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Voi.UMs 17 APRIL —JULY, 1945 NUMBERs 2—3

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The Institute for Advanced Study, Princeton, New Jersey

HE present volume to which scientists ofmany nations from three continents have

contributed, notwithstanding the adverse times,gives proof indeed that Professor Niels Bohr's60th birthday, on October t, 1945, is not onlyhis private, personal day of celebration, but aday of observance throughout the scientificcommunity of physicists. '

While many outstanding scholars of all timeshave obtained their fundamental insights insolita'ry labor secluded from the world, NielsBohr, thanks to his inspirIng personality, hasgained contact, in proportion as his scientificwork grew and shaped itself, with an ever-increasing number of people among whom hefound many collaborators and pupils. After twodecisive years in Rutherford's laboratory inManchester, he returned in I916 as a professorto his birthplace, Copenhagen, where in 1920 the"Institut for Teoretisk Fysik" was founded.Soon this institute made Copenhagen attractscientists from all parts of the planet as the"Capital of Atomic Physics. " As director of the

' Each of the authors contributing to this issue wouldlike to express his individual debt and gratitude to Pro-fessor Bohr, but editorial arrangements leave it to thisauthor to convey that message from the entire group.

The author is greatly indebted to Dr. M. Delbruck,Physics Department, Vanderbilt University, for the trans-lation of the original manuscript into English, and forsuggestions concerning its content.

laboratory which was attached to the institute,Bohr found an opportunity, along with his maintheoretical work, to supervise experimental re-search in which he had been taking a keeninterest since his early youth. The discovery inthis laboratory of the element hafnium by Costerand Hevesy was the result of a close collaborationbetween theoretical and experimental researchas well as between physics and chemistry, which,in Bohr's theory of atomic structure, v ere forthe first time founded upon common principles.As Bohr's theory united distinct branches of

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science, thus Bohr himself integrated, in lecturesat international congresses and at those carefullyplanned conferences in Copenhagen, the diversescientiFic standpoints and epistemological atti-tudes of the physicists, and thereby imparted toall participa. nts in those conferences the feelingof belonging, in spite of all their dissensions, toone large family.

Without going into the details of Bohr's workwe shall briefly characterize some aspects of thegeneral development of the fundamental con-cepts of the quantum theory of the structure ofatoms. This theory took its proper inceptionwhen Bohr succeeded in the happy synthesis ofRutherford's nuclear atom with the ideas basedoo the existence of a quantum of action whichwere implied in Planck's theory of heat radiationand the further development of these ideas in

PAULI

Einstein's interpretation of the photoelectriceffect. Bohr formulated his postulates originallyin the following form

"(1) That the dynamical equilibrium of the systems in

the stationary states can be discussed by help of theordinary mechanics, while the passing of the systemsbetween different stationary states cannot be treated on

that basis.(2) That the latter process is followed by the emission

of a homogeneous radiation, for which the relation betweenthe frequency and the amount of energy emitted is the onegiven by Planck's theory. "

With these postulates Bohr achieved a theo-retical interpretation of the previously baSingregularities of the spectra. The ambiguity of theconceptual basis —clearly expressed in Bohr'sformulation of the first postulate —by means ofwhich this interpretation was accomplished,became particularly apparent in the assumptionof two kinds of frequencies which were supposedto differ from each other in the general case,according to the two postulates, although theycoincide in the classical pictur" an objectionablefeature to many physicists. On the one handthere were the frequencies of the emitted radia-tion associated with a pair of stationary states,the initial and the final state of a "transitionprocess;" and on the other baird, the kinematicalfrequencies of the particles in the mechanicalorbits corresponding with their stationary states.

However, the later development which led tothe elimination of the concept of the mechanicalorbit from the theoretical description was fore-shadowed in Bohr's famous "correspondenceprinciple, " or "correspondence argument. " Hecould show, first for systems with simple periodicmotions, that in the limiting case of largequantum numbers where the energy values ofdifferent stationary states come to lie relativelyclose together, the emission frequencies, calcu-lated by means of the second postulate coincideasymptotically with the harmonics no of thefundamental frequency co of the periodic me-chanical orbit, if one identifies the integer r withthe difference n' n" of the value—s of the quan-tum numbers in the initial and final states,

' Phil. Mag. 26, 1 (1913), contained as Paper I in Pl).The numbers in brackets refer to the list at the end ofthis introduction.

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respectively. ' However, according to the classicalconception, these frequencies should all beemitted simultaneously; according to the quan-tum theory, the occurrence. of the various transi-tions is described by statistical laws, first givenby Einstein in their general form (spontaneousemission, induced emission, absorption). In thelimiting case of large quantum numbers, men-tioned above, the frequency of occurrence of atransition is proportional to the square of theamplitude of the "corresponding" harmonic, theamplitudes of the mechanical motion thus be-coming "amphtudes of probability. "Bohr's pupilKramers has shown how this correspondencemay be utilized for the estimation of intensitiesof spectral lines also in the case of small quantumnumbers.

Already in 1913, Bohr4 proved that the postu-late of the asymptotic identity of the mechanicalfrequencies with the frequencies given by thequotient of the energy 'differences of the station-ary states and Planck's constant suffices tocalculate the constant of Balmer's formula ofthe hydrogen spectrum, also called Rydberg'sconstant, from charge and mass of the electronand the quantum of action (including the cor-rection due to the finite mass of the nucleus).It was clear from the arguments given in thispaper that, for the calculation of this constant,the assumption of the exact validity of classicalmechanics for the stationary'states is unneces-sary, if one accepts Balmer's formula as anempirical law. On the basis of the extension ofthe rules of quantization, particularly by Som-merfeld and his students, Bohr L2$ generalizedthe correspondence principle so that it couldalso be applied to the so-called multiple periodicsystems. Simultaneously he advanced the theoryof these systems by giving the method of secularperturbations of which Kramers made interestingapplications.

In a qualitative way this theory was successfulin interpreting the properties even of complicatedatoms. One could classify their energy levels by

' Phil. Mag. 22, 506 (1914)and 28, 394 (1915),containedin L1$ as Papers VI and IX. See also especially Paper X,which was earlier withheld from publication.

4 Compare Essay I in l 3g, which is a translation of anaddress delivered before the Physical Society of Copen-hagen in December, 1913 and printed in Fysisk Tidsskrift12, 97 (1914).

NIELS BOHR ON HIS 60TH BIRTHDAY

quantum numbers, establish selection rules,interpret x-ray spectra, describe the formationof inner shells in the periodic system, includingthe rare earths. Notwithstanding these successes,it became more and more apparent that aquantitative formulation of the endeavor ex-pressed in the correspondence principle, particu-larly the calculation of transition probabilitiesand of the energy levels of atoms with more thanone electron, would be possible only if oneabandoned the idea of visualizing stationarystates by means of classical kinematics. Duringmy stay at Bohr's institute in Copenhagen in1922 and 1923, I was impressed by the cautious-ness with which these classical models were used

by Bohr in contrast to other physicists. Healways emphasized their provisional character,and in his deductions preferred to fall back onthe limiting case of large quantum numbers, forwhich alone there existed a dependable corre-spondence between classical and quantum theory.This attitude is rejected in a formulation of thefirst postulate which Bohr gave at this time I 4),and which may here be given for comparisonwith the original formulation:

"The 6rst postulate of the quantum theory for an iso-lated atomic system states that, among the kinematicallyconceivable relative motions of the particles of the atom,there exist certain states, the so-called stationary states,which are distinguished by a peculiar stability, shown bythe fact, that every permanent change in the motion ofthe isolated system must consist in a complete transitionfrom the original to another of these stationary states. "

The assumption of the validity of classicalmechanics for the stationary states was formu-lated separately from the fundamental postu-lates. There is here an example of the subtlety ofBohr's style. For those readers who are notfamiliar with the developmental history of Bohr'spapers, these shades of meaning are difficult toappreciate. He knew well what he wished not tosay when he strove in long sentences to expresshimself in his scienti6c papers.

The critical attitude towards the use ofkinematic-mechanical pictures led to anotherdevelopment. Although momentary doubts as tothe exact validity of the law of conservation ofenergy and momentum as applied to individualelementary processes were soon abandoned, thepicture of virtual oscillators introduced in this

connection as a generalization of the oscillatorsin the classical electron theory of light refractionproved useful. Using this concept, and boldlyextrapolating the result of classical mechanics,Kramers established the first law which heldexactly even for the case of small quantumnumbers, a formula which correlated dispersionphenomena with transition probabilities for thespontaneous emission of light. It was later ex-tended to the incoherent scattering of light; alsoin other cases one was able to guess correctlyquantitative rules which the energies of station-ary states and the probability amplitudes hadto ful611.

The ground was thus prepared for the decisiveadvance which came with Heisenberg's matrixtheory (1925). In this theory the probabilityamplitudes of the virtual oscillators and theenergy values of the stationary states were forthe first time derived by means of a coherentmathematical formalism. Soon thereafter (1926)Schrodinger, using de Broglie's idea of matterwaves, discovered his famous wave equation, theperiodic solutions of which proved to be equiva-lent with the matrix theory. The formal methodswere now at hand for a consistent description ofthe quantum phenomena, but many problems ofphysical interpretation had yet. to be solved inorder to elucidate the foundations of the theory.The discussions of the Solvay congress of 1927,in which Bohr participated, give a vivid pictureof these difficulties. After Born's statisticalinterpretation of Schrodinger's function and theestablishment of the general quantum-mechanicaltransformation theory which was carefullyworked out by-Dirac, the clari6cation of theissues made further progress. Finally Heisenbergdiscovered his principle of indeterminacy, andintuitively realized its great importance. It wasBohr, however, who gave the simple and correctderivation of this principle from the propertiesof wave packets, a derivation which today canbe found in all textbooks. ' He also emphasizedthe importance of the general, time-dependent,solution of Schrodinger's equation for the dis-cussion of the transition to classical mechanicsin those cases in which the scattering of thewave packets is insigni6cant.

' See Essay 1 in L6].

i00 K. PAULI

By means of a thorough discussion of numerousimaginary experiments Bohr showed that theconcept of complementarity characterizes theessential physical content of the new'theories.In harmony with the principle of indeterminacyhe defines this concept in the following words:

"Any given application of classical concepts precludesthe simultaneous use of other classical concepts which ina different connection are equally necessary for the elucida-tion of the phenomena. "'

Well-known examples of this mutual exclusionof concepts are: momentum and position of aparticle, recoil at the emission of a photon andthe coherence of light emitted in differentdirections, wave and corpuscle. According toBohr' the notion of complementarity serves

"to symbolize the fundamental limitation, met with inatomic physics, of our ingrained idea of phenomena asexisting independently of the means by which they areobserved. "

It is indeed this limitation which makes thetheory logically consistent. The "transitionprocesses" of the theory in its earlier form arenow replaced by the discontinuous selection fromthe theoretical possibilities of one case by the actof observation "here and now. " The theoreticalpossibilities themselves are subject to statisticallaws with probability amplitudes that varycontinuously as functions of time.

Bohr has always looked upon quantum me-chanics as the precise fulfillment of the programwhich he had in mind in his original formulationof the fundamental postulates. In harmony withquantum mechanics, he characterizes the "cor-respondence argument" as expressing

"our endeavor, by means of a suitably limited use ofmechanical and electromagnetic concepts, to obtain astatistical description of the atomic phenomena thatappears as a rational generalization of the classical physicaltheories, in spite of the fact that the quantum of actionfrom their point of view must be considered as an irra-tionality. "

Indeed, wave mechanics or quantum me-chanics in their present form may be consideredas the key for translating the results of classicaltheory into a quantum language compatible with

s Introductory survey in (6g, p. IO.~ See 1 5), Nature, p. 423.' See [5), Nature, p. 422.

the existence of the quantum of action. For sucha translation the canonical formalism, whichderives the form of the equations of motion fromthe so-called Hamilton function or Hamiltonian,was shown to be an excellent tool. However,quantum mechanics, in borrowing the form ofthe Hamiltonian from classical theory, takesover also a duality in its foundation, namely theconcepts of particle mechanics and the conceptsof the theory of the electromagnetic field ofMaxwell and Lorentz. As a consequence, thepresent form of quantum theory does not explainthe atomicity of electric charge and forms nological connection between the elementary quan-tum of charge and the quantum of action.

Whatever one may thirik about the foundationof quantum mechanics from an epistemologicalpoint of view, it is quite apparent from thesituation which arose by the creation of thistheory that the road for future developmentswill not lead back but forward. Clues as to thespecific direction of this way forward will come,we think, not so much from philosophic discus-sions and postulations as from new experimentalresults concerning the reactions of elementaryparticles, particularly in the high energy region,and possibly from the enrichment, by the intro-duction of new formal concepts, of the theoreticalstudy of those consequences of the theory whichreveal a limitation in the applicability of itsmathematical formalism. We meet with one suchlimitation in the application of quantum me-chanics to the interaction between electromag-netic radiation and electrons. On the one hand,this interaction when developed into a powerseries of the Fine structure constant, due to thesmallness of this constant, yields a usableapproximation for processes of emission, absorp-tion, and scattering of photons, when only thatterm of the development is used in which theparticular process first occurs. On the otherhand, in the 1ogically complete form of the theoryin which the electromagnetic field i'tself is quan-tized (quantum electrodynamics), the higherapproximations are divergent. As a result certainsmall (but experimentally measurable) effectscannot, on the basis of the present theory, becalculated accurately. As an example we maycite the infiuence of the emission of a sma11

amount of energy, in the form of many photons

NIELS BOHR ON HIS 60TH BIRTHDAY iOi

of small frequency, on the scattering cross sectionof electrons under a specified angle by a Coulombfield of force, an eEect which must give rise tocorrection terms in Rutherford's well-knownformula. Ingenious attempts of very recent dateto extend the theory to those electrodynamiceffects expected as being small do not seem to besu%ciently successful. It is therefore probablethat the divergence diAiculties of the theorycannot be overcome without directly attackingthe more basic problems which are left untouchedby the present theory. Of these the most im-

portant ones are the interpretation of the ele-mentary quantum of electric charge and thetheoretical prediction of the types of elementaryparticles occurring in nature, and of theirmasses.

It would seem that this view is also in harmonywith an interesting paper by Bohr and Rosenfeld

t 7] concerning the physical interpretation ofthe uncertainty relations as implied in quantumelectrodynamics for the electromagnetic field offree radiation. In this paper Bohr proves himself,as so often, the master in the use of imaginaryexperiments. It is shown that the uncertaintyrelations required by quantum electrodynamicsfor the values of the various components of theheld strengths, averaged over finite space-timeareas, are actually verifiable, on principle. Thispaper is a good illustration of a remark which,much earlier, Bohr once made to the presentauthor. Ile said that his interest in physics wasnot so much that of a mathematician as that ofa craftsman and of a philosopher. In the paperreferred to, this fruitful combination is reRectedin the circumstance that the complicated mecha-nisms of springs and frames are based on thesimple principle that it is permissible to use as-test-bodies extended bodies with practicallyhomogeneous distribution of charge and mass,as long as no restricting assumptions are intro-duced regarding the elementary particles occur-ring in nature. As Bohr and Rosenfeld point out,a new epistemological situation may be expectedonly if the atomic constitution of the test bodiesis made an essential feature of the argument.

Space does not permit the discussion here ofBohr's interesting applications of his epistemo-

logical point of view of complementarity to thedomains of biology and psychology. ' Physicshowever will, in all likelihood, transcending thecorrespondence argument, turn to the problemsof the elementary particles and to the closelyrelated problem of the nature of the nuclearforces. It is clear that this physics of the futurewill be in need, just as the earlier developmentof atomic physics was, of intellectual coherenceand of a unifying order. Professor Niels Bohr,whose interest in the problems of nuclear struc-ture and of radioactivity reaches back to thoseearly days which he spent with his teacher LordRutherford and his collaborators, will be calledupon, more than anybody else, to play a leadingrole in the accom'plishment of this difficult task.His friends and students may therefore be per-mitted to express, on his 60th birthday, the hopethat circumstances may permit him soon toresume the physics conferences in Copenha, gen,so fruitful and stimulating for all who partici-pated.

LIST OF N. BOHR'S PUBLICATIONS REFERRED TO

[1$ Abhandtungen uber Atombau (Friedrich Vieweg andSohn, Braunschweig, 1921); translated from thePhil. Mag. of the years 1913—1916, including apaper which was withdrawn from publication in

1916.[2) "On the quantum theory of line spectra, Parts I and

II,"Kgl. Danske Vid. Sels. Math. Fys. Medd. [8jIV, No. 1 (1918).

[3] The Theory of SPectra and Atomic Constitution (Cam-bridge University Press, Teddington, England,1922).

[4g "On the application of quantum theory to the struc-ture of atoms. Part I:The fundamental postulates. "Supplement of the Proc. Camb. Phil. Soc., 1924(translated from Zeits. f. Physik 13, 117 (1923)).

[5$ "Light and Life, " address delivered at the Interna-tional Congress on light-therapy in Copenhagen,August, 1932; Nature 131, 421 and 457 (1933).(Compare also Naturwiss. 21, 245 (1933).)

[6g Atomic Theory and the Description of Nature (Cam-bridge University Press, Teddington, England,1934).

[7g N. Bohr and L. Rosenfeld, "Zur Frage der Mess-barkeit der elektromagnetischen Feldgrossen, " Kgl.Danske Vid. Sels. Math. Fys. Medd. XII, No. 8(1933).

' See [6g, Introductory Survey, and Essays III and IV.