Hendrik Antoon Lorentz's struggle with quantum theory Kox, AJ

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Hendrik Antoon Lorentz’s struggle with quantum theory
Kox, A.J.
DOI
10.1007/s00407-012-0107-8
Publication date
2013
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Archive for History of Exact Sciences
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Kox, A. J. (2013). Hendrik Antoon Lorentz’s struggle with quantum theory. Archive for History
of Exact Sciences, 67(2), 149-170. https://doi.org/10.1007/s00407-012-0107-8
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Arch.Hist.ExactSci.(2013)67:149–170
DOI10.1007/s00407-012-0107-8
Hendrik Antoon Lorentz’s struggle with quantum
theory
A.J.Kox
Received:15June2012/Publishedonline:24July2012
©TheAuthor(s)2012.ThisarticleispublishedwithopenaccessatSpringerlink.com
Abstract A historical overview is given of the contributions of Hendrik Antoon
Lorentzinquantumtheory.Althoughespeciallyhisearlyworkisvaluable,themain
importanceofLorentz’sworkliesintheconceptualclarificationsheprovidedandin
hiscritiqueofthefoundationsofquantumtheory.
1 Introduction
TheDutchphysicistHendrikAntoonLorentz(1853–1928)isgenerallyviewedasan
icon of classical, nineteenth-century physics—indeed, as one of the last masters of
thatera.Thus,itmaycomeasabitofasurprisethathealsomadeimportantcontribu-
tions to quantum theory, the quintessential non-classical twentieth-century develop-
mentinphysics.TheimportanceofLorentz’sworkliesnotsomuchinhisconcrete
contributions to the actual physics—although some of his early work was ground-
breaking—butratherintheconceptualclarificationsheprovidedandhiscritiqueof
thefoundationsandinterpretationsofthenewideas.Especiallyinhiscorrespondence
withcolleagues,suchasMaxPlanck,WilhelmWienandAlbertEinstein,hetimeand
againtriedtoclarifythequantumprinciplesandexploretheirconsequences.
InthispaperIwillgiveanoverviewofLorentz’sworkinquantumtheory,includ-
inghisinformalcontributionsindiscussionsandcorrespondence.Iwillfirstdiscuss
Lorentz’searlyworkonradiationtheory,inwhichhegivesaderivationofaradiation
lawfromclassicalelectrontheory.ThenIwilldiscussLorentz’s1908Romelecture
Communicatedby:JedBuchwald.
B
A.J.Kox( )
InstituteforTheoreticalPhysics,UniversityofAmsterdam,
Amsterdam,TheNetherlands
e-mail:[email protected]
123
150 A.J.Kox
insometechnicaldetail,becausethetheoryLorentzdevelopsinthelectureisadaring
newapplicationofGibbs’sstatisticalmechanicsandbecauseitsoutcomeisthatthe
mostgeneralclassicaltheoryonecanthinkofleadsinescapablytotheRayleigh–Jeans
radiationlaw.Akeyelementinthisderivationisthetheoremofequipartitionofenergy.
TheRomelecturewaswidelydiscussed,bothincorrespondenceandinpapers.As
wewillsee,inthediscussionswithLorentzandalsoinhislaterworkthreequestions
willkeepcomingback.Thefirstoneisthevalidityofthelawofequipartitionofenergy
anditspossiblemodifications.Asecondtheme,howtodealwiththequantumdiscon-
tinuity(alsodiscussedinthelecture,althoughlessexplicit),wouldsoonevolveinthe
specificquestionofwheretolocalizethediscontinuity:intheether,intheinteraction
betweenmatterandether,intheresonatorsorelsewhere.Athirdtheme,notexplicitly
presentintheRomelecture,butgainingmuchprominenceinlaterwork,isthematter
ofthelightquantum.Doindependentlightquantaexist,andifso,howtoreconcile
theirexistencewithtypicalwavephenomenasuchasinterference?Thislastthemeis
inparticulardiscussedincorrespondencewithEinstein.
ThepaperconcludeswithadiscussionofthewayLorentzdealtwiththeparallel
developments of matrix mechanics and wave mechanics. He carefully studied both
theories but engaged with them in totally different ways: he extensively discussed
andcriticizedwavemechanics,especiallyincorrespondencewithErwinSchrödinger,
whereasinthecaseofmatrixmechanicshelimitedhimselftotryingtomasterthefor-
malismandgraspingitsconsequences.Althoughhehadmuchrespectandadmiration
fortheworkoftheyoungergeneration,heremainedcriticalandtotheendcouched
hisquantumworkinclassicalterms.
2 Earlyworkonradiationtheory
Lorentz’sworkonradiationtheoryischaracterizedbythesamemethodologicalcon-
sistencythatwefindthroughouthisworkandthatculminatedinhismaturetheoryof
electronsinthefirstdecadeofthetwentiethcentury.Hebaseshimselfonanontology
ofparticlesandfields,or,tousehisownterminology,onastrictseparationofmat-
ter—consistingofchargedandneutralparticles—andether.Thelatteractsascarrier
oftheelectromagneticaction,causedbythepresenceofchargedparticles.Etherand
matterareseparateentities,thatactoneachother,butmustbetreateddifferently.The
particles obey the laws of classical mechanics; the ether is governed by Maxwell’s
equations.1
ThefirstpaperIwanttodiscussdatesfrom1903,andhasthetitle:“Ontheemis-
sionandabsorptionbymetalsofraysofheatofgreatwave-lengths”(Lorentz1903).
LorentzbaseshimselfonthetheoriesofPaulDrudeandEduardRieckefortheelectri-
calconductivityofmetals,inwhichitisassumedthatmetalscontainlargequantities
offreelymovingelectrons,thatregularlycollidewiththemetalatoms.Applyinghis
electrontheorytothismodel,Lorentzcalculatestheenergydensityofradiationemit-
ted by the electrons by assuming that they only radiate when colliding with atoms,
1 InLorentz’searlyworktheetherisstilltreatedasamechanicalsystem,butgraduallyitlosesallofits
mechanicalpropertiessaveone:itsimmobility.SeeKox(1980)forfurtherdetails.
123
HendrikAntoonLorentz’sstrugglewithquantumtheory 151
limitinghimselftothecaseoflongwavelengths.Inadazzlingshowofmathematical
prowesshefindsthattheradiationisdistributedaccordingtotheRayleigh–Jeanslaw
(which,ofcourse,wasnotyetknownbythatnamein1903)andalsothatitconforms
tothelongwavelengthlimitofPlanck’sbrand-newradiationlaw:
8πkT
f(λ,T)= . (1)
λ4
In this paper Lorentz makes his first comments on Planck’s quantum hypothesis.
Hewrites:
[…]thehypothesisregardingthefinite“unitsofenergy”,whichhasledtothe
introduction of the constant h, is an essential part of the theory; also that the
questionastothemechanismbywhichtheheatofabodyproduceselectromag-
neticvibrationsintheaetherisstillleftopen.Nevertheless,theresultsofPlanck
aremostremarkable.
Andlateron,whencomparinghisresultwithPlanck’swork,hecomments:
There appears therefore to be a full agreement between the two theories in
thecaseoflongwaves,certainlyaremarkableconclusion,asthefundamental
assumptionsarewidelydifferent.
ItisinterestingtonotethatinhispaperLorentzcharacterizesPlanck’stheoryinthe
followingway:
It will suffice to mention an assumption that is made about the quantities of
energy that may be gained or lost by the resonators. These quantities are sup-
posed to be made up of a certain number of finite portions, whose amount is
fixed for every resonator; according to Planck, the energy that is stored up in
aresonatorcannotincreaseordiminishbygradualchanges,butonlybywhole
“unitsofenergy”,aswemaycalltheportionswehavejustspokenof.
AccordingtoThomasKuhn,thisisan“anomalous”readingofPlanck’swork,that
Lorentzcorrectedlater.2 CloserstudyofLorentz’spublishedandunpublishedutter-
ances shows, however, that Lorentz never strayed very far from this interpretation.
Forinstance,inhis1908Romelecture(seeSect.3),heusesalmostidenticalwords,
whereas Kuhn uses a quotation from a letter from Lorentz to Wilhelm Wien (to the
effectthatprocessesintheethertakeplaceinacontinuousway),whichwaswritten
a bit after the lecture, to argue that Lorentz had dropped his earlier interpretation.3
WhatLorentzwasuncertainabout,aswillbeshowninSect.6below,waswherethe
discontinuitylay:intheinteractionbetweenetherandmatter(i.e.,theresonators)or
intheinteractionbetweentheresonatorsandtheothermatter.
2 SeeKuhn(1978,p.138).
3 SeeKuhn(1978,p.194).Theletterinquestionisdated6June1908;itisreproducedinKox(2008)as
Letter171.SeealsoSect.4.1belowforafurtherdiscussionoftheLorentz–Wiencorrespondence.
123
152 A.J.Kox
3 TheRomelecture
FromLorentz’slaterworkonradiationtheory,itbecomesclearthatthepaperdiscussed
intheprevioussectionsetsthemethodologicalstageforlaterdevelopmentsalongsim-
ilarlinesandthatitscriticaltoneaboutthemysteryoftheunderlyingmechanismin
Planck’stheoryofenergyelementsremainsanimportanttheme.
Thefirstimportantoneofthelaterpapersisthe1908Romelecture.Itwasdelivered
atasomewhatstrangevenue,namely,the4thInternationalCongressofMathemati-
ciansinApril1908.Itsimpacthasbeenconsiderable,ifonlybecauseitmadeindis-
putablyclear thatPlanck’s energy elements werefundamentally foreigntoclassical
mechanicsandelectrodynamics.
The lecture, entitled “The distribution of energy between ponderable matter and
ether”,4startswithalengthyandverygeneraldiscussionofthefoundationsofmechan-
ics, kinetic gas theory, and electrodynamics, clearly meant for an audience of non-
physicists.ItisusefultofollowLorentz’sreasoninginsomedetail,becauseitbrings
outthesystematicwayhehassetupthispaper.
Lorentzfirstreviewsthebasicsofradiationtheory.FromKirchhoff’sworkitfollows
thatauniversalradiationlawexists:theenergydensityofradiationinthewavelength
intervalλ,λ+dλattemperatureT isgivenby:
F(λ,T)dλ, (2)
with F afunctionthatisindependent ofthespecificpropertiesofthebodythathas
producedtheradiation.
Next Lorentz discusses the law of equipartition of energy, Boltzmann’s work in
kineticgastheory,andtheatthattimenotwidelyknownstatisticalmechanicsofGibbs,
asanalternativetoBoltzmann’sapproach.Hestressesthatthephasespaceapproach
takenbyGibbsonlyworksifthesystemunderconsiderationcanbedescribedusing
Hamilton’s equations, so that the ensemble behaves like an incompressible fluid (in
otherwords,ifLiouville’stheoremholdsfortheensembledensity).Hethenintroduces
theensembledensityofthecanonicalensembleintheform:
ϕ =Ce−E/Θ (3)
andexplainshowonecandeterminemacroscopicquantitiesfromensembleaverages.
Lorentznowturnstoelectromagnetism.Hearguesthatoneneedstobasethistheory
onavariationalprincipleoftheform:
(cid:2)
δ (L−U)dt =0 (4)
4 Thelecturewaspublishedindifferentversionsandinvariousplaces;seeLorentz(1908a)inthebibliog-
raphyformoredetails.
123
HendrikAntoonLorentz’sstrugglewithquantumtheory 153
with L the magnetic energy and U the electric energy. This becomes the standard
Lagrangianfortheelectromagneticfieldifonetakes:
(cid:2)
1
L = H2dV (5)
2
and
(cid:2)
1
U = D2dV (6)
2
whereDisthedielectricdisplacementandHthemagneticforce.Notethat,although
theintegrandin(3)hastheformofa“standard”lagrangian,inthiscasetheterms L
andU donothavetheirusualmeaningsofkineticandpotentialenergy,respectively.
ItwillbecomeclearinthefollowingwhyLorentzisusingthissuggestivenotation.
Havingsetthestage,Lorentzproceedstoconsiderthemostgeneralphysicalsys-
tem he can think of. It consists of charged particles (‘electrons’), neutral particles
(‘atoms’),andether(i.e.,electricandmagneticfields),enclosedinarectangularbox.
The particles are all in motion; the electrons may be free or bound inside of atoms.
Thissystemcanbedescribedbyfoursetsofgeneralizedcoordinates:
– {q }fortheneutralparticles,
1
– {q }forthechargedparticles,
2
– {q ,q(cid:2)}fortheelectricfield.
3 3
While{q }and{q }haveastraightforwardmeaning,the‘coordinates’{q ,q(cid:2)}havea
1 2 3 3
morecomplicatedinterpretation.Foreachinstantoftimeonecansplittheelectricfield
intotwoparts:thefirstisthefieldthatwouldexistifallchargedparticleswereatrest
at their positions q , while the second part obeys the source-free Maxwell equation
2
∇·D=0.ThislatterpartcanbeexpandedinaFourierseriesofthemodesthatfitin
thebox;{q ,q(cid:2)}arethecoefficientsappearinginthisexpansion.Thus,thethethree
3 3
componentsofDcanbewrittenas:
(cid:3) uπ vπ wπ
D = (q α+q(cid:2)α(cid:2))cos xsin ysin z
x 3 3 f g h
u,v,w
(cid:3) uπ vπ wπ
D = (q β+q(cid:2)β(cid:2))sin xcos ysin z (7)
y 3 3 f g h
u,v,w
(cid:3) uπ vπ wπ
D = (q γ +q(cid:2)γ(cid:2))sin xsin ycos z.
x 3 3 f g h
u,v,w
Here f,g,harethelengthsofthesidesoftheboxandu,v,wareintegersrunningfrom
1to∞.5 Foreachcomponentandforeachset{u,v,w}threedirectionsaredefined,
perpendiculartoeachother.Oneisdeterminedbythevector(u,v,w),andtheother
f g h
two,correspondingtothetwopolarizationstatesofthefield,havethedirectioncosines
5 Theparticularchoiceofsinesandcosinesisdictatedbytheboundaryconditionsinthebox:thesidesof
theboxaresupposedtobeperfectlyconducting,whichmeansthatDisalwaysperpendiculartothesides.
123
154 A.J.Kox
α andα(cid:2),β andβ(cid:2),andγ andγ(cid:2),respectively.Thecoefficients{q ,q(cid:2)}(which,fol-
3 3
lowingLorentz’susage,willbeabbreviatedto{q }inthefollowing)obviouslydepend
3
on{u,v,w}andont.
The next step is to write the Lagrangian L −U as a function of the generalized
coordinates.BecauseLorentznowconsidersamoregeneralsystemthanjustelectro-
magneticfields,heincludeskineticenergytermsin L andpotentialenergytermsin
U,inadditiontothefieldterms.ForU hefinds
(cid:3)
1
U =U + fgh q2 (8)
0 16 3
withU0 afunctionofthecoordinatesq1 an(cid:4)dq2,accountingforthepotentialenergy
betweentheparticles;thesecondtermis 1 D2dV.
2
The term L consists in the first place of a part representing the kinetic energy of
theelectronsandoftheneutral(cid:4)particles,denotedby L0 andquadraticinq˙1 andq˙2.
Further,tofindthefieldpart 1 H2dV ithastobetakenintoaccountthatmagnetic
2
fields are generated by moving charges as well as by changing electric fields. This
givesrisetotermsinHproportionaltoq˙ andtoq˙ ,respectively,whichleadstoterms
2 3
in L proportional toq˙2,q˙2, andq˙ q˙ . The terms proportional toq˙2 are absorbed in
2 3 2 3 2
L ;theexplicitformofthepartproportionaltoq˙2isfoundbyfirstcalculatingD˙ from
0 3
(7)andthenusing∇∧H=(1/c)D˙ tofindH.Thefinalresultis:
fhg (cid:3) q˙2 (cid:3)
L = L + 3 + l q˙ q˙ . (9)
0 16c2 π2(u2/f2+v2/g2+w2/h2) ij 2i 3j
ij
In the last term the index i refers to the individual electrons; the index j abbrevi-
atesthedependenceofthequantitiesq˙ onu,v,wandthedirectioncosinesα,β,γ.
3
Accordingly,thecoefficientsl dependonu,v,w,α,β,γ andonthecoordinatesq .
ij 2i
From this Lagrangian the Lagrange equations follow easily. Lorentz explicitly
writes down the equations for q and shows that they give rise to standing waves,
3
withwavelength
2
λ= (cid:5) (10)
u2/f2+v2/g2+w2/h2
WheneverthereisavalidLagrangianformalism,onecanalsowritedownHamilto-
nianequations.ThatdoesnotmeanthatGibbsianstatisticalmechanicscanbeapplied
to the system under consideration yet. A major obstacle remains: because there are
infinitelymanytermsinthesum(7)therearealsoinfinitelymanycoordinatesq ,so
3
thatphasespacewouldbecomeinfinitelydimensional,precludingtheexistenceofa
meaningfulensembledensity.Lorentz’sworkroundsolutionistointroducewhathe
calls“fictitiousconnections”(“liaisonsfictives”)intheetherbywhichstandingwaves
withsmallerwavelengthsthansomevalueλ areexcluded.Ascanbeseenfrom(10)
0
this means that an upper limit is imposed on the values taken by u,v,w. Lorentz
justifieshisconditionbypointingoutthatonecanmakeλ assmallasonewishes.To
0
this“fictitious”systemGibbsianstatisticalmechanicsisthenapplied.
123
HendrikAntoonLorentz’sstrugglewithquantumtheory 155
Lorentznowreturnstoexpression(3)fortheensembledensity.Hefirstnotesthatin
L thetermL containstermsoftheform(1/2)mq˙2.BecauseE = L+U,theexpo-
0 1
nentialin(3)containsthesetermsaswell.Takingtheensembleaverageof(1/2)mq˙2
1
using (3) (i.e., calculating the mean kinetic energy of a neutral particle), now gives
(1/2)Θ;forthethree-dimensionalmotionoftheparticlesthisbecomes(3/2)Θ.Ear-
lierinthepaper,Lorentzhasexplainedthatoneofthemostimportantresultsofkinetic
gastheoryisthatthemeankineticenergyofamovingmoleculeoratomisequaltoαT,
withT thetemperatureandαauniversalconstant(nottobeconfusedwiththedirec-
tioncosineintroducedearlier).Thus(3/2)Θ =αT (or,inmodernnotation,Θ =kT).
Inthisway,LorentzextendsthestandardinterpretationofΘ formechanicalsystems
tohismuchmorecomplicatedsystemofparticlesandfields.
NowLorentzturnstothesecondtermin(8).Sincethetermsinthissumarequa-
draticinq ,acalculationsimilartotheoneaboveshowsthatinanensembleaverage
3
eachtermwillcontribute(1/2)Θ =(1/3)αT tothemeanelectricenergy.Takinginto
(cid:2)
accountthetwopolarizationstatesrepresentedbythecoordinatesq andq ,wegeta
3 3
totalcontributionbytheq ’sof2αT/3.Thiscanalsobeinterpretedasthecontribution
3
ofonemode(u,v,w)tothemeanelectricenergy.
Returningtotherectangularbox,itiseasytoseethatthenumberofmodeswith
wavelengthsbetweenλandλ+dλthatfitinthebox(whichissupposedtobesuffi-
cientlylarge)isequalto
4π
fghdλ. (11)
λ4
Takingintoaccounttheearlierresultforthemeanelectricenergypermode,Lorentz
finds
8παT
dλ (12)
3λ4
fortheenergydensity.Becausethemeanmagneticenergyisequaltothemeanelectric
energy,thetotalmeanelectromagneticenergydensityisgivenbytwicethisexpression,
sothattheradiationfunction(2)isnowgivenby:
16παT
F(λ,T)= (13)
3λ4
ThisistheRayleigh–Jeanslaw.
In this way, Lorentz has generalized his earlier paper on long-wave radiation in
metals,inwhichhefirstspecifiedamechanismbywhichradiationisgeneratedand
thenexplicitlycalculatedtheenergy-densityofthisradiation.
Lorentzofcourserealizestheconsequencesofhisresult.Itisclearlyincontradic-
tion with the observed radiation curve, which shows a maximum when plotted as a
functionofλ.Moreover,itimpliesthatinthecaseofamaterialbodyinequilibrium
withtheetherthelatterwillcontainaninfiniteamountofenergyandtheenergywill
123
156 A.J.Kox
becomeconcentratedinevershorterwavelengths.6 Thishadalreadybeenconcluded
byJeans.AsLorentzremarks:
[…]whenJeanspublishedhistheory,Ihadhopedthatoncloserinspectionone
couldshowthatthetheoremofequipartitionofenergyonwhichhebasedhim-
self cannot be applied to the ether and that in this way one could find a true
maximumofthefunctionF(λ,T).Theprecedingconsiderationsseemtoprove
thatthisisnotthecaseandthatJeans’sconclusionswillbeinescapableunless
thefundamentalhypothesesofthetheoryareprofoundlymodified.7
This is a crucial conclusion. To summarize: Lorentz has shown that the valid-
ity of the equipartition theorem for material particles inescapably implies its valid-
ity for his more complicated mechanical–electromagnetical system (or, using his
own words, for the ether). This then immediately leads to the Rayleigh–Jeans
law.8
Isthereawaytoreconciletheexperimentalresultswithwhathehasfound,Lorentz
wonders.Onethingiscertain:forlongwavelengthsthelawissatisfactory;theprob-
lemliesintheshort-wavelengthregime.Apossiblesolutionisthatthemaximumin
the observed curve is an artefact of the experiment, perhaps due to the fact that the
radiatingbodiesusedintheexperimentsarenotblackforsmallwavelengthsandthus
radiatemuchlessenergyforthesewavelengthsthanisassumed.Inthiswayequilib-
rium between radiation and matter will take a very long time to set in—it is in fact
neverobserved.
InthefinalparagraphsLorentzemphasizesthathedoesnotpretendtohaveprovided
thedefinitivesolutiontotheradiationproblem.Thewayoneproceedsintheoretical
physics, he argues, is to examine the relative likelihood of various hypotheses and
theoriesforagivenphenomenonandstudytheconsequencesthatfollowfromthose
hypotheses. In the case of the Planck radiation law versus the Rayleigh–Jeans law,
one has to conclude that the latter is very hard to bring in agreement with experi-
ments, whereas Planck’s law is in good agreement with them but requires a funda-
mental change in our thinking about electromagnetic phenomena. This is already
clear if one looks at a freely moving electron emitting radiation with a continu-
ousfrequencyspectrum.ThequestionremainshowtoapplyPlanck’shypothesisof
energy elements in this case. Lorentz concludes by expressing the hope that future
experiments will provide firm evidence for one or the other of the two radiation
laws.
6 ThisiswhatPaulEhrenfestdubbedthe‘ultravioletcatastrophe’.
7 “[…]lorsqueJeanspubliasathéorie,j’aiespéréqu’enyregardantdeplusprès,onpourraitdémontrerque
lethéorèmedel’“equipartitionofenergy”,surlequelils’étaitfondéestinapplicableàl’éther,etqu’ainsi
onpourraittrouverunvraimaximumdelafonctionF(λ,T).Lesconsidérationsprécédentesmesemblent
prouverqu’iln’enestrienetqu’onnepourraéchapperauxconclusionsdeJeansàmoinsqu’onnemodifie
profondémentleshypothèsesfondamentalesdelathéorie.”
8 AsEinsteinhadalreadyshown,giventhevalidityoftheequipartitionlaw,theRayleigh–Jeanslawfollows
evenwithoutinvokingtheapparatusofstatisticalmechanics.SeeSect.4.2belowfordetails.
123
HendrikAntoonLorentz’sstrugglewithquantumtheory 157
4 ReactionstotheRomelecture
4.1 WilhelmWien
OncetheRomelecture’scontentsbecameknownamongthephysicists,itstirredup
quitesomeemotion.WilhelmWienwrotetoArnoldSommerfeldon18May1908:
ThelectureLorentzdeliveredinRomehasdisappointedmegreatly.Thathedid
notdomorethanpresenttheoldtheoryofJeanswithoutpresentinganewpoint
of view is in my opinion a bit shabby. […] This time Lorentz has not shown
himselfasaleaderofscience.9
Wien points out in rather strong terms that the question of the validity of Jeans’s
law—orratheritsnon-validity—isapurelyexperimentalmatter.Heemphasizesthat
Lorentz’s theoretical views on this point are irrelevant, because experiments show
enormousdeviationsfromJeans’slawinaregionwhereonecaneasilyestablishhow
muchtheradiatingbodydeviatesfromablackbody.
WienalsocommunicatedhisobjectionstoLorentzhimself,thoughinarathermore
cautiousway,inaletterdated17May1908:10
WithmuchinterestIhavereadthelectureyougaveinRome.Ithinkthatitis
veryusefultocontinuetokeepalltheoreticalpossibilitiesinmind.ButIdonot
thinkthatanyone whohaseverdoneexperimentsinthefieldofradiationwill
admitthatthereiseventheremotestpossibilityforthetheoryofJeanstoreach
agreementwithexperience.11
He then points out that one can easily determine, by measuring their absorptive
power,thattheradiatingbodiesusedinexperimentsdepartatmostafewpercentfrom
ideal black bodies and that the discrepancies of Jeans’s law with experiment are so
largethatthereisnowaytheoryandexperimentcanbereconciled.Theletterfinishes
withanadmonitionofsorts:
Ifearthatfurtherresistanceandclingingtoviewsthataretoosimplewillbean
impedimenttotheprogressofscience.12
9 “DerVortrag,denLorentzinRomgehaltenhat,hatmichschwerenttäuscht.Daßerweiternichtsvor-
brachtealsdiealteTheorievonJeansohneirgendeinenneuenGesichtspunkthineinzubringenfindeich
etwasdürftig.[…]LorentzhatsichdiesmalnichtalseinFührerderWissenschafterwiesen.”SeeEckart
andMärker(2000,nr.132).
10 SeeKox(2008,Letter170).
11 “IchhabemitgrossemInteressedenVortraggelesendenSieinRomgehaltenhaben.Ichglaubedass
esdurchauszweckmässigistalletheoretischenMöglichkeitendauerndimAugezubehalten.Aberich
glaubenicht,dassirgendjemand,derjemalsexperimentellaufdemGebietederStrahlunggearbeitethat,
Ihnenzugebenwird,dassfürdieTheorievonJeansauchnurdieentferntesteMöglichkeitbestehtmitder
ErfahrunginÜbereinstimmungzukommen.”
12 “Ichfürchtedaher,dasseinlängeresSträubenundFesthaltenanzueinfachenVorstellungenhemmend
aufdenFortschrittderWissenschaftwirkenkann.”
123