1112.2499 popularizing atom

8/2/2019 1112.2499 Popularizing Atom

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Spreadingthegospel:TheBohratompopularised

HelgeKraghandKristianHvidtfeltNielsen*

CentreforScienceStudies,AarhusUniversity,Aarhus,Denmark

Summary

Theemergenceofquantumtheoryintheearlydecadesofthetwentiethcentury

wasaccompaniedbyawiderangeofpopularsciencebooks,allofwhich

presentedinwordsandinimagesnewscientificideasaboutthestructureoftheatom.TheworkofphysicistssuchasErnestRutherfordandNielsBohr,among

others,waspivotaltothesocalledplanetarymodeloftheatom,which,still

today,isusedinpopularaccountsandinsciencetextbooks.Inanattempttoadd

toourknowledgeaboutthepopulartrajectoryofthenewatomicphysics,this

paperexaminesonebookinparticular,coauthoredbyDanishsciencewriter

HelgeHolstandDutchphysicistandclosecollaboratorofNielsBohr,HendrikA.

Kramers.TranslatedfromDanishintofourEuropeanlanguages,thebooknot

onlypresentedcontemporaryideasaboutthequantumatom,butalsowentinto

ratherlengthydiscussionsaboutunresolvedproblems.Moreover,thebookwas

quiteexplicit

in

identifying

the

quantum

atom

with

the

atom

as

described

by

Bohrstheory.WearguethatKramersandHolstsbook,alongwithotheratomic

books,wasausefultoolforphysicistsandsciencepopularisersastheygrappled

withthenewquantumphysics.

Contents

1. Introduction

2. TheBohratomanditsreception

3. Popularexpositionsofatomictheory

4. TheCopenhagencontext:Bohr,Kramers,Holst,Klein

5. TheAtomandtheBohrTheoryofItsStructure

6. Pictorialatoms

7. Receptionanddissemination

8. Conclusion:theKramersHolstbookinapopularsciencecontext

* Emails::[email protected]@ivs.au.dk


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1. Introduction

Theearlytwentiethcenturysawtheriseofthenewphysicsofrelativityand

quantumtheoryand,acrossEuropeandtheUSA,itspopularisationthrough

numerousbooks,lectures,andarticlesaimedatageneralaudience.Althoughnever

aswidelydisseminatedanddiscussedinpublicastherelativitytheoryofAlbert

Einstein,thenewquantumtheoryoftheatom,firstproposedbyNielsBohrin1913,

wonpopularrenowninthelate1910sandearly1920sthroughtheworkofphysicists

andscience

popularisers.

As

observed

by

historians

such

as

Michael

Whitworth

and

PeterBowler,theeffortsrangedwidelyintermsofpopularity:somewere

genuinelypopularintermsofexposition,marketing,andreadership;otherswere

quitetechnicalandgenerallyobscureto,andprobablyneverintendedtoreach,

wideraudiences.1Manyprominentscientists,includingEinsteinandBohr,were

activelyengagedinthepopularisationofthenewphysics;others,suchasWerner

HeisenbergandPaulDirac,restrictedtheirinteresttotheelaborationofnew

scientificknowledge.2Asaresultofthewidespectrumofpopularscienceandthe

1MichaelWhitworth, TheClothboundUniverse:PopularPhysicsBooks,191939,PublishingHistory,40(1996),5382.PeterJ.Bowler,ScienceforAll:ThePopularizationofScienceinEarlyTwentiethCenturyBritain(Chicago:UniversityofChicagoPress,2009).2AstoEinstein,hewaskeenlyinterestedinpopularisinghistheoryofrelativity,asshown,

forexample,byhisearlysemipopularpresentationberdieSpezielleunddieallgemeineRelativittstheorie(Braunschweig:Vieweg&Sohn,1917),translatedintoEnglishasRelativity:

The

Special

and

General

Theory

(New

York:

Hartsdale

House,

1920).

Although

Einstein

had

sparednopainsinhisendeavourtopresentthemainideasinthesimplestandmost

intelligibleform,thebookpresumedastandardofeducationcorrespondingtothatofa

universitymatriculationexamination(preface,p.v).OnEinsteinasapopularsciencewriter,

seeElkeFlatau,AlbertEinsteinalswissenschaftlicherAutor,MaxPlanckInstituteforthe

HistoryofScience,Preprint293(2005).OnWernerHeisenberg,seeDavidC.Cassidy,

Uncertainty:TheLifeandScienceofWernerHeisenberg(NewYork:W.H.Freeman,1992);onPaulDirac,seeHelgeKragh,Dirac:AScientificBiography(Cambridge:CambridgeUniversityPress,1991)andGrahamFarmelo,TheStrangestMan:TheHiddenLifeofPaulDirac,QuantumGenius(London:FaberandFaber,2009).


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sustainedinterestinpopularscienceonbehalfofsomescientists,theboundary

betweenrealphysicsandpopularphysicsneverwasentirelyclearcut.Thefact

thatthenewphysics,partlybecauseofitscounterintuitiveresultsandpartlybecause

ofthehighdegreeofcomplicatedmathematicsinvolved,hasplayedanimportant

roleindistancingscientificknowledgefromlayopinionshouldnotleadusto

considerthegapbetweenrealandpopularscienceasgiven.Thehistoricalgenealogy

ofthisgapprovidesuswithimportantinsightsintofoundationalissuespertainingto

scienceand

the

public.

3

Thehistoriographyofpopularscienceconsiderspopularscienceasintegral,

evenfundamental,tothehistoryofscienceproper.4Thehistoricalinterpretationof

scientificdevelopmentsneedstotakeintoaccountthedistinctionbetween,onthe

onehand,scientificknowledgeandscientificcommunications,andontheother

hand,otherkindsofknowledgeandothermodesofcommunication.Tobesure,for

severalreasons,thenewphysicsofthetwentiethcenturymarksanimportantshiftin

thehistoryofemergingdemarcationsbetweenscienceandpopularscience.Scientists

andotherssawrelativityandquantumtheory,alongwithnonEuclidiangeometry,

asemblematicforasharpcognitivedividebetweenscientificknowledgeandpublic

opinion.5Thenewphysicsandmathematicsmadeitcleartoeveryonethatscientific

knowledgewasdifficulttoaccess,borderingontheincomprehensible.Whereas,

3BernadetteBensaudeVincent,AGenealogyoftheIncreasingGapbetweenScienceandthe

Public,PublicUnderstandingofScience,10(2001),99113.4JonathanR.Tophametal.,Focus:HistorizicingPopularScience,Isis,100(2009),310368.Forahistoriographicaldiscussionofpopularscienceanditsrelationtohistoryofscience

proper,seeRogerCooterandStephenPumfrey,SeparateSpheresandPublicPlaces:

ReflectionsontheHistoryofSciencePopularizationandScienceinPopularCulture,HistoryofScience,32(1994),237267,whodeplorethereluctanceofhistoriansofallkindstocommitthemselvestoinquiryintopopularscience(p.246).5BensaudeVincent(note3),pp.105108.


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previously,popularsciencecouldbeseenasanextensionofscientificepistemology

inpublicdomains,thenewphysicsrequiredtranslatingsophisticatedmathematics

andhighlytechnicallanguageintoeverydaylanguageandsimplecognitivemodels,

suchasimagesoftheatomasaplanetarysystem.Moreover,newvenuesofmass

communication,newtechniquesofmassproductionoftextsandimages,andthe

everincreasingdemandforpopularscience(probablyenforcedbythegrandclaims

ofthenewphysics)alsocontributedtotheboomofpopularscienceduringthe

earlydecades

of

the

twentieth

century.

6Finally,

as

Andreas

Daum

notes,

the

enactmentofagapbetweenscienceandpopularsciencenotonlyservedtodenigrate

popularscience.Onthecontrary,scientistsandpopularisersoftenhaveappealedto

thisgapinordertomakeapositivecaseforpopularscience,i.e.,topresentpopular

knowledgeassomethingpositiveandnecessary.7

Atthecoreofthispaperisanattempttoengagehistoricallywiththe

establishmentoftheboundarybetweenrealandpopularatomictheoryinthe

periodfromabout1915to1925.Duringthisdecadeatomicandquantumphysicswas

dominatedbythetheoryofatomicstructureproposedbyNielsBohrin1913,a

theorywhichalsoattractedagooddealofpublicattention.Foremostamongthe

popularexpositionsofBohrstheorywasabookpublishedbyHelgeHolstand

HendrikA.Kramersin1922,whichbookweanalyseinsomedetail.Followinga

sectionontheearlyreceptionofBohrstheoryinscientificcircleswesurveythefield

ofatomicbooks,thatis,popularbooksonatomictheory,therebyprovidinginsights

intothekindofpopularbookswrittentopresentthenewscientificmodelsofthe

6PeterBowler,citedinScottKeir,TheBoomsofPopularScience,Nature.comBlogs,[accessed4

September2011].7AndreasW.Daum,VarietiesofPopularScienceandtheTransformationsofPublic

Knowledge,Isis,100(2009),319332,onp.320.


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atomtowideraudiences.Welargelyrestrictoursurveytobookspublishedin

GermanyandEngland.ThebookauthoredbyHolstandKramerswasarare,joint

effortbetweenaDanishsciencepopulariserandoneofBohrsclosecollaborators.

Aimedatthegeneralreaderwithaninterestincontemporaryphysics,thebookwas

receivedasawelcomeadditiontothemanypopularaccountsofthenewquantum

theoryoftheatom,butalsoasavehicleforspreadingthegospelofBohrs

interpretationofquantumtheory,partsofwhichwerestillbeingdebatedbyatomic

physicists.8

TheKramersHolstbook,withitsexplicitomissionofmathematicalreasoning

anditsintroductiontovarietiesofatomictheorisingthroughouttheages,effectively

establishedaboundarybetweenrealphysics(basedonmathematicsand

experimentation)andpopularphysics(writteninclearandsimplelanguage,and

supportedbyahistoricalnarrative).Theauthorsclearlysawpopularphysicsasan

importantvenueforpresentingfundamentalideasandsignificantresults,butalsoas

anopportunityfordiscussingkeyproblemsandaddressingthephysicalmeaningof

theBohrtheory.Theywanted,inshort,thebooktoserveasastimulustofurther

studyoftheBohrtheory.9

8HistoricalcommentsontheKramersHolstbookincludeMaxDresden,H.A.Kramers:

Between

Tradition

and

Revolution

(Berlin:

Springer,

1987),

pp.

132

134,

and

Arne

Schirrmacher,

BohrscheBahneninEuropa:BilderundModellezurVermittlungdesModernenAtom,in

CharlotteBiggandJochenHennig,eds,Atombilder:IkonographiedesAtomsinWissenchaftundffentlichkeitdes20.Jahrhunderts(Munich:DeutschesMuseum,2009).DresdenfindsitnotinappropriatetodescribethebookbyKramersandHolstasatrulymissionaryventureto

spreadthegospelaccordingtoBohr(p.134).Asweshallsee,althoughitcanindeedbe

describedasmissionary,theauthorsdidnothidetheprovisionalandincompletenatureof

Bohrstheory.9H.A.KramersandH.Holst,TheAtomandtheBohrTheoryofitsStructure(London:Gyldendal,1923),p.ix.


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2. TheBohratomanditsreception

FinancedbyastipendfromtheCarlsbergFoundation,youngBohrspenttheperiod

fromSeptember1911toJuly1912inEngland,firstinCambridgewithJ.J.Thomson

andsubsequentlyinManchesterwithErnestRutherford.Itwasduringhisstayin

ManchesterthathecameupontheideaofcombiningRutherfordsnewhypothesisof

thenuclearatomwithPlancksquantumtheory,anideahedevelopedintoafull

blownatomictheoryinasequelofthreeseminalpapersthatappearedinthe

summerand

fall

of

1913.

Published

in

the

Philosophical

Magazine,he

presented

the

wellknownplanetarymodeloftheatomthatcanstillbemetinelementary

textbooksinphysicsandchemistry.10

WhatisofinterestinthepresentcontextismerelythatBohrpicturedtheatom

asconsistingofatinypositivenucleussurroundedbyoneormoreelectronsmoving

indefinite,socalledstationaryorbitsaroundit.Thismaysounduncontroversial,

muchliketheplanetsorbitingthesun,butaccordingtotheauthoritativetheoryof

classicalelectrodynamicsarevolvingelectronemitselectromagneticenergy,causing

anatomoftheBohrRutherfordtypetocollapse.Toavoidtheradiationcatastrophe,

Bohrpostulatedthatelectronsinstationaryorbitsdonotobeythelawsof

electrodynamics.Moreover,heassumedthatelectronsinhigher(excited)energy

stateswillspontaneouslyjumpfromthehighertoalowerstationarystate,bywhich

processtheatomwillemitadiscreteamountofradiation.Thefrequencyofthe

10NielsBohr,OntheConstitutionofAtomsandMolecules,PhilosophicalMagazine,26(1913),125;476502;857875.ThereareseveralhistoricalanalysesofBohrsatomictheory,seefor

exampleJagdishMehraandHelmutRechenberg,TheHistoricalDevelopmentofQuantumTheory,vol.1(NewYork:Springer,1982)andOlivierDarrigol,FromcNumberstoqNumbers:TheClassicalAnalogyintheHistoryofQuantumTheory(Berkeley:UniversityofCaliforniaPress,1992).ForamoreaccessiblereviewandafullbiographyofBohr,seeAbrahamPais,

NielsBohrsTimes,inPhysics,Philosophy,andPolity(Oxford:ClarendonPress,1991),pp.176209.


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emittedlightisgivenby E/h,where Eistheenergydifferencebetweenthetwo

statesandhisthequantumconstantintroducedbyPlanckin1900.Onlywhenthe

atomisinthelowestpossibleenergystate,knownasthegroundstate,willitbe

stableandnotemitradiation.

Basedonthetwopostulatesorassumptions,andsuppliedwithsomefurther

hypothesesthatlackedindependentjustification,Bohrsucceededinaccounting

quantitativelyforthelinespectrumofhydrogenthatuntilthenhaddefied

explanation.In

addition,

he

calculated

the

ionisation

energy

(the

energy

ittakes

to

detachtheelectronfromtheatom)inagreementwithexperimentandpredicted

severalotherphenomenathatweresoonverifiedexperimentally.Inshort,Bohrs

theorywasgreatlysuccessfulfromanempiricalpointofview.Itsimpressive

explanatoryandpredictivepowerconvincedmanyphysiciststotakeitseriouslyin

spiteofitsdoubtfulfoundationinthetwopostulates.Manyofthosewhoadopted

thetheoryuseditselectivelyandopportunistically:whiletheyacceptedthephysical

model,theyeitherdeniedorignoreditstheoreticalfoundation.AsJamesJeans

pointedlysaidatthemeetingoftheBritishAssociationfortheAdvancementof

ScienceinSeptember1913,Theonlyjustificationfortheseassumptionsisthevery

weightyoneofsuccess.11

Inspiteofinitialscepticismandscatteredopposition,Bohrstheorywas

generallyifsomewhathesitatinglywelcomedbyalargepartofthephysics

community.TheconversiontotheBohratomdidnotoccurinstantly,butlatestby

thesummerof1915thetheorywaswellknownandacceptedassuperiorto

11JamesJeans,DiscussiononRadiation,Report,BritishAssociationfortheAdvancementofScience(London:J.Murray,1914),376386,onp.379.ThiswasthemeetingatwhichBohrstheorywasfirstdiscussedinpublicandalsotheoccasionforthefirstmentionofitinthe

press.Reportingfromthemeeting,TheTimesofLondonbrieflymentionedon13SeptemberJeanssaccountofDr.Bohrsingeniousexplanationofthehydrogenspectrum.


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alternativeconceptionsoftheconstitutionoftheatom.Itfirstattractedinterest

amongEnglishphysicists,amongwhomRutherford,HenryMoseley,andOwen

Richardsonsupporteditfromanearlydate,whileJohnNicholsonandsomeother

physicistsresistedthenewtheory.12

GermanphysicistswereslowertorespondtoBohrsatom,butwhentheydid,

theydiditeffectivelyandwithgreatconsequences.Contrarytotheircolleaguesin

England,theydevelopedthetheoryscientificallyandturneditintoamoregeneral

andeven

more

powerful

theory.

This

important

development,

which

took

place

duringthedifficultwaryears,wasprimarilytheworkofArnoldSommerfeldandhis

innovativeschoolinMunich.Theresultwasthatby1918theBohr(orBohr

Sommerfeld)theorywasmuchbetterknowninGermanythaninEngland.The

furtherdevelopmentofBohrsatomictheory,largelyidenticaltowhatisknownas

theoldquantumtheory(asdistinctfromquantummechanics),wasalsodominated

byGermanphysicists.Untilthefallofthetheoryin1925,themaincentresof

quantumandatomictheorywereCopenhagen,Munich,andGttingen.Itshouldbe

notedthattheBohratomchangedconsiderablyovertime.WhereasBohroriginally

conceivedatomsasplanarconfigurationsofringspopulatedwithevenlyspaced

electrons,by1922thepicturehadchangedtoamorecomplicatedthreedimensional

modelinwhichtheelectronsmovedinellipticorbitsofdifferenteccentricitiesand

spatialorientations.

Bohrsatomictheoryneverattractedthesamekindofpublicattentionas,for

example,Einsteinstheoryofrelativity.Yetitwasknownatanearlystagenotonly

byphysicistsinterestedinthestructureofmatterbutalsobyabroadersegmentof

scientistsandlayreadersofthegeneralscienceliterature.JournalssuchasNature

12OntheBritishopposition,andtheoneofNicholsoninparticular,seeHelgeKragh,

ResistingtheBohrAtom:TheEarlyBritishOpposition,PhysicsinPerspective,13(2011),435.


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(England),Science(theUSA),andDieNaturwissenschaften(Germany)werenotonly

readbyprofessionalscientistsbutalsobymanypeoplewithageneralinterestinthe

sciences.

WhiletheearlydiscussionoftheBohratominNaturewasofatechnical

natureandofinterestmostlytophysicists,readersofScience,thejournalofthe

AmericanAssociationoftheAdvancementofScience,weremorebroadlyinformed.

Forexample,theJuly1914issueofthejournalincludedasurveyarticlebyArthurS.

Evebased

on

ameeting

of

the

Royal

Society

of

Canada

on

the

structure

of

the

atom.

Eve,aformerassistant(andlaterbiographer)ofRutherfordandsince1903professor

ofphysicsinMontreal,presentedtheideasofthebrilliantyoungDane,Bohrwhose

workisremarkableasleadingtoexcellentnumericalverification.13Halfayearlater

SciencebroughtanothersurveyarticlewhichpraisedtheBohrRutherfordmodelof

theatomasagreatadvance,evenonethatwillprobablyremain,sufferingbutlittle

changeinthefuture.14Theauthor,G.WalterStewartoftheUniversityofIowaCity,

recognisedtheweaknessesofthemodelbutdidnotfinditdamagingthatBohrs

theoryhaddifficultieswiththemorecomplexatoms:Whenonecontemplatesthe

narrowscopeofeventhisbrillianttheory,whatalimitlessfieldforresearchseems

ahead!

ThescientificallyinterestedpublicinGermanspeakingEuropemightgeta

thoroughintroductiontotheBohrtheoryinthepagesoftherecentlyfoundedDie

Naturwissenschaften,whichinMarch1914carriedalongarticleonthesubjectby

RudolfSeeliger,ayoungphysicistatthePhysikalischTechnischeReichsanstaltin

Berlin.AlthoughSeeligerwasalertthatthetheoryrestedonaproblematic

foundationandmightevennotbeconsistent,hisreviewwasgenerallypositive.Like

13ArthurS.Eve,ModernViewsontheConstitutionoftheAtom,Science,40(1914),115121.14G.WalterStewart,TheContentandStructureoftheAtom,Science,40(1914),661663.


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Stewartandseveralotherphysicists,heconcludedthattheempiricalstrengthofthe

theoryovershadowedtheconceptualproblemsassociatedwithit:Eventhoughwe

maybescepticalwithrespecttothedetails,IthinkwehaveinBohrsconsiderations

animportantandfundamentaladvanceintheknowledgeoftheoriginofspectral

linesandseries.15ContrarytothereviewsinScience,theoneofSeeligerwasofa

detailedandrathertechnicalnature,undoubtedlyappealingmoretophysiciststhan

tolayreaders.

Whilemagazines

like

Scienceand

Naturwissenschaftenprimarily

were

directed

toscientistsandscientificallycompetentcitizens,atleastinonecaseBohrstheory

alsoappearedearlyoninagenuinelypopularsciencejournal.TheUSPopularScience

Monthly,foundedin1872byEdwardYoumann,includedinthesummerof1915a

lecturethatRutherfordhadgiventotheNationalAcademyofSciencesin

WashingtonD.C.inAprilthepreviousyear.Inthisdetailedyetnontechnicalreview

Rutherfordcoveredthemostrecentdevelopmentsinatomicandsubatomicphysics,

includingnotonlythenuclearatombutalsoisotopes,Wilsonscloudchamber,and

MoseleysmeasurementsofthecharacteristicXraylinesfromelements.The

questionofthespectra,hesaid,hasbeenattackedinaseriesofremarkablepapers

byBohr,whoconcludesthatthecomplexityofthespectrumisnotduetothe

complexityoftheatombuttothevarietyofmodesinwhichanelectroncanemit

radiation.AlthoughRutherfordexpressedconfidenceinBohrsmodel,atthesame

15RudolfSeeliger,ModerneAnschauungenberdieEntstehungderSpektrallinienundder

Serienspektren,DieNaturwissenschaften,2(1914),285290,309314,onp.313.DieNaturwissenschaften,foundedin1913andpublishedbytheSpringerVerlag,wasuntil1935editedbythephysicistArnoldBerliner.AssociatedwiththeKaiserWilhelmGesellschaft,the

magazinewassubtitledWochenschriftfrdieFortschrittederNaturwissenschaften,derMedizinundderTechnik(WeeklyPublicationfortheAdvancesintheNaturalSciences,MedicineandTechnology).ItwasinmanywaystheGermanequivalenttotheBritishNatureandtheUSScience.


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timeheadmittedthatthereisroomformuchdifferenceofopinionastothe

interpretationoftheratherrevolutionaryassumptionsmadebyBohr.16

Asonemightexpect,BohrsworkattractedearlyinterestinDenmarkeven

thoughtheatomictheorywasaproductofManchesterratherthanCopenhagen.We

haveaninterestingexampleinthe25volumeencyclopaediaSalmonsens

KonversationsLeksikon,whichinitssecondeditionof1915includedanentryonNiels

Bohr(andalsooneonhisfather,thephysiologistChristianBohr,andhisyounger

brother,the

mathematician

Harald

Bohr).

The

entry

mentioned

his

early

work

on

the

electrontheoryofmetals,andalsohisrecentworkonatomictheory:

BasedonRutherfordsatomicmodel,butsupplementedbyafewremarkable

andrevolutionaryhypotheses,heexplainsmanyofthephysical,and

especiallyoptical,propertiesofmatter(particularlyinthecaseofhydrogen,

thesimplestelement).Thustheatomicmodelyieldsdirectlyand

quantitativelycorrectlythespectrumofhydrogen.Theconsiderationswhich

areestablishedinthiswayareexpectedtobegreatlyimportantforthefurther

researchintheseareas.17

16ErnestRutherford,TheConstitutionofMatterandtheEvolutionoftheElements,PopularScienceMonthly,87(August1915),104142,onpp.139140.Themagazinewasatthetimeabouttochangeitsprofile.Whiletheexistingversionwasstillofaratherscholarlynature,

oftenwithextensivearticleswrittenbyrecognisedscientists,bytheendof1915thejournal

changedtoaformatwithnumeroussmallandeasytoreadarticleswrittenbyitsreporters.

Atthesametimethenumberofillustrationsgrewdramatically.Themagazinebecame

popularinasensedifferentfromtheolderone,suchaswediscussinourintroduction.17CarlBlangstrup,ed.,SalmonsensKonversationsLeksikon,vol.3(Copenhagen:J.H.Schultz,1915).TheauthorwasthephysicistHansMariusHansen,aclosefriendofBohr.


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InthesameyearBohrstheorymadeitsentryinthestandardtextbookusedby

physicsstudentsattheUniversityofCopenhagen,arevisedfourtheditionof

ChristianChristiansenstextbookfirstpublished18921894.18

3. Popularexpositionsofatomictheory

ItwasonlyaftertheendoftheFirstWorldWarthatBohrsatomictheorywon

generalrecognitionandbecametheunquestionedbasisforresearchinatomicand

molecularstructure

such

as

communicated

in

the

physics

journals.

The

first

books

of

anonspecialistnatureexpoundingthetheorydatefromtheyearsaround1920.The

firstwasperhapsDieAtomtheoriefrom1918,asmallbookbasedonaseriesof

lecturesgivenbyLeoGraetz,professorofphysicsinMunich.IntroducingtheBohr

atomasaanentiresolarsystemwiththeelectronswhirlingaroundthenucleus

liketheearthmovesaroundthesun,Graetzemphasisedtheimportantdifference

thattheelectrons,contrarytotheplanets,couldonlymoveindiscreteorbitsgivenby

awholenumber.Remarkably,contrarytoallpreviouspicturesoftheatomthe

quantumatomdidnothaveadefinitevolume.AsBohrhadpointedoutinhis1913

trilogy,thesizeofanatominanexcitedstateincreasedwiththeassociatedquantum

number.Ahighlyexcitedatommighthaveasize,say,aradiusof0.01mm,that

madeiteasilyvisibleinamicroscope!AsGraetzpointedout,thenewatomictheory

wasbasedonarbitraryassumptions,namelythetwoquantumpostulatesthatcould

onlybejustifiedbytheirempiricalconsequencesinspectroscopy.19Ontheother

18 ChristianChristiansen,LrebogiFysik(Copenhagen:Gyldendal,1915),p.456,revisedbyMartinKnudsen,thesuccessorofChristiansenasprofessorofphysicsinCopenhagen.19LeoGraetz,DieAtomtheorieinihrerneuestenEntwickelung(Stuttgart:J.EngelhornsNachf.,1918),p.78.Thebookmusthavesoldwell,forin1922itcameoutinafourthprintingand

thesameyearitappearedinaRussiantranslation.Graetzjustifiedhispublicationbythe

generalinterestinatomictheoryhehadexperiencednotonlyfromphysicistsandchemists,


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Fig.1. TheBohrmodelofheliumandlithiumaccordingtoLeoGraetzsAtomtheorieof1918.Thenucleusisdepictedasmuchsmallerthantheelectrons,indicatingthatGraetzconceived

thechargedparticlesaselectromagneticinnature.Source:Graetz1918(note19).

hand,theseconsequenceshadbeenverifiedsoconvincinglythattherecouldbeno

doubtoftheessentialtruthofthetheory.Graetzillustratedhisbookwithseveral

picturesofatomsandmolecules,representingtheelectronsasmuchlargerbodies

thantheatomicnucleus(Figure1).20

Germanlayreaderscouldgetanupdatedandmoredetailedexpositionofthe

BohratomfromDieEntwicklungderAtomtheorie,abookof1922writtenbythe

physicsteacherPaulKirchberger.Abouthalfofthishistoricallyorganisedand

carefuldiscussionofatomismdealtwiththecompositeatomofthetwentieth

century,includinga40pagechapterontheBohrmodelwhichwasexpoundedin

considerabledetail.LikeGraetzandseveralotherauthors,Kirchbergerpointedout

thatBohrspostulatesweresomewhatarbitraryandthathismodeloftheatomwas

butalsofrommostscientificallyeducatedlaypersons.PrefacedatedAugust1918.Ofthesix

lecturesincludedinthebook,thetwolast(pp.6088)werelargelydevotedtoBohrsatomic

theory.20Thiswasaremnantoftheelectromagneticworldviewaccordingtowhichthemassofa

chargedsphericalparticlewasofelectromagneticorigin,varyingasthesquareofthecharge

overtheradius.Itfollowsthattheradiusoftheelectronmustbenearly2000timesasgreat

asthatoftheproton.Bohrdidnotacceptthisinterpretationandneverspokeofthesizeof

electrons.


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farfromvisualisable(anschaulich)whichmayhavebeenthereasonwhyhe

refrainedfromincludingpicturesoftheatom.Visualisableornot,toKirchbergerit

wasobviousthatBohrstheorywascorrectandtheonlypossiblewaytogetfurther

insightinthestrangeworldoftheatoms.21

Byfarthemostinfluentialbookonthenewquantumtheoryofatomswas

SommerfeldsAtombauundSpektrallinien,thefirsteditionofwhichwaspublishedin

1919andwhichuntil1925appearedinfoureditionsofincreasinglength.AnEnglish

translationof

the

third

edition

was

published

in

1923.

The

only

reason

to

mention

thisfamouswork,oftenreferredtoastheBibleofquantumtheory,inthepresent

contextisthatSommerfeldhimselfthoughtofitasapopularexposition.Inaletterto

EinsteinofJune1918hetoldthathehadstartedwritingapopularbookonAtomic

StructureandSpectralLines,whichinitsmaintextisforchemistsbutthe

appendicesofwhicharealsoforphysicists.22Intheprefacetothefirstedition

Sommerfeldemphasisedthathisbookwasmeanttobeaccessibletoagenerally

educatedreadership(gemeinverstndlich).However,Atombauwasnotapopularbook

inthesenseofbeingeasytoreadandunderstandforreaderswithnoscientific

training.Popularscience,toscientistslikeSommerfeld,tookonadifferentmeaning:

itprovidedavenueofcommunicationinwhichbasicideasandphysicalconcepts

couldtakecentrestage.Sommerfeldsbookwasclear,didactic,andmadeuseofonly

21PaulKirchberger,DieEntwicklungderAtomtheorie,gemeinverstndlichdargestellt(Karlsruhe:C.F.Mller,1922),prefacedatedOctober1921.Asecondrevisededitionappearedin1929.

Kirchbergeralsowrotearticlesonthenewatomictheoryforthenewspapers,forexample

ModerneAtomtheorieinBerlinerTageblattof16August1922.22ArnoldSommerfeld,AtombauundSpektrallinien(Braunschweig:Vieweg&Sohn,1919).SommerfeldtoEinstein,June1918,inMichaelEckertandKarlMrker,eds,ArnoldSommerfeld.WissenschaftlicherBriefwechsel,vol.1(Berlin:VerlagfrGeschichtederNaturwissenschaftenundderTechnik,2000),p.597.WhilethefirsteditionofAtombauhadalengthof550pages,thefourtheditionhadexpandedto862pages.


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15

fairlyelementarymathematics(bySommerfeldsstandards).Itwashardlyaccessible

toalaypublicandprobablynotreadbyit.Widereadershipwasnotoverly

importanttoauthorslikeSommerfeldwho,intimesofsomescientificcontroversy

abouttheviabilityofthenewphysicsandwithveryfewbooksavailableonthetopic,

sawpopularscienceasyetanothermeansofmakingnewphysicalknowledge

comprehensibleandaccessible.

EnglishbooksonthequantumatomappearedalittlelaterthaninGermany23

andhad

asomewhat

different

character.

Among

the

earliest

was

The

Atom,abook

by

theUSphysicist,inventorandprolificmodelbuilderAlbertCushingCrehore.

However,Crehoresbookwasofadifferentgenre,asitspurposewasnottoexpound

currentlyacceptedknowledgeaboutatomicstructurebuttopromotehisown

unorthodoxmodeloftheatom.Thishedidingreatdetail,includingsomeheavy

dosesofmathematics,andonhiswayheconfrontedwhatatthetimehadbecome

thestandardmodel,theoneofBohrandhisGermanallies.Crehoreadmittedthat

Bohrstheoryhasmadeaverystrongappealtophysicists,whowithsome

reservationsmaybesaidtohaveadopteditastheirguidingtheory,buthedidnot

finditspopularityjustified.24Likeotherphysicistsofaconservativeinclination,he

objectedthattherewasnothingintheBohratomthatvibratedwiththefrequencyof

theemittedlight.Crehoresownalternativewastomodifythelawsof

electrodynamicssoastomakethemcomplywiththequantumatom,buthis

alternativewasignoredbymainstreamphysicists.ReadersofCrehoresbookcould

23ThefirstbookwhichreferredtoBohrsatomicmodelwasactuallyEnglish,namelyabook

onXrayswrittenbyGeorgeW.C.Kaye,aphysicistattheNationalPhysicalLaboratory.G.

W.C.Kaye,Xrays:AnIntroductiontotheStudyofRntgenRays(London:Longmans,GreenandCo.,1914),onp.18,prefacedatedFebruary1914.24AlbertC.Crehore,TheAtom(NewYork:VanNostrand,1920),preface14June1919,onp.2.HisexpositionoftheBohratomappearedonpp.2430.ForCrehoreandhisviewsofatomic

structure,seeKragh2011(note12).


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16

findinitacriticalifnotunfairexpositionofthemainfeaturesoftheBohratomic

model.

OftheBritishbooksdealingwiththeBohrmodeloftheatom,weshallonly

refertofourpopularbookspublishedin1923.25Twoofthemwereextensivereviews

writtenbyphysicistsandmainlyaddressedtoanaudienceofphysicists,chemists

andengineers,althougheducatedlayreadersmightbenefitfromthemaswell.26

EdwardAndradesTheStructureoftheAtomgaveadetailedaccountofatomic

physics,both

nuclear

and

extra

nuclear,

including

alargely

qualitative

discussion

of

theBohratomanditsrelationtoexperiments.NormanRobertCampbellnotonly

coveredthesamegroundandatlargelythesamelevel,hisbookalsoappearedwith

thesametitle(bothbookswereprefacedApril1923).Thetwobookswere

informativeandcompetentoverviewsofthestateofartinatomicandquantum

physicsratherthanattemptstodisseminatethetopictoabroadaudience.Theycan

beseenasmorequalitativeandlessdemandingversionsofSommerfeldsAtombau.

Thethirdbooktobementionedwasofanaltogetherdifferentcharacter,foroncenot

writtenbyascientistbutbyasciencewriterandjournalist.

JohnW.N.Sullivanhadstudiedmathematicsandscience,butwithouttaking

adegree,beforeheturnedtoliteratureandpopularscience.Asasciencewriterhe

madehisnamewitharticlesfromthespringof1919onEinsteinsgeneraltheoryof

relativity,andhelaterwroteanumberofbooksonscience,literatureandculture.In

asmallandunpretentiousbookof1923,entitledAtomsandElectrons,hecoveredthe

25AccordingtoaCatalogueofBritishScientificandTechnicalBooksissuedbytheBritishScienceGuild,in1925therewereonly3scientificbooksonquantumtopics(asubgroupunder

SpectraandMolecularPhysics)publishedinEngland,outofatotalof318physicsbooks.

Thecorrespondingfiguresfor1921were1and269.SeeRaykumariWilliamson,TheMakingofPhysicists(Bristol:AdamHilger,1987),p.10.26EdwardN.daC.Andrade,TheStructureoftheAtom(London:G.BellandSons,1923).N.RobertCampbell,TheStructureoftheAtom(Cambridge:CambridgeUniversityPress,1923).


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moderndevelopmentsinatomictheory,payingmuchattentiontotheideasofthe

structureofatomsduetothebrilliantyoungDanishphysicist,NielsBohr.27Among

thetopicshedealtwithinsomedetailwasthenewexplanationoftheperiodic

systemintermsofelectronicorbitsthatBohrhadexpoundedinhisNobellecture

andatotheroccasions.AlthoughnotabookexclusivelyaboutBohrsatomictheory,

nearlyathirdofitwasacompetentifnaturallycondensedaccountofthistheory.

ReaderswouldgettheimpressionthatmodernatomictheorywassolelyduetoBohr:

apartfrom

abrief

reference

to

Sommerfeld,

no

other

physicists

were

mentioned

as

contributorstothetheory.

AtomsandElectronswasexplicitlywrittenasapopularphysicsbook.It

appearedinHodderandStoughtonsseriesPeoplesLibrary,theobjectofwhich

wasinsomedegreetosatisfythateverincreasingdemandforknowledgewhichis

oneofthehappiestcharacteristicsofourtime.Probablytokeepthepricelow(itsold

for2s6d),itcontainednopictures,whichwasunusualforabookofitskind.Another

popularatombookwasTheABCofAtoms,writtenbythefamousphilosopher,

mathematicianandauthorBertrandRussell,who,atthetime,supportedhimselfand

hisfamilyasawriterofallkindsofpopularbooks.28Basicallyappealingtothesame

audienceasSullivansbook,RussellsABCwassomewhatmoredemanding.Like

mostpopularisers,Russellsoughttoillustratethequiteunintelligiblefeaturesof

Bohrstheorybymeansofanalogies.AccordingtoBohr,electronsmoved

instantaneouslyandmysteriouslyfromonestationaryorbittoanother;accordingto

27JohnW.N.Sullivan,AtomsandElectrons(London:HodderandStoughton,1923),onp.121,reviewedinNature,113(1924),379380.OnSullivanasasciencewriter,seeWhitworth1996(note1),whoalsomentionsafewotherEnglishpopularbooksdealingwithatoms,including

OliverLodge,AtomsandRays:AnIntroductiontoModernViewsonAtomicStructureandRadiation(NewYork:GeorgeH.Doran,1924).28 BertrandRussell,TheAutobiographyofBertrandRussell,vol.2(London:AllenandUnwin,1968),p.152.


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Russell,Anelectronislikeamanwho,whenheisinsulted,listensatfirstapparently

unmoved,andthensuddenlyhitsout.29

Theyear1923wasagoodyearforpopularandsemipopularworksonthe

quantumatom.Afewphysicistsandsomesciencepopularisersjoinedforcesin

makingaccessibleandcomprehensiblethenewquantumtheory. Althoughtheir

effortsrangedwidelyintermsofexpositionanduserfriendliness,theyallwere

convincedthatquantumtheorywasimportantenoughtomeritpopularaccessibility

andacceptance.

Popular

quantum

theory

required

translating

mathematical

reasoningintoeverydaylanguageandimagesbasedoneverydayexperiences.In

ordertogoastepdeeperintothemeaningofpopularscienceatthetime,wenow

turntoabookpublishedinEnglishintheverysameyearasAndrades,Campbells,

Sullivans,andRussellsbooks;itwasatranslationofaDanishbookcowrittenbya

DanishlibrarianandDutchphysicist.ThestageofthebookwassetinCopenhagen.

4. TheCopenhagencontext:Bohr,Kramers,Holst,Klein

NielsBohrconsidereditimportanttoexpoundhisviewsofquantumandatomic

theorynotonlytothephysicscommunitybutalsotoabroaderscientificaudience.

Thishedidmostlyintheformoflectures,bothinDenmarkandabroad,andsomeof

theselecturesweresubsequentlypublished.Forexample,alecturegivenbeforethe

DanishPhysicalSocietyinDecember1913waspublishedintheDanishjournalFysisk

Tidsskriftin1914andseveralyearslaterinGerman,English,andFrench.InOctober

1921hedeliveredanimportantaddresstoajointmeetingofthePhysicalSocietyand

29BertrandRussell,TheABCofAtoms(London:KeganPaul,Trench,Trubner&Co.,1927),p.63.Thefirsteditionfromthesummerof1923wassoldat4s6dandprintedin3000copies(Whitworth1996,note1).Russellalsowroteapopularbookonrelativitytheory,TheABCofRelativity(London:KeganPaul,Trench,Trubner&Co.,1925),thefirsteditionofwhichwasprintedin2000copies.


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19

theChemicalSocietyinCopenhagen,andthisaddresswasalsopublished

internationally.ThesamewasthecasewithhisNobellectureinStockholmon11

December1922.However,Bohrfeltnoneed(andhadneithertime,nor,webelieve,

muchtalent)toexposehisviewsofatomicstructuretowideraudienceseitherinthe

formofmagazinearticlesorapopularbook.Hedidhoweverwriteanentryon

AtomforthethirteentheditionoftheEncyclopaediaBritannica,butwhenthevolume

appearedin1926muchofthecontentwasobsoletebecauseofthequantum

mechanicalrevolution.

30

TheclosestBohrcametowritingapopularbookonatomictheorywasThe

TheoryofSpectraandAtomicConstitution,asmallbookpublishedbyCambridge

UniversityPressin1922,whichalsoappearedinGermanandFrenchtranslations.31

Thebookwasacollectionofthreelectures,thetwoCopenhagenlecturesmentioned

above(from1913and1921,respectively)andapreviouslypublishedaddresstothe

GermanPhysicalSocietyof1920.Theprincipalobjectofthebookwastoemphasize

certaingeneralviewsinafreerformthanisusualinscientifictreatisesandtext

books,forwhichreasonreferencesandfootnoteswereleftout.32Bohr,likemany

otherphysicistsatthesame,sawpopularisationasameanstomakeclearand

30NielsBohr,Atom,EncyclopaediaBritannica,13thed.,Suppl.,vol.1(1926),262267.Itisinteresting,bothfromthepointofviewofpopularisationandthehistoryofphysics,to

compareBohrsarticlewiththefamousarticleonAtomthatMaxwellwroteforthe9th

edition

of

Encyclopaedia

Britannica

from

1875

(pp.

36

49).

Bohr

made

various

attempts

to

presentmodernatomicphysicstoageneralaudience,butmostlyinthepost1925period.See

FinnAaserud,ed.,NielsBohrCollectedWorks,vol.12(Amsterdam:Elsevier,2007).31N.Bohr,TheTheoryofSpectraandAtomicConstitution,translatedbyA.D.Udden(Cambridge:CambridgeUniversityPress,1922).N.Bohr,DreiAufstzeberSpektrenundAtombau(Braunschweig:Vieweg&Sohn,1922).N.Bohr,Lesspectresetlastructuredelatome:troisconfrences,translatedbyA.Corvisy(Paris:J.Hermann&Cie.,1923).AsecondEnglishandGermanedition,slightlyrevisedandprovidedwithacoupleofappendices,cameoutin

1924.32Bohr1922(note31,Englishedition),p.vi.


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20

accessiblethegeneraloutlineofcontemporaryatomictheory,eventhough,apart

fromBohrsconcessiontoreaderfriendliness,thebookwashighlytechnicaland,at

times,partlyobscure.YetinahighlylaudablereviewessayinNaturetheCambridge

physicistRalphFowlerevaluateditnotonlyasagreatworkbutalsoasonewhich

expoundedBohrsatomictheoryinasimplenonmathematicalwaywhichshould

becapableofbeingfollowedbyanyonewhoispreparedtoacceptthemathematical

theoremsonwhichtheworkisnecessarilybased.33Themathematicalintricacyof

atomicphysics

necessitated

anew

kind

of

popular

science

in

which

mathematical

symbolswerekepttoaminimuminfavourofthefundamentalphysicalmeaningof

themathematics.

WhatBohrdidnotdo,namely,writeacomprehensivepopularexpositionof

hisatomictheory,wasdonebyhisclosecollaborator,theDutchmanHendrik

AntonieKramers,andtheDanishphysicstrainedlibrarianandauthorHelgeHolst.

DanishreadersmightalsolearnaboutBohrstheoryfromexpositionsgivenbyother

Danishscientists,includingthedistinguishedchemistNielsBjerrum.34Before

discussingtheproductoftheKramersHolstcollaboration,TheAtomandtheBohr

TheoryofitsStructure,itwillbeusefultointroducethetwoauthors.WhileH.A.

(Hans)Kramersisnotwellknowntothepublic,inthehistoryofscienceheis

recognisedasoneofthegreattheoreticalphysicistsofthetwentiethcentury.35After

33RalphH.Fowler,TheStructureoftheAtom,Nature,111(1923),523525,onp.523.34NielsBjerrum,FysikogKemi,pp.71194inTorstenBrodn,NielsBjerrum,andElis

Strmgren,MatematikenogdeEksakteNaturvidenskaberidetNittendeAarhundrede(Copenhagen:Gyldendal,1925).Anotherexample,mostlyaimedatengineers,wasEdvardS.

Johansen,ModerneAnskuelseromElektricitetogStof(Copenhagen:Gjellerup,1920).35ThestandardbiographyofKramersisDresden(note8),whichcovershislifeandscience

inimpressivedetails.AbrieferaccountofKramersscontributionstophysicsisgivenby

HendrikCasimirinDictionaryofScientificBiography,vol.7(1973),491494.ForBohrsappreciationofKramers,seethememorialaddressinNederlandschTijdschriftvoor


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22

specialists.36Althoughby1922hehadwrittenonlyafewpopularworks,hewas

alreadyaseasonedpopulariser.Whatmattershereisthatintheearly1920shewas

BohrsclosestcollaboratorandintimatelyfamiliarwithBohrstheoryandhiswayof

thinking.NoonewasbetterqualifiedthanKramerstowriteauthoritativelyaboutthe

Bohratom.

HelgeHolstisunknowninternationally,butfarfromanuninterestingfigure.37

AfterhavinggraduatedinphysicsfromCopenhagenUniversityin1893,followedby

abrief

period

as

assistant

at

the

Polytechnic

College,

Holst

turned

to

acareer

as

writerandpublisherofpopularworksinscienceandtechnology.Theearlyyearsof

thetwentiethcenturywasinDenmark(asinmanyothercountries)aperiodinwhich

therewasagrowingmarketforpopularscience.Therewasagreatdealofinterest

amongDanishscientists,educatorsandjournaliststodisseminatethemarvelsof

modernscienceandtechnologytoanattentiveaudiencethirstingforknowledge.38

ThiswasaclimateinwhichHolst,whowasperhapsDenmarksleadingandmost

productivepopulariserintheperiod,thrived.HewaseditorofthejournalFrem,a

popularjournalofscienceandculture,andtheauthorofanumberofbooks,either

aloneorwithcoauthors.In1920HolstwasappointedlibrarianatthePolytechnic

College,inwhichpositionheremaineduntilhisdeathin1944,continuing

throughouthislifetowritearticlesandbooksonpopularscienceandtechnology.

36PeterRobertson,TheEarlyYears:TheNielsBohrInstitute19211930(Copenhagen:AkademiskForlag,1979),pp.51,9597.KramerstoBohr,12March1917,inJ.RudNielsen,

ed.,NielsBohrCollectedWorks,vol.3(Amsterdam:Elsevier,1976),p.654.KramersquicklylearnedtospeakandwriteDanish.37HansM.Hansen,HelgeHolst,FysiskTidsskrift,43(1945),14(inDanish).38OnpopularscienceinDenmarkintheearlytwentiethcentury,seeHelgeKragh,PeterC.

Kjrgaard,HenryNielsen,andKristianHvidtfeltNielsen,ScienceinDenmark:AThousandYearHistory(Aarhus:AarhusUniversityPress,2008),pp.357383.


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23

Holstsambitionswerenotlimitedtodisseminatingsciencetothegeneral

public.Healsohadaninterestinthefoundationofphysics,whichcausedhimto

revoltwhenhebecameacquaintedwithEinsteinsnewandcontroversialgeneral

theoryofrelativity.HewasthefirstDanetowritecomprehensivelyaboutEinsteins

theory,whichhedidin1919,characteristicallyinaliteraryandculturalmagazine.

ThesameyearhepublishedinGermanalengthymemoirintheproceedingsofthe

DanishRoyalAcademyofSciencesandLetters,whichhefollowedupbyapopular

bookin

Danish

and

two

papers

in

the

Zeitschrift

fr

Physik.In

these

works,

which

wereprimarilyofaphilosophicalnature,hecriticizedEinsteinstheoryand

advocatedhisownalternativeofacausalrelativitytheorybasedontheexistenceof

ahypotheticalneutralfieldgeneratedbythestars.AlthoughHolstwasnottaken

seriouslybymainstreamphysicists,hisviewswereknownanddiscussed.Ifindthe

workbyHelgeHolsttobepoor,Einsteinwroteinaletterof1920.39

InconnectionwithhisRoyalAcademymemoirof1919,Holstwasincontact

withBohr,whomheapparently(butinvain)triedtomakeinterestedinhisviews.40

NorwouldhehavefoundanysupportfromKramers,whoatthetimewastheonly

physicistinDenmarkwhohadasolidtechnicalknowledgeofgeneralrelativityand

39EinsteintoJosephPetzoldt,21July1920,inDianaK.Buchwaldetal.,eds,CollectedPapersof

Albert

Einstein,

vol.

10

(Princeton:

Princeton

University

Press,

2006),

p.

341.

In

his

authoritativereviewofrelativitytheory,WolfgangPaulireferredtoHolstsworks,

commentingthathefoundthehypothesisofacosmicneutralfieldtobeunnecessary.W.

Pauli,Relativittstheorie(Leipzig:Teubner,1921),p.560,aseparatereprintofhisarticleinEncyclopdiederMathematischenWissenschaften,vol.5,part2.40HolsttoBohr,fourlettersof1919,inArchiveforHistoryofQuantumPhysics(AHQP),

BohrScientificCorrespondence(film3,section4).SeealsoHolsttoKramers,5July1921,

AHQP,KramersCorrespondenceM/fno.8aSection6025.TheinformationaboutHolstand

thetheoryofrelativityisinpartbasedonanunpublishedMasterThesis(AarhusUniversity)

from1998byJonasCilieborg.


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24

in1920startedgivingregularcoursesonrelativitytheorytostudentsatthe

UniversityofCopenhagen.

Finally,theSwedishphysicistOskarKlein,whoreplacedKramersinwriting

andupdatingtheDanish1929editionofTheAtomandtheBohrTheory,wasanotherof

Bohrscloseassociates.41AfterhavingworkedonandoffwithBohrandKramers

from1918to1923,hewenttotheUniversityofMichigan,AnnArbor,andin1925he

returnedtoCopenhagen.Therehedidsomeveryimportantworkintheoretical

physics,including

afive

dimensional

theory

of

quanta

and

relativity

(Kaluza

Klein

theoryandKleinGordonequation),ananalysisofPaulDiracsnewtheoryofthe

electron(KleinsparadoxandKleinNishinascattering)andamajorcontribution

tothequantumtheoryofradiation(JordanKleintheory).In1930heleftDenmark

tobecomeprofessorofphysicsattheStockholmUniversityCollege.Inthepresent

contextitisrelevanttopointoutnotonlythatKleinwasBohrsfaithfullieutenant

(suchasKramerswas),butalsothatheengagedinpopularisingthenewatomic

physics.Forexample,in19221923hewroteacomprehensivesurveyofBohrs

theoryinKosmos,ayearbookpublishedbytheSwedishPhysicsAssociation.42

5. TheAtomandtheBohrTheoryofitsStructure

BeforegoingintodetailsaboutthecontentandimpactofthebookbyKramersand

Holst(Figure2),wefirstwouldliketomentionitspublicationhistory.Itwas

originallypublishedinDanishin1922,thesameyearthatBohrreceivedtheNobel

Prize.43However,atthetimeofwriting,thiswasunknown,andsothebookwasnot

41ForKleinslifeandcareer,seeAbrahamPais,TheGeniusofScience:APortraitGalleryofTwentiethCenturyPhysicists(Oxford:OxfordUniversityPress,2000),pp.122147.42OskarKlein,DenBohrskeAtomteorien,Kosmos,2(1922),5494and3(1923),72120.43ThetitlewasBohrsAtomteoriAlmenfatteligtFremstillet,meaningBohrsAtomicTheory,aPopularExposition.TheDanishtermalmenfatteligcorrespondstotheGerman


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25

Fig.2. FrontispieceofKramersandHolstsbookof1923,makingnodoubt

thatatomictheorywasthebrainchildofNielsBohr.

occasionedbytheprestigiousprizeandthemediaattentionitbroughtwithit.The

publisherwasthecountrysoldestandlargestpublishinghouse,Gyldendal,a

companynamedafteritsfounderSrenGyldendalwhoestablisheditin1770.There

islittledoubtthattheNobelPrizewasanimportantfactorinthedecisiontomakean

Englishtranslation,whichin1923waspublishedseparatelybyGyldendalin

England

and

by

Alfred

E.

Knopf

in

the

USA,

in

both

cases

with

a

foreword

by

Rutherford.ThetranslationwasdonebytheUSphysicsgraduateRobertBruce

gemeinverstndlichorliterallycommonlyintelligible.IntheDanisheditionsof1922and

1929Holstappearedasafirstauthor,whiletheorderoftheauthorsinthetranslationswas

KramersandHolst,presumablybecauseKramerswasbetterknownthanHolst.TheDanish

editionsof1922and1929werebothprintedin2000copies.Thisshouldbeseeninrelationto

thepopulationofthecountry,whichinthe1920swasabout3.3million,andmaybe

comparedwiththenumberofcopies(3000)ofRussellsABCofAtoms(note29).


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26

LindsayandhiswifeRachelTupperLindsay,whospenttheyears19221923in

CopenhagenonastipendfromtheAmericanScandinavianFoundation.44Itmayata

firstblushseemstrangethatBohrdidnotprovidetheDanisheditionwitha

foreword,butthiswouldhardlyhavebeenappropriateinabookthatcarriedhis

nameinthetitleandfocusedonhiswork.Thelackofaforeworddidnotimplyany

lackofinterestfromBohrsside.45

In1925TheAtomandtheBohrTheorywastranslatedintoGermanandSpanish,

andin

1927

itappeared

in

aDutch

translation,

possibly

occasioned

by

Kramerss

returntotheNetherlandstheyearbefore.46TheDutchversionincludedsectionson

thenewHeisenbergSchrdingerquantummechanicsanddifferedinminorrespects

fromtheearlierversions.47ThereasonwhytheKramersHolstbookwasnot

immediatelytranslatedforthelargeGermanmarketmayhavebeencompetition

44DuringhisstayinCopenhagen,R.BruceLindsayworkedunderBohrandKramers,and

thelatteraskedhimtoundertakethetranslation,muchofwhichwasactuallydonebyMrs.Lindsay.ApparentlyKramerswashimselfinvolvedinthetranslation.Ihaveusedthelast

twoweeksontheEnglishtranslationofmybookwithHolst,hewrotetoBohron11

October1923.SeeRudNielsen1976(note36),p.661.AfterhisreturntotheUSA,Lindsay

completedhisdoctoraldissertationbeguninCopenhagenandsubsequentlyentereda

distinguishedcareerinphysicsasprofessoratBrownUniversity.45Bohrdidwriteaforewordtoalaterpopularbookonatomicphysicscomingfromhis

instituteandwrittenbytwoofhiscollaborators,ChristianMllerandEbbeRasmussen.This

book,AtomerogAndreSmting[AtomsandOtherSmallThings](Copenhagen:Hisrchsprung,1938)followedthegeneralstructureoftheKramersHolstbook,butofcourse

extended

with

aspects

of

quantum

mechanics,

nuclear

physics

and

other

post

1925

developments.46TheGermanedition:DasAtomunddieBohrscheTheorieseinesBaues(Berlin:Springer,1925),translatedbyFritzArndt,aprofessorofchemistryattheUniversityofBreslau.TheSpanish

edition:EltomoysuEstructuraSegnlaTeoriadeN.Bohr(Madrid:RevistadeOccidente,1925),translatedbyTomsR.Bachiller.TheDutchedition:DeBouwderAtomen(Amsterdam:D.B.Centen,1927),translatedbyHenriC.Brinkman,reprinted1930andin1949underthe

titleDeBouwderAtomenenMoleculen.47KramerscontemplatedwritingaDutchtranslationasearlyas1923,whichappearsfrom

HolsttoKramers,29July1923,AHQP,M/fNo.8a,Sect.6026.


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27

fromsimilarbooksinGerman,inparticularKirchbergersEntwicklungder

Atomtheorie.48In1929asecond,updatededitionappearedinDanish,nowwiththe

assistanceofKlein.Thiseditionleftoutpartsofthe1922editioninfavouroftwonew

sections:oneonquantummechanicsandoneonwaveandparticledescriptionsof

lightandmatter,bothofwhichwereprimarilywrittenbyKlein.Whilethe

correspondenceprinciplewasgivenmuchattentioninthefirstedition,inthesecond

Bohrsnewprincipleofcomplementaritywassimilarlyhighlighted.

Theprefaces

of

the

two

publications

of

1922

and

1923

presented

Bohr

slightly

differently.TheDanisheditionreferredtoBohrastheyoungDane,whoin1913

advancedatheorythatnotonlyprovidedasurprisinglysimpleexplanationof

certainphysicalfacts,inthefaceofwhichphysicsuntilthenhadremained

perplexed,butalsoofferedundreamtofpossibilitiesforfutureresearch.According

totheBritishedition,ontheotherhand,Bohrsimplypavedthewayforareally

physicalinvestigationoftheproblem,namely,theproblemofexplainingintermsof

generallawsthephysicalandchemicalpropertiesoftheelements.TheDanish

prefacefurthermorestatedthatBohr,becauseoftherevolutionarycharacterofhis

ideas,forawhilehadtowalkalone,guidedbyhisextensiveknowledge,hisgreat

powerofcombinationand,notintheleast,hiscertaininstinct.Joinedbyother

physicistsinhisquestforthesecretsoftheatom,Bohrforawhilealmostseemedas

ifhewaslackingbehindtheothers,but,truly,theDanishprefaceboldlydeclared,

Bohrwassearchinginthedarkfarahead,andthus,physicalresearchtodayis

carriedoutunderthesignoftheBohriantheory.Attributingslightlylessheroismto

Bohr,theEnglishprefacefullyacknowledgedthecontributionofNielsBohr:

48ThisiswhatWaltherGrotriansuggestedinareviewof1925:W.Grotrian,DieNaturwissenschaften,13(1925),952953.


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28

Thepastdecadehaswitnessedanenormousdevelopmentatthehandsof

scientistsinallpartsoftheworldofBohrsoriginalconceptions;butthroughit

allBohrhasremainedtheleadingspirit,andthetheorywhich,atthepresent

time,givesthemostcomprehensiveviewofatomicstructuremay,therefore,

mostproperlybearthenameofBohr.

Thebookconsistsofsevenchapters,thefirstfourofwhichdetailimportanttheories

anddiscoveries

in

the

history

of

physics

and

chemistry

leading

up

to

Bohrs

theory

oftheatom.ThereismentionofDaltonsatomictheory,Mendeleevsdevelopment

oftheperiodtableofelements,Maxwellselectromagnetism,BalmersandRitzs

formulaeofatomicspectra(thebookcontainedcolourplatesofspectraproducedby

BunsenandKirchhoff49),andThomsonsandRutherfordsdiscoveriesoftheelectron

andthenucleus,respectively.Thetwoauthorsdidnotfailtopointoutseveral

contributionstophysicsmadebyDanishscientists,suchasLudvigA.Coldings

workofthe1840santicipatingtheprincipleofenergyconversation,Christian

Christiansensexperimentswithblackbodyradiationfromtheearly1880s,and

MartinKnudsensworkfromabout1915ongasesatverylowpressure.50

IntheiroutlineofthecoreofBohrstheory,KramersandHolstdwelledupon

thetwopostulatesorwhattheycalledfundamentalconcepts,thatis,theconstraint

49 Theseplatesofspectra,goingbacktotheearly1860s,werereprintedinnumeroustextson

spectrumanalysis.AccordingtoKlausHentschel,itwasthemostfrequentlyreprinted

scientificillustrationinthesecondhalfofthenineteenthcentury.K.Hentschel,MappingtheSpectrum:TechniquesofVisualRepresentationinResearchandTeaching(Oxford:OxfordUniversityPress,2002),p.48.50KramersandHolst(note9),p.25andp.33.ChristiansenwasBohrsteacherandservedas

professorofphysicsatCopenhagenUniversity18861912,afterwhichhewasfollowedby

Knudsen.


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ofstationarystatesandthefrequencycondition.51TheydepictedtheBohrmodelof

thehydrogenatominasimplifiedform,apointlikenucleussurroundedby

electronsmovingcircularly(orelliptically)instationaryorbits.Ineachofthese

orbits,theyexplained,theelectronfollowsthegeneralmechanicallawsofmotion,

butitcontradictsclassicalelectrodynamicsbyemittingnoelectromagneticwaves:

radiationisonlyemittedwhentheelectronpassesfromoneorbittoanother.

FromthebeginningoftheiroutlineofBohrstheory,KramersandHolst

emphasisedBohrs

attempts

to

preserve

and

develop

the

connection

between

quantumtheoryandclassicalphysicaltheoriesandobservations.Theydescribedthe

correspondenceprincipleasdifficulttoexplain,becauseitcannotbeexpressedin

exactquantitativelaws,anditis,onthisaccount,alsodifficulttoapply.52

Nevertheless,theauthorscitedseveralapplicationsofthecorrespondenceprinciple,

accordingtowhichthereisaformalcorrespondencebetweenthestatesdescribedby

ellipticelectronorbitsandtheradiationemitted(orabsorbed)duetotransitions

betweenthestates.However,theyalsopointedoutthatitisnotobviouswhythe

motionofanelectroninastationarystateshouldbedescribedinclassicalterms

whenthetransitionbetweenstatesisthoroughlyunclassical.KramersandHolst,

closelyfollowingBohrsowninterpretation,putitthisway:

WethenalsohereseetheoutwardsimilaritybetweentheBohrtheoryandthe

classicalelectrodynamics.Wemaysaythattheradiationoffrequency ,

producedbyasinglejump,correspondstothefundamentalharmonic

componentinthemotionoftheelectron,whiletheradiationoffrequency 2,

emittedbyadoublejump,correspondstothefirstovertone,etc.Thesimilarity

51Ibid.,pp.117118,138.52Ibid.,p.139.


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is,however,onlyofaformalnature,sincetheprocessesofradiation,

accordingtotheBohrtheory,areofaquitedifferentnaturethanwouldbe

expectedfromthelawsofelectrodynamics.53

Unsurprisingly,givenKramerssinvolvementintheformulationandapplicationof

theprincipleofcorrespondence,thetwoauthorsdescribedtheprinciplein

considerabledetail,presentingitasoneofBohrsdeepestthoughtsandchief

guides.The

principle

of

correspondence

between

quantum

and

classical

theory

not

onlyhadturnedoutbeextraordinarilyfruitfulforatomicphysicists,butalsohas

madepossibleamoreconsistentpresentationofthewholetheory,anditbidsfairto

remainthekeystoneofitsfuturedevelopment.54

Likemostotherauthorsdescribingelementsofthenewatomictheorytoa

generalaudience,KramersandHolstusedaclassicalanalogytoillustratetheBohr

atom.Theyaskedtheirreaderstocomparetheatomwithahypotheticalmusical

instrumentconsistingofaseriesofcirculardiscsplacedoneoveranother,eachdisc

beingsmallerthantheoneabove.55Aballwouldmovefrictionlessaroundanyofthe

discs,correspondingtoasysteminastationarystate.Theballmightfalldowntoany

lowerdisc,emittingasound.Passingfromonestationarystatetoanother,thesystem

53Ibid.,pp.130131.Otheraspectsofcorrespondencebetweenquantumandclassicaltheory

mentioned

in

the

book

included

the

formal

agreement

between

the

Balmer

Ritz

formula

for

thehydrogenspectrumandBohrsquantizationpostulate,theagreementbetween

calculationsofthemagnitudeofionisationpotentialsbymeansofquantumandclassical

theory,thequantumtheorybasedderivationoftheRydbergconstant,andthecalculationof

morecomplicatedelectronmotionsthanthosewhichappearsintheunperturbedhydrogen

atom(p.141).54Ibid.,p.141.55TheacousticalanalogywasprobablyduetoHolst,whoinapaperfromthespringof1922

introducedittoillustrateBohrsideaofemissionofradiation.H.Holst,OmNielsBohrs

Vrk,Tilskueren(May1922),281287.


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31

wouldloseaquantityofenergyequaltotheworknecessarytoraisetheballagain.

Theenergylostbymovingfromonestatetoanotherwouldbeemittedasasound

fromtheinstrument.Ifthesmallestdiscwasgroovedinsuchawaythattheball

couldfallnofurther,thenthisfancifulinstrumentcanprovidearoughanalogywith

theBohratom.Wemustbeware,however,ofstretchingtheanalogyfartherthanis

hereindicated.56Theanalogynicelyillustratedthecorrespondencebetweenan

atomicsystemandclassicaldescriptions,butitalsoindicatedsomeoftheproblems

ofapplying

the

correspondence

principle.

As

Kramers

and

Holst

pointed

out,

correspondenceconsiderationsareapplicableonlytocertainaspectsofthetheory,

notallofthem.Moreover,thetheoryitselfsaysnothingaboutwhentoapplythe

principleofcorrespondence.Itwastosomeextentanadhocsolutiontoahostof

theoreticalproblems,and,furthermore,itraisedanumberofadditionalproblems.

Alwayseagertospottheoreticalproblems,NielsBohrwaskeentodiscuss

difficultissuesinrelationtoquantumtheoryandthecorrespondenceprinciple.

OskarKleinrecalledthat,inconversations,Bohrpreferredtotakeupunsolved

problems,aroundwhichhisthoughtmovedincessantly.57So,mostlikely,Kramers

andHolstwereinspiredbyBohrsfondnessofopenquestionswhentheychoseto

discussparticularproblemsofBohrstheoryintheirbook.Also,thewayinwhich

theyframedtheirdiscussionofthenewdifficultieswastypicalofBohrsthinking.

Theynever,asdid,forexample,BertrandRussellinhisABCofAtoms,saidthatthe

problemswouldprobablybesolvedbyphysicistsinthefuture,nordidthey,aswas

alsocommoninpopularbooksabouttheatom,simplyneglectproblematicissues.

Rather,inlinewithBohrsownapproach,theymadeapointofwarningagainstthe

56KramersandHolst1923(note9),p.120.57O.Klein,GlimpsesofNielsBohrasScientistandThinker,pp.7493inStefanRozental,

ed.,NielsBohr:HisLifeandWorkasSeenbyhisFriendsandColleagues(Amsterdam:NorthHolland,1967),onp.77.


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ideathattheBohrtheorycouldbeusedtoderiveeverythingthathappensinthe

atomandsoallinnature.58

Eversince1913,criticsofBohrstheoryhadobjectedtowhattheyconsidered

theseriousconceptualandmethodologicalproblemsassociatedwiththetheory.59

KramersandHolstdidnoteschewtheseproblems,althoughneitherdidthey

conclude,assomecriticsdid,thattheywerereasonstodisbelieveBohrsviewofthe

constitutionofatoms.AsBohrhadhimselfemphasised,histheoryofferedno

explanationin

the

ordinary

sense

of

either

the

stationary

states

or

the

jumps

between

them.Echoingtheirmaster,KramersandHolstwrote:Weareinconceivablyfar

frombeingabletogiveadescriptionoftheatomicmechanism,suchaswouldenable

ustofollow,forexample,anelectronfromplacetoplaceduringitsentiremotion,or

toconsiderthestationarystatesaslinksinthewholeinsteadofisolatedgiftsfrom

above.60

AmongtheproblemsdealtwithbyKramersandHolstwasthepeculiarfact

thattheelectron,inmakingatransitionbetweentwo,nonadjacentenergylevels,

willnotemitalltheinterveningfrequencies,butsimplythefrequencycorresponding

totheentirejump.Rightfromthebeginningofthejump,theelectronseemsto

arrangeitsconductaccordingtothegoalofitsmotionandalsoaccordingtofuture

events.Butsuchagiftiswonttobetheprivilegeofthinkingbeingsthatcan

anticipatecertainfutureevents.61Inotherwords,theelectronmightseemtobe

58KramersandHolst1923(note9),p.132.59Ontheseproblems,seeHelgeKragh,ConceptualObjectionstotheBohrAtomicTheory

DoElectronsHaveaFreeWill?,EuropeanPhysicalJournalH(forthcoming).60KramersandHolst1923(note9),p.133.AccordingtoBohr,hisatomictheorydoesnot

attemptanexplanationintheusualsenseofthisword,butonlytheestablishmentofa

connexionbetweenfactswhichinthepresentstateofscienceareunexplained.Bohr1922

(note31),p.v.61KramersandHolst1923(note9),p.136.


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endowedwithakindoffreewill,itsmotionbeingdeterminedteleologicallyrather

thancausally.Thiswasanoldproblem,firstpointedoutbyRutherfordinaletterto

BohrofMarch1913,62andKramersandHolstmadenoattempttosolveit.Following

Bohr,theychosetoconsidertheparadoxicalbehaviourofatomicelectronsa

stimulatingchallengetoourthinkingaboutthesubatomicworldratherthanareal

problemfortheBohratom.Itindicatedthatitmightbeimpossibletoobtaina

consistentpictureofatomicprocessesinspaceandtime.

Bypresenting

the

reader

with

an

analogy

of

the

atom

and

then

proceed

to

discussitsweaknesses,KramersandHolstillustratedBohrsownwayofworking.

Bohrlikedtofullyexplorethelogicalconsequencesandcontradictionsofanymodel

orconcept,onlyinordertocomeupwithnewmodelsandnewconcepts,which

couldalsobeexploredintermsoftheirweaknessesandambiguities.ForBohr,this

wassimplythewayheworked.Inapopularbookaboutscience,however,the

discussionofuncertaintiesandunknownsinthetheoryofatomshadtobelimited.

Mostlikelybecauseoftheirlengthypresentationofsomeoftheshortcomingsofthe

Bohrmodel,KramersandHolsthadtowarntheirreadersagainsttheimpression

thattheBohrtheory,whileitgivesusaglimpseintodepthspreviouslyunsuspected,

atthesametimeleadsusintoafog,whereitisimpossibletofindtheway.63Onthe

contrary,theyargued,thebestproofthatBohrstheorywasnoblindalleyfor

physicistswasitsabilitytopredictandaccountformanyphenomenawith

remarkableaccuracyandincompleteagreementwithexperimentalobservations.To

maketheirpoint,thetwoauthors,havingpresentedtheBohrtheory,turnedtheir

attentiontothefirstgreattriumphsinwhichthetheoryshoweditsabilitytoleadthe

62 RutherfordtoBohr,20March1913,inUlrichHoyer,ed.,NielsBohr.CollectedWorks,vol.2(Amsterdam:NorthHolland,1981),p.583.Formoreonthisproblem,seeKragh(note59).63Ibid.,p.138.


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waywherepreviouslytherehadbeennopath.64Thesetriumphsincludedthe

spectroscopicverificationsofthetheoryinthecaseofthehydrogenatomandalso

theconstructionofatomicmodelsofthehigheratomsinagreementwiththeperiodic

system.Beforeturningtotheatomicmodelsandtheirpictorialrepresentations,we

wanttocommentonasectioninDasAtomunddieBohrscheTheoriewhichdidnot

appearintheearlierEnglishedition.

Duetotherapidprogressofquantumtheory,by1925theBohratomwasnot

quitethe

same

as

ithad

been

two

years

earlier.

In

an

attempt

to

update

the

content

of

theGermanedition,itwasexpandedwithanewchapterontheinteractionoflight

andmatterwrittenbyKramers.Thischapterisofinterestbecauseitgivesaclearand

nontechnicalaccountofhowBohrandhisassistantsinCopenhagenlookedatthe

radiationproblem,whichinthelastphaseoftheoldquantumtheorybecame

increasinglyimportant.Tomakealongstoryshort,bylate1923Einsteinsideaof

localizedlightquanta(laterknownasphotons)hadbecomeacceptedbyasubstantial

partofthephysicscommunity,butnotbyBohrandKramersinCopenhagen.Based

onanideaofvirtualoscillatorsproposedbytheUSphysicistJohnSlater,who

stayedatBohrsinstitutefromDecember1923toJune1924,BohrandKramers

proposedanalternativetheoryoflightemissionbasedonthewavepictureoflight

andtheradicalhypothesisthatenergyandmomentumareconservedonly

statistically.Withenergynonconservationfollowedtheequallyradicalideathatthe

principleofcausalitymightnotbevalidinthesubatomicdomain.

TheshortlivedBKS(BohrKramersSlater)theoryarousedgreatattentionin

thephysicscommunity,iflittlesympathyoutsideCopenhagen,andinMay1925it

64Ibid.,p.142.


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35

wasdisprovedbyexperimentsmadebyWaltherBotheandHansGeigerinBerlin.65

WhenKramerswrotehischaptertotheGermanedition,theprefaceofwhichwas

datedMarch1925,thetheorywasstillaliveanditfiguredprominentlyinhis

exposition.

WhilecertainlyhopingthattheBKStheory(orwhatheconsistentlycalled

Bohrsnewview)wouldturnouttobecorrect,Kramersemphasiseditsunfinished

natureandmodestlycharacteriseditasonlyanattempttothrowalittlelightinthe

greatdarkness

of

our

ignorance

about

the

course

of

the

atomic

processes

essentiallyaworkingprogrammeforthetheorists.Astotheelementofacausality,

hepreferredtoconsideritratheramatteroftaste,althoughthereislittledoubtthat

hisowntaste(andBohrsaswell)wasacausal.ToKramers,theprincipleofcausality

wasafactofexperienceratherthanalogicalnecessity,andonecouldeasilyimagine

thatitbreaksdownforatomicprocesses.Similarly,oneshouldkeepanopenmind

withrespecttoaviolationofthelawofenergyconservation.Interestingly,Kramers

suggestedthatlargescaleenergynonconservationprocessesmightgoonhereand

now.Thereareindications,hesaid,thatinthehotstars,theprincipleofenergy

conservationcannotbeusedjustlikethat,butthatinthesebodiesthereoccurs,soto

speak,aspontaneouscreationofenergywhichcontributestomaintaintheenormous

radiationofenergythatthestarspourintospace.66

65

Much

has

been

written

about

the

BKS

theory

and

its

role

in

the

final

phase

of

the

old

quantumtheory.See,forexample,Dresden(note8),pp.4178,159215andSandro

Petruccioli,Atoms,MetaphorsandParadoxes:NielsBohrandtheConstructionofaNewPhysics(Cambridge:CambridgeUniversityPress,1993),pp.111133.AccordingtoDresden,the

treatmentoftheBKStheoryintheKramersHolstbookiswithoutmuchdoubtthemost

understandableexpositionoftheBKSideas(p.195).66KramersandHolst1925(Germanedition,note46),pp.123140.Thechapteralsoappeared

asaseparatearticleinDanish,seeH.A.Kramers,OmVekselvirkningenmellemStofog

Lys,FysiskTidsskrift,23(1925),2640.TheideathatstellarenergyisrootedinprocessesviolatingenergyconservationwaslatertakenupbyBohr,whoadvocateditfromabout1929


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36

6.Pictorial

atoms

InhisNobellectureof1922aswellasatotheroccasionsBohrhadaccountedforthe

mainfeaturesoftheperiodicsystemoftheelementsbymeansofatomicmodels

basedontwoquantumnumbers.Whilein1913heonlymadeuseoftheprincipal

quantumnumbern(withintegralvalues1,2,3,),todescribeellipticorbitsitwas

necessarytotakeintoaccountalsotheazimuthalquantumnumberkintroducedby

Sommerfeldin

his

1915

generalization

of

Bohrs

theory.

An

electronic

orbit

could

thenbecharacterizedasannkorbit,wherekcanattainthevalues1,2,,n.

Geometrically,thegreaterthedifferencebetweenthetwoquantumnumbers,the

greatertheeccentricityoftheellipticorbit.Onlyinthecasek=nistheeccentricity

zero,meaningthattheellipsedegeneratesintoacircle.

KramersandHolstdescribedBohrstwoquantumconstructionofatomsin

somedetail,providingitwithanumberofpicturesplacedattheendofthebook

(Figure3).Orbitswithevennweredrawninblack,thosewithoddninred,andall

theorbitswereroughlydrawntoscale.KramersandHolstnotedthattheirdiagrams,

seductivelylookinglikeimagesofrealatoms,shouldnotbetakentooliterally:

Althoughtheattempthasbeenmadetogiveatruepictureoftheseorbitsasregards

theirdimensions,thedrawingsmuststillbeconsideredaslargelysymbolic.Thusin

realitytheorbitsdonotlieinthesameplane,butareorientedindifferentwaysin

space.Inlinewiththeirpreviousdiscussionsoftheshortcomingsofthequantum

to1933.Wellawarethattheideawasspeculative,Kramersdidnotexpounditinanyofhis

scientificpublications.Indeed,oneofthefunctionsofpopularworksisthatscientistshave

greaterlibertyinsuggestingideasofaspeculativenaturethatwouldnotbefoundacceptable

inscientificarticles.


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37

Fig.3. The88electronorbitsofaradiumatomaccordingtoBohrstheoryof1921.The

ellipticorbitsareshownclosedforsimplicity,butshouldreallybeslightlyopen,astheellipsesslowlyprecess.Source:KramersandHolst1923(note9).

theory,theyfurthernotedthattherewasstillagooddealofuncertaintyastothe

relativepositionsoftheseplanes.67

Littleisknownabouttheoriginofthediagrams,butapparentlytheywere

madeonBohrsrequestforhislecturesandnotspecificallyforthebook.68Thetable

withthepicturesofatomswasincludedinboththeDanish,English,German,and

Spanisheditions(butnotintheDutcheditionof1927).However,whiletheDanish

67KramersandHolst1923(note9),p.192.68ThisinformationcomesfromH.A.Kramers,DasKorrespondenzprinzipundder

SchalenbaudesAtoms,Naturwissenschaften,11(1923),550559,onp.556.TheNielsBohrArchiveinCopenhagenpossessesanumberofglassslidesfromtheperiodwithatomic

pictures,butitisunknownwhetherthesearetheoriginalsusedbyBohrorreproductions

fromtheKramersHolstbook.


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38

editionof1922includedelevenelements(H,He,Li,C,Ne,Na,Ar,Kr,Cu,Xe,and

Ra),thecarbonatomwithitsbeautifulspatialsymmetryoffour21valenceelectrons

wasmissingintheothereditions.Why?WesuspectthatthereasonwasthatBohr

hadcometodoubthissymmetricconfigurationofthecarbonatom,whichsoon

turnedouttobetwo21electronsandtwo22electronsintheoutershell.69Atanyrate,

KramersandHolsttookaninterestinthereproductionofthediagramsinthe

translatededitions.Thus,inalettertoKramersof29July1923,Holstexpressed

concernthat

the

format

of

the

British,

German

and

Dutch

translations

would

not

be

bigenoughtoallowthediagramstobeincluded.Ifnot,newblocksprobablywould

havetobemade.70

Thecolouredplateswithpicturesofatomsthatwereattachedtothebookby

KramersandHolstundoubtedlyappealedtomanyreadersandwerealsoeminently

usefulforpublicpresentations.Theywerereusedatanumberofoccasions,firstby

KramersinanarticleinaspecialissueofNaturwissenschaften,publishedinJuly1923

andcelebratingthefirstdecadeofBohrstheory.Apartfromadvertisingthepopular

Danishbook,Kramersrepeatedthatthepicturesshouldnotberegardedastrue

representationsofatoms.Theyweremerelymeantasaroughillustration.71Shortly

latertheCanadianphysicistJohnMcLennan,attheUniversityofToronto,usedthe

picturesinhisaddresstotheLiverpoolmeetingoftheBritishAssociationin

September1923inwhichhegaveacarefulpresentationofBohrsrecentideasof

69Bohradmittedhismistakeinanappendixtothesecond(1924)editionofBohr1922(note

31),seep.138.Whereasthesymmetricstructureofthecarbonatomwascarefullydescribed

inthe1922editionoftheKramersHolstbook,itwasnotmentionedinthelatereditions.70HolsttoKramers,29July1923,AHQP,M/fNo.8a,Sect.6026.SeealsoHolsttoKramers,7

May1925,AHQP,M/fNo.8a,Sect.6027,concerningtheplatesintheSpanishedition.71Kramers1923(note68),p.556.ReferencetotheplatesandtheKramersHolstbookwas

alsomadebytheDutchphysicistDirkCosterinhiscontributiontothespecialissue.

Characteristically,CosterworkedatthetimeatBohrsinstitute.


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atomicstructure.ThepictureshavebeencopiedfromapaperbyKramersthathas

recentlyappearedandarestatedtobesimilartothosepreparedbyBohrforusein

hisownlectures.72TheEnglishtranslationoftheKramersHolstbookhadnotyet

appeared.

TheKramersHolstpictorialmodelsofatomscanbefoundinseveralother

casesofthepopularorsemipopularliterature,notalwayswithreferenceandrarely

withpermission.AndradewereunawareoftheplateswhenhewrotehisStructureof

the

Atom,but

the

following

year,

in

acontribution

to

ageneral

work

celebrating

the

progressinchemistry,heincludedpicturesofsomeofthesimpleratomicmodels

(He,Ar,Ne,Na).73Theatomicmodelsalsoappearedinapopularbookwrittenin

1924byLarsVegard,professorofphysicsattheUniversityofOslo(thenKristiania),

whowasinternationallyknownforhisresearchonthephysicsoftheaurora

borealis.74

ThesameyeartheatomicpicturesturnedupinanarticleintheSpanish

popularsciencejournalIbercaandprobablymanyotherplaces.ThearticleinIberca

wasatranslationofRutherfordsopeningaddresstothe1923BritishAssociation

meeting,whichdidnotinfactincludeanypicturesorreferencetothem.Theeditors

oftheSpanishjournalpastedthepicturesoftheatomstothearticletomakeitmore

inviting.75

72

John

C.

McLennan,

On

the

Origin

of

Spectra,

Report,

British

Association

of

the

Advancement

ofscience(London:J.Murray,1924),2558.73E.Andrade,TheStructureoftheAtom,pp.4355inEdwardF.Armstrong,ed.,ChemistryintheTwentiethCentury(London:ErnestBenn,1924),onp.53.74 LarsVegard,StoffetsOpbygningogAtomenesIndre(Kristiania:OlafNorlisForlag,1924).AlthoughVegardpaidtributetotheDanishphysicsgeniusNielsBohr,hisbookwasless

Bohrfocusedthanmostpopularphysicsbooksatthetime.75TheSpanishtranslationofRutherfordsaddressappearedinfoursequelsinIbercanos.357,542,545,and551.Onthisjournal,seeMariaC.Bosc,SomeNotesonthe

PopularizationofQuantumandAtomicPhysicsinSpain,19141927,pp.6174inArne


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40

Asalastexample,theKramersHolstpicturesturnedupintheprinted

versionintheBayerischeRadioZeitungofalecturebroadcastedbythePolishGerman

radiochemistKasimirFajans.76ItshouldbementionedthattheCopenhagenerswere

notaloneinpresentingvisualmodelsoftheatomforpedagogicalandeducational

purposes.Thus,asearlyas1918Sommerfeldmadeasketchofthehydrogenatom

whichafewyearslater,togetherwithamodelofthepositivehydrogenmolecule

ion,wasturnedintoathreedimensionalmodeldisplayedattheDeutschesMuseum

inMunich.

SimilarbutmorecomplicatedmodelsoftheBohrorbitalatom,basedon

calculationsmadebyLawrenceBraggandDouglasHartree,wereshownatthe

BritishEmpireExhibitioninLondon19241925andlaterattheScienceMuseum.77

Moreover,theDutchphysicistHeikeKamerlinghOnnes,aNobellaureateof1913for

hisfundamentalresearchinlowtemperaturephysics,madeuseofpictorialatomsin

hisattempttounderstandwhysuperconductivityisrestrictedtoafewmetals

(Figure4).Hereceivedthepictures,whichweremoreschematicversionsofthe

KramersHolstmodels,fromKramersinCopenhagen.78

Schirrmacher,ed.,CommunicatingScienceinthe20thCentury.MaxPlanckInstituteforthe

History

of

Science,

Preprint

385.

76Wehavethisinformationfromanunpublishedtalkof2007byArneSchirrmacher,see

slide22ofthepowerpointpresentationincludedinhttp://quantumhistory.mpiwg

berlin.mpg.de/eLibrary/hq1_talks/oldqt/06_schirrmacher.77ForthemodelsinMunichandLondon,seeSchirrmacher2009(note8).78HeikeKamerlinghOnnes,Rapportssurdenouvellesexpriencesavecles

supraconducteurs,CommunicationsfromthePhysicalLaboratoryoftheUniversityofLeiden,1924,Supplement50a.ForKamerlinghOnnessinterestinatomicmodels,seeTilmanSauer,

EinsteinandtheEarlyTheoryofSuperconductivity,ArchiveforHistoryofExactSciences,61(2007),159211.


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Fig.4. Theelectronicandlatticestructureofindium,accordingtoBohrsatomictheoryand

asusedbyKamerlinghOnnesinapaperonsuperconductingmetals.Source:Kamerlingh

Onnes1924(note78).

7. Receptionanddissemination

TheKramersHolstvolumewassuccessfulandwellreceivedinthephysics

communityasafineexampleofpopularscience.AccordingtoRutherfords

forewordtotheEnglishtranslation,thebookwasnotonlyaclearlywrittenand

accurateaccountofBohrsatomictheory,itwasalsocommendablebecauseofits

plainlanguageandlackofmathematics.Thisbook,Rutherfordsaid,shouldprove

attractivenotonlytothegeneralscientificreader,butalsotothestudentwhowishes

togainabroadgeneralideaofthissubjectbeforeenteringintothedetailsofthe

mathematicaltheory.79AsnotedbyananonymousreviewerinNature,thebook

79Foreworddated8October1923.


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42

differedfromotherpopularworksonatomictheorybyitsfocusonanddevotionto

Bohrswayofconceivingquantumandatomicphysics:Wehaveadiscussionin

everypartofwhichthespiritoftheBohrtheorywalksabroad.Therevieweragreed

withRutherfordastothebookspedagogicalqualitiesandalsothatitsusewasnot

restrictedtoageneralreadership.Thequantumatomwaswidelyseenasabstruse,

butthebook[is]extremelyvaluabletothenotinconsiderablenumberofphysicists

whofeeltheneedofageneralandauthoritativeaccountofthelatestspeculationson

thesematters.

80

SomeofthethemesmentionedintheNaturereviewessayalsoappearedina

longerandhighlyappreciativereviewbyGeorgeL.Clark,achemistatthe

MassachusettsInstituteofTechnologyandaspecialistinXrayanalysis.Itisalmost

asifBohrhimselfwerespeakingasnodoubtheis,Clarkcommented,

suggestingthatthetwoDanes,KramersandHolstengagedinakindofteleological

historiographybypresentingthehistoryofatomismassettingthestageforthe

adventoftheimmeasurablygreatcontributionofNielsBohr.Likesomeother

scientistsreviewingthebook,Clarkthought(probablyunrealistically)thatitwasa

workaccessibletotheproverbialmanonthestreet:

Itcanbeunderstoodbyanyonewithaverageintelligence;infact,itshould

provefascinatingtoallagesfromtwelvetofourteenup.Itisabookforthe

homelibrarytable,forthecollegelectureroom,forthescientistsreference

shelf,fortheministerwhowouldpreachtruthandfaith.Itisthekindofbook

80Reviewessay,ScienceforthePeople,Nature,113(1924),378380,ofKramersandHolst1923(note9)andSullivan(note27).Theassessmentthatthebook,althoughofapopular

nature,wasvaluabletoscientistsbecauseofitsauthoritativestatementofBohrsview,was

repeatedinareviewbyFrankHoyt,aUSphysicistwhoknewKramersfromhisstayin

Copenhagen19221924:AstrophysicalJournal,61(1925),453.


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whichmaybereadappreciativelyatasinglesittingintwoorthreehours,or

inbits,evenonastreetcar(thereviewerhasobservedthisinthree

instances).81

Bohrspentthelatefallof1923intheUSAandCanada,lecturingonhisatomic

theoryatseveraluniversities.TheprestigiousSillimanLecturesthathegaveatYale

Universitybetween6and15Novemberattractedmuchattentionandwerecovered

bythe

The

New

York

Times.The

day

after

the

first

lecture

the

newspaper

informed

its

readersthatLikenedtosolarsystem,he[Bohr]picturestheatomwithnucleus

correspondingtosun,andelectronstoplanets.On27January1924itnotedinits

booksectionthatTherecentlecturesatYaleandColumbiabytheDanishscientist,

NielsBohr,lendadditionalinteresttothepublicationofTheAtomandthe

BohrTheoryofItsStructurebyHelgeHolstandH.A.Kramers.

GiventhattheKramersHolstbookwaspracticallydevoidofmathematics,it

isabitcuriousthatitwasreviewedinatleasttwomathematicaljournals.Oneof

thesereviews,bytheViennesephysicistOttoHalpern,foundittobeaneasyand

understandablereadbutalsopointedoutthatKramersschapteronradiationtheory

failedtomentiontheComptoneffect,whichheconsideredamajordeficiency.82

Indeeditwas,forthescatteringeffectdiscoveredbyArthurComptonin1923was

generallytakenasstrong(ifnotcompelling)evidenceforthelightquantum.Butthen

neitherKramersnorBohrbelievedinthelightquantumandtheyalsodidnotbelieve

thattheComptoneffectproveditsexistencesincetheBKStheoryprovidedan

alternativeexplanation.Still,towriteaboutlightquantaandthenatureoflightinthe

81JournaloftheAmericanChemicalSociety,46(1924),13181319.82OttoHalpern,MonatsheftefrMathematik,35(1925),3233.Theotherreview,oftheEnglishedition,wasbyR.D.CarmichaelandappearedinBulletinoftheAmericanMathematicalSociety30(1924),374.


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springof1925withoutmentioningtheComptoneffectwasanaberrationthatmight

smellofpartisanship.

WefinallymentionareviewbyWalterGrotrian,aBerlinastrophysicistand

specialistinspectroscopy,whomistakenlybelievedthatbothauthorsbelongtothe

closelyknitcirclearoundNielsBohr.Kramerswasthewellknowncollaboratorof

N.BohrandHolstwasthoughttobelongtothesamegroup.Comparingthebookto

Kirchbergers,GrotriansuggestedthattheKramersHolstworkwasabetterbuy

becauseitcombined

atruly

popular

(gemeinverstndlich)

exposition

with

an

authoritativeaccountofBohrsatomictheory.83InstarkcontrasttoEinsteinstheory

ofrelativity,Bohrstheoryoftheatomreceivedalmostnoattentionfrom

philosophers.Russellwasanexception,butthenhisABCofAtomswasnot

philosophicalinnature.AnotherofthefewexceptionswasHaroldChapmanBrown,

aphilosopheratStanfordUniversity.Beingfearfulofgettingbeyondmydepthsin

theintricaciesofmodernphysics,hetookrecoursetoTheAtomandtheBohrTheoryof

itsStructurefromwhichhecitedapassageindicatingthecompletelackofknowledge

aboutanatomduringatransitionfromonestationarystatetoanother.Brownfound

thistobearevolutionaryspeculation,foritdeprivesmatterofitseternalexistence,

anessentialattributeundertheoldconception.84

Whilethegeneralpublic,whenpresentedwiththeKramersHolstpictures,

couldhardlyavoidbelievingthatthesewerenearlyauthenticrepresentationsof

whatatomsreallylooklike,specialistsinatomictheorywerewellawarethata

83Grotrian(note48).ItshouldbementionedthatDresden(note8),p.134,referstoa1924

reviewbyMaxvonLaue,alsoinNaturwissenschaften.Thisispuzzling,fornosuchreviewexistsandyetDresdenquotesfromit!84 HaroldC.Brown,TheMaterialWorldSnarkorBoojum?JournalofPhilosophy,22(1925),197214(onp.203),basedonanaddressdeliveredtotheAmericanPhilosophicalAssociation

on28November1924.Therevolutionarypassagethatarousedthephilosophersattention

appearedinBohrandKramers(note9),pp.133134.


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modelshouldnotbeconfusedwithreality.AlthoughBohrandKramersconsidered

thepicturesassymbolicratherthanconcreterepresentations,stillin1923theyhad

littledoubtabouttherealityoftheelectronorbits.Sure,theatomdidnotlooklike

thepicture,butitmightstillbesomethinglikeit.Otherphysicists,andespeciallythe

youngstersPauliandHeisenberg,heldmoreradicalviews,doubtingthevery

legitimacyofelectronorbits.

Bythesummerof1924thevisualanalogueoftheBohrorBohrSommerfeld

atomicmodel

was

fading

and

no

longer

considered

as

aviable

image

of

the

real

structureofatoms.Theconstitutionoftheatomintermsofatinypositivenucleus

surroundedatgreatdistancesbyasystemofelectronswasleftuntouched,andso

wasthepostulateofstationarystates;butfewleadingphysicistsbelievedinthe

planetaryanalogy,thattheelectronsactuallymovedindefiniteorbitswhose

geometrywascharacterizedbyquantumnumbers.Objectionstotheorbitalmodel

hadbeenaroundforsometime,raisedinparticularbyPauli,whoreachedthe

conclusionthattheconceptionofdefiniteandunambiguouslydeterminedelectron

orbitsintheatomcanhardlybesustained,ashewrotetoSommerfeld.85Itwasasif

suchmodelsemotionallyoffendedhim,andheseemstohaveassociatedthemwith

KramersratherthanBohr.InalettertoBohrof12December1924hepokedfunat

ourgoodfriendKramersandhiscolourfulpicturebooks,obviouslyareferenceto

theKramersHolstbookanditspictorialatomicmodels.86AsPaulisawit,insofar

onecouldspeakofatomicmodelsatall,ithadtobeamathematicalandnota

pictorialmodel.

85PaulitoSommerfeld,6December1924,inMichaelEckertandKarlMrker,eds,ArnoldSommerfeld.WissenschaftlicherBriefwechsel,vol.2(Berlin:VerlagfrGeschichtederNaturwissenschaftenundderTechnik,2004),p.177.86PaulitoBohr,12December1924,inKlausStolzenburg,ed.,NielsBohr.CollectedWorks,vol.5(Amsterdam:NorthHolland,1984),p.427.


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Ofcourse,withtheadventofquantummechanicsPaulisviewbecame

generallyacceptedandthepictorialorbitalmodelslostwhatevercredibilitythere

wasleft.YetthepictureslivedonintheDanish1929editionoftheKramersHolst

bookwhichwasrevisedbyOskarKleinandsupplementedwithachapteronthe

newquantummechanicsandBohrsinterpretationofit.Thetwocolourplates,

scientificallyunjustifiedastheywere,wereapparentlyfoundtobetoogoodtobeleft

out.

8. Conclusion:TheKramersHolstbookinapopularsciencecontext

Whilewebegintohaveahistoricalunderstandingofthescientificreceptionofthe

BohrtheoryindifferentEuropeancontexts,thepopularexpositionandreceptionof

theBohrtheorystillremainsrelativelyunexplored.Moreover,wehavelittle

understandingoftheinteractionbetweenatomicphysicsproperandpopularphysics

inthisperiod.Itisrelativelyeasytounderstandwhysomephysicistsandscience

popularisersattemptedtomakequantumtheorycomprehensibleinnon

mathematicallanguageandvisualimages.Theyviewedpopularscienceasawayin

whichtopropoundsomeofthelatestscientificideasaboutthestructureoftheatom;

physicistsdidsoastheyweregrapplingwiththemathematicalandconceptual

developmentofquantumtheory,sciencepopularisersastheywerestrugglingto

1112.2499 popularizing atom

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