitestate.Themoststrenuousobjection to this ideahascomefrompeoplewhocannot

stomachtheideaoftheUniverseconstantlysplittingintonewversionsofitselfeverytimeitisconfrontedbyaquantum“choice.”AsIshalldescribeinChapter14,thisobjectionhasnowbeenovercome,althoughSchrödingerdidnotlivetoseeithappen.Buthedidlivetoseewidespreadrecognitionofanotherpieceofhislaterwork—hisideasaboutthenatureoflife.

Notes

1TherearetwouniversitiesbecauseoriginallyTrinityCollegeDublin(TCD)wasforProtestants,andtheNationalUniversity,ofwhichUniversityCollegeispart,forCatholics;noCatholicsattendedTCDuntilthe1960s.2QuotedbyBitbol,Schrödinger’sPhilosophyofQuantumMechanics.OtherSchrödingerquotesinthissectioncomefromthesamesourceunlessotherwiseindicated.

ChapterTwelve

WhatIsLife?

Schrödinger had a lifelong interest in the process of heredity, having learnedaboutbiologyfromhisbotanistfatherandreadwidelyaboutevolutionaryideasduring his time as an undergraduate, when the recently rediscovered work ofGregor Mendel (1822–84) on inheritance was being widely discussed. Hisinterests inphilosophyandEastern religion, addressing thenatureof themindandsoul,andquestionssuchas thepossibleexistenceofagroupunconscious,formedpartof the same tapestryof thought.ToSchrödinger, thecontinuityofthegeneticlineisakindofimmortality,andhealwaysregrettedneverhavingason.Sowhenthetimecamearoundforanotherseriesofpubliclectures,in1943,Schrödingerdecidedtotreathisaudiencetohisthoughtsaboutthenatureoflifeandinheritance, jumpingofffromapaperco-writtenbyMaxDelbrück(1906–81), whom Schrödinger knew from his time in Berlin, when Delbrück wasworking at theKaiserWilhelm Institute forChemistry.Although the twomayhave discussed Delbrück’s work in the early 1930s, the key paper was notpublisheduntil1935,afterSchrödingerhadleftBerlin,andtheninarelativelyobscurejournal.SchrödingerprobablysawitonlyashorttimebeforehedecidedtomakethisworkthebasisofhispubliclecturesatTCDinFebruary1943.Today “everybody knows” about DNA, and the term “genetic code” has

becomepartof thecommonlanguage. It isdifficult tostandbackand imaginetheimpactoftheideasofDelbrück,asinterpretedbySchrödinger,inthe1940s,and ridiculous to try to write about these events without acknowledging howmuchmorewenowknow.So,toputtheimpactofSchrödinger’sbookWhatIsLife?inperspectiveitseemsbesttogetaclearideafirstofjustwhatitisthatwedonowknowaboutDNA,thegeneticcode,andinheritance.

LifeitselfDNA is a long molecule found in the cells of every living thing. The most

important feature ofDNA is that strung out along the length of themoleculethere is a series of chemical subunits called bases, which are denoted by thelettersA, C, T, andG. Strings of these four bases can convey information inwhatisusuallycalledacode,butwhichIprefertothinkofasalanguage,inthesameway that the twenty-six lettersof thealphabetareused in longstrings toconvey information in this book. But DNAmolecules do not usually exist inisolation.Theycomeinpairs,withonelongmoleculetwinedarounditspartnerinthefamousdoublehelixarrangement.Thetwomoleculesineachhelixarenotidentical, but are likemirror imagesof one another; everywhereonemoleculehasanA,itspartnerhasaT;everywhereonemoleculehasaC,itspartnerhasaG; everywhere one molecule has a G, its partner has a C; everywhere onemoleculehasaT,itspartnerhasanA.Soundertherightcircumstances(whichoccurwhen a living cell divides) the twohalves of thehelix canunwind, andeach single strand can build itself a new partner from the chemical materialsurrounding it inside thecell,bymakingappropriate linksbetweenbases.Theresult is two identical double helices, and one copygoes into eachof the twocellsformedbythedivision.Whensexcells(spermoregg)arebeingmanufacturedbythebody,aslightly

more complicated process occurs inwhich pieces ofDNA get cut out of onehelix and spliced into another, so that offspring inherit a slightly differentarrangementofgeneticmaterialfromtheirparents.AllofthismattersbecausethecodeorlanguagecarriedbytheDNAcontains

theinstructionsfortheconstructionofanorganismfromasinglecell,andfortheoperationof theorganism.Thecode/language is translatedand the instructionsareputintoactioninsidealivingcellwiththeaidofamoleculeverysimilartoDNA,calledRNA.Intheprocess,asectionofDNAdoublehelixuntwists,andtherelevantsectionofcodeiscopiedintoasingle-strandedRNAmolecule.ThisRNA“message”isthenused,bythemachineryofthecell,tobuildupmoleculescalledaminoacids,whicharelinkeduptoformproteins.Someproteinsprovidethestructureofyourbody, thingslikemuscleandhair,whileothers,knownasenzymes, act as catalysts, encouraging (or in some cases inhibiting) chemicalreactionsgoingoninsideyourcells.Proteins are so important in the body that in the early 1940s, when

Schrödingerwaswritinghisbook,theywerewidelythoughttobethemoleculesoflife,andDNAwasthoughttobemerelysomekindofscaffoldingonwhichproteinchemistrycouldtakeplace,withoutcontributingdirectlytotheprocess.But it was known that the genetic information is packed into entities called

chromosomes—each individualhumanhas23pairsofchromosomes,withonememberofeachpairinheritedfromeachparent(itisactuallychromosomesthatare broken apart and joined together in new arrangements when sex cells aremade). Genes are sections of chromosomes, and it is a change in a gene(sometimescalledamutation)thatproduceschangesinindividualmembersofaspeciesonwhichevolutioncanact.Buthowbigdoesachangeinthemoleculeoflife(whateveritmaybe)havetobeinordertoproduceasignificantchangeintheindividual?Inthe1935paperthatsointriguedSchrödinger,Delbrückandhiscolleagues,usingdatafromexperimentsinwhichmutationswerecausedinfruitflies(drosophila)byX-rays,suggestedthatamutationcanbecausedbyasinglechangeatoneplaceinamolecule—inmodernterminology,achangeassimpleaschanginganAtoaGinaDNAhelix.Thescientificpaperthatconveyedthisdramatic information became known, from the colour of the cover on thereprints that circulated (increasingly after Schrödinger drew attention to it), as“thegreenpamphlet.”But just as Schrödinger’s What Is Life? drew on the green pamphlet, so

DelbrückandhiscolleaguesdrewonSchrödinger’searlierwork,sincethekindof biology they were concerned with is part of chemistry, and by the 1930schemistry had become part of physics—specifically, part of quantum physics.AndtheversionofquantumphysicsthatchemistsusedwasSchrödinger’swavemechanics.

QuantumchemistryChemistry is concernedwith theway atoms join together tomakemolecules.This involvesasharingofelectrons (whichhavenegativecharge)between thepositivelychargednucleiofdifferentatoms.Inthesimplestexample,twoatomsof hydrogen, which each consist of a single proton associated with a singleelectron,jointogethertomakeasinglemoleculeofhydrogen,inwhichinsomeway the two electrons “surround” both of the protons (the atomic nuclei).Molecules form in this way because the molecular state represents a lower-energy state than the two atoms on their own. But how could two electronssurround twoprotons? It’s likesaying that twosmallchildren“surround” theirparents.Clearly, it is much easier to visualize this sharing of electrons, in which a

coupleofelectronscaninsomesensesurroundapairofatomicnuclei,usingthe

ideaofwavesratherthanthatofparticles.Thisdoesbegthequestionofhowtheelectric charge associated with the electrons gets “smeared out,” and leadsstraight to Born’s idea that the wave represents a probability of finding theelectroninaparticularplace,butthattheelectronactuallyexistsasaparticle—theinterpretationthatSchrödingerhated.Forthepurposesofchemistry,though,such puzzles can be left to the philosophers and interpreters of quantummechanics. The chemists’ concern, once Schrödinger had discovered wavemechanics, was to find ways to use the equations to calculate the change inenergythatoccurswhenhydrogenatomscombinetomakemolecules,andthento extend this kind of calculation to more complicated systems, so that theycould predictwhich arrangements of atomswould form stablemolecules, andhowstrongthebondsbetweenthemwouldbe.The theory of the electron bond was developed, using Schrödinger’s wave

equation,fromtheindependentworkin1927oftheAmericanEdwardCondon(1902–74) and the team ofWalter Heitler and Fritz London. That summer of1927Heitler andLondonwere inZürich, andbenefited fromdiscussionswithSchrödingerbothintheformalsettingoftheuniversityandduringlongwalksinthewoods.LinusPauling(1901–94),whowas tobecomethe leadingquantumchemist,wasalsoinZürichthatsummer,buthadlittlecontactwithSchrödinger.1When Heitler and London calculated the difference in energy between twohydrogen atoms and one hydrogenmolecule, they came upwith a value veryclose to theamountofenergywhichchemistsalreadyknew, fromexperiment,was required to break such a molecule apart. This was a dramatic discovery,sinceitshowedthatthearrangementsofatomsinmoleculesarenotarbitrary,butare indeed the arrangements with least energy, and therefore the most stablearrangements.ItwasPaulingwhodevelopedacomplete,coherent,andaboveallquantitative

descriptionofthechemicalbasisofbiologyoverthenextfewyears,inparticularusingwavemechanics toexplain thechemicalbehaviourof carbon, the singlemostimportantatominthechemistryoflife—soimportantforlifethattheterms“carbon chemistry” and “organic chemistry” are synonymous. His book TheNature of theChemicalBond, published in 1939, became themost influentialchemistrytextbookofthetwentiethcentury.In1954PaulingreceivedtheNobelPrizeforthiswork,withthecitationspecifying“hisresearchintothenatureofthe chemical bond and its application to the elucidation of the structure ofcomplexsubstances.”Butitsinfluencehadbeguntospreadwellbeforethebookappeared; indeed, his research into the nature of the chemical bond had

essentially been completed by 1935—which is why the authors of the greenpamphletwereable torelate theenergycarriedby individualX-rayphotons totheenergyrequiredtobreakdifferentkindsofchemicalbond.

ThegreenpamphletInfact, thesectionof thegreenpamphlet thatdiscussedtheX-rayexperimentswas written by Delbrück’s colleague Nikolai Timofeev-Ressovsky (1900–81).The“thirdman”wasamorejuniorcolleague,KarlZimmer(1911–88),whousedthedatafromtheexperimentstocalculatehowmuchenergyisneededtocauseamutation,and,bycomparing thiswith thebondenergiesofcarboncompoundscalculatedusingquantumchemistry, concluded that a single“hit”byanX-rayphoton could produce a mutation. It later turned out that some of theassumptionsinhiscalculationwerewrong;butfortunatelythisdidnotaffectthemain conclusion. This was that a chemical change involving at most a fewhundred atoms and perhaps equivalent to the breaking of a single molecularbond(followedbytheformationofanewanddifferentbond)couldproduceageneticmutation. Thiswas one of the first pieces of evidence that genes are,indeed,molecules,andnotmorecomplicatedstructuresliketinyversionsofthecell; it led first Delbrück, in his section of the green pamphlet, and thenSchrödingertotheideaofthegeneticcode.MaxDelbrückhadbeenborn inBerlin in1906andworkedhiswaythrough

the German educational system, studying mathematics, physics, andastrophysics.HeemergedwithaPhDin1930andthereafterspentshortspellsinEnglandattheUniversityofBristol’sH.H.WillsPhysicsLaboratory,withNielsBohr inCopenhagen,andwithWolfgangPauli inZürich,beforesettlingat theKaiser Wilhelm Institute for Chemistry in Berlin. He was one of the firstphysiciststomakethemovethroughchemistryintobiologyinthewakeofthedevelopmentofquantummechanics;thistrenddidnotgainpaceuntilaftertheSecondWorldWar.In1935DelbrückhimselfwasworkingasanassistanttothephysicistLiseMeitner;hisbiologicalinterestswereatthattimestillsecondarytohismainresearch,althoughthreedecadeslaterhewouldreceiveashareoftheNobel Prize for his work on the genetics of viruses. The impact of the newphysics on biology is, though, neatly encapsulated in the title of Delbrück’ssectionofthepamphlet—“AModelofMutationBasedonAtomicPhysics.”2

Thedirect inspirationfor thisworkwasa lectureDelbrückattended,entitled

“LightandLife,”givenbyBohrinCopenhagenin1932andpublishedinNaturethefollowingyear.Bohrsaid:Theexistenceoflifemustbeconsideredasanelementaryfactthatcannotbeexplained,butmustbetakenasastartingpointinbiology,inasimilarwayas the quantumof action,which appears as an irrational element from thepoint of view of classical mechanical physics, taken together with theexistence of elementary particles, forms the foundation of atomic physics.The asserted impossibility of a physical or chemical explanation of thefunctionpeculiartolifewouldbe. . .analogoustotheinsufficiencyofthemechanicalanalysisfortheunderstandingofthestabilityofatoms.ButBohrinsistedthattherewasnoneedtoinvokeamysterious“lifeforce”to

explainthedifferencebetweenlivingandnon-livingthings.“Ifwewereabletopushtheanalysisofthemechanismoflivingorganismsasfarasthatofatomicphenomena,” he argued, “we should scarcely expect to find any featuresdifferingfromthepropertiesofinorganicmatter.”ItwastheideaofpushingtheanalysisofthemechanismoflivingorganismstothislimitthatledDelbrückintogenetics.One of the reasonswhy hewas attracted to the jobwithMeitner inBerlinwasthattheKaiserWilhelmInstitutesweresetupincloseproximitytoone another, to encourage the spread of ideas across disciplines;Berlin in theearly1930swastheidealplaceforaphysicistwhowasinterestedinbiology.Inthegreenpamphlet,Delbrücksuggestedthatgeneticmutationsresultfrom

the transitionsofmoleculesfromonequantumstate toanother.Genesmustbevery stablemolecules,hepointedout, inorder to transmit characteristics fromonegenerationtothenext.Raremutations,thekindonwhichnaturalselectionacts, can occur as a result of the molecules absorbing energy from theirsurroundings, perhaps simply through the action of heat energy jostling themoleculesabout;morefrequentmutationscanbecausedbyaddingenergyintheform of X-rays or (as Delbrück speculated but was later proved) ultravioletradiation.Itistherearrangementofthegeneticmaterial(whateveritmaybe)inquantumprocessesthatcausesmutations.Inotherwords,mutationisaquantumprocess that involvesmoleculesbeingpushed fromonestableconfiguration toanother stableconfigurationoveranenergybarrier.Butwhatare thegenes? Itwastoosoontosay,andinDelbrück’swords:Weleaveopenthequestionwhetherasinglegeneisapolymericentitythatarises by the repetition of identical atomic structures or whether suchperiodicity is absent; and whether individual genes are separate atomic

assemblies or largely autonomous parts of a large structure, i.e.whether achromosome contains a row of separate genes like a string of pearls, or aphysico-chemicalcontinuum.Apolymerissimplyalongmoleculecontainingverymanyatomsstrungout

likea—well, likeastring.Delbrück’s introductionof the ideaof thegeneasapolymericmoleculeisakeystepinthedevelopmentofanunderstandingofthemechanismsoflife.Youshouldn’tbeconfused,though,byhisreferenceto“therepetitionofidenticalatomicstructures”;iftheywereallliterallyidenticalthentheywouldnotconveyanyinformation,justasthestringoflettersAAAAA...conveysno information,andheclearlymeans the repetitionofa few identicalunits,butindifferentorders,likedifferentwordswrittenusingthesamelettersofthealphabet.As a result of the work described in the green pamphlet, Delbrück was

awardedaRockefellerfellowshipwhichtookhimtoCaliforniain1937,initiallytoworkwiththegeneticistThomasHuntMorgan(1866–1945)atPasadena.Heremained based in the United States for the rest of his life, and became anAmerican citizen in 1945. While in California, he also worked with LinusPauling, and together they wrote a paper, published in the journal Science in1940, in which they pointed out that two molecules with complementarystructure(usingatermclearlyborrowedfromquantummechanics,butmeaningthesameasmyuseoftheterm“mirrorimagemolecules”)lyingalongsideeachotherwould form a particularly stable configuration.They said that studies ofthisformofcomplementarityshouldreceiveahighpriorityintheinvestigationoftheworkingsofthecell.PaulingandDelbrückseemtohavebeenunaware,atthetimetheywrotetheir

paper,of a suggestionmade in1937by theBritishgeneticist J.B.S.Haldane(1892–1964), thenbasedatUniversityCollege inLondon.Hesaid:“Wecouldconceive of a [copying] process [of the gene] analogous to the copying of agramophone recordby the intermediationof a negative, perhaps related to theoriginalasanantibodyistoanantigen.”3Thisisexactlythekindofprocessthat,as I explained earlier, operates when DNA is copied in the cell, or when itsmessageistranslatedusingRNA.ItmatchesupbeautifullywiththesuggestionmadebyPaulingandDelbrück.ButSchrödingerseemstohavebeenunawareofeitherofthesesuggestionswhenhewroteWhatIsLife?

Schrödinger’svariationonthethemeThe heart of Schrödinger’s book is a reworking of the ideas from the greenpamphlet, presenting the quantum-mechanical evidence followed by a chaptertitled“Delbrück’sModelDiscussedandTested.”Hesaysthatithas“oftenbeenasked”howthetinyspeckofmaterialthatisafertilizedegg“couldcontainanelaborate code-script involving all future development of the organism.” Hisansweristhat“thenumberofatomsinsuchastructureneednotbeverylargetoproduceanalmostunlimitednumberofpossiblearrangements,”andhegivestheexampleofakindofsuperMorsecode,withthreesignsinsteadoftheusualdotand dash, which, used in groups of not more than ten, “could form 88,572different ‘letters’; with five signs and groups up to 25 the number is372,529,029,846,191,405.”ThereisalsoabiologicalexamplethatSchrödingermighthaveused,ifhehad

been a biologist himself, and familiarwith the latestwork.By the end of the1930s, it had been found that all proteins in living things are made up fromdifferentarrangementsofjust20differentamino-acidbuildingblocks.Therearepotentially about 24 × 1017 (24 followed by 17 zeroes) ways of arranging the“letters”ina20-character“alphabet,”meaningthattherearepotentially24×1017

different possible proteins.Only a tiny fraction of these potential proteins areactuallyexpressedinlivingthings.Thegene,saidSchrödinger,islike“anaperiodiccrystal.”Hepointsoutthatin

an ordinary (periodic) crystal of a substance such as common salt there is anendless repetition of the same basic unit in a perfectly regular pattern thatconveysverylittleinformation,andcontraststhiswith“say,aRaphaeltapestry,whichshowsnodullrepetition,butanelaborate,coherent,meaningfuldesign,”eventhoughitismadeupofafewsimple,identicalunits(inthiscase,different-colouredthreads).ThisideaofanaperiodiccrystalisessentiallywhatDelbrückmeantby“apolymerthatarisesbytherepetitionofidenticalatomicstructures,”butnodoubtSchrödingerwantedtouseadifferentanalogy.Andhecertainlyputthemessageacrossforcefully:Incallingthestructureofthechromosomefibresacode-scriptwemeanthattheall-penetratingmind,onceconceivedbyLaplace,towhicheverycausalconnectionlayimmediatelyopen,couldtellfromtheirstructurewhethertheegg would develop, under suitable conditions, into a black cock or aspeckledhen,intoaflyoramaizeplant,arhododendron,abeetle,amouse

orawoman.Towhichwemayadd,thattheappearancesoftheeggcellsareveryoftenremarkablysimilar;...

Buttheterm“code-script”is,ofcourse,toonarrow.Thechromosomestructuresare at the same time instrumental in bringing about the development theyforeshadow.Theyarelaw-codeandexecutivepower—or,touseanothersimile,theyarearchitect’splanandbuilder’scraft—inone.Apart frompromoting the ideaof a genetic code (without, it has to be said,

offeringanyexplanationofhowthecodemightbecopied),Schrödinger’sbookwas important because it introduced the idea that life feeds off “negativeentropy.” This line of argument drew on Schrödinger’s long-term interest inthermodynamics, which tells us that the entropy of a closed system alwaysincreases—thatorderedsystemsbecomedisordered.Lifeisclearlyworkingtheotherway;itseemstocreateorderoutofdisorder,orinSchrödinger’swordsit“evades the decay to equilibrium.” Schrödinger seems to suggest that livingthings take in “negativeentropy” from their surroundings in the formof food,which is in an ordered state. “The essential thing in metabolism is that theorganismsucceedsinfreeingitselffromalltheentropyitcannothelpproducingwhilealive.”I say he “seems to” suggest this because this section of his book is very

confused,andhasdrawna lotofcriticism.Theobviousquestion is,wheredidthe negative entropy in the food come from? But in spite of the confusion,Schrödinger was pointing in the right direction. Life does feed off negativeentropy,whichcomesfromtheSun;overall, theentropyof thesolarsystemisincreasing,inlinewiththelawsofthermodynamics.AsmalldecreaseinentropyassociatedwiththepresenceoflifeonEarthisvastlyoffsetbythehugeincreaseinentropyassociatedwiththewayheatfromtheSunflowsoutintothecoldofspace,warming the Earth on itsway. The key point is that the Earth is not aclosed system in the thermodynamic sense. In fact, Boltzmann himself saidnearly the same thing as far back as 1886, when he referred to the need ofbiologicalorganisms“forentropywhichbecomesavailablebythetransitionofenergy from the hot sun to the cold earth.”4 Confused (or not) thoughSchrödinger’sdiscussionmayhavebeen,theterm“negativeentropy”caughton—whenhisbookeventuallygotpublished.Thepath topublicationwascomplicatedbecausewhenhe turnedhis lecture

materialintobookformSchrödingeraddedanEpilogue,“OnDeterminismandFreeWill,”inwhichhedrewonEasternreligionandphilosophytoexpresshisversion of the idea that the individual, personal self is only a facet of the

universal self. “It is daring,” he said, “to give to this conclusion the simplewording that it requires. In Christian terminology to say: ‘Hence I am GodAlmighty’ sounds both blasphemous and lunatic.”Hewas right—it did soundblasphemous,andwashardlyasensiblethingtosayinabookbeingpublishedinDublininthe1940s.Surprisingly, perhaps, the book had got past the stage of being typeset (this

wasinthedaysofmetaltypesetoutbyhand,letterbyletter)andwasinpageproofwiththepublisherCahill&Companybeforeanythinghitthefan.Atthatpoint, somebody reading the proof (almost certainly Paddy Browne, who hadbeenhelpingSchrödingerturnhislecturenotesintothekindofEnglishthoughtappropriate for a book)went ballistic and drew the attention of themanagingdirectoratCahill,JohnO’Leary,totheEpilogue.O’Learyrefusedtopublishthebook unless the Epilogue was removed; Schrödinger refused to remove theEpilogue; the typewas literallybrokenup; andeventually (in1944) thebook,complete with Epilogue, was published by Cambridge University Press—ironically,amuchbetterhomeforthebook,helpingtoensurethatitwaswidelyread.

ThedoublehelixWhatIsLife?hasoftenbeencriticized(accurately)onthegroundsthatwhatisgoodinthebookisnotoriginal,andthatwhatisoriginalinthebookisnotgood.Thismisses thepoint thatyoudonothave tobeoriginal tobe influential,andinfluential the book certainly was—no passage more so than this: “FromDelbrück’s general picture of the hereditary substance it emerges that livingmatter,whilenoteludingthe‘lawsofphysics’asestablisheduptodate,islikelytoinvolve‘otherlawsofphysics’hithertounknown,which,however,oncetheyhave been revealed, will form just as integral a part of this science as theformer.”Theprospectofnewapplicationsofphysicswasimmenselyappealingtoawholegenerationofphysicists,weariedbywarand inmanycasesdeeplyconcerned about the part the old physics had played in what happened toHiroshima and Nagasaki.Working for life hadmore appeal than working fordeath.Nothing shows this upsurge of enthusiasm—and Schrödinger’s influence—

moreclearly thanaconferencewhich tookplaceunder theauspicesof theUSNationalAcademyofSciencesinWashington,DC,intheautumnof1946,just

aboutassoonassuchaconferencecouldhavebeenorganizedafter theendofthewar.Thetitlewas“BorderlineProblemsinPhysicsandBiology,”andintheopeningaddresstothemeetingMaxDelbrücknotedthatWhatIsLife?hadbeenthestimulus thathadbrought themtogether. It isnatural thatphysicistsshouldhave had their eyes opened to the biological possibilities of their work bySchrödinger’sbook;butfromamodernperspectiveit looksatfirstsightrathermoresurprisingthatithadanequallyprofoundimpactonbiologists.Youhavetoremember that in the mid-1940s, only a few years after the publication ofPauling’sgreatbook,andwithwarintervening,veryfewbiologistsknewmuch(ifanything)aboutthenatureofthechemicalbondorthermodynamics.Thisisnottheplacetogointoallthedetailsofhowthemessagespread,butitissurelyworth looking at the direct influence on the two scientists credited withdiscoveringthestructureofDNA,FrancisCrickandJamesWatson.Crick,whowasborninavillagenearNorthamptonin1916(hediedin2004),

was the senior member of the team in terms of age. He graduated fromUniversityCollegeinLondonwithadegreeinphysicsin1938,buthisplanstocarry out research for a physics PhD were interrupted by the war, when heworkedfortheAdmiralty(upuntil1947,infact)onthedesignofacousticandmagneticmines.His interest in theapplicationofphysics tobiologywas firedfirst bySchrödinger’s book; “itwasonly later,” hewrote inhismemoirWhatMadPursuit,“thatIcametoseeitslimitations—likemanyphysicists,heknewnothingofchemistry—buthecertainlymadeitseemasifgreatthingswerejustaroundthecorner.”Theflamesofthisinterestwerefannedbyanarticlewrittenin the journalChemical and Engineering News by Linus Pauling in 1946. In1947Crick beganworking at the Strangeways Laboratory in Cambridge on astudyofthewaymagneticparticlesmoveincells,andin1949hetransferredtotheCavendishLaboratorytobegin,atthelateageofthirty-three,researchforaPhD,involvingX-raystudiesofproteins.It was at the Cavendish that Crick met Watson. Watson had been born in

Chicago in 1928 and graduated from the university there, having studiedzoology, at the age of nineteen. Crick moved from physics into biophysics;Watsonmoved from biology into biophysics. He had also read Schrödinger’sbook, in 1946 while still an undergraduate, and it was instrumental indetermininghis future careerpath.He said in1984, in a talkgiven at IndianaUniversity: “From the moment I read Schrödinger’sWhat Is Life? I becamepolarisedtowardsfindingoutthesecretofthegene.”Withtypicalchutzpah,healso said: “It was clear in those days that physicists were brighter than

biologists.” Although he started working for a PhD on drosophila at IndianaUniversity,inBloomington,hesoonswitchedtoX-raystudiesofatypeofvirusknownasabacteriophage.ArmedwithafreshPhDandstillonlytwenty-two,in1950 Watson travelled to Copenhagen, where he carried out more work onbacteriophage,andthen,in1951,toCambridge,wherehemetupwithCrickattheCavendish—throughthepurechanceof theirhappening tosharearoomatthelaboratory.At that time, the idea that biologicalmoleculesmight have helical structure

wasintheair.In1951,Pauling’steampublishedanastonishingseriesofsevenscientific papers describing the structure ofmany different proteins (in thingslikehair, feathers,muscle,silk,andhorn) in termsofastructureknownas thealpha-helix. By that time, it was also clear that the important molecules inchromosomeswereintheformofDNA,andWatson,inparticular,wasinspiredbyPauling’sworktolookforahelicalstructureinDNA,recruitingCricktothecauseanddeflectinghimfromhisproteinwork.Thewaytofindsuchastructurewas using X-ray crystallography, a technique with which neither Crick norWatsonhadanyexpertise.ButatKing’sCollege inLondonRosalindFranklin(1920–58)wascarryingoutexactlythiskindofstudyofDNA.Asisnowverywell known, Crick andWatson obtained some of Franklin’s key data by notentirelyethicalmeans,andusedthismaterialasthebasisfortheirfamousmodelofDNAasadoublehelix.5ThediscoverywaspublishedintheissueofNaturedated25April1953(ayearbeforeCrickobtainedhisPhD);bythetimeitwasrecognized by the award of aNobel Prize, in 1962, Franklinwas dead (fromcancer,possiblyrelatedtoherworkwithX-rays)andcouldnotsharethehonour.CrickandWatsonwerewellawareoftheimportanceoftheirdiscoveryforan

understandingofthewayDNAmolecules(andthereforegenes)replicate.Neartheendoftheirpaper,theywrote:“Ithasnotescapedournoticethatthespecificpairingwehavepostulatedimmediatelysuggestsapossiblecopyingmechanismfor thegeneticmaterial.”But thediscoveryof thestructureofDNA,andeventhe hint of how it replicates, was not the end of the story. The question stillremainedofhowtheinformationwascodedintheDNAmoleculesthatmadeupthegenesinchromosomes,andhowtheinformationinthegeneswastransferredandputtousebythemechanismsofthecell.CrickwouldgoontoplayakeypartincrackingtheDNAcode.Although he was delighted by the impact his book had in the 1950s,

Schrödinger didn’t quite live to see the completion of this vindication of theideaspresentedinWhatIsLife?:hediedinJanuary1961,afewmonthsbefore

the news broke thatCrick had broken the code—just five years after his longdelayedreturntoVienna.

Notes

1SeePauling’scontributiontoKilmister,ed.,Schrödinger.2ItsoundsevenbetterintheoriginalGerman—“AtomphysikalischesModellderMutation.”3CitedbyMaxPerutz,inKilmister,ed.,Schrödinger.4CitedbyMaxPerutz,inKilmister,ed.,Schrödinger.5SeemybookInSearchoftheDoubleHelix.

ChapterThirteen

BacktoVienna

The complications that delayed Schrödinger’s permanent return to Austriaresulted from the antipathy between the Western Allies in the war againstHitler’sGermanyand theSovietUnion.Unitedonlyby theiropposition to theNazis,EastandWestweresoonembroiledinaColdWar,neitherwillingtogiveupterritorytotheother.LikeGermany,Austriawasdividedintoseparatezonesofoccupationafter thewar,with theAmericans,British,French,andRussianseach responsible forpartof thecountry; and likeBerlin,Viennawas similarlydivided,asvividlyportrayed in thefilmTheThirdMan. It tookuntil1990forGermany to be reunified, and from that perspectiveAustriawas lucky. But itdidn’tfeellikealuckycountryintheyearsimmediatelyafter1945.In someways, the immediate aftermath of thewarwas like a replay of the

aftermathoftheFirstWorldWar.Severewinters,especiallyin1946–47,broughtfood shortages and street riots. There was an unsuccessful Communist coupattempt inMay 1947, and in February 1948 theCommunists seized power inneighbouring Czechoslovakia. Anticipating that Austria would be the nextdomino to fall, Josef Stalin, the Soviet leader, stalled the negotiations for anAustrianpeace treaty.But therewasavitaldifferencebetween thesituation in1948 and that of 1918. Instead of punishing Austria more severely, after theattemptedcoupofMay1947aid(intheformoftheMarshallPlan)pouredin,asAmericasoughttobolsterthisbulwarkagainsttheadvanceofcommunism.Oneside-effectof thiswas that inaspiritof reconciliation,outside theSovietzonemanyformerNaziswereallowedtoremain,orreturnto,theirpostsinthecivilserviceandacademia;thiswasnotpossiblefortheformerJewishpopulation,90percentofwhomhadbeenmurderedorexiled.It was against this background that Schrödinger became a regular visitor to

Austriaintheearly1950s.HeevenmanagedtolectureinVienna,althoughnotwithout, on at least one occasion, some harassment by border guards whilegetting out of the Soviet zone (getting into the Soviet zone was easy!).WithAnny’sboutsofdepression,andErwin’sdeclininghealth,ithadbeguntolookas

iftheymightendtheirdaysinDublinafterall.ButinMarch1953Stalindied,andhissuccessor,NikitaKhrushchev,soondecidedthathehadnothingtolose,andmightgainpolitically,byclearingtheairoverAustria.ThebasisforthenewtreatylayinanagreementknownastheMoscowDeclaration,signedduringtheMoscowConference ofOctober 1943 by the foreignministers of theUK, theUSA,andtheUSSR.Thesectionof thedeclarationregardingAustriastatedthat theannexationof

AustriabyGermanywasnullandvoid,andcalledfortheestablishmentofafreeAustriaafterthevictoryoverNaziGermany:TheGovernmentsoftheUnitedKingdom,theSovietUnionandtheUnitedStates of America are agreed that Austria, the first free country to fall avictimtoHitleriteaggression,shallbeliberatedfromGermandomination.TheyregardtheannexationimposeduponAustriabyGermanyonMarch15,1938,asnullandvoid.Theyconsiderthemselvesasinnowayboundbyanychanges effected inAustria since that date.Theydeclare that theywish tosee re-established a free and independentAustria, and thereby to open thewayfortheAustrianpeoplethemselves,aswellasthoseneighbouringstateswhich will be faced with similar problems, to find that political andeconomicsecuritywhichistheonlybasisforlastingpeace.Thepainstakingnegotiationsoverapeacetreatystillwentonformonthsafter

Khrushchev’s decision to proceed, but itwas duly signed on 15May 1955; itofficially came into force on 27 July, and by early November the occupyingforces had left Austrian soil. In between, Schrödinger was appointed to aprofessorial post specially created for him at the University of Vienna—receivingthenewswhileononeofhisregularsummerjaunts.

FarewelltoDublinInJune1955,SchrödingergaveatalkinPisatoameetingoftheItalianPhysicalSociety. Anny accompanied him, and they spent a week touring in Tuscanybefore heading up into theAlps to escape the summer heat. From Innsbruck,where they collected a new Fiat 2000, they drove to the Tyrol, where theyreceivedformalconfirmationofErwin’sappointmenttotheViennapostinJuly,while staying atNeustift. The appointmentwas to take effect from 1 January1956—with,crucially,fullpensionrights,eventhoughSchrödingerwasonlyacouple of years short of retirement age—but he was not required to take up

residenceinViennauntillaterintheyear.Withallhisfinancialworriesresolved,Schrödingerwasabletoenjoytherest

ofwhatturnedouttobehislastrealholidayinreasonablygoodhealth,withtwoweeksatLakeGardafollowedbyavisittoAlpbach,takinginthesightsofthemountains thatheandAnny loved.Then itwasback toDublin, toprepare forthe last bigmove of their lives. Itwas not a happy return, and things did notimprove through the autumn and winter. Almost immediately, Anny admittedherself toherusualclinicfor tendaystoreceivemoretreatment,andalthoughRuthMarchcametohelpwiththepreparationsforthemove,Erwinwasstruckdownbyanattackofphlebitis,whichpreventedhimtravellingtoCambridgeinJanuary to give a planned series of lectures. Although he recovered, AnnyneededmoretreatmentinthenewyearandbythetimeshewashomeagainRuthhad returned to Innsbruck—just as Erwin was hit with a severe attack ofbronchitis.On 11 February, a Sunday, hewashed down a cocktail of sleepingpills with a large quantity of whisky. It is unlikely that this was an accident.WhenAnnyhad troublewakinghimon theMondaymorning, shecalled theirdoctor,underwhosesupervisionherecoveredwithouthavingtogotohospital,althoughhewasnotallowedtogetupuntilthefollowingSaturday.Schrödinger’srecoveryfromall thiswashardlyhelpedbytheensuinground

ofpartiesandformalfarewellstohiscolleaguesandotherluminariesinDublin,includingDevandtheIrishPresident,anditwasanexhaustedmanandhiswifewhofinallytooktheferryacrosstheIrishSeaon23March1956onthefirstlegof their journey, via London, where they stayed for two nights, to Innsbruck,wheretheyarrivedonthetwenty-eighth.Ruthhadherhandsfullathome,whereArthurMarchwasseriouslyillandHildewastoodistractedtobemuchhelp,sotheydidn’tlingerbutdroveontoVienna,wheretheroundofwelcomeswasasexhaustingas,ifmorecheerfulthan,theroundoffarewellshadbeen.

HomeistheheroThe return of Austria’s greatest scientist to his native land was doublysignificant:notonlyfront-pagenewsin itsownright,butasignof thebelatednormalizationofAustrian society, a full tenyearsafter theSecondWorldWarhadended.Schrödingergavehisinauguralprofessoriallecture,on“TheCrisisoftheAtomicConcept,” to apackedaudience at theUniversityofViennaon13April1956.Thethemewashisfamiliarmessageaboutthenatureofrealityand

thesuperiorityofthewavemodeltothewave-particledualityoftheCopenhagenInterpretation—buthecouldhavebeenreadingfromthetelephonedirectoryandstillhave receivedanovation fromtheaudienceofscientists,civicdignitaries,andoldfriendseagertowelcomehimhome.Another,morepersonal,causeforcelebrationwasthemarriageofRuthMarch,inMay1956,toArnulfBraunizer;thiswassoonfollowedbythenewsthatshewasexpectingababy,Erwin’sfirstgrandchild,dueinFebruary1957.ArealhomeforErwinandAnnyproveddifficulttofind,though,andwhilethe

festivities continued the Schrödingers were unable to put down roots: at firstthey had to live in the Atlanta Hotel, conveniently situated for the PhysicsInstitutebut, inAnny’seyesat least,wildlyextravagantatacostequivalent to£2.50perdayforthepairofthemonhalf-board.Eventually,theywereabletosettle down in a five-room apartment on the third floor of a block onPasteurgasse,akilometreorsofromtheinstitute.Itcostthemjustover£2,000,butaswellasbeingconvenientlylocatedthebuildinghada lift,bynowakeyrequirement for Erwin. The apartment needed refurbishing before they couldoccupyit,sothemovewasdelayeduntilaftertheirnowregularsummerholidayinAlpbach.Schrödinger’s teachingdutieswere light.Hegave lectures twice aweek, on

“GeneralRelativity”andon“ExpandingUniverses,”buttheclassesweresmallandinformal;asfortheweeklyseminar,itwas“morelikeahigherkindergarten,notliketheDublinSeminar.”1Vienna,however,haddelightsthatDublincouldnot compete with, not least the theatre, which the Schrödingers attendedfrequently,and theproximityof themountains.But it isdebatablewhether the“mountainair”reallywasgoodforErwin’shealth,orwhetherhighaltitudewasonthecontrarydetrimentalforamanwithheartandlungproblems.Althoughheenjoyedanextendedsummerholiday inAlpbachwithAnnythatyear,headingforthehillsassoonasthetermwasover,inSeptemberErwinwassoillthathehad to cancel his planned lectures in Cambridge, already postponed fromJanuary. Instead, these talks,knownas theTarnerLectures,werepresentedbytheProfessorofPhilosophy,JohnWisdom,readingfromSchrödinger’stext.ThelectureswerepublishedbyCambridgeUniversityPressin1958,underthetitleMindandMatter; thisbookwas latercombinedwithWhatIsLife? inasinglevolume,firstpublishedin1967andstillinprint.Mind and Matter is significant as an example of Schrödinger’s thinking

towardstheendofhislife,butisotherwiseunremarkable.Headdressestheoldquestionofwhetheranobjectiverealityexistsifitisnotbeingobserved,which

leadshimintoadiscussionofwhethertheworldwouldexistifitwerenotbeingobservedby“higheranimals,”asking:“Woulditotherwisehaveremainedaplaybeforeemptybenches,notexistingforanybody,thusquiteproperlyspeakingnotexisting?” His answer is that such a conclusion is nonsense, and thatconsciousness is somehow associated with the process of learning—includingthe“learning”about its environment involved in theevolutionofaplant (oramicrobe)tofititsecologicalniche.Thisleadshimintomurkywaters:“Wefindthebehaviouroftheindividualsofaspecieshavingaverysignificantinfluenceonthetrendofevolution,andthusfeigningasortofsham-Lamarckism.”Schrödingerisconcernedthatthisprocesscouldadverselyaffecttheevolution

ofourownspecies:NowIbelievethattheincreasingmechanizationand“stupidization”ofmostmanufacturing processes involves the serious danger of a generaldegenerationofourorganofintelligence.Themorethechancesinlifeofthecleverandoftheunresponsiveworkerareequalledoutbytherepressionofhandicraft and the spreading of tedious and boringwork on the assemblyline, the more will a good brain, clever hands and a sharp eye becomesuperfluous. Indeed the unintelligentman, who naturally finds it easier tosubmit to the boring toil,will be favoured; he is likely to find it easier tothrive, tosettledownandtobegetoffspring.Theresultmayeasilyamounteventoanegativeselectionasregardstalentsandgifts....Instead of letting the ingenious machinery we have invented produce anincreasingamountofsuperfluousluxury,wemustplantodevelopitsothatit takesoff humanbeings all theunintelligent,mechanical, “machine-like”handling.Themachinemust takeover the toil forwhichman is toogood,notmantheworkforwhichthemachineistooexpensive.

Well,maybeSchrödinger’sconclusionwasright,althoughpossiblynotreachedfortherightreason!Elaboratinghisdiscussionof thenatureofreality,Schrödingerthenbemoans

the fact that in physical science, since the time of the ancient Greeks, “amoderately satisfying picture of the world has only been reached at the highpriceoftakingourselvesoutofthepicture,steppingbackintotheroleofanon-concerned observer.” Jung, he says, was right when he pointed out that allscienceis“afunctionofthesoul,inwhichallknowledgeisrooted.Thesoulisthegreatestofallcosmicmiracles,itistheconditiosinequanonoftheworldasan object.” Schrödinger’s own conclusion is that “subject and object are only

one.Thebarrierbetweenthemcannotbesaidtohavebrokendownasaresultofrecentexperiencesinthephysicalsciences,forthisbarrierdoesnotexist.”The consciousness that Schrödinger refers to is, as ever, not an individual

consciousness,butthecollectiveconsciousnessofwhichweareallapart.Andhisfinallectureaddressesissuesofstrikingpersonalrelevance—religionandlifeafter death. I won’t spell out his argument, which is based on a statisticalinterpretationoftime,buttheconclusion,nodoubtappealingtosomeoneinhisseventiethyear,wasthat“wemay,orsoIbelieve,assertthatphysicaltheoryinitspresentstagestronglysuggeststheindestructibilityofMindbyTime.”

DecliningyearsThroughoutmostofhisadultlife,oneofSchrödinger’sdrivingmotivationshadbeentheneedtosecurehisandAnny’s—particularlyAnny’s—financialfuture.Hehadatlastachievedit,butattheageofsixty-ninehadlittleelse.“TheonlythingIhaveenoughofnow,”hewrote,“ismoney.”2

Thereasonforthisgloomycommentwasessentiallyhisdeclininghealth.ThecoldanddampofwinterinViennaexacerbatedhisheartandlungproblems,andwiththebloodsupplytohisbrainrestricted,aftergivinglectureshebecameverytired,andonseveraloccasionsconfusedandrambling—that is,whenhecouldgivehislecturesatall.AlthoughAnnyalwaysdrovehimtheshortdistancefromtheirapartmenttotheinstituteandbackagain,inthewintertermhewasabletoteachfewerthanhalfhisclasses.ItwasintheapartmentthatSchrödingerheldcourt, when he was well enough, receiving many friends from the artisticcommunityaswellasscientists.Evenhere,afterNovember1956,whenSoviettanks crushed the uprising in Hungary, the atmosphere was marred by thewidespread fear that Austria, so recently freed from occupation,might be thenextinline.Decemberalsobroughtgloomynews,butatamorepersonallevel.Onavisit

toVienna,Ruth,nowsevenmonthspregnant,broughtword thatArthurMarchwas terminally ill,with cancer of the throat. Ruth and her new husbandwerelooking after things forHilde in Innsbruck; theSchrödingers gave them somemoneytoreducetheirworriesatthisdifficulttime.Having “enough”money alsomeant that in spite of everythingAnny could

enjoytheChristmasfestivities.ShewrotetoherfriendElisabethUllmann:What an experience when I came on December 29 to Fritz the Baker’s.

WhenonehaslivedtwentyyearsintheBritishIslesonethinkssuchbountyis impossible,a little shopwithabout20servinggirlsand theChefwhomtheytreatlikealord[.Itis]quiteexpensiveandeveryvarietyofbakedgoodscan be found, croissants, rolls, salt rolls, kümmel buns, sour breads,sandwich bread and different kinds of black breads, brioches,milk sticks,pretzelsandbosniaks,nottoforgetsixdifferentkindsoftarts.

Clearly,Anny liked her baked goods, and no doubt someof these found theirwayontothetablewhentheSchrödingersentertainedalargepartyoffriendson31 December; but the festivities were short-lived for Erwin, who went downwithanotherattackofbronchitisastheoldyeargavewaytothenew.Althoughseverely ill, he was saved with the help of aureomycin, the first of thetetracyclines,penicillin-likedrugsdevelopedaftertheSecondWorldWar.SohewasaswellashecouldnowexpecttobewhenRutharrivedinFebruarytostaywiththeSchrödingerswhileawaitingthearrivalofherbaby;shehadbeensentaway from the March household by Arnulf, to get her away from the dyingArthurMarchandthedistraughtHildewhileheheldthefortthere.Erwin’s grandson,AndreasBraunizer,was born at theUniversity ofVienna

Clinicon28February1957.Afewweekslater,on17April,ArthurMarchdied.In a letter to Hilde, Erwin wrote of his belief that a dying person should beallowedtoslipawaypeacefully,aidedbydosesofopium,ratherthansuffertheindignityofprolonginglifeforafewextradaysjustforthesakeofit.Hewasclearly contemplating his own fate, but told her: “I am glad of the few years[left],fortheworldisvery,verybeautiful.”Thosefewyearsalmostbecameafewweeks.InMay,Annywasbeingtreated

forasthmaataclinicnearInnsbruckwhenshewassummonedbacktoErwin’sbedside:hewasclosetodeathwithasevereboutofpneumonia,andwassavedonly by a cocktail of the new antibiotics, including penicillin, streptomycin,Terramycin,andMagnamycin.Tenyearsearlierhewouldsurelyhavedied;asitwas,bytheendofthemonthhehadturnedthecorner.Therewasdoublecausefor celebration on 31May—for the same day Germany’s top civil order, the“Pour le Mérité,”3 was formally conferred on Schrödinger at a ceremony inBonn, although of course he had known about the award for some time. HisfriendLiseMeitner received thedecorationat thesame time—only thesecondwomantobehonouredinthisway.Because of his poor health, Schrödingerwas formally excused any teaching

forhislastyearasaprofessorinVienna,1957–58.ButhewaswellenoughtovisitthePhysicsInstitutefromtimetotime,andtoparticipateinajointmeeting

of theAustrian Physical Society and theChemical–Physical Society inMarch1958.Itwasthere,on26March,thathegavehislastscientificlecture,attheageof seventy.The themewentbackhalfa lifetime to focuson the linksbetweenenergyandentropy,andtoarguethat the lawofconservationofenergyis trueonlyinastatisticalsense.But entropy, statistical or not,was fast catching upwithSchrödinger. In the

springof1958,hesufferedanattackofphlebitiswhichrequiredhospitalizationand then lengthy bed rest at home; he recovered just in time for the regularsummer visit to Alpbach. By now formally retired, on 30 September 1958, amonth after his seventy-first birthday, Schrödinger was appointed to thehonorarypostofprofessoremeritusattheUniversityofVienna.Hewouldhavejustovertwoyearstoenjoythesecureoldagehehadstrivensohardtoachieve.

ThetriumphofentropyThefirstofthoseyearswaseverythingSchrödingerhadhopeditmightbe.Afterenjoying the role ofGrandOldMan inVienna, in the summer he took off asusualfortheTyrolwithAnny;hestayedthereforfourmonths,attimesenjoyingthecompanyofoldfriends,includingLiseMeitner.InOctobertheSchrödingersstayedintheItaliancityofBolzano,thelargestcityoftheSouthTyrol(andnowthe home of the ice mummy “Ötzi”), where their delight at the beautifulmountainscenerywasoffsetbyarecurrenceofErwin’sbronchitisastheautumnfadedintowinter.Oneside-effectofthisboutofill-healthwasthat,oftenunableto sleep, he spent many long night hours writing letters, one of which inparticular provides an insight into his thoughts at this time about quantummechanics.The letter was sent to John Synge (1897–1995), a distinguished Irish

mathematicianandphysicistwhohadjoinedtheDublinInstituteforAdvancedStudiesasaseniorprofessor in1948,andwasoneof its leading lights for therest of his career.Schrödinger’s letter castigatedphysicists ingeneral for their(ashesawit)unthinkingacceptanceoftheCopenhagenInterpretation:“Withavery few exceptions (such asEinstein andLaue) all the rest of the theoreticalphysicists were unadulterated asses and I was the only sane person left.” Hecomplained that his efforts to get people to take the puzzle of wave-particleduality seriously had fallen on stony ground because his colleagues “haveformed the opinion that I am—naturally enough—in love with ‘my’ great

success in life [and] therefore, so they say, I insist upon the view that ‘all iswaves.’”Intheirview,old age dotage closes my eyes towards the marvelous discovery of“complementarity.” So unable is the good average theoretical physicist tobelievethatanysoundpersoncouldrefusetoaccepttheKopenhagenoracle[NielsBohr]....IfIwerenotthoroughlyconvincedthatthemanishonestandreallybelievesintherelevanceofhis[idea]Ishouldcallitintellectuallywicked.

Nothingcouldbeclearer,andSchrödingerwouldsurelybedelightedtoseetheway the Copenhagen Interpretation has fallen from favour today, although hemightnotapproveofalltheideasthatareofferedasalternatives.The letter to Synge was just about Schrödinger’s last word on quantum

mechanics.As themountains grew colder,Erwin andAnnymoved down intoItalyforthreeweeks,stoppingatMantova,Cremona,Piacenza,Parma,Verona,andVenice before returning to Vienna to hole up for the winter. Schrödingerstoicallyputupwiththerespiratoryproblemsthathehadbecomeusedto,butbythe spring of 1960 itwas clear that the problem this timewasmore than justbronchitis, and tests revealed a recurrence of the tuberculosis that he hadsufferedintheearly1920s.Atleasttherewerenoweffectivedrugstotackletheproblem, but part of the treatment still involved the old idea of fresh air andsunshine.SoSchrödingerwaspackedofftoAlpbachtostay.There,hetooktheopportunity to finish the second part of what became his final book, whichwouldbepublishedinGermanasMeineWeltansichtandinEnglishasMyViewoftheWorld.The first part of the book was essentially the essay on metaphysics, the

Vedanta, and consciousness written in 1925, shortly before SchrödingersucceededPlanckasprofessorinBerlin.Norwasthe“new”materialreallynew,beingmorearestatementofSchrödinger’sideasabouttherelationshipbetweenmind and matter, addressing the question “What is real?” and endorsing thebelief that“we livingbeingsallbelong tooneanother, thatweareallactuallymembersoraspectsofasinglebeing,whichwemayinwesternterminologycallGod,whileintheUpanishadsitiscalledBrahman.”Schrödingersaysthathehas“nohesitationindeclaringquitebluntlythattheacceptanceofareallyexistingmaterialworld,astheexplanationofthefactthatweallfindintheendthatweare empirically in the same environment, is mystical and metaphysical.”Although anyone who wishes to take that view is at liberty to do so, “he

certainly does not have the right to pillory other positions asmetaphysical ormysticalonthesuppositionthathisownisfreefromsuch‘weakness.’”During his “cure” at Alpbach, Schrödinger also had plenty of time towrite

letterstohiswidecircleoffriendsandacquaintances.Intermsofhislongbattlewithwhatmightberegardedasthequantum-mechanicalestablishment,themostsignificantofthesewasalettertohisoldsparringpartnerMaxBorn.“Ido,”hesaid,need togiveyouoncea thoroughheadwashing. . . .The impudencewithwhich you assert time and again that the Copenhagen Interpretation ispractically universally accepted, assert itwithout reservations, even beforeanaudienceofthelaity—whoarecompletelyatyourmercy—it’satthelimitoftheestimable....Areyousoconvincedthatthehumanracewillsuccumbbeforelongtoyourownfolly?

AssomeonewhowastaughtthegospeloftheCopenhagenInterpretationjustafewyearslater,andonlymuchlaterstillappreciatedthenatureofitsfolly,IfindthesewordsfromSchrödingerin1960strikeclosetomyheart!By the beginning of November, Erwin had had enough of Alpbach, and

decidedtogobacktoVienna;Annyhadbeentakenseriouslyillwithasthmaandrushedtohospitalon20October.Hereturnedtotheirapartmenton9November,driven in theSchrödinger carby a friend. In truth, hewasnotwell enough tolook after himself, and struggled along, with help fromAnny’s sister and thecouplewholookedaftertheapartmentbuilding,onlyuntil2December,whenhewas admitted to hospital. Just a few days later, Annywaswell enough to gohome—she would live for another four years—and Erwin now demanded toreturnhomehimself,saying,“IwasbornathomeandI’lldieathome.”Hiswishwasnotimmediatelygranted,andashisconditiondeterioratedoverthenextfewweeksheremainedinhospital,withAnnyathisbedside,holdinghishand.Buthewasatlastreturnedtohisownbedonthemorningof3January1961.Hediedthefollowingday,at6:55p.m.Thecauseofdeathwassimplygivenasoldage;hewasseventy-three.Schrödinger had asked to be buried in the little churchyard atAlpbach.The

priestat firstdemurred,on thenotunreasonablegrounds thatErwinwasnotaCatholic;butwhenhewasadvisedthatSchrödingerhadbeenamemberofthePontifical Academy he relented, and the interment took place on Sunday, 10January.Schrödingerwasgone,buthisscientificlegacylivedon.

Notes

1LetterquotedbyMooreinSchrödinger:LifeandThought.2QuotedbyMooreinSchrödinger:LifeandThought.3Amilitaryversionofthehonour,knownastheBlueMax,existedpriortotheendoftheFirstWorldWar.

ChapterFourteen

Schrödinger’sScientificLegacy

Themostsignificantdevelopmentinquantumphysicssince1960—arguablythemost significant development in science in the twentieth century—was theresolution of the EPR “Paradox” and experimental confirmation that quantumentanglement(atermcoinedbySchrödinger)isreal.Apartfromitsimplicationsfor our understanding of the Universe we live in, this has led to practicalbenefits, including huge economic and commercial benefits, that are justbeginning to be realized.The story beginswith anAmericanCommunistwhosharedSchrödinger’sdislikeoftheCopenhagenInterpretation,developsthroughtheworkofanIrishmathematicianwhoknewbetterthantobelieveeverythinghereadinbooks,andreachesaclimax(althoughnotanend)inthelaboratoryofaFrenchmanwhoriskedhiscareerbyattemptingtoprovewhatothersregardedasimpossible.

Hiddenrealityandamathematician’smistake

DavidBohm (1917–92)was anAmerican physicistwhowrote a classic bookpresentingtheCopenhagenInterpretation,butasaresultofhiscarefulanalysisof this view decided that it was nonsense, and developed an alternativeunderstandingofthequantumworld.Hisbook,QuantumTheory,waspublishedin 1951, when Bohm was under a cloud following an investigation by thenotoriousUn-AmericanActivitiesCommittee.Hehadbrieflybeenamemberofthe Communist Party, in 1942 (when the USA and USSR were allies in theSecond World War), and although he was cleared of any “un-American”behaviour, suchwas the atmosphere of paranoia at the time that he had beendismissedfromhispostatPrincetonUniversityandwashoundedintoexilenotlongafterthebookwaspublished.HeworkedforatimeinBrazil,theninIsrael,

andattheUniversityofBristol,inEngland,beforesettling,in1961,atBirkbeckCollegeoftheUniversityofLondon.Bohm’suneasewiththeCopenhagenInterpretationstemmedfromdiscussions

withEinsteinatPrincetonfollowingthepublicationofhisbook.EvenbeforehelefttheUSA,andinspiteoftheturmoilinhisprivatelife,Bohmhadwrittentwopapers, published early in 1952, that outlined his alternative understanding ofquantummechanics.Thiswasessentiallyamorethoroughlyworked-outversionofthepilotwaveideathathadbeensuggestedbyLouisdeBrogliebackin1927,buthadbeenunjustifiablyignoredbecauseofthewayBohrandhiscolleagueshad steamrollered all opposition to theCopenhagen Interpretation. Indeed, thesteamrollering had been so effective that Bohm was unaware of de Broglie’spilot wave model when he worked out his own variation on the theme. Inessence, the idea is that entities such as electrons are real particles,which areguidedbyawavewhichobeystheSchrödingerequation.Verycrudelyspeaking,asIhavementioned,ananalogycanbemadewithasurferridingawaveontheocean.Thesnagwiththisideaisthatthepilotwavehasto“know”abouteverything

likely to affect the trajectories of the particles (in principle, everything in theUniverse) in order to guide each particle to its destination. It is said to beinfluenced by so-called “hidden variables.” If we knew what the hiddenvariables were, we could use them to calculate the quantum behaviour ofelectrons and other particles without resorting to the collapse of the wavefunctionorthestatisticalinterpretation.AstheOxfordphysicistDavidDeutsch(b. 1953) has put it, “a non-local hidden variable theory means, in ordinarylanguage,atheoryinwhichinfluencespropagateacrossspaceandtimewithoutpassing through the space in between: [in other words] they propagateinstantaneously.”1

Apart fromthemomentumof theCopenhagen juggernaut, therewasanotherreasonwhymostphysicistsdidnottakehiddenvariablestheoryseriouslyinthe1950s.In1932,JohnvonNeumann(1903–57),aHungarian-bornmathematicalgenius, had published a book inwhich, among other things, he “proved” thathiddenvariablestheoriescouldnotwork.HiscontemporariesweresoinaweofvonNeumann’s ability that for a generation this proofwas barely questioned,anditwaswidelycitedasgospel,withoutbeingspelledoutinfull,instandardtextssuchasMaxBorn’sNaturalPhilosophyofCauseandChance,publishedin1949. Born praised von Neumann’s “brilliant book” which proved that “noconcealed parameters can be introduced with the help of which the

indeterministicdescriptioncouldbetransformedintoadeterministicone.”OneofthepeoplewhowasdeeplyimpressedbythiswhenhereadBorn’sbook,justafteritwaspublished,wasayoungmaninhisfinalyearasastudentinBelfast—JohnBell(1928–90).ButsinceBelldidnotreadGerman,andvonNeumann’sbookhadnotbeenpublishedinEnglish,hehadto takeBorn’swordfor it thatvonNeumannknewwhathewastalkingabout.Bell,whohadbeenborn inBelfast, came froma “poor but honest” family.2

With an older daughter and two younger sons besides John, his parents couldbarelyaffordforonechildtogotosecondaryschool,butJohn’sabilitywassoobviousatanearlyagethattheydeterminedtogivehimeveryopportunitytheycould. Their struggle was rewarded when John qualified to study at Queen’sUniversityattheageofsixteen,ayearbeforehewasoldenoughtoenrolthere.Afterworkingasalabassistantwhilewaitingtostarthiscourse,hewentontoobtain a degree in experimental physics in 1948 and another degree inmathematics in 1949, the year he read Born’s book. When he had firstencounteredquantummechanicsasanundergraduate,hehadbeenoutraged.“Ididnotdaretothinkitwasfalse,”helatertoldJeremyBernstein,“butIknewit[theCopenhagenInterpretation]wasrotten.”3

After graduating, Bell worked for the UK Atomic Energy ResearchEstablishment until 1960, when he moved to the European particle physicsresearchcentreCERN,inGeneva,wherehestayedfortherestofhiscareer.HehadreadBohm’spapersonhiddenvariablestheoryandbeenimpressedbythem,sohewasalreadyhavingdoubtsaboutvonNeumann’s“proof.”Helaterwrote:“In1952Isawtheimpossibledone.ItwasinthepapersbyDavidBohm.Bohmshowed explicitly how parameters could indeed be introduced into non-relativistic wave mechanics, with the help of which the indeterministicdescriptioncouldbetransformedintoadeterministicone.”4

WhenhegotaGerman-speakingcolleaguetotranslatetherelevantpartofvonNeumann’sbookforhim,hesawatoncewherevonNeumannhadgonewrong.ButBelldidnothaveanopportunity to lookdeeply into the implicationsuntil1963–64,when,havingtakenasabbaticalyearofffromhisworkatCERN,hevisited the Stanford Linear Accelerator Center (SLAC) and other academiccentresintheUnitedStates.VonNeumannhadperpetratedahowler.His“proof”didn’tworkbecausehehadmadearidiculousassumption,equivalenttosayingthatiftheaverageheightofagroupofchildrenis1.2metrestheneachchildhasaheightof1.2metres.Ifthatsoundssillytoyou,youareingoodcompany:Bellthought soaswell. In1988hesaid:“ThevonNeumannproof, ifyouactually

cometogripswithit,fallsapartinyourhands!Thereisnothingtoit.It’snotjustflawed,it’ssilly!...Whenyoutranslate[it]intotermsofphysicaldisposition,they’renonsense.Youmayquotemeonthat:TheproofofvonNeumannisnotmerelyfalsebutfoolish!”5

ButthefactthatvonNeumannwaswrongdidn’tnecessarilymeanthatBohmwasright.Belldecidedtogobacktotherootsofthenon-localitydebate,startingoutfromtheEPRthoughtexperiment,toseewhetherornotnon-localitywasafundamental feature of all hidden variables theories. This was the first steptowards themostprofoundchange inourunderstandingof thequantumworldsincetherevolutionof1926–27.

TheBelltestandtheAspectexperiment

BellstartedoutfromaversionoftheEPRexperimentdevisedbyBohmandhiscolleagueYakirAharonov (b. 1932)whileBohmwasworking in Israel in thelate 1950s. In this version of the experiment, instead of thinking in terms ofmomentum and position the imaginary experiment deals with the propertyknownasspin—ortheequivalentpropertyofphotons,polarization.Simplifyingthe argument somewhat, there are circumstances in which quantum processeswillproducetwoelectronswhichflyoffindifferentdirections,andwhichhaveacombinedspinofzero.Soifonehasspinup,theotherhasspindown,andsoon.Thereisanextradegreeofvariabilitybecausethespincanbemeasuredinanydirection(forexample,horizontallyorvertically,oranyangleinbetween).Ifthespinofoneelectronismeasuredinanyparticularorientation,thenweknowthatthespinoftheotherelectronmustbetheopposite,forthatparticularorientation.But how does the other electron know this? The naive answer is that the

electronssetoutontheirrespectivejourneyswithwell-definedbutoppositespinstates.Butamoresubtleexperimentremovesthispossibility.Ifthespinofoneelectron ismeasured for one orientation, and the spin of the other electron ismeasured for a different orientation, the situation is not so simple. Therelationship between the measured spins can be predicted from quantummechanics in a well-defined statistical way, but the predictions do not matchthoseof“commonsense.”WhenBellcalculatedtheappropriatenumbersforthecorrelation,hefoundadifferencebetweenthepredictionofquantummechanics

andthepredictionsofanytheorybasedonlocalrealityandhiddenvariables.Heexpressed this in termsofa relationcalledBell’s inequality,whichsays that iflocal reality holds, one set of numbers determined by experiment must besmallerthananothersetofnumbersdeterminedbyexperiment.Thisisabitlikesaying that in the everydayworld the number of red-hairedmenmust be lessthanthetotalnumberofmenandwomen.Butifquantummechanicsiscorrect,andlocalrealitydoesnothold,thenBell’sinequalityisviolated,asifthereweremorered-hairedmenintheworldthanallofthemenandwomenputtogether.“I got that equation into my head and out on to paper within about one

weekend,” he later told Paul Davies. “But in the previous weeks I had beenthinking intenselyall around thesequestions.And in thepreviousyears it hadbeenatthebackofmyheadcontinually.”Bellwaswellawarethat,unlikethesituationoriginallydescribedbyEinstein,

Podolsky, and Rosen, his hypothesis could actually be tested by experiment,takingtheEPRdebateoutoftherealmsofphilosophyandintothelab.Inthepaperhewrotedescribingtheseresultshesaid:“Itrequireslittleimaginationtoenvisage the measurements involved actually being made.” But few peoplenoticedthepaper,orthisextraordinaryclaim,becauseitappearedinanobscurejournal.Such an important theoretical discovery should have been published in the

prestigious Physical Review. But Phys Rev, as it is known, charged forpublication,onthebasisofthenumberofpagesprinted.AlthoughBell’spaperwasjustsixpageslong,asavisitortoBrandeisUniversity(wherehehadarrivedinthecourseofhissabbaticaltrip)hefeltdiffidentaboutaskingtheinstitutetopay, and sent it to the journal Physics, which didn’t levy page charges.Unfortunately, it didn’t havemany readers, either. So itwas five years beforeBell received a letter from JohnClauser (b. 1942), aBerkeley-basedphysicistwhohadreadthepaperandintendedtocarryoutanexperimenttotestwhetherornotBell’sinequalitywasviolated.Bellenthusiasticallyrepliedthat:Inviewofthegeneralsuccessofquantummechanics,itisveryhardformeto doubt the outcomeof such experiments.However, Iwould prefer theseexperiments, inwhich thecrucialconceptsareverydirectly tested, tohavebeen done and the results on record. Moreover, there is always the slimchanceofanunexpectedresult,whichwouldshaketheworld!6

Butitwas1972beforeClauserandhiscolleaguesreportedthattheirexperiment(actuallyusingphotonsratherthanelectrons)hadindeedproducedresultsinline

withthepredictionsofquantumtheory,andagainstlocalreality.Exciting though theseconclusionswere, theexperimentswerenotdefinitive.

They involved using beams of photons, rather than individual pairs, and thedetectors used could detect only a fraction of the photons in the beams.Conceivably,alltheundetectedphotonswerebehavinginadifferentmannerthatwould lead todifferent conclusions.Clauser’s experimentwas apointer to theway ahead, rather than the last word on the subject. But the fact that theexperiment had been carried out at all was a triumph,which stimulated otherresearchers to attempt improvementson the theme.Theonewhoachieved themoststrikingsuccesswasaFrenchman,AlainAspect(b.1947),whospentthreeyearsdoingvoluntarywork(aversionofFrenchnationalservice)asateacherinCameroonafterobtaininghisdegree,andreaduponquantumphysics,includingtheEPRParadoxanditsimplications,duringhissparetimeinAfrica.WhenhereturnedtoFrancein1974,hewasdeterminedtomakeanexperimentaltestoftheBellinequalityforhisdoctoralworkattheUniversityofParis–South.WhenhevisitedBellinGenevatodiscusshisplans,Bell’sfirstquestionwas“Doyouhavetenure?,”meaning“Doyouhaveasecurepermanentpost?”WhenAspectrepliedthat,farfromhavingtenure,hewasstillonlyaPhDstudent,Bellreplied:“Youmustbeverycourageous.”7HemeantthatifAspectfailedinhisquesttocarryoutthedifficultexperimenthemightendupwithnoPhDandnoprospectof a career in physics. But although it took longer than he had anticipated,Aspecteventuallyachievedhisgoal.The important featureof all suchexperiments is thatmeasurementsmadeof

photonbeamAproducea setof randomnumbers.ThemeasurementsmadeofphotonbeamBalsoproduceasetofrandomnumbers,sonoinformationaboutphotonbeamAcanbegleanedjustbylookingatthosenumbers.Butwhenthetwo sets of numbers are put together and compared, it is possible to see acorrelationbetweenthem—toseethatthe“answers”obtainedfromphotonbeamBdependonthe“questions”asked,simultaneously,ofphotonbeamA,nomatterhowfarawayphotonbeamAis.Theonlywaytomakethiscomparison,though,is to convey information fromA toB by conventionalmeans (meaning,moreslowlythanthespeedoflight),sothereisnoconflictwithrelativitytheory.Inthefirstversionsofthiskindofexperiment,therewasapossibleloophole.

Theexperimentsweresetupso that theentangledphotonswent their separatewaysandpassedthroughtwodifferentsetsofdetectors.Butthewholesetupwasfixedinadvance,soitwaspossibletoarguethatthisdeterminedtheoutcomeoftheexperiments,withnoneedforany“spookyactionatadistance”linkingthe

partsoftheexperiment.Aswellasgreatlyimprovingtheexperimentalstatistics,Aspectclosedthis loopholebydevisingasystemwhichchangedthesettingofthe polarizing filter used to measure the photon beam at random while thephotons were in flight through the experiment. The two sets of measuringequipmentwere13metresapart,sotheswitchinghadtotakeplaceinlesstimethan it takes for amessage travelling at the speed of light to cross 13metres,which is about 43 nanoseconds (1 nanosecond is 1 thousand-millionth of asecond). In roundnumbers, the switchingbetween settings actually tookplaceonceevery10nanoseconds(every10thousand-millionthsofasecond).Inthatway,therewasnopossibilitythatthesetupatdetectorBcould“know”whatthesettingofdetectorAwasatthemomentphotonBarrived.Aspecthimselfsaid:What these experiments have shown is first that they violate Bell’sinequalities, and on the other hand that these results are in very goodagreementwith the predictions of quantummechanics. Sowe assume thatquantummechanics is still a very good theory. [But] even in this kind ofexperiment it is not possible to send any messages or useful informationfasterthanlight.8

Every subsequent refinement of this kind of experiment has confirmed theaccuracyofthisstatement.TheresultsofAspect’sexperimentswerepublishedin1981and1982,andhe

receivedhisPhDin1983. Itwas thisdefinitiveconfirmationof thevalidityofquantummechanics,closing the lastmajor loophole for local realistic theories,that prompted me to write my book In Search of Schrödinger’s Cat, whichappeared in1984,offeringahistoricalaccountof thedevelopmentofquantumphysics.Iwas(andstillam)happytoaccepttheevidencethat“itisnotpossibleto send any messages or useful information faster than light.” But a fewmaverickphysicistsmadeaseriesofwrong-headedbutsophisticatedattemptstoprove that entanglementoffers away to sendmessages faster than light.Theywereultimatelyprovedwrong,butresearchpartlystimulatedbytheirquesthasledquantumphysicsintothealmostequallyexoticrealmsofcryptographyandteleportation.

Quantumcryptographyandthe“nocloning”theorem

One of the people who tried to devise a way to use entanglement to sendmessages faster than light wasNickHerbert, an American physicist who hadcompletedaPhDatStanfordUniversityin1967,buthadbeenunabletogetanacademicpostandhadworkedinavarietyofjobswhilepursuinghisinterestinquantumphysicsinhissparetime,togetherwithagroupoflike-mindedthinkersbased in Berkeley, California. The details of Herbert’s design for faster-than-light (FTL) signallingdonotmatter, except foronekeypoint. It dependedonmaking exact copies of photons—“clones,” in the vernacular. A copy ofHerbert’s paper found its way to Wojciech Zurek (b. 1951), a Polish-bornAmericanphysicistwhofoundtheflawintheargument.TogetherwithWilliamWootersheprovedthat“asinglephotoncannotbecloned,”andusedthatphraseasthetitleforapaperpublishedinNatureinOctober1982whichbegan:“Notethat if photons could be cloned, a plausible argument could be made for thepossibility of faster-than-light communication.” Although it ruled out FTLsignalling, itwas the “no cloning theorem,” also discovered independently bytheDutch physicistDennisDieks, that opened theway to the practical use ofquantumentanglementtocreateuncrackablecodes—quantumcryptography.There are several approaches to the problem of quantum cryptography, but

they all depend on code systems that use a “key” of random numbers. Thedescriptionhere is adapted frommybookSchrödinger’sKittens, since I couldnotseeanywaytoimproveonit.The kind of code I want to describe is familiar from spy stories. The two

peopleusingthecode(alwaysreferredtobycryptologistsas“Alice”and“Bob”)areeachequippedwithan identical listof randomnumbers,aso-called“pad,”whichcanbeasthickasatelephonebook.Thepersonsendingthemessageturnsitintonumbers(perhapsassimplyasbyallottingthenumber1toletterA,2toB,andsoon),andthenchoosesoneof thepagesofrandomnumbersfromthepad. The numbers on the pad are then written out under the numberscorrespondingtothelettersinthemessage,andthepairsofnumbersareaddedtogether.Thecodedmessage is then sent, alongwith informationaboutwhichpageonthepadwasused,andattheotherendthesamesetofrandomnumbersaresubtractedfromthecodedsignaltorestoretheoriginalmessage.ThecodeiscalledtheVernamcipher,aftertheAmericanGilbertVernam,whodevelopeditduringtheFirstWorldWar,andissometimesreferredtoasthe“one-timepad”technique, because spies were supplied with the random number book in theformofatear-offpad,sothateachsheetcouldbeusedonceandthendestroyed(if the same set of randomnumbers from the samepageof thepad is used to

codemorethanonemessage,patternsrecurwhichmakeitpossibletocrackthecode).Thiskindofcodecannotbebroken,unless thepersonwho intercepts italso

hasacopyof the sameone-timepad.Thesnag is thatunder theconditions inwhichespionageagentsusuallyoperateitisalltoolikelythattheinterestedthirdpartywill get holdof apad;worse, it is possible for the thirdparty tohave acopyofthepad,andtobebreakingthecode,withoutthetwousersofthecodeknowing.Quantumphysicsoffersawayaroundbothproblems.Thereisnoneedtokeep

the coded messages themselves secret, because they are useless without theinformation thatcomesoveraquantumchannel—thekey.What isneeded isawaytocommunicatethekeyitself—astringofrandomnumbers—fromAlicetoBobinanuncrackableway.Tomakethingsassimpleaspossible,thestringofnumberscanbeinbinaryarithmetic,astringof0sand1slikethecodeusedbycomputers; so the key can be transmitted as any system of on/off, either/orsignals.Charles Bennett, of the IBMResearch Center at YorktownHeights in New

York,andhiscolleaguesshowedthatyoucandothisusingpolarizedlight.ThetechniqueinvolvesAlicesendingBobastreamofphotons,polarizedeitheruporacrossoneoftwoagreedorientations(at45degreestoeachother),butwiththepolarizationofeachphotonchosenatrandom.Bobmeasuresthepolarizationoftheincomingphotons,butforeachmeasurementhecanonlyalignhisdetectorwithoneof theagreeddirectionsofpolarization—again,chosenat random. Ineachcase,hewillgetan“answer’correspondingeithertovertical(binary1)orhorizontal (binary 0) polarization relative to his detector. He then tells Alicewhich orientations he used for eachmeasurement, and she tells himwhich ofthese match the way the photons were sent (this communication can be byemail).BobandAlicethenthrowoutallthemeasurementsforwhichBobchosethe“wrong”polarization,andareleftwithastringof1sand0s,theirsecurekeyinbinarycode.Itsoundslikeatediousprocesswhenspelledoutlikethis,butintherealworldanyoneusingsuchasystemwouldavoidthetediumbyrunningitthroughacomputerwhichdidthedonkeywork.Thegreatbeautyofthetechniqueisthattheonlywayathirdpartycanfindout

what code Alice and Bob are using is to “eavesdrop” on the quantumcommunication channel, and measure the polarization of the photons as theypassthrough.Buttheactofmeasuringthepolarizationofaphotonchangesthepolarization!Thephotoncannotbecopied(cloned)andleftunchanged.Evenif

theeavesdroppercopiesthemeasuredphotonandsendsitontoBob,itwillhavebeen randomized. Bob and Alice can check for this interference by standardtechniqueswhich,ineffect,compareeveryfifth,oreveryseventh,orwhatever,letterofthekey,withoutrevealingthewholekey.ArturEkert(b.1961),aPolishphysicistnowattheUniversityofOxford(who

has also collaborated with Bennett), found another way to achieve the sameends,showinghowtherequiredrandomstringofdigitscouldbeobtainedfromavariation on the EPR experiment itself. The EPR photons are fired off inoppositedirections,suitablyentangledbutasyetunmeasured,onebeamtoAliceand one to Bob. Alice and Bob can each measure the polarization of theirphotons, using detectors oriented at random along one of a set of previouslyagreed polarization directions. They then tell each other, over any ordinarypublic communications channel, which measurements they made, but not theresults of those measurements. Finally, they discard the measurements wheretheyuseddifferentorientations,andconstructtheirsecurekeyoutoftheresultsof themeasurementswhere their polarization detectorswere aligned the sameway—makingallowance,ofcourse,forthefactthatthemembersofeachpairofEPRphotonshavetheoppositepolarization,oncetheyhavebeenmeasured,sothatBobalwaysgetsa1whereAlicegetsa0,andviceversa.And,onceagain,any attempt to “tap” the quantum communication channel by looking at thephotonsbeforetheygettoBobandAlicewillscrambleuptheirpolarizationsina detectableway. It’sworthmentioningEkert’s variation on the theme if onlybecauseitledtoamemorableencounterbetweenhimandJohnBell,whenBellwasonavisittoOxfordandEkertwasjustagraduatestudent.AfteratalkBellgave, Ekert was able to meet him briefly and explain his idea. Bell wasastonished.“Areyou tellingme that thiscouldbeofpracticaluse?”heasked.Ekertsaiditcould.“Well,”saidBell,“it’sunbelievable.”9

It may all sound far-fetched and improbable; but even by the timeSchrödinger’sKittens was published, in 1995, Bennett and his colleagues hadactuallybuiltasystemwhichworksinthisway.Admittedly,intheprototypethecodedmessageswereonlysentacrossadistanceof30centimetres;but that isbecausetheybuiltitonadesk-top.Iwrotein1995that“inprinciple,polarisedphotonscouldbesentunalteredthroughseveralkilometresofopticalfibre.Andafterall,whenJohnLogieBairdbuiltthefirsttelevisiontransmitteritonlysentapictureoveradistanceofacoupleofmetres.”The quantum cryptographers have sincemore thanmetmy expectations. In

2004, appropriately enough in Schrödinger’s home city of Vienna, a team of

physicists headed byAntonZeilinger (b. 1945) carried out the first electronicbanktransferofmoneyusingquantumcryptographytoensurethesecurityofthedata.Thiswasn’tjustacasualexperimentinvolvingonephysicisttransferringasmallamountintoanotherphysicist’saccountbutafull-blowntransferofofficialfunds between amajor bank and themayor’s office. In 2007, during a Swisselection, quantum encryption was used to ensure the security of votes castelectronicallyinGeneva.Beforelong,thisislikelytobethewaythesecurityofinformation routinely transmitted over the Internet is assured.And it need notjustbeinformationthatistransmitted.

Quantumteleportationandclassicalinformation

Quantum teleportation also uses the “no cloning” theorem, but in a slightlydifferent way. A photon—or other quantum entity—cannot be duplicated(cloned), but all of its properties can be transferred to a second photon eventhough(indeed,because)thefirstphotonischanged.Ineffect,thesecondphotonhasbecomethefirstphoton.Entanglement and action at a distance are at the heart of the technique of

quantum teleportation, which was also proposed by Charles Bennett, andpublishedinthejournalPhysicalReviewLettersin1993.In theclassical,everydayworld,sendingcopiesof things todistantplaces is

routine.Theobvious analogywith teleportation is the faxmachine,whichhastheaddedadvantageofleavingtheoriginalcopyintactatitsstartingplacewhileproducingaduplicateatthedestination.Newspapersandbooksarereproducedin editions containinghundredsof thousandsof essentially identical copies, asfarastheirinformationcontentisconcerned.Butat thequantumlevel,copyingruns intodifficulties.Thefirst issimplya

questionofdetail.Theuncertaintyprinciplemakesitimpossibletoknoweverydetail abouteveryatom in, say,a sheetofpaper,oreven theexactpositionofeverymoleculeofinkintheprintingonthepaper;sothefaxed“copy”canonlyeverbeanapproximation.Inaddition,scanninganobjectat thequantumlevelchanges its quantum state. But this apparent problem iswhatmakes quantumteleportationpossible!Evenifyoudidobtaintheinformationneededtobuildacopyofaquantumsystem,theoriginalwouldbedestroyed.Thisismorelikethe

science-fictionversionof teleportation(“Beammeup,Scotty”) than thewayafaxmachineworks.Classicalinformationcanbecopied,butcanonlybetransmittedatthespeed

of light (or less);quantum informationcannotbecopied,but sometimes, as intheEPRexperiment, itseemstopropagateinstantlyfromoneplacetoanother.Bennett and his colleagues used a mixture of these classical and quantumfeaturesofasystemtodevisetheirteleportationdevice.Theydescribethisintermsoftwopeople—again,AliceandBob—whowant

to teleport an object. In this teleportation for beginners, the object to beteleported is simply a single particle—perhaps an electron—in a particularquantumstate.Atthebeginningoftheexperiment,AliceandBobareeachgivenaboxcontainingonememberofapairofentangledobjects,equivalenttotheireachcarryingoneofthephotonsfromtheEPRexperiment,withoutmeasuringits polarization. Then, they go off on their travels across the Universe. Sometime later—perhapsmany years later—Alicewants to send another particle toBob. All she has to do is to allow the “new” particle to interact with herentangled particle, and tomeasure the outcome of their interaction. This bothestablishesandchanges thestateofherentangledparticle,and instantaneouslyestablishes and changes the state of Bob’s entangled particle in an equivalentway.Bobdoesn’tknowthisyet,becauseheissomewhereontheothersideofthe

Universe.SonowAlicehastosendhimamessage,perhapsbyradio,orperhapsbyputtinganotice in thenewspaper thatBob readseveryday, tellinghim theresultofhermeasurement.Thismessage contains only classical information, so she can send asmany

copies as she likes in as many newspapers or radio broadcasts as she likes.Eventually,Bobwillgetthemessage.Armedwiththeinformationabouthowtheinteraction betweenAlice’s two particles turned out,Bob can now look at hisownentangledparticleandusetheinformationto“subtractout”theinfluenceofhisownoriginalparticlefromitspresentstate.Whatheis leftwithisanexactcopyof theotherparticle—theone thatAlicewanted tosend tohim.AndshehasdonethiswithoutknowingwhereBobis,orevenspeakingtohimdirectly.The original version of the third particlewas destroyed (changed into anotherquantumstate)whenAlicecarriedouthermeasurementonit,soBob’sversionisunique,unlikeanewspaper,andheisfullyentitledtoregarditastheoriginalparticle,conveyedtohimbyacombinationofclassicalmessageandactionatadistance.

This process, Bennett stresses, defies no physical laws, and only permitsteleportation to take place at less than the speed of light—Bob needs Alice’s“classical”messageinordertountanglehisparticleproperly,andifhelooksathisparticletoosoonhewillchangeitsquantumstateanddestroyanyprospectofuntangling it in the right way. “Alice’s measurement forces the other EPRparticletochangeinsuchawaythattheclassicalinformationthatcomesoutofhermeasurementenablessomeoneelsetoproduceaperfectcopyofwhatwentin,”but“itcannottakeplaceinstantaneously.”10Itis,asmorethanonewaghasremarked, “teleportation, Jim, but not aswe know it.”Andonce again, in theyears since 1995 experimenters have put the idea into practice on animpressively largescale,althoughnotyet fromonesideof theUniverse to theother.Thefirstsuccessfulquantumteleportationexperimentsonthelaboratoryscale

(overaboutametre)werecarriedoutinInnsbruckin1997,byZeilinger’steam.Thiswassoonextendedtoarangeofafewhundredmetres,usingfibreoptics,andby2004differentteamswerecarryingoutpartialteleportationofthestatesofwholeatoms.11InMay2010,ateamofChinesescientistsreportedinNaturesuccessful quantum teleportation over a range of 16 kilometres sending laserbeamsthroughtheair;andtherearealreadyplans(butnofunding)forasatellitetobelaunchedcarryingphotonsinanentangledstatethatcanbeteleportedbackto Earth from orbit. But all of these ideas pale in comparison with the mostimportantpracticalapplicationofentanglement,whichusesthesametechnologythatisneededforquantumcryptographyandquantumteleportation.Thisisthedevelopmentofthequantumcomputer,apracticalpropositionas“unbelievable,”in the sense usedby JohnBell that day inOxford, as anydevelopment in theapplicationofsciencetotechnology.

ThequantumcomputerandtheMultiverse

Ihavedescribed thebackground to thedevelopmentofquantumcomputers indetailinmybookInSearchoftheMultiverse,butthemind-blowingimplicationscan be understood without going into the nuts and bolts of the quantumengineering.Theessenceofmodernelectroniccomputersis thattheycarryoutcalculationsusingbinarycode,whichcanberepresentedasastringof0sand1s,

orinpracticaltermsasanarrayofswitcheswhichcanbeeitheronoroff.Each“on/off”unitiscalledabit.Eightbitsmakeabyte,andthepowerofacomputeris often expressed in terms of the number of bytes in its “brain”—these days,many gigabytes in even a modest laptop or smart phone. The essence of aquantum computer is that each of the switches—each bit—can exist in asuperpositionof states,withoutanycollapseof thewave function, so that it isbothonandoff(storingboth1and0)atthesametime.Crucially,suchswitches(or“stores”)canalsobeentangled,sothatapairoftheseso-calledqubitsmaybeguaranteedtobeeitherbothinthestate1orbothinthestate0,eventhoughneitherofthequbitscanbesaidtobedefinitelyinthestate0ordefinitelyinthestate1.Inprinciple,eachqubitcouldbeasingleatomorapolarizedphoton;asyet, in practice molecules containing several atoms are used, and each bit ofinformationisstoredinbillionsofcopiesofeachmolecule.All of this means that the power of a quantum computer is literally

exponentiallygreaterthanthepowerofanequivalentconventionalcomputer.Aquantum computer using n qubits is 2n times as powerful as a conventionalcomputerwithnbits.Forexample,with2qubitsaquantumcomputerwouldbeequivalent to a conventional computer with 4 bits, with 4 qubits a quantumcomputerwouldbeequivalenttoaconventionalcomputerwith16bits,andwithjust 10 qubits a quantum computer would be equivalent to a conventionalcomputer with 1,024 bits, or one kilobit.12 The crucial point is that modestquantumcomputers havebeenbuilt anddowork as expected, confirming thattheyoperateinlinewiththerulesofquantumphysics,includingentanglement.ThemostdramaticclaimsforsuccessinthisfieldhavecomefromaCanadian

commercialcompany,D-WaveSystems,whichannounced inMay2011 that ithad sold a 128-qubit quantum computer to a security firm, LockheedMartin.Nobody outside the company knows exactly how the computerworks, exceptthat it involves linking sixteen 8-qubit units, because details have been keptsecretforcommercialreasons.Thishasledtodoubtsamongsomescientistsastowhetheritreallyoperatespurelyonquantumprinciples.Butitcertainlydoessomething—the Lockheed Martin people are no fools, and spent a yearreviewingthemachinebeforebuyingit.Andevenifitturnedoutthat“only”the8-qubitunitsare reallyoperatingpurelyasquantumprocessors,which there isno reason to doubt since similar mini-processors have beenmade to work inseverallabs,thatstrikesattheheartofourunderstandingofrealityandleadsusstraightbacktoSchrödinger’sviewoftheworld.DavidDeutsch,who is apioneerof the theoryofquantumcomputation,has

asked:Wheredothecalculationscarriedoutonaquantumcomputertakeplace?Remember that there is no collapse of the wave function, exactly like thesituationintheSchrödinger’scatthoughtexperimentbeforetheboxisopened.Sobothpossibilitiesarereal.Ifaquantumcomputerusing8qubitsisequivalenttoaconventionalcomputerusing256bits,thatisbecausethereare256separatecomputers corresponding to each possible quantum state of the processorcarryingoutthecomputationin256differentuniverses—the“parallelworlds”ofscience fiction. They work on the problem together, solve it, and share theanswer.“That’swhatthelawsofphysicstellus,”saysDeutsch.“Itcan’tbethattherearemultipleuniversesatthelevelofatomsbutonlyasingleuniverseatthelevelofcats.”13

Thisdoesnotmean that theUniverse somehow“splits” into—in thiscase—256copiesof itselfwhenyou run thecomputer.TheMultiverse ideasays thattherealwayswere256universes,identicaltooneanotheruptothepointwherethe computation is run, and that the identical experimenters in each of thoseuniverseseachdecidetocarryoutthesameexperiment—hardlysurprising,sincethey are identical. And this “no collapse” picture is very close to whatSchrödingersuggestedin1952(seeChapter11),althoughwhatbecameknownas the Many Worlds Interpretation (MWI) of quantum mechanics is usuallycredited to theAmericanphysicistHughEverett (1930–82),whoproposed itafew years later; he was unaware of Schrödinger’s earlier work, and(unfortunately) did see theMWI in termsof the repeated “splitting”of realityintodifferentbranches.Inmyview,themostimportantthingtotakeawayfromtheconceptoftheMultiverse,whichistheonlysatisfactorywaytoexplainwhyquantum computers work, is Schrödinger’s idea that the wave function nevercollapses,andthatallrealitiesare(andalwayswere)equallyreal.Fromthere,itisbutashortsteptoSchrödinger’sothergreatinterest.

QuantumphysicsandrealityThe big problem with the Copenhagen Interpretation, even if you arecomfortablewiththeideaofcollapsingwavefunctions,hasalwaysbeenwhereyoudraw the line between the quantumworld and the everydayworld. In theclassic thought experiment, it is implicitly assumed that it takes theconsciousnessofahumanbeing to trigger thecollapseanddeterminewhetherthecatisdeadoralive.Butisn’tthecatitselfcompetenttotellwhetheritisalive

ordead?Couldananttriggerthecollapse?Orarobot?JohnBellexpressedthisbeautifullyinanarticleinPhysicsWorldin1990.He

wrote: “What exactly qualifies some physical system to play the role of‘measurer’?Wasthewavefunctionoftheworldwaitingtojumpforthousandsofyearsuntilasingle-celled livingcreatureappeared?Ordid ithave towaitalittle longer, for some better qualified system [a person]with a Ph.D.?”WhatBell set out as a reductio ad absurdum some scientists take literally. StevenWeinberg (b. 1933), interviewed in the November 2010 edition of ScientificAmerican,said:“TheuniversemaybelikeagiantSchrödinger’scat:Whenthecatisalivethecatknowshe’salive(therearescientiststorecordwhat’sgoingonintheuniverse);andintheotherstate,thecatdoesn’tknowanything(thereare no scientists to observe what’s going on).” This is the CopenhagenInterpretationtakentoitslogicalextreme—theUniverseonlyexistsbecauseweare here to observe it. But I’m with Bell on this—what such a notion reallyindicatesistheabsurdityoftheCopenhagenInterpretation.Therehavebeenmanyattempts—apart fromtheManyWorlds Interpretation

—togetroundthisproblembyremovingtheroleoftheconsciousobserver.Themost fashionable in recent years has been something called “decoherence.”According to this idea, although a single quantum entity such as an atom canexist in a superposition of states, if this entity becomes entangled with amacroscopic object containing large numbers of atoms the complexity of thesystem forces the quantum superposition to “decohere” as the informationdescribing the individual quantum entity gets lost among the vast number ofpossible combinations of interactions between all of the atoms in themacroscopicsystem.Putmoresimply, thedecoherenceoccursbecause there isno such thing as an isolated quantum entity; everything is entangledwith theoutside world. This has always seemed to me at best a variation on theCopenhagenInterpretationandatworstmumbojumbo.Ifasingleatomcanexistinaquantumstatebutmydesk,say,cannot,wheredoyoudrawtheline?Willtwoatoms formaquantumsystem?Experiments show theydo.Sohowmanyatomsdoesittaketomakethesystemdecohere?Three?Seventeen?Forty-two?Itisexactlythesame,butonasmallerscale,astheSchrödinger’sCatpuzzle.Buttheideaofdecoherencedoessuggestanotherwayoflookingattheworld,

onemoreinkeepingwithSchrödinger’sphilosophy.Proponentsofdecoherence,looking from the outside in, say that entanglementmakes the quantumworldclassical; looking from the inside out, however, it is equally valid to say thatentanglement makes the classical world quantum. And in recent years

experimenters have detected an increasing number of examples of quantumeffects—in particular, entanglement—operating in macroscopic systems. Itseemsthatthereisno“outsideworld.”Oneofthepioneersofthislineofwork,Oxford-basedphysicistVlatkoVedral

(b. 1971), summarized the evidence in the June 2011 issue of ScientificAmerican. Throughout the first decade of the twenty-first century, variousresearchers carried out a series of experiments in which they studiedentanglement in increasingly large samplesofmaterial. In someof theearlieststudies,crystalswere tweakedbymagnetic fields. Inessence, theatoms in thesampleswereseentolinethemselvesupwiththemagneticfieldsmorequicklythan they could havewithout the help of entanglement. The early versions oftheseexperimentsrequiredverylowtemperatures,closetoabsolutezero(minus273°C),toavoidinterferencebythejigglingofatomsduetothermalmotion;butbytheendofthedecadevariouskindsofentanglementexperimentswerebeingcarriedoutattemperatureswellabove0°C.Themostimpressiveevidenceofmacroscopicentanglementsofarcomesfrom

studiesofmigratorybirds.Insomespecies,theeyeofthebirdcontainsatypeofmoleculeinwhichtwoelectronsformanentangledpair.Whenthismoleculeisexposed to light, the entangled electrons become sensitive tomagnetic fields.Experimentsconfirmthat thischanges thechemistryof theprocessesaffectingvision.Ithasbeensuggested,butnotyetprovedconclusively,thatthealterationin the chemistry of the photo-receptors means that an image of the magneticfieldisproducedinthebird’sbrain—thatitcanseethemagneticfield.Other evidence of entanglement at work in living systems comes from the

chemistryofphotosynthesis.Vedral says that it isno longerpossible toacceptthat “large numbers of particles spontaneously behave classically . . .experiments now leavevery little room for suchprocesses to operate . . . fewphysicistsnowthinkthatclassicalphysicswilleverreallymakeacomebackonany scale.”And “the implications ofmacroscopic objects such as us being inquantumlimbo[are]mind-blowing.”And if there are no boundaries between the macroscopic world and the

quantumworld,ifthereisnocollapseofthewavefunction,andifeverythingisentangledwitheverythingelse,thephysicist’sviewoftheworldis,afterall,notsodifferentfromSchrödinger’sVedanticvisionofreality.

Notes

1InterviewinDaviesandBrown,TheGhostintheAtom.2InterviewinBernstein,QuantumProfiles.3Bernstein,QuantumLeaps.4Bell,SpeakableandUnspeakableinQuantumMechanics.5InterviewinOmnimagazine,May1988.UnknowntoBellatthetimehefoundthesillymistake,theflawinvonNeumann’sargumenthadalsobeenpointedoutbyGreteHermann,in1935,butignored.6QuotedbyAczel,Entanglement.7QuotedbyAczel,Entanglement.8InterviewinDaviesandBrown,TheGhostintheAtom.9QuotedbyGilder,TheAgeofEntanglement(youhavetoimagineBell’ssoftIrishaccent,especiallyontheword“unbelievable”).10QuotesfromScienceNews,10April1993.11ThedetailsareinZeilinger’sbook,DanceofthePhotons.12Withjust100qubits,youwouldhavetheequivalentof1,267billionbillionbillionbits.13SeeBrown,Minds,Machines,andtheMultiverse.

Postscript

QuantumGenerationsInthesummerof2011,aftercompletingthemaintextofthisbook,IwasabletomeetTerryRudolphanddiscussthefoundationsofquantumphysicswithhiminhisoffice,perchedtwelvefloorsupatImperialCollege,withspectacularviewsacross London. First, he told me about the circuitous route by which he hadarrived there, and the surprise he experienced when he learned who hisgrandfatherwas.Terry was born in Zimbabwe in 1973, and spent his childhood in southern

Africa during a time of political turbulence. His immediate family (he has abrotherandtwosisters)movedtoMalawiin1979,buthisgrandmotherstayedinZimbabwe, and although he saw her once or twice, moving around southernAfricaatthattimewas,asheputsit,“problematic”;after1979,hesaid,“mostofmymemories of her are via letters.”When the Rudolph familymoved on toAustralia in themid-1980s, she stayed inZimbabwe, anddiedabout tenyearslater.As a teenager in Australia, Terry was much more interested in sport

(particularlysquash) thanacademicstudies,andspentmanyhours (up tosixaday) trainingwhen he should have been studying, in the hope of becoming aprofessional.“Iwasverycompetitive,”hesays,“IguessIstillam.”Inspiteofhissportingobsession,hegraduatedfromtheUniversityofQueenslandin1993,majoringinmathematicsandphysics,havingchosenphysicsbecauseitseemedlikethehardestsubject—thoughhepointsoutthathisfather(nowretired)wasachemistandteacher,andplayedabigpartinhisbecomingascientist.Itwasinthefinalweeksofhisfirst“ordinary”degree thatTerrybecamehookedon thefundamental puzzle of the foundations of quantum physics. It happenedwhenoneof theprofessorsgavea lecture—the last lectureofhisdegreecourse—onBell’sinequalityandtheAspectexperiment.ThiswasTerry’sintroductiontotheideaofentanglementandnon-locality, and (likemanyothers) at firsthecouldnotbelieve it.He spent twoweeks trying to find the flaw in the argument, soobsessedwithitthatheignoredhisrevisionandnearlyfailedhisfinalexamasa

result.Having failed to finda flaw,he realized thatherewas something reallydifficultandprofound,somethingworthmakingtheefforttotrytogettogripswith;beforethis,hehadreallyfoundphysicstooeasytobeinteresting.Theimmediateresultofthisnewobsessionwasathesisleadingtoanhonours

degreefromQueenslandin1994.Then,itseemedlikeagoodtimetotakeayearoutandtraveltheworldbeforesettlingdown.Terryknewthathismotherhadahalf-sisterinAustria,RuthBraunizer,andnaturallyheplannedtovisitherontheEuropean legofhis travels. Itwasat thispoint thathismother realized itwastimeshetoldTerrywhohisgrandfatherwas.“Wewerehavingbreakfast,andmymum just said, ‘There’s something you should know. My father was ErwinSchrödinger.’”Thenewscameasacompletesurprisetothetwenty-one-year-oldwould-bequantumphysicist,whohadjustwrittenhisfirstscientificpaper.Asheputittome,“I’devenreadyourbook[InSearchofSchrödinger’sCat]beforeIknewwhomygrandfatherwas.”Afterhisgapyear,whichincludedmeetingupwiththeAustrianbranchofthe

family,TerryobtainedaPhDfromYorkUniversityinCanada(awardedin1998)andworkedattheUniversityofToronto,theUniversityofVienna(collaboratingwith,amongothers,AntonZeilinger), andBellLaboratories,before settling in2003atImperial,whereheisnowCo-Director,CentreforDoctoralTraininginControlledQuantumDynamics.Thismeansthatheisinchargeofsomeofthebrightest students around, addressing the foundations of quantum theory,although he is also interested in practical applications, such as quantumcomputing. He is now easy about being Schrödinger’s grandson, and neithermakesanyfussaboutitnorfindsituncomfortable;buthemakesapointofneverreading any biographies of his grandfather (including this one) because hedoesn’twanttobeinfluenced,consciouslyorunconsciously,byanawarenessofhisantecedents.“Idon’twanttosecond-guessmyself,”hesays.TerryRudolphisverymuchhisownman,andalthoughhappyenoughtobringmeuptospeedonhisbackground,reallywantedtotalkaboutquantumreality—whichwasfinebyme.One aspect of this work which particularly intrigued me involves

entanglement, thermodynamics, and thearrowof time. It is exactly the sortofthing thatSchrödinger,withhisdeepappreciationofBoltzmann’swork,mighthavebeeninvolvedwithifhewerestillaround.TerryRudolphandhiscolleagueDavidJenningshaveshownthatitishardtodecidewhatismeantbyanarrowoftimeforentangled“multipartite”systems,andhavesuggestedwaystotesttheseideasusingsystemscomposedofasmallnumberofqubits,wheretimemightbe

seen tobegoingbackwards, in thesenseofdecreasingentropy.Goingbeyondthose simple experiments into an area of special interest to me with mybackgroundincosmology,theyhavespeculatedthatintheearly,denseUniversetheextremeconditionsmighthave“allow[ed]anyrandomphysicalinteractionsto exploit the correlations present, producing a gradual disappearance of thethermodynamicarrowthecloserwegettotheinitialstateoftheUniverse.”1 Inotherwords,therewasnotimeintheBigBang!But the most important work that Terry is involved with—and the most

relevant to this book—concerns the possibility that Einstein and Bohm wereright,andthatthereisanunderlying“reality”whichisdescribedimperfectlybyquantum mechanics. “I’m a fairly conservative physicist,” he says. “In thecommunityIworkin,therearealotofpeoplewhobelieveinthingslikeManyWorlds, but I’mnot prepared to entertain that until I am sure there’s no otheroption.”HealsosharesSchrödinger’sdisdainfortheCopenhagenInterpretation,evenifhewasn’tinfluencedbyhisgrandfatherinreachingthisposition.Askedif he regards himself as interested in theory for theory’s sake, or rather inpractical applications like quantum computing, he replies: “Mainly, theory fortheory’ssake;butit’simportanttoappreciatethatquantummechanicsisn’tjustsomeabstractmathematicaltheory,butdoeshaveabearingonreality.Quantummechanics is about reality, it isn’t about consciousness, or observers, orwhatever.IthinkEinsteinhadagoodpoint—quantummechanicsisincomplete.I’msurethere’ssomethingdeeper.”Thebasicquestioniswhetherthereisaone-to-onemappingbetweenstatesof

reality and quantum states—something Einstein discussed in correspondencewithSchrödinger.Inotherwords,isitpossiblefortwo(ormore)quantumstatestobeassociatedwiththesamesinglestateofreality—or,conversely,fortwoormore states of reality to be described by the same quantum state? “Maybequantum mechanics doesn’t capture everything that’s really going on,” saysTerry:IfIknowthestateofreality,isitpossibleformetoinferwhatthequantumstateis?Ifit’snot,thenmanydifferentelementsofrealitycanbeassociatedwith one quantum state. Moreover, the same element of reality can beassociatedwithtwoquantumstates.Soyoucanhaveadistributionofrealityelements corresponding to one quantum state, and a distribution of realityelementscorrespondingtoanotherquantumstate,andthe twodistributionsmayoverlap,sothatsomeoftheelementsofrealitycanbeassociatedwithboththequantumstates.Forthoserealityelementsyoucan’tbesurewhich

quantumstateapplies.Theoverlappointsareambiguousinsomesense—thedescriptionofrealityisambiguous.For a long time, it proved impossible to find amathematical description of

quantum mechanics that allowed this kind of overlapping. In a classicdemonstration of how science sometimes develops, Terry spent a long timetrying toprove thatsuchoverlapping is impossible,andindoingsoeventuallyfoundanexamplewhichworked:Thatexamplehadonepathologicalfeature.Ithasafundamentalkindofnon-separability.Evenifyouhavetwosystemsthathaveneverinteracted,itisn’tenoughtoknoweverythingaboutsystemAandeverythingaboutsystemBseparately in order to predict how theywill behave in future. Theories inwhichthedistributionsoverlaphaveafundamentalnon-separabilitytothem.It’sentanglement,butnotintheusualsense.Terryisstilltryingtocometogripswiththeconsequencesofthisdiscovery—

at the moment it’s just a mathematical proof. But it seems to rule out wholeclassesofhiddenvariablestheories.This is just one example of the way in which the foundations of quantum

mechanics still—or perhaps I should say, once again—attract some of thebrightestmindsinscience.There’sayoungergenerationinspiredbytheideasofquantum information theory. “I’m about the oldest of them,” says Terry.“They’re young guys, very enthusiastic, free from the old wrangling aboutinterpretationsandsuchlike,andwhattheydohaspracticalapplications.Alotofprogressisbeingmade,butyoudon’talwayshearaboutit.It’sanalivefield.”Whatbetternoteonwhichtoend?Schrödingeralwayswantedason,andsaw

thecontinuityofthegeneticlineasakindofimmortality;hewouldsurelyhavebeendelightedtoknowabouthisgrandson,andabouthisworkatthefrontiersofquantummechanics.

Notes

1PhysicalReviewE,Vol.81(2010),p.061130.

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Pauli, Wolfgang (ed.),Niels Bohr and the Development of Physics (London:Pergamon,1955)Pauling,Linus,andPeterPauling,Chemistry(SanFrancisco:Freeman,1975)Planck,Max,ScientificAutobiographyandOtherPapers, trans.FrankGaynor(London:Williams&Norgate,1950)Price,W.C.,S.S.ChissikandT.Ravensdale(eds),WaveMechanics:TheFirstFiftyYears(London:Butterworth,1973)Rae, Alastair,Quantum Physics: Illusion or Reality? (Cambridge: CambridgeUniversityPress,1986)Santesson, Carl Gustaf (ed.), Les Prix Nobel en 1933 (Stockholm: Norstedt,1934); see alsohttp://nobelprize.org/nobel_prizes/physics/laureates/1933/schrodinger-speech.htmlSchrödinger,Erwin,FourLecturesonWaveMechanics(London:Blackie,1928)Schrödinger, Erwin,Collected Papers on Wave Mechanics (London: Blackie,1928)Schrödinger, Erwin, Science and the Human Temperament (London: Allen &Unwin,1935)Schrödinger, Erwin,What Is Life? (Cambridge: Cambridge University Press,1944)Schrödinger, Erwin, Statistical Thermodynamics (Cambridge: CambridgeUniversityPress,1946)Schrödinger, Erwin, Space–Time Structure (Cambridge: Cambridge UniversityPress,1950)Schrödinger,Erwin,ScienceandHumanism:Physics inourTime (Cambridge:CambridgeUniversityPress,1951)Schrödinger,Erwin,NatureandtheGreeks (Cambridge:CambridgeUniversityPress,1954)Schrödinger, Erwin,Expanding Universes (Cambridge: Cambridge UniversityPress,1956)Schrödinger,Erwin,Science,TheoryandMan(NewYork:Dover,1957)Schrödinger,Erwin,MindandMatter(Cambridge:CambridgeUniversityPress,1959)

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IndexactionatadistanceAharonov,YakirAigentler,HenriettevonAlpbachAmericanPhilosophicalSocietyAnderson,CarlAnnalenderPhysikAnnalesdephysiqueanti-particlesArosaArzberger,HansArzberger,Rhoda(néeBauer,aunt)Aspect,Alainatoms: Bohr model; Boltzmann’s work; concept; Copenhagen Interpretation;decoherence; Einstein’s work; entanglement experiments; “green pamphlet”;Mach’sview;Maxwell’swork;nuclearmodel;Planck’swork;Poincaré’swork;quantum chemistry; quantum computing; quantum physics; quantum spin ofelectron; quantum teleportation experiments;Rutherford’swork; Schrödinger’swork;structureAustria:Anschluss (1938); army;FirstWorldWar and aftermath; InternationalAtomic Energy Agency representation; Nazism; religion; Schrödinger’s flightfrom;Schrödinger’sreturnto;SecondWorldWaraftermathAustria-HungaryAustrianEmpireAustrianPhysicalSocietyBaird,JohnLogieBallot,ChristophBuysBamberger,Emily(Minnie,néeBauer,aunt)Bamberger,Helga(cousin)Bamberger,MaxBär,Richard

Bauer,Alexander(grandfather)Bauer,Alexander(great-grandfather)Bauer,Emily(Minnie,aunt),seeBambergerBauer,Emily(Minnie,néeRussell,grandmother)Bauer,Friedrich(Fritz)Bauer,Georgie,seeSchrödingerBauer,Johanna(Hansi),seeBohmBauer,Josepha(néeWittmann-Denglass,great-grandmother)Bauer,Rhoda(aunt),seeArzbergerBBCBecquerel,HenriBell,JohnBell’sinequalityBennett,CharlesBerlin: Academy of Sciences; Kaiser Wilhelm Institute for Chemistry;Schrödinger’s departure; Schrödinger’s professorship; Schrödinger’s work;UniversityofBernstein,JeremyBertel,Annemarie(Anny),seeSchrödingerBesso,Michelebirds,visionBitbol,MichelBlackett,PatrickBlair,LindaBloch,FelixBohm,DavidBohm,FranzBohm,Johanna(Hansi,néeBauer):escapefromAustriatoLondon;escapefromGermany to London; marriage; memories of Schrödinger; pregnancy;relationshipwithSchrödinger;inViennaBohr, Niels: on collapse of wave function; on complementarity; CopenhagenInstitute; Copenhagen Interpretation; Einstein’s views of his work; Festival;honours; influence; “Light andLife” lecture;model of the atom;Nobel Prize;quantization rules; relationship with Schrödinger; Schrödinger’s views of hiswork;workwithHeisenberg

Boltzmann, Ludwig: background; career; depression; education; on entropy;influence on Schrödinger; on international nature of physics; marriage;relationshipwithMach;research;statisticalapproach;Stefan–BoltzmannLawofblackbodyradiation;suicide;workonatoms;workonthermodynamicsBorn, Max: background and education; in Cambridge; career; on chance andprobability;onCopenhagenschool;onDirac’swork;Edinburghprofessorship;in Göttingen; Heisenberg’s studies; in Italy; matrix mechanics; NaturalPhilosophyofCauseandChance;Nobelcontroversy;NobelPrize;onquantummechanics; quantum revolution; relationship with Schrödinger; retirement;sacked under Nazis; Schrödinger’s response to his work; statistics; on vonNeumann’swork;workonwavefunctionBose,SatyendraNathBose–EinsteinstatisticsbosonsBragg,LawrenceBragg,WilliamBraunizer,Andreas(grandson)Braunizer,ArnulfBraunizer,Ruth(néeMarch,daughter): inBelgium;birth;birthofson;careofArthur; in Dublin; in Graz; half-sisters; in Innsbruck; marriage; in Oxford;pregnancy; relationship with Anny; relationship with father; relationship withmotherBrecht,BertoltBreslauBristolUniversityBrown,RobertBrowne,MonsignorPaddyBrownianmotionBunsen,RobertCahill&CompanyCalifornia:InstituteofTechnology;UniversityofCambridge:Bornin;CavendishLaboratory;Heisenberg’slectures;Maxwellat;Newtonat;PhilosophicalSociety;Schrödinger’svisits;TarnerLecturesCambridgeUniversityPress(CUP)“Can Quantum Mechanical Description of Physical Reality Be Considered

Complete?”(EPRpaper)CERNCharles,EmperorChemicalandEngineeringNewsChemical–PhysicalSocietyChicagochromosomesClauser,JohnClausius,RudolfcloudchamberCockcroft,JohnColdWarcolourvisionColumbiaUniversityComoconference(1927)complementarityCompton,ArthurComptoneffectCondon,EdwardCongressofVienna(1913)Copenhagen,NielsBohrInstituteCopenhagenInterpretation;author’sview;Bell’sview;Bohm’sview;Bornon;consensus view; Einstein’s view; origins; package; predictions; presentation;probabilityin;Schrödinger’sviewCosmicCode,The(Pagels)cosmicrayscosmologyCramer,JohnCrick,FranciscryptographyCurie,MarieandPierreCzernowitzD-WaveSystemsDarwin,Charles

Darwin,Charles(grandsonofabove)Davies,PaulDavy,Humphryde Broglie, Louis: background and education; Einstein’s view of his work;influence;pilotwavemodel;SolvayCongress;thesisdeBroglie,MauriceDemagnete(Gilbert)Demotucorporumingyrum(Newton)de Valera, Éamon (“Dev”): background and career; Dublin Institute forAdvanced Studies; invitation to Schrödinger; Schrödinger’s departure;Schrödinger’slecturesdeValera,Sinéad(néeFlanagan)Debye,PeterdecoherenceDelbrück,MaxDescartes,RenéDeutsch,DavidDewar,KatherineMaryDieks,DennisdiffusionequationDirac,Paul:appearanceandcharacter;inCambridge;DiracEquation;Directionsin Physics; Dublin colloquium; education; Fermi–Dirac statistics; influence;Nobel Prize; Solvay Congress; transformation theory; view of interpretation;workonquantummechanicsDiracEquationDirectionsinPhysics(Dirac)DNADollfuss,EngelbertDoppler,JohannChristianDopplereffectDora(cousin)doubleslitexperimentDublin: Austrian community; Institute for Advanced Studies (DIAS);Schrödinger in; Schrödinger “family life” in; Schrödinger’s arrival;Schrödinger’sdeparture;TrinityCollege(TCD);UniversityCollege

Eckart,CarlEddington,ArthurEdinburghUniversityEhrenfest,PaulEinstein,Albert:on“actionatadistance”;annusmirabilis;Berlinprofessorship;Bose–Einsteinstatistics;Bose’swork;childhood;CongressofVienna;Cramer’swork; on de Broglie’swork; on double slit experiment; education and career;EPR Paradox; experiences of anti-Semitism; experiences of Nazism; onFeynman’swork;general theoryof relativity; influenceonHeisenberg’swork;influenceonSchrödinger’swork;onMountWilsonexperiment;NobelPrize;atPrinceton;relationshipwithSchrödinger;onSchrödinger;onSchrödinger’scat;SolvayCongress; special theory of relativity; on underlying “reality”; viewofchanceandprobability;viewofCopenhagenInterpretation;workonBrownianmotion;workonlightquanta;workonquantumtheoryofradiationEkert,Arturelectromagneticoscillatorselectromagnetismelectron(s):Bohr’swork;bond;Born’swork; “collapseof thewave function”;Compton’s work; Copenhagen Interpretation; Copenhagen scientists’ work; deBroglie’swork;Dirac’swork;Einstein’swork;energy;entangled;Fermi–Diracstatistics; Feynman’s work; Heisenberg’s work; interaction between; Lenard’swork;measurementofchargeon;Millikan’swork;negative;orbits;pilotwavemodel; quantum teleportation; quantum “transaction”; radiation resistance;Rutherford’s work; Schrödinger’s work; sharing of; Solvay Congress (1927);spin; “spooky action at a distance”; Thomson’s work; trajectory in cloudchamber;waveequation;wavesandparticlesentanglement: decoherence; experimental confirmation of; FTL signalling;macroscopic; quantum computing; quantum cryptography; quantumteleportation;Rudolph’swork;Schrödinger’swork;termentropyEPRParadoxEpstein,PaulETH(EidgenössicheTechnischeHochschule),seeZürichEttinghausen,AndreasEverett,Hughevolution

Exner,FranzFaraday,MichaelFarmelo,Grahamfaster-than-light(FTL)communication(signalling)Fermi,EnricoFermi–DiracstatisticsfermionsFeynman,RichardFirstWorldWarForsterfamilyFowler,RalphFranklin,RosalindFranzFerdinand,ArchdukeFranzJosef,EmperorFraunhofer,JosefvonfreewillFresnel,AugustinFriedman,DennisFriedrichWilhelmIII,KingofPrussiaFrimmel,FranzGalileoGalileigasinsealedboxgases,kinetictheoryGeiger,Hansgenes: changes in; copying process; Delbrück’s work; DNA; Haldane’ssuggestion;molecules;Schrödinger’sworkGhent,UniversityofGibbs,WillardGilbert,WilliamGordon,GeorgeGöttingengravity:Einstein’swork;Newton’swork;Schrödinger’sworkGraz: Boltzmann at; Nazism; Schrödinger’s dismissal; Schrödinger’s lectures;Schrödinger’sprofessorship;Schrödinger’sresearch

“greenpamphlet”Greene,BlathnaidNicolette(Schrödinger’sdaughter)Greene,DavidHabicht,ConradHabsburgfamilyHaldane,J.B.S.Halifax,LordHalley,EdmondHamilton,WilliamHasenöhrl,Friedrich(Fritz)HeidelbergHeisenberg, Werner: concept of half-integer quantum numbers; concept ofquantum uncertainty; Copenhagen Interpretation; education and career;influence;matrixmechanics;NobelPrize;PhysicsandBeyond;relationshipwithSchrödinger; Schrödinger’s view of his work; Solvay Congress; theory ofquantumworld;workonquantumjumpsHeisenberg’sUncertaintyPrincipleHeitler,WalterHeligolandHemingway,ErnestHerbert,NickheredityHertz,HeinrichHess,VictorHibben,JohnhiddenvariablesHindenberg,FieldMarshalHiroshima,nuclearbombingHitler, Adolf: Austrian policy; defeat of France; imprisonment; invasion ofAustria;invasionofSovietUnion;lettertoSchrödinger;risetopowerHooke,RobertHoover,HerbertHumboldt,AlexandervonHuygens,Christiaanhydrogenatom

IBMResearchCenterICI(ImperialChemicalIndustries)imaginarynumbersInSearchoftheMultiverse(Gribbin)InSearchofSchrödinger’sCat(Gribbin)Innitzer,CardinalInnsbruck: March household; meeting of German scientists (1924);professorshipoffer;quantumteleportationexperiments;SchrödingeratinterferencepatternInternationalAtomicEnergyAgencyInwardBound(Pais)IrishTimesItalianPhysicalSocietyIthi,seeJungerJeans,JamesJenaJennings,DavidJews: anti-Semitism; in Austria; Einstein’s career; Hansi’s background;Lindemann’s aid to scientists; Nazism in Austria; Nazism in Germany;Schrödinger’spositionJohnsHopkinsUniversityJordan,PascualJung,CarlJunger,Itha(Ithi)Kavanagh,PatrickKepler,JohannesKhrushchev,NikitakinetictheoryKing’sCollege,LondonKirchhoff,RobertKlein,OskarKlimt,GustavKohlrausch,FritzKolbe,Ella

Krauss,FelicieKrauss,KarlandJohannaLandé,AlfredLangevin,PaulLaplace,Pierre-SimonLargeHadronColliderlasersLaue,Maxvon:career;Schrödinger’svisit;viewofCopenhagenInterpretation;workonX-raycrystallographylawsofmotionLean,LenaLehrbuchderPhysikLeidenLeipzigLemaître,GeorgesLenard,Philipplight: Einstein’s work; faster-than-light communication; momentum; Newton’swork; particle theory; Planck’s work; polarized; quanta, see photons;Schrödinger’swork;spectroscopy;speed;wavetheoryLindemann,FrederickAlexanderListener,TheLockheedMartinLockyer,JosephLondon,FritzLondon:ImperialCollege;King’sCollege;UniversityCollegeLoschmidt,JosefMacEntee,BarbaraMacEntee,MáireMacEntee,Margaret(néeBrowne)MacEntee,SeámusMach,ErnstMcCrea,WilliamMadisonMadrid

magnetismManyWorldsInterpretation(MWI)March, Arthur: death; illness; in Innsbruck; Italian holiday; marriage; Oxfordpost;Princetonquestion;relationshipwithSchrödinger;returntoInnsbruckMarch, Hilde: Arthur’s death; Arthur’s illness; in Belgium; birth of daughter;birth of grandson; in Dublin; education; in Graz; marriage; in Oxford;pregnancy;relationshipwithSchrödinger;returntoInnsbruckMarch,RuthGeorgeErica(Schrödinger’sdaughter),seeBraunizerMark,HermannMarsden,ErnestmatricesmatrixmechanicsMaxwell,JamesClerk:achievements;background;death;educationandcareer;influence; marriage; Maxwell distribution; statistical techniques; theory ofelectromagnetism;TreatiseonElectricityandMagnetism;workonlightMay,SheilaMeitner,LiseMendel,GregorMichelson,AlbertMillikan,RobertAndrewsMinkowski,Hermannmolecules: arrangements of atoms; Bohr’s work; Boltzmann’s work;CopenhagenInterpretation;DNA;formation;genes;Heisenberg’swork;helicalstructure; “of life”; Loschmidt’s work; macroscopic entanglement; Maxwell’swork;quantumcomputing;quantumteleportation;RNA;Schrödinger’sworkmomentum:Bohr’swork;Compton’swork;deBroglie’swork;Einstein’swork;EPR Paradox; Heisenberg’s work; law of conservation of; matrix mechanics;Newton’slaws;Schrödinger’sworkMoore,WalterMorgan,ThomasHuntMorley,EdwardMoscowDeclaration(1943)MountWilsonexperiment(1921)MultiverseMussolini,Benito

mutationMyles,seeO’NolanNagasaki,nuclearbombingNapoleonNationalAcademyofSciences,USNationalUniversityofIrelandNaturalPhilosophyofCauseandChance(Born)NatureNatureoftheChemicalBond,The(Pauling)Naturwissenschaften,DieNernst,WaltherNewYorkNewton,Isaac:educationandcareer;lawsofmotion;lawsofphysics;Opticks;Principia;theoryofgravity;workonlightNobelCommitteeNobel Prize: Blackett (1948); Bohr (1922); Born (1954); Cockcroft (1951);Compton(1927);Crick(1962);Delbrück(1969);Dirac(1933);Einstein(1921);Heisenberg(1932);Hess(1936);Laue(1914);Millikan(1923);Pauling(1954);Planck (1918);Rutherford (1908);Schrödinger (1933);Walton (1951);Watson(1962);Wilson(1927)Nolan,KatenuclearphysicsO’Brien,ConorCruiseO’Nolan,Brian(“Myles”)Opticks(Newton)Ortega,JoséOstwald,WilhelmOxfordPagels,HeinzPais,Abrahamparticlemechanicsparticletheoryparticles: alpha; anti-particles; beta; Bohr’s work; Born’s work; Bose’s work;bosons;CopenhagenInterpretation;Crick’swork;deBroglie’swork;Einstein’swork; entangled; fermions; Heisenberg’s work; Maxwell’s work; momentum;

negatively charged (electrons); Newtonian physics; Newton’s work on light;number in Universe; phase space; photons; positively charged (protons);quantum chemistry; quantum teleportation; quantum transaction; radiationresistance; Schrödinger’s work; Solvay Congress; spin; “spooky action at adistance”; statisticalmechanics; subatomic trajectory in cloud chamber;wavesand;Young’sworkPauli,Wolfgang:career;Dublinvisit;Feynman’sPrincetontalk;onhalf-integerquantum numbers; Heisenberg’s letters; on matrix mechanics and wavemechanics;onmeasurementofatom;SolvayCongressPauling,LinusphasespacePhilosophicalMagazinephotons: Aspect’s experiments; Bell’s work; Bose–Einstein statistics; Bose’swork; Clauser’s experiment; clones of; Compton’s work; Einstein’s work;entangled; green pamphlet on; light quanta; momentum; Planck’s work;polarization; quantum computing; quantum cryptography; quantumteleportation;Schrödinger’swork;SolvayCongress(1927);termphotosynthesisPhysicaPhysicalReviewPhysicalReviewLettersPhysicsPhysicsandBeyond(Heisenberg)PhysicsInstitutePhysicsWorldpilotwavemodelPisaPlanck, Max: career; discovery of “energy elements” (quanta); honours;influence; Nobel Prize; relationship with Schrödinger; Solvay Congress;successor at Berlin; work on black body radiation; work on electromagneticradiationPlanck’sConstantPodolsky,BorisPoincaré,HenriPontificalAcademyofSciences

positronPrinceton: Bohm’s dismissal; Einstein Archive; Einstein at; Feynman at;InstituteofAdvancedStudy;Schrödinger’slecturesPrincipia(Newton)probabilities: Born’s work; Copenhagen Interpretation; de Broglie’s work;Einstein’s work; Heisenberg’s work; quantum world; Schrödinger’s work;statisticalrulesprobabilitywaveProceedingsoftheAmericanPhilosophicalSocietyProceedingsoftheCambridgePhilosophicalSocietyProceedingsoftheRoyalIrishAcademyProceedingsoftheRoyalSocietyproteinsPrussianAcademyquanta: Bohr’s work; Einstein’s work; light, see photons; Millikan’sexperiments;Planck’senergyelementsquantumchemistryquantumcomputersquantumcryptographyquantumentanglement,seeentanglementquantumjumpsquantummechanics:Aspect’sexperiments;Bell’swork;Bohm’swork;BornandJordan’swork;CopenhagenInterpretation;Cramer’swork;development;Dirac’swork; Eddington’s work; Einstein’s work; Heisenberg’s work; Innsbruckmeeting (1924); interpretations of; Many Worlds Interpretation; and reality;Schrödinger’s cat; Schrödinger’swork; SolvayCongress (1927); superpositionofstates;term;transactionalinterpretation;transformationtheoryquantumnumbersquantum physics: absurdity of; accuracy of; archives; Bohr’s work; “centralmystery”;chemistry;chessboardanalogy;deBroglie’swork;developmentof;Einstein’s work; first version; Heisenberg’s work; lasers; and reality;Schrödinger’swork;secondquantumrevolutionquantumrealityquantumrevolution:first;secondquantumspin,seespin

quantumstatesquantumstatisticsquantumteleportationquantumtheory:birthof;Bohr’swork;Clauser’sexperiments;cosmologyand;education in;Einstein’swork; founding fathers;Heisenberg’swork;Rudolph’swork;Schrödinger’swork;statisticalapproachandQuantumTheory(Bohm)QuantumTheoryandMeasurement(ed.WheelerandZurek)quantumuncertaintyradiation:alphaandbeta;background;behaviourof;blackbody;Bose’swork;cavity; Doppler effect; Einstein’s work; Feynman’s work; gamma; Planck’swork; resistance; Rutherford’s work; Thomson’s work; ultraviolet; Wheeler–FeynmantheoryradiowavesradioactivityRathenau,WaltherRatnowsky,SimonRay,LucieRayleigh,LordRayleigh–JeansLawreality: Bell’s work; Bohm’s work; Bohr’s view; Copenhagen Interpretation;Einstein’s view; EPR Paradox; Heisenberg’s view; local; many worlds; ofmeasurements; quantum physics and; Rudolph’s work; Schrödinger’s view;VedanticvisionredshiftReichelt,Hansrelativistichydrogenequationrelativity:generaltheory;Schrödinger’swork;specialtheory;theoryRella,LotteRella,TonioReviewsofModernPhysicsRibbentrop,JoachimvonRNARosen,NathanRoyalIrishAcademy(RIA)

RoyalSocietyRudolph,Terry(Schrödinger’sgrandson)Russell,Ann(néeForster,great-grandmother)Russell,BertrandRussell,Emily(Minnie,grandmother),seeBauerRussell,LindaMaryTherese(daughter)Russell,William(grandfather)Russell,William(great-grandfather)Rutherford,ErnestSalpeter,JakobSalten,FelixSantander“scattering”experimentsScherrer,PaulSchiele,EgonSchopenhauer,ArthurSchrödinger, Anny (née Bertel, wife): in Arosa; depression; in Dublin; earlyrelationship with Schrödinger; employment; engagement; flight from Nazis;friendships; health; holidays in Ireland; holidays in Italy; holidays in Tyrol;husband’s death; Irish citizenship; London flat; marriage; mother in Vienna;mother-in-law’s illnessanddeath; inOxford;postwar travels; relationshipwithHilde; relationshipwithRuth; relationshipwithWeyl; return toVienna; sociallifeinZürich;inSpain;suicideattempt;UStripSchrödinger,Erwin: family background; birth; childhood; education;militarytraining; assistant to Exner; research; Privatdozent appointment; Congress ofVienna (1913); first lecture course; war service; first papers (1914); papers(1917); engagement; father’s death; Jena assistant professorship; marriage;papers (1920); Stuttgart associate professorship; mother’s death; Breslauprofessorship;Zürichprofessorship;TBandconvalescence;inaugurallectureatZürich; papers (1922); papers (1922–26); Solvay Congress (1924); life inZürich; Innsbruck meeting (1924); Mount Wilson experiment controversy;MeineWeltansicht (My View of theWorld); work on quantum statistics;waveequation; wave mechanics; Zürich colloquium (1925); Zürich colloquium(1926); papers on wavemechanics (1926); relationship with Ithi; response toHeisenberg’smatrixmechanics;discussionswithBohrandHeisenberg;responseto Heisenberg’s Uncertainty Principle; US tour (1927); Berlin professorship

question; SolvayCongress (1927);Berlin professorship; PrussianAcademy ofSciences;papers(1930,1931);paper“OntheReversalofNaturalLaws”(1931);relationshipwithHildeMarch;decisiontoleaveGermany;Oxfordappointment;NobelPrize(1933);Princetonlectures;familylifeinOxford;birthofdaughterRuth; lectures in Spain; resignation of Berlin professorship; “cat in the boxthought experiment”; Edinburgh professorship question; Graz professorship;familylifeinGraz;interestincosmology;letterrecantingoppositiontoNazism;dismissalfromViennesepost;dismissalfromGraz;flightfromNazis;arrivalinOxford; Dublin offer; Ghent visiting professorship; Ghent honorary degree;arrival inDublin;DublinInstituteforAdvancedStudies;familylife inDublin;DIASinternationalcolloquium;searchforunifiedfieldtheory;birthofdaughterBlathnaid Nicolette; birth of daughter Linda Mary Therese; postwar travels;wife’ssuicideattempt;healthproblems;FellowofRoyalSociety;at InnsbruckUniversity;workoninterpretationofquantummechanics;WhatIsLife?;returnto Vienna; inaugural professorial lecture; daughter Ruth’s marriage; life inVienna; birth of grandson; last lecture; retirement; ill health; death; grave;scientificlegacyFAMILY:children;father;grandchildren;mother;wifeFINANCES: after First World War; army pay; attitude to financial security;difficulties during period of inflation; Edinburgh offer; flight fromNazis; ICIfunding; Irish income; Jena University salary; money kept in Sweden; NobelPrize; in old age; Princeton lecture fees; Vienna University income; ZürichUniversitysalaryHEALTH: APPENDICITIS; bronchitis; cataracts; declining health; phlebitis;pneumonia;sleepingpilloverdose;tuberculosisHONOURS: Berlin professor emeritus; Fellow of Royal Society; Ghenthonorarydegree;NobelPrize;PontificalAcademyofSciences;“PourlaMérité”award; Prussian Academy of Science; TCD honorary doctorate; torchlightprocession;ViennaUniversityprofessoremeritusLECTURESANDTALKS:BBCtalks(1949,1950);“TheCrisisoftheAtomicConcept”; “Elementary Wave Mechanics”; “Equality and Relativity ofFreedom”; “Expanding Universes”; “The Fundamental Idea of WaveMechanics”; “General Relativity”; “Interference Phenomena of X-rays”; lastlecture; “Nature and theGreeks”; on quantummechanics; Spanish tour; “TheSpirit of Science”; Tarner Lectures; US tour; on wave mechanics; “What IsLife?”;“WhatIsaPhysicalLaw?”LOVELIFE:adolescentcrushonLotte;Anny;diaryentries;EllaKolbe;Felicie

Krauss;HansiBohm;HildeMarch; importance tohis scientific creativity; IthiJunger; “Kate Nolan”; Lucie Ray; notebook record of lovers; Sheila May;unknowngirlfriendfromViennaPERSON: APPEARANCE; interest in heredity; languages; philosophicalstudies;politicalviews;religion;reputation;theatre-goingWRITINGS: “Are There Quantum Jumps?”; The Interpretation of QuantumMechanics (ed. Bitbol); letter to Synge on quantum mechanics; MeineWeltansicht (MyViewof theWorld);MindandMatter; “On theConductionofElectricityontheSurfaceofInsulatorsinMoistAir”;“OnDeterminismandFreeWill”; “On the Reversal of Natural Laws” paper (1931); papers (1914–15);papers (1917); papers (1920); papers (1922); papers (1922–6); papers (1926);papers (1930,1931);paper (1939);poetry; “ThePresentSituation inQuantumMechanics”; Space–Time Structure; Statistical Thermodynamics; “AnUndulatory Theory of theMechanics of Atoms andMolecules”; “The VisualSensations”;WhatIsLife?;“WhatIsReal?”Schrödinger, Georgine (Georgie, née Bauer, mother): birth; death; familybackground;funeral;health;holidayinEngland;homeinVienna;marriageSchrödinger,Josef(grandfather)Schrödinger,Maria(grandmother)Schrödinger,Marie(aunt)Schrödinger,Rudolf (father):birth;career;death; familybackground; finances;health;influenceonson;lifeinVienna;marriageSchrödinger’sKittens(Gribbin)Schrödinger’sPhilosophyofQuantumMechanics(Bitbol)Schulhof,AlfredSchuschnigg,KurtScienceScientificAmericanSoddy,FrederickSolvay,ErnestSolvayCongress:(1924);(1927);(1933);(1948)Sommerfeld,ArnoldSpace–Time–Matter(Weyl)spectroscopyspin

“spookyactionatadistance,”seeactionatadistanceStalin,JosephStanfordLinearAcceleratorCenter(SLAC)statistical approach: Bell’s work; Boltzmann’s work; Born’s work; Bose–Einstein statistics; Copenhagen Interpretation; Einstein’s work; Fermi–Diracstatistics; Heisenberg’s work; Maxwell’s work; Planck’s work; quantumstatistics;Schrödinger’sworkstatisticalmechanicsStefan,JosefStefan–BoltzmannLawStuttgart“substitution”superpositionSynge,JohnTarnerLecturesteleportationthermodynamics: Boltzmann’s work; Loschmidt’s work; Maxwell’s work;Planck’s work; Rudolph’s work; Schrödinger’s work; second law; statistical;Stefan’sworkThirring,HansThomson,J.J.time: absolute; “arrow of”; Cramer’s work; Einstein’s work; hidden variablestheory; Newton’s view; reversibility; Schrödinger’s work; statisticalinterpretationofTimofeev-Ressovsky,NikolaitransactionalinterpretationtransformationtheoryTreatiseonElectricityandMagnetism(Maxwell)Trimmer,JohnUKAtomicEnergyResearchEstablishmentUllmann,ElisabethultravioletcatastropheunifiedfieldtheoryVedantaVedral,Vlatko

Vernam,GilbertVernamcipherVienna: Allied occupation; art; blockade (1918–19); climate; Congress of(1913); history; Hitler’s entry; Nazism; physics; quantum cryptography;Schrödinger Archive; Schrödinger’s childhood; Schrödinger’s education;Schrödinger’sretirement;Schrödinger’sreturnto;sociallife;theatreVienna,University of:Boltzmann’swork;Doppler’swork;Loschmidt’swork;PhysicsInstitute;Rudolph’scareer;Schrödinger’scareer;Schrödinger’sstudies;Stefan’sworkVolta,AlessandrovonNeumann,JohnWalton,ErnestWashingtonconference(1946)Watson,Jameswave equation: classical mechanics; control of wave function; CopenhagenInterpretation;Maxwell’s work; “probability wave”; Schrödinger’s work; spinissue;timeand;useofwave function: Born’s work; collapse of the; control of; CopenhagenInterpretation; de Broglie’s interpretation; entangled; Schrödinger’s work;superpositionof;timeandwave mechanics: Bohm’s work; de Broglie’s work; matrix mechanics and;quantummechanics;Schrödinger’slectures;Schrödinger’swork;statusofwavelengthswaves: “advanced” and “retarded”; amplitude; de Broglie’s work;electromagnetic; Huygens’ work; imaginary numbers; light; Maxwell’s work;particles and; “phase space”; pilot wave model; Planck’s work; probability;radio; Schrödinger’s work; Sommerfeld’s work; time and; wave packet;Wollaston’swork;Young’sworkWeill,KurtWeinberg,SteveWeyl,HellaWeyl,Hermann(Peter)WhatMadPursuit(Crick)Wheeler,JohnWheeler–Feynmantheoryofradiationresistance

Wien,WilhelmWien’sLawWilson,CharlesWisconsin,UniversityofWisdom,JohnWittgenstein,LudwigWittmann-Denglass,AntonWolfke,MieczyslawWollaston,WilliamWooters,WilliamWren,ChristopherX-raycrystallographyX-raysYoung,ThomasZeilinger,AntonZeitschriftfürPhysikZimmer,KarlZurek,WojciechZürich:ETH (EidgenössicheTechnischeHochschule); history; Schrödinger in;Universityof

JohnGribbingainedaPhDfromtheInstituteofAstronomyinCambridge(thenunder the leadershipofFredHoyle)beforeworkingas a science journalist forNature and later New Scientist. He is the author of a number of bestsellingpopular sciencebooks, including In Search of Schrödinger’sCat, In Search ofthe Multiverse, Science: A History, and The Universe: A Biography. He is aVisitingFellowattheUniversityofSussexandin2000waselectedaFellowoftheRoyalSocietyofLiterature.