STANFORD LINEAR ACCELERATOR CENTER · *Ab raham Pais, Subtle is the Lord: Science and the Life of Albert Einstein, Oxford U. Press,1982. MaxPlanck,circa 190 (Courtesy AIP EmilioSegrèVisualArchives)

STAN F O RD L I N EAR ACCELERATO R CE NTERSummer/Fall 2000, Vol. 30, No. 2

EditorsRENE DO NALDSO N , BILL KIRK

Contributing EditorsMICHAEL RIORDAN , GORDO N FRASER

JU DY JACKSO N , AKIHIRO MAKIPEDRO WALOSCHEK

Editorial Advisory BoardPATRICIA BURCHAT, DAVID BURKE

LA N CE DIXO N , GEORGE SMO OTGEORGE TRILLIN G, KARL VAN BIBBER

HERMA N WINICK

IllustrationsTERRY AN DERSO N

DistributionCRYSTAL TILGHMA N

A PERIODICAL OF PARTICLE PHYSICS

SU M MER /FALL 2000 VOL. 30, N U MBER 2

Printed on recycled paper

The Bea m Line is published quarterly by t heStanford Linear Accelerator Cen ter, Box 4349,Stanford, CA 94309. Telephone: (650) 926-2585.EMAIL: beam [email protected]: (650) 926-4500

Issues of the Bea m Line are accessible electroni-cally on t he World Wide Web at h t tp:/ /www.slac.stanford.edu /pubs/beamline. SLAC is operated byStanford University under con tract with the U.S.Depart m en t of Energy. The opinions of t he au thorsdo not necessarily reflect the policies of t heStanford Linear Accelerator Cen ter.

Cover: “Einstein and the Quantum Mechanics,” by artistDavid Martinez © 1994. The original is acrylic on canvas,16” 20”. Martinez’s notes about the scene are reproducedin the adjoining column, and you can read more about hisphilosophy in the “Contributors” section on page 60. Hiswebsite is http://members.aol.com/elchato/index.html andfrom there you can view more of his paintings. The BeamLine is extremely grateful to him and to his wife Terry forallowing us to reproduce this imaginative and fun image.

Werner Heisenberg illustrates his Uncertainty Principle bypointing down with his right hand to indicate the location ofan electron and pointing up with his other hand to its waveto indicate its momentum. At any instant, the more certain weare about the momentum of a quantum, the less sure we areof its exact location.

Niels Bohr gestures upward with two fingers to empha-size the dual, complementary nature of reality. A quantum issimultaneously a wave and a particle, but any experimentcan only measure one aspect or the other. Bohr argued thattheories about the Universe must include a factor to accountfor the effects of the observer on any measurement ofquanta. Bohr and Heisenberg argued that exact predictionsin quantum mechanics are limited to statistical descriptionsof group behavior. This made Einstein declare that he couldnot believe that God plays dice with the Universe.

Albert Einstein holds up one finger to indicate his beliefthat the Universe can be described with one unified fieldequation. Einstein discovered both the relativity of time andthe mathematical relationship between energy and matter.He devoted the rest of his life to formulating a unified fieldtheory. Even though we must now use probabilities todescribe quantum events, Einstein expressed the hopethat future scientists will find a hidden order behind quantummechanics.

Richard Feynman plays the bongo drums, with Feynmandiagrams of virtual particles rising up like music notes. Oneof his many tricks was simplifying the calculation of quantumequations by eliminating the infinities that had prevented realsolutions. Feynman invented quantum electrodynamics, themost practical system for solving quantum problems.

Schrödinger’s cat is winking and rubbing up to Bohr. Theblue woman arching over the Earth is Nut, the Sky Goddessof Egypt. She has just thrown the dice behind Einstein’sback. Nut is giving birth to showers of elementary particleswhich cascade over the butterflies of chaos.

—David Martinez

Einstein and The Quantum Mechanics

FEAT U RES

2 FOREWORDTHE FUTURE OF THE QUANTUMTHEORYJames Bjorken

6 THE ORIGINS OF THE QUAN TUMTHEORYThe first 25 years of the cent ury radicallytransform ed our ideas abou t Nat ure.

Cathryn Carson

20 THE LIGHT THAT SHINESSTRAIGHTA Nobel laureate recounts the inventionof the laser and the birth of quan tu melectronics.

Charles H. Townes

29 THE QUAN TUM AN D THECOSMOSLarge-scale structure in the U niverse beganwith tin y quan tu m fluctuations.

Rocky Kolb

34 GETTIN G TO KN OW YOURCO NSTITUEN TSHu m an kind has wondered since thebeginning of history w hat are thefundam ental constituents of m atter.Robert L. Jaffe

41 SUPERCO N DUCTIVITY:A MACROSCOPIC QUAN TU MPHEN OMEN O NQ uantu m mechanics is crucial tounderstanding and using supercond uctivityJohn Clarke

DEPA RTMEN TS

49 THE U NIVERSE AT LARGEThe Ratios of S m all Whole N u m bers:Misadvent ures in Astrono mical Q uantizationVirginia Trimble

58 CO N TRIBUTORS

61 DATES T O REMEMBER

C O N TEN TS

2 SU MMER/FALL 2000

FO REW O RD

N THIS ISSUE of the Beam Line, we cele-brate t he one hundredth anniversary of thebirth of t he quan tu m theory. The story of

how Max Planck started it all is one of the mostmarvelous in all of science. It is a favorite ofmine, so m uch so that I have already writ tenabout it (see “Par ticle Physics—Where Do We GoFrom Here?” in t he Winter 1992 Bea m Line,Vol. 22, No. 4). Here I will only quote again whatthe late Abraham Pais said abou t Planck: “Hisreasoning was mad, bu t his madness had thatdivine quality t hat only the greatest transitionalfigures can bring to science.”*

A cen tury later, t he m adness has not yet com-pletely disappeared. Science in general has a wayof producing results which defy hu man in tuition.But it is fair to say that the winner in th iscategory is the quan tu m theory. In my mindquantu m paradoxes such as t he Heisenberguncer tainty principle, Schrödinger’s cat,

“collapse of the wave packet,” and so forth are far more perplexing andchallenging than those of relativity, whether t hey be the twin paradoxes ofspecial relativity or the black hole physics of classical general relativity. It isoften said that no one really understands quan tu m theory, and I would bethe last to disagree.

In the con tribu tions to this issue, the knot ty questions of the in terpreta-tion of quantum theory are, mercifully, not addressed. There will be nomention of the debates between Einstein and Bohr, nor the later at tempts by

T he Fu t ure of t he Q uan t u m Tby JAMES BJORKEN

*A braha m Pais, Subtle is t he Lord: Science and t he Life of Albert Einstein , O xford U. Press, 1982.

Max Planck, circa 1910(Courtesy AIP Emilio Segrè Visual Archives)

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Boh m, Everet t, and others to find inter-pre tations of the theory different fromthe original “Copenhagen in terpreta-t ion” of Bohr and his associates. Instead,what is rightfully emphasized is theoverwhelming practical success of theserevolu tionary ideas. Quantum theoryworks. It never fails. And the scope ofthe applications is enor mous. As LeonLeder man, N obel Laureate and DirectorEmeritus of Fer milab, likes to point ou t,more than 25 percen t of t he grossnational product is dependen t upontechnology that springs in an essen tialway from quan tu m phenomena.*

Nevertheless, it is hard not to sympa-thize with Einstein and feel t hat there issomething incomplete abou t t he presen tstat us of quan tu m theory. Perhaps theequations defining the theory are not ex-act ly correct, and corrections will even-tually be defined and their effectsobserved. This is not a popular point ofview. Bu t t here does exist a m inorityschool of though t which asser ts that

only for sufficien tly small systems is the quan tu m theory accurate, and thatfor large complex quantu m systems, hard to follow in exquisite detail, there

heory

Albert Einstein and Neils Bohr in the late 1920s.(Courtesy AIP Emilio Segrè Visual Archives)

*Leon Lederm an, The God Part icle (If the U niverse is t he Answer, What is t he Question?),Hough ton Miffl in, 1993.

Paul

Ehre

nfes

t

4 SU MMER/FALL 2000

may be a small amoun t of some kind of extra in trinsic “noise” term or non-linearity in the fundamental equations, which effectively eliminates para-doxes such as t he “collapse of t he wave packet.”

Down through history most of the debates on the foundations of quan tu mtheory produced many words and very lit tle action, and remained closer tothe philosophy of science than to real experimental science. John Bellbrough t some freshness to the subject. T he famous theorem that bears hisnam e initiated an experimental program to test som e of t he fundamentals.Never theless, it would have been an enor mous shock, at least to m e, if anydiscrepancy in such experiments had been found, because the searchesinvolved simple atomic systems, not so differen t from elementary particlesystems within which very subtle quan tu m effects have for some time beenclearly demonstrated. A worthy challenge to the quan tu m theory in myopinion must go much fur ther and deeper.

What migh t such a challenge be? At presen t, one clear possibili ty which isactively pursued is in the realm of string theory, which at tempts an exten-sion of Einstein gravity in to the domain of very short distances, where quan-tu m effects dominate. In the presen t incarnations, it is t he t heory of gravitythat yields ground and undergoes modifications and generalizations, with thequantu m theory left essen tially in tact. Bu t it seems to me that t he alterna-tive m ust also be entertained—that the quantu m theory i tself does not sur-vive the synthesis. This, however, is easier said than done. And the problemwith each option is tha t t he answer needs to be found with precious lit tleassistance from experimen t. This is in s tark contrast with t he developmentof quantu m theory itself, which was driven from ini tiation to completion bya huge nu mber of experimen ts, essen tially guiding the theorists to the finalequations.

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Another approach has been recen tly laid ou t by Frank Wilczek in a veryin teresting essay in Physics Today .* He compares the development of theequations of quan tu m theory with those of Maxwell’s electrodynamics. Bothwere first laboriously pu t together from experimen tal evidence. In both casesthe in terpretations of what the equations meant came la ter. In t he case ofelectrodynamics, the ultimate verdict on Maxwell’s equations is that at adeep level t hey express statements abou t sym metry. (In physics jargon,Maxwell’s equations express the fact that electrodynamics is gauge invariantand Lorentz covarian t.) Wilczek notes that t here is no similar deep basis forthe equations of quan tu m mechanics, and he looks forward to statemen ts ofsym metry as the fu ture expression of the t rue meaning of the quantu mtheory. Bu t if t here are such sym metries, they are not now known or at leastnot yet recognized. Wilczek does cite a pioneering suggestion of Her mannWeyl, which migh t provide at least a clue as to what might be done. Buteven if Wilczek is on t he righ t track, there is again t he problem that theo-rists will be largely on their own, with very lit t le help to be expected fromexperiment.

There is, however, a data-driven approach on the horizon. It is a conse-quence of the infor mation revolu tion. In principle, quantu m systems may beused to create much more powerful computers than now exist. So there is astrong push to develop the concepts and the technology to create large-scalequan tu m computers. If t his happens, the foundations of quan tu m mechanicswill be tested on larger and larger, m ore complex physical systems. And ifquan tu m mechanics in the large needs to be m odified, t hese computers m aynot work as they are supposed to. If t his happens, it will be just one more ex-ample of how a revolu tion in technology can lead to a revolu tion in funda-men tal science.

*Fran k Wilczek, Physics Today, June 2000, Vol. 53, No. 6, p. 11.

6 SU MMER/FALL 2000

by CATHRYN CARSO N

HAT IS A QUAN TUM THEORY? We have

been asking that question for a long time, ever

since Max Planck in troduced the ele men t of dis-

con tinuity we call the quantu m a century ago. Since then,

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

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

has prompted a fundamental rethinking of physical theory.

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

culiar behaviors manifested principally at microscopic levels.From its beginning, t he new regime was symbolized by Planck’s constan t

h , in troduced in his famous paper of 1900. Measuring the world’s departurefrom smooth, continuous behavior, h proved to be a very small nu mber, butdifferen t from zero. Wherever it appeared, st range phenomena came with i t.What it really meant was of course mysterious. While the quantu m era wasinaugurated in 1900, a quan tu m theory would take m uch longer to jell. Int ro-ducing discon tinui ty was a tentative step, and only a first one. And eventhereafter, the recasting of physical t heory was hesitan t and slow. Physicistspondered for years what a quan tu m theory migh t be. Wondering how to in te-grate it with t he powerful apparatus of nineteenth-cen tury physics, they alsoasked what relation it bore to existing, “classical” theories. For some theanswers crystallized with quantu m mechanics, t he result of a quarter-cen tury’s labor. Others held ou t for further rethinking. If t he ou tcome wasnot to t he satisfaction of all, st ill the quantu m theory proved remarkably

T HE ORIGIN SOF T HE Q UA N T U M T HEORY

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

IN TRODUCIN G h

The story began inconspicuously enough on December 14, 1900. Max Planckwas giving a talk to the German Physical Society on the con tinuous spec-tru m of t he frequencies of ligh t e mit ted by an ideal heated body. Some twomonths earlier this 42-year-old theorist had presented a for m ula capturingsome new experimen tal results. Now, with leisure to think and more ti me athis disposal, he sough t to provide a physical justification for his for m ula.Planck pict ured a piece of mat ter, idealizing it somewhat, as equivalent to acollection of oscillating electric charges. He then imagined distributing itsenergy in discrete chunks proportional to t he frequencies of oscillation. Theconstant of propor tionality he chose to call h; we would now write e = hf.The frequencies of oscillation deter mined the frequencies of t he emit tedligh t. A twisted chain of reasoning then reproduced Planck’s postulatedfor m ula, which now involved the same natural constan t h.

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

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Loo k i ng bac k on t he eve n t , we m igh t expec t revol u t i o nar yfanfare. Bu t as so of ten in h is t ory, m at te rs were m ore a m bigu-ous. Planck did not call h is energy elem ents quanta and was notinclined to stress their discreteness, w hich made li t t le sense in anyfamiliar ter m s. So t he meaning of his procedure only gradually be-cam e apparen t. Alt hough the proble m he was t reat ing was pivotalin i ts day, i ts im plicat ions were at first t hought to be confined.

BLACKBODIES

T he behavior of light in i ts in teraction with m at ter was indeed akey proble m of nineteen t h-cen tury physics. Planck was in teres t-ed in the two theories that overlapped in this domain. The first waselect rodynam ics, t he theory of elect rici ty, m agnetis m, and ligh twaves, brought to final for m by James Clerk Maxwell in the 1870s.T h e second, da t ing fro m roughly t he sa m e period, was t her m o-dynam ics and sta tistical mechanics, governing transform at ions ofenergy and its behavior in t i me. A pressing ques tion was whet herthese two grand theories could be fused in to one, since they startedfro m different fu nda men tal notions.

Begin ning in the mid-1890s, Planck took up a seemingly narrowproble m , t h e in terac t io n of an oscil la t ing ch arge wi t h i t s elec-tro m agnet ic field. T hese st udies, however, brough t h i m in to con-tact with a long tradit ion of work on the emission of light. Decadesearlier i t had been recogn ized t ha t perfec tly absorbing (“ black ”)bodies provided a s tan dard for e m ission as wel l. T hen over t heyears a s m all in d us t ry h ad gro w n u p arou n d t h e s t u dy of s uc hobjec t s (and their real-world subst i tu t es, like soot). A sm all groupof t h eor is t s occ upied t h e m selves wi t h t h e t her m odyn a m ics ofradia tion, w hile a hos t of experim en ters labored over hea ted bod-ie s t o fix t e m pera t u re, de t e r m in e in t en s i ty, and c ha rac t e rizedeviations from blackbody ideality (see t he graph above). After sci-entists pushed the practical realization of an old idea—that a closedt ube wi t h a s m all hole cons ti t u ted a near-ideal blackbody—this“cavity radiation” allowed ever m ore reliable measure men ts. (Seeillustration a t left .)

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

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

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Now Planck’s oscillating charges emit ted and absorbed radiation,so they could be used to model a blackbody. Thus everything seemedto fall in to place in 1899 when he reproduced a for m ula that a col-league had derived by less secure means. That was convenient; every-one agreed that Willy Wien’s form ula matched the observations. Thetrouble was that im mediately afterwards, experi menters began find-ing devia t io ns. At low frequ encies, Wien’s expression beca m eincreasingly untenable, while elsewhere it continued to work wellenough. Infor med of the results in t he fall of 1900, on shor t noticePlanck came up with a reasonable in terpolation. With i ts adjustableconstan ts his for m ula seemed to fi t t he experim ents (see graph a tright). Now the question became: Where might i t come from? Whatwas i ts 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 in to elemen ts e = hf. T he derivation wasa success and splendidly reproduced the experimental data. Its mean-ing was less clear. After all, Maxwell’s theory already gave a beau-t iful accou nt of ligh t—and trea ted i t as a wave traveling in a con-tin uous mediu m. Planck did not take the constan t h to indicate aphysical discontin uity, a real atomicity of energy in a substan tivesense. None of his colleagues made much of this possibility, either,until Albert Einstein took i t up five years later.

MAKIN G LIG HT QUAN TA REAL

Of Einstein’s three great papers of 1905, the one “On a Heuristic Poin tof View Concerning t he Production and Transfor mat ion of Ligh t”was the piece that the 26-year-old patent clerk labeled revolu tionary.It was peculiar, he noted, that the electrom agnet ic t heory of lightassu med a continuu m, while current accounts of mat ter started fromdiscrete atoms. Could discontinuity be productive for light as well?However indispensable Maxwell’s equations might seem, for somein teres t ing phen o m ena t hey proved inadeq uat e. A key exa m plewas blackbody radiation, which Einstein now looked at in a way dif-ferent from Planck. Here a rigorously classical treat ment, he showed,

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

10 SU MMER/FALL 2000

yielded a result not only wrong but also absurd. Even where Wien’slaw was approximately right (and Planck’s modification unnecessary),elemen tary thermodynamics forced light to behave as though it werelocalized in discrete chunks. Radiation had to be parcelled in to whatEinstein called “energy quanta.” Today we would write E = hf.

Discontinuity was t hus endemic to the electrom agnetic world.Interestingly, Einstein did not refer to Planck’s constant h, believinghis approach to be differen t in spirit . Where Planck had looked atoscillat ing charges, Einstein applied ther modynamics to the ligh ti t self. It was only la ter t ha t Einstein went back and showed howPlanck’s 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 emit ted and absorbed inthat fashion. A few easy considerat ions then yielded a law for thephotoelectric effect , in which ligh t ejects elect rons fro m t he sur-face of a metal. Einstein provided not only a tes table 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, i t was far from trivial. So it would remain

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

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for m ore t h an a decade. Eve n af ter Rober t Mill ikan confir m edEinstein’s prediction, he and others balked at the underlying quan-tum hypothesis. It still violated everything known about light’s wave-like behavior (no tably, in terference) and hardly seem ed reconcil-able with Maxwell’s equations. When Einstein was awarded the NobelPrize, he owed the honor largely to the photoelectric effect. But theci tat ion specifically no ted his discovery of the law, not the expla-nat ion that he proposed.

The relation of the quantu m to the wave theory of light would re-main a poin t 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 at tributing to light a w hole panoplyof particulate proper ties. The particle-like quan tu m, 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-part icle d uali ty could be taken seriously, discon t in u i tyhad to demonstrate i ts wor th elsewhere.

BEYO N D LIGHT

As it tu rned ou t, the earliest welco me given to t he new quantu mconcepts came in fields far removed from t he troubled theories ofradiation. The firs t of these domains, though hardly the most obvi-ous, was the t heory of specific heats. The specific heat of a substancedetermines how much of its energy changes when its temperat ure israised. At low temperat ures, solids display peculiar behavior. HereEinstein suspected—again we meet Einstein—that the deviance mightbe explicable on quantum grounds. So he reform ulated Planck’s prob-lem to handle a lat t ice of independently vibrating atoms. From thishighly sim plistic model, he obtained quite reasonable predict ionsthat involved the same quantity hf, now translated in to the solid-state context.

T here th ings s tood for another t hree years. It took t he suddenatten tion of the physical che mist Walther Nernst to bring quan tu m

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


t heories of specific heats to general significance. Feeling his waytowards a new law of ther modynamics, Nernst not only bolsteredEins tein’s ideas wi t h experi m en tal resul ts, bu t also pu t t he m onthe agenda for widespread discussion. It was no accident, and to alarge degree Nernst’s doing, tha t the first Solvay Congress in 1911dealt precisely wit h radia tion t heory and quanta (see photographbelow). Eins tein spoke on specific heat s, offering additional com-ments on electromagnetic radiation. If the quantu m 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 quan tizing oscillat ions 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 im mensely fromone substance to the next. Bu t t he regulari ties evident even in thewelter of the lines provided fert ile mat ter for quantu m 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. Poincaré.Standing (left toright):R. Goldschmidt,M. Planck,H. Rubens,A. Sommerfeld,F. Lindemann,M. de Broglie,M. Knudsen,F. Hasenöhrl,G. Hostelet,E. Herzen, J. Jeans,E. Rutherford,H. KamerlinghOnnes, A. Einstein,P. Langevin. (FromCinquantenaire duPremier Conseil dePhysique Solvay,1911–1961).

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the quantu m’s second decade. Slower to take off, but ult imately evenmore productive, was the quan tizat ion of motions within the atomitself. Since no one had m uch sense of the atom’s constitu tion, theventure in to atomic spectra was allied to speculative model-building.U nsurprisingly, m ost of t he guesses of the early 1910s t urned outto be wrong. T hey nonetheless sounded out t he possibili t ies. T heorbital energy of electrons, their angular momentu m (something likerota tional inertia), or the frequency of their small oscillations aboutequilibriu m: all these were fair game for quantizat ion. 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 t he elect ron theory of m etals, Bohr had beco m e fascinated byits failures and instabili ties. He thought they suggested a new typeof stabilizing force, one fundam entally differen t from those famil-iar in classical physics . Suspect ing t he quan t u m was so m ehowimplicated, he could not figure out how to work it in to the theory.

T he in t u i t ion rem ained wi t h h i m, however, as he t ransfer redhis postdoctoral at ten tion from metals to Rutherford’s atom. Whenit got started, the nuclear atom (its dense positive center circled byelec t rons) was si mply one of several m odels on offer. Bohr beganworking on it during downtime in Rutherford’s lab, thinking he couldimprove on its treatment of scat tering. When he noticed that it oughtto be u nst able, however, his a t t en t ion was capt ured for good. Tostabilize t he model by fiat, he set abou t imposing a quantu m con-dition, according to the standard practice of the day. Only after a col-league directed his at ten tion to spectra did he begin to think abouttheir significance.

The famous Balm er series of hydrogen was m anifes tly news toBohr. (See illust rat ion above.) He soon realized, however, t hat hecould fi t i t to his m odel—if he changed his model a bit. He recon-ceptualized light emission as a transit ion between discontinuous or-bits, with the emit ted frequency determined by DE = hf. To get t he

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


orbits’ energies right, Bohr had to in troduce some rather ad hoc rules.These he eventually justified by quan tization of angular momentu m,which now came in units of Planck’s 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.N ot only did a quan t u m condit ion describe t ransit ions be t weenlevels, but the “stationary states,” too, were fixed by nonclassicalfiat. Electrons certainly revolved in orbits, but their frequency of rev-olu tion had nothing to do with the emit ted light. Indeed, their os-cilla t ions were postu lated not to produce radiation. T here was nopredic ting when they m igh t ju mp between levels. And transitionsgenerated frequencies according to a quan t u m relat ion, bu t Bohrproved hesitant to accept anything like a photon.

T he model, u nders tandably, was not ter ribly persuasive—t hatis, until new experimental results began coming in on X rays, energylevels, and spectra. What really convinced the skept ics was a smallm odification Bohr made. Because the nucleus is not held fixed inspace, i ts mass enters in a small way in to the spectral frequencies.The calculations produced a prediction that fi t to 3 parts in 100,000—pret ty good, even for t hose days when so m any nu m erical coinci-dences proved to be misleading.

The w heel 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 am ong Planck’s blackbody law, discreteenergy levels, and quant ized emission and absorption of radiation.Einstein further stressed that transit ions 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 QUAN TUM THEORY

What Bohr’s model provided, like Einstein’s account of specific heats,was a way to embed the quantu m in a more general t heory. In fact,the study of atomic structure would engender something plausiblycalled a quantu m theory, one that began reaching towards a full-scalereplacemen t for classical physics. T he relat ion bet ween the old and

What Was BohrUp To?

BOHR’S PATH to his atomicmodel was highly indirect. Therules of the game, as played in1911–1912, 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/n 2).

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.

BEA M LINE 15

t he new beca m e a key issue. For so m e fea t ures of Bohr’s m odelpreserved classical t heories, while others presupposed their break-down. Was this consistent or not? And why did it work?

By the late 1910s physicists had refined Bohr’s model, providinga relativist ic treat ment of the electrons and in troducing addit ional“quan tu m nu mbers.” The simple quan tization condition on angularmo ment u m could be broadly generalized. Then t he 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 magnet ic fields.And abetted by t heir elders, Bohr, Arnold Som merfeld, 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, pract iced a tightrope kind of theo-rizing. Facing resistant experimental data, they balanced the empiricalevidence from the spectra against the am biguit ies of the prescrip-tions for applying the quantu m rules.

Within this increasingly dense body of work, an in teresting strat-egy began to jell. In treat ing any physical system, the first task wasto ident ify the possible classical motions. T hen at op t hese classi-cal motions, quantu m conditions would be imposed. Quant izationbeca m e a regu lar procedure, m aking con t in ual if puzzli ng refer-ence back to classical results. In another way, too, classical physicsserved as a touchstone. Bohr’s famous “correspondence principle”

Above: Bohr’s 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 inGöttingen, 1922. (Courtesy Emilio Segre Visual Archives,Archive for the History of Quantum Physics)

16 SUMMER/FALL 2000

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 quantu m nu mbers and small differences in en-ergy, t he radiation from transi t ions 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?

N ot t ha t t he solu t io n was ye t in sigh t . T heold quantu m theory’s growing sophistication madeits failures ever plainer. By the early 1920s the the-oris t s fou nd t h em selves increasingly in difficu l-t ies. N o single proble m was fatal, bu t t heir accu-m ulation was dau nting. 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 transit ion

probabilit ies and emit ted radiation, since those might be more reli-ably knowable. “At the moment,” Pauli st ill remarked in the springof 1925, “physics is again very m uddled; in any case, i t is far toodifficult for me, and I wish I were a movie comedian or something ofthe sor t and had never heard of physics.”

QUAN TUM MEC HANICS

Discontinuity, abstraction from the visualizable, a positivist ic t urntowards observable quanti ties: these preferences indicated one pat hto a fu ll quant u m theory. So, however, did t heir opposi tes. Whenin 1925–1926 a true quan tu m mechanics was finally achieved, twoseemingly distinct alternatives were on offer. Both took as a leit motifthe relation to classical physics, bu t they offered differen t ways ofworking ou t the theme.

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

BEA M LINE 17

Heisenberg’s famous paper of 1925, celebrated for lau nching thetransformations to come, bore the title “On the Quantum-TheoreticalRein terpretat ion of Kinem at ical and Mechanical Relat ions.” T hepoint of departure was Bohr’s tradit ion of atomic s tructure: discretestates remained fundamental, but now dissociated from in tuitive rep-resentation. T he transfor mat ive in ten t was even broader from thestart . Heisenberg translated classical notions in to quantu m ones int he bes t correspo ndence-princ iple s ty le. In h is new quan t u mmechanics, familiar quan ti ties behaved s trangely; m ul tiplicat iondepended on t he order of the ter ms. The deviat ions, however, werecalibrated by Planck’s constant, thus gauging the depart ure from clas-sical nor mality.

So me gree ted the new t heory wit h ela t ion; o thers fou nd i t u n-satisfactory and disagreeable. For as elegan t as Heisenberg’s trans-la tion m igh t be, i t took a very par tial view of t he problem s of t hequan tu m. Instead of the quant u m theory of atomic structure, onemight also star t from the wave-particle duality. Here another youngtheorist, Louis de Broglie, had advanced a speculative proposal in 1923that Heisenberg and his colleagues had made li t t le of. Thinking overthe discontinuous, particle-like aspects of ligh t, 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 in to the quan tu m conditions for Bohr’s orbi ts. It also,by a sideways route, gave Erwin Schrödinger the idea for his brillian tpapers of 1926.

Im agin ing t h e disc re te a llowed s ta tes of any sys te m of par t i-c les as s i m ply t h e s table for m s of con t in u ou s m a t t er waves,Schrödinger sought con nections to a well-developed branch of clas-sical physics. The techniques of continuu m mechanics allowed himto for m ula te an equat ion for h is waves. It too was buil t aro u n dthe constan t h . Bu t now the basic concepts were differen t, and soalso the fu ndamen tal m eaning. Schrödinger had a distas te for thediscontinuity of Bohr’s atomic models and the lack of in tuit ive pic-turabil i ty of Heisenberg’s quant u m m echanics. To his m ind, t hequan tu m did not imply any of these things. Indeed, i t showed theopposi t e: t h a t t h e apparen t a to m ic i ty of ma t te r d isgu ised anunderlying contin uu m.

The Quantum inQuantum Mechanics

ICONICALLY we now writeHeisenberg’s 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-berg’s uncertainty principle of1927: DpDq ≥ h/4p.) The sig-nificance of the approach, andits rearticulation as a matrixcalculus, was made plain byMax Born, Pascual Jordan, andWerner Heisenberg. Its fullprofundity was revealed byPaul Dirac.


Thus a familiar model connected to physical in tuition, but con-st it u ting mat ter of some ill-understood sort of wave, confronted anabs tract m athemat ics wit h see m ingly bizarre variables, insisten tabou t discon tin ui ty and suspending space-ti m e pict ures. Unsur-prisingly, the coexistence of al ternative theories generated debate.The fact, soon demonstrated, of their mathe matical equivalence didnot resolve the in terpretat ive dispu te. For fu ndamen tally differentphysical pictures were on offer.

In fact, in place of Schrödinger’s mat ter waves and Heisenberg’suncom promising discreteness, a conventional understanding set tledin t ha t so m ew hat spli t t he difference. However, t he t h in king ofthe old quantu m theory school still dominated. Born dematerializedSchrödinger’s waves, turning them in to pure densities of probabilityfor finding discrete par ticles. Heisenberg added his uncer tainty prin-ciple, limiting the very possibili ty of measurement and under min-ing the law of causali ty. The pict ure was capped by Bohr’s 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 ErwinSchrödinger, with Wolfgang Pauli andWerner Heisenberg next to each otherbehind Max Born. (From Cinquantenairedu Premier Conseil de Physique Solvay,1911–1961)

BEA M LINE 19

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

Labeled the Copenhagen In terpretation after Bohr’s decisive in-fluence, it s success (to his mind) led the Danish theorist to charac-terize quan tu m mechanics as a rat ional generalizat ion of classicalphysics. Not everyone agreed that th is was the end poin t. Indeed,Einstein, Schrödinger, and others were never reconciled. Even Bohr,Heisenberg, and Pauli expected further changes—though in a newdo m ain , t h e quan t u m t heory of fie lds, w hich took quan t u mmechanics to a higher degree of complexity. But their expectationsof fu ndam en tal transfor m at ion in t he 1930s and beyond, charac-terized by analogies to t he old quan t u m t heory, fou nd li t t le reso-nance outside of their circle.

Ironically enough, just as for their an ti-Copen hagen colleagues,their demand for furt her rethinking did not make m uch headway. Ift he physical m eaning of the quan t u m re mained, to so m e, ra t herobscure, i ts pract ical u tili ty could not be denied. Whatever lessonsone took from quantu m mechanics, i t seemed to work. It not onlyi ncorporated gracefu lly t h e previou s q uan t u m ph eno m ena, bu topened 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, t he quantu m had been built in to t he founda-tions of physical theory.

SUGGESTIONSFOR FURTHER READING

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 on“One Hundred Years ofQuantum Physics.” To seethe full text of this article, goto http://www.sciencemag.org/cgi/content/full/289/5481/893.


by CHARLES H. TOWNES

O N JULY 21, 1969, astronauts Neil Ar mstrong andEdwin “Buzz” Aldrin set up an array of small reflectors onthe m oon, facing them toward Earth. At the same t ime, twoteams of astrophysicists, one at the Universi ty of California’sLick Observatory and the other at the Universi ty of Texas’sMcDonald Observatory, were preparing small inst ru mentson two big telescopes. Ten days later, the Lick team pointedits telescope at t he precise location of t he reflectors on themoon and sent a small pulse of power into t he hardware theyhad added to it. A few days after that, the McDonald teamwent through the same steps. In t he heart of each telescope,a narrow bea m of extraordinarily pure red ligh t emergedfrom a syn thet ic ruby crystal, pierced the sky, and enteredthe near vacuu m of space. The two rays were still only athousand yards wide after traveling 240,000 miles to illu mi-nate the m oon-based reflectors. Sligh tly more than a secondafter each ligh t beam hit i ts target, the crews in Californiaand Texas detected its fain t reflection. The brief time in ter-val between launch and detection of these ligh t pulses per-mit ted calculation of the distance to the moon to within aninch—a measuremen t of unprecedented precision.

The ruby crystal for each ligh t source was the heart of alaser (an acronym for ligh t amplification by stim ulated e mis-sion of radiation), which is a device first de monstrated in1960, just nine years earlier. A laser beam reflected from themoon to measure its distance is only one dramatic illustra-tion of the spectacular quality of laser ligh t. There are manyother more m undane, practical uses such as in surveyingland and grading roads, as well as myriad everyday uses—

T H E L I G H T T H A T S H I N

Adapted by Michael Riordan from HowThe Laser Happened: A dven tures of aScien tis t , by Charles H. Townes.Reprin ted by per mission of OxfordUniversi ty Press.

A Nobel laureate recounts

the invention of the laser

and the birth of quantum

electronics.

BEA M LINE 21

ranging from compact disc play-ers to grocery-store checkoutdevices.

The smallest lasers are so tinyone cannot see them without amicroscope. Thousands can bebuilt on semiconductor chips.The biggest lasers consu me asm uch electricity as a smalltown. About 45 miles from my office in Berkeley is theLawrence Liver more National Laboratory, which has someof the world’s most powerful lasers. One set of t hem, collec-tively called N OVA, produces ten individual laser beams thatconverge to a spot t he size of a pinhead and generate temper-atures of many millions of degrees. Such in tensely concen-trated energies are essen tial for experimen ts t hat can showphysicists how to create conditions for n uclear fusion. TheLiver more team hopes thereby to find a way to generate elec-tricity efficien tly, with lit tle pollu tion or radioactive wastes.

For several years after the laser’s invention, colleaguesliked to tease me about it , saying, “That’s a great idea, bu ti t’s a solu tion looking for a problem.” The tru th is, none ofus who worked on the first lasers ever imagined how manyuses there might eventually be. Bu t that was not our motiva-tion. In fact, many of today’s practical technologies have re-sulted from basic scientific research done years to decadesbefore. The people involved, motivated mainly by curiosity,often have li t tle idea as to where t heir research will eventu-ally lead.

N E S S T R A I G H T

Lasers are commonly used in eyesurgery to correct defective vision.

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LIKE THE TRANSISTOR,the laser and its progenitor themaser (an acronym for micro-

wave a m plificat ion by s t i m ulat edemission of radiation) resulted fromt h e appl icat io n of qu an t u m m e-chan ics to elect ron ics after WorldWar II. Together with other advances,they helped spawn a new disciplinein applied physics known since t helate 1950s as “quantum electronics.”

Since early in the twentieth cen-tury, physicists such as N iels Bohr,Louis de Broglie, and Albert Einsteinlearned how m olecules and a tom sabsorb and emit light—or any otherelectrom agnet ic radiat ion—on t hebasis of the newly discovered laws ofquantum mechanics. When atoms orm olecu les absorb ligh t , one m igh tsay that part s of t he m wiggle backand fort h or twirl wi t h new, addedenergy. Quantum mechanics requirest hat t hey s tore energy in very spe-cific ways, with precise, discrete lev-els of energy. An atom or a moleculecan exist in either its ground (lowest)energy state or any of a set of higher(quantized) levels, but not at energiesbetween those levels. Therefore theyon ly absorb ligh t of cer tain wave-lengths, and no ot hers, because thewavelength of ligh t deter mines theenergy of its individual photons (seebox on right). As atoms or moleculesdrop from higher back to lower en-ergy levels, they emit photons of thesa m e energies or wavelengt hs asthose they can absorb. This processis usually spontaneous, and this kindof ligh t is nor m ally e m it ted whenthese atoms or molecules glow, as ina fluorescent light bulb or neon lamp,radiating in nearly all directions.

Einstein was the first to recognizeclearly, from basic t her m odynam ic

principles, t ha t if photons can beabsorbed by atoms and boost t hemto higher energy states, then light canalso prod an a to m to give up i t sen ergy and drop dow n to a lowerlevel. One photon hits the atom, andt wo come ou t. When t his happens,t he e m it ted photon takes off inprecisely the sam e direction as thelight that stim ulated the energy loss,wit h the t wo waves exact ly in step(or in the same “phase”). This “stim-ulated emission” results in coherentamplifica tion, or a mplification of awave at exactly the same frequencyand phase.

Bot h absorption and s ti m ulatedemission can occur sim ultaneously.As a light wave comes along, it cant hus excite so m e atom s t hat are inlower energy states into higher statesand, at t he same time, induce someof those in higher states to fall backdow n to lower s ta t es. If t here aremore atoms in the upper states t hanin t he lower s ta t es, m ore ligh t isemit ted than absorbed. In short, theligh t gets s t ronger. I t com es ou tbrighter t han it went in.

T he reason w hy ligh t is usuallyabsorbed i n m at erials is t ha t sub-s tances al m ost always have m oreatoms and molecules sitting in lowerenergy sta tes t han in higher ones:m ore pho tons are absorbed t hane mit ted. Thus we do not expect toshine a ligh t through a piece of glassand see i t com e ou t t he ot her sidebrigh ter t han it went in. Yet t his isprecisely what happens with lasers.

The t rick in making a laser is toproduce a m aterial in w hich t heenergies of t he atoms or moleculespresen t have bee n pu t in a veryabnor m al condit ion, wit h m ore oft he m in exci ted sta tes t han in t he

An early small laser made of semicon-ducting material (right) compared with aU.S. dime.

BEA M LINE 23

BECAUSE OF QUANTUMmechanics, atoms and moleculescan exist only in discrete states with

very specific values of their total energy.They change from one state to another byabsorbing or emitting photons whose ener-gies correspond to the difference betweentwo such energy levels. This process, whichgenerally occurs by an electron jumpingbetween two adjacent quantum states, isillustrated in the accompanying drawings.

How Lasers Work(a)

(b)

(c)

(d)

(e)

Stimulated emission of photons, the basisof laser operation, differs from the usual ab-sorption and spontaneous emission. Whenan atom or molecule in the “ground” stateabsorbs a photon, it is raised to a higherenergy state (top). This excited state maythen radiate spontaneously, emitting a pho-ton of the same energy and reverting backto the ground state (middle). But an excitedatom or molecule can also be stimulated toemit a photon when struck by an approach-ing photon (bottom). In this case, there isnow a second photon in addition to thestimulating photon; it has precisely thesame wavelength and travels exactly inphase with the first.

Lasers involve many atoms or mole-cules acting in concert. The set of drawings(right) illustrates laser action in an optical-quality crystal, producing a cascade of pho-tons emitted in one direction.

(a) Before the cascade begins, the atoms in the crystal are in their ground state.(b) Light pumped in and absorbed by these atoms raises most of them to the excitedstate. (c) Although some of the spontaneously emitted photons pass out of the crys-tal, the cascade begins when an excited atom emits a photon parallel to the axis ofthe crystal. This photon stimulates another atom to contribute a second photon, and(d) the process continues as the cascading photons are reflected back and forth be-tween the parallel ends of the crystal. (e) Because the right-hand end is only partiallyreflecting, the beam eventually passes out this end when its intensity becomes greatenough. This beam can be very powerful.


to find a way to generate wavesshorter than those produced by t heklystrons and magnetrons developedfor radar in World War II. One day Isuddenly had an idea—use moleculesand t he st i m ula ted e m ission fromt he m. Wit h graduate s t uden t Ji mGordon and postdoc Herb Zeiger, Idecided to experiment first with am-monia (N H3) molecules, which emitradiat ion a t a wavelengt h of abou t1 cen timeter. After a couple of yearsof effort, the idea worked. We chris-te ned t his device t he “ m aser.” Itproved so interesting that for a whileI pu t off my original goal of trying togenerate even shorter wavelengths.

In 1954, shortly after Gordon andI built our second maser and showedthat the frequency of its microwaveradiat ion was indeed re m arkablypure, I visi t ed Den m ark and sawN iels Bohr. As we were walk ingalong t he street toget her, he askedme what I was doing. I described themaser and its amazing performance.

“But t hat is not possible!” he ex-claimed. I assured him it was.

Si m ilarly, a t a cock tail par ty inPrinceton, New Jersey, t he Hungar-ian mat he m at ician John von Neu-man n asked what I was working on.I told him abou t the maser and t hepurity of its frequency.

“That can’t be right!” he declared.Bu t i t was, I replied, telling hi m i thad already been demonstrated.

Such pro test s were no t offhandopin ions abou t obscure aspec ts ofphysics; they came from the marrowof t hese m en’s bones. T heir objec-tions were founded on principle—theHeisenberg uncer tain ty pri nciple.A central tenet of quantu m mechan-ics, this principle is among the coreachievem ents that occurred during

ground, or lower, sta tes. A wave ofelectromagnetic energy of the properfrequency traveling t hrough such apeculiar substance will pick up ratherthan lose energy. The increase in thenu m ber of photons associa ted wit hthis wave represents amplification—ligh t a m plificat ion by st i m ula tedemission of radiation.

If t his a m plificat ion is not verylarge on a si ngle pass of t he wavethrough the material, there are waysto beef i t up. For example, two par-allel m irrors—bet ween w hich t helight is reflected back and forth, withexcited molecules (or atoms) in t hemiddle—can build up the wave. Get-ting the highly directional laser beamout of t he device is just a mat ter ofone m irror being m ade par t iallytransparen t, so t hat when the inter-nal ly reflec t i ng bea m ge ts s t rongenough, a substan tial amount of itspower shoots righ t on t hrough oneend of t he device.

The way th is man ipula t ion ofphysical laws ca me about, with themany false starts and blind alleys onthe way to its realization, is the sub-ject of my book, How the Laser Hap-pened. Briefly sum marized in this ar-ticle, it also describes my odyssey asa scien tist and its unpredictable andperhaps nat ural pat h to t he m aserand laser. This story is in terwovenwit h t he way t he field of quan t u melectronics grew, rapidly and strik-ingly, owing to a variety of importantcon tributors, t heir cooperat ion andcompetitiveness.

D URIN G THE LATE 1940sand early 1950s, I was exam-ining molecules with micro-

waves at Columbia University—do-ing microwave spectroscopy. I tried

None of us w ho w orked

on the first lasers ever

imagined ho w many uses

there might eventually be.

Many of today’s practical

technologies have resulted

from basic scientific

research done years

to decades before.

BEA M LINE 25

a phenomenal burst of creativi ty inthe first few decades of the twentiethcen tury. As its na me implies, it de-scribes the i mpossibility of achiev-ing absolu te knowledge of all the as-pects of a system’s condition. Thereis a price to be paid i n a t te m ptingto m easure or define one aspect ofa specific part icle to very great ex-actness. One m ust surrender knowl-edge of, or con trol over, some otherfeature.

A corollary of t his principle, onw hich t he m aser’s doubters s t u m-bled, is that one cannot measure anobject’s frequency (or energy) to greataccuracy in an arbitrarily short timeinterval. Measurements made over afinite period of t im e au tom aticallyimpose uncer tain ty on the observedfrequency.

To many physicists steeped in theu ncer tain ty principle, t he m aser’sperfor mance, at first blush, made nosense at all. Molecules race throughi t s cavi ty, spending so li t t le t im et here—about one ten-thousandth ofa second—that it seemed impossiblefor the frequency of the ou tput mi-crowave radiation to be so narrowlydefined. Yet that is exactly what hap-pens in the maser.

There is good reason that t he un-certainty principle does not apply sosimply here. The maser (and by anal-ogy, the laser) does not tell you any-t hing abou t t he energy or frequen-cy of any specific m olecule. Whena molecule (or atom) is stim ulated toradiate, it m ust produce exactly thesa m e frequency as t he s ti m ulat ingradiation. In addition, this radiationrepresents the average of a large num-ber of m olecules (or a to m s) work-ing together. Each individual mole-cu le re m ains a nony m ous, not

accurately measured or tracked. Theprecision arises fro m factors t hatmollify the apparent demands of theuncertainty principle.

I am not sure that I ever did con-vince Bohr. On that sidewalk in Den-mark, he told me emphatically t hatif m olecules zip t hrough the maserso quickly, their emission lines m ustbe broad. After I persis ted, howev-er, he relented.

“Oh, well, yes,” he said; “Maybeyou are righ t.” Bu t m y i m pressionwas that he was just trying to be po-lite to a younger physicist.

After our first chat at that Prince-ton party, von N eu mann wanderedoff and had anot her drink. In abou tfifteen minutes, he was back.

“Yes, you’re righ t,” he snapped.Clearly, he had seen the point.

NOVA, the world’s largest and most pow-erful laser, at the Lawrence LivermoreNational Laboratory in California. Its 10laser beams can deliver 15 trillion wattsof light in a pulse lasting 3 billionths of asecond. With a modified single beam, ithas produced 1,250 trillion watts for halfa trillionth of a second. (CourtesyLawrence Livermore NationalLaboratory)


drive any specific resonant frequencyinside a cavity.

As I played wi t h t he var ie ty ofpossible molecular and atomic t ran-si t ions, and t he m e t hods of exci t-ing them, what is well-known todaysudden ly beca m e clear to m e: i t isjust as easy, and probably easier, togo righ t on dow n t o real ly shor twavelengths—to the near-infrared oreven optical regions—as to go downone smaller step at a time. This wasa revelation, like stepping t hrougha door in to a room I did not suspectexisted.

The Doppler effect does indeed in-creasingly smear ou t the frequencyof response of an atom (or molecule)as one goes to shorter wavelengths,bu t t here is a co m pensat ing fac torthat comes into play. The number ofatoms required to amplify a wave bya given a m ount does not increase,because atom s give up their quan tamore readily at higher frequencies.And while the power needed to keepa certain number of atoms in excitedstates increases wit h the frequency,

He seemed very interested, and heasked me about the possibility of do-ing so m et h ing si m ilar a t shor terwavelengths using semiconductors.O n ly la ter did I lear n fro m h isposthumous papers, in a September1953 let ter he had writ ten to EdwardTeller, that he had already proposedproducing a cascade of stim ulated in-frared radia tion in sem iconductorsby exci t ing elect rons wi t h in tenseneutron bombardment. His idea wasal m ost a laser, bu t he had nott hough t of e m ploying a reflec t ingcavity nor of using the coherent prop-erties of stim ulated radiation.

IN T HE LATE SU MMER of1957, I fel t i t was high t i m e Imoved on to the original goal that

fostered the m aser idea: oscillatorst hat work at wavelengths apprecia-bly shorter than 1 millimeter, beyondw hat s tandard elec tronics couldachieve. For so m e t i m e I had beent hin king off and on about this goal,hoping that a great idea would popin to my head. But since nothing hadspon taneously occurred to me, I de-cided I had to take ti me for concen-trated t hough t.

A major problem to overcome wasthat the rate of energy radiation froma m olecule increases as t he four t hpower of the frequency. Thus to keepm olecules or a to m s excit ed in aregime to amplify at a wavelength of,say, 0.1 millimeter instead of 1 cen-timeter requires an increase in pump-ing power by m any orders of m ag-nitude. Another problem was that forgas molecules or atoms, Doppler ef-fects increasingly broaden t he emis-sion spectrum as the wavelength getssmaller. That means there is less am-plification per molecule available to

t he total power required—even toam plify visible ligh t—is not neces-sarily prohibitive.

N ot only were t here no clearpenalties in such a leapfrog to veryshort wavelengths or high frequencies,this approach offered big advantages.In t he near-infrared and visible re-gions, we already had plen ty of ex-perience and equipment. By contrast,wavelengths near 0.1 m m and tech-n iques to handle t he m were rela-tively unknown. It was time to takea big step.

Still, there remained another ma-jor concern: t he resonant cavity. Tocontain enough atoms or molecules,t he cavity would have to be m uchlonger t han t he wavelengt h of t heradiat ion—probably thousands oft i mes longer. T his m ean t, I feared,that no cavity could be very selectivefor one and only one frequency. Thegrea t size of the cavi ty, co m paredto a single wavelengt h, m ean t t hatmany closely spaced but slightly dif-ferent wavelengt hs would resonate.

By grea t good fort une, I got helpand anot her good idea before I pro-ceeded any further. I had recently be-gu n a consul t ing job a t Bell Labs,where my brother-in-law and formerpostdoc Arthur Schawlow was work-ing. I nat urally told hi m t hat I hadbeen t h in ki ng abou t such op t icalm asers, and he was very in terestedbecause he had also been thinking inthat very direction.

We talked over t he cavi ty prob-le m , and Art ca m e up wit h the so-lu t ion. I had been considering arather well-enclosed cavity, with mir-rors on t he ends an d holes i n t hesides only large enough to providea way to pu m p energy in to t he gasand to kill some of the directions in

The development

of the laser follo w ed

no script excep t

to he w to the nature

of scientists groping

to understand,

to explore, and

to create.

BEA M LINE 27

which the waves might bounce. Hesuggested instead t hat we use justt wo plates, two simple mirrors, andleave off t he sides al toget her. Sucharrangements of parallel mirrors werealready used a t t he t i m e in opt ics;t hey are called Fabry–Perot in terfer-ometers.

Art recognized that withou t t hesides, m any oscillat ing modes t hatdepend on internal reflections wouldeliminate themselves. Any wave hit-t ing ei t her end m irror at an anglewould even tually walk itself ou t oft he cavi ty—and so not build up en-ergy. The only modes that could sur-vive a nd oscilla t e, t hen, wo u ld bewaves reflected exactly straight backand forth bet ween the two mirrors.

More detailed studies showed thatt he size of t he m irrors and the dis-tance between t hem could even bechosen so t hat only one frequencywould be likely to oscilla te. To besure, any wavelength that fi t an ex-act n u m ber of t i m es be t w een t hemirrors could resonate in such a cav-ity, just as a piano string produces notjus t one pure frequency bu t alsom any higher har m onics. In a well-designed system, however, only onefrequency will fall squarely a t t het ransi t io n energy of t he m edi u mwithin it. Mathematically and phys-ically, it was “neat.”

Art and I agreed to write a paperjointly on optical masers. It seem edclear t hat we could act ually buildone, but it would take time. We spentnine mont hs working on and off inour spare time to write the paper. Weneeded to clear up t he engineeringand som e specific det ails, such aswhat m aterial to use, and to clarifythe theory. By August 1958 the man-uscript was com plete, and the Bell

Labs patent lawyers told us that theyhad done t heir job pro tect i ng i t sideas. The Physical Review publishedi t in the Dece mber 15, 1958, issue.

In September 1959 the first scien-tific meeting on quantum electronicsand resonance phenomena occurredat the Shawanga Lodge in New York’sCatskill Mountains. In retrospect, itrepresen ted the for mal bir t h of t hemaser and its related physics as a dis-t inct subdiscipline. At t hat m ee t-ing Schawlow delivered a general talkon optical m asers.

Lis t eni ng wi t h in teres t wasTheodore Maiman from t he HughesResearch Laboratories in Culver City,Califor nia. He had been workingwith ruby masers and says he was al-ready t hinking abou t using ruby asthe mediu m for a laser. Ted listenedclosely to t he rundown on t he pos-sibili t y of a solid-st a te ruby laser,about which Art was not too hope-ful. “It may well be that more suit-able solid materials can be found,”he no ted, “and we are look ing forthem.”

James Gordon, Nikolai Basov, HerbertZeiger, Alexander Prokhorov, and authorCharles Townes (left to right) attendingthe first international conference onquantum electronics in 1959.

28 SUMMER/FALL 2000

tist s recen t ly hired after t heir uni-versi ty research in t he field of mi-crowave a nd radio spect roscopy—st uden ts of Willis La m b, Polyk arpKusch, and myself, who worked to-get her i n t he Colu m bia Radia t ionLaboratory, and of Nicholas Bloem-bergen a t Harvard. The whole fieldof quan tu m elect ronics grew out ofthis approach to physics.

T he develop m e nt of t he m aserand laser followed no script exceptto hew to t he nat ure of scien t is tsgroping to understand, explore andcreate. As a striking example of howi mportant technology applied to hu-man interests can grow out of basicuniversi ty research, t he laser’s de-velopm ent fi ts a pat tern t hat couldnot have been predicted in advance.

What research planner, wanting amore in t ense ligh t source, wou ldhave started by studying moleculeswit h microwaves? What industrial-ist, looking for new cutting and weld-ing devices, or what doctor, wantinga new surgical tool as the laser hasbecome, would have urged the studyof microwave spec troscopy? T hewhole field of quan tu m electronicsis truly a textbook example of broad-ly applicable technology growing un-expectedly ou t of basic research.

Maiman felt t hat Schawlow wasfar too pessimstic and left t he meet-ing in ten t on building a solid-stateruby laser. In subsequent months Tedm ade st rik ing m easure m e nt s onruby, showing that its lowest energylevel could be part ially emptied byexci ta t ion wi t h in tense light . Het hen pushed on toward still brighterexcitation sources. On May 16, 1960,he fired up a flash la m p wrappedaround a ruby crystal abou t 1.5 cmlong and produced the first operatinglaser.

The evidence that it worked wasso m ew hat indirec t . T he H ughesgroup did not set it up to shine a spotof ligh t on the wall. No such flash ofa bea m had been seen, w hich leftroom for doubt abou t just what theyhad obtained. Bu t t he ins tru m en tshad show n a substan tial change int he fluorescence spect ru m of t heruby; i t beca m e m uch narro wer, aclear sign t ha t e m ission had beenstimulated, and the radiation peakedat jus t t he wavelengt hs t ha t weremost favored for such action. A shortw hile la ter, bo t h t he H ughes re-searchers and Schawlow at Bell Labsindependently demonstrated power-ful flashes of directed light that madespo ts on t he wall—clear in t u i t iveproof t hat a laser is indeed working.

IT IS NOTEWORTHY that al-most all lasers were first built inindustrial labs. Part of the reason

for industry’s success is that once itsi m por tance becom es apparen t, in-dustrial laboratories can devote moreresources and concen trated effort toa proble m t han can a u niversi t y.When the goal is clear, industry canbe effective. Bu t the first lasers wereinven ted and buil t by young scien-

BEA M LINE 29

O NE N ORMALLY THINKS that quan tu m mechanics is onlyrelevan t on submicroscopic scales, operating in the domain ofatomic, nuclear, and part icle physics. But if our most excitingideas about the evolu tion of the early Universe are correct, t henthe imprin t of the quantu m world is visible on astronomicalscales. T he possibili ty that quantu m mechanics shaped thelargest structures in the Universe is one of the theories to comefrom the marriage of the quan tu m and the cosmos.

The Quantum

by ROCKY KOLB

WHAT’S OUT THERE?

O n a dar k clear nigh t t he sky offersmuch to see. With the unaided eye onecan see things in our solar system suchas planets, as well as extrasolar objectslike stars. Nearly everything visible byeye resides within our own Milky WayGalaxy. Bu t with a lit tle patience andskill i t’s possible to find a few extra-galac t ic objec t s. The Andro m edaGalaxy, 2.4 million light-years distant,is visible as a fain t nebu lous region,and fro m t he Sou t hern He m ispheretwo s mall nearby galaxies (if 170,000

ligh t-years can be considered nearby),t he Magellan ic Clou ds, can also beseen with the unaided eye.

While the preponderance of objectsseen by eye are galac t ic, t he viewth rough large telescopes reveals t heuniverse beyond the Milky Way. Evenwith the telescopes of t he nineteen thcen tury, t he great Brit ish astronomerSir William Herschel discovered about2,500 galaxies, and h is son, Sir Joh nHerschel, discovered an addi t ionalt housand (al t hough nei t her of t heHerschels knew that the objects theydiscovered were ex t ragalac t ic). As

& The Cosmos

“When one

tugs at a

single thing

in Nature, he

finds it

hitched to

the rest of the

Universe.”

—John Muir

(Courtesy Jason Ware, http://www.galaxyphoto.com)


several t housand galaxies. Clustersof galaxies are par t of even largerassocia t ions cal led superclus ters,containing dozens of clusters spreadou t over 100 m illion ligh t-years ofspace. Even superclusters may not bet he larges t t hings in t he U niverse.The largest surveys of the Universesuggest t o so m e as t ron o m ers t h atgalaxies are organ ized on t wo-di m ensional sheet-like struct ures,while others believe that galaxies liealong extended one-dimensional fil-am en t s. The exac t nat ure of howgalaxies are arranged in the Universeis still a matter of debate among cos-mologists. A picture of t he arrange-ment of galaxies on the largest scalesis only now emerging.

Not all of the Universe is visibleto t he eye. In addit ion t o pat t ernsin the arrangement of mat ter in thevisible Universe, there is also a struc-ture to t he background radiat ion.

The Universe is awash in a ther-m al bat h of radia t io n, wi t h a te m-perat ure of three degrees above ab-solute zero (3 K or - 270 C). Invisibleto the h u m an eye, t he backgroundradiat ion is a re m na n t of t he hotprimeval fireball. First discovered in1965 by Ar no Penzias and Rober tWilson, it is a funda mental predic-tion of the Big Bang theory.

Soon after Penzias and Wilson dis-covered t he background radiat ion,the search began for variations in thete m perat ure of t he u niverse. Fornearly 30 years, as t rophysicis t ssearched in vain for regions of the dis-tan t Un iverse tha t were ho t t er orcolder than average. It was not un til1992 that a team of astronomers us-ing the Cosmic Background ExplorerSat elli t e (C OBE) discovered an i n-trinsic pat tern in the temperature of

astronomers buil t larger telescopesand looked deeper in to space, t henu m ber of k now n galaxies grew.Alt hough no one has ever bot heredto coun t, ast ronomers have iden t i-fied about four million galaxies. Andthere are a lot more out there!

O ur deepes t view in to t he U ni-verse is t he Hubble Deep Field. Theresult of a 10-day exposure of a verysm all region of t he sky by N ASA’sHubble Space Telescope, the HubbleDeep Field reveals a universe full ofgalaxies as far as Hubble’s eye can see(photo above). If the Space Telescopecould take the time to survey the en-t ire sky to t he dep t h of t he DeepField, it would find more than 50 bil-lion galaxies.

Alt hough large galaxies con tainat least 100 billion stars and stretchacross 100,000 ligh t-years or m oreof space, t hey aren’t t he bigges tthings in t he Universe. Just as starsare part of galaxies, galaxies are partof larger struct ures.

Many galaxies are m em bers ofgroups con taining a few dozen to ahundred galaxies, or even larger assem-blages known as clusters, containing

Galaxies fill the Hubble Deep Field, oneof the most distant optical views of theUniverse. The dimmest ones, some asfaint as 30th magnitude (about four bil-lion times fainter than stars visible to theunaided eye), are very distant and rep-resent what the Universe looked ike inthe extreme past, perhaps less than onebillion years after the Big Bang. To makethis Deep Field image, astronomers se-lected an uncluttered area of the sky inthe constellation Ursa Major and pointedthe Hubble Space Telescope at a singlespot for 10 days accumulating and com-bining many separate exposures. Witheach additional exposure, fainter objectswere revealed. The final result can beused to explore the mysteries of galaxyevolution and the early Universe.(Courtesy R. Williams, The HDF Team,STScl, and NASA)

BEA M LINE 31

t he Universe. Since the t ime of t heC OBE discovery, a pa t t ern of te m-pera t u re variat ions has been m ea-sured wit h increasing precision bydozens of balloon-borne and terres-trial observations. A new era of pre-cision cosmological observations iss tar t ing. So m et i m e in 2001 N ASAwill lau nch a new sa t elli te, t heMicrowave Anisotropy Probe (MAP),and sometime in 2007 t he EuropeanSpace Agency will launch an evenm ore a m bit ious effor t , t he PlanckExplorer, to st udy temperature vari-a t ions in t he cos m ic bac kgrou ndradiation.

Even if our eyes were sensitive tomicrowave radiation, we would havea hard t im e discerning a pat tern oftem perat ure fluctuat ions since t hehot tes t and coldes t regions of t hebackground radiation are only abou tone-t housandt h of a percen t hot terand colder than average.

Although small in magnitude, thebackground temperature fluctuationsare large in im portance since t heygive us a snapshot of structure in theUniverse when the background pho-t ons las t sca t t ered, abou t 300,000years after the Bang.

WHY IS IT T HERE?

A really good answer to a deep ques-t ion usually leads to even deeperquestions. Once we discover what’sin t he Universe, a deeper ques t ionarises: Why is it there? Why are starsarranged in to galaxies, galaxies in toclusters, clusters in to superclusters,and so on? Why are there small vari-ations in the temperature of the Uni-verse?

Part of the answer involves grav-ity. Everything we see in the Universe

is t he resul t of gravi ty. Every t i m eyou see a star the imprint of gravityis shining at you. Today we observenew stars forming within giant in ter-stellar gas clouds, such as those foundat the center of the Orion Nebula just1,500 ligh t-years away (see photo onnext page).

Interstellar clouds are not smoothand u nifor m ; they con tain regionswhere the density of material is largert han in su rrou nding regions. T hedense regions wit hin the clouds aret he seeds around which stars growthrough the irresist ible force of grav-ity. The dense regions pull in nearbymaterial through the force of gravity,which compresses the material un-til i t becomes hot and dense enoughfor nuclear react ions to com menceand form stars.

About five billion years ago in ourlit t le corner of the Milky Way, grav-i ty started to pull toget her gas anddust to for m our solar system. T hisfashioning of s truct ure in our localneighborhood is just a small par t ofa process that started about 12 billionyears ago on a grander scale through-out the Universe.

For the first 300 centuries after theBig Bang, t he Universe expanded toorapidly for gravity to fashion st ruc-t ure. Finally, 30,000 years after t heBang (30,000 AB), t he expansion hadslowed enough for gravi ty to beginthe long relentless process of pullingtogether matter to form the Universewe see today.

We are quite confiden t that grav-i ty shaped t he Universe becauseas trophysicis t s ca n si m ula te in amat ter of days what Nature required12 billion years to accomplish. Start-ing wi t h t he U niverse as i t existed30,000 AB, large supercomputers can

The microwave radiation from the sky, asseen by COBE. The radiation has anaverage temperature of 2.73 degreesCentigrade above absolute zero. Herethe dark and light spots are 1 part in100,000 warmer or colder than the rest.They reveal gigantic structures stretch-ing across enormous regions of space.The distinct regions of space arebelieved to be the primordial seeds pro-duced during the Big Bang. Scientistsbelieve these anomalous regionsevolved into the galaxies and largerstructures of the present-day Universe.(Courtesy Lawrence BerkeleyLaboratory and NASA)


formation within the Orion Nebulaif t he gas and du s t were perfec t lyuniform, structure would never havefor m ed if t he en t ire U niverse wascom pletely u nifor m. Wit hou t pri-m ordial seeds in t he Universe30,000 AB, gravity would be u nableto shape the Universe in to the formwe now see. A seedless u n iversewould be a pret ty boring place to live,because mat ter wou ld re m ain per-fect ly u n ifor m ra t her t han asse m-bling into discrete structures.

The pat tern of structure we see inthe Universe today reflects the pat-tern of initial seeds. Seeds have to beinserted by hand into the computersim ulations of the formation of struc-ture. Since the aim of cosmology isto unders tand the s tr uct ure of t heU niverse on t he basis of physicallaws, we just can’t end the story bysaying structure exists because therewere pri m ordial seeds. For a co m-plete answer to the questions of whyare t here t hings in the Universe, wehave to know what planted the pri-mordial seeds.

In the m icroworld of subato m icphysics, there is an inheren t uncer-tain t y abou t t he posi t ions andenergies of par t icles. According tothe uncertainty principle, energy isn’t

calculate how small primordial seedsgrew to become t he gian t galaxies,clus ters of galaxies, superclusters,walls, and filamen ts we see through-out the Universe.

Gravi ty alone can not be the finalanswer to the question of why mat-ter in t he U niverse has such a richand varied arrangement. For the forceof gravi ty to pu ll t hi ngs toge t herrequires small initial seeds where thedensity is larger t han the surround-ing regions. In a very real sense, t hefact there is anything in the Universeat all is because there were primor-dial seeds in the Universe. While theforce of gravity is inexorable, struc-ture cannot grow without the seedsto cu l t ivate. Jus t as t hough t herewouldn’t be any seeds to t rigger star

Galaxies and galaxy clusters are notevenly distributed throughout the Uni-verse, instead they are arranged in clus-ters, filaments, bubbles, and vast sheet-like projections that stretch acrosshundreds of millions of light-years ofspace. The goal of the Las CampanasRedshift Survey is to provide a largegalaxy sample which permits detailedand accurate analyses of the propertiesof galaxies in the local universe. Thismap shows a wedge through the Uni-verse containing more than 20,000galaxies (each dot is a galaxy).(Courtesy Las Campanas RedshiftSurvey)

The Orion nebula, one of the nearbystar-forming regions in the Milky Waygalaxy. (Courtesy StScl and NASA)

BEA M LINE 33

always conserved—it can be violatedfor a brief per iod of t i m e. Beca usequan t u m m echanics applies to t hem icroworld, on ly t iny am oun ts ofenergy are involved, and t he t i m eduring which energy is out of balanceis exceedingly short.

O ne of t he consequences of t heuncertainty principle is that a regionof seemingly empty space is not reallye m pty, bu t is a seet hing frot h inwhich every sort of fundamental par-t icle pops ou t of e m pty space for abrief instant before annihilating withits an tiparticle and disappearing.

Em pt y space on ly looks l ike aquiet, cal m place because we can’tsee N at ure operating on submicro-scopic scales. In order to see t hesequantu m fluctuations we would haveto take a sm all region of space andblow it up in size. Of course that isnot possible in any terrest rial labo-ratory, so to observe t he quan t u mfluct uations we have to use a labo-ratory as large as the entire Universe.

In the early-Universe theory knownas inflation, space once exploded sorapidly that the pattern of microscopicvacu u m quan t u m flu ct uat ions be-came frozen in to the fabric of space.T he expansion of t he U niversestretched the microscopic pat tern ofquantu m fluctuations to astronom-ical size.

Much later, t he pat tern of whatonce were quan tu m fluctuations ofthe vacuum appear as small fl uctua-t ions in t he m ass de nsi ty of t heUniverse and variations in the tem-perature of the background radiation.

If this theory is correct, then seedsof s tructure are not hing more t hanpat t erns of quan t u m fluc t uat ionsfrom t he infla tionary era. In a very

real sense, quan tu m fluc t uat ionswould be the origin of everything wesee in t he Universe.

When viewi ng asse m blages ofstars in galaxies or galaxies in galac-tic clusters, or when viewing the pat-ter n of flu ct ua t ions i n t he bac k-grou nd radia t ion, you are act uallyseeing quant um fluctuations. Wit h-out the quantum world, the Universewould be a boring place, devoid ofstructures like galaxies, stars, plan-ets, people, poodles, or petunias.

This deep connection between thequantum and the cosmos may be theultimate expression of the true unityof science. The study of the very largeleads to the study of the very small.Or as the great American naturalistJohn Muir stated, “When one tugs ata single thing in Nature, he finds ithitched to the rest of the Universe.”

One of several computer simulations ofthe large-scale structure of the Universe(spatial distribution of galaxies) carriedout by the VIRGO collaboration. Thesesimulations attempt to understand theobserved large-scale structure by test-ing various physics models. (CourtesyVIRGO Collaboration)

For Additional Information on the Internet

Rocky Kolb. http://www-astro-theory.fnal.gov/Personal/rocky/welcome.html

Jason Ware. http://www.galaxyphoto.com

Hubble Space Telescope Public Pictures. http://oposite.stsci.edu/pubinfo/Pictures.html

NASA Image eXchange. http://nix.nasa.gov/

VIRGO Consortium. http://star-www.dur.ac.uk/~frazerp/virgo/virgo.html

COBE Sky Map. http://www.lbl.gov/LBL-PID/George-Smoot.html

Las Campanas Redshift Survey.http://manaslu.astro.utoronto.ca/~lin/lcrs.html

Sloan Digital Sky Survey. http://www.sdss.org


THE URGE TO REDUCE THE FORMS of mat ter to afew elemen tary consti tuents m ust be very ancien t. By450 BCE, Empedocles had already developed or inherited a“standard model” in which everything was composed offour elemen ts—Air, Ear th, Fire, and Water. T hinking aboutthe materials available to him, t his is not a bad lis t. Bu t as apredict ive model of N ature, it has some obvious shor tcom-ings. Successive generations have evolved increasinglysophis ticated standard models, each with its own list of“fu ndamental” consti tuen ts. The length of t he list has fluc-tuated over t he years, as shown on the next page. TheGreeks are actually t ied for t he minim u m with four. T hechemists of the 19t h cen tury and the par ticle physicists ofthe 1950s and 1960s pushed the nu mber up toward 100 beforesome revolu tionary development reduced it dramatically.Today’s list includes abou t 25 elemen tary par ticles, t houghit could be ei ther higher or lower depending on how youcoun t. Tomorrow’s list—the product of t he next generationof accelerators—pro mises to be longer still, with no end insight. In fact, modern speculat ions always seem to increaserather than decrease the n u mber of fu ndamental con-stit uen ts. Superst ring theoris ts dream of unifying all theforces and forms of mat ter in to a single essence, bu t so farthey have lit tle clue how the diversity of our observed worldwould devolve fro m this perfect for m. Others have poin tedou t that Nature at t he shor test distances and highest ener-gies might be qui te random and chaotic, and that the forceswe feel and t he par ticles we observe are special only in t hatthey persist longer and propagate fur ther t han all t he res t.

Two lessons stand ou t in t his cartoon his tory. First, whatserves as a “fundamental consti tuen t” changes with timeand depends on what sor ts of questions one asks. T he older

Get ting to Know Yby ROBERT L. JAFFE

Humankind has

w ondered since the

beginning of history

w hat are the funda-

mental constituents

of mat ter. Today’s list

includes about 25

elementary particles.

Tomorro w ’s lis t

promises to be longer

still, w ith no end

in sight.

Fire

Dry

Wet

Cold

Hot

Water

Eart

h

Air

BEA M LINE 35

models are not really inferior to today’s Standard Modelwithin the con text of t he world they set ou t to describe.And, second, there always seems to be another layer. In t heearly years of t he 21st cen tury par t icle physicists will beprobing deeply in to the physics of the curren t StandardModel of par ticle physics with new accelerators like theB-factories of SLAC and KEK and the Large Hadron Colliderat CERN . Now seems like a good t ime to reflect on w hat toexpect.

It is no acciden t, nor is it a sign of our stupidity, t hat wehave constructed “atomic” descrip tions of Nature onseveral differen t scales on ly to learn that our “atoms” werecomposed of yet more funda-mental constit uen ts. Quan tu mmechanics i tself gives rise tothis apparen tly layered textureof N ature. It also gives us verysophisticated tools and testswith which to probe our con-st it uents for substructure. Look-ing back at the “atoms” of pre-vious genera tions, we can seewhere the hin ts of substructurefirst appeared and how our pre-decessors were led to the nextlayer. Looking forward from ourpresen t crop of elemen tary par-ticles, we see some suggest ionsof deeper structure beneath,but—tan talizingly—other signssuggest t hat today’s fundamen talconsti tuents, nu merous as they

1000

100

10

1

Molecules

Atoms Hadrons

StandardModel

Num

ber

ofEl

emen

tary

Part

icle

s

500 BCE,A,F,W

Distance (cen timeters)

1 meV 1 eV 1 keV 1 MeV 1 GeV 1 TeV 1 PeV

Energy (electron volts)

100 10–4 10–8 10–12 10–16 10–20

ca.1

970

ca.1

930

ca.1

800

p,n,e,ne,g

A schematic history of the concept of anelementary constituent, from the fourelements of the Greeks to today’sStandard Model. The number has goneup and down over the years.

Your Constituen ts


are, may be more fundamental thanyesterday’s.

BEFORE LO OKIN G atwhere we are today, let’s takea brief tou r of t he two m ost

useful “atomic” descriptions of thepast: the standard models of che m-istry and nuclear physics, shown be-low. Both provide very effective de-scriptions of phenomena within theirrange of applicabili ty. Act ually theter m “effec t ive” has a tec hn icalmeaning here. For physicists an “ef-fective theory” is one based on build-ing blocks k nown not to be elemen-tary, bu t which can be t reated as if

they were, in the case at hand. “Ef-fect ive” is t he r igh t word becauseit means bot h “ useful” and “stand-ing in place of,” both of which applyin this case. The chemical elementsare very useful tools to understandeveryday phenom ena, and they“stand in place of” the complex mo-t ions of electrons arou nd ato m icnuclei, which are largely irrelevan tfor everyday applications.

C he m is try and n uclear physicsare both “effective theories” becausequan t u m m echanics shields t he mfro m t he co m plexit y t hat lies be-neath. This feat ure of quan tum me-chanics is largely responsible for theorderliness we perceive in t he phys-ical world, and it deserves more dis-cussio n. Consider a fa m iliar sub-stance such as water. At the simplestlevel, a che m is t views pure wa teras a vast n u mber of iden tical mole-cules, each composed of two hydro-gen atoms bound to an oxygen atom.Deep wit hin t he a to ms are n uclei:eight protons and eight neu trons foran oxygen n ucleus, a single protonfor hydrogen. Within the protons andneu trons are quarks and gluons.Within the quarks and gluons, whoknows what? If classical mechanicsdescribed t he world, each degree offreedom in this teeming microcosmcould have an arbi t rary a m ou n t ofexcitation energy. When disturbed,for exam ple by a col lision wi t hanot her m olecule, all t he motionswithin t he water molecule could beaffected. In just t his way, t he Eart han d everyt hi ng on i t would bethoroughly perturbed if our solar sys-tem collided with another.

Chemistry

N uclear

Hadronic

Standard Model

92 Elements

p,n,e,ne,g

p,n,L ,S,p,r ,...

Quarks, Leptons

Antiquity ~ 1900

1900–1950

1950–1970

1970–?

>~ 10–8 cm>~ 10–12 cm>~ 10–13 cm>~ 10–17 cm

Scheme ConstituentsDate of

DominanceDomain of

Applicability

Energy All energiesavailable.Fine structureapparent evenat low energy.

Energy levelsdiscrete.Characterizedby natural scalesof system.

Energy Levels ofa Classical System

Energy Levels ofa Quan tum System

DE1

DE2

DE3

Below: The “elementary” particles of thefour schemes that have dominatedmodern science.

Left: A schematic view of the energylevels of classical and quantumsystems.

BEA M LINE 37

Q uan tu m mechan ics, on theot her hand, does not allow arbitrarydisr up t ion. All exci ta t ions of t hem olecule are quan tized, each wi t hi ts own characterist ic energy. Mo-t ions of t he molecule as a whole—rota tions and vibrat ions—have t helowest energies, in t he 1–100 milli-electron volt regime (1 meV = 10- 3 eV).An electron volt, abbreviated eV, ist he energy an electron gains fallingt hrough a poten t ial of one vol t andis a convenient unit of energy for fun-damental processes. Excitation of theelectrons in t he hydrogen and oxy-gen a to ms come next, wit h charac-teristic energies ranging from abou t10- 1 to 103 eV. Nuclear excitations inoxygen require millions of electronvol ts (106 eV = 1 MeV), and exci ta-t ions of t he quarks inside a protonrequire hundreds of MeV. Collisionsbe t ween water m olecules a t roomte mperat ure transfer energies of or-der 10- 2 eV, enough to excite rotationsand perhaps vibrations, but too smallto involve any of the deeper excita-tions except very rarely. We say thatt hese variables—t he elect rons, t henuclei, the quarks—are “frozen.” Theenergy levels of a classical and quan-t um system are compared in the bot-tom illustration on the previous page.They are inaccessible and unimportant.They are not static—the quarks insidethe nuclei of water molecules arewhizzing about at speeds approachingthe speed of light—however their stateof motion cannot be changed by every-day processes. Thus there is an excel-lent description of molecular rotationsand vibrations that knows lit tle aboutelectrons and nothing about nuclearstructure, quarks, or gluons. Ligh tqua n t a m a ke a par t ic ularly goodprobe of this “quan tu m ladder,” as

Victor Weisskopf called it. As su m-m arized in t he illu s t ra t ion above,as we shorten the wavelength of lightwe increase t he e nergy of ligh tquan ta in direct propor tion. As wem ove fro m m icrowaves to visiblel igh t to X rays to ga m m a rays weprobe successively deeper layers oft he s t ruct ure of a water m olecule.T he appropria te cons t i t uen t de-scription depends on the scale of theprobe. At one ex trem e, we can nothope to describe the highest energyexcitations of water without know-ing about quarks and gluons; on theother hand, no one needs quarks andgluons to describe t he way water isheated in a microwave oven.

PERHAPS T HE M OST ef-fect ive t heory of all was theone inven ted by t he n uclear

physicists in the 1940s. It reigned foronly a few years, before the discov-ery of m yriad excited sta tes of t heproton and neu tron led to i ts aban-don ment and even tual replacemen twi t h today’s Standard Model ofquarks and leptons. The nuclear stan-dard m odel was based on three con-stituen ts: the proton (p); the neu tron(n); and t he electron (e). The neutri-no (ne) plays a bit part in radioactivedecays, and perhaps one should countt he photon (g), t he quan t u m of t heelectromagnet ic field. So t he basiclist is three, four, or five, roughly asshort as Empedocles’ and far more ef-fective at explaining Nature. Most ofnuclear physics and astrophysics and

Molecular

Atomic

N uclear

Hadronic

Active

Frozen

Frozen

Frozen

Irrelevant

Active

Frozen

Frozen

Irrelevant

Irrelevant

Active

Frozen

Irrelevant

Irrelevant

Irrelevant

Active

States of Water

meV eV MeV GeV

microwavevisib

le soft

g–ray hard

g–ray

The “quantum ladder” of water—theimportant degrees of freedom changewith the scale on which it is probed,described here by the wavelength oflight.


is emit ted. This suggest that protonsand neutrons, like hydrogen, have in-ner workings capable of excita tionand de-excitation. Of course, if onlyfeeble energies are available, the in-ternal struct ure cannot be exci ted,and i t wi ll not be possible to tellwhether or not the particle is com-posi te. So an experim en ter needs ahigh-energy accelerator to probe com-positeness by looking for excitations.

Co m plex force law s. We have adeep prejudice t hat t he forces be-tween ele m en tary part icles shouldbe simple, like Coulomb’s law for theelectrost a t ic force bet ween poin tcharges: F12 = q1q2/r 2

12. Because t heyderive from the complex motion of theelectrons within the atom, forces be-tween atoms are not simple. Nor, itturns out, are the forces between pro-tons and neutrons. They depend onthe relative orientation of the parti-cles and their relative velocities; theyare complicated functions of the dis-tance between them. Nowadays theforces between t he proton and neu-tron are sum marized by pages of ta-bles in the Physical Review. We nowunderstand that they derive from the

all of a to m ic, m olecu lar, a nd con-densed m at ter physics can be un-derstood in terms of these few con-s t i tuen t s. The nuclei of a to ms arebuilt up of protons and neutrons ac-cording to fa irly si m ple em piricalrules. Atoms, in turn, are composedof electrons held in orbit around nu-clei by electromagnetism. All the dif-feren t che mical elem en ts from hy-drogen (the lightest) to uraniu m (theheaviest naturally occurring) are justdifferen t organizat ions of electronsaround nuclei with different electriccharge. Even the radioactive process-es that transm ute one elemen t in toa no t her are well descr ibed i n t hepneneg world.

T he nuclear m odel of t he worldwas soon replaced by another. Cer-tain tell-tale signatures that emergedearly in t he 1950s made it clear thatt hese “ele m en t ary” co ns t i t uen tswere not so elementary after all. Thesa m e signa t ures of com positenesshave repeated every t ime one set ofconstit uents is replaced by another:

Excitat ions. If a part icle is com-posite, when it is hit hard enough itscomponent parts will be excited intoa quasi-s table s t a te, w hic h la terdecays by emitting radiation. The hy-drogen a to m provides a classicexample. When hydrogen atoms areheated so that t hey collide with oneanother violently, light of character-istic frequencies is emit ted. As soonas i t was understood t hat the ligh tcomes from the de-exci tat ion of itsinner workings, hydrogen’s days asan ele m en tary par t icle were over.Similarly, during the 1950s physicistsdiscovered t ha t w hen a pro ton orneu tron is h it hard enough, excitedstates are for med and characteristicradiation (of ligh t or other hadrons)

com plex quark and gluon substruc-ture within protons and neutrons.

The complicated features of forcelaws die away quickly with distance.So if an experi menter looks at a par-t icle from far away or wi t h lowresolu t ion, it is not possible to tellw he t her i t is com posi t e. A h igh-energy accelerator is needed to probeshort distances and see the deviationsfrom si mple force laws that are tell-tale signs of compositeness.

For m factors. Whe n t wo s t ruc-tureless particles scat ter, t he resultsare deter mined by the simple forcesbetween them. If one of the particleshas subs tru ct ure, t he scat tering ismodified. In general the probabilityof the scat tered particle retaining itsiden ti ty—t his is known as “elas ticsca t t ering”—is reduced, becausethere is a chance that the particle willbe excited or conver ted in to som e-thing else. The factor by which theelas t ic scat tering probabili ty isdiminished is known as a “form fac-tor.” Rober t Hofstadter first discov-ered that the proton has a for m fac-tor in exper i m e n t s perfor m ed a tStanford in t he 1950s. T his was in-controvertible evidence that the pro-ton is com posite.

If, however, one scat ters ligh t lyfrom a com posite par ticle, not hingnew is exci ted, and no form factor isobserved. Once again, a high-energyaccelera tor is necessary to sca t terhard enough to probe a particle’s con-st ituents.

Deep inelast ic scat teri ng. T hebes t proof of com posi teness is, ofcourse, to det ect direc t ly t he sub-cons t i t uen ts ou t of wh ich a par t i-cle is co mposed. Ru t herford foundthe nucleus of the a tom by scat ter-ing a par t icles from a gold foil and

There is

tantalizing

evidence

that ne w

relationships

a w ait discovery.

BEA M LINE 39

fi nding t hat som e were sca t t ereddirect ly back wards, a resul t t hatwould on ly be possible if t he goldatoms contained a heavy concentra-tion of mass—the nucleus—at theircore. The famous SLAC experimentsled by Jerom e Fried m a n, HenryKendall, and Richard Taylor foundt he analogous result for the proton:w hen t hey scat tered elect ron s a tlarge angles they found tell tale evi-dence of pointlike quarks inside.

By t he early 1970s m oun tains ofevidence had forced the physics com-m u nit y t o concl ude t hat pro to ns,neu trons, and t heir ilk are not fun-damental, bu t are instead composedof quarks and gluo ns. During t hatdecade Burton Richter and Sam Tingand their collaborators separately dis-covered t he char m quark; LeonLeder man led the team that discov-ered t he bot tom quark; and Mart inPerl’s group discovered the third copyof t he elec tron, t he ta u-lep ton ort auon. The m edia tors of t he wea kforce, t he W and Z bosons, were dis-covered at CERN . The final ingredi-en ts in our presen t Standard Modelare t he top quark, recen t ly discov-ered at Fer m ilab, and t he Higgsboson, soon to be discovered at Fer-milab or CERN . As these final blocksfall into place, we have a set of about25 constituents from which all mat-ter is built up.

T HE STAN DARD Modelof particle physics is incred-ibly successful an d pre-

dictive, but few believe it is t he lastword. There are too many particles—abou t 25—and too m any para m-eters—also abou t 25 masses, in ter-act ion s trengt hs, a nd orien ta t ionangles—for a fu nda m en tal t heory.

Particle physicists have spent the lastquarter cen tury looking for signs ofwhat com es next. So far, t hey havecom e up em pty—no signs of an ex-ci ta t ion spectru m , com plex forcelaws, or form factors have been seenin any experiment. T he sit uation issu m m arized above. T he StandardModel was discovered when physi-cists at tempted to describe the worldat distances smaller than t he size ofthe proton, abou t 10- 13 cm. Moder nexperiments have probed to distancesabo u t fou r orders of m agni t udesmaller, 10- 17 c m, without evidencefor substructure.

There is tantalizing evidence thatnew relat ionships await discovery.For exa m ple, t he Standard Modeldoes not require the electric chargesof the quarks to be related to the elec-tric charge of the electron. However,the sum of the electric charges of thethree quarks that make up t he pro-ton has been m easured by experi-ment to be the exact opposite of thecharge on the electron to bet ter thanone part in 1020. Such a relationshipwo uld follow nat urally ei t her ifquarks and electrons were composedof com m on const i t uen ts or if t heywere differen t exci ta t ions states ofsome “ ur” par ticle. Equally in trigu-ing is t ha t each q uark and lep tonseems to come in three versions withidentical properties, differing only inmass. The three charged leptons, theelectron, t he m uon and the tauon,

Yes

Yes

No

92 Elemen ts

p,n,e

Standard Model

Yes

Yes

No

Yes

Yes

No

ExcitationSpectru m

FormFactors

ComplexForce Laws

Evidence for underlying structure inmodels of elementary constituents.


lept ons are ge neralizat ions ofCoulomb’s Law. They all follow fromsym metry considerations known as“gauge principles.” Even gravi ty,which rests uneasily in the StandardModel, follows from the gauge prin-ciple that Eins tein called “generalcovariance.” The si m plici ty of t heforces i n t he Standard Model hasbeen m istaken for evidence t hat atlast we have reached truly ele men-tary const it uen ts, and that there isno furt her substructure to be found.After all, t he argum ent goes, “Howcould co mposite part icles behave sosimply?” Unfortunately, it turns outt hat it is qui te nat ural for compos-ite par ticles to m i mic fundamentalones if we do not probe them deeplyenough. The forces bet ween a tomsand nuclei look simple if one doesno t look too closely. Models wi t hqui te arbitrary in teractions definedat very short distances produce t heki nd of forces we see in t he St an-dard Model w hen viewed fro m faraw ay. In a tech n ical se nse, t hedeviations from the forces that fol-low fro m t he “gauge principle” aresuppressed by fac t ors l i ke L / l ,where l is t he typical lengt h scaleprobed by an exper i m en t (l scaleslike t he inverse of t he energy of thecolliding particles), and L is t he dis-tance scale of the substructure. Hol-gar N ie lsen a nd h is col labora t orshave followed this thread of logic toan extre me, by exploring the extentto which an essentially random the-ory defined at the shortest distancescales will present itself to our eyeswi t h gauge in t erac t ions l ik e t heStandard Model and gravity. T heseexercises s how how m uch roo mt here is for surprise when we probe

are the best-known example, but thesame holds for the up, charm, and topquarks, the down, s trange, and bot-tom quarks, and t he neu t rinosassociated with each lepton. The pat-tern looks very m uch like one of in-ternal excitation—as if the muon andtauon are “excited electrons”. How-ever, extre mely careful experi mentshave not been able to excite an elec-tron into a muon or a tauon. The lim-its on these excitation processes arenow ex tre m ely s t rong a nd pre t tym uch rule ou t si m ple m odels inwhich the electron, muon, and tauonare “m ade up of” t he same subcon-stituents in a straightforward way.

Building structures that relate theelementary particles of the StandardModel to one another is the businessof m oder n par t icle t heory. Super-sy m m etry (SUSY) co m bin ed wit hGrand U nificat ion is perhaps t hemost promising approach. It removesso m e of t he m ost t roubling incon-gruities in the Standard Model. How-ever, t he cos t is high—if SUSY isrigh t, a huge nu mber of new par t i-cles await discovery at the LHC or att he N ext Linear Collider. T he listof “elemen tary constituen ts” wouldmore than double, as would the num-ber of para m eters necessary to de-scribe their interactions. The situa-t ion would rese m ble t he s ta te ofche mistry before the understandingof atoms, or of hadron physics beforethe discovery of quarks: a huge num-ber of constituents, grouped into fam-ilies, awai ting t he next si mplifyingdiscovery of substructure.

One of the most st riking proper-ties of the Standard Model is the sim-plici ty of the force laws. All t hek now n forces bet ween quarks and

t he next level beyond t he StandardModel.

We are poised rather uncomfort-ably upon a rung on Viki Weisskopf’sQ uan t u m Ladder. T he world ofquarks, leptons, and gauge in terac-t io ns does a wonderfu l job of ex-plaining t he rungs below us: t hen uclear world of pneneg, t he worldof atom s, and che mist ry. However,the in ternal consistency of the Stan-dard Model and t he propensi ty ofquan t u m m echan ics to sh ield usfrom what lies beyond, leave us with-ou t enough wisdo m to guess w hatwe will find on the next rung, or if,indeed, t here is anot her rung to befound. Hin t s fro m t he Sta ndardModel suggest that new constituentsawait discovery wit h the next roundof accelera tor experim en ts. Hopefrom past exam ples motivates the-orists to seek simplifications beyondt his proliferat ion. Past experiencecautions that we are a long way fromthe end of this exploration.

BEA M LINE 41

N THE NETHERLAN DS IN 1911, abou t adecade after the discovery of quan tu m theory bu tmore than a decade before the in troduction of quan-

tu m mechanics, Heike Kamerlingh Onnes discovered super-conductivity. This discovery came three years after he suc-ceeded in liquefying heliu m, thus acquiring the refrigerationtechnique necessary to reach temperatures of a few degreesabove absolu te zero. The key feature of a superconductor isthat i t can carry an electrical curren t forever with no decay.The microscopic origin of superconductivity proved to beelusive, however, and it was not until 1957, after 30 years ofquan tu m m echanics, that John Bardeen, Leon Cooper, andRober t Schrieffer elucidated their famous theory of supercon-ductivity which held that t he loss of electrical resistance wasthe result of electron “pairing.” (See photograph on next page.)

In a nor mal metal, electrical curren ts are carried by elec-trons which are scat tered, giving rise to resistance. Sinceelectrons each carry a negative electric charge, they repeleach other. In a superconductor, on the other hand, t here isan at tractive force between electrons of opposite momentu mand opposite spin that overcomes this repulsion, enablingthem to for m pairs. These pairs are able to move through thematerial effectively without being scat tered, and thus carry asupercurrent with no energy loss. Each pair can be describedby a quan tu m mechanical “wave function.” T he remarkableproper ty of t he superconductor is that all electron pairs have

by JOH N CLARKE

A MacroscopicQ uantu m

Phenom enon

Drawing of Heike Kamerlingh Onnes made in1922 by his nephew, Harm Kamerlingh Onnes.(Courtesy Kamerlingh Onnes Laboratory,Leiden University)

Upper left: Plot made by Kamerlingh Onnes ofresistance (in ohms) versus temperature (inkelvin) for a sample of mercury. The sharp dropin resistance at about 4.2 K as the temperaturewas lowered marked the first observation ofsuperconductivity.

I

uperconduct ivi ty


Sure enough, th is quan t u m me-chanical phenom enon, cal led t he“Josephson effect ,” was observedshortly afterwards at Bell TelephoneLaboratories.

Bet ween t h e t wo t u n neling dis-coveries, in 1961 , t here occurredanot her discovery that was to haveprofound implications: flux quanti-zat ion. Because supercurren t s arelossless, they can flow indefinitelyarou nd a superconduct ing loop,t hereby m ain tain ing a per m a nen tm agnet ic field. This is t he princi-ple of t he high-field m agnet . How-ever, the magnetic flux threading thering cannot take arbitrary values, butinstead is quan tized in units of theflux quan tu m. The superconductorconsequently mimics familiar quan-tu m effects in atoms but does so ona macroscopic scale.

For m os t of t he cen t u ry, super-conductivity was a pheno menon ofliquid heliu m temperatures; a com-pound of n iobiu m and ger m aniu mhad the highest transition tempera-t ure, abou t 23 K. In 1986, however,Alex M ueller and Georg Bednorzs taggered t he ph ysics world wit ht heir an nou nce m en t of supercon-ductivity a t 30 K in a layered oxideof the elements lanthanum, calcium,copper, and oxygen. Their am azingbreakthrough unleashed a worldwiderace to discover materials with high-er critical te mperatures. Shortly af-terwards, the discovery of supercon-ductivity in a compound of yt triu m,bariu m, copper, and oxygen at 90 Kushered in the new age of supercon-ductors for which liqu id n i t rogen,boiling at 77 K, could be used as thecryogen. Today the highest transitiontemperature, in a mercury-based ox-ide, is abou t 133 K.

the same wave function, t hus for m-i ng a m acroscopic q uan t u m s ta tewit h a phase coheren ce ext endi ngthroughout the material.

There are two types of supercon-ductors. In 1957, Alexei Abrikosovshowed that above a certain t hresh-old magnetic field, type II supercon-ductors ad m i t field in t he for m ofvor t ices. Each vor tex con tains onequan tu m of m agnetic flux (productof magnetic field and area). Becausesupercurren ts can flow around t hevortices, these materials remain su-perconducting to vastly higher mag-net ic fields t han t heir type I coun-terpar ts . Type II m aterials are theenabling t ech nology for h igh-fieldmagnets.

Shor t ly aft erwards cam e a suc-cession of even ts t hat heralded theage of superconducting electronics.In 1960, Ivar Giaever discovered t hetunneling of electrons through an in-sulating barrier separating two thinsuperconducting fil m s. If t he insu-la tor is sufficien t ly t hin, elect ronswill “ tunnel” through it. Building onthis notion, in 1962 Brian Josephsonpredicted t hat elect ron pairs couldtunnel through a barrier between twosuperconductors, giving the junctionweak superconduct ing proper t ies.

John Bardeen, Leon Cooper, and RobertSchrieffer (left to right) at the Nobel Prizeceremony in 1972. (Courtesy EmilioSegre Visual Archives)

BEA M LINE 43

Why do these new materials havesuch high transit ion temperatures?Amazingly, some 13 years after theirdiscovery, nobody knows! While i tis clear that hole pairs carry the su-percurren t, it is unclear what gluest he m toge t her. T he nat ure of t hepairing mechanism in high-temper-at ure superconductors remains oneof the great physics challenges of thenew millenniu m.

LARGE-SCALE APPLICATIO NS

Copper-clad wire made from an alloyof niobiu m and titaniu m is t he con-ductor of choice for magnetic fieldsup to 10 tesla. Magnets made of thiswire are widely used in experimentsranging from high-field nuclear mag-netic resonance to the study of howelectrons behave in t he presence ofextremely high magnetic fields. Thelargest scale applicat ions of super-conduc ting wire, however, are inmagnets for particle accelerators andm agnet ic resonance imaging (MRI).Other prototype applications includecables for power transmission, largeinductors for energy storage, powergenerators and electric motors, mag-net ically levitated trains, and bear-ings for energy-s toring flyw heels.Higher m agnet ic fields ca n beachieved with other niobiu m alloysinvolving tin or aluminum, but thesematerials are brit tle and require spe-cial handling. Much progress has beenm ade wit h m ult ifilam en tary wiresconsist ing of t he high te m perat uresuperconductor bism uth-strontium-calcium-copper-oxide sheathed in sil-ver. Such wire is no w available inlengt hs of several h u ndred m etersand has been used in demonstrationssuch as elect ric m otors and power

transmission. At 4.2 K t his wirere mains superconducting to highermagnetic fields t han the niobiu malloys, so that it can be used as aninsert coil to boost the magnetic fieldproduced by low-temperature magnets.

T he world’s most powerful par-t icle accelerat ors rely on m agnetswound with superconducting cables.This cable con tains 20–40 niobiu m-titaniu m wires in parallel, each con-taining 5,000–10,000 fi laments capa-ble of carrying 10,000 a m peres (seeJudy Jackson’s article “Down to theWire” in the Spring 1993 issue).

The first superconducting accel-erator to be built was t he Tevatronat Ferm i Nat ional Accelera tor Lab-oratory in 1984. This 1 TeV machine

Tevatron superconducting dipolemagnets and correction assemblyin Fermilab’s Main Ring tunnel.(Courtesy Fermi National AcceleratorLaboratory)


examples, it becomes clear that thedem anding requirem en ts of accel-era tors have been a m ajor drivi ngforce behind t he development of su-perconducting m agnets. Their cru-cial advantage is that they dissipatevery little power compared with con-ventional magnets.

Millions of people arou nd t heworld have been surrounded by a su-perconducting magnet while havinga m agnet ic reson ance i m age (MRI)taken of t hem selves. T housands ofMRI machines are in everyday use,each containing tens of kilom etersof superconducting wire wound intoa persisten t-curren t solenoid. Them agnet is cooled ei t her by liqu idheliu m or by a cryocooler. Once thecurren t has bee n s tored in t he su-perconduct ing coil, t he m agnet icfield is very stable, decaying by as lit-tle as a part per million in a year.

Conven tional MRI relies on t hefact t hat pro tons possess spin andthus a magnetic moment. In the MRIm achine, a radiofrequency pulse ofmagnetic field induces protons in thepatient to precess about the directionof t he static magnetic field suppliedby t he supercondu ting magnet. Forthe workhorse machines with a fieldof 1.5 T, t he precessional frequency,which is precisely proportional to thefield, is abou t 64 M Hz. T hese pre-cessing magnetic moments induce aradiofrequency voltage in a receivercoil t hat is amplified and stored forsubsequen t analysis. If the magneticfield were unifor m, all t he protonswould precess at the same frequency.The key to obtaining an image is theuse of m agne t ic field gradien ts todefine a “voxel,” a volu me typically3 m m across. O ne dis t i ngu ishesstruct ure by vir t ue of the fact that,

i ncorporates 800 superconduct ingmagnets. Other superconducting ac-celera tors incl ude HERA a t t heDeutsches Elek tronen Synchrot ronin Germany, the Relativistic HeavyIon Collider nearing co mpletion a tBrookhaven National Laboratory inN ew York, and t he Large HadronCollider (LHC) which is being buil tin t he t u nnel of t he exist ing LargeElec tron Posi tron r ing a t CER N i nSwitzerland. The LHC, scheduled forcom plet ion in 2005, is designed for14 TeV collision energy and, wi t hquadrupole and corrector m agnets,will involve more t han 8,000 super-conducting magnets. The dipole fieldis 8.4 tesla. T he ill-fated Supercon-ducting Super Collider was designedfor 40 TeV and was to have involved4,000 superconduct ing dipole m ag-nets. At the other end of the size andenergy scale is Helios 1 , a 0.7 GeVsynchrotron X-ray source for lit ho-graphy operating at IBM. From these

A 1.5 tesla MRI scanner at Stanford Uni-versity for a functional neuroimagingstudy. The person in the foreground isadjusting a video projector used to pre-sent visual stimuli to the subject in themagnet. (Courtesy Anne Marie Sawyer-Glover, Lucas Center, StanfordUniversity)

BEA M LINE 45

for example, fat and muscle and greyand white mat ter produce differentsignal strengths.

MRI has become a clinical tool ofgrea t im por t ance and is used in awide variety of modes. The develop-m en t of funct ional m agnetic reso-nan t im aging enables one to locatesom e sit es in the brain t hat are in-volved in body function or t hough t.During brain activity, there is a rapid,momentary increase in blood flow toa specific site, thereby increasing thelocal oxygen concentration. In turn,t he presence of t he oxygen modifiest he local MRI signal relative to thatof t he surrounding tissue, enablingone to pinpoint the neural activi ty.Applicat ions of th is tech nique in-cl ude m apping t he brain and pre-operat ive surgical planning.

SMALL-SCALE APPLICATIO NS

At the lower end of the size scale (lessthan a millimeter) are extremely sen-sitive devices used to measure mag-net ic fields. Called “SQ UIDS” forsuperconducting quant u m in terfer-ence devices, they are the most sen-sitive type of detector known to sci-ence, and can t u rn a cha nge in amagnetic field, something very hardto measure, in to a change in voltage,somet hing easy to measure. The dcSQUID consists of two junctions con-nect ed in parallel to for m a super-conducting loop. In t he presence ofan appropriate current, a voltage isdeveloped across the junctions. If onechanges the magnetic field threadingthe loop, this voltage oscillates backand for t h wit h a period of one fluxquan t u m. O ne detects a change inm agnetic field by m easuring theresulting change in voltage across the

SQUID using conventional electronics.In essence, t he SQ UID is a flux-to-voltage transducer.

Squ ids are fabricat ed fro m t hi nfil ms using photolithographic tech-niques to pat tern t hem on a siliconwafer. In the usual design, they con-sist of a square washer of niobiu mcon tain ing a sli t o n ei t her side ofwhich is a tu nnel junction. T he up-per electrodes of t he junct ions areconnected to close the loop. A spiralniobium coil with typically 50 turnsis deposited over the top of the wash-er, separated from it by an insulatinglayer. A curren t passed through thecoil efficien t ly couples flux to t heSQUID. A typical SQUID can detectone part per million of a flux quan-tu m, and it is this remarkable sen-sitivity that makes possible a host ofapplications.

Generally, SQUIDs are coupled toauxiliary co m pone n t s, such as asuperconducting loop connected tot h e in pu t ter m i nals of t h e coil t oform a “flux transformer.” When weapply a magnet ic field to t his loop,flux quan tizat ion induces a super-current in the transformer and hencea flux in t he SQUID. The flux trans-for mer functions as a sort of “hear-i ng aid,” enabling one t o detec t a

Current

Curren t

Voltage

Voltage

Superconductor

Magnetic Field

JosephsonJunction

Top: A dc SQUID configuration showingtwo Josephson junctions connected inparallel. Bottom: A high transition tem-perature SQUID. The yttrium-barium-copper-oxide square washer is 0.5 mmacross.


m agnet ic field as m uch as eleve norders of magnitude below that of them agn et ic field of t he ear t h. If, in-s t ead, we con nec t a resis t ance i nseries wit h the SQ UID coil, we cre-ate a volt meter that readily achievesa voltage noise six orders of magni-t ude below t hat of sem iconductoramplifiers.

It is likely that most SQUIDs evermade are used for studies of t he hu-man brain. Com mercially availablesystems contain as many as 306 sen-sors arranged in a helmet containingl iquid heliu m t hat fi t s arou nd t heback, top, and sides of the pat ien t’sskull. This completely non-invasivetechnique enables one to detect t he

t i ny m agnet ic fields produced bythousands of neurons fir ing inconcert. Although the fields ou tsidet he head are qu i te large by SQ UIDstandards, they are minuscule com-pared with environmental magneticnoise—cars, elevators, television sta-t io ns. To el i m i nat e t h ese noisesources, t he pat ien t is usu ally en-closed in a m agnet ically-shieldedroom . In addit ion, t he flu x trans-for m ers are generally configured asspatial gradiom eters t hat discri m i-nate against distant noise sources infavor of nearby signal sources. Com-pu ter processing of the signals fromt he array of SQUIDs enables one tolocate the source to wit hin 2–3 m m.

T here are t wo broad classes ofsignal: s t i m ula ted, t he brain’s re-sponse to an external stim ulus; andspon taneous, self-generated by thebrain. An example of the first is pre-surgical screening of brain t u mors.By applying stimuli, one can map outthe brain function in the vicinity ofthe tu mor, thereby enabling the sur-geon to choose the leas t da m agingpat h to re m ove i t . An exa m ple ofspon taneous signals is t heir use toidentify the location of epileptic foci.T he fas t te m poral response of t heSQUID , a few m illiseconds, enableson e t o de m o ns t ra t e t h at so m epatients have two foci, one of whichstim ulates the other. By locating theepileptic focus non-invasively beforesurgery, one can make an infor meddecision about the type of treatment.Research is also under way on otherdisorders, including Alzheimer’s andParkinson’s diseases, an d recoveryfrom stroke.

There are many other applicationsof low-temperature SQUIDs, rangingfrom the ultra-sensitive detection of

System containing 306 SQUIDs for thedetection of signals from the humanbrain. The liquid helium that cools thedevices needs to be replenished onlyonce a week. The system can be rotatedso as to examine seated patients. Themagnetic images are displayed on aworkstation (not shown). (Courtesy 4D-Neuroimaging)

BEA M LINE 47

ischem ia (localized tissue anem ia);anot her is to locat e t he si te of a narrhythmia. Although extensive clin-ical t rials would be required t ode m onstra te i t s efficacy, M C G isen t irely non-invasive and m ay becheaper and faster than current tech-niques.

Ground-based and airborne hightemperature SQUIDs have been usedsuccessfully in geophysical survey-ing trials. In Ger many, high temper-at ure SQ UID s are used t o exa m i necom mercial aircraft wheels for pos-sible flaws produced by the stress andheat generated at landing.

The advan tage of the h ighero pe ra t i ng t e m pera t u r e of h ig htem perature SQUIDs is exemplified

n uclear m agnet ic resonance tosearches for magnetic monopoles andstudies of the reversal of the Ear th’sm agnet ic field in ancien t t i m es. Arecen t example of the SQUID’s ver-satility is the proposal to use it as ahigh-frequency a m plifier in an up-graded axion detector at LawrenceLivermore National Laboratory. Theaxion is a candidate particle for thecold dark mat ter that consti tu tes alarge fraction of the mass of the Uni-verse (see article by Leslie Rosenbergand Karl van Bibber in the Fall 1997Beam Line, Vol. 27, No. 3).

W i t h t h e a d v e n t o f h i g h -temperature superconductivity, manygroups around t he world chose t heSQ UID to develop t heir t h in-fil mtechnology. Yttrium-barium-copper-oxygen dc SQUIDs operating in liq-uid nitrogen achieve a magnetic fieldsensit ivi ty wit hin a factor of 3–5 oft heir liquid-heliu m cooled cousins.High-temperature SQUIDs find novelapplications in which t he potent ialeconom y and convenience of cool-ing wit h liqu id ni t rogen or a cryo-cooler are st rong incent ives. Mucheffort has been expended to developt he m for m agnet ocardiography(M C G) in an u nshielded environ-men t. The magnetic signal from thehear t is easily detected by a SQ UIDin a shielded enclosure. However, toreduce the system cost and to makeMCG more broadly available, it is es-sen t ial to el i m i nat e t he sh ieldedroom. This challenge can be met bytaking spatial derivatives, often witha combination of hardware and soft-ware, to reduce external interference.What advan tages does M C G offerover conventional electrocardiogra-phy? O ne po ten t ially im por t an tapplica t ion is t he det ect ion of

Localization of sources of magneticspikes in a five-year-old patient withLandau-Kleffner syndrome (LKS). Thesources, shown as arrows at left andright, are superimposed on a magneticresonance image of the brain. LKS iscaused by epileptic activity in regions ofthe brain responsible for understandinglanguage and results in a loss oflanguage capabilities in otherwisenormal children. (Courtesy 4D-Neuroimaging and Frank Morrell, M.D.,Rush-Presbyterian-St. Luke’s MedicalCenter)


in “SQ UID microscopes,” in w hicht he device, mounted in vacuum justbelow a thin window, can be broughtvery close to sam ples at room tem-perat ure and pressure. Such micro-scopes are used to det ect flaws insemiconductor chips and to monitort he gyrations of magnetotactic bac-teria, which con tain a tiny magnetfor navigational purposes.

Alt hough SQ UIDs dom inate t hesmall-scale arena, ot her devices areimportant. Most national standardslaboratories around the world use theac Josephson effect to main tain thestandard vol t. Superconducting de-tectors are revolu tionizing submil-li meter and far infrared astronomy.Mixers involving a low tempera t u res u p e r c o n d u c t o r - i n s u l a t o r -superconductor (SIS) tunnel junctionprovide u nrivaled sensi t ivi ty tonarrow-ba nd signals, for exa m ple,t hose produced by rota tional t ran-si t ions of m olecules in in ters tellarspace. Rough ly 100 SIS m ixers areoperat ional on ground-based radiot elescopes, and a radio-t elescopearray planned for Chile will requireabou t 1000 such m ixers. When onerequires broadband detec tors—forexa m ple, for t he detect ion of t hecosm ic background radia tion—t helow tem perat ure superconduct ing-t ransi t io n-edge bolom eter is t hedevice of choice in the submillimeterrange. T he bolometer absorbs inci-dent radiation, and the resulting risein its temperat ure is detected by thechange in resistance of a supercon-ductor at its transition; this changeis read ou t by a SQ UID . Arrays of1,000 or even 10,000 such bolometersare contemplated for satellite-basedtelescopes for rapid mapping of t hecosmos—not only in the far infrared

but also for X-ray astronomy. Super-conduct ing detectors are poised toplay a crucial role in radio and X-rayastronomy.

A rapidly growing nu mber of cel-lular base stations use multipole hightemperature filters on their receivers,yielding sharper bandwidt h defini-t ion and lower noise t han conven-t ional fil t ers. T h is tech nology en-ables t he provider to pack m orecha nnels i n t o a given frequencyalloca t ion in u rba n environ m en tsand to extend the distance betweenrural base stations.

THE NEXT MILLEN NIUM

The major fundamental questions are“Why are h igh te m perat u re super-conductors superconducting?” and“ Can we achieve st ill higher t e m-perat ure superconductors?” On theapplications front, the developmentof a high tem perature wire that canbe manufact ured cost effectively insufficien t lengths could revolution-ize power generation, transmission,and u t ilizat ion. On the small-scaleend, superconducting detector arrayson satellites may yield new insightsinto the origins of our Universe. Hightemperature filters will provide rapidinternet access from our cell phones.T he co m bi na t io n of SQ UID arraysand MRI will revolu t ionize ourunderstanding of brain function. Andperhaps a SQUID will even catch anaxion.

BEA M LINE 49

by VIRGINIA TRIMBLE

THE U NIVERSE AT LA RGE

O D MADE THE IN TEGERS; all else is the work of Man. Sosaid Kronecker of the del ta. And indeed you can do many

things with the in tegers if your tastes run in that direction. A uni-for m density stretched string or a pipe of unifor m bore will pro-duce a series of tones that sound pleasant together if you stop thestring or pipe in to lengths that are the ratios of small whole nu m-bers. Some nice geometrical figures, like the 3-4-5 right triangle,can also be made this way. Such things were known to Pythagorasin the late sixth cen tury BCE and his followers, the Pythagoreans.They extended the concept to the heavens, associating particularnotes with t he orbits of the planets, which therefore sang ahar mony or music of the spheres, finally transcribed in moderntimes by Gustav Holtz.

A fondness for small whole nu mbers and structures made ofthem, like the regular or Platonic solids, persisted for centuries. Itwas, in its way, like our fondness for billions and billions, a fash-ion. George Bernard Shaw claimed early in the twentieth centurythat it was no more rat ional for his con temporaries to think theywere sick because of an invasion by millions of germs than fortheir ancestors to have at tributed the problem to an invasion byseven devils. Most of us would say that the germ theory of diseasetoday has a firmer epistomological basis than the seven devilstheory. But the insight that there are fashions in nu mbers and math-ematics, as m uch as fashions in art and govern men t, I think stands.

The Ratios of Small Whole N u mbers:Misadventures in Astronomical Quantization

This is also Part III of “Astrophysics Faces the Millennium,”but there are limits to the number of sub titles that can dance

on the head of an editor.

G


KEPLER’S LAWS AN D LAURELS

Some of the heroes of early modern astronomy remainedpart of the seven devils school of natural philosophy. Welaud Johan nes Kepler (1571–1630) for his t hree laws ofplanetary motion that were later shown to follow directly

from a Newtonian, inverse-square law of gravity, but hehad tr ied m a ny co m bina-t ions of s m all w hole nu m-bers before showing that theorbit periods and orbit sizesof the planet s were con-nected by P2 = a3. And t hesame 1619 work, Harmony ofthe Worlds, that enunciatedthis relation also showed thenotes sung by the planets, ina no ta t ion that I do noten tirely understand. Venushu m med a single high pitch,and Mercury ran up a gli s-sando and down an arpeggio,w h i l e Ea r t h m o a n e dm i(seria), fa(mes), mi(seria).T he range of not es in eachm elody depended on t herange of speeds of the planetin i t s orbi t, w hic h Kepler,with his equal areas law, hadalso correctly described.

Kepler’s planets were,however, six, t hough Coper-nicus and Tycho had clung tos ev e n , b y c o u n t i ng t h em o o n , e v e n a s t h e y r e-arranged Sun and Earth. Whysix planet s carried on six

spheres? Why, because t here are precisely five regularsolids to separate t he spheres: cube, pyra mid, octahe-dron, dodecahedron, and icosahedron. With t igh t pack-ing of sequen tial spheres and solids in t he righ t order,

Kepler could approxi mately reproduce t he rela tive or-bit sizes (se mi-major axes) required to move t he plan-e t s to t he posi t ions on t he sky w here we see t he m.T hough this schem e appears in his 1596 CosmographicMystery and so belongs to Kepler’s geo m etric you t h,he does no t appear to have abandoned i t i n h is alge-braic mat urity.

EXCESSIVELY U NIVERSAL GRAVITATIO N

Newton (1643–1727) was born the year after Galileo diedand died only two years before James Bradley recognizedaberra t ion of starligh t, t hereby dem onst rating una m-biguously that the Earth goes around the Sun and t hatlight travels abou t 104 times as fast as the Eart h’s orbitspeed (N O T a ra t io of sm all whole n u m bers!) Bu t t heSWN ideal persisted many places. Galileo had found fourmoons orbiting Jupiter (which Kepler himself noted alsofollowed a P2 = a3 pat tern around their central body), andt he Eart h had one. Mars m ust then naturally have two.So said Jonathan Swift in 1726, at tributing the discoveryto Lapu tian* astronomers, t hough it was not act uallym ade u n t il 1877 by Asaph Hall of t he U.S. N avalObservatory.

Attempts to force-fi t Newtonian gravity to the entiresola r sys te m have led t o a couple of ghos t planets,begin ni ng wi t h Vulcan, whose job was to accelera tethe rotation of the orbit of Mercury (“advance of the per-ihelion ”) un t il Eins tein an d General Relat ivity wereready to take it on. Planet X, ou t beyond Plu to, wherei t m igh t influence t he orbi ts of co mets, and Ne mesis,s t ill fur t her ou t and prone to sending co m ets in wardto impact the Earth every 20 million years or so, are morerecen t exa m ples. T hey have not been observed, and,according t o dyna m icis t Pe ter Vandervoor t of t heUniversity of Chicago, the Nemesis orbit is dynamicallyvery interesting; it just happens not to be occupied.

*It is, I suspect, not hing m ore t han bad dict ion t hat leadsto the frequen t false at tribu tion of t he discovery toLillipu tian astrono m ers, w hen their cult ure m ust surelyhave specialized in m icroscopy.

The music of the spheres accordingto Kepler. Saturn (upper left) isscored on the familiar bass clef, withF on the second line from the top,and Venus (beneath Saturn) on atreble clef with G on the second linefrom the bottom. The others are F, G,and C clefs with the key notes onother lines, not now generally in use.(Copyright © 1994, UK ATC, TheRoyal Observatory, Edinburgh.)

BEA M LINE 51

THE GREGORY-WOLFF-BO N NET LAW

Meanwhile, t he sm all whole n um bers folk were look-ing again at the known planetary orbits and trying to de-scribe t heir relative sizes. Proportional to 4, 7, 10, 15, 52,and 95, said David Gregory of Oxford in 1702. The num-bers were published again, in Ger m any, by C hris t ianWolff and picked up in 1766 by a chap producing a Ger-m an translation of a French volu me on natural historyby Charles Bonnet. T he t ransla tor, w hose na m e wasJohann Titius (of Wit tenberg) added the set of nu mbersto Bonnet’s text, improving them to 4, 7, 10, 16, 52, and100, t hat is 4+0, 4+3, 4+6 , 4+12 , 4+48 , and 4+96, or 4+(3¥0,1,2,4,16,32). A second, 1712, edition of the transla-t ion reached Johann Eler t Bode, who also liked the se-ries of num bers, published them yet again in an in tro-duction to astronomy, and so gave us the standard nameBode’s Law, not, as you will have remarked, either a lawor invented by Bode.

Bode, a t leas t, expected t here to be a planet a t 4 +3¥8 units (2.8 AU), in t he region t hat New ton though tthe creator had left empty to protect the inner solar sys-tem from disruption by the large masses of Jupiter andSat urn. Closely related seven teen t h cen t ury explana-t ions of t he large separat ion from Mars to Jupi ter in-cluded plu ndering of t he region by Jupiter and Saturnand collisional disruptions. Don’t forget these completely,since we’ll need them again. Great, however, was the re-joicing in the small whole nu mbers camp when WilliamHerschel spotted Uranus in 1781 in an orbit not far from4 + 192 units from the sun.

Among the most impressed was Baron Franz Xaver vonZach of Got ha (notice the extent to which this sort ofnu merical/positional astronomy seems to have been aGer man enterprise). After a few years of hunting the skieswhere an a = 28 unit planet might live, he and few col-leagues decided to enlist a bunch of European colleaguesas “celest ial police,” each to patrol a fixed part of thesky in search of t he missing planet. Hegel, of the sam egeneration and cul ture, on the ot her hand, objected topotential additional planets, on the ground that Uranushad brough t us back up to seven, equal to t he nu mber

of holes in the average human head, and so the correctnu mber.*

Even as von Zach was organ izing t h ings, Ital ianastronomer Giuseppe Piazzi, working independently ona s tar catalog, found, on New Year’s Day 1801, a newm oving object t hat he a t first took to be a com et be-fore losing it behind the sun in February. Some high pow-ered m a t he m at ics by t he you ng Ga uss (w homastronomers think of as the inventor of the least squaresmethod in this context) provided a good enough orbit forZach to recover the wanderer at the end of the year. Sureenough, it had a roughly circular orbit of abou t t he sizet hat had been Boded. But it was smaller than our ownmoon and, by 1807, had acquired three stablemates. These(Ceres, Juno, Pallas, and Vesta) were, of course, the firs tfour of many thousands of asteroids, whose total m assis nevertheless still not enough to make a decent moon.I do not k now whet her Piazzi m ade his discovery int he sky sector t hat von Zach had assigned to hi m orwhether, if not, the person who was supposed to get thatsector was resentful, though the lat ter seems likely.

Neptune and Pluto entered the planetary inven torywith orbits quite different and smaller than the next twoter ms in the Titius-Bode sequence. Strong expectationt hat t hey should fall at the sequence posit ions proba-bly retarded the searches for them (which were based onirregularities in the motion of Uran us).

In recent years, the orbits of triplets of planets aroundone pulsar and one normal star (Ups And) have also beenclaim ed as following som ething like a Gregory-Wolff-Titius sequence. Notice however that it takes two orbitsto define t he sequence, even in co m pletely arbi t raryunits.

What is t he sta t us of Bode’s Law today? T he tableon the next page shows the actual orbit semi-major axesand the fi t ted nu mber sequence. All agree to abou t five

*It is lef t as an exercise for t he reader to form ulate anappropriate snide re m ark about Hegel having t hus physio-logically an ticipated the discovery of N ept une, w hich hedid not in fact live to see.


percen t u n t il you reach N ept u ne. Bu t curren t t heorycomes m uch closer to w hat N ew ton and his con te m-poraries said than to orbit quantization. The process offormation of the planets and subsequent stability of theirorbi ts are possible only if t he planets fur ther from t hesu n, where the gravi ta t ional effec t of the su n isprogressively weaker, are also further from each other.

BI- AN D MULTI-MODALITIES

T he m in i m u m require m e n t for quan t izat ion is t woen tities with different values of something. With threeyou get eggroll, and t wen tieth cent ury astronomy hasseen a grea t m any divisio ns of i t s sources in to t wodiscrete classes. Exam ples include galact ic stars in topopulations I and II; star formation processes into thosem aking high and low m ass s tars; binary sys te m s in topairs with co mponen ts of nearly equal vs. very u nequalm asses; stellar velocities in to t wo streams; and super-novae in to types I and II (occ urring in popula t ions IIand I respectively).

None of these has achieved the status of true crank-iness. Rather, most have eventually either smoothed outin to so m e kind of con t i nu u m , fro m which ear ly

investigations had snatched t wo widely separated sub-sets (stellar populations, for instance), or n-furcated into“ m an y,” each wi t h honorably differen t u nderlyingphysics (including supernova types). A few, like t he dis-tinction between novae and supernovae, turned ou t tobe wildly differen t sort s of t hings, ini tially perceivedas similar classes because of some major misconception(t hat t heir dis tances were si m ilar, in t he nova-super-nova case).

T hus t o explore t he ex tre m i t ies of weirdness inastronomical quan tization, we m ust ju mp all t he wayfrom the solar syste m to the wilder reaches of quasarsand cosmology. Here will we find fractals, universes withperiodic boundary condit ions, non-cosm ological (andindeed non-Doppler and non-gravitational redshifts), andgalaxies t hat are per m it ted to ro ta te on ly a t cer ta indiscrete speeds.

FRACTAL, TOPOLOGICALLY-COMPLEX,AN D PERIODIC U NIVERSES

In t he cosm ological con tex t, frac tal st ruct u re wouldappear as a clustering heirarchy. That is, the larger thescale on which you looked at the distribu tion of galax-ies (etc.), the larger the structures you would find. Manypre-Einsteinian pictures of the Universe were like this,including ones conceived by Thomas Wright of Durham,Im manuel Kant, and Johann Lambert (all eighteenth cen-t ury). Since we have global solu tions for t he equationsof GR only for t he case of ho m ogenei ty and iso t ropyon average, it is not ent irely clear what a general rela-tivistic fractal universe ough t to look like.

Bu t it probably doesn’t mat ter. Observations of dis-tances and locations of galaxies curren tly tell us t hatt here are clusters and superclusters of galaxies (oftensheet-like or fila men tary) wit h voids between, havingsizes up to 100–200 million parsecs. This is less than 10percen t of the distance to galaxies with large redshifts.No honest survey of galaxy positions and distances hasfou nd s tructu re larger than th is, t hough a couple ofgroups continue to reanalyze other people’s data and re-por t fractal or heirarchical st ruct ure ou t to billions of

Planetary Orbit Sizes

Astronomical Mean Orbit Size in Actual Semi-MajorObject Titius-Bode sequence Axis in AU¥10

Mercury 4 3.87Venus 7 7.32Earth 10 10.0 (definition)Mars 16 15.24

Asteroid belt (mean) 28 26.8Jupiter 52 52.03Saturn 100 95.39.Uranus 196 191.9Neptune 388 301

Pluto 722 395

BEA M LINE 53

parsecs. A naive plot of galaxies on the sky indeed appearsto have a sort of quadrupole, but the cause is dust in ourown galaxy absorbing t he ligh t co m ing from galaxiesin the direction of t he galactic plane, not struct ure onthe scale of the whole observable Universe.

A non-artist’s impression of a hierarchical or fractal universe inwhich observations on ever-increasing length scales revealever-larger structure. In this realization, the first order clusterseach contain seven objects, the next two orders have threeeach, and the fourth order systems (where we run off the edgeof the illustration) at last four. Immanuel Kant and others in theeighteenth century proposed this sort of structure, but modernobservations indicate that there is no further clustering forsizes larger than about 150 million parsecs. (Adapted fromEdward R. Harrison’s Cosmology, The Science of the Universe,Cambridge University Press, second edition, 2000. Reprintedwith the permission of Cambridge University Press)

Coming at the problem from the other side, the thingsthat we observe to be very isotropic on t he sky, includ-ing bright radio sources, the X-ray background, gam maray bursts, and, most notoriously, the cosmic microwaveradiation background have been used by Jim Peebles ofPrinceton to show that eit her (a) the large scale fractaldimension d = 3 to a part in a thousand (that is, in effect,homogeneity over t he distances to t he X-ray and radiosources), or (b) we live very close indeed to the cen terof an i nho m oge neous b u t sp herically sy m m etric(isotropic) universe.

Several of the early solvers of the Einstein equations,including Georges Lemaitre, Alexander Friedmann, andWillem de Sit ter, considered at least briefly the idea ofa universe with topology more co mplex than the min-im u m needed to hold it together.

Connecting li t t le, rem ote bi ts of universe togetherwith worm holes, Einstein-Rosen bridges, or whatever isnot a good strategy, at least for the time and space scalesover which we observe t he cos m ic m icrowave back-ground. If you peered through such a connection in onedirect ion an d not in t he patch of sky nex t to i t , t he

A plot of the distribution of nearby galaxies on the sky, datingfrom before the confirmation that other galaxies exist and thatthe Universe is expanding. Most of the small clumps are realclusters, but the concentration toward the poles and dearth atthe equator (in galactic coordinates) result from absorption oflight by dust in the plane of our own Milky Way. [From C. V. L.Charlier, Arkiv. for Mat. Astron., Fys 16, 1 (1922)]


QUAN TIZED VELOCITIES AN D REDSHIFTS

T he ideas along these lines that still bounce around thelitera ture all see m to date from after t he discovery ofquasars, though the quantization intervals are as smallas 6 k m /sec. The topic is closely coupled (a) wi th red-sh ifts w hose origi ns are no t due to t he expan sion ofthe Universe, strong gravitation, or relative motion, butto some new physics and (b) wi th alternatives to stan-dard hot Big Bang comology, especially steady state andits more recent offspring. The number of people activelyworking on and supporting these ideas does not seem tobe more than a few dozen (of a world wide astronomicalcom m unity of more than 10,000), and most of the paperscome from an even smaller group. This is not, of course,equivalent to the ideas being wrong. But they have beenout in the scholarly marketplace for many years with-out at tracting vast numbers of buyers.

The underlying physics that might be responsible fornew kinds of wavelengt h shifts and/or quantized wave-length shifts have not been worked ou t in anything liket he m at he m atical de tail of t he Sta ndard Model a ndprocesses. One suggestion is t hat new mat ter is addedto the Universe in such a way that the particles initiallyhave zero rest mass and gradually grow to the values wesee. This will certainly result in longer wavelengths fromyounger matter, since the expression for the Bohr energylevels has t he elect ron rest m ass upstairs. Quan tizedor preferred redsh ifts t hen require so m e addi t ionalassu mption about mat ter not entering the Universe ata constant rate.

The first quasar redshift, Dl / l = 0.16 for 3C 273, wasmeasured in 1963 by Maarten Sch m idt and others. By1968–1969, about 70 were known, and Geoffrey and Mar-garet Burbidge re marked, first, that t here seemed to bea great many objects with z = 1.95 and, second, that therewas anot her m ajor peak a t z = 0.061 and sm aller onesat its m ultiples of 0.122, 0.183, and so on up to 0.601. The“z = 1.95” effect was amenable to two semi-conventional

photons from the t wo directions would have differen tredshlfts, that is different temperatures. The largest tem-perat u re fluct uat ions we see are par ts in 105, so t heligh t t ravel t im e t hrough t he wor m hole m ust not dif-fer from t he t ravel t im e wit hou t it by more t han t hatfract ion of the age of t he Universe, anot her conclusionexpressed clearly by Peebles.

A periodic u n iverse, i n w hich al l t he pho t ons goaround m any t im es, is harder to rule ou t. Indeed it hasbeen invoked a nu m ber of t i m es. T he firs t ca m p in-cludes people who have thought they had seen the sameobject or st ruct u re by looking a t differen t direct ionsin t he sky and t hose w ho have poin ted ou t t hat wedo not see such duplicate s truct ures, t hough we m igh twell have, and, t herefore, t hat t he cell size of periodicuniverse m ust be larger t han t he distance ligh t t ravelsi n a Hubble t i m e. T he second ca m p includes peoplew ho wa n t to use periodic bou ndary co ndi t io ns t oexpla in t he cos m ic m icrowave bac kgrou nd (i t’s ou row n galaxy seen sim ultaneously around t he Universei n a ll direct ions), h igh energy cos m ic rays (pho tonsw hich have been around many t im es, gaining energyas t hey go), or t he cen ters of quasars (brigh t becauset hey illu minate them selves).

Desce nding a bi t fro m t hat l as t peak of t er m inalweirdness, we note t hat a periodic universe, wi th cellsize m uch sm aller t han the distance light goes in 10–20billion years, au tom atically guaran tees t hat t he radioand X-ray sources will be seen qui te isotropicaIly ont he sky. I t also has no part icle horizon, if t hat is t hesor t of t hing t hat bot hers you.

Each year, t he ast rono m ical lit era t u re incl udes afew cosm ological ideas about which one is te m pted tosay (wit h Pauli?) t hat i t isn’t even wrong. A couple ofm y favori tes from t he 1990s are a universe wit h octe-h edral geo m e t ry ( t he adver t ised ca use is m agne t icfields) and one wi t h a metric that oscillates at a periodof 160 minutes (accoun ting for fluctuations in t he ligh tof t he Sun and certain variable stars).

BEA M LINE 55

explanations. The first was that z = 2 was the maxim umthat could be expected from a strong gravitational fieldif the object was to be stable. The second was that z = 1.95m igh t correspond to the epoch duri ng w hich aFriedmann-Lemaitre universe (one with a non-zero cos-mological constant) was coasting at almost constant size,so t hat we would observe lo ts of space (hence lots ofobjects) with that redshift.

00

10

20

30

40

50

60

0.8 1.6 2.4 3.2 4.0

Mg II & [O III]

Mg II & Hb

C III] & Mg IIC IV & C III]

La & C IVO VI & La

[Ne V] [O II] [NeIII]

Redshift

Nu

mbe

r

Histogram of redshifts of quasars initially identified as radiosources. This removes many (not all) of the selection effectsassociated with the apparent colors of sources at different z’sand with the present or absence of strong emission lines in thewavelength ranges usually observed from the ground. Theredshift ranges in which various specific lines are usable isindicated. C IV, for instance (rest wavelength 1909 A) disap-pears into the infrared at z = 3.4. Geoffrey Burbidge con-cludes that the sharp peaks in the distribution are not the re-sult of selection effects arising from availability of lines tomeasure redshifts. (Courtesy G. R. Burbidge)

R

t

t

R

Flat Space

The scale factor, R(t), for universes with non-zero cosmologi-cal constant. The case (upper diagram) with flat space, nowthought to be the best bet, goes from deceleration to acceler-ation through an inflection point (which probably happenednot much before z = 1) and so has no coasting phase to pileup redshifts at a preferred value, as would happen in a uni-verse with negative curvature (lower diagram). In either case,we live at a time like X, so that the Hubble constant (tangent tothe curve) gives the impression of the Universe being youngerthan it actually is. The early expansion has R proportional tot2/3 and the late expansion has exponential R(t).

56 SUMMER/FALL 2000

In the interim, gravitational redshifts have been pret tyclearly ruled out (you can’t keep enough low density gasat a single level in your potential well to emit the pho-tons we see), and the peak in N(z) has been dilu ted as thenumber of known redshifts has expanded beyond 2000.A cosmological constant is back as part of many people’sfavorite universes, but (if space is flat) in a form that doesnot produce a coasting phase, but only an inflection pointin R(t).

No conven t ional explanat ion for the periodici ty atDz = 0.061 has ever surfaced, and the si tuation was noti mproved over t he next decade when, as t he data basegrew, Geoffrey R. Burbidge repor ted addi t ional peaksat z = 0.30, 0.60, 0.96, and 1.41 and a colleague showedthat the whole set, including 1.95, could be fi t by Dlog(1+z)= 0.089. Meanwhile, and apparently independently, ClydeCowan, venturing out of his usual territory, found quitedifferent peaks separated by Dz = 1/15 and 1/6. As recentlyas 1997, ano ther group found several sta tist ically sig-nifican t peaks in N (z) between 1.2 and 3.2.

Any attempt to assign statistical significance to theseapparen t st ruct ures in N (z) m ust take accoun t of t woconfounders. Firs t, t he observed sam ple is not draw nuniformly from the real population. Quasars have onlya few strong emission line from which redshifts can bem easured, a nd t hese m ove in to, t h rough, a nd ou t ofobservable ranges of wavelengt h as redshift increases.Second, you m ust somehow m ultiply by the probabilityof all the other si milar effects that you didn’t find butthat would have been equally surprising. The 0.061 effectstill appears in the larger data bases of the 1990s, at leastwhen t he analysis is done by other suppor ters of non-cosmological redshifts and quasi-steady-state univers-es. It does, however, need to be said (and I say it out fromunder a recently-resigned editorial hat) that t he analy-ses require a certain amount of work, and that it is ratherdifficul t to persuade peopIe w ho are not violen t ly foror against an unconventional hypothesis to do the work,even as referees.

At the same time the Burbidges were reporting z = 1.95and 0.061 structures, another major player was sneakingup on quan tization with m uch finer in tervals. William

Tifft of the University of Arizona had star ted out by try-ing to measure very accurately the colors of normal galax-ies as a function of distance from their cen ters (one wayof probing t he ages, m asses, and heavy ele ment abun-dances of t he stars t hat con tribu te m ost of t he ligh t).In the process, he ended up wit h n umbers he trusted fort he total apparen t brigh tnesses of his program galaxies.He proceeded to graph apparent brigh tness vs. redshiftas Hubble and many others had done before him. Lo andbehold! His plots were stripy, and, in 1973 he announcedthat the velocities of ordinary nearby galaxies were quan-t ized in steps of abou t 72 k m /sec (z = 0.00024). Adm it-tedly, many of t he velocities were uncer tain by com-parable a m ounts, and t he m otion of t he solar sys te mit se lf (abou t 30 k m /sec rela t ive t o nearby s tars,220 k m / sec arou nd t he cen ter of the Milky Way, andso for t h) was no t negl igible on t h is scale. In t hein tervening quar ter of a cen t ury, he has con tin ued toexamine more and more data for more and more galax-ies, ellipticals as well as spirals, close pairs, and mem-bers of rich clusters, as well as nearly isolated galaxies,and even the distribu tions of velocit ies of stars wit hinthe galaxies. He has also devoted at tention to collectingdata wit h u ncer tain t ies less t han his qua n t izat ionin terval and to taking ou t t he con tribu tion of our ownmany motions to velocities seen in different directions

00 72 144 216

5

1059 Radio Pairs

Delta V

N

A data sample showing redshift quantization on the (roughly)72 km/sec scale. The points represent differences in velocitiesbetween close pairs of galaxies. An extended discussion ofthe development of the observations and theory of quantiza-tion at intervals like 72 and 36 km/sec is given by William Tifft inJournal of Astrophysics and Astronomy 18, 415 (1995). The ef-fects become clearer after the raw data have been modified invarious ways. [Courtesy William G. Tifft, Astrophysics andSpace Science 227, 25 (1997)].

BEA M LINE 57

in the sky. Some sort of quantization always appears in theresults. The interval has slid around a bit between 70 and75 km /sec and some subm ultiples have appeared in dif-ferent contexts, including 36 and 24 km/sec and even some-thing close to 6 km/sec. But the phenomenon persists.

A pair of as t rono m ers a t t he Royal Observat oryEdinburgh looked independen tly at some of the samplesin 1992 and 1996. They found sligh tly different intervals,for exa m ple, 37.22 k m /sec, bu t quan tizat ion none theless. A 1999 varian t from another aut hor includes peri-odicity (described as quantization) even in the rotationspeeds of normal spiral galaxies.

Tifft’s Arizona colleague W. John Cocke has providedso me par ts of a theoret ical fram ework for the 72 (etc.)k m /sec quant izat ion. It has (a) an exclusion principle,so that iden tical velocities for galaxies in close pairs areat least very rare if not forbidden and (b) som e aspectsanalogous to bou nd discrete levels on the atom ic scale,with continua possible only for velocity differences largert han some particular value. The quan tization is, then,responsible for the large range of velocities observed inrich clusters of galaxies which would then not requireadditional, dark mat ter to bind them.

Am I prepared to say that there is nothing meaning-fuI in any of t hese peaks and periods? No, t hough liket he race being to the swift and the bat tle to t he strong,t hat’s how I would bet if it were compulsory. There is,however, a differen t kind of prediction possible. Most oft he m ajor players on t he u nconven t ional tea m (s) areat, beyond, or rapidly approaching standard retirementages. T his i ncl udes Cocke and Tifft as well as t heBurbidges, H. C. (Ch ip) Arp, a fir m exponen t of non-cosm ological (t hough not necessarily quan tized) red-shifts, and the t hree founders of Steady State Cosmol-ogy, Fred Hoyle, T hom as Gold, and Her m ann Bondi.Meanw hile, very few young as t ronom ers are rallyingto th is particular set of flags. Whether th is reflects goodjudgm en t, fear of os tracis m by t he m ainstream astro-nomical com m unity, or som ething else can be debated.But it does, I t hink m ean that periodic, quant ized, andnon-cosmological redshifts will begin to disappear fromt he astronomical literature fairly soon.

QUAN TUM GRAVITY, QUAN TUM COSMOLOGY,AN D BEYO N D

The further back you try to look into our universal past,the further you diverge from the regimes of energy, den-si ty, and so for t h a t w hich exis t ing physics h as beentested. General relativity is said to be non-renormalizableand nonquan tizable, so t hat som e ot her description ofgravity m ust become necessary and appropriate at leastw hen t he age of t he Universe is comparable wit h thePlanck t i m e of 10- 43 sec, and perhaps long after. Oneprong of t he search for new a nd bet ter physics goest hrough at te mpts (via st ring t heory and m uch else) tounify all four forces, arguably in a space of many moret han three dimensions.

A very differen t approach is t hat of quan t u m cos-m ology, a t te m pting to wri te down a Schrödinger-like(Klein-Gordon) equation for the entire Universe and solveit. It is probably not a coincidence that the Wheeler (JohnArchibald)-DeWit t (Bryce S.) equation, governing t hewave fu nct ion of t he U niverse, co m es also fro m1967–1968, when t he first claim s of periodic and quan-tized redshifts were being made. The advent of quasarswith redshifts larger than one and of the microwave back-ground had quickly m ade t he very large, the very old,and t he very spooky all sound exciting.

The difference between the quanta in this short sectionand in t he previous long ones is t hat quan tu m gravi tyand quantum cosmology are respectable part-time activitiesfor serious physicists. The papers appear in different sortsof journals, and the authors include famous names (Hawk-ing, Linde, Wit ten, Schwartz, Greene, Vilenkin, and oth-ers) some of whose bearers are considerably younger thanthe velocity quantizers and the present author.

This last adventure in astronomical quantization stillhas most of its brigh t future ahead of it.

Where to find more:P. J. E. Peebles, Principles of Physical Cosmology, Princeton University Press,1993 is the repository of how the conventional models work and why someplausible sounding alternatives do not. Some early fractal cosmologies arediscussed by E. R. Harrison in Cosmology: The Science of the Universe, 2ndedition, Cambridge University Press, 2000. The lead up to Bode’s law ap-pears in M. A. Hoskin, The Cambridge Concise History of Astronomy, CambridgeUniversity Press, 1999.

58 SUMMER/FALL 2000

CATHRYN CARSO N is a histo-rian of science at the University ofCalifornia,Berkeley, w here she di-rects the Office for History of Scienceand Technology. Her in terest in thehistory of quantum mechanics beganwith an undergraduate thesis at theUniversity of Chicago on the pecu-liar notion of exchange forces. By thatpoint she had realized that she pre-ferred h is tory to science, bu t sh efound herself unable to stop takingphysics classes and ended up wit ha master’s degree. She did her grad-uat e work at Harvard U niversi ty,where she earned a Ph.D. in historyof science. At Berkeley she teachest he his tory of physics an d t he h is-tory of American science.

Recently she has been working onWerner Heisenberg's public role inpost-1945 Germany, the history of thescience behind nuclear waste man-agement, and theories and practicesof research management.

C O N TRIBU T O RS

CHARLES H. TOWNES receivedt he 1964 Nobel Prize in physics forhis role in the invention of the maserand t he laser. He is presen tly a pro-fessor in t he Graduate School at theUniversity of California, Berkeley,an d engaged i n research in as tro-physics.

Townes received his Ph.D. in 1939from the California Institute of Tech-nology and was a member of the BellTelephone Laborat ories techn icalstaff from 1939 to 1947. He has alsoheld professorships at Columbia Uni-versity and the Massachuset ts Insti-tu te of Technology, and served as anadvisor to t he U .S. governmen t.

His many me mberships includethe National Academy of Sciences,the National Academy of Engineer-ing, and The Royal Society of London.His many awards include t heN ational Medal of Science, t heNational Academy’s Comstock Prize,and the Niels Bohr International GoldMedal, as well as honorary degreesfrom 25 colleges and universities.

JAMES BJORKEN (Bj) is bes tknown for playing a cen tral role inthe development of the quark-partonmodel at SLAC from 1963 to 1979. Agraduate s t uden t at Stanford U ni-versity, he emigrated to SLAC withhis t hesis advisor, Sidney Drell, in1961. D uring t ha t period t hey col-laborated on a pair of tex tbooks,of w hich Relat iv is t ic Q uan t u mMechanics is the more beloved.

In 1979 Bj left for a ten-year hiatusat Fer milab where he served as As-sociate Director of Physics. Shortlyafter returning to SLAC, he becameinvolved in an experim en tal ini tia-tive at the SSC. Since then he has re-t urned to t he world of t heoret icalphysics.

Bj was influen t ial in reva m pingt he Bea m Li ne a nd served on t heEditorial Advisory Board for a recordseven years. He retired from SLAC in1999 and is currently building a housein Driggs, Idaho.

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Master of the Universe, EDWARDW. KOLB (known to most as Rocky),is head of the NASA/Fer milab Astro-physics Group at the Fermi NationalAccelera tor Laboratory as well as aProfessor of Astronom y and Astro-physics at The University of Chicago.He is a Fellow of the American Phys-ical Socie ty and has served on edi-torial boards of several internationalscientific journals as well as the mag-azine Astrono m y .

The field of Kolb’s research is theapplicat ion of ele m en tary par t iclephysics to the very early Universe.In addition to over 200 scientific pa-pers, he is a co-au thor of The EarlyU niverse, t he standard textbook onparticle physics and cosm ology. Hisnew book for t he general public,Blind Watchers of the Sk y , winnerof t he 1996 Em m e award fro m t h eAmerican Astronom ical Society, isthe story of the people and ideas thatshaped our view of the Universe.

ROBERT L. JAFFE is Professor ofPhysics and Director of t he Cen terfor Theoretical Physics at the Mass-achuset ts Inst i t u te of Tech nology.His research specialty is the physicsof ele m en tary par t icles, especiallythe dynamics of quark confinemen tand the Standard Model. He has alsoworked on t he quan t u m t heory oftubes, the astrophysics of dense mat-ter, and many problems in scat teringt h eory. He t each es qu an t u m m e-chanics, field theory, mechanics, andelectrodynamics at the advanced un-dergraduate and graduate levels.

Jaffe is a Fellow of the AmericanPhysical Society and t he AmericanAssociation for the Advancement ofScience. He has been a warded t heScience Council Prize for Excellencei n Teach ing U ndergradua tes, t heGraduate Studen t Council TeachingAward, and the Physics Depart men tBuechner Teaching Prize.

JO H N CLARKE has been in thePhysics Depart men t at t he Univer-sity of California, Berkeley and at theLawrence Berkeley N at ional Labo-ratory since 1968. He has spent mostof his career doing experim en ts onsuperconductors, developing super-conduct ing quan t u m in t erferencedevices (SQUIDS), and using them toconduct a wide variety of measure-men ts. Am ong his curren t interestsare more sensitive detectors for ax-ions, detecting magnetically labeledcells, and mapping m agnetic fieldsfrom the heart.

He is a Fellow of the Royal Soci-ety of London. He was named Cali-fornia Scien t ist of the year in 1987,and he received the Keithley Awardfrom the American Physical Societyin 1998 and t he Co mstock Prize inPhysics from the National Academyof Sciences in 1999.


VIRGINIA TRIMBLE’s first pub-lished paper deal t wi t h t he slopesof the so-called air shafts in Cheops’pyra m id and t hei r possible ast ro-nomical significance. An alternativeexplanation is that the slopes are aninevitable consequence of the height:dept h ratio of the stone blocks used(a ratio of small whole numbers). Thedrawing, in t he s tyle of a Copt ictom b por t rai t, was done in 1962 incolored chalk by the originator of theproject, t he la te Alexandre MikhailBadawy.

A recurring t he m e in cover ar t is tDAVID MARTINEZ ' s work is t hel in k bet ween m oder n scie n t ificknowledge and ancien t m agicalvision. His t he m es are drawn frombot h m odern and ancien t sources,and he is equally inspired by pio-neering scien t is ts and by Mot herNature in her various guises. He be-came interested in mathematics andphysics in his teens but only devel-oped his artistic talents in middle age.

Mar t inez has been ac t ive formany years wit h La Peña, a Lat inoarts organizat ion in Aus tin, Texas.He developed “The Legends Project”wi t h t he m to teac h ar t a nd s tory-telling to at-risk children. He is cur-rently doing research for two pain t-ings, one abou t Gaston Julia and theo t her abou t co m pu ters fea t u ringJoh n von N e u m an, Alan Turi ng,John Mauchly, and Presper Eckert.

BEA M LINE 61

D ATES T O REMEMBER

Nov. 6–9 22nd Advanced ICFA Beam Dynamics Workshop on Ground Motion in Fut ure Accelerators,Menlo Park, CA ([email protected] or ht tp:/ / www-project.slac.stanford.edu/lc/wkshp/G M2000 /)

Nov. 6–10 2000 Meeting of the High Energy Astrophysics Division (HEADS) of the American AstronomicalSociety (AAS), Honolulu, Hawaii (Eureka Scientific Inc. Dr. John Vallerga, 2452 Delmer St., Ste.100, Oakland, CA 94602-3017 or [email protected])

Nov. 11–21 International School of Cosmic Ray Astrophysics. 12t h Course: High Energy Pheno mena inAstrophysics and Cosm ology, Erice, Sicily (Et tore Majorana Centre, Via Guarnot ta 26, I-91016Erice, Sicily, Italy or [email protected] and ht tp:/ /www.ccsem.infn.it /)

Nov. 12–15 10t h Astronomical Data Analysis Software and Systems (ADASS 2000), Boston, Massachuset ts([email protected] or h t tp:/ /hea-www.harvard.edu/ADASS/)

Dec 2–7 International School of Quan tu m Physics. Third Course: Advances in Quant um Struct ures 2000,Erice, Sicily (Et tore Majorana Centre, Via Guarnot ta 26, I-91016 Erice, Sicily or [email protected] and ht tp:/ /www.ccsem.infn.it /)

Dec 3–8 11t h Conference on Computational Physics 2000: New Challenges for the New Millenniu m(CCP 2000), Brisbane, Australia (ht tp:/ /www.physics.uq.edu.au/CCP2000 /)

Dec 11–15 20t h Texas Symposium on Relativistic Astrophysics, Austin, Texas ([email protected] texas.eduor ht tp:/ / www.texas-symposiu m.org/)

Dec 18–22 International Symposium on T he Quan tu m Century: 100 Years of Max Planck’s Discovery, NewDelhi, India (Director: Cen tre for Philosophy and Foundations of Science, S-527 Greater Kailash-II, New Delhi, 110048, India or [email protected] and h t tp:/ /education.vsnl.com /cpfs/q100.h tml)

2001Jan 8–Mar 16 Joint Universities School. Course 1: Physics, Technologies, and Applications of Particle Acceler-

ators (JUAS 2001), Archamps, France (ESI/JUAS, Cen tre Universitaire de Formation et deRecherche, F-74166, Archamps, France or [email protected] and ht tp:/ /juas.in2p3.fr/)

Jan 15–26 US Particle Accelerator School (USPAS 2001), Houston, Texas (US Particle Accelerator School,Fermilab, MS 125, Box 500, Batavia, IL 60510, USA or [email protected] and h t tp:/ /www.indiana-edu/~uspas/programs/)

Feb 19–23 4 th International Conference on B Physics and CP Violation (BC4), Ago Town, Mie Prefecture,Japan (A. I. Sanda, Theoretical Physics, Nagoya University, Furo-cho, Chik usa-ku, Nagoya City,Aichi Prefecture, Japan or [email protected] and h t tp:/ /www.hepl.phys.nagoya-u.ac.jp/public/bcp4)

Documents

STANFORD LINEAR ACCELERATOR CENTER · *Ab raham Pais, Subtle is the Lord: Science and the Life of Albert Einstein, Oxford U. Press,1982. MaxPlanck,circa 190 (Courtesy AIP EmilioSegrèVisualArchives)