TheHistoricalandPhysicalFoundations ofQuantumMechanics
RobertGolub NorthCarolinaStateUniversity,Raleigh,NC,USA
StevenK.Lamoreaux YaleUniversity,NewHaven,CT,USA
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Preface
Thereisanenormousnumberofbooksandotherwritingsconcernedwithexplaining andinterpretingquantummechanics.Standardtextstendtoconcentrateonmethodologyandapplicationstospecificproblems,whilediscussionsofinterpretationandthe historicaldevelopmenttendtocontainaminimumofmathematics.Theideabehind thisbookisthattogainarealunderstandingofthesubject,someacquaintancewith thehistoricaldevelopmentisessential;afterall,thathistoryisthenarrativeofhow humanitylearnedquantummechanics.Theideaswerenotfoundwrittenontablets onafarmine.g.,NewYorkState,butwereslowlyandpainstakinglydevelopedby peoplejustlikeus.Wealsoprovideaccompanyingdiscussionsforthevariousinterpretationsthathavebeensuggested,providingsufficientmathematicalillustrationsthat highlighttherespectivefeaturesanddifferences.
Acknowledgements
Wewouldliketothankourfriendsandfamilyfortheirunderstandingandsupportas ourattentionwasdrawnawaytothewritingofthisbook.
R.G.wouldliketothankhiswifeEkaterinaKorobkina,E.DavidDavisforcontributionstoChapter21andhelpwiththebook,andRolandG¨ahler.Inaddition,he thanksProf.ChuengJifordiscussionsattheearlystagesofthebook.
S.K.L.thankshiswife,Melissa,anddaughter,Zoe,hisFridayOwlShopcigar friendsCarlJ.FranoandJamesSurprenant,andDr.SidneyB.Cahnfortheirunfailingandunflappablemoralsupport.HealsothanksMr.EdwardS.McCatty(B.A. (Amherst),M.Div.(Yale),M.A.Lit.(UCL))foreditorialcommentsonChapter1and forprovidinginspirationthroughouttheproject.
WeespeciallythankDr.YuliaGurevich,whoseexpertediting,togetherwithher vastknowledgeofphysics,clarifiedandstrengthenedmanypartsofthisbook.Her artistictalentisevidentinmanyofthefigures.
YaleUniversityprovidedsupportforthepreparationandeditingofthemanuscript. NCSUalsoprovidedsupportwithasabbaticalforR.G.
5Furtherstepstoquantummechanics:LouisdeBroglieand
Contents
6Theinventionofquantummechanics—matrixmechanics 87 6.1Introduction 87 6.2Heisenbergrediscoversmatrices 88
6.3ThefoundingofmatrixmechanicsbyBorn,Jordan, andHeisenberg 90 6.4Furtherdevelopments 101 6.5Conclusion
7Schr¨odingerandthedevelopmentofwavemechanics
7.1Ideasleadingtowavemechanics
7.2ThedevelopmentofwavemechanicsaspresentedinSchr¨odinger’s publications 111
7.3Firstapplicationsofthewaveequation
7.4Therelationbetweenmatrixandwavemechanics
8FurtherdevelopmentsofwavemechanicsbySchr¨odinger
8.2Perturbationtheory
8.3Thetime-dependentSchr¨odingerequation
9Quantumstatisticsandtheoriginofwavemechanics
9.1Bose-Einsteinstatistics
9.2Fermi-Diracstatistics
10Earlyattemptsatinterpretationofthetheory
10.3Born’sinsightandthelossofdeterminacyinphysics
10.4Heisenberg’suncertaintyprinciple
10.5NielsBohrandcomplementarity:theCopenhageninterpretation ofquantummechanics
10.6Conflictingviewsonquantumjumps 216
10.7ChronologyofBohr–Heisenberg–Schr¨odingerdiscussions 220
11Thefinalsynthesisofquantummechanics:the“transformationtheory”andDiracnotation 221 11.1Introduction 221
11.2Sturm-Liouvilletheory,Hilbertspace,andlinearoperators 224
11.3Dirac’sbra-ketnotation
11.4GeneralfeaturesofthetheoryandDiracnotation
12DiracandJordancommit“sinsquared”:secondquantization andthebeginningofquantumfieldtheory 245
12.1Introduction 245
12.2Dirac’sq-numbers,operators,andthequantummechanicsofDirac, Jordan,andvonNeumann 246
12.3Thebeginningofquantumfieldtheory
12.4Ehrenfest’stheoremandtheclassicallimitofquantummechanics
13The“completionofquantummechanics”—thefifthSolvay ConferenceonPhysics,October1927
13.1Introduction
13.2Thecollapseofthewavefunctionanditsmeaning—themeasurementproblem
13.3Wave-particleduality
13.4EinsteinandBohr:thebattleofthecentury?
14VonNeumann’smathematicalfoundationsofquantum mechanics:redux
14.2VonNeumann’smeasurementtheory
14.3Nohiddenparametersproof
14.4VonNeumannentropy
15EinsteinandSchr¨odingerrenewtheassaultonquantummechanics
16Weimarcultureandquantummechanics
17Furtherdevelopmentoftheinterpretationofquantumtheory
17.5HughEverettIIIandtheworld’ssecondmostimportantPhD thesis(?)
xii Contents
17.7(Spontaneous)Directwavefunctioncollapse 489
17.8Secondquantizationandparticle-waveduality 493
17.9Conclusion 494
PARTIIAPPLICATIONSOFQUANTUMMECHANICS
18Operatortechniquesandthealgebraicsolutionsofproblems 501
18.1Introduction 501
18.2Uncertaintyrelationshipsviaoperatortechniques 502
18.3Pictures 504
18.4Ladderoperators 512
18.5Harmonicoscillator 513
18.6Coherentstates 517
18.7Two-dimensionalharmonicoscillator 537
18.82DharmonicoscillatorsolutiontotheHatom 540
18.9Sumrulesandsummationtechniques 542
18.10Benzenemolecule 559
18.11Angularmomentum:anoperatorapproach 561
18.12Algebraicderivationofthehydrogenspectrum 583
18.13TheWKBapproximation:boundaryconditionsbycomplexanalysis 591
19Spin-1/2andtwo-levelsystems 597
19.1Larmor’stheorem 597
19.2Paulimatrices 605
19.3Vectorrepresentationofspinandspinorrotationsymmetry 606
19.4Theeffectsofnear-resonantoscillatingmagneticfields 610
19.5Effectsoftime-dependent,nonresonantvariations ofthepotential 612
19.6Thedensitymatrix 621
19.7Generalapplicationtotwo-levelsystems:fictitiousspin-1/2 628
20Pathintegralsandscattering 635
20.1Introduction 635
20.2Pathintegrals 635
20.3Anintroductiontoscatteringofnonrelativisticparticles byamany-bodysystem 643
20.4Conclusion 657
21Introductiontoquantumcomputing(withtheassistanceof EdwardD.Davis) 659
21.1Overview 659
21.2Thebasicideas 668
21.3Unitaryoperations 672
21.4Aphysicalmodelofaquantumcomputer 676
21.5Someadditionalalgorithms 679
21.6Factoring—theHolyGrailofquantumcomputing 683
21.7Conclusion 693
Introduction
“Youhavenothingtodobutmentionthequantumtheoryandpeoplewilltakeyourvoicefor thevoiceofscienceandbelieveanythingyousay.”GeorgeBernardShaw,19381
1.1 Overview
AsearchonAmazon.comforbookson“quantumtheory”returnsover10,000hits whilesearchingfor“quantumphysics”returnsover20,000.Thiscorrespondstoone bookadayfor30years.Thesebooksrangefromadvancedmathematicaltreatises tobookswithoutasingleequation,fromdeepphilosophicaldebatesbetweenauthors withdifferentunderstandingsofthesubjecttotextbooksteachingthemethodology andvariousapplications.Inaddition,therearevastnumbersofpapersinhistorical andphilosophicaljournalsconcernedwiththedevelopmentandphilosophicalimplicationsofthetheory.Forthoseinterested,therearealsomanyvolumesofcollected correspondenceandmanyonlinearchivesoforalandwrittenmaterial.2
Whilethereislittledisputeoverthemathematicalapparatusofthetheoryandits applicationtophysicalproblemsthereisawidespectrumofdivergentopinionsabout whatthetheoryistryingtotellusconcerningthenatureofreality.Foralongtime followingWWII,therewaslittleinterestamongphysicistsforsuchquestionsasattentionwasturnedtothefreneticdevelopmentofdifferenttechnologies.However,recent decadeshaveseen,inadditiontoanamazingrangeofapplicationsofthetheory,an ever-increasingattentiontowhatiscalledthe“interpretation”ofquantummechanics. Thereisnowabewilderingforestoftheseinterpretationseachofwhichhasagroupof supportersaswellasopponents.As,tothisdate,noneoftheinterpretationshasbeen abletoconvinceamajorityofworkingphysicists(who,itshouldbesaid,mostlyignore thesediscussions,anattitudethathasbeensummedupas“shutupandcalculate”) ofitscorrectnessornecessity.Itisalmostasifphysicsissplittingintoanumberof cultsunitingsupportersandcriticsinanever-endingembrace.
Itisstrikingthatalloftheproposedinterpretationsareconcernedwiththeoriginal formofthetheory,theSchr¨odingertheorysupplementedbytheDiractransformation theory,seeminglyignoringthemostadvancedformofthetheory,i.e.,thatinvolvingthe
1QuotedbySimon,D.R.,OnthePowerofQuantumComputation,35thAnnualSymposiumon theFoundationsofComputerScience,(1994)SantaFe,NMandatwww.greatest-quotations.com.
2Seee.g.,AmericanPhilosophicalSocietyLibrary:SourcesfortheHistoryofQuantumPhysics, 1898-1950,https://search.amphilsoc.org/collections/view?docId=ead/Mss.530.1.Ar2-ead.xml.
TheHistoricalandPhysicalFoundationsofQuantumMechanics.RobertGolubandStevenK.Lamoreaux,OxfordUniversityPress. c ⃝ RobertGolubandStevenK.Lamoreaux(2023).DOI:10.1093/oso/9780198822189.003.0001
quantizationofthenon-relativisticSchr¨odingerequation,introducedbyJordan,with thesupportofPauliandWigneramongothers,thathecalled“secondquantization.” Aswewillsee,thisformulationsolvesseveralproblemsassociatedwiththeoriginal formofthetheoryandalmostsuppliesitsowninterpretation,asdoesrelativistic quantumfieldtheorywherequestionsofinterpretation,essentiallywhetherparticles orwavesareprior,aremuchlessprominent.3 Thisconcentrationonanotfully maturedversionofthetheorymightbeconsideredbysomeasanindicationthatthe interpretationdiscussioniscaughtinatime-warp,devotingitsattentiontoatheory thatcouldbeviewedasalreadysuperseded.
Thepurposeofthisbookistotakeastepbackandattempttoretracethedevelopmentofthetheorybyinvestigatingoriginalsources,theoriginalpublishedpapers andletters,oftheparticipants.Thisisthepathbywhichhumanitylearnedquantum mechanicsandfollowingitmighthopefullyleadtoanimprovedunderstanding.Of course,theattemptbyphysiciststhemselvestoapproachthehistoryoftheirsubject isanexercisefraughtwithdifficulties,ashasbeenrecognizedbyseveralpractitioners. Forexample,SilvanSchweber,atheoreticalphysicistturnedhistorianofscience,recognizes4 that“thehistoryofsciencecannotescapesomeformofwhiggism.Thedata issorichthatsomeselectionmustbemade.”Awhighistoryofscienceistheview ofthescientificwinnerswhowriteasiftheirtriumphwasaninevitableresultofthe correctnessoftheirideas.Whighistoryofsciencedisplaysthehistoricaldevelopment asproceedingfromapastruledbyignorancetoagloriouspresentwithouttaking accountoftheactualstateofknowledgeinthepast.
WecanseetheresultoftryingtoovercomethelimitationmentionedbySchweberandincludeallrelevantpublicationsalongwithbiographicalinformationonthe manyactorsandexcerptsfromcorrespondence,intheheroicworkmadebyMehra andRechenberg,whohavecompletedaninevolumetreatise,“TheHistoricalDevelopmentofQuantumMechanics,”publishedbetween1982and2001.5 Thishasbeen anenormoushelpinwritingthepresentvolume
S.A.Goudsmit,thecodiscovererofelectronspin,6 wasskepticalastotheutility ofthehistoryofscience:7 “Manyhistorianshavewrittenveryprettystoriesabout howadiscoveryshouldhavebeenmade,butitisunfortunatelyveryimprobablethat thedevelopmentwasaslogicalasthesefabricatedstorieswouldindicate.Luckand randomeventsplayamuchlargerrolethanpeoplearereadytoadmit.”Inaddition hecomplainsthat:“They(thehistoriansofphysics)presentthingsasifthewholeof physicswascreatedbyahandfulofgeniuses.Thisiscompletelyunfairtothemany physicistswhoseworkenablesthegreatdiscoveriesofthegeniuses.”
3Weinberg,S. TheQuantumTheoryofFields,Vol.1,Foundations,CUP,(1995)
4Schweber,S.S., QEDandtheMenWhoMadeIt:Dyson,Feynman,SchwingerandTomonaga, Princeton,1994
5Mehra,J.andRechenberg,H., TheHistoricalDevelopmentofQuantumMechanicsVolumes 1–6,comprisingninevolumesintotalassomeofthevolumesareprintedintwoparts,SpringerVerlag1982–2001.
6Uhlenbeck,G.F.andGoudsmit,S.,Naturwissenschaften,13,953,(1925)and SpinningElectrons andthestructureofSpectra,Nature,117,264(1926)
7Goudsmit,S.A., TheDiscoveryoftheElectronSpin (inGerman),Phys.Blaetter,10,4345(1965)
Hethengoesontostate“Historiansareoftenunjustwithrespecttotheexperimentalphysicists.Eventhoughtheevolutionofideasisveryimportantforhistory,we shouldnotneglectthegeniusesamongtheexperimentalphysicistswhosediscoveries andresultsareabsolutelynecessaryfornewideasandtheirverification,”andfurther makesthepointthat“Publishedarticlesarenotveryreliableashistoricalsources.In agoodarticle,theauthortriestoconvincethereadersoheoftenchoosesadifferent trainofthoughtasthatbywhichhecameupontheidea.”Thisissomethingthatcan beattestedtobyanyexperiencedresearcher.
StevenWeinberg(op.cit.)explicitlydisdainsthehistoricalapproachtoteaching physicaltheories,preferringalogicaldevelopmentofthetheoryasitispresently understood.This,ofcourse,vitiatestheimportanceofdirectobservationofnatural phenomena,andthefactthatcurrentphysicaltheorieswereatonetimetenuous hypothesesthatrequiredtestingviathescientificmethod.Assuch,abandoningthe historicalapproachappearsasathrowbacktowardScholasticismwithitsbasisin dogmatism.
AlbertEinsteinwasalsoskepticalofahistoricalapproach:
Onlythosewhohavesuccessfullywrestledwithproblematicsituationsoftheirownagecan haveadeepinsightintothosesituations,unlikelaterhistorianswhofinditdifficulttomake abstractionsfromthoseconceptsandviewswhichappeartohisgenerationasestablishedor evenselfevident.8
Whilethereiscertainlyalargedegreeoftruthinallofthisthefactisthatthe originalpublishedpapersareclosertotheoriginalideasthanathird-generationtextbookandcanbeexpectedtoreflectsomethingofthethen-contemporaryzeitgeistas theresultoftheauthor’sstatedwishtopersuadehisreaders.Wealsomakeuseof lettersandcontemporaryaccountswhenappropriate.
Thus,inthisbook,whilebeingawareoftheseissues,wewillattempttotracethe mainlinesofthedevelopmentwiththehopethatthisreturntotherootswillcast somelightonwhataretodayconsideredthedifficultiesofthetheory.
1.2 ThePrehistoryofQuantumMechanics:atomism
Quantummechanicshasitsfundamentalbasisintheatomictheoryofmatter,which hasitsrootsinatomism.Atomismwasoriginallya philosophical theorythatmaterial objectsarediscontinuous,beingconstructedofindivisibledistincttypesofatoms— equivalently,quantizedunitsofmatter,thatserveasbuildingblocks.Atomsarenow understoodtobeoflimitedvariability(chemicalelements,isotopes,periodictable), buteachtypeofatomhasuniqueandfixedproperties,andallatomsofagiventype arenowunderstoodtobeidenticalandindistinguishable.
Theconceptofatomismhasalongcheckeredifnottortuoushistory,onethatis rarelyexpoundeduponinphysicsbooks.Wewillpresentaveryabbreviatedoverview ofthedevelopmentofmodernideas,andthesearefromaveryWesternperspective. Therewaslikelywidespreadcommunicationintheancientworldthatallowedideasto bespread,anditisnotimpossiblethatGreekatomismhaditsoriginwiththeIndian
8Einstein,A.,ReplytocriticismsinSchilpp,P.A.,ed., AlbertEinsteinPhilosopher-Scientist, Vol.II,Harper,1949,1951.
sageandphilosopherAcharyaKanad(Kashyap)whoaround600BCEspeculatedon thelimitofdivisibilityofmatterandproposedparticlesthatcouldnotbedivided further, anu or atoms.Perhapsitstandstoreasonthatanysocietywithamerchant classhasspeculatedonthedegreeofdivisibility(henceminimummarketableunit)of materialbodies;avastbodyofhistoryisneverrecorded,orlost—inthewordsofRoy Batty—liketearsintherain.
Intheteachingofphysics,inthoserareinstanceswherehistoryismentioned,Democritus(ca.450BCE)isoftencreditedwiththeoriginalformulationoftheatomic hypothesis,andthatisit,nothingmore.Thestoryisalmostinfinitelymorecomplicated,andwewillattempttoprovidesomehighlights.Democrituswasastudentof Lucretius(ca.475BCE)withwhomtheatomicideahasitsroots,whichheformulated inresponsetoParmenides’deductionthatrealityisanillusion.9
AccordingtoParmenides,foranobjecttomovefromonelocationtoanother,it wouldneedtobedestroyedatthefirstlocationandrecreatedatthenewlocation. Asthisappearstobeanimpossibility,Parmenidesmadethelogicalleapthatreality isanillusion.Thenotionthatthereisnoreality,thatallthatexistsisillusion,has comeupmanytimessincetheancientGreekphilosophers—Shakespeare’s“Allthe worldisastage,”andmorerecently,thenotionthatwearelivinginacomputer simulationisbeingtakenseriously10 andisanessentialformofIdealism.Thevarious ZenoparadoxeswereputforwardinsupportofParmenides’assertion,toshowthat thephysicaluniverseaswebelieveweareobservingitisindeedanimpossibility.Of course,itiseasytobelieveeverythingisanillusionuntilaseveretoothachestartsona Saturdaynight;realityisofteninconflictwithourbeliefs,expectations,andprejudices, thatareformedintheechochambersofourminds,colleagues,andnowadays,social media(FacebookandTwitter).
Lucretius,followedby,andembellishedby,Democritus,answeredParmenides’ claimbyinventingatoms,andequallyimportant,the void,inwhichatomsmove. Thevoidisnothingness,andtheargumentagainstitsexistencecontinuestodaybecausewearefacedwiththeproblemofinventingadescriptionforsomethingthatdoes notexist,whichisanapparentself-contradiction.Nonetheless,thecompleteatomic picturewaslaidoutbyDemocritus,inwhichobjectsareconstructedofatomsof varyingcharacteristics,andtheseatoms,collectedtogetherasobjects,movetogether freelyinthevoid.Thesearethebasictenetsofthemodernpictureoftheuniverseand matter,perhapscoincidentally,asthiswasaphilosophicaltheory.
Jumpingaheadsome100years,Aristotletookastepbackwardinhisadoption ofEmpedocles’notion(450BCE)thatthematerialworldcomprisesfourelements, earth,wind,fire,water,andfurthersurmisedthatthenaturalstateofmatterwas atrest.(TheGreeknotionofelementsmighthavealsobeenderivedfromtheHindu Veda whichexistedinoralformfrom2millenniaBCEandinwrittenformfrom1 millenniaBCE,inwhichthesamefourelementsplusafifth,theall-importantvoid, arepostulated.)
9AlthoughitistemptingtoascribethediscontinuityofmatterasassumedbyDemocritusas resultingfromalackofunderstandingofmathematicalcontinuity,however,thedevelopmentofthe earlyphilosophicaltheoriesfollowsamorecomplicatedpath.See,forexample,BernardPullman, The AtomintheHistoryofHumanThought (OxfordUniversityPress,2001).
10Bostrom,Nick(2003). AreYouLivinginaComputerSimulation?.PhilosophicalQuarterly 53, (211):243-255.doi:10.1111/1467-9213.00309.
Afifthelement,quintessence,wasintroducedastheelementfromwhichheavenly bodiesareconstructed.Bythemedievalages,anewnotion(aformofMonism)was introducedthateverythingwasaquintessence-likeelement,scrapedtogetherintoa particularform,atwhichpointthequintessenceassumedthepropertiesoftheform, e.g.,apencilsharpener,thekeyboardonwhichIamtyping,etc.Thisnotionwastaken asacentralprincipleortenetbytheCatholicChurch,andprovidesamechanismfor transubstantiation.Thistenetwasimportantenoughthatatomismwasspecifically addressedbytheCouncilofTrent(1545to1563)asanathema(heretical).
Galileoisofcourseknownforthetrialsheenduredconcerninghispromotingthe heliocentricmodelofthesolarsystem.ThemostpuzzlingaspectoftheentireGalileo affairisthathehadbeenwellreceivedbyPopeUrbanVIII,whowasfullyawareof andstudiedGalileo’swritings.TheresultsofGalileo’sfirsttrialin1616werelimited toorderstoceaseholding,teaching,ordefendingheliocentricideas.Uptothistime, GalileohadagoodrelationshipwiththeJesuits,eventhefactioninchargeofimposingchurchdoctrine,whichincludedthecanonsoftheCouncilofTrent;thisfaction wasalsoinchargeofgeneraleducation.Galileo’steachingswereatoddswithAristotleandScholasticism,sothatafactionofJesuits(forwhomAristotelianteachings wereeducationalcanon)becameincreasinglyhostiletowardGalileo;thishostilityonly increasedwiththeminimalresultsofGalileo’sfirsttrial,especiallywhenhedidnot ceasepromotinghisscientificideasandcontinuedtowritebooks.PopeUrbanVIII,to appeasetheseJesuitsinhiseffortstoconsolidatepower,accededtotheirdemandsthat Galileobeagainbroughttotrial,beforetheInquisition,forheresy.Recentdiscoveries intheVaticanrecordsshowthatmorecharges,inadditiontothoseassociatedwith heliocentrictheories,werebeingpreparedtobringupGalileo’sembracingatomism asanadditionalheresy.11 Tofurtherinflamethesituation,Simplicioin Dialogueon theTwoWorldSystems wassuggestedasmodeledonUrbanVIII.In1632,thePope orderedanotherinvestigationagainstGalileo.Thistimehewasprosecutedfollowing thenormalmethodsoftheInquisition,however,Galileowasthenofadvancedage andwasthereforenotsubjecttotortureanddeathforbeingfoundguiltyofheresy, butconsequentlywasplacedunderhousearrestfortherestofhislife.Ayounger man,GiordanoBruno,who30yearsearlier(duringthetenureofPopeClementVIII) embracedheliocentricity,atomism,andmanyotherhereticalscientificandsociologicalnotions,andtaughtthemwithabandon,wasdecreedguiltyofheresyandon17 February1600washungupsidedownnakedbeforebeingburnedatthestake.
OneinterestingandimportantasideisthatGalileo’sandBruno’swritingswere preservedintheVaticanArchives;thisisoneparticularlyastonishingaspectofthe CatholicChurchinthatthewritingsofenemieswereveryoftenpreserved,unlikemost humaninstitutionswherethememoriesofadversariesareerasedasapatheticpanacea againstfuturethreats.TheChurchdidnotinitiateacampaigntocollectupGalileo’s booksandritualisticallydestroythem,incontradistinctionto,forexample,theNazis’ handlingtheworksofenemiesofthestatebyburningbooksinwell-publicizedbonfires, ortheMemoryHoleofOrwell’s1984.Thisisnottosaythatit never happened,but itappearsthepreservationwasageneralmatterofcourse.
11PietroRedondi(RaymondRosenthal,Translator), Galileo-Heretic (PrincetonUniversityPress, 1989).
Theabove,ofcourse,ispresentedwiththecaveatthattheunderstandingofhistoricaleventsisfraughtwithdifficulties;dowehavethecompletepicture?Whatwereall participantsintheeventthinking?Whatwerethefundamentalmotivations,e.g.,consolidationofpower,controllingthemasses,etc.?RegardingGalileo,ArthurKoestler comments:
ButthereexistedapowerfulbodyofmenwhosehostilitytoGalileoneverabated:theAristoteliansattheuniversities.Theinertiaofthehumanmindanditsresistancetoinnovation aremostclearlydemonstratednot,asonemightexpect,bytheignorantmasswhichiseasily swayedonceitsimaginationiscaught—butbyprofessionalswithavestedinterestintradition andinthemonopolyoflearning.Innovationisatwofoldthreattoacademicmediocrities:it endangerstheiroracularauthority,anditevokesthedeeperfearthattheirwhole,laboriously constructedintellectualedificemightcollapse.Theacademicbackwoodsmenhavebeenthe curseofgeniusfromAristarchustoDarwinandFreud;theystretch,asolidandhostilephalanxofpedanticmediocrities,acrossthecenturies.Itwasthisthreat,notBishopDantiscus orPopePaulIIIwhichhadcowedCanonKoppernigkintolifelongsilence.InGalileo’scase, thephalanxresembledmorearearguard—butarearguardstillfirmlyentrenchedinacademic chairsandpreachers’pulpits.
asquotedinPullman,op.cit.,p128.,fromArthurKoestler.12
Onakindernote,asaphilosophicaltheory,Aristotelianismisperfectlyinternally consistent.However,thisdoesnotmeanitrepresentsreality;asBertrandRussell quipped,13
Aphilosophy[ofnature]thatisnotself-consistentcannotbeentirelycorrect,butonethatis self-consistentmaywellbecompletelyfalse.
AccordingtoJeroenvanDongen,“Kuhnhimselfmentionedakindofepiphany hehadexperiencedwhenassistingConantinteachingthehistoryofscience:Reading Aristotle,heshockinglydiscoveredthathisownNewtonianexpectationswereblocking himfromseeingtheconsistencyandintegrityofAristotle’sphysics.Thisexperience puthimonthepath”tohisfamousbookintroducingtheconceptofparadigms.14 Koestler,again,waslesskind,
Aristotelianphysicsisreallyapseudoscience,outofwhichnotasinglediscovery,invention ornewinsighthascomeintwothousandyears;norcoulditevercomeandthatwasits secondprofoundattraction.Itwasastaticsystem,describingastaticworld,inwhichthe naturalstateofthingswastobeatrest,ortocometorestattheplacewherebynaturethey belonged,unlesspushedordragged;andthisschemeofthingswastheidealfurnishingfor thewalled-inuniverse,withitsimmutablyfixedScaleofBeing.
However,thiswasnotAristotle’sfault;toagainquoteBertrandRussell, Inreadinganyimportantphilosopher,butmostofallinreadingAristotle,itisnecessary tostudyhimintwoways:withreferencetohispredecessors,andwithreferencetohis successors.Intheformeraspect,Aristotle’smeritsareenormous;inthelatter,hisdemerits areequallyenormous.Forhisdemerits,however,hissuccessorsaremoreresponsiblethanhe is.HecameattheendofthecreativeperiodinGreekthought,andafterhisdeathitwas twothousandyearsbeforetheworldproducedanyphilosopherwhocouldberegardedas approximatelyhisequal.Towardtheendofthislongperiodhisauthorityhadbecomealmost asunquestionedasthatoftheChurch,andinscience,aswellasinphilosophy,hadbecomea seriousobstacletoprogress.Eversincethebeginningoftheseventeenthcentury,almostevery seriousintellectualadvancehashadtobeginwithanattackonsomeAristoteliandoctrine;
12Koestler,A., TheSleepwalkers:AHistoryofMan’sChangingViewoftheUniverse (London, Arkana,1959);theabovequoteisapparentlyaback-translationfromFrench.
13BertrandRussell, HistoryofWesternPhilosophy (FirstpublishedbyGeorgeAllenandUnwin Ltd,London.1946).
14vanDongen,J. InEurope,PhysicsinPerspective22,3-25(2020).
ThePrehistoryofQuantumMechanics:atomism 9
inlogic,thisisstilltrueatthepresentday.Butitwouldhavebeenatleastasdisastrous ifanyofhispredecessors(exceptperhapsDemocritus)hadacquiredequalauthority.Todo himjustice,wemust,tobeginwith,forgethisexcessiveposthumousfame,andtheequally excessiveposthumouscondemnationtowhichitled.
Andfinally,Crescenzo(asquotedbyPullman 15)states, ForbothPlatoandAristotle,whowereconstantlyinsearchoftheprimecauseandultimate purpose,itisasthoughDemocritushadtoldthemtheplotofacomedywhileskippingthe firstandlastscenes.
WhatGalileobroughtforward,asbegunbyCopernicusandKepler,isthepossibilityoftheuseofmathematicstodescribephysicalsystems,andmotionordynamics, inparticular.Thisapplicabilityandeffectivenessofmathematicsinthisendeavoris thebasisofmodernphysicalsciencesandengineering,anditisnotobviousthatthis shouldbepossible.16 Newton’swork(circa1700)carriedtheapplicationofmathematicstoarevolutionarynewlevel,andwasaharbingeroftheendofAristotelian dominanceinWesternthinking.
Evensomealchemistsatthistimehadmovedonfromthenotionthateverythingis composedofthefourprimordialelements,earth,air,water,heat.Forexample,instead ofcombiningelementstoformgold,theGermanalchemistHenningBrandattempted toextractexistinggoldfromurine;hereasonedthatbecauseurineisnormallygolden, itmustcontaingold,ormightholdthekeytofindingthePhilosopher’sStone.Some timearound1669,heembarkedontheAugeantaskofboilingdown5,700litersof putrefiedhumanurine(thereisnorecordofhowheobtainedthisquantity),andthen subjectingtheresiduetoheatinthepresenceofcarbon,whichreducedphosphates toelementalphosphorus,ataskthatbringstomindMarieandPierreCurie’slater Augeantaskofextractingafractionofagramofradiumfromtonsofpitchblende.
Phosphoruswasthefirstelementtobediscoveredthatwasnotalreadyknownin ancienttimes,andtheappearanceofacontinuousglowmusthavebeenastounding andawe-inspiringtothealchemist.Brand,ofcourseintypicalalchemistfashion,kept hisdiscoverysecretbutendedupsellingtherecipe–andalsotippedoffRobertBoyle (whosoonfiguredouthisownextractionmethod)astothesourceofphosphorus.
ThefinalmajorblowtoAristotelianismcamewiththediscoverythatwatercould becreatedbycombininghydrogenandoxygen,mostnotablyasdescribedbyLavoisier in1789;hesurmisedthatwateris85%oxygenand15%hydrogenbyweight–andis thereforehardlyanelement.Lavoisier’soxygentheoryofcombustionalsobrought downthephlogistontheoryofcombustion,andledtothelawofconservationofmass.
OneofthereasonsforourdelvingintothishistoryisthatScholasticism(education basedonAristotelianprecepts)dominatedmuchofWesternEuropefrombeforethe twelfthcenturythroughtheeighteenthandwellintothenineteenthcenturyinsome regions,andhadaprofoundeffectonthedevelopmentofatomictheoryinphysics, butlesssoonchemistry.Oneofthelasttimesthatsomeoneofnotemademention oftheprimordialelementswasNapoleon,whoquipped,“Godcreatedafifthelement especiallyforPoland–mud,”afterhisarmywasmiredduringthe1806campaigninto
15Pullman, loc.cit.,p.56
16EugeneWigner, TheUnreasonableEffectivenessofMathematicsintheNaturalSciences,CommunicationsinPureandAppliedMathematics, 13,1(1960).
Fig.1.1 TheAlchemistDiscoveringPhosphorus byJosephWrightofDerby(1771,reworked 1795)(PublicDomain).
Poland.17 Bythemid-nineteenthcentury,Aristotelianismwasrelegatedtoajoke,in particular,Melvillein MobyDick describesthestateofthe Pequod,whenherupper deckswereoverloadedduringthesearchforaleakingwhale-oilcaskstoreddeepbelow deck,as,“Top-heavywastheshipasadinnerlessstudentwithallAristotleinhis head.”
Itisnoteworthythatteachingatomismwascontroversialandassociatedwithaprogressiveoutlookformorethanamillennium.Aslateas1624thecourtofKingLouis VIIIofFrancethreatenedtheteachingofatomismwiththedeathpenalty.General
17F.LorainePetre, Napoleon’sCampaigninPoland (SampsonLow,MarstonandCompany:London,1901).p.51.
questionsabouttheinfinitesimalwerefrowneduponwellintothenineteenthcentury(suchnotionswereatoddswithAristotelianismandScholasticism),forexample, BernardBolzano(1781–1848)wasviewedasaprogressiveradical,thusunacceptable totheAustrianrulers(HouseofHapsburg-Lorraine)ofBohemiaandwasejectedfrom hisuniversityposition;itwas50yearsafterhisdeaththatKarlWeierstraussfoundin hiswritingsthefoundationoftheBolzano-Weirstrausstheorem,whichisessentialto thenotionofcontinuityandoneofthetheoreticalunderpinningsofcalculus.
Aswehavealreadystated,thisbookisnotahistoryofscience,butanattemptto placethedevelopmentofquantummechanicsinahistoricalframework.Asasociety, welikenicestoriesofhowideasweredevelopedandintroduced,butthetruthisalmost alwaysmorecomplicated.Asillyexampleisthesupposedinventionofthesandwichby JohnMontague,the4thEarlofSandwich.Itishardtobelievethatinthe30millennia thatbreadexistedinoneformoranother,nobodyeverplacedasliceofmeatbetween twopiecesofbread.Whatthegoodearlaccomplishedwastomaketheconsumption ofsuchacceptableinpolitecompany.
EventherelativelyrecentworkofPlanckhasbeenhotlyarguedamongscience historians.Inparticular,MartinKleinandThomasKuhnreallycouldnotagreeon Planck’spersonality;washecarefullyconservativeorarecklessrevolutionary?18 In fact,botharecorrecttosomedegree.Humansarecomplex,andoftenexpressdifferent andseeminglyincompatibleviewsdependingonthesituation.
1.3 Religionandscience
TheseparationbetweenscienceandreligionthatdevelopedduringthisperiodinEurope,thatis,fromtheeleventhtotheeighteenthcentury,andevenintothenineteenth century,isquiteremarkableandperhapsuniqueinthedevelopmentofhumansocietiesandcultures.BythetimeofNewton,theneedforreconciliationbetweenscientific observationwiththeBiblelargelydisappearedfromscientificliterature;whatisespeciallyremarkableisthatNewtonhadaliteralistinterpretationoftheBibleandwrote extensivelyonthesubject,however,heheldhisnotionsinclosesecretashisembracingmonotheismwasatoddswiththedoctrineofTrinityCollege,whereheheldhis facultyposition,astherewerepotentialseriousconsequencesforholdingsuchviews.
Howthisseparationcameaboutremainsamystery,althoughsomecreditFrancis Baconwithdevelopingtheconceptofempiricismandwiththedevelopmentofthe scientificmethod,however,hewasacontemporaryofGalileo,andtheywerecertainly awareofeachother’swork,soitappearsdifficulttoassigncredittoeither.Bacon wasespeciallyagainstAristotle’ssyllogismandrulesofinductiveenquiry;forGalileo, Aristotelianphysicswassimplyincompatiblewithreality.19 Otherspavedtheway;recallGiordanoBruno,whoperishedforhisscienceteachingsomeyearsbeforeGalileo’s predicament.Oftentheyoungaretheonesleadingthewaytowardrevolution.Compare thesituationofBrunoandGalileowiththeanti-VietnamwarmovementintheUSA, originallyfomentedprincipallybycollegestudentsuntilthefundamentalhypocrisy
18JeroenvanDongen, InEurope,loc.cit.
19W.Mays, ScientificMethodinGalileoandBacon, IndianPhilosophicalQuarterly 1,vol.3,217 (1974).
andpathologyofthewarwerefinallyrevealedthroughtheKentStateMassacreand thePentagonPapers.
Itisalsowrongtosaythatbeforee.g.,FrancisBacontherewasnosuchthing asthescientificmethod.Testingbytrialanderrorispartofthehumanpsycheand hasexistedsincethebeginningofconsciousthought.TheEgyptianscouldnothave constructedthepyramidsandotherstructuresiftheydidnothaveasystemtostudy nature,recordobservationsandmethods,andtransmitknowledgebetweengenerations.RecordssuggestthattheEgyptianculturestagnatedinthatnewideaswerenot allowedtodevelop,andthusthesocietycouldnotkeepupwithachangingenvironment,orthreatsfromexternalpoliticalforces.
TheseparationprobablywastheresultofScholasticismdominatingmonasticmedievalteaching,acriticalmethodofphilosophicalanalysispredicateduponAristotle, withaLatinCatholictheismbeingseparateandnotsubjectedtologicalargument andanalysisbutwhichwastobeacceptedasinfallibleandinvariantdoctrine.Such curriculadominatedteachingintheEuropeanmedievaluniversitiesfromabout1100 to1700.ThoseinterestedinscientificobservationhadtoskirtaroundAristotle,and indoingso,bypassedreligiousscrutinyanddebate.Theproblemsscientistsfacedare bestillustratedbyGalileo’sinteractionwiththeChurch;aslongasGalileocalledhis observationsandconclusions“theoretical”therewasnoconflictwiththeChurchor withitsdoctrine.Inthissense,theconflictwithGalileowasabattletodecidewho getstointerpretscripture,oralternatively,whohaspoliticalcontrol.
InthehistoryofWesternscience,allofthisledtosciencebeingdoneoutsideof religiousconsiderations,originallyclearlytoavoidconflictwiththeChurch,andalso withpolitics,whichisalmostthesamething.Laterthisseparationbecameamatter ofcourseandpartofournowacceptedscientificculture.
InnationsgovernedbyShariaLaw,scienceanddoctrineareexpectedtobe,and toremain,mutuallycompatible.DuringtheSovietera,Russianscientistshadtoat leastobliquelyacknowledgedialecticalmaterialism.Awell-knownanecdotetellsof BeriaapproachingKurchatov,theheadscientistoftheSovietatomicbombproject, regardingthefallaciesofEinstein’stheoryofrelativityasitisincompatiblewith thefundamentalnotionsofdialecticalmaterialism.Kurchatovrepliedthatwithout relativity,therecannotbeanatomicbomb.Apparently,theSovietphilosopherswere abletounifyawaytheincompatibilities.
Thescientist-as-atheistisamodernWesternnotionthathaditsbeginningsfrom dancingaroundtheChurchandAristotle,butwaslateramplifiedbyDarwin’stheoryofevolution.Darwindidnotsetatimelineforevolution,becauseherealized thatestimatesfortheageoftheSun(30millionofyears),duetotheenergyreleasedfromgravitationalinteractions,werenotsufficientlylong.Biologistsarguedthat thereneededtobeanotherenergysourcefortheSun,asdidgeologistswhoneeded moretimefortheirsedimentaryrockstoform,andtheywerecorrect.20 Theageof theearthduetoOldTestamentgenealogyandtheJewishcalendarisabout6,000 years,andthisisviewedbymanyasaconflictbetweenscienceandreligionthatarises fromtakingtheancientscripturesliterally,insteadofseriously.Itisworthnoting
20Bethe,H.A., EnergyProductionintheStars,NobelLecture,Dec.11,1967.https://www. nobelprize.org/uploads/2018/06/bethe-lecture.pdf.
thatsomeKabbalistsfromSpaininthetwelfthtothirteenthcenturiescalculatedthe Earth’sageasintherangeof1millionto2.5billionyears.21
Thefundamentalincompatibilitybetweenscience,religion,andpoliticsisthat thebasisofscienceisfalsification.Asacademics,wetendtoviewconflictsbetween doctrineandscientificobservationasbeingduetosemanticissues,e.g.,thesixdays ofcreationrefersnottodays,butperhapstovasteons;themodernreaderhasno ideaofwhattheoriginalwriterhadinmind.Thisisaboutthebestthatcanbedone underthenotionoftheinfallibilityofancientscripture.Andwhatdowemeanby falsification?Inscience,thebreadthofthisnotiongoesfromtwomeasurementsofthe samequantitybeinginconsistentduetoexperimentalerrors,toanentiretheoretical constructbeingincorrect.
InresponsetoEinstein’sfamousremark,“GoddoesnotplaydicewiththeUniverse,”Bohrsaid“Einstein,stoptellingGodwhattodo.”Perhapsthisisalesson regardingthestrictinterpretationofhistoricalandphilosophicaldocuments.
1.4 Birthofthemodernatomictheoryofmatter
ThefirstmodernkinetictheoryofgasesisduetoJamesHermann,whoin1716deduced thatthepressureexertedbyagasisproportionaltotheaveragesquaredvelocityof thegasparticlestimesthenumberdensity.
In1729Eulerattemptedtomathematicallyexplainthebehaviorofgaseswith akinetictheorybasedonRobertBoyle’sgasdatafrom1662.Heassumedthatthe gasparticleswouldallmoveatthesamespeed.DanielBernoulliformulatedakinetic theoryofgases,withthenotionthatthevelocitieswouldbestatisticallydistributed, butdidnotspecifythedistribution,however,heanticipatedtheworkofJamesClerk Maxwellacenturylater.Bernoulli’sworkwasnotwidelyaccepted,inpartbecause
Fig.1.2 Bernoulli’ssketchofgasmoleculesholdingupaweightviatheforceexertedona piston,asstillseentodayinelementarythermodynamicsbooks.(PublicDomain)
21DovGinsberg, TheAgeoftheEarthFromJudaicTraditionalLiterature,EarthSciencesHistory 3,vol.(2),169,173(1984).
conservationofenergyhadnotyetbeenestablishedanditwasnotobviousthatcollisionsbetweenparticlescouldbeperfectlyelastic.RogerBoskovich,aCroatianJesuit, carriedthescientificatomictheoryfurtherbysurmisingthatatomsareinfluencedby interatomicpotentialsmodeledonNewtoniangravity(1758)andprovidedthefirst insightthatcollisionsmightbeelastic.
ItisofinteresttonotethatBenjaminFranklinwasveryinterestedinoilfilms onwater,mostlybecauseoftheirbothanecdotalandactualeffectstoreducethe amplitudeofwind-drivenwaves.Franklinwouldcarryvialsofoilwithhimwhichhe wouldsometimespourontopondsorlakestostudytheeffectsoffilms.Henoticedthat ateaspoonofoliveoilwouldspreadtoanareaofaboutone-halfanacre.Hedidnot estimatethesizeofamoleculebasedonthis,butthisresultimpliesamolecularsize ofaboutananometer.22 Later,AgnesPockels(circa1885)wasthefirsttoestimate thesizeofoilmoleculesbasedonhermeasurementsoffilms.
Experimentswithgasesthatfirstbecamepossibleattheturnofthenineteenth centuryledJohnDalton(1766–1844)in1803toproposethebasisofmodernatomic theorybasedonthefollowingassumptions:
1. Matterismadeupofatomsthatareindivisibleandindestructible.
2. Allatomsofanelementareidentical.
3. Atomsofdifferentelementshavedifferentweightsanddifferentchemicalproperties.
4. Atomsofdifferentelementscombineinsimplewholenumberstoformcompounds.
5. Atomscannotbecreatedordestroyed.Whenacompounddecomposes,theatoms arerecoveredunchanged.
ThisissupplementedwithAvogadro’shypothesis,namedafterAmedeoAvogadro, who,in1812,statedthattwogivensamplesofaperfectgas,withthesamevolume andatthesametemperatureandpressure,containthesamenumberofmolecules.
Atthispoint,thedevelopmentofatomictheoryinphysicsdeviatesfromitsdevelopmentinchemistry.Withfewnotableexceptions,forchemistsatthistimeatoms werebecomingveryrealandbroughtnewunderstandingtochemicalreactionsand compounds.Physicistswereoflessuniformopinionastotherealityofatoms,astate thatpersisteduntilwellintothetwentiethcentury.
In1828thechemistFrederichW¨ohlersynthesizedureafrominorganiccompounds, anddisprovedthevitalisthypothesisthat“organic”compoundscouldbemadeonly bylivingthings.In1855,AugustKekul`eformulatedtheringstructureofBenzene. Whenisomersofdibromobenzenewerenotdiscovered,heproposedthatthedouble bondsintheringsoscillatebetweencarbonatompairs—doesthismarktheinvention ofquantummechanics?
In1869,theRussianchemistDmitriMendeleevdevelopedaframeworkthatwould becomethemodernperiodictable.Whilearrangingtheelementsaccordingtotheir atomicweight,hefoundthattheytendedtofallintocolumnargroupswithsimilar
22See,e.g.,JoostMertens, Oilontroubledwaters:BenjaminFranklinandthehonorofDutch Seamen,PhysicsToday 59,1,36(2006);https://doi.org/10.1063/1.2180175.Also,W.M.Klipstein,J.S.RadnichandS.K.Lamoreaux, Thermallyexcitedliquidsurfacewavesandtheirstudy throughthequasielasticscatteringoflight,AmericanJournalofPhysics64,758(1996);online: https://doi.org/10.1119/1.18174.
Fig.1.3 a.1,2-Dibromobenzenewithfixedbondsinthering,comparedtob.wherethebonds locationsaredelocalized,andconsideredtobethecorrectformulabecausethenon-existence oftwoisomersof1,2-Dibromobenzene.
properties,andheinsertedgapsforelementsthathesuspectedwerenotyetdiscovered. Basedonthepropertiesofagroup,Mendeleevpredictedthepropertiesofsomeundiscoveredelementsandgavethemnamessuchas“eka-aluminum”forananticipated elementwithpropertiessimilartoaluminum.Eka-aluminumwaslaterdiscoveredas gallium.However,discrepanciesremained;thepositionofcertainelements,suchas iodineandtellurium,couldnotbeexplaineduntilthediscoveryofisotopes.
Bythistime,chemicalindustrieswereburgeoning,particularlyinEnglandand theUnitedStates,andespeciallyinGermany.Theacceptanceofatomsandatomism bychemistswasprofitablyproductive;thewealthcondensedintheflasksoforganic chemistshelpedinspireandsecurethefundingofscienceingeneral.Assuch,therejectionofatomsbymanyphysicistsappearsasparticularlyintellectuallyschizophrenic.
1.5 Atomismandphysics
In1860,JamesClerkMaxwell,afterreadingapaperbyClausius23 thatintroducedthe notionofthemeanfreepath,beganhisstudiesofkinetictheoryanddeterminedthe velocityspectrumofspeedsinanidealizedgasbyuseofheuristicmethodsthatwere laterfullydevelopedbyBoltzmann.Atthetime,thenotionofavelocitydistribution wentagainsttheconventionaltheory,whichwasthatarangeofvelocitieswouldbe equalizedbymolecularcollisions.Maxwellalsoinvestigatedkinetictheoryingeneral, anddiscovered“thecuriousresult”thatviscosityisindependentofpressure,which wasunexpected.Hepublishedanestimateofthemeanfreepathbasedonairviscosity measurementthathadbeendonebyStokes.24 MaxwellandKatherineClerkMaxwell (hiswife)madethefirstreliablemeasurementsofthedependenceofgasviscosityon temperatureandpressure.Thesemeasurementswereperformedintheatticoftheir house,withthetemperaturecontrolledbyselectivestokingofthefireplace.Their results,reportedin1866,supportedthekinetictheoryofgasviscosityandprovided thefirstaccuratemeasurementoftheeffectivediameteroftheatomsormoleculesthe gascomprises,basedonLoschmidt’swork,citedbelow.
23Clausius,R.(1857),“UeberdieArtderBewegung,welchewirW¨armenennen,”Annalender Physik,100(3):353-379.Englishtranslation TheNatureoftheMotionwhichwecallHeat,PhilosophicalMagazine,Vol.14,pp.108-27(1857).
24Maxwell,J.C.(1860) Illustrationsofthedynamicaltheoryofgases.PartI.Onthemotionsand collisionsofperfectlyelasticspheres,PhilosophicalMagazine,4thseries,19:19-32.Maxwell,J.C. (1860) Illustrationsofthedynamicaltheoryofgases.PartII.Ontheprocessofdiffusionoftwoor morekindsofmovingparticlesamongoneanother,PhilosophicalMagazine,4thseries,20:21-37.
