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1
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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