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by CATHRYN CARSON

HAT IS A QUANTUM THEORY? We have

been asking that question for a long time, ever

since Max Planck introduced the element of dis-

continuity we call the quantum a century ago. Since then,

the chunkiness of Nature (or at least of our theories about

it) has been built into our basic conception of the world. It

has prompted a fundamental rethinking of physical theory.

At the same time it has helped make sense of a whole range of pe-

culiar behaviors manifested principally at microscopic levels.From its beginning, the new regime was symbolized by Plancks constant

h, introduced in his famous paper of 1900. Measuring the worlds departurefrom smooth, continuous behavior, h proved to be a very small number, butdifferent from zero. Wherever it appeared, strange phenomena came with it.What it really meant was of course mysterious. While the quantum era wasinaugurated in 1900, a quantum theory would take much longer to jell. Intro-ducing discontinuity was a tentative step, and only a first one. And eventhereafter, the recasting of physical theory was hesitant and slow. Physicistspondered for years what a quantum theory might be. Wondering how to inte-grate it with the powerful apparatus of nineteenth-century physics, they alsoasked what relation it bore to existing, classical theories. For some theanswers crystallized with quantum mechanics, the result of a quarter-centurys labor. Others held out for further rethinking. If the outcome wasnot to the satisfaction of all, still the quantum theory proved remarkably

THE ORIGINS OF THE QUANTUM THEORY

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successful, and the puzzlement along the way, despite its frustrations, canonly be called extraordinarily productive.

INTRODUCING h

The story began inconspicuously enough on December 14, 1900. Max Planckwas giving a talk to the German Physical Society on the continuous spec-trum of the frequencies of light emitted by an ideal heated body. Some twomonths earlier this 42-year-old theorist had presented a formula capturingsome new experimental results. Now, with leisure to think and more time athis disposal, he sought to provide a physical justification for his formula.Planck pictured a piece of matter, idealizing it somewhat, as equivalent to acollection of oscillating electric charges. He then imagined distributing itsenergy in discrete chunks proportional to the frequencies of oscillation. Theconstant of proportionality he chose to call h; we would now write e = hf.The frequencies of oscillation determined the frequencies of the emittedlight. A twisted chain of reasoning then reproduced Plancks postulatedformula, which now involved the same natural constant h.

Two theorists,Niels Bohr andMax Planck, at theblackboard.(Courtesy EmilioSegre` VisualArchives,Margrethe BohrCollection)

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Looking back on the event, we might expect revolutionaryfanfare. But as so often in history, matters were more ambigu-ous. Planck did not call his energy elements quanta and was notinclined to stress their discreteness, which made little sense in anyfamiliar terms. So the meaning of his procedure only gradually be-came apparent. Although the problem he was treating was pivotalin its day, its implications were at first thought to be confined.

BLACKBODIES

The behavior of light in its interaction with matter was indeed akey problem of nineteenth-century physics. Planck was interest-ed in the two theories that overlapped in this domain. The first waselectrodynamics, the theory of electricity, magnetism, and lightwaves, brought to final form by James Clerk Maxwell in the 1870s.The second, dating from roughly the same period, was thermo-dynamics and statistical mechanics, governing transformations ofenergy and its behavior in time. A pressing question was whetherthese two grand theories could be fused into one, since they startedfrom different fundamental notions.

Beginning in the mid-1890s, Planck took up a seemingly narrowproblem, the interaction of an oscillating charge with its elec-tromagnetic field. These studies, however, brought him into con-tact with a long tradition of work on the emission of light. Decadesearlier it had been recognized that perfectly absorbing (black)bodies provided a standard for emission as well. Then over theyears a small industry had grown up around the study of suchobjects (and their real-world substitutes, like soot). A small groupof theorists occupied themselves with the thermodynamics ofradiation, while a host of experimenters labored over heated bod-ies to fix temperature, determine intensity, and characterizedeviations from blackbody ideality (see the graph above). After sci-entists pushed the practical realization of an old ideathat a closedtube with a small hole constituted a near-ideal blackbodythiscavity radiation allowed ever more reliable measurements. (Seeillustration at left.)

An ideal blackbody spectrum(Schwarzer Krper) and its real-worldapproximation (quartz). (From ClemensSchaefer, Einfhrung in die TheoretischePhysik, 1932).

Experimental setup for measuring black-body radiation. (The blackbody is thetube labeled C.) This design was a prod-uct of Germanys Imperial Institute ofPhysics and Technology in Berlin, wherestudies of blackbodies were pursuedwith an eye toward industrial standardsof luminous intensity. (From Mller-Pouillets Lehrbuch der Physik, 1929).

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Now Plancks oscillating charges emitted and absorbed radiation,so they could be used to model a blackbody. Thus everything seemedto fall into place in 1899 when he reproduced a formula that a col-league had derived by less secure means. That was convenient; every-one agreed that Willy Wiens formula matched the observations. Thetrouble was that immediately afterwards, experimenters began find-ing deviations. At low frequencies, Wiens expression becameincreasingly untenable, while elsewhere it continued to work wellenough. Informed of the results in the fall of 1900, on short noticePlanck came up with a reasonable interpolation. With its adjustableconstants his formula seemed to fit the experiments (see graph atright). Now the question became: Where might it come from? Whatwas its physical meaning?

As we saw, Planck managed to produce a derivation. To get theright statistical results, however, he had to act as though the energyinvolved were divided up into elements e = hf. The derivation wasa success and splendidly reproduced the experimental data. Its mean-ing was less clear. After all, Maxwells theory already gave a beau-tiful account of lightand treated it as a wave traveling in a con-tinuous medium. Planck did not take the constant h to indicate aphysical discontinuity, a real atomicity of energy in a substantivesense. None of his colleagues made much of this possibility, either,until Albert Einstein took it up five years later.

MAKING LIGHT QUANTA REAL

Of Einsteins three great papers of 1905, the one On a Heuristic Pointof View Concerning the Production and Transformation of Lightwas the piece that the 26-year-old patent clerk labeled revolutionary.It was peculiar, he noted, that the electromagnetic theory of lightassumed a continuum, while current accounts of matter started fromdiscrete atoms. Could discontinuity be productive for light as well?However indispensable Maxwells equations might seem, for someinteresting phenomena they proved inadequate. A key examplewas blackbody radiation, which Einstein now looked at in a way dif-ferent from Planck. Here a rigorously classical treatment, he showed,

Experimental and theoretical results onthe blackbody spectrum. The datapoints are experimental values; Plancksformula is the solid line. (Reprinted fromH. Rubens and F. Kurlbaum, Annalender Physik, 1901.)

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yielded a result not only wrong but also absurd. Even where Wienslaw was approximately right (and Plancks modification unnecessary),elementary thermodynamics forced light to behave as though it werelocalized in discrete chunks. Radiation had to be parcelled into whatEinstein called energy quanta. Today we would write E = hf.

Discontinuity was thus endemic to the electromagnetic world.Interestingly, Einstein did not refer to Plancks constant h, believinghis approach to be different in spirit. Where Planck had looked atoscillating charges, Einstein applied thermodynamics to the lightitself. It was only later that Einstein went back and showed howPlancks work implied real quanta. In the meantime, he offered a fur-ther, radical extension. If light behaves on its own as though com-posed of such quanta, then perhaps it is also emitted and absorbed inthat fashion. A few easy considerations then yielded a law for thephotoelectric effect, in which light ejects electrons from the sur-face of a metal. Einstein provided not only a testable hypothesis butalso a new way of measuring the constant h (see table on the nextpage).

Today the photoelectric effect can be checked in a college labo-ratory. In 1905, however, it was far from trivial. So it would remain

Pieter Zeeman, Albert Einstein, and PaulEhrenfest (left to right) in ZeemansAmsterdam laboratory. (Courtesy EmilioSegre` Visual Archives, W. F. MeggersCollection)

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for more than a decade. Even after Robert Millikan confirmedEinsteins prediction, he and others balked at the underlying quan-tum hypothesis. It still violated everything known about lights wave-like behavior (notably, interference) and hardly seemed reconcil-able with Maxwells equations. When Einstein was awarded the NobelPrize, he owed the honor largely to the photoelectric effect. But thecitation specifically noted his discovery of the law, not the expla-nation that he proposed.

The relation of the quantum to the wave theory of light would re-main a point of puzzlement. Over the next years Einstein would onlysharpen the contradiction. As he showed, thermodynamics ineluctablyrequired both classical waves and quantization. The two aspects werecoupled: both were necessary, and at the same time. In the process,Einstein moved even closer to attributing to light a whole panoplyof particulate properties. The particle-like quantum, later named thephoton, would prove suggestive for explaining things like the scat-tering of X rays. For that 1923 discovery, Arthur Compton would winthe Nobel Prize. But there we get ahead of the story. Before notionsof wave-particle duality could be taken seriously, discontinuityhad to demonstrate its worth elsewhere.

BEYOND LIGHT

As it turned out, the earliest welcome given to the new quantumconcepts came in fields far removed from the troubled theories ofradiation. The first of these domains, though hardly the most obvi-ous, was the theory of specific heats. The specific heat of a substancedetermines how much of its energy changes when its temperature israised. At low temperatures, solids display peculiar behavior. HereEinstein suspectedagain we meet Einsteinthat the deviance mightbe explicable on quantum grounds. So he reformulated Plancks prob-lem to handle a lattice of independently vibrating atoms. From thishighly simplistic model, he obtained quite reasonable predictionsthat involved the same quantity hf, now translated into the solid-state context.

There things stood for another three years. It took the suddenattention of the physical chemist Walther Nernst to bring quantum

(From W. W. Coblentz, Radiation,Determination of the Constants andVerification of the Laws in A Dictionaryof Applied Physics, Vol. 4, Ed. SirRichard Glazebrook, 1923)

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theories of specific heats to general significance. Feeling his waytowards a new law of thermodynamics, Nernst not only bolsteredEinsteins ideas with experimental results, but also put them onthe agenda for widespread discussion. It was no accident, and to alarge degree Nernsts doing, that the first Solvay Congress in 1911dealt precisely with radiation theory and quanta (see photographbelow). Einstein spoke on specific heats, offering additional com-ments on electromagnetic radiation. If the quantum was born in 1900,the Solvay meeting was, so to speak, its social debut.

What only just began to show up in the Solvay colloquy was theother main realm in which discontinuity would prove its value. Thetechnique of quantizing oscillations applied, of course, to line spec-tra as well. In contrast to the universality of blackbody radiation, thediscrete lines of light emission and absorption varied immensely fromone substance to the next. But the regularities evident even in thewelter of the lines provided fertile matter for quantum conjectures.Molecular spectra turned into an all-important site of research during

The first SolvayCongress in 1911assembled thepioneers ofquantum theory.Seated (left toright): W. Nernst,M. Brillouin,E. Solvay,H. A. Lorentz,E. Warburg,J. Perrin, W. Wien,M. Curie,H. Poincar.Standing (left toright):R. Goldschmidt,M. Planck,H. Rubens,A. Sommerfeld,F. Lindemann,M. de Broglie,M. Knudsen,F. Hasenhrl,G. Hostelet,E. Herzen, J. Jeans,E. Rutherford,H. KamerlinghOnnes, A. Einstein,P. Langevin. (FromCinquantenaire duPremier Conseil dePhysique Solvay,19111961).

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the quantums second decade. Slower to take off, but ultimately evenmore productive, was the quantization of motions within the atomitself. Since no one had much sense of the atoms constitution, theventure into atomic spectra was allied to speculative model-building.Unsurprisingly, most of the guesses of the early 1910s turned outto be wrong. They nonetheless sounded out the possibilities. Theorbital energy of electrons, their angular momentum (something likerotational inertia), or the frequency of their small oscillations aboutequilibrium: all these were fair game for quantization. The observedlines of the discrete spectrum could then be directly read off from theelectrons motions.

THE BOHR MODEL OF THE ATOM

It might seem ironic that Niels Bohr initially had no interest in spec-tra. He came to atomic structure indirectly. Writing his doctoral thesison the electron theory of metals, Bohr had become fascinated byits failures and instabilities. He thought they suggested a new typeof stabilizing force, one fundamentally different from those famil-iar in classical physics. Suspecting the quantum was somehowimplicated, he could not figure out how to work it into the theory.

The intuition remained with him, however, as he transferredhis postdoctoral attention from metals to Rutherfords atom. Whenit got started, the nuclear atom (its dense positive center circled byelectrons) was simply one of several models on offer. Bohr beganworking on it during downtime in Rutherfords lab, thinking he couldimprove on its treatment of scattering. When he noticed that it oughtto be unstable, however, his attention was captured for good. Tostabilize the model by fiat, he set about imposing a quantum con-dition, according to the standard practice of the day. Only after a col-league directed his attention to spectra did he begin to think abouttheir significance.

The famous Balmer series of hydrogen was manifestly news toBohr. (See illustration above.) He soon realized, however, that hecould fit it to his modelif he changed his model a bit. He recon-ceptualized light emission as a transition between discontinuous or-bits, with the emitted frequency determined by DE = hf. To get the

The line spectrum of hydrogen. (FromG. Herzberg, Annalen der Physik, 1927)

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orbits energies right, Bohr had to introduce some rather ad hoc rules.These he eventually justified by quantization of angular momentum,which now came in units of Plancks constant h. (He also used an in-teresting asymptotic argument that will resurface later.)

Published in 1913, the resulting picture of the atom was rather odd.Not only did a quantum condition describe transitions betweenlevels, but the stationary states, too, were fixed by nonclassicalfiat. Electrons certainly revolved in orbits, but their frequency of rev-olution had nothing to do with the emitted light. Indeed, their os-cillations were postulated not to produce radiation. There was nopredicting when they might jump between levels. And transitionsgenerated frequencies according to a quantum relation, but Bohrproved hesitant to accept anything like a photon.

The model, understandably, was not terribly persuasivethatis, until new experimental results began coming in on X rays, energylevels, and spectra. What really convinced the skeptics was a smallmodification Bohr made. Because the nucleus is not held fixed inspace, its mass enters in a small way into the spectral frequencies.The calculations produced a prediction that fit to 3 parts in 100,000pretty good, even for those days when so many numerical coinci-dences proved to be misleading.

The wheel made its final turn when Einstein connected the Bohratom back to blackbody radiation. His famous papers on radiativetransitions, so important for the laser (see following article by CharlesTownes), showed the link among Plancks blackbody law, discreteenergy levels, and quantized emission and absorption of radiation.Einstein further stressed that transitions could not be predicted inanything more than a probabilistic sense. It was in these same papers,by the way, that he formalized the notion of particle-like quanta.

THE OLD QUANTUM THEORY

What Bohrs model provided, like Einsteins account of specific heats,was a way to embed the quantum in a more general theory. In fact,the study of atomic structure would engender something plausiblycalled a quantum theory, one that began reaching towards a full-scalereplacement for classical physics. The relation between the old and

W h a t W a s B o h rU p To ?

BOHRS PATH to his atomicmodel was highly indirect. Therules of the game, as played in19111912, left some flexibilityin what quantum condition oneimposed. Initially Bohr appliedit to multielectron states,whose allowed energies henow broke up into a discretespectrum. More specifically, hepicked out their orbital fre-quencies to quantize. This isexactly what he would laterproscribe in the final version ofhis model.

He rethought, however, inthe face of the Balmer seriesand its simple numericalpattern

fn = R (1/4 - 1/n2).

Refocusing on one electronand highlighting excited states,he reconceptualized lightemission as a transition. TheBalmer series then resultedfrom a tumble from orbit n toorbit 2; the Rydberg constantR could be determined interms of h. However, remnantsof the earlier model stillappeared in his paper.

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the new became a key issue. For some features of Bohrs modelpreserved classical theories, while others presupposed their break-down. Was this consistent or not? And why did it work?

By the late 1910s physicists had refined Bohrs model, providinga relativistic treatment of the electrons and introducing additionalquantum numbers. The simple quantization condition on angularmomentum could be broadly generalized. Then the techniques ofnineteenth-century celestial mechanics provided powerful theoret-ical tools. Pushed forward by ingenious experimenters, spectroscopicstudies provided ever more and finer data, not simply on the basicline spectra, but on their modulation by electric and magnetic fields.And abetted by their elders, Bohr, Arnold Sommerfeld, and Max Born,a generation of youthful atomic theorists cut their teeth on such prob-lems. The pupils, including Hendrik Kramers, Wolfgang Pauli, WernerHeisenberg, and Pascual Jordan, practiced a tightrope kind of theo-rizing. Facing resistant experimental data, they balanced the empiricalevidence from the spectra against the ambiguities of the prescrip-tions for applying the quantum rules.

Within this increasingly dense body of work, an interesting strat-egy began to jell. In treating any physical system, the first task wasto identify the possible classical motions. Then atop these classi-cal motions, quantum conditions would be imposed. Quantizationbecame a regular procedure, making continual if puzzling refer-ence back to classical results. In another way, too, classical physicsserved as a touchstone. Bohrs famous correspondence principle

Above: Bohrs lecture notes on atomic physics, 1921. (Originalsource: Niels Bohr Institute, Copenhagen. From OwenGingerich, Ed., Album of Science: The Physical Sciences inthe Twentieth Century, 1989.)

Left: Wilhelm Oseen, Niels Bohr, James Franck, Oskar Klein(left to right), and Max Born, seated, at the Bohr Festival inGttingen, 1922. (Courtesy Emilio Segre` Visual Archives,Archive for the History of Quantum Physics)

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first found application in his early papers, where it pro-vided a deeper justification of his quantization con-dition. In the classical limit, for large orbits withhigh quantum numbers and small differences in en-ergy, the radiation from transitions between adja-cent orbits should correspond to the classical radiationfrequency. Quantum and classical results must matchup. Employed with a certain Bohrian discrimination,the correspondence principle yielded detailed infor-mation about spectra. It also helped answer the ques-tion: How do we build up a true quantum theory?

Not that the solution was yet in sight. Theold quantum theorys growing sophistication madeits failures ever plainer. By the early 1920s the the-orists found themselves increasingly in difficul-ties. No single problem was fatal, but their accu-mulation was daunting. This feeling of crisis wasnot entirely unspecific. A group of atomic theorists,centered on Bohr, Born, Pauli, and Heisenberg, hadcome to suspect that the problems went back to elec-tron trajectories. Perhaps it was possible to abstractfrom the orbits? Instead they focused on transition

probabilities and emitted radiation, since those might be more reli-ably knowable. At the moment, Pauli still remarked in the springof 1925, physics is again very muddled; in any case, it is far toodifficult for me, and I wish I were a movie comedian or something ofthe sort and had never heard of physics.

QUANTUM MECHANICS

Discontinuity, abstraction from the visualizable, a positivistic turntowards observable quantities: these preferences indicated one pathto a full quantum theory. So, however, did their opposites. Whenin 19251926 a true quantum mechanics was finally achieved, twoseemingly distinct alternatives were on offer. Both took as a leitmotifthe relation to classical physics, but they offered different ways ofworking out the theme.

Paul Dirac and Werner Heisenbergin Cambridge, circa 1930. (CourtesyEmilio Segre` Visual Archives, PhysicsToday Collection)

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Heisenbergs famous paper of 1925, celebrated for launching thetransformations to come, bore the title On the Quantum-TheoreticalReinterpretation of Kinematical and Mechanical Relations. Thepoint of departure was Bohrs tradition of atomic structure: discretestates remained fundamental, but now dissociated from intuitive rep-resentation. The transformative intent was even broader from thestart. Heisenberg translated classical notions into quantum ones inthe best correspondence-principle style. In his new quantummechanics, familiar quantities behaved strangely; multiplicationdepended on the order of the terms. The deviations, however, werecalibrated by Plancks constant, thus gauging the departure from clas-sical normality.

Some greeted the new theory with elation; others found it un-satisfactory and disagreeable. For as elegant as Heisenbergs trans-lation might be, it took a very partial view of the problems of thequantum. Instead of the quantum theory of atomic structure, onemight also start from the wave-particle duality. Here another youngtheorist, Louis de Broglie, had advanced a speculative proposal in 1923that Heisenberg and his colleagues had made little of. Thinking overthe discontinuous, particle-like aspects of light, de Broglie suggest-ed looking for continuous, wave-like aspects of electrons. His notion,while as yet ungrounded in experimental evidence, did provide sur-prising insight into the quantum conditions for Bohrs orbits. It also,by a sideways route, gave Erwin Schrdinger the idea for his brilliantpapers of 1926.

Imagining the discrete allowed states of any system of parti-cles as simply the stable forms of continuous matter waves,Schrdinger sought connections to a well-developed branch of clas-sical physics. The techniques of continuum mechanics allowed himto formulate an equation for his waves. It too was built aroundthe constant h. But now the basic concepts were different, and soalso the fundamental meaning. Schrdinger had a distaste for thediscontinuity of Bohrs atomic models and the lack of intuitive pic-turability of Heisenbergs quantum mechanics. To his mind, thequantum did not imply any of these things. Indeed, it showed theopposite: that the apparent atomicity of matter disguised anunderlying continuum.

T h e Q u a n t u m i nQ u a n t u m M e c h a n i c s

ICONICALLY we now writeHeisenbergs relations as

pq - qp = - ih/2p.

Here p represents momentumand q represents position. Forordinary numbers, of course,pq equals qp, and so pq - qpis equal to zero. In quantummechanics, this difference,called the commutator, is nowmeasured by h. (The samething happens with Heisen-bergs uncertainty principle of1927: DpDq ! h/4p.) The sig-nificance of the approach, andits rearticulation as a matrix calculus, was made plain by Max Born, Pascual Jordan, andWerner Heisenberg. Its full profundity was revealed by Paul Dirac.

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Thus a familiar model connected to physical intuition, but con-stituting matter of some ill-understood sort of wave, confronted anabstract mathematics with seemingly bizarre variables, insistentabout discontinuity and suspending space-time pictures. Unsur-prisingly, the coexistence of alternative theories generated debate.The fact, soon demonstrated, of their mathematical equivalence didnot resolve the interpretative dispute. For fundamentally differentphysical pictures were on offer.

In fact, in place of Schrdingers matter waves and Heisenbergsuncompromising discreteness, a conventional understanding settledin that somewhat split the difference. However, the thinking ofthe old quantum theory school still dominated. Born dematerializedSchrdingers waves, turning them into pure densities of probabilityfor finding discrete particles. Heisenberg added his uncertainty prin-ciple, limiting the very possibility of measurement and undermin-ing the law of causality. The picture was capped by Bohrs notion

Old faces and new at the 1927 SolvayCongress. The middle of the second rowlines up Hendrik Kramers, Paul Dirac,Arthur Compton, and Louis de Broglie.Behind Compton stands ErwinSchrdinger, with Wolfgang Pauli andWerner Heisenberg next to each otherbehind Max Born. (From Cinquantenairedu Premier Conseil de Physique Solvay,19111961)

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of complementarity, which sought to reconcile contradictory conceptslike waves and particles.

Labeled the Copenhagen Interpretation after Bohrs decisive in-fluence, its success (to his mind) led the Danish theorist to charac-terize quantum mechanics as a rational generalization of classicalphysics. Not everyone agreed that this was the end point. Indeed,Einstein, Schrdinger, and others were never reconciled. Even Bohr,Heisenberg, and Pauli expected further changesthough in a newdomain, the quantum theory of fields, which took quantummechanics to a higher degree of complexity. But their expectationsof fundamental transformation in the 1930s and beyond, charac-terized by analogies to the old quantum theory, found little reso-nance outside of their circle.

Ironically enough, just as for their anti-Copenhagen colleagues,their demand for further rethinking did not make much headway. Ifthe physical meaning of the quantum remained, to some, ratherobscure, its practical utility could not be denied. Whatever lessonsone took from quantum mechanics, it seemed to work. It not onlyincorporated gracefully the previous quantum phenomena, butopened the door to all sorts of new applications. Perhaps this kindof success was all one could ask for? In that sense, then, a quarter-century after Planck, the quantum had been built into the founda-tions of physical theory.

S U G G E S T I O N SF O R F U R T H E R R E A D I N G

Olivier Darrigol, From c-Numbers to q-Numbers: The Classical Analogy inthe History of QuantumTheory (Berkeley: U.C.Press, 1992).

Helge Kragh, Quantum Gen-erations: A History ofPhysics in the TwentiethCentury (Princeton, Prince-ton University Press, 1999).

Abraham Pais, Subtle is theLord ...: The Science andthe Life of Albert Einstein(Oxford, Oxford UniversityPress, 1982).

Helmut Rechenberg, Quantaand Quantum Mechanics,in Laurie M. Brown,Abraham Pais, and SirBrian Pippard, Eds.,Twentieth CenturyPhysics, Vol. 1 (Bristol andNew York, Institute ofPhysics Publishing andAmerican Institute ofPhysics Press, 1995),pp. 143-248.

The August 11, 2000, issue ofScience (Vol. 289) containsan article by Daniel Klep-pner and Roman Jackiw onOne Hundred Years ofQuantum Physics. To seethe full text of this article, goto http://www.sciencemag.org/cgi/content/full/289/5481/893.