4462827 stanford linear accelerator center beamline summer fall 2000

8/8/2019 4462827 Stanford Linear Accelerator Center Beamline Summer Fall 2000

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STAN FO RD LI N EAR ACCELERATO R CEN TER

Summer/Fall 2000, Vol. 30, N


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Editors

RENE DONALDSON, BILL KIRK

Cont ributing Editors

MICHAEL RIORDAN , GORDON FRASER

JUDY JACKSON , AKIHIRO MAKI

PEDRO WALOSCHEK

Editorial Advisory BoardPATRICIA BURCH AT, DAVID BURKE

LANCE DIXON , GEORGE SMOOT

GEORGE TRILLING , KARL VAN BIBBER

HERMAN WINICK

Illustrations

TERRY ANDERSON

Distribution

CRYSTAL TILGHM AN

A PERIODICAL OF PARTICLE PHYSICS

SUMMER/FALL 2000 VO L. 30, N UMBER 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: beam [email protected] ford.edu

FAX: (650) 926-4500

Issues of the Beam Line are accessible electroni-

cally on th e World Wide Web at ht tp://ww w.slac.

stanford.edu/pubs/beamline. SLAC is operated by

Stanford University under contract with the U.S.

Departm ent of Energy. The opinions of the au th ors

do not necessarily reflect th e policies of the

Stanford Linear Accelerator C enter.

Cover: Einstein and the Quantum Mechanics, by artist

David Martinez 1994. The original is acrylic on canvas,

16 20. Martinezs notes about the scene are reproduced

in the adjoining column, and you can read more about his

philosophy in the Contributors section on page60. His

website is http://members.aol.com/elchato/index.html and

from there you can view more of his paintings. TheBeam

Lineis extremely grateful to him and to his wife Terry for

allowing us to reproduce this imaginative and fun image.

Werner Heisenberg illustrates his Uncertainty Principle by

pointing down with his right hand to indicate the location of

an electron and pointing up with his other hand to its wave

to indicate its momentum. At any instant, the more certain we

are about the momentum of a quantum, the less sure we are

of its exact location.

Niels Bohr gestures upward with two fingers to empha-

size the dual, complementary nature of reality. A quantum is

simultaneously a wave and a particle, but any experiment

can only measure one aspect or the other. Bohr argued that

theories about the Universe must include a factor to account

for the effects of the observer on any measurement of

quanta. Bohr and Heisenberg argued that exact predictionsin quantum mechanics are limited to statistical descriptions

of group behavior. This made Einstein declare that he could

not believe that God plays dice with the Universe.

Albert Einstein holds up one finger to indicate his belief

that the Universe can be described with one unified field

equation. Einstein discovered both the relativity of time and

the mathematical relationship between energy and matter.

He devoted the rest of his life to formulating a unified field

theory. Even though we must now use probabilities to

describe quantum events, Einstein expressed the hope

that future scientists will find a hidden order behind quantum

mechanics.

Richard Feynman plays the bongo drums, with Feynman

diagrams of virtual particles rising up like music notes. Oneof his many tricks was simplifying the calculation of quantum

equations by eliminating the infinities that had prevented real

solutions. Feynman invented quantum electrodynamics, the

most practical system for solving quantum problems.

Schrdingers cat is winking and rubbing up to Bohr. The

blue woman arching over the Earth is Nut, the Sky Goddess

of Egypt. She has just thrown the dice behind Einsteins

back. Nut is g iving birth to showers of elementary particles

which cascade over the butterflies of chaos.

David Martinez

Einstein and The Quantum Mechanics


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FEATURES

2 FOREWORDTHE FUTURE OF THE QUANTUM

THEORY

James Bjorken

6 TH E ORIGIN S OF TH E QU AN TU M

THEORYTh e first25 years of t he cent ury radically

transform ed our ideas about N ature.

Cathryn Carson

20 TH E LIGHT TH AT SHINESSTRAIGHT

A N obel laureate recount s the invention

of the laser and the b irth of quantu m

electronics.

Ch arles H. Townes

29 THE QUANTUM AN D THECOSMOS

Large-scale structu re in t he U niv erse began

with t iny quantum fluctuat ions.

Rocky Kolb

34 GETTIN G TO KNO W YOURCONSTITUENTS

Hum ankind has wondered s ince the

beginning of history w hat are th e

fundam ental constituent s of m atter.

Robert L. Jaffe

41 SUPERCONDUCTIVITY:

A MACROSCOPIC QUANTUMPHENOMENON

Q uantum m echanics is crucial to

und erstanding and using superconductivity

John Clarke

DEPARTMENTS

49 TH E UN IVERSE AT LARGE

The Ratios of Sm all W hole N um bers:Misadventu res in Astronom ical Q uantizat ion

Virginia Trim ble

58 CONTRIBUTORS

61 DATES TO REMEMBER

CONTENTS


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FOREWORD

N THIS ISSUE of th e Beam Line , we cele-

brate the one hu ndredth ann iversary of th e

birth of th e quantu m th eory. The story of

how M ax Planck started it all is one of the m ost

m arvelous in all of science. It is a favorite of

m ine, so m uch so th at I have already written

about it (see Particle Ph ysicsWhere Do We Go

From H ere? in t he Winter 1992Beam Line,

Vol. 22 , No. 4). Here I will only quot e again w hat

th e late Abraham Pais said about Planck: H is

reasoning was mad, but h is madness had th at

divine quality th at only t he greatest transitional

figures can bring to science.*

A century later, th e madness has not yet com-

pletely disappeared. Science in general h as a w ay

of producing results wh ich defy hum an int uition.

But it is fair to say that th e winn er in this

category is the quant um th eory. In m y min d

quant um paradoxes such as the H eisenberg

un certain ty principle, Schrdingers cat,

collapse of th e wave packet , an d so forth are far m ore perplexing and

challenging than th ose of relativity, wh ether t hey be th e tw in paradoxes of

special relativit y or th e black h ole physics of classical general relativity. It isoften said that no one really un derstands quant um th eory, and I would be

th e last to disagree.

In t he contributions t o this issue, th e knott y questions of th e interpreta-

tion of quant um th eory are, m ercifully, not addressed. There w ill be no

m ention of th e debates between Einstein and Bohr, nor the later att em pts by

T h e Fu t u re of t h e Q u an t u m by JAM ES BJO RKEN

*Ab raham Pais, Subtle is the Lord: Science and the Life of Albert Einstein, Ox ford U . Press, 1982.

Max Planck, c irca1910

(CourtesyAIPEmilio Segr Visual Archives)

I


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Bohm , Everett , and oth ers to fin d int er-

pretat ions of the t heory different from

th e original Copenhagen interpreta-

tion of Bohr an d his associates. Inst ead,

wh at is right fully em phasized is the

overwhelming practical success of these

revolutionary ideas. Qu antu m th eory

work s. It n ever fails. And th e scope of

th e applications is enorm ous. As Leon

Lederman, Nobel Laureate and Director

Em eritus of Ferm ilab, likes to point out,

m ore than 25 percent of th e gross

national product is dependent upon

techn ology th at springs in an essent ial

way from quantu m phenomena.*

N everth eless, it is hard not t o sympa-

th ize with Einstein and feel that t here is

somet hing incomplete about th e present

statu s of quant um th eory. Perhaps th e

equations defining the t heory are not ex-

actly correct, and corrections will even-

tu ally be defin ed and th eir effects

observed. Th is is not a popular point ofview. But th ere does exist a min ority

school of th ought w hich asserts that

only for sufficiently sm all systems is th e quantu m th eory accurate, and th at

for large complex quant um systems, hard t o follow in exquisite detail, th ere

eory

Albert Einstein and Neils Bohr in the late1920s.(CourtesyAIPEmilio Segr Visual Archives)

*Leon Lederm an, The G od Particle (If th e Universe is the Answ er, What is t he Qu estion?),

Houghton M ifflin, 1993.

PaulEhrenfest


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m ay be a sm all am ount of some kin d of extra intrinsic noise term or non-

linearity in t he fundam ental equat ions, which effectively eliminat es para-

doxes such as the collapse of th e wave packet.

Dow n t hrough history most of the debates on the foun dations of quant um

th eory produced many w ords and very little action, and rem ained closer toth e philosophy of science th an t o real experim ent al science. John Bell

brought some freshness to th e subject. The fam ous th eorem th at bears his

nam e initiated an experim ental program t o test some of th e fun dament als.

N everth eless, it w ould have been an enorm ous shock, at least t o m e, if any

discrepancy in such experimen ts h ad been foun d, because th e searches

involved sim ple atom ic system s, not so different from element ary particle

systems w ithin wh ich very subtle quant um effects have for som e tim e been

clearly dem onstrated. A worth y challenge to th e quantu m th eory in m y

opinion m ust go mu ch further and deeper.

What m ight such a challenge be? At present, one clear possibility w hich is

actively pursued is in th e realm of string theory, which attem pts an exten-

sion of Einstein gravity in to t he dom ain of very short distances, wh ere quan-

tu m effects domin ate. In th e present incarnations, it is t he t heory of gravity

th at yields ground and un dergoes modifications and generalizations, wit h t he

quant um th eory left essentially intact. But it seem s to me th at th e alterna-

tive m ust also be entertainedthat t he quant um th eory itself does not sur-

vive the synt hesis. This, how ever, is easier said th an done. And th e problem

wit h each option is that t he answer needs to be found w ith precious little

assistance from experim ent. Th is is in stark contrast wit h t he development

of quant um th eory itself, which w as driven from in itiation to com pletion by

a hu ge nu m ber of experim ents, essent ially guiding the t heorists t o th e final

equations.


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Anot her approach has been recently laid out by Frank Wilczek in a very

int eresting essay in Phy sics Today .* He compares the development of th e

equations of quantu m th eory with th ose of Maxwells electrodynam ics. Both

were first laboriously put together from experimental evidence. In both cases

th e interpretations of wh at th e equations m eant cam e later. In t he case ofelectrodynamics, the u ltim ate verdict on M axwells equations is that at a

deep level th ey express statem ent s about sym m etry. (In ph ysics jargon,

Maxw ells equation s express th e fact t hat electrodynam ics is gauge invariant

and Lorent z covariant .) Wilczek n otes t hat th ere is no sim ilar deep basis for

th e equations of quant um m echanics, and he looks forward to statemen ts of

symm etry as the fut ure expression of th e true m eaning of th e quantu m

th eory. But if th ere are such sym m etries, th ey are not now kn own or at least

not yet recognized. Wilczek does cite a pion eering suggestion of Herm ann

Weyl, which m ight provide at least a clue as to w hat m ight be done. But

even if Wilczek is on th e right track, th ere is again th e problem t hat th eo-

rists will be largely on th eir own, with very little help t o be expected from

experiment.

Th ere is, how ever, a data-driven approach on t he h orizon. It is a conse-

quence of th e inform ation revolution. In principle, quant um systems m ay be

used to create m uch m ore powerful com puters th an now exist. So there is a

stron g push t o develop th e concepts and th e techn ology to create large-scale

quant um comput ers. If th is happens, the foundations of quant um m echanics

will be test ed on larger and larger, m ore complex physical system s. And if

quant um m echanics in t he large needs to be modified, these compu ters may

not work as they are supposed to. If th is happens, it will be just one m ore ex-

am ple of how a revolution in t echnology can lead to a revolution in fun da-

m ental science.

*Frank Wilczek, Physics Today, June 2000, Vol. 53, N o. 6, p. 11 .


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by CATHRYN CARSON

H AT IS A Q UAN T U M T HEO RY? We have

been asking th at qu estion for a long tim e, ever

since Max Planck int roduced th e elem ent of dis-

continuity w e call the quant um a cent ury ago. Since then,

th e chu nk iness of N atu re (or at least of our th eories about

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

has prompt ed a fun dam ent al reth ink ing of physical th eory.

At t he sam e tim e it has helped m ake sense of a wh ole range of pe-

culiar behaviors manifested principally at microscopic levels.

From its beginn ing, th e new regime w as symbolized by Planck s constan t

h , introdu ced in his fam ous paper of1900. Measurin g the w orlds departu re

from sm ooth, continu ous behavior, h proved to be a very sm all num ber, but

different from zero. Wherever it appeared, stran ge phenom ena cam e wit h it .

What it really meant was of course mysterious. While the quant um era was

inaugurated in 1900, a quant um th eory would take m uch longer to jell. Int ro-

ducing discont inuit y was a tent ative step, and only a first on e. And eventh ereafter, th e recastin g of physical th eory was hesitan t an d slow. Physicists

pondered for years what a quant um th eory might be. Wondering how t o inte-

grate it w ith th e powerful apparatu s of nineteenth -centu ry physics, they also

asked what relation it bore to existing, classical theories. For some the

answers crystallized with quant um m echanics, th e result of a quarter-

centurys labor. Others held out for further rethinking. If the outcome was

not to t he satisfaction of all, still th e quant um th eory proved remarkably

T H E O RIG IN S

O F T H E Q UAN T U M T H EO RY

W


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successful, and the puzzlement along the way, despite its frustrations, can

only be called extraordinarily product ive.

INTRODUCING h

Th e story began inconspicuously enough on D ecember 14 , 1900. Max Planck

was giving a talk t o th e Germ an Physical Society on t he contin uous spec-

tru m of th e frequencies of light emit ted by an ideal heated body. Some tw o

months earlier this 42-year-old theorist h ad present ed a form ula captu ring

some new experim ental results. N ow, with leisure to thin k and m ore tim e at

his disposal, he sought to provide a physical just ificat ion for his form ula.Planck pictured a piece of matter, idealizing it somewhat, as equivalent to a

collection of oscillating electric charges. He t hen im agined distribut ing its

energy in discrete chu nk s proportion al to th e frequencies of oscillation. Th e

constant of proportionality he chose to call h ; we wou ld now write e = hf.

Th e frequencies of oscillation determin ed th e frequencies of th e em itt ed

light . A twist ed chain of reasoning then reproduced Planck s postulat ed

form ula, which now involved th e sam e natural constant h .

Two theorists,

Niels Bohr and

Max Planck, at the

blackboard.

(Courtesy Emilio

Segre Visual

Archives,

Margrethe Bohr

Collection)


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Looking back on t he event , we m ight expect revolu t ion ary

fanfare. But as so often in h is tory, m at t ers were m ore ambigu-

ous. Planck did not call his energy elemen ts quant a and was not

inclined to stress their discreteness, which m ade litt le sense in any

fam iliar term s. So th e m eaning of his procedure only gradually be

came apparent. Although th e problem h e was treating was pivotal

in i ts day, its im plications were at first th ought t o be confined.

BLACKBODIES

The behavior of l ight in i ts interaction w ith m atter w as indeed a

key problem of nineteenth -centu ry physics. Planck was interest-

ed in th e two t heories that overlapped in t his domain. Th e first was

electrodynam ics, th e th eory of electricity, m agnet ism, and light

waves, brought t o final form by Jam es Clerk Maxw ell in the 1870s

Th e second, dat ing from roughly the same period, was th erm o

dynam ics and statist ical m echanics, governing transform ations of

energy and its behavior in t ime. A pressing question was w heth er

th ese two grand t heories could be fused into one, since th ey started

from different fundam ental n otions.

Beginn ing in th e m id-1890s, Planck t ook up a seemin gly narrow

problem, th e interact ion of an osci l lat ing charge with i ts elec

trom agnet ic field. Th ese studies, however, brought him into con-

tact w ith a long tradition of work on t he em ission of light. D ecades

earlier i t had been recognized th at perfectly absorbing (black

bodies provided a s tan dard for em ission as w el l . Then over the

years a smal l indus t ry had grown u p around th e s tudy of such

objects (and t heir real-world subst itu tes, like soot). A sm all group

of theor i s t s occupied them selves wi th t he th erm odynamics o

radiation, while a host of experiment ers labored over heated bod-

i e s t o f i x t em perat u re , de t e rm i ne i n t ens i t y, and ch a rac t e ri ze

deviation s from black body ideality (see th e graph above). After sci-

ent ists push ed the pract ical realization of an old ideath at a closed

tube with a small hole consti tuted a near-ideal blackbodythis

cavit y radiation allowed ever more reliable m easurem ent s. (See

il lustration at left .)

An ideal blackbody spectrum

(Schwarzer Krper) and its real-worldapproximation (quartz). (From Clemens

Schaefer, Einfhrung in die Theoretische

Physik, 1932).

Experimental setup for measuring black-

body radiation. (The blackbody is the

tube labeledC.) This design was a prod-

uct of Germanys Imperial Institute of

Physics and Technology in Berlin, where

studies of blackbodies were pursued

with an eye toward industrial standards

of luminous intensity. (FromMller-

Pouillets Lehrbuch der Physik, 1929).


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BEA M LIN E

N ow Planck s oscillating charges emit ted an d absorbed radiation,

so they could be u sed to m odel a blackbody. Thu s everything seem ed

to fall into place in 1899 when h e reproduced a form ula th at a col-

league had derived by less secure means. Th at was convenien t; every-

one agreed th at Willy Wiens form ula m atched t he observations. The

trouble was that im m ediately afterwards, experim ent ers began fin d-

ing deviations. At low frequencies, Wiens expression became

increasingly unt enable, while elsewhere it continu ed to work w ell

enough. Informed of the results in th e fall of1900, on short n otice

Planck cam e up with a reasonable interpolation. With its adjust ableconstan ts his formu la seemed to fit the experimen ts (see graph at

right ). N ow th e question becam e: Where might it come from ? What

was its physical meaning?

As we saw, Planck m anaged to produce a derivation. To get t he

right statist ical results, how ever, he had t o act as though t he energy

involved were divided up int o element s e = hf. The derivation was

a success and splendidly reproduced th e experim ental data. Its m ean-

ing was less clear. After all, Ma xwells th eory already gave a beau-

tiful account of light and treat ed it as a wave traveling in a con-

tinuous m edium . Planck did not take the constant h to indicate a

physical discontin uit y, a real atom icity of energy in a su bstant ive

sense. Non e of his colleagues m ade mu ch of this possibility, either,

until Albert Einstein took it up five years later.

MAKIN G LIGH T Q UAN TA REAL

Of Einst eins th ree great papers of1905, the one O n a H euristic Point

of View C oncern ing the Product ion and Transformat ion of Light

was the piece that t he 26-year-old patent clerk labeled revolution ary.

It was peculiar, he n oted, that th e electrom agnet ic theory of light

assumed a continuu m , while current account s of m atter started from

discrete atom s. Could discont inu ity be productive for light as well?

How ever indispensable Maxw ells equations m ight seem , for some

interes t ing phenom ena th ey proved inadequate. A key exam ple

was blackbody radiation, wh ich Einstein now looked at in a w ay dif-

ferent from Planck. Here a rigorously classical treatm ent, h e showed,

Experimental and theoretical results on

the blackbody spectrum. The data

points are experimental values; Plancks

formula is the solid line. (Reprinted from

H. Rubens and F. Kurlbaum, Annalen

der Physik, 1901.)


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yielded a result not only w rong but also absurd. Even w here Wiens

law w as approxim ately right (and Planck s m odification u nnecessary)

element ary therm odynamics forced light to behave as though it w ere

localized in discrete ch un ks. Radiation had t o be parcelled into w hat

Einstein called energy quanta. Today we wou ld write E= hf.

Discontinu ity was thu s endemic to th e electrom agnetic world

Interestingly, Einstein did not refer to Plancks constan t h , believing

his approach to be different in spirit. Where Planck h ad looked at

oscillatin g charges, Einstein applied th erm odynam ics to th e light

itself. It w as only later th at Einstein wen t back and show ed how

Plancks work im plied real quanta. In th e m eantim e, he offered a fur-

th er, radical extension. If light behaves on its ow n as t hough com -

posed of such qu anta, th en perhaps it is also emitt ed and absorbed in

th at fashion. A few easy considerations th en yielded a law for th e

photoelectric effect, in w hich l ight ejects electrons from th e sur-

face of a m etal. Einst ein provided not on ly a testable hypothesis but

also a new way of m easuring the constant h (see table on t he n ext

page).

Today the photoelectric effect can be checked in a college labo-

rator y. In 1905, however, it w as far from t rivial. So it w ould rem ain

Pieter Zeeman, Albert Einstein, and Paul

Ehrenfest (left to right) in Zeemans

Amsterdam laboratory. (Courtesy Emilio

Segre Visual Archives, W. F. Meggers

Collection)


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BEA M LIN E 1

for m ore than a decade. Even after Robert Mil l ikan confirm ed

Einsteins prediction, he and others balked at the underlying quan-

tum hypoth esis. It still violated everything known about light s wave-

like behavior (notably, interference) and hardly seemed reconcil-

able with Maxwells equations. When Einstein w as awarded the N obel

Prize, he owed t he h onor largely to th e photoelectric effect. But th e

citation specifically noted his discovery of the law, not th e expla-

nation t hat he proposed.

The relation of the quantu m to th e wave theory of light would re-

m ain a point of puzzlemen t. Over th e next years Einstein w ould onlysharpen t he contradiction. As he showed, therm odynam ics ineluctably

required both classical waves and quan tization . The tw o aspects were

coupled: both w ere necessary, and at th e same t im e. In t he process,

Einstein m oved even closer to attribut ing to light a wh ole panoply

of particulate properties. The particle-like quant um , later named t he

photon , would prove suggestive for explaining things like th e scat-

terin g ofX rays. For th at 1923 discovery, Arth ur Com pton wou ld win

th e N obel Prize. But th ere we get ahead of th e story. Before not ions

of wave-particle duality could be tak en seriously, discontin uit y

had to demonstrate its worth elsewhere.

BEYON D LIGHT

As it tu rned out, the earliest welcome given to t he new quan tum

concepts cam e in fields far removed from th e troubled th eories of

radiation. The fi rst of these domains, though h ardly th e m ost obvi-

ous, was th e th eory of specific h eats. The specific heat of a substance

determines how m uch of its energy changes when its tem perature is

raised. At low t em peratu res, solids display peculiar behavior. Here

Einstein su spectedagain we m eet Einsteinthat the deviance m ight

be explicable on quan tu m groun ds. So he reformu lated Planck s prob-

lem t o handle a latt ice of independen tly vibrating atom s. From t his

highly simplistic m odel, he obtain ed quite reasonable predictions

that involved the sam e quantity hf, now translated int o the solid-

state context.

Th ere thin gs stood for anoth er three years. It took th e sudden

attent ion of th e physical chem ist Walther N ernst to bring quant um

(From W. W. Coblentz, Radiation,

Determination of the Constants and

Verification of the Laws in A Dictionary

of Applied Physics, Vol. 4, Ed. Sir

Richard Glazebrook, 1923)


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th eories of specific heat s to general significance. Feeling his way

towards a new law of thermodynamics, Nernst not only bolstered

Einstein s ideas with experim ent al result s, but also put t hem on

th e agenda for widespread discussion. It w as no accident, an d to a

large degree Nernsts doing, that the first Solvay Congress in 1911

dealt precisely with radiation th eory and quan ta (see photograph

below). Einst ein spok e on specific heat s, offering additional com -

m ents on electromagnetic radiation. If the quantu m was born in 1900

th e Solvay meetin g was, so to speak, its social debut.

What on ly just began to show up in t he Solvay colloquy was th eother m ain realm in wh ich discontinuity w ould prove its value. The

tech nique of quantizin g oscillations applied, of course, to line spec

tra as well. In cont rast to t he u niversality of blackbody radiation, th e

discrete lines of light em ission an d absorption varied imm ensely from

one substance to th e next. But th e regularities evident even in th e

welter of th e lines provided fertile m att er for quantu m con jectu res

Molecular spectra turn ed into an all-im portant site of research during

The first Solvay

Congress in1911

assembled the

pioneers of

quantum theory.

Seated (left to

right): W. Nernst,

M. Brillouin,

E. Solvay,

H. A. Lorentz,

E. Warburg,

J. Perrin, W. Wien,

M. Curie,

H. Poincar.

Standing (left to

right):

R. Goldschmidt,

M. Planck,

H. Rubens,

A. Sommerfeld,

F. Lindemann,

M. de Broglie,

M. Knudsen,F. Hasenhrl,

G. Hostelet,

E. Herzen, J. Jeans,

E. Rutherford,

H. Kamerlingh

Onnes, A. Einstein,

P. Langevin. (From

Cinquantenaire du

Premier Conseil de

Physique Solvay,

19111961).


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BEA M LIN E 1

th e quant um s second decade. Slower to t ake off, but ultim ately even

m ore productive, was the quant ization of motions with in th e atom

itself. Since no one had much sense of the atoms constitution, the

vent ure int o atom ic spectra was allied to speculative m odel-building.

Un surprisingly, most of th e guesses of th e early 1910s turned out

to be wrong. They nonetheless sounded out the possibilities. The

orbital energy of electrons, their angular mom entu m (somet hing like

rotation al inertia), or the frequency of their sm all oscillations about

equilibrium : all these w ere fair gam e for quant ization. Th e observed

lines of the discrete spectrum could th en be directly read off from th eelectrons motions.

TH E BOH R MO DEL OF TH E ATOM

It m ight seem ironic th at N iels Bohr initially had no interest in spec-

tra. He cam e to atom ic structu re indirectly. Writing his doctoral thesis

on t he electron t heory of m etals, Bohr had becom e fascinated by

its failures and instabilities. He thought they suggested a new type

of stabilizing force, one fundamentally different from those famil-

iar in class ical physics . Suspect ing the quan tu m was som ehow

implicated, he could not figure out how t o work it into t he th eory.

Th e intui t ion remained with him , however, as he t ransferred

his postdoctoral attent ion from m etals to Ruth erfords atom . When

it got started, th e nuclear atom (its dense positive center circled by

electron s) was sim ply one of several m odels on offer. Bohr began

workin g on it during downt im e in Rut herfords lab, th inkin g he could

improve on its treatm ent of scattering. When he not iced that it ought

to be un stable, however, his atten tion w as captured for good. To

stabilize th e m odel by fiat, he set about im posing a quant um con-

dition, according to th e standard practice of th e day. On ly after a col-

league directed his attention to spectra did he begin to think about

their significance.

Th e fam ous Balm er series of hydrogen was m anifestly news t o

Bohr. (See illustrat ion above.) He soon realized, however, th at h e

could fit it t o his m odelif he ch anged his model a bit. He recon-

ceptualized light em ission as a transition betw een discontinu ous or-

bits, with t he em itted frequency determ ined by DE= hf. To get t he

The line spectrum of hydrogen. (From

G. Herzberg, Annalen der Physik, 1927)


16/63


orbits energies right , Bohr had to int roduce som e rath er ad hoc rules

These he eventu ally justified by quant ization of angular m omen tu m

wh ich now cam e in unit s of Plancks constant h . (He also u sed an in -

teresting asymptotic argument that will resurface later.)

Published in 1913, the resulting picture of the atom was rather odd

N ot only did a quant um condi t ion describe t ransi t ions between

levels, but th e stat ionary states, t oo, were fixed by nonclassica

fiat . Electron s certainly revolved in orbits, but t heir frequency of rev

olution h ad noth ing to do with th e emit ted light . Indeed, their os-

cillations were postulated not to produce radiation. There was nopredicting when t hey m ight jum p between levels. And transitions

generated frequencies according to a quant um relation, but Bohr

proved hesitant t o accept an ything like a photon.

Th e m odel, un derstandably, was not t erribly persuasiveth at

is, un til new experim ent al results began coming in on X rays, energy

levels, and spectra. What really convinced th e skeptics was a sm all

m odification Bohr m ade. Because th e nu cleus is not held fixed in

space, its m ass enters in a small way in to t he spectral frequencies

Th e calculations produced a prediction th at fit to 3 parts in 100,000

pretty good, even for those days when so many numerical coinci-

dences proved to be m isleading.

The w heel made its final tu rn w hen Einstein connected th e Bohr

atom back t o blackbody radiation. His fam ous papers on radiative

transit ions, so importan t for th e laser (see following article by Charles

Townes), showed the link among Plancks blackbody law, discrete

energy levels, and quantized emission and absorption of radiation

Einstein furth er stressed th at t ransitions could not be predicted in

anyth ing more than a probabilistic sense. It was in these sam e papers

by the way, that h e form alized the not ion of particle-like quant a.

THE OLD Q UAN TUM THEORY

What Bohrs m odel provided, like Einst eins accoun t of specific heat s

was a way to em bed the quant um in a m ore general theory. In fact

the study of atomic structu re would engender someth ing plausibly

called a quan tu m th eory, one th at began reaching towards a full-scale

replacemen t for classical physics. Th e relation between t he old and

What Was Bohr

Up To?

BOHRS PATH to his atomicmodel was highly indirect. The

rules of the game, as played in

19111912, 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 discretespectrum. 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.


17/63

BEA M LIN E 15

th e new becam e a key issue. For some featu res of Bohrs m odel

preserved classical theories, while others presupposed their break-

down. Was th is consistent or not? And why did it work?

By th e late 1910s physicist s had refined Bohrs m odel, providing

a relativistic treatm ent of the electrons and int roducing additional

quantu m num bers. T he simple quantization condition on angular

m omen tum could be broadly generalized. Then the t echniques of

nineteent h-centu ry celestial m echanics provided powerful theoret-

ical tools. Push ed forward by ingenious experim ent ers, spectroscopic

studies provided ever more and finer data, not sim ply on th e basic

line spectra, but on t heir m odulation by electric and m agnet ic fields.

And abett ed by th eir elders, Bohr, Arnold Somm erfeld, and Max Born,

a generation of youth ful atom ic theorists cut th eir teeth on such prob-

lem s. The pupils, inclu ding Hendrik Kram ers, Wolfgang Pauli, Werner

Heisenberg, and Pascual Jordan, practiced a tight rope kind of th eo-

rizing. Facing resistant experim ental data, they balanced the em pirical

evidence from th e spectra against t he am biguit ies of th e prescrip-

tions for applying the quantu m rules.

Within t his increasingly dense body of work , an interestin g strat-

egy began t o jell. In treatin g any physical system , the fi rst task was

to ident ify the possible classical m otions. Th en atop th ese classi-

cal motions, quantum conditions would be imposed. Qu antization

becam e a regular procedure, m akin g cont inu al if puzzling refer-

ence back t o classical results. In anot her w ay, too, classical physics

served as a touchstone. Bohrs famous correspondence principle

Above: Bohrs lecture notes on atomic physics, 1921. (Original

source: Niels Bohr Institute, Copenhagen. From Owen

Gingerich, Ed., Album of Science: The Physical Sciences in

the Twentieth Century, 1989.)

Left: Wilhelm Oseen, Niels Bohr, James Franck, Oskar Klein

(left to right), and Max Born, seated, at the Bohr Festival in

Gttingen, 1922. (Courtesy Emilio Segre Visual Archives,Archive for the History of Quantum Physics)


18/63

16 SU MM ER/FA LL 2000

first found application in his early papers, where it pro

vided a deeper justifi cation of his quant ization con-

dition. In th e classical lim it, for large orbits with

high quan tum num bers and sm all differences in en-

ergy, th e radiation from tran sitions betw een adja-

cent orbits should correspond t o the classical radiation

frequency. Quant um and classical results m ust m atch

up. Em ployed wit h a certain Bohrian discrimin ation

the correspondence principle yielded detailed infor-

m ation about spectra. It also helped answer th e question: How do we build up a true quant um theory?

N ot tha t the so lu t ion was yet in s igh t . Th e

old quan tu m t heorys growing sophisticat ion m ade

its failures ever plainer. By the early 1920s the the-

orists found th em selves increasingly in difficul-

t ies. No single problem w as fatal , but t heir accu-

m ulat ion was daun tin g. This feeling of crisis was

not ent irely un specific. A group of atom ic theorists

cent ered on Bohr, Born, Pau li, and H eisenberg, had

come to suspect th at th e problem s went back t o elec-

tron trajectories. Perhaps it w as possible to abstract

from th e orbits? Instead they focused on transition

probabilities and emit ted radiation, since those might be m ore reli

ably know able. At th e m oment , Pauli still rem arked in t he spring

of1925, ph ysics is again very m uddled; in any case, i t is far too

difficu lt for me, and I wish I were a movie com edian or somet hing of

th e sort and h ad never heard of physics.

QUANTU M MECHANICS

Discont inu ity, abstraction from t he visualizable, a positivistic tu rn

tow ards observable quant ities: th ese preferences indicated one pat h

to a full quantum theory. So, however, did their opposites. When

in 19251926 a true quantum mechanics was finally achieved, two

seem ingly distinct altern atives were on offer. Both took as a leitm otif

the relation to classical physics, but they offered different ways of

working out the th eme.

Paul Dirac and Werner Heisenberg

in Cambridge, circa1930. (Courtesy

Emilio Segre Visual Archives, Physics

TodayCollection)


19/63

BEA M LIN E 17

Heisen bergs fam ous paper of1925, celebrated for launch ing the

transformations to come, bore the title On the Q uantu m -Theoretical

Reinterpretation of Kinem atical and Mechanical Relations. Th e

point of departure w as Bohrs tradition of atom ic struct ure: discrete

states remained fundament al, but now dissociated from intuit ive rep-

resentation. The transformative intent was even broader from the

start. Heisenberg translated classical not ions into quantu m ones in

the best correspondence-principle s tyle. In his new quantum

m echanics, fam iliar quan tit ies behaved strangely; m ultiplication

depended on the order of the terms. The deviations, however, werecalibrated by Planck s constan t, th us gauging the depart ure from clas-

sical normality.

Som e greeted the new th eory with elation; others found it u n-

satisfactory an d disagreeable. For as elegant as Heisen bergs tran s-

lation m ight be, it took a very partial view of th e problem s of th e

quant um . Instead of th e quant um t heory of atom ic struct ure, one

m ight also start from t he wave-particle duality. Here another youn g

th eorist, Louis de Broglie, had advan ced a speculat ive proposal in 1923

th at H eisenberg and his colleagues had m ade little of. Think ing over

th e discont inu ous, part icle-like aspects of light , de Broglie suggest-

ed looking for contin uou s, wave-like aspects of electrons. His notion ,

wh ile as yet un groun ded in experim ent al evidence, did provide sur-

prising insight in to t he qu ant um conditions for Bohrs orbits. It also,

by a sideways rout e, gave Erwin Schrdin ger th e idea for his brilliant

papers of1926.

Imagining th e discrete al lowed s tat es of any system of part i -

c les as s imply the s tab le fo rms of con t inuous mat ter waves ,

Schrdinger sought con nect ions to a well-developed branch of clas-

sical physics. Th e techniqu es of contin uu m m echanics allowed him

to formu late an equat ion for his waves. I t too was bui l t around

the constant h . But now th e basic concepts w ere different , and so

also the fundam ent al mean ing. Schrdinger had a distaste for the

discontin uity of Bohrs atom ic m odels and t he lack of int uitive pic-

tu rability of Heisenbergs quant um m echanics. To his m ind, the

quantum did not imply any of these things. Indeed, it showed the

oppos i te : tha t the apparen t a tomici ty o f mat ter d i sgu ised an

underlying continuu m .

The Quantum in

Quantum Mechan ics

ICONICALLY we now writeHeisenbergs 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 - qp

is equal to zero. In quantum

mechanics, this difference,

called the commutator, is now

measured by h. (The same

thing happens with Heisen-

bergs uncertainty principle of

1927: DpDq 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.


20/63


Thu s a familiar model connected to physical intu ition, but con-

stitu tin g m att er of som e ill-un derstood sort of wave, confront ed an

abstract m athem atics with seemingly bizarre variables, insistent

about discontinu ity and suspending space-tim e pictu res. Un sur-

prisingly, the coexistence of alternative theories generated debate

The fact, soon demonstrated, of their m athem atical equivalence did

not resolve th e int erpretative dispute. For fundam entally different

physical pictures w ere on offer.

In fact, in place of Schrdingers m att er w aves and Heisen bergs

un comprom ising discreteness, a convent ional understanding settled

in th at som ewhat spl it t he difference. However, the thin king of

th e old quant um th eory school still domin ated. Born dem aterialized

Schrdingers waves, tu rnin g them into pure densit ies of probability

for fin ding discrete particles. Heisenberg added his un certaint y prin-

ciple, lim iting the very possibility of m easurement and un dermin-

ing th e law of causality. The picture was capped by Bohrs not ion

Old faces and new at the1927Solvay

Congress. The middle of the second row

lines up Hendrik Kramers, Paul Dirac,

Arthur Compton, and Louis de Broglie.

Behind Compton stands Erwin

Schrdinger, with Wolfgang Pauli and

Werner Heisenberg next to each other

behind Max Born. (From Cinquantenaire

du Premier Conseil de Physique Solvay,

19111961)


21/63

BEA M LIN E 19

of complem entarity, which sought t o reconcile contradictory concepts

like waves and particles.

Labeled the Copenhagen Interpretation after Bohrs decisive in-

fluence, its success (to his mind) led the Danish theorist to charac-

terize quant um m echanics as a rational generalization of classical

physics. N ot everyone agreed that t his was th e end point. Indeed,

Einst ein, Schrdinger, and ot hers w ere never recon ciled. Even Bohr,

Heisenberg, and Pauli expected further changesth ough in a new

domain , the quantum theory of f i e lds , which took quantum

m echan ics to a higher degree of com plexity. But t heir expectat ionsof fundam ental t ransformat ion in th e 1930s and beyond, charac-

terized by analogies to t he old quan tum th eory, found li t t le reso-

nance outside of their circle.

Ironically enough, just as for their anti-Copenhagen colleagues,

their deman d for furt her rethink ing did not m ake m uch h eadway. If

the physical meaning of the quantu m remained, to some, rather

obscure, its practical ut ility could not be denied. Whatever lessons

one took from quantum m echanics, it seemed to w ork. It n ot only

incorporated graceful ly the previous quan tu m ph enom ena, but

opened the door to all sorts of new applications. Perhaps this kin d

of success was all one could ask for? In that sense, then, a quarter-

centu ry after Planck, the quantu m h ad been built into the founda-

tion s of physical th eory.

SUGGESTIONS

FOR FURTHER READING

Olivier Darrigol, From c-

Numbers to q-Numbers:

The Classical Analogy in

the History of Quantum

Theory (Berkeley: U.C.

Press, 1992).

Helge Kragh, Quantum Gen-

erations: A History of

Physics in the Twentieth

Century (Princeton, Prince-ton University Press, 1999).

Abraham Pais, Subtle is the

Lord ...: The Science and

the Life of Albert Einstein

(Oxford, Oxford University

Press, 1982).

Helmut Rechenberg, Quanta

and Quantum Mechanics,

in Laurie M. Brown,

Abraham Pais, and SirBrian Pippard, Eds.,

Twentieth Century

Physics, Vol. 1 (Bristol and

New York, Institute of

Physics Publishing and

American Institute of

Physics Press, 1995),

pp. 143-248.

The August 11, 2000, issue of

Science (Vol. 289) contains

an article by Daniel Klep-

pner and Roman Jackiw on

One Hundred Years of

Quantum Physics. To see

the full text of this article, go

to http://www.sciencemag.org/

cgi/content/full/289/5481/893.


22/63


by CHARLES H . TOWNES

ON JULY 21, 1969, astronaut s N eil Arm strong andEdwin Buzz Aldrin set u p an array of sm all reflectors on

th e moon, facing th em t oward Earth. At th e sam e tim e, tw o

team s of astrophysicists, one at th e Un iversity of Californias

Lick O bservatory and th e oth er at t he U niversity of Texass

McDon ald Observatory, were preparing sm all instrum ents

on t wo big telescopes. Ten days later, the Lick team point ed

its t elescope at t he precise location of th e reflectors on th e

m oon and sent a sm all pulse of power into th e hardware they

had added to it . A few days after t hat, t he M cDonald team

went th rough t he sam e steps. In t he h eart of each telescope,

a narrow beam of extraordinarily pure red light em ergedfrom a synth etic ru by crystal, pierced th e sky, and ent ered

th e near vacuu m of space. The tw o rays were still only a

th ousand yards wide after t raveling 240,000 m iles to illumi-

nate t he m oon-based reflectors. Slight ly m ore than a second

after each light beam h it it s target, th e crews in C alifornia

and Texas detected its faint reflection. The brief tim e int er-

val betw een launch and detection of these light pulses per-

m itted calculation of th e distance to the m oon to with in an

incha m easurem ent of unprecedented precision.

Th e ruby crystal for each light source was th e heart of a

laser (an acronym for light am plification by stim ulated em is-

sion of radiation), wh ich is a device first dem onst rated in

1960, just nin e years earlier. A laser beam reflected from t he

m oon to m easure its distance is only one dramatic illustra-

tion of th e spectacu lar quality of laser light. Th ere are m any

other m ore mu ndane, practical uses such as in surveying

land an d grading roads, as well as m yriad everyday uses

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

Adapted by Michael Riordan from How

The Laser Happened: A dven tures of a

Scientist, by Charles H. Townes.

Reprinted by perm ission of Oxford

University Press.

A Nob el laureate recounts

the invention of the laser

and t he birth of quantum

electronics.


23/63

BEA M LIN E 2

ranging from com pact disc play-

ers to grocery-store ch eckou t

devices.

Th e sm allest lasers are so tiny

one cannot see them without a

m icroscope. Thousands can be

built on sem iconductor chips.

Th e biggest lasers consu m e as

m uch electricity as a small

town. About 45 m iles from m y office in Berkeley is the

Lawrence Livermore National Laboratory, which has some

of th e worlds m ost powerful lasers. One set of th em , collec-tively called NOVA, produces ten individual laser beams that

converge to a spot t he size of a pinhead an d generate t em per-

atu res of m any m illions of degrees. Such int ensely concen-

trated energies are essential for experiments that can show

physicists h ow to create conditions for nuclear fusion. Th e

Livermore team hopes thereby to fi nd a w ay to generate elec-

tricity efficient ly, wit h little pollution or radioactive wastes.

For several years after the lasers invention, colleagues

liked to t ease me about it, saying, T hat s a great idea, but

its a solut ion lookin g for a problem. Th e tru th is, none of

us wh o worked on the first lasers ever imagined how m any

uses there m ight eventually be. But th at was not ou r m otiva-

tion . In fact, m any of todays practical t echn ologies have re-

sult ed from basic scient ific research done years to decades

before. The people involved, m otivat ed m ainly by curiosity,

often have little idea as to w here th eir research w ill eventu -

ally lead.

ES S T R A I G H T

Lasers are commonly used in eye

surgery to correct defective vision.

Will&DeniMcIntyre,

P4219FPhotoResearchers


24/63


LIKE THE TRANSISTOR ,th e laser and its progenitor th e

m aser (an acronym for m icro-

wave amplif icat ion by s t imu lated

em ission of radiation) result ed from

the appl ica t ion of quantum me-

chanics to electronics after World

War II. Together w ith other advances,

they h elped spawn a n ew discipline

in applied physics known since the

late 1950s as quant um electronics.

Since early in th e twen tieth cen-tu ry, physicists such as N iels Bohr,

Louis de Broglie, and Albert Einst ein

learned how molecules and atom s

absorb and em it lightor any oth er

electromagnetic radiationon the

basis of th e new ly discovered laws of

quantum mechanics. When atoms or

molecules absorb light, one might

say that parts of them wiggle back

and forth or twirl wit h n ew, added

energy. Qu antum m echanics requires

th at th ey store energy in very spe-

cific w ays, with precise, discrete lev-

els of energy. An atom or a molecu le

can exist in either its ground (lowest)

energy stat e or any of a set of higher

(quan tized) levels, but n ot at energies

between th ose levels. Therefore they

only absorb l ight of cer tain wave-

lengths, and no others, because the

wavelength of light determines the

energy of its in dividual phot ons (see

box on right ). As atom s or molecules

drop from higher back to lower en-

ergy levels, they em it phot ons of thesame energies or wavelengths as

those t hey can absorb. This process

is usually spontaneous, and th is kind

of l ight is norm ally em it ted wh en

th ese atom s or molecules glow, as in

a fluorescent light bulb or neon lamp,

radiating in nearly all directions.

Einstein was th e first to recognize

clearly, from basic thermodynamic

principles , that i f photon s can be

absorbed by atoms an d boost them

to higher energy states, th en light can

also prod an atom to give up i ts

energy and drop down to a lower

level. One phot on hits th e atom, and

two com e out. When this happens

the emit ted photon takes off in

precisely th e same direction as t he

light t hat stim ulated th e energy loss

with the t wo waves exactly in step

(or in the sam e phase). This stimulated emission results in coherent

am plification, or am plification of a

wave at exactly the sam e frequency

and phase.

Both absorption and stimulated

emission can occur sim ultan eously

As a light wave com es along, it can

thu s excite some atom s that are in

lower energy states in to h igher states

and, at t he same t ime, induce some

of th ose in higher stat es to fall back

down to lower s tat es . If there are

more atoms in the u pper states than

in the lower s tates , more l ight is

emit ted than absorbed. In short, th e

l ight gets s t ronger . I t comes out

brighter than it went in.

Th e reason wh y light is usu ally

absorbed in m ater ials is that sub-

stances almost always have more

atom s and m olecules sitting in lower

energy s tates th an in h igher ones

more photons are absorbed than

emit ted. Thu s we do not expect to

shin e a light th rough a piece of glassand see it com e out th e other s ide

brighter than it w ent in . Yet th is is

precisely what happens w ith lasers

The t rick in m aking a laser is to

produce a mater ia l in which the

energies of the atom s or m olecules

present have been put in a very

abnormal condi t ion, wi th m ore o

them in exci ted sta tes than in th e

An early small laser made of semicon-ducting material (right) compared with a

U.S. dime.


25/63

BEA M LIN E 2

BECAUSE OF QUANTUMmechanics, atoms and molecules

can exist only in discrete states with

very specific values of their total energy.

They change from one state to another by

absorbing or emitting photons whose ener-

gies correspond to the difference between

two such energy levels. This process, which

generally occurs by an electron jumping

between two adjacent quantum states, is

illustrated in the accompanying drawings.

How Lasers Work

(a)

(b)

(c)

(d)

(e)

Stimulated emission of photons, the basis

of laser operation, differs from the usual ab-

sorption and spontaneous emission. When

an atom or molecule in the ground state

absorbs a photon, it is raised to a higher

energy state (top). This excited state may

then radiate spontaneously, emitting a pho-

ton of the same energy and reverting back

to the ground state (middle). But an excited

atom or molecule can also be stimulated to

emit a photon when struck by an approach-

ing photon (bottom). In this case, there is

now a second photon in addition to the

stimulating photon; it has precisely the

same wavelength and travels exactly in

phase 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 excited

state. (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 of

the 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 partially

reflecting, the beam eventually passes out this end when its intensity becomes great

enough. This beam can be very powerful.


26/63


to f ind a way to generate waves

shorter than those produced by the

klystrons and m agnetron s developed

for radar in World War II. One day

suddenly had an ideause m olecules

and the s t im ulated emission from

them. With graduate s tudent J im

Gordon an d postdoc Herb Z eiger,

decided to experimen t fi rst with am

monia (N H3) m olecules, wh ich em it

radiation at a wavelength of about

1 centim eter. After a couple of yearsof effort, the idea w orked. We chris

tened this device the maser . It

proved so interestin g that for a while

I put off my original goal of trying to

generate even sh orter wavelengths.

In 1954, short ly after Gordon and

I built ou r second m aser and show ed

th at th e frequency of its m icrowave

radiat ion was indeed remarkably

pure, I vis i ted Denmark and saw

Niels Bohr . As we were walking

along the street together, he askedm e wh at I was doing. I described the

m aser and its am azing performan ce

But th at is not possible! he ex

claimed. I assured him it w as.

Similarly, at a cock tail party in

Princeton, N ew Jersey, the H un gar

ian math emat ician John von N eu

m ann asked what I was working on

I told him about t he m aser and the

purit y of its frequency.

That cant be right ! he declared

But i t w as, I replied, tell ing him it

had already been dem onstrated.

Such protests were not offhand

opinions about obscure aspects o

physics; th ey came from t he m arrow

of th ese men s bones. Th eir objec

tions were foun ded on principlethe

Heisenberg uncertainty pr inciple

A central tenet of quantu m m echan

ics, this principle is am ong the core

achievem ents th at occurred during

ground, or lower, states. A w ave of

electromagnetic en ergy of the proper

frequency traveling through such a

peculiar substan ce will pick up rather

th an lose energy. Th e increase in th e

num ber of photons associated w ith

th is wave represents amplification

l ight amplif icat ion by s t imulated

emission of radiation.

If th is amplification is not very

large on a single pass of the wave

through th e m aterial, there are waysto beef it up. For example, tw o par-

al lel mirrorsbetween which the

light is reflected back and forth, wit h

excited m olecules (or atom s) in t he

middlecan build up the wave. Get-

ting the highly directional laser beam

out of th e device is just a m atter of

one mirror being made par t ial ly

transparent, so that wh en th e inter-

nal ly ref lect ing beam gets s t rong

enough, a substantial amount of its

power shoots right on t hrough oneend of th e device.

The way th i s manipula t ion of

physical laws came about, with the

m any false start s and blind alleys on

the w ay to its realization, is the sub-

ject of my book ,How t he Laser Hap-

pened. Briefly sum m arized in this ar-

ticle, it also describes my odyssey as

a scient ist and its un predictable and

perhaps na tura l path to th e m aser

and laser. Th is story is interwoven

with the w ay the f ield of quantum

electronics grew, rapidly and strik -

ingly, owing to a variety of im portan t

contributors, their cooperation and

competitiveness.

DURING THE LATE 1940sand early 1950s, I was exam -

ining molecules with m icro-

waves at Colum bia Universitydo-

ing microwave spectroscopy. I tried

None of us w ho w orked

on the first lasers ever

imagined how many uses

there might ev entually b e.

Many of today s p ractical

technologies have resulted

from basic scientific

research done years

to decad es before.


27/63

BEA M LIN E 2

a phenom enal burst of creativity in

the first few decades of the t went ieth

centu ry. As its nam e implies, it de-

scribes the im possibility of achiev-

ing absolute k now ledge of all the as-

pects of a system s condition. There

is a price to be paid in at tem pting

to m easure or define one aspect of

a specific particle to very great ex-

actness. On e must surrender knowl-

edge of, or control over, some other

feature.A corollary of this principle, on

which the m aser s doubters s tum -

bled, is that on e cannot m easure an

objects frequen cy (or energy) to great

accuracy in an arbitrarily short t ime

interval. Measurements m ade over a

finite period of t ime autom atically

impose uncertaint y on the observed

frequency.

To many ph ysicists steeped in the

un certainty pr inciple, the maser s

performan ce, at fi rst blush, made nosense at all. Molecules race th rough

i ts cavi ty, spending so l it t le t im e

thereabout one ten-thousandth of

a secondthat it seemed im possible

for the frequency of the out put m i-

crowave radiation t o be so narrowly

defined. Yet th at is exactly what hap-

pens in the m aser.

Th ere is good reason th at th e un-

certaint y principle does not apply so

simply here. Th e m aser (and by anal-

ogy, the laser) does not tell you an y-

th ing about th e energy or frequen-

cy of any specific m olecule. When

a m olecule (or atom ) is stimu lated to

radiate, it m ust produce exactly the

same frequency as the s t im ulat ing

radiation. In addition, th is radiation

represent s th e average of a large num -

ber of molecules (or atoms) work-

ing together. Each individual m ole-

cule remains anonymous , not

accurately measu red or tracked. The

precision arises from factors that

m ollify the apparent dem ands of the

un certainty principle.

I am not su re that I ever did con-

vince Bohr. On t hat sidewalk in D en-

mark, he t old me em phatically that

if molecules zip through th e m aser

so quickly, their emission lines m ust

be broad. After I persisted, howev-

er, he relented.

Oh , well, yes, he said; Maybeyou are right. But m y im pression

was th at he was just trying to be po-

lite to a younger physicist.

After our fi rst chat at th at Prince-

ton party, von N eum ann w andered

off and h ad anoth er drink. In about

fi fteen m inut es, he was back.

Yes, you re right, he snapped.

Clearly, he had seen th e point.

NOVA, the worlds largest and most pow-

erful laser, at the Lawrence Livermore

National Laboratory in California. Its10

laser beams can deliver15trillion watts

of light in a pulse lasting3billionths of a

second. With a modified single beam, it

has produced1,250trillion watts for half

a trillionth of a second. (Courtesy

Lawrence Livermore National

Laboratory)


28/63


drive any specific resonant frequency

inside a cavity.

As I played with t he var iety of

possible molecular and atom ic tran-

si t ions, and the m ethods of exci t -

ing them , what is well-known todaysuddenly becam e clear to m e: i t is

just as easy, and probably easier, to

go r ight on down to real ly short

wavelengthsto the near-infrared or

even optical regionsas to go down

one smaller step at a tim e. This was

a revelation, l ike stepping through

a door into a room I did not suspect

existed.

Th e Doppler effect does indeed in-

creasingly smear out the frequency

of response of an atom (or m olecule)

as one goes to shorter wavelengths,

but there is a compensat ing factor

that comes into play. The nu m ber of

atom s required to am plify a wave by

a given am ount does not increase,

because atoms give up th eir quanta

m ore readily at h igher frequen cies.

And wh ile the power needed to keep

a certain num ber of atom s in excited

states increases with th e frequency,

He seemed very interested, and he

asked m e about t he possibility of do-

ing something s imilar at shorter

wavelengths using semiconductors.

Only later did I learn from his

posthum ous papers, in a Septem ber

1953 letter he had written to Edward

Teller, th at h e had already proposed

producing a cascade of stim ulat ed in-

frared radiation in semiconduct ors

by excit ing electrons w ith intense

neutron bom bardm ent. His idea wasalmost a laser , but he had not

th ought of em ploying a ref lect ing

cavity nor of using the coherent prop-

erties of stim ulated radiation.

IN T H E LAT E SU M MER of1957, I fel t i t was high t ime I

m oved on to the original goal that

fostered th e m aser idea: oscillators

that work at wavelengths apprecia-

bly shorter th an 1 millim eter, beyond

what s tandard electronics couldachieve. For some t im e I had been

th inkin g off and on about t his goal,

hoping that a great idea would pop

into m y head. But since nothin g had

spontaneously occurred to m e, I de-

cided I had to t ake tim e for concen-

trated thought.

A m ajor problem to overcome was

that th e rate of energy radiation from

a molecu le increases as the fourth

power of the frequency. Thu s to k eep

molecules or atoms exci ted in a

regim e to am plify at a wavelength of,

say, 0.1 m illim eter instead of 1 cen-

timet er requires an increase in pum p-

ing power by man y orders of m ag-

nitude. Another problem was th at for

gas m olecules or atom s, Doppler ef-

fects increasingly broaden t he em is-

sion spectrum as the w avelength gets

smaller. That m eans there is less am-

pl ification per m olecule available to

th e total power requiredeven t o

am plify visible light is not n eces

sarily prohibitive.

Not only were there no c lear

penalties in such a leapfrog to very

short w avelengths or high frequencies

th is approach offered big advant ages

In th e n ear-infrared and visible re

gions, we already had plent y of ex

perience and equipment . By contrast

wavelengths near 0.1 mm and tech

niques to handle them were re latively unkn own. It was tim e to take

a big step.

Still, there remained anoth er ma-

jor concern: the resonant cavity. To

contain enough atom s or molecules

the cavi ty would have to be much

longer than t he wavelength of the

radiation probably thousands o

tim es longer. This m eant, I feared

that no cavity could be very selective

for one an d only on e frequency. The

great size of the cavity, comparedto a single wavelength , meant th at

m any closely spaced but slight ly dif

ferent w avelengths w ould resonate

By great good fortune, I got help

and an oth er good idea before I pro

ceeded any furt her. I had recently be

gun a consulting job at Bell Labs

wh ere my brother-in-law and form er

postdoc Arthu r Schawlow w as work

ing. I natu rally told him th at I had

been t h inking about such opt ica

m asers, and he w as very interested

because he had also been t hink ing in

that very direction.

We talked over th e cavity prob

lem, and Art came up with the so

lut ion. I had been consider ing a

rather well-enclosed cavity, with m ir

rors on th e ends and holes in the

sides only large enough t o provide

a way to pu m p energy into t he gas

and to k ill som e of the directions in

The dev elopment

of the laser follow ed

no script excep t

to hew to t he nature

of scientist s groping

to understand ,

to explore, and

to create.


29/63

BEA M LIN E 2

which t he waves might bounce. He

suggested instead that we u se just

tw o plates, tw o simple mirrors, and

leave off th e sides altogeth er. Such

arrangem ent s of parallel mirrors were

already used at the t ime in opt ics;

th ey are called FabryPerot interfer-

ometers.

Art recognized that with out th e

sides, man y oscillating modes th at

depend on internal reflections would

eliminate th emselves. Any wave hit-t ing ei ther end m irror at an an gle

would eventually walk itself out of

the cavityand so not build up en-

ergy. Th e only modes th at could sur-

vive and oscil late , then, w ould be

waves reflected exactly straight back

and forth between the t wo m irrors.

More detailed studies showed th at

th e size of the m irrors and th e dis-

tance between t hem could even be

chosen so that only one frequency

wou ld be likely to oscillate. To besure, any wavelength t hat fi t an ex-

ac t num ber of t imes between th e

m irrors could resonate in such a cav-

ity, just as a piano string produces not

just one pure f requency but also

m any higher harm onics. In a well-

designed system , how ever, only one

frequency will fall squarely at the

transi t ion energy of the medium

with in it. Mathem atically and phys-

ically, it w as neat.

Art an d I agreed to w rite a paper

jointly on optical masers. It seemed

clear th at we could actu al ly bui ld

one, but it w ould take tim e. We spent

nine m onth s working on and off in

our spare time to w rite the paper. We

needed to clear up the engineering

and som e specific detai ls , such as

wh at m aterial to use, and to clarify

th e th eory. By August 1958 the man-

uscript was com plete, and the Bell

Labs patent lawyers told us that t hey

had done their job protect ing i ts

ideas. The Physical Rev iew published

it in the D ecem ber 15 , 1958, issue.

In Septem ber 1959 the fi rst scien-

tific meeting on quantum electronicsand resonance phenomen a occurred

at t he Shawan ga Lodge in N ew Yorks

Catskill Mou ntains. In retrospect, it

represented th e form al birth of the

m aser and its related physics as a dis-

t inc t subdisc ip l ine . At t ha t m eet -

ing Schaw low delivered a general talk

on optical m asers.

Listening with interest was

Theodore Maiman from t he H ughes

Research Laboratories in Cu lver City,

Cal i fornia. He had been working

with ruby m asers and says he was al-

ready thin king about using ruby as

the m edium for a laser. Ted listened

closely to the run down on t he pos-

sibili ty of a solid-stat e ruby laser,

about which Art w as not too hope-

ful. It m ay well be that more suit-

able solid materials can be found,

he noted , and w e are looking for

them.

James Gordon, Nikolai Basov, Herbert

Zeiger, Alexander Prokhorov, and author

Charles Townes (left to right) attending

the first international conference on

quantum electronics in1959.


30/63

28 SU MMER /FA LL 2000

t ists recently hired after th eir uni-

versity research in th e field of m i-

crowave and radio spectroscopy

stu dent s of Willis Lamb, Polykarp

Kusch, and myself, who w orked to-

geth er in the Colum bia Radiat ion

Laboratory, and of N icholas Bloem -

bergen at H arvard. The w hole field

of quantum electronics grew out of

this approach to physics.

The deve lopment of the m aser

and laser followed n o script exceptto hew to th e na ture of scien t i s t s

groping to understand, explore and

create. As a striking exam ple of how

important technology applied to hu -

m an int erests can grow out of basic

un iversity research, the laser s de-

velopment fi ts a pattern th at could

not h ave been predicted in advance.

What research planner, want ing a

more intense l ight source, would

have started by studying molecules

with microwaves? What industrial-ist, looking for new cu tt ing and weld-

ing devices, or what doctor, wan ting

a new surgical tool as the laser has

becom e, would have urged the stu dy

of microwave spectroscopy? The

whole field of quantum electronics

is truly a text book exam ple of broad-

ly applicable techn ology growing un-

expectedly out of basic research.

Maiman felt that Schawlow was

far too pessimst ic and left t he m eet-

ing intent on bu ilding a solid-state

ruby laser. In subsequen t m onth s Ted

made s t r ik ing measurements on

ruby, showin g that it s lowest energy

level could be partially emptied by

exci ta t ion wi th in tense l ight . H e

then pushed on tow ard still bright er

excitation sources. On May 16, 1960,

he f i red up a f lash lamp wrapped

around a ru by crystal about 1.5 cmlong and produced the fi rst operating

laser.

The evidence that i t worked was

somewhat indi rec t . The Hughes

group did not set it up t o shine a spot

of light on th e wall. No such flash of

a beam h ad been seen, which lef t

room for doubt about just wh at th ey

had obtained. But the inst rum ents

had shown a substant ial chan ge in

the f luorescence spectrum of the

ruby; i t became m uch n arrower, aclear sign t hat em ission h ad been

stim ulated, and the radiation peaked

at jus t the w avelengths t ha t w ere

m ost favored for such action. A short

while later , both the Hughes re-

searchers and Schaw low at Bell Labs

independently dem onstrated power-

ful flashes of directed light th at m ade

spots on th e wal lclear intu i t ive

proof th at a laser is indeed workin g.

IT IS NOTEWORTHY that al-m ost all lasers were fi rst built in

indu strial labs. Part of th e reason

for indust rys success is that once its

importance becomes apparent , in-

dust rial laboratories can devote more

resources and concentrated effort t o

a problem than can a universi ty.

When th e goal is clear, industry can

be effective. But th e fi rst lasers were

invented and bu ilt by young scien-


31/63

BEA M LIN E 2

ON E N ORMALLY THIN KS that quantu m m echanics is only

relevant on su bm icroscopic scales, operating in t he dom ain of

atom ic, nuclear, and particle physics. But if our m ost exciting

ideas about th e evolut ion of the early Universe are correct, th en

th e im print of th e quantu m world is visible on astronom ical

scales. The possibility that quantu m m echanics shaped th e

largest stru ctu res in t he U niverse is one of th e th eories to com e

from t he m arriage of th e quantu m and th e cosm os.

The Quan tu m

by ROCKY KOLB

WHATS OU T THERE?

On a dark clear night th e sky offers

m uch t o see. With t he un aided eye one

can see thin gs in our solar system such

as planet s, as well as extrasolar objects

like stars. N early everyth ing visible by

eye resides with in our own M ilky WayGalaxy. But with a little patience and

skill it s possible to find a few extra-

galactic objects. The Andromeda

Galaxy, 2.4 m illion light -years distant ,

is visible as a faint nebu lous region,

and from t he Sout hern H emisphere

tw o sm all nearby galaxies (if170,000

light-years can be considered nearby),

th e Magellanic Clou ds, can also be

seen with th e unaided eye.

While t he preponderance of objects

seen by eye are galactic, the view

th rough large telescopes reveals th e

un iverse beyond t he M ilky Way. Even

wit h t he telescopes of th e nineteent hcentu ry, th e great British astronom er

Sir William Herschel discovered about

2,500 galaxies, and h is son , Sir John

Herschel, discovered an addit ional

thousand (a l though nei ther of the

Herschels kn ew th at th e objects they

discovered were extragalactic) . As

& Th e Cosm os

When one

tugs at a

single thing

in Nature, he

finds it

hitched tothe rest of the

Universe.

John Muir

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


32/63


several thousan d galaxies. Clu sters

of galaxies are part of even larger

associat ions cal led superclusters

cont ainin g dozens of clust ers spread

out over 10 0 m illion light -years o

space. Even su perclusters m ay not be

the largest th ings in t he U niverse

Th e largest surveys of the U niverse

suggest to some astronom ers that

galaxies are organized on two

dimensional sheet- l ike s t ructures

wh ile others believe that galaxies liealong extended on e-dimen sional fil

ament s . The exac t na ture of how

galaxies are arranged in t he Un iverse

is still a matt er of debate am ong cos

mologists. A picture of the arrange

m ent of galaxies on t he largest scales

is only now em erging.

N ot all of the Un iverse is visible

to th e eye. In addi t ion to pat t erns

in the arrangement of m atter in the

visible Universe, there is also a stru c

tu re to the backgroun d radiation.Th e Universe is awash in a th er

m al bath of radiat ion, wi th a tem

peratu re of th ree degrees above ab

solut e zero (3 K or -270 C). Inv isible

to the hu m an eye, the background

radiat ion is a remnant of the hot

prim eval fireball. First discovered in

1965 by Arno Penzias and Robert

Wilson, i t is a fundam ental predic

tion of the Big Bang th eory.

Soon after Penzias and Wilson dis

covered the background radiation

th e search began for variations in th e

temperature of the universe. For

near ly 30 years , as t rophysicis ts

searched in vain for regions of th e dis

tan t U niverse tha t were hot te r or

colder th an average. It w as not u nt i

1992 that a team of astronom ers us

ing th e C osmic Backgroun d Explorer

Satelli te (COBE) discovered an in-

trinsic pattern in t he tem perature o

astronom ers built larger telescopes

and looked deeper into space, the

number of known galaxies grew.

Although no one has ever bothered

to count , astronom ers have identi-

fied about four m illion galaxies. And

there are a lot m ore out there!

Ou r deepest view int o the Un i-verse is the H ubble Deep Field. The

result of a 10-day exposure of a very

small region of the sk y by NASAs

Hu bble Space Telescope, the Hu bble

Deep Field reveals a un iverse full of

galaxies as far as Hu bbles eye can see

(phot o above). If th e Space Telescope

could take the time t o survey the en-

t i re sky to the depth of the Deep

Field, it would fi nd m ore than 50 bil-

lion galaxies.

Although large galaxies contain

at least 100 billion st ars and stretch

across 100,000 l ight-years or more

of space, they arent the biggest

thin gs in t he U niverse. Just as stars

are part of galaxies, galaxies are part

of larger structures.

Many galaxies are members of

groups containing a few dozen to a

hundred galaxies, or even larger assem -

blages kn own as clusters, containin g

Galaxies fill the Hubble Deep Field, one

of the most distant optical views of the

Universe. The dimmest ones, some as

faint as30th magnitude (about four bil-

lion times fainter than stars visible to the

unaided eye), are very distant and rep-

resent what the Universe looked ike in

the extreme past, perhaps less than one

billion years after the Big Bang. To makethis Deep Field image, astronomers se-

lected an uncluttered area of the sky in

the constellation Ursa Major and pointed

the Hubble Space Telescope at a single

spot for10days accumulating and com-

bining many separate exposures. With

each add itional exposure, fainter objects

were revealed. The final result can be

used to explore the mysteries of galaxy

evolution and the early Universe.

(Courtesy R. Williams, TheHDFTeam,

STScl, andNASA)


33/63

BEA M LIN E 3

the U niverse. Since the t ime of the

COBE discovery, a pat tern of tem-

perature var iat ions has been m ea-

sured wit h in creasing precision by

dozens of balloon-borne and terres-

trial observation s. A new era of pre-

cision cosmological observations is

s tar t ing. Sometime in 2 00 1 N A SA

wil l l aunch a new sa te l l i t e , the

Microwave An isotropy Probe (MAP),

and sometime in 2007 the European

Space Agency w ill launch an evenm ore ambit ious effor t , the Planck

Explorer, to stu dy tem perature vari-

at ions in the cosmic background

radiation.

Even if our eyes were sen sitive to

m icrowave radiation, we would have

a hard tim e discerning a pattern of

temperature fluctuations since the

hot t est and coldest regions of th e

background radiation are only about

one-thou sandth of a percent hott er

and colder than average.Although small in magnitude, the

background tem perature flu ctuations

are large in importance since they

give us a snapshot of structu re in the

Universe when th e background pho-

tons last scat tered, about 300,000

years after th e Bang.

WHY IS IT TH ERE?

A really good answ er to a deep ques-

t ion usual ly leads to even deeper

questions. On ce we discover what s

in th e Universe, a deeper quest ion

arises: Why is it th ere? Why are stars

arranged int o galaxies, galaxies int o

clusters, clusters into su perclusters,

and so on? Why are th ere small vari-

ations in the tem perature of the Uni-

verse?

Part of the answer involves grav-

ity. Everything we see in the Un iverse

is th e result of gravity. Every tim e

you see a star the im print of gravity

is shining at you. Today we observe

new stars form ing within giant inter-

stellar gas clouds, such as th ose found

at th e center of the O rion N ebula just

1,500 light-years away (see phot o on

next page).

Interstellar clouds are not sm ooth

and un iform; th ey contain regions

wh ere the density of mat erial is larger

than in surrounding regions. Thedense regions with in th e clouds are

th e seeds around w hich st ars grow

th rough t he irresistible force of grav-

ity. The dense regions pull in nearby

m aterial th rough th e force of gravity,

which com presses the material un-

til it becomes hot an d dense enough

for nuclear reactions to com m ence

and form stars.

About fi ve billion years ago in our

litt le corner of the M ilky Way, grav-

ity started to pu ll togeth er gas anddust to form our solar system. This

fashioning of structure in our local

neighborhood is just a sm all part of

a process that started about 12 billion

years ago on a grander scale th rough-

4462827 stanford linear accelerator center beamline summer fall 2000

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