STANFORD LINEAR ACCELERATOR CENTERSummer/Fall 2000, Vol. 30, No. 2

EditorsRENE DONALDSON, BILL KIRK

Contributing EditorsMICHAEL RIORDAN, GORDON FRASER

JUDY JACKSON, AKIHIRO MAKIPEDRO WALOSCHEK

Editorial Advisory BoardPATRICIA BURCHAT, DAVID BURKE

LANCE DIXON, GEORGE SMOOTGEORGE TRILLING, KARL VAN BIBBER

HERMAN WINICK

IllustrationsTERRY ANDERSON

DistributionCRYSTAL TILGHMAN

A PERIODICAL OF PARTICLE PHYSICS

SUMMER/FALL 2000 VOL. 30, NUMBER 2

Printed on recycled paper

The Beam Line is published quarterly by the Stanford Linear Accelerator Center, Box 4349, Stanford, CA 94309. Telephone: (650) 926-2585. EMAIL: beamline@slac.stanford.eduFAX: (650) 926-4500

Issues of the Beam Line are accessible electroni-cally on the World Wide Web at http://www.slac.stanford.edu/pubs/beamline. SLAC is operated byStanford University under contract with the U.S.Department of Energy. The opinions of the authorsdo not necessarily reflect the policies of theStanford Linear Accelerator Center.

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 wave to 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

FEATURES

2 FOREWORD

THE FUTURE OF THE QUANTUMTHEORYJames Bjorken

6 THE ORIGINS OF THE QUANTUMTHEORYThe first 25 years of the century radically

transformed our ideas about Nature.

Cathryn Carson

20 THE LIGHT THAT SHINES STRAIGHTA Nobel laureate recounts the invention

of the laser and the birth of quantum

electronics.

Charles H. Townes

29 THE QUANTUM AND THECOSMOSLarge-scale structure in the Universe began

with tiny quantum fluctuations.

Rocky Kolb

34 GETTING TO KNOW YOUR CONSTITUENTSHumankind has wondered since the

beginning of history what are the

fundamental constituents of matter.

Robert L. Jaffe

41 SUPERCONDUCTIVITY: A MACROSCOPIC QUANTUM PHENOMENONQuantum mechanics is crucial to

understanding and using superconductivity

John Clarke

DEPARTMENTS

49 THE UNIVERSE AT LARGEThe Ratios of Small Whole Numbers:Misadventures in Astronomical QuantizationVirginia Trimble

58 CONTRIBUTORS

61 DATES TO REMEMBER

CONTENTS

2 SUMMER/FALL 2000

FOREWORD

N THIS ISSUE of the Beam Line, we cele-brate the one hundredth anniversary of thebirth of the quantum 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 much so that I have already writtenabout it (see “Particle Physics—Where Do We GoFrom Here?” in the Winter 1992 Beam Line,Vol. 22, No. 4). Here I will only quote again whatthe late Abraham Pais said about Planck: “Hisreasoning was mad, but his madness had thatdivine quality that only the greatest transitionalfigures can bring to science.”*

A century later, the madness has not yet com-pletely disappeared. Science in general has a wayof producing results which defy human intuition.But it is fair to say that the winner in thiscategory is the quantum theory. In my mindquantum paradoxes such as the Heisenberguncertainty principle, Schrödinger’s cat,

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

In the contributions to this issue, the knotty questions of the interpreta-tion of quantum theory are, mercifully, not addressed. There will be nomention of the debates between Einstein and Bohr, nor the later attempts by

The Future of the Quantum Tby JAMES BJORKEN

*Abraham Pais, Subtle is the Lord: Science and the Life of Albert Einstein, Oxford U. Press, 1982.

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

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Bohm, Everett, and others to find inter-pretations of the theory different fromthe original “Copenhagen interpreta-tion” of Bohr and his associates. Instead,what is rightfully emphasized is theoverwhelming practical success of theserevolutionary ideas. Quantum theoryworks. It never fails. And the scope ofthe applications is enormous. As LeonLederman, Nobel Laureate and DirectorEmeritus of Fermilab, likes to point out,more than 25 percent of the grossnational product is dependent upontechnology that springs in an essentialway from quantum phenomena.*

Nevertheless, it is hard not to sympa-thize with Einstein and feel that there issomething incomplete about the presentstatus of quantum theory. Perhaps theequations defining the theory are not ex-actly correct, and corrections will even-tually be defined and their effectsobserved. This is not a popular point ofview. But there does exist a minorityschool of thought which asserts that

only for sufficiently small systems is the quantum theory accurate, and thatfor large complex quantum 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 Lederman, The God Particle (If the Universe is the Answer, What is the Question?),Houghton Mifflin, 1993.

Pau

l Ehr

enfe

st

4 SUMMER/FALL 2000

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

Down through history most of the debates on the foundations of quantumtheory produced many words and very little action, and remained closer tothe philosophy of science than to real experimental science. John Bellbrought some freshness to the subject. The famous theorem that bears hisname initiated an experimental program to test some of the fundamentals.Nevertheless, it would have been an enormous shock, at least to me, if anydiscrepancy in such experiments had been found, because the searchesinvolved simple atomic systems, not so different from elementary particlesystems within which very subtle quantum effects have for some time beenclearly demonstrated. A worthy challenge to the quantum theory in myopinion must go much further and deeper.

What might such a challenge be? At present, one clear possibility which isactively pursued is in the realm of string theory, which attempts an exten-sion of Einstein gravity into the domain of very short distances, where quan-tum effects dominate. In the present incarnations, it is the theory of gravitythat yields ground and undergoes modifications and generalizations, with thequantum theory left essentially intact. But it seems to me that the alterna-tive must also be entertained—that the quantum theory itself does not sur-vive the synthesis. This, however, is easier said than done. And the problemwith each option is that the answer needs to be found with precious littleassistance from experiment. This is in stark contrast with the developmentof quantum theory itself, which was driven from initiation to completion bya huge number of experiments, essentially guiding the theorists to the finalequations.

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Another approach has been recently laid out by Frank Wilczek in a veryinteresting essay in Physics Today.* He compares the development of theequations of quantum theory with those of Maxwell’s electrodynamics. Bothwere first laboriously put together from experimental evidence. In both casesthe interpretations of what the equations meant came later. In the case ofelectrodynamics, the ultimate verdict on Maxwell’s equations is that at adeep level they express statements about symmetry. (In physics jargon,Maxwell’s equations express the fact that electrodynamics is gauge invariantand Lorentz covariant.) Wilczek notes that there is no similar deep basis forthe equations of quantum mechanics, and he looks forward to statements ofsymmetry as the future expression of the true meaning of the quantumtheory. But if there are such symmetries, they are not now known or at leastnot yet recognized. Wilczek does cite a pioneering suggestion of HermannWeyl, which might provide at least a clue as to what might be done. Buteven if Wilczek is on the right track, there is again the problem that theo-rists will be largely on their own, with very little help to be expected fromexperiment.

There is, however, a data-driven approach on the horizon. It is a conse-quence of the information revolution. In principle, quantum 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-scalequantum computers. If this happens, the foundations of quantum mechanicswill be tested on larger and larger, more complex physical systems. And ifquantum mechanics in the large needs to be modified, these computers maynot work as they are supposed to. If this happens, it will be just one more ex-ample of how a revolution in technology can lead to a revolution in funda-mental science.

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

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by CATHRYN CARSON

HAT IS A QUANTUM THEORY? We have

been asking that question for a long time, ever

since Max Planck introduced the element of dis-

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

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

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

has prompted a fundamental rethinking of physical theory.

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

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

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

THE ORIGINS OF THE QUANTUM THEORY

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

INTRODUCING h

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

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

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

BLACKBODIES

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

Beginning in the mid-1890s, Planck took up a seemingly narrowproblem, the interaction of an oscillating charge with its elec-tromagnetic field. These studies, however, brought him into con-tact with a long tradition of work on the emission of light. Decadesearlier it had been recognized that perfectly absorbing (“black”)bodies provided a standard for emission as well. Then over theyears a small industry had grown up around the study of suchobjects (and their real-world substitutes, like soot). A small groupof theorists occupied themselves with the thermodynamics ofradiation, while a host of experimenters labored over heated bod-ies to fix temperature, determine intensity, and characterizedeviations from blackbody ideality (see the graph above). After sci-entists pushed the practical realization of an old idea—that a closedtube with a small hole constituted a near-ideal blackbody—this“cavity radiation” allowed ever more reliable measurements. (Seeillustration at 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 emitted and absorbed radiation,so they could be used to model a blackbody. Thus everything seemedto fall into place in 1899 when he reproduced a formula that a col-league had derived by less secure means. That was convenient; every-one agreed that Willy Wien’s formula matched the observations. Thetrouble was that immediately afterwards, experimenters began find-ing deviations. At low frequencies, Wien’s expression becameincreasingly untenable, while elsewhere it continued to work wellenough. Informed of the results in the fall of 1900, on short noticePlanck came up with a reasonable interpolation. With its adjustableconstants his formula seemed to fit the experiments (see graph atright). Now the question became: Where might it come from? Whatwas its physical meaning?

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

MAKING LIGHT QUANTA REAL

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

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

10 SUMMER/FALL 2000

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

Discontinuity was thus endemic to the electromagnetic world.Interestingly, Einstein did not refer to Planck’s constant h, believinghis approach to be different in spirit. Where Planck had looked atoscillating charges, Einstein applied thermodynamics to the lightitself. It was only later that Einstein went back and showed 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 emitted and absorbed inthat fashion. A few easy considerations then yielded a law for thephotoelectric effect, in which light ejects electrons from the sur-face of a metal. Einstein provided not only a testable hypothesis butalso a new way of measuring the constant h (see table on the nextpage).

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

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

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

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

BEYOND LIGHT

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

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

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

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theories of specific heats to general significance. Feeling his waytowards a new law of thermodynamics, Nernst not only bolsteredEinstein’s ideas with experimental results, but also put them onthe agenda for widespread discussion. It was no accident, and to alarge degree Nernst’s doing, that the first Solvay Congress in 1911

dealt precisely with radiation theory and quanta (see photographbelow). Einstein spoke on specific heats, offering additional com-ments on electromagnetic radiation. If the quantum was born in 1900,the Solvay meeting was, so to speak, its social debut.

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

The first SolvayCongress in 1911assembled thepioneers ofquantum theory.Seated (left toright): W. Nernst,M. Brillouin,E. Solvay,H. A. Lorentz,E. Warburg,J. Perrin, W. Wien,M. Curie,H. 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 quantum’s second decade. Slower to take off, but ultimately evenmore productive, was the quantization of motions within the atomitself. Since no one had much sense of the atom’s constitution, theventure into atomic spectra was allied to speculative model-building.Unsurprisingly, most of the guesses of the early 1910s turned outto be wrong. They nonetheless sounded out the possibilities. Theorbital energy of electrons, their angular momentum (something likerotational inertia), or the frequency of their small oscillations aboutequilibrium: all these were fair game for quantization. The observedlines of the discrete spectrum could then be directly read off from theelectrons’ motions.

THE BOHR MODEL OF THE ATOM

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

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

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

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

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orbits’ energies right, Bohr had to introduce some rather ad hoc rules.These he eventually justified by quantization of angular momentum,which now came in units of 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.Not only did a quantum condition describe transitions betweenlevels, but the “stationary states,” too, were fixed by nonclassicalfiat. Electrons certainly revolved in orbits, but their frequency of rev-olution had nothing to do with the emitted light. Indeed, their os-cillations were postulated not to produce radiation. There was nopredicting when they might jump between levels. And transitionsgenerated frequencies according to a quantum relation, but Bohrproved hesitant to accept anything like a photon.

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

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

THE OLD QUANTUM THEORY

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

What Was BohrUp To?

BOHR’S PATH to his atomic

model was highly indirect. The

rules of the game, as played in

1911–1912, left some flexibility

in what quantum condition one

imposed. Initially Bohr applied

it to multielectron states,

whose allowed energies he

now broke up into a discrete

spectrum. More specifically, he

picked out their orbital fre-

quencies to quantize. This is

exactly what he would later

proscribe in the final version of

his model.

He rethought, however, in

the face of the Balmer series

and its simple numerical

pattern

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

Refocusing on one electron

and highlighting excited states,

he reconceptualized light

emission as a transition. The

Balmer series then resulted

from a tumble from orbit n to

orbit 2; the Rydberg constant

R could be determined in

terms of h. However, remnants

of the earlier model still

appeared in his paper.

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

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

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

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

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

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

QUANTUM MECHANICS

Discontinuity, abstraction from the visualizable, a positivistic turntowards observable quantities: these preferences indicated one pathto a full quantum theory. So, however, did their opposites. Whenin 1925–1926 a true quantum mechanics was finally achieved, twoseemingly distinct alternatives were on offer. Both took as a leitmotifthe relation to classical physics, but they offered different ways ofworking out the theme.

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

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

Some greeted the new theory with elation; others found it un-satisfactory and disagreeable. For as elegant as Heisenberg’s trans-lation might be, it took a very partial view of the problems of thequantum. Instead of the quantum theory of atomic structure, onemight also start from the wave-particle duality. Here another youngtheorist, Louis de Broglie, had advanced a speculative proposal in 1923

that Heisenberg and his colleagues had made little of. Thinking overthe discontinuous, particle-like aspects of light, de Broglie suggest-ed looking for continuous, wave-like aspects of electrons. His notion,while as yet ungrounded in experimental evidence, did provide sur-prising insight into the quantum conditions for Bohr’s orbits. It also,by a sideways route, gave Erwin Schrödinger the idea for his brilliantpapers of 1926.

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

The Quantum inQuantum Mechanics

ICONICALLY we now writeHeisenberg’s relations as

pq - qp = - ih/2p.

Here p represents momentum

and q represents position. For

ordinary numbers, of course,

pq equals qp, and so pq - qpis equal to zero. In quantum

mechanics, this difference,

called the commutator, is now

measured by h. (The same

thing happens with Heisen-

berg’s uncertainty principle of

1927: DpDq ³ h/4p.) The sig-

nificance of the approach, and

its rearticulation as a matrix

calculus, was made plain by

Max Born, Pascual Jordan, and

Werner Heisenberg. Its full

profundity was revealed by

Paul Dirac.

18 SUMMER/FALL 2000

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

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

BEAM LINE 19

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

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

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

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 T wentiethCentury (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.

20 SUMMER/FALL 2000

by CHARLES H. TOWNES

ON JULY 21, 1969, astronauts Neil Armstrong andEdwin “Buzz” Aldrin set up an array of small reflectors onthe moon, facing them toward Earth. At the same time, twoteams of astrophysicists, one at the University of California’sLick Observatory and the other at the University of Texas’sMcDonald Observatory, were preparing small instrumentson two big telescopes. Ten days later, the Lick team pointedits telescope at the precise location of the reflectors on themoon and sent a small pulse of power into the hardware theyhad added to it. A few days after that, the McDonald teamwent through the same steps. In the heart of each telescope,a narrow beam of extraordinarily pure red light emergedfrom a synthetic ruby crystal, pierced the sky, and enteredthe near vacuum of space. The two rays were still only athousand yards wide after traveling 240,000 miles to illumi-nate the moon-based reflectors. Slightly more than a secondafter each light beam hit its target, the crews in Californiaand Texas detected its faint reflection. The brief time inter-val between launch and detection of these light pulses per-mitted calculation of the distance to the moon to within aninch—a measurement of unprecedented precision.

The ruby crystal for each light source was the heart of alaser (an acronym for light amplification by stimulated emis-sion of radiation), which is a device first demonstrated 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 light. There are manyother more mundane, practical uses such as in surveyingland and grading roads, as well as myriad everyday uses—

THE LIGHT THAT SHIN

Adapted by Michael Riordan from HowThe Laser Happened: Adventures of aScientist, by Charles H. Townes.Reprinted by permission of OxfordUniversity Press.

A Nobel laureate recounts

the invention of the laser

and the birth of quantum

electronics.

BEAM LINE 21

ranging from compact disc play-ers to grocery-store checkout devices.

The smallest lasers are so tinyone cannot see them without a microscope. Thousands can be built on semiconductor chips. The biggest lasers consume as much electricity as a small town. About 45 miles from my office in Berkeley is theLawrence Livermore National Laboratory, which has someof the world’s most powerful lasers. One set of them, collec-tively called NOVA, produces ten individual laser beams thatconverge to a spot the size of a pinhead and generate temper-atures of many millions of degrees. Such intensely concen-trated energies are essential for experiments that can showphysicists how to create conditions for nuclear fusion. TheLivermore team hopes thereby to find a way to generate elec-tricity efficiently, with little pollution or radioactive wastes.

For several years after the laser’s invention, colleaguesliked to tease me about it, saying, “That’s a great idea, butit’s a solution looking for a problem.” The truth is, none ofus who worked on the first lasers ever imagined how manyuses there might eventually be. But 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 little idea as to where their research will eventu-ally lead.

NES STRAIGHT

Lasers are commonly used in eyesurgery to correct defective vision.

Will

& D

eni M

cInt

yre,

P42

19F

Pho

to R

esea

rche

rs

22 SUMMER/FALL 2000

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

wave amplification by stimulatedemission of radiation) resulted fromthe application of quantum me-chanics to electronics after WorldWar II. Together with other advances,they helped spawn a new disciplinein applied physics known since thelate 1950s as “quantum electronics.”

Since early in the twentieth cen-tury, physicists such as Niels Bohr,Louis de Broglie, and Albert Einsteinlearned how molecules and atomsabsorb and emit light—or any otherelectromagnetic radiation—on thebasis of the newly discovered laws ofquantum mechanics. When atoms ormolecules absorb light, one mightsay that parts of them wiggle backand forth or twirl with new, addedenergy. Quantum mechanics requiresthat they store 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 theyonly absorb light of certain wave-lengths, and no others, because thewavelength of light determines theenergy of its individual photons (seebox on right). As atoms or moleculesdrop from higher back to lower en-ergy levels, they emit photons of thesame energies or wavelengths asthose they can absorb. This processis usually spontaneous, and this kindof light is normally emitted 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 thermodynamic

principles, that if photons can beabsorbed by atoms and boost themto higher energy states, then light canalso prod an atom to give up itsenergy and drop down to a lowerlevel. One photon hits the atom, andtwo come out. When this happens,the emitted photon takes off inprecisely the same direction as thelight that stimulated the energy loss,with the two waves exactly in step(or in the same “phase”). This “stim-ulated emission” results in coherentamplification, or amplification of awave at exactly the same frequencyand phase.

Both absorption and stimulatedemission can occur simultaneously.As a light wave comes along, it canthus excite some atoms that are inlower energy states into higher statesand, at the same time, induce someof those in higher states to fall backdown to lower states. If there aremore atoms in the upper states thanin the lower states, more light isemitted than absorbed. In short, thelight gets stronger. It comes outbrighter than it went in.

The reason why light is usuallyabsorbed in materials is that sub-stances almost always have moreatoms and molecules sitting in lowerenergy states than in higher ones:more photons are absorbed thanemitted. Thus we do not expect toshine a light through a piece of glassand see it come out the other sidebrighter than it went in. Yet this isprecisely what happens with lasers.

The trick in making a laser is toproduce a material in which theenergies of the atoms or moleculespresent have been put in a veryabnormal condition, with more ofthem in excited states than in the

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

BEAM 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.

24 SUMMER/FALL 2000

to find a way to generate wavesshorter than those produced by theklystrons and magnetrons developedfor radar in World War II. One day Isuddenly had an idea—use moleculesand the stimulated emission fromthem. With graduate student JimGordon and postdoc Herb Zeiger, Idecided to experiment first with am-monia (NH3) molecules, which emitradiation at a wavelength of about1 centimeter. After a couple of yearsof effort, the idea worked. We chris-tened this device the “maser.” Itproved so interesting that for a whileI put 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 microwaveradiation was indeed remarkablypure, I visited Denmark and sawNiels Bohr. As we were walkingalong the street together, he askedme what I was doing. I described themaser and its amazing performance.

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

Similarly, at a cocktail party inPrinceton, New Jersey, the Hungar-ian mathematician John von Neu-mann asked what I was working on.I told him about the maser and thepurity of its frequency.

“That can’t be right!” he declared.But it was, I replied, telling him ithad already been demonstrated.

Such protests were not offhandopinions about obscure aspects ofphysics; they came from the marrowof these men’s bones. Their objec-tions were founded on principle—theHeisenberg uncertainty principle.A central tenet of quantum mechan-ics, this principle is among the coreachievements that occurred during

ground, or lower, states. A wave ofelectromagnetic energy of the properfrequency traveling through such apeculiar substance will pick up ratherthan lose energy. The increase in thenumber of photons associated withthis wave represents amplification—light amplification by stimulatedemission of radiation.

If this amplification is not verylarge on a single pass of the wavethrough the material, there are waysto beef it up. For example, two par-allel mirrors—between which thelight is reflected back and forth, withexcited molecules (or atoms) in themiddle—can build up the wave. Get-ting the highly directional laser beamout of the device is just a matter ofone mirror being made partiallytransparent, so that when the inter-nally reflecting beam gets strongenough, a substantial amount of itspower shoots right on through oneend of the device.

The way this manipulation ofphysical laws came 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 summarized in this ar-ticle, it also describes my odyssey asa scientist and its unpredictable andperhaps natural path to the maserand laser. This story is interwovenwith the way the field of quantumelectronics grew, rapidly and strik-ingly, owing to a variety of importantcontributors, their cooperation andcompetitiveness.

DURING 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 who worked

on the first lasers ever

imagined how many uses

there might eventually be.

Many of today’s practical

technologies have resulted

from basic scientific

research done years

to decades before.

BEAM LINE 25

a phenomenal burst of creativity inthe first few decades of the twentiethcentury. As its name implies, it de-scribes the impossibility of achiev-ing absolute knowledge of all the as-pects of a system’s condition. Thereis a price to be paid in attemptingto measure or define one aspect ofa specific particle to very great ex-actness. One must surrender knowl-edge of, or control over, some otherfeature.

A corollary of this principle, onwhich the maser’s doubters stum-bled, is that one cannot measure anobject’s frequency (or energy) to greataccuracy in an arbitrarily short timeinterval. Measurements made over afinite period of time automaticallyimpose uncertainty on the observedfrequency.

To many physicists steeped in theuncertainty principle, the maser’sperformance, at first blush, made nosense at all. Molecules race throughits cavity, spending so little timethere—about one ten-thousandth ofa second—that it seemed impossiblefor the frequency of the output mi-crowave radiation to be so narrowlydefined. Yet that is exactly what hap-pens in the maser.

There is good reason that the un-certainty principle does not apply sosimply here. The maser (and by anal-ogy, the laser) does not tell you any-thing about the energy or frequen-cy of any specific molecule. Whena molecule (or atom) is stimulated toradiate, it must produce exactly thesame frequency as the stimulatingradiation. In addition, this radiationrepresents the average of a large num-ber of molecules (or atoms) work-ing together. Each individual mole-cule remains anonymous, not

accurately measured or tracked. Theprecision arises from factors thatmollify 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 thatif molecules zip through the maserso quickly, their emission lines mustbe broad. After I persisted, howev-er, he relented.

“Oh, well, yes,” he said; “Maybeyou are right.” But my impressionwas that he was just trying to be po-lite to a younger physicist.

After our first chat at that Prince-ton party, von Neumann wanderedoff and had another drink. In aboutfifteen minutes, he was back.

“Yes, you’re right,” 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)

26 SUMMER/FALL 2000

drive any specific resonant frequencyinside a cavity.

As I played with the variety ofpossible molecular and atomic tran-sitions, and the methods of excit-ing them, what is well-known todaysuddenly became clear to me: it isjust as easy, and probably easier, togo right on down to really shortwavelengths—to the near-infrared oreven optical regions—as to go downone smaller step at a time. This wasa revelation, like stepping througha door into a room I did not suspectexisted.

The Doppler effect does indeed in-creasingly smear out the frequencyof response of an atom (or molecule)as one goes to shorter wavelengths,but there is a compensating factorthat comes into play. The number ofatoms required to amplify a wave bya given amount does not increase,because atoms give up their quantamore readily at higher frequencies.And while the power needed to keepa certain number of atoms in excitedstates increases with the frequency,

He seemed very interested, and heasked me about the possibility of do-ing something similar at shorterwavelengths using semiconductors.Only later did I learn from hisposthumous papers, in a September1953 letter he had written to EdwardTeller, that he had already proposedproducing a cascade of stimulated in-frared radiation in semiconductorsby exciting electrons with intenseneutron bombardment. His idea wasalmost a laser, but he had notthought of employing a reflectingcavity nor of using the coherent prop-erties of stimulated radiation.

IN THE LATE SUMMER of1957, I felt it was high time Imoved on to the original goal that

fostered the maser idea: oscillatorsthat work at wavelengths apprecia-bly shorter than 1 millimeter, beyondwhat standard electronics couldachieve. For some time I had beenthinking off and on about this goal,hoping that a great idea would popinto my head. But since nothing hadspontaneously occurred to me, I de-cided I had to take time for concen-trated thought.

A major problem to overcome wasthat the rate of energy radiation froma molecule increases as the fourthpower of the frequency. Thus to keepmolecules or atoms excited 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 many orders of mag-nitude. Another problem was that forgas molecules or atoms, Doppler ef-fects increasingly broaden the emis-sion spectrum as the wavelength getssmaller. That means there is less am-plification per molecule available to

the total power required—even toamplify visible light—is not neces-sarily prohibitive.

Not only were there no clearpenalties in such a leapfrog to veryshort wavelengths or high frequencies,this approach offered big advantages.In the near-infrared and visible re-gions, we already had plenty of ex-perience and equipment. By contrast,wavelengths near 0.1 mm and tech-niques to handle them were rela-tively unknown. It was time to takea big step.

Still, there remained another ma-jor concern: the resonant cavity. Tocontain enough atoms or molecules,the cavity would have to be muchlonger than the wavelength of theradiation—probably thousands oftimes longer. This meant, I feared,that no cavity could be very selectivefor one and only one frequency. Thegreat size of the cavity, comparedto a single wavelength, meant thatmany closely spaced but slightly dif-ferent wavelengths would resonate.

By great good fortune, I got helpand another good idea before I pro-ceeded any further. I had recently be-gun a consulting job at Bell Labs,where my brother-in-law and formerpostdoc Arthur Schawlow was work-ing. I naturally told him that I hadbeen thinking about such opticalmasers, and he was very interestedbecause he had also been thinking inthat very direction.

We talked over the cavity prob-lem, and Art came up with the so-lution. I had been considering arather well-enclosed cavity, with mir-rors on the ends and holes in thesides only large enough to providea way to pump energy into the gasand to kill some of the directions in

The development

of the laser followed

no script except

to hew to the nature

of scientists groping

to understand,

to explore, and

to create.

BEAM LINE 27

which the waves might bounce. Hesuggested instead that we use justtwo plates, two simple mirrors, andleave off the sides altogether. Sucharrangements of parallel mirrors werealready used at the time in optics;they are called Fabry–Perot interfer-ometers.

Art recognized that without thesides, many oscillating modes thatdepend on internal reflections wouldeliminate themselves. Any wave hit-ting either end mirror at an anglewould eventually walk itself out ofthe cavity—and so not build up en-ergy. The only modes that could sur-vive and oscillate, then, would bewaves reflected exactly straight backand forth between the two mirrors.

More detailed studies showed thatthe size of the mirrors and the dis-tance between them could even bechosen so that only one frequencywould be likely to oscillate. To besure, any wavelength that fit an ex-act number of times between themirrors could resonate in such a cav-ity, just as a piano string produces notjust one pure frequency but alsomany higher harmonics. In a well-designed system, however, only onefrequency will fall squarely at thetransition energy of the mediumwithin it. Mathematically and phys-ically, it was “neat.”

Art and I agreed to write a paperjointly on optical masers. It seemedclear that we could actually buildone, but it would take time. We spentnine months working on and off inour spare time to write the paper. Weneeded to clear up the engineeringand some specific details, such aswhat material to use, and to clarifythe theory. By August 1958 the man-uscript was complete, and the Bell

Labs patent lawyers told us that theyhad done their job protecting itsideas. The Physical Review publishedit in the December 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, itrepresented the formal birth of themaser and its related physics as a dis-tinct subdiscipline. At that meet-ing Schawlow delivered a general talkon optical masers.

Listening with interest wasTheodore Maiman from the HughesResearch Laboratories in Culver City,California. He had been workingwith ruby masers and says he was al-ready thinking about using ruby asthe medium for a laser. Ted listenedclosely to the rundown on the pos-sibility of a solid-state ruby laser,about which Art was not too hope-ful. “It may well be that more suit-able solid materials can be found,”he noted, “and we are looking 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

tists recently hired after their uni-versity research in the field of mi-crowave and radio spectroscopy—students of Willis Lamb, PolykarpKusch, and myself, who worked to-gether in the Columbia RadiationLaboratory, and of Nicholas Bloem-bergen at Harvard. The whole fieldof quantum electronics grew out ofthis approach to physics.

The development of the maserand laser followed no script exceptto hew to the nature of scientistsgroping to understand, explore andcreate. As a striking example of howimportant technology applied to hu-man interests can grow out of basicuniversity research, the laser’s de-velopment fits a pattern that couldnot have been predicted in advance.

What research planner, wanting amore intense light source, wouldhave started by studying moleculeswith 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 spectroscopy? Thewhole field of quantum electronicsis truly a textbook example of broad-ly applicable technology growing un-expectedly out of basic research.

Maiman felt that Schawlow wasfar too pessimstic and left the meet-ing intent on building a solid-stateruby laser. In subsequent months Tedmade striking measurements onruby, showing that its lowest energylevel could be partially emptied byexcitation with intense light. Hethen pushed on toward still brighterexcitation sources. On May 16, 1960,he fired up a flash lamp wrappedaround a ruby crystal about 1.5 cmlong and produced the first operatinglaser.

The evidence that it worked wassomewhat indirect. The Hughesgroup did not set it up to shine a spotof light on the wall. No such flash ofa beam had been seen, which leftroom for doubt about just what theyhad obtained. But the instrumentshad shown a substantial change inthe fluorescence spectrum of theruby; it became much narrower, aclear sign that emission had beenstimulated, and the radiation peakedat just the wavelengths that weremost favored for such action. A shortwhile later, both the Hughes re-searchers and Schawlow at Bell Labsindependently demonstrated power-ful flashes of directed light that madespots on the wall—clear intuitiveproof that 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 itsimportance becomes apparent, in-dustrial laboratories can devote moreresources and concentrated effort toa problem than can a university.When the goal is clear, industry canbe effective. But the first lasers wereinvented and built by young scien-

BEAM LINE 29

ONE NORMALLY THINKS that quantum mechanics is onlyrelevant on submicroscopic scales, operating in the domain ofatomic, nuclear, and particle physics. But if our most excitingideas about the evolution of the early Universe are correct, thenthe imprint of the quantum world is visible on astronomicalscales. The possibility that quantum mechanics shaped thelargest structures in the Universe is one of the theories to comefrom the marriage of the quantum and the cosmos.

The Quantum

by ROCKY KOLB

WHAT’S OUT THERE?

On a dark clear night the 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. But with a little patience andskill it’s possible to find a few extra-galactic objects. The AndromedaGalaxy, 2.4 million light-years distant,is visible as a faint nebulous region,and from the Southern Hemispheretwo small nearby galaxies (if 170,000

light-years can be considered nearby),the Magellanic Clouds, can also beseen with the unaided eye.

While the preponderance of objectsseen by eye are galactic, the viewthrough large telescopes reveals theuniverse beyond the Milky Way. Evenwith the telescopes of the nineteenthcentury, the great British astronomerSir William Herschel discovered about2,500 galaxies, and his son, Sir JohnHerschel, discovered an additionalthousand (although neither of theHerschels knew that the objects theydiscovered were extragalactic). 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)

30 SUMMER/FALL 2000

several thousand galaxies. Clustersof galaxies are part of even largerassociations called superclusters,containing dozens of clusters spreadout over 100 million light-years ofspace. Even superclusters may not bethe largest things in the Universe.The largest surveys of the Universesuggest to some astronomers thatgalaxies are organized on two-dimensional sheet-like structures,while others believe that galaxies liealong extended one-dimensional fil-aments. The exact nature of howgalaxies are arranged in the Universeis still a matter of debate among cos-mologists. A picture of the arrange-ment of galaxies on the largest scalesis only now emerging.

Not all of the Universe is visibleto the eye. In addition to patternsin the arrangement of matter in thevisible Universe, there is also a struc-ture to the background radiation.

The Universe is awash in a ther-mal bath of radiation, with a tem-perature of three degrees above ab-solute zero (3 K or -270 C). Invisibleto the human eye, the backgroundradiation is a remnant of the hotprimeval fireball. First discovered in1965 by Arno Penzias and RobertWilson, it is a fundamental predic-tion of the Big Bang theory.

Soon after Penzias and Wilson dis-covered the background radiation,the search began for variations in thetemperature of the universe. Fornearly 30 years, astrophysicistssearched in vain for regions of the dis-tant Universe that were hotter orcolder than average. It was not until1992 that a team of astronomers us-ing the Cosmic Background ExplorerSatellite (COBE) discovered an in-trinsic pattern in the temperature of

astronomers built larger telescopesand looked deeper into space, thenumber of known galaxies grew.Although no one has ever botheredto count, astronomers have identi-fied about four million galaxies. Andthere are a lot more out there!

Our deepest view into the Uni-verse is the Hubble Deep Field. Theresult of a 10-day exposure of a verysmall region of the sky by NASA’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-tire sky to the depth of the DeepField, it would find more than 50 bil-lion galaxies.

Although large galaxies containat least 100 billion stars and stretchacross 100,000 light-years or moreof space, they aren’t the biggestthings in the Universe. Just as starsare part of galaxies, galaxies are partof larger structures.

Many galaxies are members ofgroups containing 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)

BEAM LINE 31

the Universe. Since the time of theCOBE discovery, a pattern of tem-perature variations has been mea-sured with increasing precision bydozens of balloon-borne and terres-trial observations. A new era of pre-cision cosmological observations isstarting. Sometime in 2001 NASAwill launch a new satellite, theMicrowave Anisotropy Probe (MAP),and sometime in 2007 the EuropeanSpace Agency will launch an evenmore ambitious effort, the PlanckExplorer, to study temperature vari-ations in the cosmic backgroundradiation.

Even if our eyes were sensitive tomicrowave radiation, we would havea hard time discerning a pattern oftemperature fluctuations since thehottest and coldest regions of thebackground radiation are only aboutone-thousandth of a percent hotterand colder than average.

Although small in magnitude, thebackground temperature fluctuationsare large in importance since theygive us a snapshot of structure in theUniverse when the background pho-tons last scattered, about 300,000years after the Bang.

WHY IS IT THERE?

A really good answer to a deep ques-tion usually leads to even deeperquestions. Once we discover what’sin the Universe, a deeper questionarises: Why is it there? Why are starsarranged into galaxies, galaxies intoclusters, clusters into 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 the result of gravity. Every timeyou see a star the imprint of gravityis shining at you. Today we observenew stars forming within giant inter-stellar gas clouds, such as those foundat the center of the Orion Nebula just1,500 light-years away (see photo onnext page).

Interstellar clouds are not smoothand uniform; they contain regionswhere the density of material is largerthan in surrounding regions. Thedense regions within the clouds arethe seeds around which stars growthrough the irresistible force of grav-ity. The dense regions pull in nearbymaterial through the force of gravity,which compresses the material un-til it becomes hot and dense enoughfor nuclear reactions to commenceand form stars.

About five billion years ago in ourlittle corner of the Milky Way, grav-ity started to pull together gas anddust to form our solar system. Thisfashioning of structure in our localneighborhood is just a small part ofa process that started about 12 billionyears ago on a grander scale through-out the Universe.

For the first 300 centuries after theBig Bang, the Universe expanded toorapidly for gravity to fashion struc-ture. Finally, 30,000 years after theBang (30,000 AB), the expansion hadslowed enough for gravity to beginthe long relentless process of pullingtogether matter to form the Universewe see today.

We are quite confident that grav-ity shaped the Universe becauseastrophysicists can simulate in amatter of days what Nature required12 billion years to accomplish. Start-ing with the Universe as it 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)

32 SUMMER/FALL 2000

formation within the Orion Nebulaif the gas and dust were perfectlyuniform, structure would never haveformed if the entire Universe wascompletely uniform. Without pri-mordial seeds in the Universe30,000 AB, gravity would be unableto shape the Universe into the formwe now see. A seedless universewould be a pretty boring place to live,because matter would remain per-fectly uniform rather than assem-bling into discrete structures.

The pattern of structure we see inthe Universe today reflects the pat-tern of initial seeds. Seeds have to beinserted by hand into the computersimulations of the formation of struc-ture. Since the aim of cosmology isto understand the structure of theUniverse on the basis of physicallaws, we just can’t end the story bysaying structure exists because therewere primordial seeds. For a com-plete answer to the questions of whyare there things in the Universe, wehave to know what planted the pri-mordial seeds.

In the microworld of subatomicphysics, there is an inherent uncer-tainty about the positions andenergies of particles. According tothe uncertainty principle, energy isn’t

calculate how small primordial seedsgrew to become the giant galaxies,clusters of galaxies, superclusters,walls, and filaments we see through-out the Universe.

Gravity alone cannot be the finalanswer to the question of why mat-ter in the Universe has such a richand varied arrangement. For the forceof gravity to pull things togetherrequires small initial seeds where thedensity is larger than the surround-ing regions. In a very real sense, thefact 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 cultivate. Just as though therewouldn’t be any seeds to trigger 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 Redshift Survey)

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

BEAM LINE 33

always conserved—it can be violatedfor a brief period of time. Becausequantum mechanics applies to themicroworld, only tiny amounts ofenergy are involved, and the timeduring which energy is out of balanceis exceedingly short.

One of the consequences of theuncertainty principle is that a regionof seemingly empty space is not reallyempty, but is a seething froth inwhich every sort of fundamental par-ticle pops out of empty space for abrief instant before annihilating withits antiparticle and disappearing.

Empty space only looks like aquiet, calm place because we can’tsee Nature operating on submicro-scopic scales. In order to see thesequantum fluctuations we would haveto take a small region of space andblow it up in size. Of course that isnot possible in any terrestrial labo-ratory, so to observe the quantumfluctuations 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 microscopicvacuum quantum fluctuations be-came frozen into the fabric of space.The expansion of the Universestretched the microscopic pattern ofquantum fluctuations to astronom-ical size.

Much later, the pattern of whatonce were quantum fluctuations ofthe vacuum appear as small fluctua-tions in the mass density of theUniverse and variations in the tem-perature of the background radiation.

If this theory is correct, then seedsof structure are nothing more thanpatterns of quantum fluctuationsfrom the inflationary era. In a very

real sense, quantum fluctuationswould be the origin of everything wesee in the Universe.

When viewing assemblages ofstars in galaxies or galaxies in galac-tic clusters, or when viewing the pat-tern of fluctuations in the back-ground radiation, you are actuallyseeing quantum fluctuations. With-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

34 SUMMER/FALL 2000

THE URGE TO REDUCE THE FORMS of matter to afew elementary constituents must be very ancient. By450 BCE, Empedocles had already developed or inherited a“standard model” in which everything was composed offour elements—Air, Earth, Fire, and Water. Thinking aboutthe materials available to him, this is not a bad list. But as apredictive model of Nature, it has some obvious shortcom-ings. Successive generations have evolved increasinglysophisticated standard models, each with its own list of“fundamental” constituents. The length of the list has fluc-tuated over the years, as shown on the next page. TheGreeks are actually tied for the minimum with four. Thechemists of the 19th century and the particle physicists ofthe 1950s and 1960s pushed the number up toward 100 beforesome revolutionary development reduced it dramatically.Today’s list includes about 25 elementary particles, thoughit could be either higher or lower depending on how youcount. Tomorrow’s list—the product of the next generationof accelerators—promises to be longer still, with no end insight. In fact, modern speculations always seem to increaserather than decrease the number of fundamental con-stituents. Superstring theorists dream of unifying all theforces and forms of matter into a single essence, but so farthey have little clue how the diversity of our observed worldwould devolve from this perfect form. Others have pointedout that Nature at the shortest distances and highest ener-gies might be quite random and chaotic, and that the forceswe feel and the particles we observe are special only in thatthey persist longer and propagate further than all the rest.

Two lessons stand out in this cartoon history. First, whatserves as a “fundamental constituent” changes with timeand depends on what sorts of questions one asks. The older

Getting to Know Yby ROBERT L. JAFFE

Humankind has

wondered since the

beginning of history

what are the funda-

mental constituents

of matter. Today’s list

includes about 25

elementary particles.

Tomorrow’s list

promises to be longer

still, with no end

in sight.

Fire

Dry

Wet

Cold

Hot

Water

Ear

th

Air

BEAM LINE 35

models are not really inferior to today’s Standard Modelwithin the context of the world they set out to describe.And, second, there always seems to be another layer. In theearly years of the 21st century particle physicists will beprobing deeply into the physics of the current StandardModel of particle physics with new accelerators like theB-factories of SLAC and KEK and the Large Hadron Colliderat CERN. Now seems like a good time to reflect on what toexpect.

It is no accident, nor is it a sign of our stupidity, that wehave constructed “atomic” descriptions of Nature onseveral different scales only to learn that our “atoms” werecomposed of yet more funda-mental constituents. Quantummechanics itself gives rise tothis apparently layered textureof Nature. It also gives us verysophisticated tools and testswith which to probe our con-stituents for substructure. Look-ing back at the “atoms” of pre-vious generations, we can seewhere the hints of substructurefirst appeared and how our pre-decessors were led to the nextlayer. Looking forward from ourpresent crop of elementary par-ticles, we see some suggestionsof deeper structure beneath,but—tantalizingly—other signssuggest that today’s fundamentalconstituents, numerous as they

1000

100

10

1

Molecules

Atoms Hadrons

StandardModel

Nu

mbe

r of

Ele

men

tary

Par

ticl

es

500 BCE,A,F,W

Distance (centimeters)

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 Constituents

36 SUMMER/FALL 2000

are, may be more fundamental thanyesterday’s.

BEFORE LOOKING atwhere we are today, let’s takea brief tour of the two most

useful “atomic” descriptions of thepast: the standard models of chem-istry and nuclear physics, shown be-low. Both provide very effective de-scriptions of phenomena within theirrange of applicability. Actually theterm “effective” has a technicalmeaning here. For physicists an “ef-fective theory” is one based on build-ing blocks known not to be elemen-tary, but which can be treated as if

they were, in the case at hand. “Ef-fective” is the right word becauseit means both “useful” and “stand-ing in place of,” both of which applyin this case. The chemical elementsare very useful tools to understandeveryday phenomena, and they“stand in place of” the complex mo-tions of electrons around atomicnuclei, which are largely irrelevantfor everyday applications.

Chemistry and nuclear physicsare both “effective theories” becausequantum mechanics shields themfrom the complexity that lies be-neath. This feature of quantum me-chanics is largely responsible for theorderliness we perceive in the phys-ical world, and it deserves more dis-cussion. Consider a familiar sub-stance such as water. At the simplestlevel, a chemist views pure wateras a vast number of identical mole-cules, each composed of two hydro-gen atoms bound to an oxygen atom.Deep within the atoms are nuclei:eight protons and eight neutrons foran oxygen nucleus, a single protonfor hydrogen. Within the protons andneutrons are quarks and gluons.Within the quarks and gluons, whoknows what? If classical mechanicsdescribed the world, each degree offreedom in this teeming microcosmcould have an arbitrary amount ofexcitation energy. When disturbed,for example by a collision withanother molecule, all the motionswithin the water molecule could beaffected. In just this way, the Earthand everything on it would bethoroughly perturbed if our solar sys-tem collided with another.

Chemistry

Nuclear

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 Quantum 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.

BEAM LINE 37

Quantum mechanics, on theother hand, does not allow arbitrarydisruption. All excitations of themolecule are quantized, each withits own characteristic energy. Mo-tions of the molecule as a whole—rotations and vibrations—have thelowest energies, in the 1–100 milli-electron volt regime (1 meV = 10-3 eV).An electron volt, abbreviated eV, isthe energy an electron gains fallingthrough a potential of one volt andis a convenient unit of energy for fun-damental processes. Excitation of theelectrons in the hydrogen and oxy-gen atoms come next, with charac-teristic energies ranging from about10-1 to 103 eV. Nuclear excitations inoxygen require millions of electronvolts (106 eV = 1 MeV), and excita-tions of the quarks inside a protonrequire hundreds of MeV. Collisionsbetween water molecules at roomtemperature 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 thatthese variables—the electrons, thenuclei, the quarks—are “frozen.” Theenergy levels of a classical and quan-tum 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 little aboutelectrons and nothing about nuclearstructure, quarks, or gluons. Lightquanta make a particularly goodprobe of this “quantum ladder,” as

Victor Weisskopf called it. As sum-marized in the illustration above,as we shorten the wavelength of lightwe increase the energy of lightquanta in direct proportion. As wemove from microwaves to visiblelight to X rays to gamma rays weprobe successively deeper layers ofthe structure of a water molecule.The appropriate constituent de-scription depends on the scale of theprobe. At one extreme, we cannothope to describe the highest energyexcitations of water without know-ing about quarks and gluons; on theother hand, no one needs quarks andgluons to describe the way water isheated in a microwave oven.

PERHAPS THE MOST ef-fective theory of all was theone invented by the nuclear

physicists in the 1940s. It reigned foronly a few years, before the discov-ery of myriad excited states of theproton and neutron led to its aban-donment and eventual replacementwith today’s Standard Model ofquarks and leptons. The nuclear stan-dard model was based on three con-stituents: the proton (p); the neutron(n); and the electron (e). The neutri-no (ne) plays a bit part in radioactivedecays, and perhaps one should countthe photon (g), the quantum of theelectromagnetic field. So the 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

Nuclear

Hadronic

Active

Frozen

Frozen

Frozen

Irrelevant

Active

Frozen

Frozen

Irrelevant

Irrelevant

Active

Frozen

Irrelevant

Irrelevant

Irrelevant

Active

States of Water

meV eV MeV GeV

microwavevisi

ble 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.

38 SUMMER/FALL 2000

is emitted. This suggest that protonsand neutrons, like hydrogen, have in-ner workings capable of excitationand de-excitation. Of course, if onlyfeeble energies are available, the in-ternal structure cannot be excited,and it will not be possible to tellwhether or not the particle is com-posite. So an experimenter needs ahigh-energy accelerator to probe com-positeness by looking for excitations.

Complex force laws. We have adeep prejudice that the forces be-tween elementary particles shouldbe simple, like Coulomb’s law for theelectrostatic force between pointcharges: F12 = q1q2/r2

12. Because theyderive 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 the proton and neu-tron are summarized by pages of ta-bles in the Physical Review. We nowunderstand that they derive from the

all of atomic, molecular, and con-densed matter physics can be un-derstood in terms of these few con-stituents. The nuclei of atoms arebuilt up of protons and neutrons ac-cording to fairly simple empiricalrules. Atoms, in turn, are composedof electrons held in orbit around nu-clei by electromagnetism. All the dif-ferent chemical elements from hy-drogen (the lightest) to uranium (theheaviest naturally occurring) are justdifferent organizations of electronsaround nuclei with different electriccharge. Even the radioactive process-es that transmute one element intoanother are well described in thepneneg world.

The nuclear model of the worldwas soon replaced by another. Cer-tain tell-tale signatures that emergedearly in the 1950s made it clear thatthese “elementary” constituentswere not so elementary after all. Thesame signatures of compositenesshave repeated every time one set ofconstituents is replaced by another:

Excitations. If a particle is com-posite, when it is hit hard enough itscomponent parts will be excited intoa quasi-stable state, which laterdecays by emitting radiation. The hy-drogen atom provides a classicexample. When hydrogen atoms areheated so that they collide with oneanother violently, light of character-istic frequencies is emitted. As soonas it was understood that the lightcomes from the de-excitation of itsinner workings, hydrogen’s days asan elementary particle were over.Similarly, during the 1950s physicistsdiscovered that when a proton orneutron is hit hard enough, excitedstates are formed and characteristicradiation (of light or other hadrons)

complex quark and gluon substruc-ture within protons and neutrons.

The complicated features of forcelaws die away quickly with distance.So if an experimenter looks at a par-ticle from far away or with lowresolution, it is not possible to tellwhether it is composite. A high-energy accelerator is needed to probeshort distances and see the deviationsfrom simple force laws that are tell-tale signs of compositeness.

Form factors. When two struc-tureless particles scatter, the resultsare determined by the simple forcesbetween them. If one of the particleshas substructure, the scattering ismodified. In general the probabilityof the scattered particle retaining itsidentity—this is known as “elasticscattering”—is reduced, becausethere is a chance that the particle willbe excited or converted into some-thing else. The factor by which theelastic scattering probability isdiminished is known as a “form fac-tor.” Robert Hofstadter first discov-ered that the proton has a form fac-tor in experiments performed atStanford in the 1950s. This was in-controvertible evidence that the pro-ton is composite.

If, however, one scatters lightlyfrom a composite particle, nothingnew is excited, and no form factor isobserved. Once again, a high-energyaccelerator is necessary to scatterhard enough to probe a particle’s con-stituents.

Deep inelastic scattering. Thebest proof of compositeness is, ofcourse, to detect directly the sub-constituents out of which a parti-cle is composed. Rutherford foundthe nucleus of the atom by scatter-ing a particles from a gold foil and

There is

tantalizing

evidence

that new

relationships

await discovery.

BEAM LINE 39

finding that some were scattereddirectly backwards, a result thatwould only be possible if the goldatoms contained a heavy concentra-tion of mass—the nucleus—at theircore. The famous SLAC experimentsled by Jerome Friedman, HenryKendall, and Richard Taylor foundthe analogous result for the proton:when they scattered electrons atlarge angles they found telltale evi-dence of pointlike quarks inside.

By the early 1970s mountains ofevidence had forced the physics com-munity to conclude that protons,neutrons, and their ilk are not fun-damental, but are instead composedof quarks and gluons. During thatdecade Burton Richter and Sam Tingand their collaborators separately dis-covered the charm quark; LeonLederman led the team that discov-ered the bottom quark; and MartinPerl’s group discovered the third copyof the electron, the tau-lepton ortauon. The mediators of the weakforce, the W and Z bosons, were dis-covered at CERN. The final ingredi-ents in our present Standard Modelare the top quark, recently discov-ered at Fermilab, and the 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.

THE STANDARD Modelof particle physics is incred-ibly successful and pre-

dictive, but few believe it is the lastword. There are too many particles—about 25—and too many param-eters—also about 25 masses, inter-action strengths, and orientationangles—for a fundamental theory.

Particle physicists have spent the lastquarter century looking for signs ofwhat comes next. So far, they havecome up empty—no signs of an ex-citation spectrum, complex forcelaws, or form factors have been seenin any experiment. The situation issummarized above. The StandardModel was discovered when physi-cists attempted to describe the worldat distances smaller than the size ofthe proton, about 10-13 cm. Modernexperiments have probed to distancesabout four orders of magnitudesmaller, 10-17 cm, without evidencefor substructure.

There is tantalizing evidence thatnew relationships await discovery.For example, the 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 the pro-ton has been measured by experi-ment to be the exact opposite of thecharge on the electron to better thanone part in 1020. Such a relationshipwould follow naturally either ifquarks and electrons were composedof common constituents or if theywere different excitations states ofsome “ur” particle. Equally intrigu-ing is that each quark and leptonseems to come in three versions withidentical properties, differing only inmass. The three charged leptons, theelectron, the muon and the tauon,

Yes

Yes

No

92 Elements

p,n,e

Standard Model

Yes

Yes

No

Yes

Yes

No

ExcitationSpectrum

FormFactors

ComplexForce Laws

Evidence for underlying structure inmodels of elementary constituents.

40 SUMMER/FALL 2000

leptons are generalizations ofCoulomb’s Law. They all follow fromsymmetry considerations known as“gauge principles.” Even gravity,which rests uneasily in the StandardModel, follows from the gauge prin-ciple that Einstein called “generalcovariance.” The simplicity of theforces in the Standard Model hasbeen mistaken for evidence that atlast we have reached truly elemen-tary constituents, and that there isno further substructure to be found.After all, the argument goes, “Howcould composite particles behave sosimply?” Unfortunately, it turns outthat it is quite natural for compos-ite particles to mimic fundamentalones if we do not probe them deeplyenough. The forces between atomsand nuclei look simple if one doesnot look too closely. Models withquite arbitrary interactions definedat very short distances produce thekind of forces we see in the Stan-dard Model when viewed from faraway. In a technical sense, thedeviations from the forces that fol-low from the “gauge principle” aresuppressed by factors like L/l ,where l is the typical length scaleprobed by an experiment (l scaleslike the inverse of the energy of thecolliding particles), and L is the dis-tance scale of the substructure. Hol-gar Nielsen and his collaboratorshave followed this thread of logic toan extreme, by exploring the extentto which an essentially random the-ory defined at the shortest distancescales will present itself to our eyeswith gauge interactions like theStandard Model and gravity. Theseexercises show how much roomthere is for surprise when we probe

are the best-known example, but thesame holds for the up, charm, and topquarks, the down, strange, and bot-tom quarks, and the neutrinosassociated with each lepton. The pat-tern looks very much like one of in-ternal excitation—as if the muon andtauon are “excited electrons”. How-ever, extremely careful experimentshave not been able to excite an elec-tron into a muon or a tauon. The lim-its on these excitation processes arenow extremely strong and prettymuch rule out simple models inwhich the electron, muon, and tauonare “made up of” the same subcon-stituents in a straightforward way.

Building structures that relate theelementary particles of the StandardModel to one another is the businessof modern particle theory. Super-symmetry (SUSY) combined withGrand Unification is perhaps themost promising approach. It removessome of the most troubling incon-gruities in the Standard Model. How-ever, the cost is high—if SUSY isright, a huge number of new parti-cles await discovery at the LHC or atthe Next Linear Collider. The listof “elementary constituents” wouldmore than double, as would the num-ber of parameters necessary to de-scribe their interactions. The situa-tion would resemble the state ofchemistry before the understandingof atoms, or of hadron physics beforethe discovery of quarks: a huge num-ber of constituents, grouped into fam-ilies, awaiting the next simplifyingdiscovery of substructure.

One of the most striking proper-ties of the Standard Model is the sim-plicity of the force laws. All theknown forces between quarks and

the next level beyond the StandardModel.

We are poised rather uncomfort-ably upon a rung on Viki Weisskopf’sQuantum Ladder. The world ofquarks, leptons, and gauge interac-tions does a wonderful job of ex-plaining the rungs below us: thenuclear world of pneneg, the worldof atoms, and chemistry. However,the internal consistency of the Stan-dard Model and the propensity ofquantum mechanics to shield usfrom what lies beyond, leave us with-out enough wisdom to guess whatwe will find on the next rung, or if,indeed, there is another rung to befound. Hints from the StandardModel suggest that new constituentsawait discovery with the next roundof accelerator experiments. Hopefrom past examples motivates the-orists to seek simplifications beyondthis proliferation. Past experiencecautions that we are a long way fromthe end of this exploration.

BEAM LINE 41

N THE NETHERLANDS IN 1911, about adecade after the discovery of quantum theory butmore than a decade before the introduction of quan-

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

In a normal metal, electrical currents are carried by elec-trons which are scattered, giving rise to resistance. Sinceelectrons each carry a negative electric charge, they repeleach other. In a superconductor, on the other hand, there isan attractive force between electrons of opposite momentumand opposite spin that overcomes this repulsion, enablingthem to form pairs. These pairs are able to move through thematerial effectively without being scattered, and thus carry asupercurrent with no energy loss. Each pair can be describedby a quantum mechanical “wave function.” The remarkableproperty of the superconductor is that all electron pairs have

by JOHN CLARKE

A Macroscopic Quantum

Phenomenon

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

Superconductivity

42 SUMMER/FALL 2000

Sure enough, this quantum me-chanical phenomenon, called the“Josephson effect,” was observedshortly afterwards at Bell TelephoneLaboratories.

Between the two tunneling dis-coveries, in 1961, there occurredanother discovery that was to haveprofound implications: flux quanti-zation. Because supercurrents arelossless, they can flow indefinitelyaround a superconducting loop,thereby maintaining a permanentmagnetic field. This is the princi-ple of the high-field magnet. How-ever, the magnetic flux threading thering cannot take arbitrary values, butinstead is quantized in units of theflux quantum. The superconductorconsequently mimics familiar quan-tum effects in atoms but does so ona macroscopic scale.

For most of the century, super-conductivity was a phenomenon ofliquid helium temperatures; a com-pound of niobium and germaniumhad the highest transition tempera-ture, about 23 K. In 1986, however,Alex Mueller and Georg Bednorzstaggered the physics world withtheir announcement of supercon-ductivity at 30 K in a layered oxideof the elements lanthanum, calcium,copper, and oxygen. Their amazingbreakthrough unleashed a worldwiderace to discover materials with high-er critical temperatures. Shortly af-terwards, the discovery of supercon-ductivity in a compound of yttrium,barium, copper, and oxygen at 90 Kushered in the new age of supercon-ductors for which liquid nitrogen,boiling at 77 K, could be used as thecryogen. Today the highest transitiontemperature, in a mercury-based ox-ide, is about 133 K.

the same wave function, thus form-ing a macroscopic quantum statewith a phase coherence extendingthroughout the material.

There are two types of supercon-ductors. In 1957, Alexei Abrikosovshowed that above a certain thresh-old magnetic field, type II supercon-ductors admit field in the form ofvortices. Each vortex contains onequantum of magnetic flux (productof magnetic field and area). Becausesupercurrents can flow around thevortices, these materials remain su-perconducting to vastly higher mag-netic fields than their type I coun-terparts. Type II materials are theenabling technology for high-fieldmagnets.

Shortly afterwards came a suc-cession of events that heralded theage of superconducting electronics.In 1960, Ivar Giaever discovered thetunneling of electrons through an in-sulating barrier separating two thinsuperconducting films. If the insu-lator is sufficiently thin, electronswill “tunnel” through it. Building onthis notion, in 1962 Brian Josephsonpredicted that electron pairs couldtunnel through a barrier between twosuperconductors, giving the junctionweak superconducting properties.

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

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Why do these new materials havesuch high transition temperatures?Amazingly, some 13 years after theirdiscovery, nobody knows! While itis clear that hole pairs carry the su-percurrent, it is unclear what gluesthem together. The nature of thepairing mechanism in high-temper-ature superconductors remains oneof the great physics challenges of thenew millennium.

LARGE-SCALE APPLICATIONS

Copper-clad wire made from an alloyof niobium and titanium is the 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 the presence ofextremely high magnetic fields. Thelargest scale applications of super-conducting wire, however, are inmagnets for particle accelerators andmagnetic resonance imaging (MRI).Other prototype applications includecables for power transmission, largeinductors for energy storage, powergenerators and electric motors, mag-netically levitated trains, and bear-ings for energy-storing flywheels.Higher magnetic fields can beachieved with other niobium alloysinvolving tin or aluminum, but thesematerials are brittle and require spe-cial handling. Much progress has beenmade with multifilamentary wiresconsisting of the high temperaturesuperconductor bismuth-strontium-calcium-copper-oxide sheathed in sil-ver. Such wire is now available inlengths of several hundred metersand has been used in demonstrationssuch as electric motors and power

transmission. At 4.2 K this wireremains superconducting to highermagnetic fields than the niobiumalloys, so that it can be used as aninsert coil to boost the magnetic fieldproduced by low-temperature magnets.

The world’s most powerful par-ticle accelerators rely on magnetswound with superconducting cables.This cable contains 20–40 niobium-titanium wires in parallel, each con-taining 5,000–10,000 filaments capa-ble of carrying 10,000 amperes (seeJudy Jackson’s article “Down to theWire” in the Spring 1993 issue).

The first superconducting accel-erator to be built was the Tevatronat Fermi National Accelerator Lab-oratory in 1984. This 1 TeV machine

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

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examples, it becomes clear that thedemanding requirements of accel-erators have been a major drivingforce behind the development of su-perconducting magnets. Their cru-cial advantage is that they dissipatevery little power compared with con-ventional magnets.

Millions of people around theworld have been surrounded by a su-perconducting magnet while havinga magnetic resonance image (MRI)taken of themselves. Thousands ofMRI machines are in everyday use,each containing tens of kilometersof superconducting wire wound intoa persistent-current solenoid. Themagnet is cooled either by liquidhelium or by a cryocooler. Once thecurrent has been stored in the su-perconducting coil, the magneticfield is very stable, decaying by as lit-tle as a part per million in a year.

Conventional MRI relies on thefact that protons possess spin andthus a magnetic moment. In the MRImachine, a radiofrequency pulse ofmagnetic field induces protons in thepatient to precess about the directionof the static magnetic field suppliedby the superconduting magnet. Forthe workhorse machines with a fieldof 1.5 T, the precessional frequency,which is precisely proportional to thefield, is about 64 MHz. These pre-cessing magnetic moments induce aradiofrequency voltage in a receivercoil that is amplified and stored forsubsequent analysis. If the magneticfield were uniform, all the protonswould precess at the same frequency.The key to obtaining an image is theuse of magnetic field gradients todefine a “voxel,” a volume typically3 mm across. One distinguishesstructure by virtue of the fact that,

incorporates 800 superconductingmagnets. Other superconducting ac-celerators include HERA at theDeutsches Elektronen Synchrotronin Germany, the Relativistic HeavyIon Collider nearing completion atBrookhaven National Laboratory inNew York, and the Large HadronCollider (LHC) which is being builtin the tunnel of the existing LargeElectron Positron ring at CERN inSwitzerland. The LHC, scheduled forcompletion in 2005, is designed for14 TeV collision energy and, withquadrupole and corrector magnets,will involve more than 8,000 super-conducting magnets. The dipole fieldis 8.4 tesla. The ill-fated Supercon-ducting Super Collider was designedfor 40 TeV and was to have involved4,000 superconducting dipole mag-nets. At the other end of the size andenergy scale is Helios 1, a 0.7 GeVsynchrotron X-ray source for litho-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)

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

MRI has become a clinical tool ofgreat importance and is used in awide variety of modes. The develop-ment of functional magnetic reso-nant imaging enables one to locatesome sites in the brain that are in-volved in body function or thought.During brain activity, there is a rapid,momentary increase in blood flow toa specific site, thereby increasing thelocal oxygen concentration. In turn,the presence of the oxygen modifiesthe local MRI signal relative to thatof the surrounding tissue, enablingone to pinpoint the neural activity.Applications of this technique in-clude mapping the brain and pre-operative surgical planning.

SMALL-SCALE APPLICATIONS

At the lower end of the size scale (lessthan a millimeter) are extremely sen-sitive devices used to measure mag-netic fields. Called “SQUIDS” forsuperconducting quantum interfer-ence devices, they are the most sen-sitive type of detector known to sci-ence, and can turn a change in amagnetic field, something very hardto measure, into a change in voltage,something easy to measure. The dcSQUID consists of two junctions con-nected in parallel to form a super-conducting loop. In the presence ofan appropriate current, a voltage isdeveloped across the junctions. If onechanges the magnetic field threadingthe loop, this voltage oscillates backand forth with a period of one fluxquantum. One detects a change inmagnetic field by measuring theresulting change in voltage across the

SQUID using conventional electronics.In essence, the SQUID is a flux-to-voltage transducer.

Squids are fabricated from thinfilms using photolithographic tech-niques to pattern them on a siliconwafer. In the usual design, they con-sist of a square washer of niobiumcontaining a slit on either side ofwhich is a tunnel junction. The up-per electrodes of the junctions 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 current passed through thecoil efficiently couples flux to theSQUID. A typical SQUID can detectone part per million of a flux quan-tum, and it is this remarkable sen-sitivity that makes possible a host ofapplications.

Generally, SQUIDs are coupled toauxiliary components, such as asuperconducting loop connected tothe input terminals of the coil toform a “flux transformer.” When weapply a magnetic field to this loop,flux quantization induces a super-current in the transformer and hencea flux in the SQUID. The flux trans-former functions as a sort of “hear-ing aid,” enabling one to detect a

Current

Current

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.

46 SUMMER/FALL 2000

magnetic field as much as elevenorders of magnitude below that of themagnetic field of the earth. If, in-stead, we connect a resistance inseries with the SQUID coil, we cre-ate a voltmeter that readily achievesa voltage noise six orders of magni-tude below that of semiconductoramplifiers.

It is likely that most SQUIDs evermade are used for studies of the hu-man brain. Commercially availablesystems contain as many as 306 sen-sors arranged in a helmet containingliquid helium that fits around theback, top, and sides of the patient’sskull. This completely non-invasivetechnique enables one to detect the

tiny magnetic fields produced bythousands of neurons firing inconcert. Although the fields outsidethe head are quite large by SQUIDstandards, they are minuscule com-pared with environmental magneticnoise—cars, elevators, television sta-tions. To eliminate these noisesources, the patient is usually en-closed in a magnetically-shieldedroom. In addition, the flux trans-formers are generally configured asspatial gradiometers that discrimi-nate against distant noise sources infavor of nearby signal sources. Com-puter processing of the signals fromthe array of SQUIDs enables one tolocate the source to within 2–3 mm.

There are two broad classes ofsignal: stimulated, the brain’s re-sponse to an external stimulus; andspontaneous, self-generated by thebrain. An example of the first is pre-surgical screening of brain tumors.By applying stimuli, one can map outthe brain function in the vicinity ofthe tumor, thereby enabling the sur-geon to choose the least damagingpath to remove it. An example ofspontaneous signals is their use toidentify the location of epileptic foci.The fast temporal response of theSQUID, a few milliseconds, enablesone to demonstrate that somepatients have two foci, one of whichstimulates the other. By locating theepileptic focus non-invasively beforesurgery, one can make an informeddecision about the type of treatment.Research is also under way on otherdisorders, including Alzheimer’s andParkinson’s diseases, and 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)

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ischemia (localized tissue anemia);another is to locate the site of anarrhythmia. Although extensive clin-ical trials would be required todemonstrate its efficacy, MCG isentirely non-invasive and may becheaper and faster than current tech-niques.

Ground-based and airborne hightemperature SQUIDs have been usedsuccessfully in geophysical survey-ing trials. In Germany, high temper-ature SQUIDs are used to examinecommercial aircraft wheels for pos-sible flaws produced by the stress andheat generated at landing.

The advantage of the higheroperating temperature of hightemperature SQUIDs is exemplified

nuclear magnetic resonance tosearches for magnetic monopoles andstudies of the reversal of the Earth’smagnetic field in ancient times. Arecent example of the SQUID’s ver-satility is the proposal to use it as ahigh-frequency amplifier in an up-graded axion detector at LawrenceLivermore National Laboratory. Theaxion is a candidate particle for thecold dark matter that constitutes 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).

With the advent o f h igh-temperature superconductivity, manygroups around the world chose theSQUID to develop their thin-filmtechnology. Yttrium-barium-copper-oxygen dc SQUIDs operating in liq-uid nitrogen achieve a magnetic fieldsensitivity within a factor of 3–5 oftheir liquid-helium cooled cousins.High-temperature SQUIDs find novelapplications in which the potentialeconomy and convenience of cool-ing with liquid nitrogen or a cryo-cooler are strong incentives. Mucheffort has been expended to developthem for magnetocardiography(MCG) in an unshielded environ-ment. The magnetic signal from theheart is easily detected by a SQUIDin a shielded enclosure. However, toreduce the system cost and to makeMCG more broadly available, it is es-sential to eliminate the shieldedroom. This challenge can be met bytaking spatial derivatives, often witha combination of hardware and soft-ware, to reduce external interference.What advantages does MCG offerover conventional electrocardiogra-phy? One potentially importantapplication is the detection 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)

48 SUMMER/FALL 2000

in “SQUID microscopes,” in whichthe device, mounted in vacuum justbelow a thin window, can be broughtvery close to samples at room tem-perature and pressure. Such micro-scopes are used to detect flaws insemiconductor chips and to monitorthe gyrations of magnetotactic bac-teria, which contain a tiny magnetfor navigational purposes.

Although SQUIDs dominate thesmall-scale arena, other devices areimportant. Most national standardslaboratories around the world use theac Josephson effect to maintain thestandard volt. Superconducting de-tectors are revolutionizing submil-limeter and far infrared astronomy.Mixers involving a low temperatures 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 unrivaled sensitivity tonarrow-band signals, for example,those produced by rotational tran-sitions of molecules in interstellarspace. Roughly 100 SIS mixers areoperational on ground-based radiotelescopes, and a radio-telescopearray planned for Chile will requireabout 1000 such mixers. When onerequires broadband detectors—forexample, for the detection of thecosmic background radiation—thelow temperature superconducting-transition-edge bolometer is thedevice of choice in the submillimeterrange. The bolometer absorbs inci-dent radiation, and the resulting risein its temperature is detected by thechange in resistance of a supercon-ductor at its transition; this changeis read out by a SQUID. Arrays of1,000 or even 10,000 such bolometersare contemplated for satellite-basedtelescopes for rapid mapping of thecosmos—not only in the far infrared

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

A rapidly growing number of cel-lular base stations use multipole hightemperature filters on their receivers,yielding sharper bandwidth defini-tion and lower noise than conven-tional filters. This technology en-ables the provider to pack morechannels into a given frequencyallocation in urban environmentsand to extend the distance betweenrural base stations.

THE NEXT MILLENNIUM

The major fundamental questions are“Why are high temperature super-conductors superconducting?” and“Can we achieve still higher tem-perature superconductors?” On theapplications front, the developmentof a high temperature wire that canbe manufactured cost effectively insufficient lengths could revolution-ize power generation, transmission,and utilization. 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.The combination of SQUID arraysand MRI will revolutionize ourunderstanding of brain function. Andperhaps a SQUID will even catch anaxion.

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by VIRGINIA TRIMBLE

THE UNIVERSE AT LARGE

OD MADE THE INTEGERS; all else is the work of Man. Sosaid Kronecker of the delta. And indeed you can do many

things with the integers if your tastes run in that direction. A uni-form density stretched string or a pipe of uniform bore will pro-duce a series of tones that sound pleasant together if you stop thestring or pipe into lengths that are the ratios of small whole num-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 century BCE and his followers, the Pythagoreans.They extended the concept to the heavens, associating particularnotes with the orbits of the planets, which therefore sang aharmony or music of the spheres, finally transcribed in moderntimes by Gustav Holtz.

A fondness for small whole numbers 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 rational for his contemporaries to think theywere sick because of an invasion by millions of germs than fortheir ancestors to have attributed 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 numbers and math-ematics, as much as fashions in art and government, I think stands.

The Ratios of Small Whole Numbers: Misadventures in Astronomical Quantization

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

on the head of an editor.

G

50 SUMMER/FALL 2000

KEPLER’S LAWS AND LAURELS

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

from a Newtonian, inverse-square law of gravity, but hehad tried many combina-tions of small whole num-bers before showing that theorbit periods and orbit sizesof the planets were con-nected by P2 = a3. And thesame 1619 work, Harmony ofthe Worlds, that enunciatedthis relation also showed thenotes sung by the planets, ina notation that I do notentirely understand. Venushummed a single high pitch,and Mercury ran up a glis-sando and down an arpeggio,while Earth moanedmi(seria), fa(mes), mi(seria).The range of notes in eachmelody depended on therange of speeds of the planetin its orbit, which Kepler,with his equal areas law, hadalso correctly described.

Kepler’s planets were,however, six, though Coper-nicus and Tycho had clung toseven, by counting themoon, even as they re-arranged Sun and Earth. Whysix planets carried on six

spheres? Why, because there are precisely five regularsolids to separate the spheres: cube, pyramid, octahe-dron, dodecahedron, and icosahedron. With tight pack-ing of sequential spheres and solids in the right order,

Kepler could approximately reproduce the relative or-bit sizes (semi-major axes) required to move the plan-ets to the positions on the sky where we see them.Though this scheme appears in his 1596 CosmographicMystery and so belongs to Kepler’s geometric youth,he does not appear to have abandoned it in his alge-braic maturity.

EXCESSIVELY UNIVERSAL GRAVITATION

Newton (1643–1727) was born the year after Galileo diedand died only two years before James Bradley recognizedaberration of starlight, thereby demonstrating unam-biguously that the Earth goes around the Sun and thatlight travels about 104 times as fast as the Earth’s orbitspeed (NOT a ratio of small whole numbers!) But theSWN ideal persisted many places. Galileo had found fourmoons orbiting Jupiter (which Kepler himself noted alsofollowed a P2 = a3 pattern around their central body), andthe Earth had one. Mars must then naturally have two.So said Jonathan Swift in 1726, attributing the discoveryto Laputian* astronomers, though it was not actuallymade until 1877 by Asaph Hall of the U.S. NavalObservatory.

Attempts to force-fit Newtonian gravity to the entiresolar system have led to a couple of ghost planets,beginning with Vulcan, whose job was to acceleratethe rotation of the orbit of Mercury (“advance of the per-ihelion”) until Einstein and General Relativity wereready to take it on. Planet X, out beyond Pluto, whereit might influence the orbits of comets, and Nemesis,still further out and prone to sending comets inwardto impact the Earth every 20 million years or so, are morerecent examples. They have not been observed, and,according to dynamicist Peter Vandervoort of theUniversity of Chicago, the Nemesis orbit is dynamicallyvery interesting; it just happens not to be occupied.

*It is, I suspect, nothing more than bad diction that leadsto the frequent false attribution of the discovery toLilliputian astronomers, when their culture must surelyhave specialized in microscopy.

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.)

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THE GREGORY-WOLFF-BONNET LAW

Meanwhile, the small whole numbers folk were look-ing again at the known planetary orbits and trying to de-scribe their 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 Germany, by ChristianWolff and picked up in 1766 by a chap producing a Ger-man translation of a French volume on natural historyby Charles Bonnet. The translator, whose name wasJohann Titius (of Wittenberg) added the set of numbersto Bonnet’s text, improving them to 4, 7, 10, 16, 52, and100, that 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-tion reached Johann Elert Bode, who also liked the se-ries of numbers, published them yet again in an intro-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, at least, expected there to be a planet at 4 +3´8 units (2.8 AU), in the region that Newton thoughtthe creator had left empty to protect the inner solar sys-tem from disruption by the large masses of Jupiter andSaturn. Closely related seventeenth century explana-tions of the large separation from Mars to Jupiter in-cluded plundering of the 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 numbers 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 Gotha (notice the extent to which this sort ofnumerical/positional astronomy seems to have been aGerman 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 “celestial police,” each to patrol a fixed part of thesky in search of the missing planet. Hegel, of the samegeneration and culture, on the other hand, objected topotential additional planets, on the ground that Uranushad brought us back up to seven, equal to the number

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

Even as von Zach was organizing things, Italianastronomer Giuseppe Piazzi, working independently ona star catalog, found, on New Year’s Day 1801, a newmoving object that he at first took to be a comet be-fore losing it behind the sun in February. Some high pow-ered mathematics by the young Gauss (whomastronomers 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 about the sizethat 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 firstfour of many thousands of asteroids, whose total massis nevertheless still not enough to make a decent moon.I do not know whether Piazzi made his discovery inthe sky sector that von Zach had assigned to him orwhether, if not, the person who was supposed to get thatsector was resentful, though the latter seems likely.

Neptune and Pluto entered the planetary inventorywith orbits quite different and smaller than the next twoterms in the Titius-Bode sequence. Strong expectationthat they should fall at the sequence positions proba-bly retarded the searches for them (which were based onirregularities in the motion of Uranus).

In recent years, the orbits of triplets of planets aroundone pulsar and one normal star (Ups And) have also beenclaimed as following something like a Gregory-Wolff-Titius sequence. Notice however that it takes two orbitsto define the sequence, even in completely arbitraryunits.

What is the status of Bode’s Law today? The tableon the next page shows the actual orbit semi-major axesand the fitted number sequence. All agree to about five

*It is left as an exercise for the reader to formulate anappropriate snide remark about Hegel having thus physio-logically anticipated the discovery of Neptune, which hedid not in fact live to see.

52 SUMMER/FALL 2000

percent until you reach Neptune. But current theorycomes much closer to what Newton and his contem-poraries said than to orbit quantization. The process offormation of the planets and subsequent stability of theirorbits are possible only if the planets further from thesun, where the gravitational effect of the sun isprogressively weaker, are also further from each other.

BI- AND MULTI-MODALITIES

The minimum requirement for quantization is twoentities with different values of something. With threeyou get eggroll, and twentieth century astronomy hasseen a great many divisions of its sources into twodiscrete classes. Examples include galactic stars intopopulations I and II; star formation processes into thosemaking high and low mass stars; binary systems intopairs with components of nearly equal vs. very unequalmasses; stellar velocities into two streams; and super-novae into types I and II (occurring in populations IIand I respectively).

None of these has achieved the status of true crank-iness. Rather, most have eventually either smoothed outinto some kind of continuum, from which early

investigations had snatched two widely separated sub-sets (stellar populations, for instance), or n-furcated into“many,” each with honorably different underlyingphysics (including supernova types). A few, like the dis-tinction between novae and supernovae, turned out tobe wildly different sorts of things, initially perceivedas similar classes because of some major misconception(that their distances were similar, in the nova-super-nova case).

Thus to explore the extremities of weirdness inastronomical quantization, we must jump all the wayfrom the solar system to the wilder reaches of quasarsand cosmology. Here will we find fractals, universes withperiodic boundary conditions, non-cosmological (andindeed non-Doppler and non-gravitational redshifts), andgalaxies that are permitted to rotate only at certaindiscrete speeds.

FRACTAL, TOPOLOGICALLY-COMPLEX,AND PERIODIC UNIVERSES

In the cosmological context, fractal structure wouldappear as a clustering heirarchy. That is, the larger thescale on which you looked at the distribution 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,Immanuel Kant, and Johann Lambert (all eighteenth cen-tury). Since we have global solutions for the equationsof GR only for the case of homogeneity and isotropyon average, it is not entirely clear what a general rela-tivistic fractal universe ought to look like.

But it probably doesn’t matter. Observations of dis-tances and locations of galaxies currently tell us thatthere are clusters and superclusters of galaxies (oftensheet-like or filamentary) with voids between, havingsizes up to 100–200 million parsecs. This is less than 10percent of the distance to galaxies with large redshifts.No honest survey of galaxy positions and distances hasfound structure larger than this, though a couple ofgroups continue to reanalyze other people’s data and re-port fractal or heirarchical structure out 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 196 191.9

Neptune 388 301Pluto 722 395

BEAM 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 the light coming from galaxiesin the direction of the galactic plane, not structure 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 the sky, includ-ing bright radio sources, the X-ray background, gammaray bursts, and, most notoriously, the cosmic microwaveradiation background have been used by Jim Peebles ofPrinceton to show that either (a) the large scale fractaldimension d = 3 to a part in a thousand (that is, in effect,homogeneity over the distances to the X-ray and radiosources), or (b) we live very close indeed to the centerof an inhomogeneous but spherically symmetric(isotropic) universe.

Several of the early solvers of the Einstein equations,including Georges Lemaitre, Alexander Friedmann, andWillem de Sitter, considered at least briefly the idea ofa universe with topology more complex than the min-imum needed to hold it together.

Connecting little, remote bits of universe togetherwith wormholes, Einstein-Rosen bridges, or whatever isnot a good strategy, at least for the time and space scalesover which we observe the cosmic microwave back-ground. If you peered through such a connection in onedirection and not in the patch of sky next to it, the

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)]

54 SUMMER/FALL 2000

QUANTIZED VELOCITIES AND REDSHIFTS

The ideas along these lines that still bounce around theliterature all seem to date from after the discovery ofquasars, though the quantization intervals are as smallas 6 km/sec. The topic is closely coupled (a) with red-shifts whose origins are not due to the expansion ofthe Universe, strong gravitation, or relative motion, butto some new physics and (b) with 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 astronomicalcommunity 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 attracting vast numbers of buyers.

The underlying physics that might be responsible fornew kinds of wavelength shifts and/or quantized wave-length shifts have not been worked out in anything likethe mathematical detail of the Standard Model andprocesses. One suggestion is that new matter 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 the electron rest mass upstairs. Quantizedor preferred redshifts then require some additionalassumption about matter not entering the Universe ata constant rate.

The first quasar redshift, Dl/l = 0.16 for 3C 273, wasmeasured in 1963 by Maarten Schmidt and others. By1968–1969, about 70 were known, and Geoffrey and Mar-garet Burbidge remarked, first, that there seemed to bea great many objects with z = 1.95 and, second, that therewas another major peak at z = 0.061 and smaller onesat its multiples 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 two directions would have differentredshlfts, that is different temperatures. The largest tem-perature fluctuations we see are parts in 105, so thelight travel time through the wormhole must not dif-fer from the travel time without it by more than thatfraction of the age of the Universe, another conclusionexpressed clearly by Peebles.

A periodic universe, in which all the photons goaround many times, is harder to rule out. Indeed it hasbeen invoked a number of times. The first camp in-cludes people who have thought they had seen the sameobject or structure by looking at different directionsin the sky and those who have pointed out that wedo not see such duplicate structures, though we mightwell have, and, therefore, that the cell size of periodicuniverse must be larger than the distance light travelsin a Hubble time. The second camp includes peoplewho want to use periodic boundary conditions toexplain the cosmic microwave background (it’s ourown galaxy seen simultaneously around the Universein all directions), high energy cosmic rays (photonswhich have been around many times, gaining energyas they go), or the centers of quasars (bright becausethey illuminate themselves).

Descending a bit from that last peak of terminalweirdness, we note that a periodic universe, with cellsize much smaller than the distance light goes in 10–20billion years, automatically guarantees that the radioand X-ray sources will be seen quite isotropicaIly onthe sky. It also has no particle horizon, if that is thesort of thing that bothers you.

Each year, the astronomical literature includes afew cosmological ideas about which one is tempted tosay (with Pauli?) that it isn’t even wrong. A couple ofmy favorites from the 1990s are a universe with octe-hedral geometry (the advertised cause is magneticfields) and one with a metric that oscillates at a periodof 160 minutes (accounting for fluctuations in the lightof the Sun and certain variable stars).

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explanations. The first was that z = 2 was the maximumthat could be expected from a strong gravitational fieldif the object was to be stable. The second was that z = 1.95might correspond to the epoch during which aFriedmann-Lemaitre universe (one with a non-zero cos-mological constant) was coasting at almost constant size,so that we would observe lots 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 & [OIII]

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 prettyclearly 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 diluted 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 conventional explanation for the periodicity atDz = 0.061 has ever surfaced, and the situation was notimproved over the next decade when, as the data basegrew, Geoffrey R. Burbidge reported additional peaksat z = 0.30, 0.60, 0.96, and 1.41 and a colleague showedthat the whole set, including 1.95, could be fit 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, another group found several statistically sig-nificant peaks in N(z) between 1.2 and 3.2.

Any attempt to assign statistical significance to theseapparent structures in N(z) must take account of twoconfounders. First, the observed sample is not drawnuniformly from the real population. Quasars have onlya few strong emission line from which redshifts can bemeasured, and these move into, through, and out ofobservable ranges of wavelength as redshift increases.Second, you must somehow multiply by the probabilityof all the other similar 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 the analysis is done by other supporters 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 the analy-ses require a certain amount of work, and that it is ratherdifficult to persuade peopIe who are not violently 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 quantization with much finer intervals. William

Tifft of the University of Arizona had started out by try-ing to measure very accurately the colors of normal galax-ies as a function of distance from their centers (one wayof probing the ages, masses, and heavy element abun-dances of the stars that contribute most of the light).In the process, he ended up with numbers he trusted forthe total apparent brightnesses of his program galaxies.He proceeded to graph apparent brightness 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-tized in steps of about 72 km/sec (z = 0.00024). Admit-tedly, many of the velocities were uncertain by com-parable amounts, and the motion of the solar systemitself (about 30 km/sec relative to nearby stars,220 km/sec around the center of the Milky Way, andso forth) was not negligible on this scale. In theintervening quarter of a century, he has continued 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 distributions of velocities of stars withinthe galaxies. He has also devoted attention to collectingdata with uncertainties less than his quantizationinterval and to taking out the contribution 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)].

BEAM 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 submultiples 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 astronomers at the Royal ObservatoryEdinburgh looked independently at some of the samplesin 1992 and 1996. They found slightly different intervals,for example, 37.22 km/sec, but quantization none theless. A 1999 variant from another author includes peri-odicity (described as quantization) even in the rotationspeeds of normal spiral galaxies.

Tifft’s Arizona colleague W. John Cocke has providedsome parts of a theoretical framework for the 72 (etc.)km/sec quantization. It has (a) an exclusion principle,so that identical velocities for galaxies in close pairs areat least very rare if not forbidden and (b) some aspectsanalogous to bound discrete levels on the atomic scale,with continua possible only for velocity differences largerthan some particular value. The quantization is, then,responsible for the large range of velocities observed inrich clusters of galaxies which would then not requireadditional, dark matter to bind them.

Am I prepared to say that there is nothing meaning-fuI in any of these peaks and periods? No, though likethe race being to the swift and the battle to the strong,that’s how I would bet if it were compulsory. There is,however, a different kind of prediction possible. Most ofthe major players on the unconventional team(s) areat, beyond, or rapidly approaching standard retirementages. This includes Cocke and Tifft as well as theBurbidges, H. C. (Chip) Arp, a firm exponent of non-cosmological (though not necessarily quantized) red-shifts, and the three founders of Steady State Cosmol-ogy, Fred Hoyle, Thomas Gold, and Hermann Bondi.Meanwhile, very few young astronomers are rallyingto this particular set of flags. Whether this reflects goodjudgment, fear of ostracism by the mainstream astro-nomical community, or something else can be debated.But it does, I think mean that periodic, quantized, andnon-cosmological redshifts will begin to disappear fromthe astronomical literature fairly soon.

QUANTUM GRAVITY, QUANTUM COSMOLOGY,AND BEYOND

The further back you try to look into our universal past,the further you diverge from the regimes of energy, den-sity, and so forth at which existing physics has beentested. General relativity is said to be non-renormalizableand nonquantizable, so that some other description ofgravity must become necessary and appropriate at leastwhen the age of the Universe is comparable with thePlanck time of 10-43 sec, and perhaps long after. Oneprong of the search for new and better physics goesthrough attempts (via string theory and much else) tounify all four forces, arguably in a space of many morethan three dimensions.

A very different approach is that of quantum cos-mology, attempting to write down a Schrödinger-like(Klein-Gordon) equation for the entire Universe and solveit. It is probably not a coincidence that the Wheeler (JohnArchibald)-DeWitt (Bryce S.) equation, governing thewave function of the Universe, comes also from1967–1968, when the first claims 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 made the very large, the very old,and the very spooky all sound exciting.

The difference between the quanta in this short sectionand in the previous long ones is that quantum gravityand 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, Witten, 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 bright 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 CARSON is a histo-rian of science at the University ofCalifornia,Berkeley, where she di-rects the Office for History of Scienceand Technology. Her interest 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 history to science, but shefound herself unable to stop takingphysics classes and ended up witha master’s degree. She did her grad-uate work at Harvard University,where she earned a Ph.D. in historyof science. At Berkeley she teachesthe history of physics and the his-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.

CONTRIBUTORS

CHARLES H. TOWNES receivedthe 1964 Nobel Prize in physics forhis role in the invention of the maserand the laser. He is presently a pro-fessor in the Graduate School at theUniversity of California, Berkeley,and engaged in research in astro-physics.

Townes received his Ph.D. in 1939from the California Institute of Tech-nology and was a member of the BellTelephone Laboratories technicalstaff from 1939 to 1947. He has alsoheld professorships at Columbia Uni-versity and the Massachusetts Insti-tute of Technology, and served as anadvisor to the U.S. government.

His many memberships includethe National Academy of Sciences,the National Academy of Engineer-ing, and The Royal Society of London.His many awards include theNational Medal of Science, theNational Academy’s Comstock Prize,and the Niels Bohr International GoldMedal, as well as honorary degreesfrom 25 colleges and universities.

JAMES BJORKEN (Bj) is bestknown for playing a central role inthe development of the quark-partonmodel at SLAC from 1963 to 1979. Agraduate student at Stanford Uni-versity, he emigrated to SLAC withhis thesis advisor, Sidney Drell, in1961. During that period they col-laborated on a pair of textbooks,of which Relativistic QuantumMechanics is the more beloved.

In 1979 Bj left for a ten-year hiatusat Fermilab where he served as As-sociate Director of Physics. Shortlyafter returning to SLAC, he becameinvolved in an experimental initia-tive at the SSC. Since then he has re-turned to the world of theoreticalphysics.

Bj was influential in revampingthe Beam Line and served on theEditorial 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/Fermilab Astro-physics Group at the Fermi NationalAccelerator Laboratory as well as aProfessor of Astronomy and Astro-physics at The University of Chicago.He is a Fellow of the American Phys-ical Society and has served on edi-torial boards of several internationalscientific journals as well as the mag-azine Astronomy.

The field of Kolb’s research is theapplication of elementary particlephysics to the very early Universe.In addition to over 200 scientific pa-pers, he is a co-author of The EarlyUniverse, the standard textbook onparticle physics and cosmology. Hisnew book for the general public,Blind Watchers of the Sky, winnerof the 1996 Emme award from theAmerican Astronomical Society, isthe story of the people and ideas thatshaped our view of the Universe.

ROBERT L. JAFFE is Professor ofPhysics and Director of the Centerfor Theoretical Physics at the Mass-achusetts Institute of Technology.His research specialty is the physicsof elementary particles, especiallythe dynamics of quark confinementand the Standard Model. He has alsoworked on the quantum theory oftubes, the astrophysics of dense mat-ter, and many problems in scatteringtheory. He teaches quantum me-chanics, field theory, mechanics, andelectrodynamics at the advanced un-dergraduate and graduate levels.

Jaffe is a Fellow of the AmericanPhysical Society and the AmericanAssociation for the Advancement ofScience. He has been awarded theScience Council Prize for Excellencein Teaching Undergraduates, theGraduate Student Council TeachingAward, and the Physics DepartmentBuechner Teaching Prize.

JOHN CLARKE has been in thePhysics Department at the Univer-sity of California, Berkeley and at theLawrence Berkeley National Labo-ratory since 1968. He has spent mostof his career doing experiments onsuperconductors, developing super-conducting quantum interferencedevices (SQUIDS), and using them toconduct a wide variety of measure-ments. Among his current interestsare more sensitive detectors for ax-ions, detecting magnetically labeledcells, and mapping magnetic fieldsfrom the heart.

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

60 SUMMER/FALL 2000

VIRGINIA TRIMBLE’s first pub-lished paper dealt with the slopesof the so-called air shafts in Cheops’pyramid and their possible astro-nomical significance. An alternativeexplanation is that the slopes are aninevitable consequence of the height:depth ratio of the stone blocks used(a ratio of small whole numbers). Thedrawing, in the style of a Coptictomb portrait, was done in 1962 incolored chalk by the originator of theproject, the late Alexandre MikhailBadawy.

A recurring theme in cover artistDAVID MARTINEZ's work is thelink between modern scientificknowledge and ancient magicalvision. His themes are drawn fromboth modern and ancient sources,and he is equally inspired by pio-neering scientists and by MotherNature in her various guises. He be-came interested in mathematics andphysics in his teens but only devel-oped his artistic talents in middle age.

Martinez has been active formany years with La Peña, a Latinoarts organization in Austin, Texas.He developed “The Legends Project”with them to teach art and story-telling to at-risk children. He is cur-rently doing research for two paint-ings, one about Gaston Julia and theother about computers featuringJohn von Neuman, Alan Turing,John Mauchly, and Presper Eckert.

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DATES TO REMEMBER

Nov. 6–9 22nd Advanced ICFA Beam Dynamics Workshop on Ground Motion in Future Accelerators,Menlo Park, CA (robbin@slac.stanford.edu or http://www-project.slac.stanford.edu/lc/wkshp/GM2000/)

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 head2k@netcom.com)

Nov. 11–21 International School of Cosmic Ray Astrophysics. 12th Course: High Energy Phenomena inAstrophysics and Cosmology, Erice, Sicily (Ettore Majorana Centre, Via Guarnotta 26, I-91016Erice, Sicily, Italy or hq@emcsc.ccsem.infn.it and http://www.ccsem.infn.it/)

Nov. 12–15 10th Astronomical Data Analysis Software and Systems (ADASS 2000), Boston, Massachusetts(adass@cfa.harvard.edu or http://hea-www.harvard.edu/ADASS/)

Dec 2–7 International School of Quantum Physics. Third Course: Advances in Quantum Structures 2000,Erice, Sicily (Ettore Majorana Centre, Via Guarnotta 26, I-91016 Erice, Sicily or hq@emcsc.cc-sem.infn.it and http://www.ccsem.infn.it/)

Dec 3–8 11th Conference on Computational Physics 2000: New Challenges for the New Millennium(CCP 2000), Brisbane, Australia (http://www.physics.uq.edu.au/CCP2000/)

Dec 11–15 20th Texas Symposium on Relativistic Astrophysics, Austin, Texas (wheel@hej3.as.utexas.eduor http://www.texas-symposium.org/)

Dec 18–22 International Symposium on The Quantum Century: 100 Years of Max Planck’s Discovery, NewDelhi, India (Director: Centre for Philosophy and Foundations of Science, S-527 Greater Kailash-II, New Delhi, 110048, India or q100@cpfs.org and http://education.vsnl.com/cpfs/q100.html)

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

ators (JUAS 2001), Archamps, France (ESI/JUAS, Centre Universitaire de Formation et deRecherche, F-74166, Archamps, France or juas@esi.cur-archamps.fr and http://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 uspas@fnal.gov and http://www.indiana-edu/~uspas/programs/)

Feb 19–23 4th International Conference on B Physics and CP Violation (BC4), Ago Town, Mie Prefecture,Japan (A. I. Sanda, Theoretical Physics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya City,Aichi Prefecture, Japan or sanda@eken.phys.nagoya-u.ac.jp and http://www.hepl.phys.nagoya-u.ac.jp/public/bcp4)