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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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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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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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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)
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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.
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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)
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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)
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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.
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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)
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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.
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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.
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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
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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.
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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.
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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.
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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)
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26 SU MMER/FA LL 2000
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.
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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.
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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-
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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)
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30 SU MM ER/ FA LL 2000
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)
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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-