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量子未来
一本专门介绍量子力学的英文科技文献,讲述了量子力学的发展以利未来的展望。
CONTENTS
FEATURES
2
FOREWORD
34
GETTING TO KNOW YOUR CONSTITUENTS
Humankind has wondered since the beginning of history what are the fundamental
constituents of matter. Robert L. Jaffe
THE FUTURE OF THE QUANTUMTHEORY
James Bjorken
6
THE ORIGINS OF THE QUANTUMTHEORY
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The ?rst 25years of the century radicallytransformed our ideas about Nature.Cathryn
Carson
41
SUPERCONDUCTIVITY:
AMACROSCOPIC QUANTUM PHENOMENON
Quantum mechanics is crucial to
understanding and using superconductivityJohn Clarke
20
THE LIGHT THAT SHINES STRAIGHT
A Nobel laureate recounts the invention of the laser and the birth of quantum
electronics.Charles H. Townes
DEPARTMENTS
49
THE UNIVERSE AT LARGE
The Ratios of Small Whole Numbers:
Misadventures
in
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Astronomicahttp://www.51wendang.com/doc/f25c1567573777508636613al
QuantizationVirginia Trimble
29
THE QUANTUM AND THECOSMOS
Large-scale structure in the Universe began
58 CONTRIBUTORS
FOREWORD
The Future of the Quantum T
byJAMES BJORKEN
brate the one hundredth anniversary of thebirth of the quantum theory. The story ofhow
MaxPlanck started it all is one of the mostmarvelous in all of science. It is a favorite
ofmine, so much so that I have already written
about it (see “Particle Physics—Where Do We GoFrom Here?” in the Winter 1992Beam
Line,
Vol.22, No. 4). Here I will only quote again whatthe late Abraham Pais said about
Planck: “Hisreasoning was mad, but his madness had thatdivine quality that only the
greatest transitional?gures can bring to science.”*
A century later, the madness has not yet com-pletely disappeared. Science in general
has
a
wayof
producing
results
which
defy
human
intuition.But
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ihttp://www.51wendang.com/doc/f25c1567573777508636613at is fair to say that the
winner in thiscategory is the quantum theory. In my mindquantum paradoxes such as
the HeisenbergMax Planck, circa 1910
(Courtesy AIPEmilio Segrè Visual Archives)uncertainty principle, Schr?dinger’s
cat,
“collapse of the wave packet,” and so forth are far more perplexing andchallenging
than those of relativity, whether they be the twin paradoxes ofspecial relativity
or the black hole physics of classical general relativity. It isoften said that no
one reallyunderstands quantum theory, and I would bethe last to disagree.
In the contributions to this issue, the knotty questions of the interpreta-tion of
quantum theory are, mercifully, not addressed. There will be no
mention of the debates between Einstein and Bohr, nor the later attempts by
*Abraham Pais, Subtle is the Lord: Science and the Life of Albert Einstein, Oxford
U. Press, 1982.
I
NTHISISSUhttp://www.51wendang.com/doc/f25c1567573777508636613aEof the Beam Line,
we cele-
2SUMMER/FALL 2000
heory
Bohm, Everett, and others to ?nd inter-pretations of the theory different fromthe
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original “Copenhagen interpreta-tion” of Bohr and his associates. Instead,what is
rightfully emphasized is theoverwhelming practical success of theserevolutionary
ideas. Quantum theoryworks. It never fails. And the scope ofthe applications is
enormous. As LeonLederman, Nobel Laureate and DirectorEmeritus of Fermilab, likes
to point out,more than 25 percent of the grossnational product is dependent
upontechnology that springs in an essentialway from quantum phenomena.*
Nevertheless, it is hard not to sympa-thize with Einstein and feel that there
issomething incomplete about the presentstatus of quantum theory. Perhaps thet
seequations de?ning the theory are not ex-fnerhEactly correct, and corrections will
even- luaPtually be de?ned and their effects
http://www.51wendang.com/doc/f25c1567573777508636613aAlbert Einstein and Neils
Bohr in the late 1920s.
observed. This is not a popular point of(Courtesy AIPEmilio Segrè Visual
Archives)view. But there does exist a minority
school of thought which asserts that
only for suf?ciently small systems is the quantum theory accurate, and thatfor large
complex quantum systems, hard to follow in exquisite detail, there
*Leon Lederman, The God Particle (If the Universe is the Answer, What is the
Question?),Houghton Mif?in, 1993.
BEAM LINE3
may be a small amount of some kind of extra intrinsic “noise” term or non-linearity
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in the fundamental equations, which effectively eliminates para-doxes such as the
“collapse of the wave packet.”
Down through history most of the debates on the foundations of quantumtheory produced
many words and very little action, and remained closer tothe philosophy of science
than
to
real
experimental
science.
Johttp://www.51wendang.com/doc/f25c1567573777508636613ahn Bell
brought some freshness to the subject. The famous theorem that bears hisname initiated
an experimental program to test some of the fundamentals.Nevertheless, it would have
been an enormous shock, at least to me, if anydiscrepancy in such experiments had
been found, because the searchesinvolved simple atomic systems, not so different from
elementary particlesystems within which very subtle quantum effects have for some
time beenclearly demonstrated. A worthy challenge to the quantum theory in myopinion
must go much further and deeper.
What might such a challenge be? At present, one clear possibility which isactively
pursued is in the realm of string theory, which attempts an exten-sion of Einstein
gravity into the domain of very short distances, where quan-tum effects dominate.
In the present incarnations, it is the theory of gravitythat yields ground and
undergoes
modi?cations
and
generalizations,
thequhttp://www.51wendang.com/doc/f25c1567573777508636613aantum
theory
with
left
essentially intact. But it seems to me that the alterna-tive must also be
entertained—that the quantum theory itself does not sur-vive the synthesis. This,
however, is easier said than done. And the problemwith each option is that the answer
needs to be found with precious littleassistance from experiment. This is in stark
contrast with the developmentof quantum theory itself, which was driven from
initiation to completion bya huge number of experiments, essentially guiding the
theorists to the ?nalequations.
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4SUMMER/FALL 2000
*Frank Wilczek, Physics Today, June 2000, Vol. 53, No.6, p. 11.
BEAM LINE5
THE ORIGINS
OF THE QUANTUM THEORY
by CATHRYN
CARSON
W
HATISAQUANTUMTHEORY?We have
been asking that question for a long time, eversince Max Planck introduced the element
of dis-
continuity
we
call
the
quantum
ago.http://www.51wendang.com/doc/f25c1567573777508636613a
a
century
Since
then,the
chunkiness of Nature (or at least of our theories aboutit) has been built into our
basic conception of the world. Ithas prompted a fundamental rethinking of physical
theory.At the same time it has helped make sense of a whole range of pe-culiar
behaviors manifested principally at microscopic levels.
From its beginning, the new regime was symbolized by Planck’s constanth, introduced
in his famous paper of 1900. Measuring the world’s departurefrom smooth, continuous
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behavior, hproved to be a very small number, butdifferent from zero. Wherever it
appeared, strange phenomena came with it.What it really meant was of course mysterious.
While the quantum era wasinaugurated in 1900, a quantum theory would take much longer
to jell. Intro-ducing discontinuity was a tentative step, and only a ?rst one. And
eventhereafter,
the
Physicistspondered
recasting
of
for
physical
theory
was
years
quantumhttp://www.51wendang.com/doc/f25c1567573777508636613a
hesitant
and
slow.
what
theory
a
might
be.
Wondering how to inte-grate it with the powerful apparatus of nineteenth-century
physics, they alsoasked what relation it bore to existing, “classical” theories.
For some theanswers crystallized with quantum mechanics, the result of a
quarter-century’s labor. Others held out for further rethinking. If the outcome
wasnot to the satisfaction of all, still the quantum theory proved remarkably
6SUMMER/FALL 2000
successful, and the puzzlement along the way, despite its frustrations, canonly be
called extraordinarily productive.
INTRODUCINGh
The story began inconspicuously enough on December 14, 1900. Max Planckwas giving
a talk to the German Physical Society on the continuous spec-trum of the frequencies
of light emitted by an ideal heated body. Some twomonths earlier this 42-year-old
theorist had presented a formula capturingsome new experimental results. Now, with
leisure to think anhttp://www.51wendang.com/doc/f25c1567573777508636613ad more
time athis disposal, he sought to provide a physical justi?cation for his
formula.Planck pictured a piece of matter, idealizing it somewhat, as equivalent to
acollection of oscillating electric charges. He then imagined distributing itsenergy
in discrete chunks proportional to the frequencies of oscillation. Theconstant of
proportionality he chose to call h; we would now write e= hf.The frequencies of
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oscillation determined the frequencies of the emittedlight. A twisted chain of
reasoning then reproduced Planck’s postulatedformula, which now involved the same
natural constant h.
Two theorists,Niels Bohr andMax Planck, at theblackboard.(Courtesy EmilioSegre`
VisualArchives,
Margrethe Bohr
Collection)
BEAM LINE7
An ideal blackbody spectrum
(Schwarzer K?rper) and its real-worldapproximation (quartz). (From ClemensSchaefer,
Einführung in die TheoretischePhysik, 1932).
http://www.51wendang.com/doc/f25c1567573777508636613aExperimental
setup
for
measuring black-body radiation. (The blackbody is thetube labeled C.) This design
was a prod-uct of Germany’s Imperial Institute ofPhysics and Technology in Berlin,
wherestudies of blackbodies were pursuedwith an eye toward industrial standardsof
luminous intensity. (From Müller-Pouillets Lehrbuch der Physik, 1929).
8SUMMER/FALL 2000
Looking back on the event, we might expect revolutionaryfanfare. But as so often in
history, matters were more ambigu-ous. Planck did not call his energy elements quanta
and was notinclined to stress their discreteness, which made little sense in
anyfamiliar terms. So the meaning of his procedure only gradually be-came apparent.
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Although the problem he was treating was pivotalin its day, its implications were
at first thought to be confined.
BLACKBODIES
The behavior of light in its interaction with matter was indeed akey problem of
nineteenth-cehttp://www.51wendang.com/doc/f25c1567573777508636613antury physics.
Planck was interest-ed in the two theories that overlapped in this domain. The first
waselectrodynamics, the theory of electricity, magnetism, and lightwaves, brought
to final form by James Clerk Maxwell in the 1870s.The second, dating from roughly
the same period, was thermo-dynamics and statistical mechanics, governing
transformations ofenergy and its behavior in time. A pressing question was
whetherthese two grand theories could be fused into one, since they startedfrom
different fundamental notions.
Beginning in the mid-1890s, Planck took up a seemingly narrowproblem, the interaction
of an oscillating charge with its elec-tromagnetic field. These studies, however,
brought him into con-tact with a long tradition of work on the emission of light.
Decadesearlier it had been recognized that perfectly absorbing (“black”)bodies
provided a standard for emission as well. Then over theyears a small industry had
grohttp://www.51wendang.com/doc/f25c1567573777508636613awn up around the study of
suchobjects (and their real-world substitutes, like soot). A small groupof theorists
occupied themselves with the thermodynamics ofradiation, while a host of
experimenters labored over heated bod-ies to fix temperature, determine intensity,
and characterizedeviations from blackbody ideality (see the graph above). After
sci-entists pushed the practical realization of an old idea—that a closedtube with
a small hole constituted a near-ideal blackbody—this“cavity radiation” allowed
ever more reliable measurements. (See
illustration at left.)
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Now Planck’s oscillating charges emitted and absorbed radiation,so they could be
used to model a blackbody. Thus everything seemedto fall into place in 1899 when he
reproduced a formula that a col-league had derived by less secure means. That was
convenient;
every-one agreed that Willy Wien’s formula matched the observations.
Thetrouble
was
that
immediatelhttp://www.51wendang.com/doc/f25c1567573777508636613ay
afterwards,
experimenters began ?nd-ing deviations. At low frequencies, Wien’s expression
becameincreasingly untenable, while elsewhere it continued to work wellenough.
Informed of the results in the fall of 1900, on short noticePlanck came up with a
reasonable interpolation. With its adjustableconstants his formula seemed to fit the
experiments (see graph atright). Now the question became:
Where might it come from?
Whatwas its physical meaning?
As we saw, Planck managed to produce a derivation. To get theright statistical results,
however, he had to act as though the energyinvolved were divided up into elements
e= hf. The derivation wasa success and splendidly reproduced the experimental data.
Its mean-ing was less clear. After all, Maxwell’s theory already gave a beau-tiful
account of light—and treated it as a wave traveling in a con-tinuous medium. Planck
did
not
take
the
constant
hto
indicate
aphysical
discontinuity,
http://www.51wendang.com/doc/f25c1567573777508636613aa real atomicity of energy in
a substantivesense. None of his colleagues made much of this possibility,
either,until Albert Einstein took it up ?ve years later.
MAKING LIGHT QUANTA REAL
Of Einstein’s three great papers of 1905, the one “On a Heuristic Pointof View
Concerning the Production and Transformation of Light”was the piece that the
26-year-old patent clerk labeled revolutionary.It was peculiar, he noted, that the
electromagnetic theory of lightassumed a continuum, while current accounts of matter
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started fromdiscrete atoms. Could discontinuity be productive for light as
well?However indispensable Maxwell’s equations might seem, for someinteresting
phenomena they proved inadequate. A key examplewas blackbody radiation, which
Einstein now looked at in a way dif-
ferent from Planck. Here a rigorously classical treatment, he showed,
Experimental
and
theoretical
results
onthe
blackbody
spectrum.http://www.51wendang.com/doc/f25c1567573777508636613a The data
points are experimental values; Planck’sformula is the solid line. (Reprinted fromH.
Rubens and F. Kurlbaum,Annalender Physik, 1901.)
BEAM LINE9
Pieter Zeeman, Albert Einstein, and PaulEhrenfest (left to right) in Zeeman’s
Amsterdam
laboratory.
(Courtesy
EmilioSegre`
Visual
Archives,
W.
F.
MeggersCollection)
yielded a result not only wrong but also absurd. Even where Wien’slaw was
approximately
right
(and
Planck’s
modi?cation
unnecessary),elementary
thermodynamics forced light to behave as though it werelocalized in discrete chunks.
Radiation had to be parcelled into whatEinstein called “energy quanta.” Today we
would write E= hf.
Discontinuity was thus endemic to the electromagnetic world.Interestingly, Einstein
did not refer to Planck’s constant h, believinghis approach to be different in spirit.
Where
Planck
had
looked
atoscillating
charges,
Einstein
thermodynhttp://www.51wendang.com/doc/f25c1567573777508636613aamics
applied
to
the
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lightitself. It was only later that Einstein went back and showed howPlanck’s work
implied real quanta. In the meantime, he offered a fur-ther, radical extension. If
light behaves on its own as though com-posed of such quanta, then perhaps it is also
emitted and absorbed inthat fashion. A few easy considerations then yielded a law
for thephotoelectric effect, in which light ejects electrons from the sur-face of
a metal.
Einstein provided not only a testable hypothesis butalso a new way of
measuring the constant h(see table on the nextpage).
Today the photoelectric effect can be checked in a college labo-ratory. In 1905
, however, it was far from trivial. So it would remain
10SUMMER/FALL 2000
for more than a decade. Even after Robert Millikan confirmedEinstein’s prediction,
he and others balked at the underlying quan-tum hypothesis. It still violated
everything
known
about
light’s
wavehttp://www.51wendang.com/doc/f25c1567573777508636613a-like behavior (notably,
interference) and hardly seemed reconcil-able with Maxwell’s equations. When
Einstein was awarded the NobelPrize, he owed the honor largely to the photoelectric
effect. But thecitation specifically noted his discovery of the law, not the
expla-nation that he proposed.
The relation of the quantum to the wave theory of light would re-main a point of
puzzlement. Over the next years Einstein would onlysharpen the contradiction. As he
showed, thermodynamics ineluctablyrequired both classical waves and quantization.
The two aspects werecoupled: both were necessary, and at the same time. In the
process,Einstein moved even closer to attributing to light a whole panoplyof
particulate properties. The particle-like quantum, later named thephoton, would
prove suggestive for explaining things like the scat-tering of Xrays. For that
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1923discovery, Arthur Compton would winthe Nobel Prize. But there we get ahead of
http://www.51wendang.com/doc/f25c1567573777508636613athe story. Before notionsof
wave-particle duality could be taken seriously, discontinuityhad to demonstrate its
worth elsewhere.
BEYOND LIGHT
As it turned out, the earliest welcome given to the new quantumconcepts came in fields
far removed from the troubled theories ofradiation. The ?rst of these domains, though
hardly the most obvi-ous, was the theory of speci?c heats. The speci?c heat of a
substancedetermines how much of its energy changes when its temperature israised.
At low temperatures, solids display peculiar behavior. HereEinstein suspected—again
we meet Einstein—that the deviance mightbe explicable on quantum grounds. So he
reformulated Planck’s prob-lem to handle a lattice of independently vibrating atoms.
From thishighly simplistic model, he obtained quite reasonable predictionsthat
involved the same quantity hf, now translated into the solid-state context.
There
things
stood
for
another
three
yhttp://www.51wendang.com/doc/f25c1567573777508636613aears. It took the sudden
attention of the physical chemist Walther Nernst to bring quantum
(From W. W. Coblentz, Radiation,Determination of the Constants andVeri?cation of the
Lawsin
A Dictionaryof Applied Physics,Vol. 4, Ed. SirRichard Glazebrook, 1923)
BEAM LINE11
The ?rst SolvayCongress in 1911assembled thepioneers of
quantum
theory.Seated
(left
toright):
W.
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Nernst,M.Brillouin,E.Solvay,H.A.Lorentz,E.Warburg,
J.Perrin, W. Wien,M. Curie,H.Poincaré.Standing (left toright):
R.Goldschmidt,M.Planck,H.Rubens,A.Sommerfeld,F.Lindemann,M.de
Broglie,M.Knudsen,F.Hasen?hrl,G.Hostelet,
E.Herzen, J. Jeans,E. Rutherford,H.Kamerlingh
Onnes, A.Einstein,P.Langevin. (FromCinquantenaire duPremier Conseil dePhysique
Solvay,1911–1961).
theories of specific heats to general significance. Feeling his waytowards a new law
of
thermodynamics,
Nernst
not
only
bolsteredEhttp://www.51wendang.com/doc/f25c1567573777508636613ainstein’s
ideas
with experimental results, but also put them onthe agenda for widespread discussion.
It was no accident, and to alarge degree Nernst’s doing, that the first Solvay
Congress
in
1911dealt
precisely
with
radiation
theory
and
quanta
(see
photographbelow). Einstein spoke on specific heats, offering additional com-ments
on electromagnetic radiation. If the quantum was born in 1900,the Solvay meeting was,
so to speak, its social debut.
What only just began to show up in the Solvay colloquy was theother main realm in
which discontinuity would prove its value. Thetechnique of quantizing oscillations
applied, of course, to line spec-tra as well. In contrast to the universality of
blackbody radiation, thediscrete lines of light emission and absorption varied
immensely fromone substance to the next. But the regularities evident even in
thewelter of the lines provided fertile matter for quantum conjectures.
Molechttp://www.51wendang.com/doc/f25c1567573777508636613aular
spectra
turned
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into an all-important site of research during
12SUMMER/FALL 2000
the quantum’s second decade. Slower to take off, but ultimately evenmore productive,
was the quantization of motions within the atomitself. Since no one had much sense
of the atom’s constitution, theventure into atomic spectra was allied to speculative
model-building.Unsurprisingly, most of the guesses of the early 1910s turned outto
be wrong. They nonetheless sounded out the possibilities. Theorbital energy of
electrons, their angular momentum (something likerotational inertia), or the
frequency of their small oscillations aboutequilibrium: all these were fair game for
quantization. The observedlines of the discrete spectrum could then be directly read
off from theelectrons’ motions.
THE BOHR MODEL OF THE ATOM
It might seem ironic that Niels Bohr initially had no interest in spec-tra. He came
to
atomic
ihttp://www.51wendang.com/doc/f25c1567573777508636613andirectly.
structure
Writing
his
doctoral thesison the electron theory of metals, Bohr had become fascinated byits
failures and instabilities. He thought they suggested a new typeof stabilizing force,
one fundamentally different from those famil-iar in classical physics. Suspecting
the quantum was somehowimplicated, he could not ?gure out how to work it into the
theory.The intuition remained with him, however, as he transferredhis postdoctoral
attention from metals to Rutherford’s atom. Whenit got started, the nuclear atom
(its dense positive center circled byelectrons) was simply one of several models on
offer. Bohr beganworking on it during downtime in Rutherford’s lab, thinking he
couldimprove on its treatment of scattering. When he noticed that it oughtto be
unstable, however, his attention was captured for good. Tostabilize the model by fiat,
he set about imposing a quantum con-dition, according to the standard practice of
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the
day.
Only
http://www.51wendang.com/doc/f25c1567573777508636613aafter
a
col-league directed his attention to spectra did he begin to think abouttheir
signi?cance.
The famous Balmer series of hydrogen was manifestly news toBohr. (See illustration
above.) He soon realized, however, that hecould fit it to his model—if he changed
his model a bit. He recon-ceptualized light emission as a transition between
discontinuous or-bits, with the emitted frequency determined by DE= hf
. To get the
The line spectrum of hydrogen. (FromG.Herzberg, Annalen der Physik, 1927)
BEAM LINE
13
What Was Bohr
Up To?
BOHR’SPATHto his atomic
model was highly indirect. Therules of the game, as played in1911–1912, left
some ?exibilityin what quantum condition oneimposed. Initially Bohr appliedit to
multielectron states,whose allowed energies henow broke up into a discretespectrum.
More
speci?cally,
hepicked
out
their
orbital
quantihttp://www.51wendang.com/doc/f25c1567573777508636613aze.
what he would laterproscribe in the ?nal version ofhis model.
fre-quencies
This
to
isexactly
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He rethought, however, inthe face of the Balmer seriesand its simple numericalpattern
fn= R(1/4 -1/n2).Refocusing on one electronand highlighting excited states,he
reconceptualized lightemission as a transition. TheBalmer series then resultedfrom
a tumble from orbit ntoorbit 2; the Rydberg constantRcould be determined in
terms of h. However, remnantsof the earlier model stillappeared in his paper.
14SUMMER/FALL 2000
orbits’ energies right, Bohr had to introduce some rather ad hoc rules.These he
eventually justi?ed by quantization of angular momentum,which now came in units of
Planck’s constant h. (He also used an in-teresting asymptotic argument that will
resurface later.)
Published in 1913, the resulting picture of the atom was rather odd.Not only did a
quantum
condition
describe
betweenlhttp://www.51wendang.com/doc/f25c1567573777508636613aevels,
transitions
but
the
“stationary states,” too, were fixed by nonclassical?at. Electrons certainly
revolved in orbits, but their frequency of rev-olution had nothing to do with the
emitted light. Indeed, their os-cillations were postulated notto produce radiation.
There was nopredicting when they might jump between levels. And transitionsgenerated
frequencies according to a quantum relation, but Bohrproved hesitant to accept
anything like a photon.
The model, understandably, was not terribly persuasive—thatis, until new
experimental results began coming in on Xrays, energylevels, and spectra. What really
convinced the skeptics was a smallmodification Bohr made. Because the nucleus is not
held fixed inspace, its mass enters in a small way into the spectral frequencies.The
calculations produced a prediction that ?t to 3parts in 100,000—pretty good, even
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for those days when so many numerical coinci-dences proved to be misleading.
://www.51wendang.com/doc/f25c1567573777508636613aparThe wheel made its ?nal turn
when Einstein connected the Bohratom back to blackbody radiation.
His famous papers
on radiativetransitions, so important for the laser (see following article by
CharlesTownes), showed the link among Planck’s blackbody law, discreteenergy levels,
and quantized emission and absorption of radiation.Einstein further stressed that
transitions could not be predicted inanything more than a probabilistic sense. It
was in these same papers,by the way, that he formalized the notion of particle-like
quanta.
THE OLD QUANTUM THEORY
What Bohr’s model provided, like Einstein’s account of speci?c heats,was a way to
embed the quantum in a more general theory. In fact,the study of atomic structure
would engender something plausiblycalled a quantum theory, one that began reaching
towards a full-scalereplacement for classical physics. The relation between the old
and
Above: Bohr’s lecture nohttp://www.51wendang.com/doc/f25c1567573777508636613ates
on atomic physics, 1921. (Originalsource: Niels Bohr Institute, Copenhagen. From Owen
Gingerich, Ed., Album of Science: The Physical Sciences inthe Twentieth Century,
1989.)
Left: Wilhelm Oseen, Niels Bohr, James Franck, Oskar Klein(left to right), and Max
Born, seated, at the Bohr Festival inG?ttingen, 1922. (Courtesy Emilio Segre`
Archives,
Archive for the History of Quantum Physics)
Visual
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the new became a key issue. For some features of Bohr’s modelpreserved classical
theories, while others presupposed their break-down. Was this consistent or not? And
why did it work?
By the late 1910s physicists had refined Bohr’s model, providinga relativistic
treatment of the electrons and introducing additional“quantum numbers.” The simple
quantization condition on angularmomentum could be broadly generalized. Then the
techniques
ofnineteenth-century
celestial
mechanics
provided
powerful
theorhttp://www.51wendang.com/doc/f25c1567573777508636613aet-ical tools. Pushed
forward by ingenious experimenters, spectroscopicstudies provided ever more and
finer data, not simply on the basicline spectra, but on their modulation by electric
and magnetic ?elds.And abetted by their elders, Bohr, Arnold Sommerfeld, and Max
Born,a generation of youthful atomic theorists cut their teeth on such prob-lems.
The pupils, including Hendrik Kramers, Wolfgang Pauli, WernerHeisenberg, and Pascual
Jordan, practiced a tightrope kind of theo-rizing. Facing resistant experimental data,
they balanced the empiricalevidence from the spectra against the ambiguities of the
prescrip-tions for applying the quantum rules.
Within this increasingly dense body of work, an interesting strat-egy began to jell.
In treating any physical system, the ?rst task wasto identify the possible classical
motions. Then atop these classi-cal motions, quantum conditions would be imposed.
Quantizationbecame
a
regular
prochttp://www.51wendang.com/doc/f25c1567573777508636613aedure, making continual
if puzzling refer-ence back to classical results. In another way, too, classical
physics
served as a touchstone. Bohr’s famous “correspondence principle”
BEAM LINE15
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Paul Dirac and Werner HeisenberginCambridge, circa 1930. (CourtesyEmilio Segre`
Visual Archives, PhysicsTodayCollection)
?rst found application in his early papers, where it pro-vided a deeper justi?cation
of his quantization con-dition. In the “classical limit,” for large orbits withhigh
quantum numbers and small differences in en-ergy, the radiation from transitions
between adja-cent orbits should correspond to the classical radiationfrequency.
Quantum and classical results must matchup. Employed with a certain Bohrian
discrimination,the correspondence principle yielded detailed infor-mation about
spectra. It also helped answer the ques-tion: How do we build up a true quantum theory?
Not that the solhttp://www.51wendang.com/doc/f25c1567573777508636613aution was yet
in sight. Theold quantum theory’s growing sophistication madeits failures ever
plainer. By the early 1920s the the-orists found themselves increasingly in
difficul-ties. No single problem was fatal, but their accu-mulation was daunting.
This
feeling
of
crisis
wasnot
entirely
unspeci?c.
A
group
of
atomic
theorists,centered on Bohr, Born, Pauli, and Heisenberg, hadcome to suspect that the
problems went back to elec-tron trajectories. Perhaps it was possible to abstractfrom
the orbits? Instead they focused on transition
probabilities and emitted radiation, since those might be more reli-ably knowable.
“At the moment,” Pauli still remarked in the springof 1925, “physics is again very
muddled; in any case, it is far toodif?cult for me, and I wish I were a movie comedian
or something ofthe sort and had never heard of physics.”
QUANTUM MECHANICS
Discontinuity,
abstraction
from
the
visualizable,
poshttp://www.51wendang.com/doc/f25c1567573777508636613aitivistic
a
turntowards
observable quantities: these preferences indicated one pathto a full quantum theory.
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So, however, did their opposites. Whenin 1925–1926a true quantum mechanics was
finally achieved, twoseemingly distinct alternatives were on offer. Both took as a
leitmotifthe relation to classical physics, but they offered different ways ofworking
out the theme.
16SUMMER/FALL 2000
Heisenberg’s famous paper of 1925, celebrated for launching thetransformations to
come, bore the title “On the Quantum-TheoreticalReinterpretation of Kinematical and
Mechanical Relations.” Thepoint of departure was Bohr’s tradition of atomic
structure: discretestates remained fundamental, but now dissociated from intuitive
rep-resentation. The transformative intent was even broader from thestart.
Heisenberg
translated
correspondence-principle
classical
style.
notions
In
his
into
quantum
ones
inthe
new
quantummechanics,
best
familiar
qhttp://www.51wendang.com/doc/f25c1567573777508636613auantities behaved strangely;
multiplicationdepended on the order of the terms. The deviations, however,
werecalibrated by Planck’s constant, thus gauging the departure from clas-sical
normality.
Some greeted the new theory with elation; others found it un-satisfactory and
disagreeable. For as elegant as Heisenberg’s trans-lation might be, it took a very
partial view of the problems of thequantum. Instead of the quantum theory of atomic
structure,
onemight also start from the wave-particle duality. Here another
youngtheorist, Louis de Broglie, had advanced a speculative proposal in 1923that
Heisenberg and his colleagues had made little of. Thinking overthe discontinuous,
particle-like aspects of light, de Broglie suggest-ed looking for continuous,
wave-like aspects of electrons. His notion,while as yet ungrounded in experimental
evidence, did provide sur-prising insight into the quantum conditions for Bohr’s
orbits. It also,http://www.51wendang.com/doc/f25c1567573777508636613aby a sideways
route, gave Erwin Schr?dinger the idea for his brilliantpapers of 1926.
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Imagining the discrete allowed states of any system of parti-cles as simply the stable
forms of continuous matter waves,Schr?dinger sought connections to a well-developed
branch of clas-sical physics. The techniques of continuum mechanics allowed himto
formulate an equation for his waves. It too was built aroundthe constant h. But now
the basic concepts were different, and soalso the fundamental meaning. Schr?dinger
had a distaste for thediscontinuity of Bohr’s atomic models and the lack of intuitive
pic-turability of Heisenberg’s quantum mechanics. To his mind, thequantum did not
imply any of these things. Indeed, it showed theopposite: that the apparent atomicity
of matter disguised anunderlying continuum.
The Quantum inQuantum Mechanics
ICONICALLYwe now write
Heisenberg’s relations as
pq-qp= -ih/2p.://www.51wendang.com/doc/f25c1567573777508636613ar
Here prepresents momentumand qrepresents position. Forordinary numbers, of
course,pqequals qp, and so pq-qpisequal to zero. In quantummechanics, this
difference,called the commutator, is nowmeasured by h. (The samething happens with
Heisen-berg’s uncertainty principle of1927: DpDq?h/4p.) The sig-ni?cance of the
approach, andits rearticulation as a matrix calculus, was made plain by Max Born,
Pascual Jordan, andWerner Heisenberg. Its full profundity was revealed by Paul Dirac.
BEAM LINE17
Old faces and new at the 1927SolvayCongress. The middle of the second rowlines up
Hendrik Kramers, Paul Dirac,Arthur Compton, and Louis de Broglie.Behind Compton
stands Erwin
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Schr?dinger, with Wolfgang Pauli andWerner Heisenberg next to each otherbehind Max
Born. (From Cinquantenairedu Premier Conseil de Physique Solvay,1911–1961)
Thus a familiar model connected to physical intuition, but con-stituting
mattehttp://www.51wendang.com/doc/f25c1567573777508636613ar
of
some
ill-understood sort of wave, confronted anabstract mathematics with seemingly
bizarre variables, insistentabout discontinuity and suspending space-time pictures.
Unsur-prisingly, the coexistence of alternative theories generated debate.The fact,
soon
demonstrated,
of
their
mathematical
equivalence
didnot
resolve
the
interpretative dispute. For fundamentally differentphysical pictures were on offer.
In fact, in place of Schr?dinger’s matter waves and Heisenberg’suncompromising
discreteness, a conventional understanding settledin that somewhat split the
difference. However, the thinking ofthe old quantum theory school still dominated.
Born dematerializedSchr?dinger’s waves, turning them into pure densities of
probabilityfor ?nding discrete particles. Heisenberg added his uncertainty
prin-ciple, limiting the very possibility of measurement and undermin-
ing
the
law
of
causality.
The
picture
was
capped
by
Bohrhttp://www.51wendang.com/doc/f25c1567573777508636613a’s notion
18SUMMER/FALL 2000
SUGGESTIONS
FOR FURTHER READINGOlivier Darrigol, From c-Numbers to q-Numbers: The Classical
Analogy inthe History of QuantumTheory(Berkeley: U.C.Press, 1992).Helge Kragh,
Quantum Gen-erations: AHistory ofPhysics in the TwentiethCentury(Princeton,
Prince-ton University Press, 1999).Abraham Pais, “Subtle is theLord ...”: The
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Science andthe Life of Albert Einstein(Oxford, Oxford UniversityPress, 1982).Helmut
Rechenberg, “Quantaand Quantum Mechanics,”in Laurie M. Brown,Abraham Pais, and
SirBrian Pippard, Eds.,Twentieth Century
Physics, Vol. 1(Bristol andNew York, Institute ofPhysics Publishing andAmerican
Institute
ofPhysics
Press,
1995),pp.
143-248.The
August
11,
2000,
issue
ofScience(Vol. 289) containsan article by Daniel Klep-pner and Roman Jackiw on“One
Hundred Years ofQuantum Physics.” To seethe full text of this article, goto
http://www.sciencemag.org/cgi/content/fullhttp://www.51wendang.com/doc/f25c15675
73777508636613a/289/5481/893.
BEAM LINE19
THE LIGHT THAT SHIN
by CHARLES
H. TOWNES
A Nobel laureate recounts
the invention of the laserand the birth of quantum
electronics.Adapted by Michael Riordan from HowThe Laser Happened: Adventures of a
Scientist, by Charles H. Townes.
Reprinted by permission of Oxford
University Press.20
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SUMMER/FALL 2000
ONJULY21, 1969, astronauts Neil Armstrong and
Edwin “Buzz” Aldrin set up an array of small re?ectors on
the moon, facing them toward Earth. At the same time, two
teams of astrophysicists, one at the University of California’sLick Observatory and
the other at the University of Texas’s
McDonald Observatory, were preparing small instrumentson two big telescopes. Ten days
later, the Lick team pointed
its
telescope
at
the
precise
location
of
the
re?ectors
on
the://www.51wendang.com/doc/f25c1567573777508636613apar
moon and sent a small pulse of power into the hardware theyhad added to it. A few
days after that, the McDonald teamwent through the same steps. In the heart of each
telescope,a narrow beam of extraordinarily pure red light emergedfrom a synthetic
ruby crystal, pierced the sky, and enteredthe near vacuum of space. The two rays were
still only athousand yards wide after traveling 240,000miles to illumi-nate the
moon-based re?ectors. Slightly more than a secondafter each light beam hit its target,
the crews in Californiaand Texas detected its faint re?ection. The brief time
inter-val between launch and detection of these light pulses per-mitted calculation
of the distance to the moon to within aninch—a measurement of unprecedented
precision.
The ruby crystal for each light source was the heart of alaser (an acronym for light
ampli?cation by stimulated emis-sion of radiation), which is a device ?rst
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demonstrated
in1960http://www.51wendang.com/doc/f25c1567573777508636613a,
just
nine years earlier. A laser beam re?ected from the
moon to measure its distance is only one dramatic illustra-tion of the spectacular
quality of laser light. There are many
other more mundane, practical uses such as in surveyingland and grading roads, as
well as myriad everyday uses—
NES STRAIranging from compact disc play-s
rehers to grocery-store checkout rcaesdevices.
eR otoThe smallest lasers are so tiny
hP F9one cannot see them without a 124P ,microscope. Thousands can be reytnIbuilt
on semiconductor chips. cM inThe biggest lasers consume as eD & llimuch electricity
as a small
Wtown. About 45miles from my of?ce in Berkeley is theLasers are commonly used in
eyeLawrence Livermore National Laboratory, which has somesurgery to correct
defective vision.
of the world’s most powerful lasers. One set of them, collec-tively called NOVA,
produces
ten
individualhttp://www.51wendang.com/doc/f25c1567573777508636613a
laser beams thatconverge to a spot the size of a pinhead and generate temper-atures
of many millions of degrees. Such intensely concen-trated energies are essential for
experiments that can showphysicists how to create conditions for nuclear fusion.
TheLivermore team hopes thereby to ?nd a way to generate elec-tricity ef?ciently,
with little pollution or radioactive wastes.For several years after the laser’s
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invention, colleaguesliked to tease me about it, saying, “That’s a great idea,
butit’s a solution looking for a problem.” The truth is, none ofus who worked on
the ?rst lasers ever imagined how manyuses there might eventually be. But that was
not our motiva-tion. In fact, many of today’s practical technologies have re-sulted
from basic scienti?c research done years to decadesbefore. The people involved,
motivated mainly by curiosity,often have little idea as to where their research will
eventu-ally lead.
BEAM LINE
://www.51wendang.com/doc/f25c1567573777508636613aar21
L
IKETHETRANSISTOR,
the laser and its progenitor themaser (an acronym for micro-wave amplification by
stimulatedprinciples, that if photons can beabsorbed by atoms and boost themto higher
energy states, then light canalso prod an atom to give up itsAn early small laser
made of semicon-ducting material (right) compared with aU.S.dime.
22SUMMER/FALL 2000
emission of radiation) resulted fromthe application of quantum me-chanics to
electronics after WorldWar II. Together with other advances,they helped spawn a new
disciplinein
applied
physics
known
since
thelate
1950s
as
“quantum
electronics.”Since early in the twentieth cen-tury, physicists such as Niels
Bohr,Louis de Broglie, and Albert Einsteinlearned how molecules and atomsabsorb and
emit light—or any otherelectromagnetic radiation—on thebasis of the newly
discovered laws ofquantum mechanics. When atoms ormolecules absorb light,
onehttp://www.51wendang.com/doc/f25c1567573777508636613a mightsay that parts of
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them wiggle backand forth or twirl with new, addedenergy. Quantum mechanics
requiresthat they store energy in very spe-ci?c ways, with precise, discrete lev-els
of energy. An atom or a moleculecan exist in either its ground (lowest)energy state
or any of a set of higher(quantized) levels, but not at energiesbetween those levels.
Therefore theyonly absorb light of certain wave-lengths, and no others, because
thewavelength of light determines theenergy of its individual photons (seebox on
right). As atoms or moleculesdrop from higher back to lower en-ergy levels, they emit
photons of thesame energies or wavelengths asthose they can absorb. This processis
usually spontaneous, and this kindof light is normally emitted whenthese atoms or
molecules glow, as ina ?uorescent light bulb or neon lamp,radiating in nearly all
directions.Einstein was the ?rst to recognizeclearly, from basic thermodynamic
energy andhttp://www.51wendang.com/doc/f25c1567573777508636613a drop down to a
lowerlevel. One photon hits the atom, andtwo come out. When this happens,the emitted
photon takes off inprecisely the same direction as thelight that stimulated the energy
loss,with the two waves exactly in step(or in the same “phase”). This “stim-ulated
emission” results in coherentamplification, or amplification of awave at exactly
the same frequencyand phase.
Both absorption and stimulatedemission can occur simultaneously.As a light wave comes
along, it canthus excite some atoms that are inlower energy states into higher
statesand, at the same time, induce someof those in higher states to fall backdown
to lower states. If there aremore atoms in the upper states thanin the lower states,
more light isemitted than absorbed. In short, thelight gets stronger. It comes
outbrighter than it went in.
The reason why light is usuallyabsorbed in materials is that sub-stances almost always
have moreatoms and mhttp://www.51wendang.com/doc/f25c1567573777508636613aolecules
sitting in lowerenergy states than in higher ones:more photons are absorbed
thanemitted. Thus we do not expect toshine a light through a piece of glassand see
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it come out the other sidebrighter than it went in. Yet this isprecisely what happens
with lasers.The trick in making a laser is toproduce a material in which theenergies
of the atoms or moleculespresent have been put in a veryabnormal condition, with more
of
them in excited states than in the
How Lasers Work
B
ECAUSEOFQUANTUM
mechanics, atoms and moleculescan exist only in discrete states withvery speci?c
values of their total energy.They change from one state to another byabsorbing or
emitting photons whose ener-gies correspond to the difference betweentwo such energy
levels. This process, whichgenerally occurs by an electron jumpingbetween two
adjacent quantum states, isillustrated in the accompanying drawings.
(http://www.51wendang.com/doc/f25c1567573777508636613aa)
Stimulated emission of photons, the basisof laser operation, differs from the usual
ab-sorption and spontaneous emission. Whenan atom or molecule in the “ground”
stateabsorbs a photon, it is raised to a higherenergy state (top). This excited state
maythen radiate spontaneously, emitting a pho-ton of the same energy and reverting
backto the ground state (middle). But an excitedatom or molecule can also be
stimulated toemit a photon when struck by an approach-ing photon (bottom). In this
case, there isnow a second photon in addition to thestimulating photon; it has
precisely thesame wavelength and travels exactly inphase with the ?rst.
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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
groundhttp://www.51wendang.com/doc/f25c1567573777508636613a state.
(b)Light pumped in and absorbed by these atoms raises most of them to the excitedstate.
(c) Although some of the spontaneously emitted photons pass out of the crys-tal, the
cascade begins when an excited atom emits a photon parallel to the axis ofthe crystal.
This photon stimulates another atom to contribute a second photon, and(d) the process
continues as the cascading photons are re?ected back and forth be-tween the parallel
ends of the crystal. (e) Because the right-hand end is only partiallyre?ecting, the
beam eventually passes out this end when its intensity becomes greatenough. This beam
can be very powerful.
BEAM LINE23
None of us who workedon the ?rst lasers everimagined how many usesthere might
eventually be.Many of today’s practicaltechnologies have resulted
from basic scienti?cresearch done yearsto decades before.
24
SUMMER/FALL 2000
ground, or lower, shttp://www.51wendang.com/doc/f25c1567573777508636613atates. A
wave ofelectromagnetic energy of the properfrequency traveling through such
apeculiar substance will pick up ratherthan lose energy. The increase in thenumber
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of photons associated withthis wave represents ampli?cation—light amplification by
stimulatedemission of radiation.
If this amplification is not verylarge on a single pass of the wavethrough the material,
there are waysto beef it up. For example, two par-allel mirrors—between which
thelight is re?ected back and forth, withexcited molecules (or atoms) in
themiddle—can build up the wave. Get-ting the highly directional laser beamout of
the device is just a matter ofone mirror being made partiallytransparent, so that
when the inter-nally reflecting beam gets strongenough, a substantial amount of
itspower shoots right on through oneend of the device.
The way this manipulation ofphysical laws came about, with themany false starts and
blind alleys onthe wayhttp://www.51wendang.com/doc/f25c1567573777508636613a to its
realization, is the sub-ject of my book, How the Laser Hap-pened. Brie?y summarized
in this ar-ticle, it also describes my odyssey asa scientist and its unpredictable
andperhaps natural path to the maserand laser. This story is interwovenwith the way
the field of quantumelectronics grew, rapidly and strik-ingly, owing to a variety
of importantcontributors, their cooperation andcompetitiveness.
D
URINGTHELATE1940s
and early 1950s, I was exam-ining molecules with micro-waves at Columbia
University—do-ing microwave spectroscopy. I tried
to find a way to generate wavesshorter than those produced by theklystrons and
magnetrons developedfor radar in World War II. One day Isuddenly had an idea—use
moleculesand the stimulated emission fromthem. With graduate student JimGordon and
postdoc Herb Zeiger, Idecided to experiment ?rst with am-monia (NHradiation at a
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wavelength
of
about3)
molecules,
which
http://www.51wendang.com/doc/f25c1567573777508636613aemit1 centimeter. After a
couple of yearsof effort, the idea worked. We chris-tened this device the “maser.”
Itproved so interesting that for a whileI put off my original goal of trying togenerate
even shorter wavelengths.In 1954, shortly after Gordon andI built our second maser
and showedthat the frequency of its microwaveradiation was indeed remarkablypure,
I visited Denmark and sawNiels Bohr. As we were walkingalong the street together,
he askedme what I was doing. I described themaser and its amazing performance.“But
that is not possible!” he ex-claimed. I assured him it was.
Similarly, at a cocktail party inPrinceton, New Jersey, the Hungar-ian mathematician
John von Neu-mann asked what I was working on.I told him about the maser and thepurity
of its frequency.
“That can’t be right!” he declared.But it was, I replied, telling him ithad already
been
demonstrated.Such
protests
were
not
offhandopinions
about
obscuhttp://www.51wendang.com/doc/f25c1567573777508636613are aspects ofphysics;
they came from the marrowof these men’s bones. Their objec-tions were founded on
principle—theHeisenberg
uncertainty
principle.A
central
tenet
of
quantum
mechan-ics, this principle is among the coreachievements that occurred during
a phenomenal burst of creativity inthe ?rst few decades of the twentiethcentury. As
its name implies, it de-scribes the impossibility of achiev-ing absolute knowledge
of all the as-pects of a system’s condition. Thereis a price to be paid in
attemptingto measure or define one aspect ofa specific particle to very great
ex-actness. One must surrender knowl-edge of, or control over, some otherfeature.
A corollary of this principle, onwhich the maser’s doubters stum-bled, is that one
cannot measure anobject’s frequency (or energy) to greataccuracy in an arbitrarily
short
timeinterval.
Measurements
made
over
afinite
period
of
time
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automaticallyimpose
uncertainty
on
the
obhttp://www.51wendang.com/doc/f25c1567573777508636613aservedfrequency.
To many physicists steeped in theuncertainty principle, the maser’sperformance,
at ?rst blush, made nosense at all. Molecules race throughits cavity, spending so
little timethere—about one ten-thousandth ofa second—that it seemed impossiblefor
the frequency of the output mi-crowave radiation to be so narrowlyde?ned. Yet that
is exactly what hap-pens in the maser.
There is good reason that the un-certainty principle does not apply sosimply here.
The maser (and by anal-ogy, the laser) does not tell you any-thing about the energy
or frequen-cy of any specific molecule. Whena molecule (or atom) is stimulated
toradiate, it must produce exactly thesame frequency as the stimulatingradiation.
In addition, this radiationrepresents the average of a large num-ber of molecules
(or atoms) work-ing together. Each individual mole-cule remains anonymous, not
accurately
measured
or
tracked.
arihttp://www.51wendang.com/doc/f25c1567573777508636613ases
Theprecision
from
factors
thatmollify the apparent demands of theuncertainty principle.
I am not sure that I ever did con-vince Bohr. On that sidewalk in Den-mark, he told
me emphatically thatif molecules zip through the maserso quickly, their emission
lines mustbe broad. After I persisted, howev-er, he relented.
“ Oh, well, yes,” he said; “Maybeyou are right.” But my impressionNOVA, the
world’s largest and most pow-
was that he was just trying to be po-erful laser, at the Lawrence Livermorelite to
a younger physicist.
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National Laboratory in California. Its 10After our ?rst chat at that Prince-laser
beams can deliver 15trillion wattston party, von Neumann wanderedof light in a pulse
lasting 3billionths of aoff and had another drink. In aboutsecond. With a modi?ed
single beam, it?fteen minutes, he was back.
has produced 1,250trillion watts for half“Yes, you’re right,” he snapped.
a trillionthttp://www.51wendang.com/doc/f25c1567573777508636613ah of a second.
(CourtesyLawrence Livermore NationalClearly, he had seen the point.
Laboratory)
BEAM LINE25
The developmentof the laser followedno script except
He seemed very interested, and heasked me about the possibility of do-ing something
similar at shorterwavelengths using semiconductors.Only later did I learn from
hisposthumous papers, in a September1953letter he had written to EdwardTeller, that
he had already proposedproducing a cascade of stimulated in-frared radiation in
semiconductorsby exciting electrons with intenseneutron bombardment. His idea
wasalmost a laser, but he had notthought of employing a reflectingcavity nor of using
the coherent prop-erties of stimulated radiation.
I
NTHELATESUMMERof
1957, I felt it was high time I
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moved on to the original goal thatfostered the maser idea: oscillatorsthat work at
wavelengths
apprecia-bly
shorter
http://www.51wendang.com/doc/f25c1567573777508636613amillimeter,
than
1
beyondwhat
standard electronics couldachieve. For some time I had beenthinking off and on about
this goal,hoping that a great idea would popinto my head. But since nothing
hadspontaneously occurred to me, I de-cided I had to take time for concen-trated
thought.
A major problem to overcome wasthat the rate of energy radiation froma molecule
increases as the fourthpower of the frequency. Thus to keepmolecules or atoms excited
in aregime to amplify at a wavelength of,say, 0.1millimeter instead of 1 cen-timeter
requires an increase in pump-ing power by many orders of mag-nitude. Another problem
was that forgas molecules or atoms, Doppler ef-fects increasingly broaden the
emis-sion spectrum as the wavelength getssmaller. That means there is less
am-pli?cation per molecule available to26
SUMMER/FALL 2000
to hew to the naturethe total power required—even toamplify visible light—is not
neces-sarily prohhttp://www.51wendang.com/doc/f25c1567573777508636613aibitive.
of scientists gropingNot only were there no clearpenalties in such a leapfrog to
veryshort wavelengths or high frequencies,to understand,this approach offered big
advantages.In the near-infrared and visible re-gions, we already had plenty of ex-to
explore, andperience and equipment. By contrast,wavelengths near 0.1mm and
tech-niques to handle them were rela-to create.
tively unknown. It was time to takea big step.
Still, there remained another ma-jor concern: the resonant cavity. Tocontain enough
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atoms or molecules,the cavity would have to be muchdrive any speci?c resonant
frequencylonger than the wavelength of theinside a cavity.
radiation—probably thousands ofAs I played with the variety oftimes longer. This
meant, I feared,possible molecular and atomic tran-that no cavity could be very
selectivesitions, and the methods of excit-for one and only one frequency. Theing
them,
what
is
well-khttp://www.51wendang.com/doc/f25c1567573777508636613anown
todaygreat size of the cavity, comparedsuddenly became clear to me: it isto a single
wavelength, meant thatjust as easy, and probably easier, tomany closely spaced but
slightly
dif-go
right
on
down
to
really
shortferent
wavelengths
would
resonate.wavelengths—to the near-infrared orBy great good fortune, I got helpeven
optical regions—as to go downand another good idea before I pro-one smaller step
at a time. This wasceeded any further. I had recently be-a revelation, like stepping
throughgun a consulting job at Bell Labs,a door into a room I did not suspectwhere
my brother-in-law and formerexisted.
postdoc Arthur Schawlow was work-The Doppler effect does indeed in-ing. I naturally
told him that I hadcreasingly smear out the frequencybeen thinking about such
opticalof response of an atom (or molecule)masers, and he was very interestedas one
goes to shorter wavelengths,because he had also been thinking inbut there is a
chttp://www.51wendang.com/doc/f25c1567573777508636613aompensating factorthat very
direction.
that comes into play. The number ofWe talked over the cavity prob-atoms required to
amplify a wave bylem, and Art came up with the so-a given amount does not
increase,lution. I had been considering abecause atoms give up their quantarather
well-enclosed cavity, with mir-more readily at higher frequencies.rors on the ends
and holes in theAnd while the power needed to keepsides only large enough to providea
certain number of atoms in exciteda way to pump energy into the gasstates increases
with the frequency,
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and to kill some of the directions in
which the waves might bounce. Hesuggested instead that we use justtwo plates, two
simple mirrors, andleave off the sides altogether. Sucharrangements of parallel
mirrors werealready used at the time in optics;they are called Fabry–Perot
interfer-ometers.
Art
recognized
that
without
thesides,
many
oscillating
thatdhttp://www.51wendang.com/doc/f25c1567573777508636613aepend
on
modes
internal
re?ections wouldeliminate themselves. Any wave hit-ting either end mirror at an
anglewould eventually walk itself out ofthe cavity—and so not build up en-ergy. The
only modes that could sur-vive and oscillate, then, would bewaves re?ected exactly
straight backand forth between the two mirrors.More detailed studies showed thatthe
size of the mirrors and the dis-tance between them could even bechosen so that only
one frequencywould be likely to oscillate. To besure, any wavelength that ?t an ex-act
number of times between themirrors could resonate in such a cav-ity, just as a piano
string produces notjust one pure frequency but alsomany higher harmonics. In a
well-designed system, however, only onefrequency will fall squarely at thetransition
energy of the mediumwithin it. Mathematically and phys-ically, it was “neat.”
Art and I agreed to write a paperjointly on optical masers. It seemedclear that we
could achttp://www.51wendang.com/doc/f25c1567573777508636613atually buildone, but
it would take time. We spentnine months working on and off inour spare time to write
the paper. Weneeded to clear up the engineeringand some specific details, such aswhat
material to use, and to clarifythe theory. By August 1958the man-uscript was complete,
and the Bell
Labs patent lawyers told us that theyJames Gordon, Nikolai Basov, Herberthad done
their job protecting itsZeiger, Alexander Prokhorov, and authorideas. The Physical
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ReviewpublishedCharles Townes (left to right) attendingit in the December 15, 1958,
issue.the ?rst international conference onIn September 1959the ?rst scien-quantum
electronics in 1959.
ti?c meeting on quantum electronicsand resonance phenomena occurredat the Shawanga
Lodge in New York’sCatskill Mountains. In retrospect, itrepresented the formal birth
of themaser and its related physics as a dis-tinct subdiscipline. At that meet-ing
Schawlow
delivered
a
general
talkohttp://www.51wendang.com/doc/f25c1567573777508636613an optical masers.
Listening with interest wasTheodore Maiman from the HughesResearch Laboratories in
Culver City,California. He had been workingwith ruby masers and says he was al-ready
thinking about using ruby asthe medium for a laser. Ted listenedclosely to the rundown
on the pos-sibility of a solid-state ruby laser,about which Art was not too hope-ful.
“It may well be that more suit-able solid materials can be found,”he noted, “and
we are looking forthem.
”
BEAM LINE27
Maiman felt that Schawlow wasfar too pessimstic and left the meet-ing intent on
building a solid-stateruby laser. In subsequent months Tedmade striking measurements
onruby, showing that its lowest energylevel could be partially emptied byexcitation
with intense light. Hethen pushed on toward still brighterexcitation sources. On May
16, 1960,he fired up a flash lamp wrappedaround a ruby crystal about 1.5cmlong and
produced
the
?rshttp://www.51wendang.com/doc/f25c1567573777508636613at
operatinglaser.
The evidence that it worked wassomewhat indirect. The Hughesgroup did not set it up
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to shine a spotof light on the wall. No such ?ash ofa beam had been seen, which leftroom
for doubt about just what theyhad obtained. But the instrumentshad shown a substantial
change inthe fluorescence spectrum of theruby; it became much narrower, aclear sign
that emission had beenstimulated, and the radiation peakedat just the wavelengths
that weremost favored for such action. A shortwhile later, both the Hughes
re-searchers and Schawlow at Bell Labsindependently demonstrated power-ful ?ashes
of directed light that madespots on the wall—clear intuitiveproof that a laser is
indeed working.
I
TISNOTEWORTHYthat al-
most all lasers were ?rst built inindustrial labs. Part of the reasonfor industry’s
success is that once itsimportance becomes apparent, in-dustrial laboratories can
devote
moreresources
ahttp://www.51wendang.com/doc/f25c1567573777508636613and
concentrated effort toa problem than can a university.When the goal is clear, industry
canbe effective. But the ?rst lasers wereinvented and built by young scien-
28
SUMMER/FALL 2000
The Quantum
&The Cosmos
(Courtesy Jason Ware, http://www.galaxyphoto.com)
ONENORMALLYTHINKSthat quantum mechanics is only
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“ When onetugs at asingle thinginNature, he?nds ithitched to the rest of
theUniverse.”
—John Muir
relevant on submicroscopic scales, operating in the domain ofatomic, nuclear, and
particle physics. But if our most excitingideas about the evolution of the early
Universe are correct, thenthe imprint of the quantum world is visible on
astronomicalscales. The possibility that quantum mechanics shaped the
largest structures in the Universe is one of the theories to comefrom the marriage
of the quantum and the cosmos.WHAT’S OUT THERE?
On a dhttp://www.51wendang.com/doc/f25c1567573777508636613aark clear night the sky
offersmuch to see. With the unaided eye onecan see things in our solar system suchas
planets, as well as extrasolar objectslike stars. Nearly everything visible byeye
resides within our own Milky WayGalaxy. But with a little patience andskill it’s
possible to find a few extra-galactic objects. The AndromedaGalaxy, 2.4million
light-years distant,is visible as a faint nebulous region,and from the Southern
Hemispheretwo small nearby galaxies (if 170,000
light-years can be considered nearby),the Magellanic Clouds, can also beseen with
the unaided eye.
While the preponderance of objectsseen by eye are galactic, the viewthrough large
telescopes reveals theuniverse beyond the Milky Way. Evenwith the telescopes of the
nineteenthcentury, the great British astronomerSir WilliamHerschel discovered
about2,500galaxies, and his son, Sir JohnHerschel, discovered an additionalthousand
(although
neither
of
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thhttp://www.51wendang.com/doc/f25c1567573777508636613aeHerschels knew that the
objects theydiscovered were extragalactic). As
BEAM LINE
29
Galaxies ?ll the Hubble Deep Field, oneastronomers built larger telescopes
of the most distant optical views of theUniverse. The dimmest ones, some asand looked
deeper into space, thefaint as 30th magnitude (about four bil-number of known galaxies
grew.lion times fainter than stars visible to theAlthough no one has ever
botheredunaided eye), are very distant and rep-to count, astronomers have
identi-resent what the Universe looked ike in?ed about four million galaxies. Andthe
extreme past, perhaps less than onethere are a lot more out there!
billion years after the Big Bang. To makeOur deepest view into the Uni-this Deep Field
image, astronomers se-verse is the Hubble Deep Field. Thelected an uncluttered area
of the sky inthe constellation Ursa Major and pointedresult of a 10-day exposure of
a
verythe
Hubbhttp://www.51wendang.com/doc/f25c1567573777508636613ale
Space
Telescope at a singlesmall region of the sky by NASA’sspot for 10days accumulating
and com-Hubble Space Telescope, the Hubblebining many separate exposures. WithDeep
Field reveals a universe full ofeach additional exposure, fainter objectsgalaxies
as far as Hubble’s eye can seewere revealed. The ?nal result can be(photo above).
If the Space Telescopeused to explore the mysteries of galaxycould take the time to
survey the en-evolution and the early Universe.
(Courtesy R. Williams, The tire sky to the depth of the DeepHDFTeam,STScl, and NASA)
Field, it would ?nd more than 50bil-lion galaxies.
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Although large galaxies containat least 100billion stars and stretchacross
100,000light-years or moreof space, they aren’t the biggestthings in the Universe.
Just as starsare part of galaxies, galaxies are partof larger structures.
Many
galaxies
are
members
ofgroups
containing
a
few
dozen
gahttp://www.51wendang.com/doc/f25c1567573777508636613alaxies,
or
to
even
ahundred
larger
assem-blages known as clusters, containing
30SUMMER/FALL 2000
several thousand galaxies. Clustersof galaxies are part of even largerassociations
called superclusters,containing dozens of clusters spreadout over 100million
light-years ofspace. Even superclusters may not bethe largest things in the
Universe.The largest surveys of the Universesuggest to some astronomers thatgalaxies
are organized on two-dimensional sheet-like structures,while others believe that
galaxies liealong extended one-dimensional ?l-aments. The exact nature of
howgalaxies are arranged in the Universeis still a matter of debate among
cos-mologists. A picture of the arrange-ment of galaxies on the largest scalesis only
now emerging.
Not all of the Universe is visibleto the eye. In addition to patternsin the arrangement
of matter in thevisible Universe, there is also a struc-ture to the background
radiation.The
Univhttp://www.51wendang.com/doc/f25c1567573777508636613aerse
is
awash in a ther-mal bath of radiation, with a tem-perature of three degrees above
ab-solute zero (3 K or -270 C). Invisibleto the human eye, the backgroundradiation
is a remnant of the hotprimeval ?reball. First discovered in1965by Arno Penzias and
RobertWilson, it is a fundamental predic-tion of the Big Bang theory.
Soon after Penzias and Wilson dis-covered the background radiation,the search began
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for
variations
in
thetemperature
of
the
universe.
Fornearly
30years,
astrophysicistssearched in vain for regions of the dis-tant Universe that were hotter
orcolder than average. It was not until1992that a team of astronomers us-ing the
Cosmic Background ExplorerSatellite (COBE) discovered an in-trinsic pattern in the
temperature of
the Universe. Since the time of theCOBEdiscovery, a pattern of tem-perature
variations has been mea-sured with increasing precision bydozens of balloon-borne
and
terres-trial
observatihttp://www.51wendang.com/doc/f25c1567573777508636613aons. A new era of
pre-cision cosmological observations isstarting. Sometime in 2001NASAwill launch a
new satellite, theMicrowave Anisotropy Probe (MAP),and sometime in 2007the
EuropeanSpace Agency will launch an evenmore ambitious effort, the PlanckExplorer,
to study temperature vari-ations in the cosmic backgroundradiation.
Even if our eyes were sensitive tomicrowave radiation, we would havea hard time
discerning a pattern oftemperature fluctuations since thehottest and coldest regions
of thebackground radiation are only aboutone-thousandth of a percent hotterand colder
than average.
Although small in magnitude, thebackground temperature ?uctuationsare large in
importance since theygive us a snapshot of structure in theUniverse when the
background pho-tons last scattered, about 300,000years after the Bang.
WHY IS IT THERE?
A
really
good
answer
to
a
deep
ques-tion
usually
leads
deeperquestihttp://www.51wendang.com/doc/f25c1567573777508636613aons.
to
Once
even
we
discover what’sin the Universe, a deeper questionarises: Why is it there? Why are
starsarranged into galaxies, galaxies intoclusters, clusters into superclusters,and
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so on? Why are there small vari-ations in the temperature of the Uni-verse?
Part of the answer involves grav-ity. Everything we see in the Universe
is the result of gravity. Every timeyou see a star the imprint of gravityis shining
at you. Today we observenew stars forming within giant inter-stellar gas clouds, such
as those foundat the center of the Orion Nebula just1,500light-years away (see photo
onnext page).
Interstellar clouds are not smoothand uniform; they contain regionswhere the density
of material is largerthan in surrounding regions. Thedense regions within the clouds
arethe seeds around which stars growthrough the irresistible force of grav-ity. The
dense
regions
pull
in
nearbymaterial
through
the
force
of
gravity,whichttp://www.51wendang.com/doc/f25c1567573777508636613ah compresses the
material un-til it becomes hot and dense enoughfor nuclear reactions to commenceand
form stars.
About ?ve billion years ago in ourlittle corner of the Milky Way, grav-ity started
to pull together gas anddust to form our solar system. Thisfashioning of structure
in our localneighborhood is just a small part ofa process that started about
12billionyears ago on a grander scale through-out the Universe.
For the ?rst 300centuries after theBig Bang, the Universe expanded toorapidly for
gravity to fashion struc-ture. Finally, 30,000years after theBang (30,000AB), the
expansion hadslowed enough for gravity to beginthe long relentless process of
pullingtogether matter to form the Universewe see today.
We are quite con?dent that grav-ity shaped the Universe becauseastrophysicists can
simulate in amatter of days what Nature required12billion years to accomplish.
Start-ing
with
the
Universe
as
it
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existhttp://www.51wendang.com/doc/f25c1567573777508636613aed30,000AB
, large supercomputers can
The microwave radiation from the sky, asseen by COBE. The radiation has anaverage
temperature of 2.73degreesCentigrade above absolute zero. Herethe dark and light
spots are 1part in100,000warmer or colder than the rest.They reveal gigantic
structures stretch-ing across enormous regions of space.The distinct regions of space
are
believed to be the primordial seeds pro-duced during the Big Bang. Scientistsbelieve
these anomalous regionsevolved into the galaxies and largerstructures of the
present-day Universe.(Courtesy Lawrence BerkeleyLaboratory and NASA)
BEAM LINE31
Galaxies and galaxy clusters are notcalculate how small primordial seeds
evenly distributed throughout the Uni-grew to become the giant galaxies,verse,
instead they are arranged in clus-ters, ?laments, bubbles, and vast sheet-clusters
of
galaxies,
superclusters,like
thahttp://www.51wendang.com/doc/f25c1567573777508636613at
projections
stretch
acrosswalls,
and ?laments we see through-hundreds of millions of light-years ofout the Universe.
space. The goal of the Las CampanasGravity alone cannot be the ?nalRedshift Survey
is to provide a largeanswer to the question of why mat-galaxy sample which permits
detailedter in the Universe has such a richand accurate analyses of the propertiesand
varied arrangement. For the forceof galaxies in the local universe. Thisof gravity
to pull things togethermap shows a wedge through the Uni-verse containing more than
20,000requires small initial seeds where thegalaxies (each dot is a galaxy).density
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is larger than the surround-(Courtesy Las Campanas Redshift ing regions. In a very
real sense, theSurvey)
fact there is anything in the Universeat all is because there were primor-dial seeds
in the Universe. While theforce of gravity is inexorable, struc-ture cannot grow
without
the
seedsto
cultivate.
Just
as
though
thttp://www.51wendang.com/doc/f25c1567573777508636613aherewouldn’t be any seeds
to trigger star
32SUMMER/FALL 2000
The Orion nebula, one of the nearbystar-forming regions in the Milky Waygalaxy.
(Courtesy StScl and NASA)
formation within the Orion Nebulaif the gas and dust were perfectlyuniform, structure
would never haveformed if the entire Universe wascompletely uniform. Without
pri-mordial seeds in the Universe30,000AB, gravity would be unableto shape the
Universe into the formwe now see. A seedless universewould be a pretty boring place
to live,because matter would remain per-fectly uniform rather than assem-bling into
discrete structures.
The pattern of structure we see inthe Universe today re?ects the pat-tern of initial
seeds. Seeds have to beinserted by hand into the computersimulations of the formation
of struc-ture. Since the aim of cosmology isto understand the structure of theUniverse
on
the
basis
of
physicallaws,
we
just
stohttp://www.51wendang.com/doc/f25c1567573777508636613ary
can’t
bysaying
end
the
structure
exists because therewere primordial seeds. For a com-plete answer to the questions
of whyare there things in the Universe, wehave to know what planted the pri-mordial
seeds.
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In the microworld of subatomicphysics, there is an inherent uncer-tainty about the
positions andenergies of particles. According tothe uncertainty principle, energy
isn’t
always conserved—it can be violatedfor a brief period of time. Becausequantum
mechanics applies to themicroworld, only tiny amounts ofenergy are involved, and the
timeduring which energy is out of balanceis exceedingly short.
One of the consequences of theuncertainty principle is that a regionof seemingly empty
space is not reallyempty, but is a seething froth inwhich every sort of fundamental
par-ticle pops out of empty space for abrief instant before annihilating withits
antiparticle
and
disappearing.Empty
space
only
looks
like
aquiet,
calm
plachttp://www.51wendang.com/doc/f25c1567573777508636613ae because we can’tsee
Nature operating on submicro-scopic scales. In order to see thesequantum ?uctuations
we would haveto take a small region of space andblow it up in size. Of course that
isnot possible in any terrestrial labo-ratory, so to observe the quantumfluctuations
we have to use a labo-ratory as large as the entire Universe.In the early-Universe
theory knownas in?ation, space once exploded sorapidly that the patternof
microscopicvacuum quantum fluctuations be-came frozen into the fabric of space.The
expansion of the Universestretched the microscopic pattern ofquantum ?uctuations to
astronom-ical size.
Much later, the pattern of whatonce were quantum ?uctuations ofthe vacuum appear as
small ?uctua-tions in the mass density of theUniverse and variations in the
tem-perature of the background radiation.If this theory is correct, then seedsof
structure
are
nothing
more
thanpatterns
of
quantum
fluctuationsfrom
the
inflathttp://www.51wendang.com/doc/f25c1567573777508636613aionary era. In a very
One
of
several
computer
simulations
ofthe
large-scale
structure
of
the
Universe(spatial distribution of galaxies) carriedout by the VIRGOcollaboration.
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Thesesimulations attempt to understand theobserved large-scale structure by test-ing
various physics models. (CourtesyVIRGOCollaboration)
For Additional Information on the Internet
Rocky
Kolb.
http://www-astro-theory.fnal.gov/Personal/rocky/welcome.htmlJason
Ware. http://www.galaxyphoto.com
Hubble
Space
Telescope
Public
Pictures.
http://oposite.stsci.edu/pubinfo/Pictures.html
NASAImage eXchange. http://nix.nasa.gov/
VIRGOConsortium. http://star-www.dur.ac.uk/~frazerp/virgo/virgo.htmlCOBESky Map.
http://www.lbl.gov/LBL-PID/George-Smoot.html
Las Campanas Redshift Survey.
http://manaslu.astro.utoronto.ca/~lin/lcrs.htmlSloan
Digital
Sky
Survey.
http://www.sdss.org
BEAM LINE33
Gehttp://www.51wendang.com/doc/f25c1567573777508636613atting to Know Y
Humankind haswondered since the beginning of historywhat are the funda-mental
constituentsof
matter.
Today’s
listincludes
about
particles.Tomorrow’s listpromises to be longerstill, with no end
in sight.
25elementary
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34SUMMER/FALL 2000
by ROBERT
L. JAFFE
THEURGETOREDUCETHEFORMSofmatter to a
few elementary constituents must be very ancient. By450BCE, Empedocles had already
developed or inherited a“standard model” in which everything was composed offour
elements—Air, Earth, Fire, and Water. Thinking aboutthe materials available to him,
this is not a bad list. But as apredictive model of Nature, it has some obvious
shortcom-ings. Successive generations have evolved increasinglysophisticated
standard models, each with its own list of“fundamental” constituents. The length
of the list has ?uc-tuated over the years, as shown on the next page. TheGreeks are
actuallhttp://www.51wendang.com/doc/f25c1567573777508636613ay tied for the minimum
with four. Thechemists of the 19th century and the particle physicists ofthe 1950s
and 1960s pushed the number up toward 100beforesome revolutionary development reduced
it dramatically.Today’s list includes about 25elementary particles, thoughit could
be either higher or lower depending on how youcount. Tomorrow’s list—the product
of the next generationof accelerators—promises to be longer still, with no end
insight. In fact, modern speculations always seem to increaserather than decrease
the number of fundamental con-stituents. Superstring theorists dream of unifying all
theforces and
forms of matter into a single essence, but so farthey have little clue
how the diversity of our observed worldwould devolve from this perfect form. Others
have pointedout that Nature at the shortest distances and highest ener-gies might
be quite random and chaotic, and that the forceswe feel and the particles we observe
are spechttp://www.51wendang.com/doc/f25c1567573777508636613aial only in thatthey
persist longer and propagate further than all the rest.Two lessons stand out in this
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cartoon history. First, whatserves as a “fundamental constituent” changes with
timeand depends on what sorts of questions one asks. The older
BEAM LINE
35
they were, in the case at hand. “Ef-fective” is the right word becauseit means both
“useful” and “stand-EFORELOOKINGating in place of,” both of which applywhere we
are today, let’s takein this case. The chemical elementsa brief tour of the two
mostare very useful tools to understand
useful “atomic” descriptions of theeveryday phenomena, and theypast: the standard
models of chem-“stand in place of” the complex mo-istry and nuclear physics, shown
be-tions of electrons around atomiclow. Both provide very effective de-nuclei, which
are
largely
irrelevantscriptions
applications.range
of
phenomena
within
of
Actuallyhttp://www.51wendang.com/doc/f25c1567573777508636613a
theirfor
everyday
applicability.
theChemistry
and
nuclear physicsterm “effective” has a technicalare both “effective theories”
becausemeaning here. For physicists an “ef-quantum mechanics shields themfective
theory” is one based on build-from the complexity that lies be-Below: The
“elementary” particles of the
ing blocks known not to be elemen-neath. This feature of quantum me-four schemes that
have dominated
tary, but which can be treated as ifchanics is largely responsible for themodern
science.
orderliness we perceive in the phys-
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ical world, and it deserves more dis-cussion. Consider a familiar sub-stance such
as water. At the simplestlevel, a chemist views pure wateras a vast number of identical
mole-cules, each composed of two hydro-gen atoms bound to an oxygen atom.Deep within
the atoms are nuclei:eight protons and eight neutrons foran oxygen nucleus, a single
protonfor
hydrogen.
Within
the
protons
andneutrons
are
quarks
ahttp://www.51wendang.com/doc/f25c1567573777508636613and gluons.Within the quarks
and gluons, whoknows what? If classical mechanicsdescribed the world, each degree
offreedom in this teeming microcosmcould have an arbitrary amount ofexcitation energy.
When disturbed,for example by a collision withanother molecule, all the motionswithin
the water molecule could beaffected. In just this way, the Earth
and everything on it would be
thoroughly perturbed if our solar sys-tem collided with another.
are, may be more fundamental than
yesterday’s.
B
Left: A schematic view of the energylevels of classical and quantumsystems.
36SUMMER/FALL 2000
Quantum mechanics, on the
other hand, does not allow arbitrarydisruption. All excitations of themolecule are
quantized, each withits own characteristic energy. Mo-tions of the molecule as a
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whole—rotations
and
vibrations—have
thelowest
1–100milli-electron
energies,
in
the
volt
rhttp://www.51wendang.com/doc/f25c1567573777508636613aegime (1meV = 10-3eV).An
electron volt, abbreviated eV, isthe energy an electron gains fallingthrough a
potential of one volt andis a convenient unit of energy for fun-damental processes.
Excitation of theelectrons in the hydrogen and oxy-gen atoms come next, with
charac-teristic energies ranging from about10-1to 103eV. Nuclear excitations
inoxygen require millions of electronvolts (106eV = 1MeV), and excita-tions of the
quarks inside a protonrequire hundreds of MeV. Collisionsbetween water molecules at
roomtemperature transfer energies of or-der 10-2eV, enough to excite rotationsand
perhaps vibrations, but too smallto involve any of the deeper excita-tions except
very rarely. We say thatthese variables—the electrons, thenuclei, the quarks—are
“frozen.” Theenergy levels of a classical and quan-tum system are compared in the
bot-tom illustration on the previous page.They are inaccessible and unimportant.They
are
not
static—the
quarks
http://www.51wendang.com/doc/f25c1567573777508636613ainsidethe nuclei of water
molecules arewhizzing about at speeds approachingthe speed of light—however their
stateof motion cannot be changed by every-day processes. Thus there is an excel-lent
description of molecular rotationsand vibrations that knows little aboutelectrons
and nothing about nuclearstructure, quarks, or gluons. Lightquanta make a
particularly goodprobe of this “quantum ladder,” as
States of Water
vemeV
eV
GeV
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ow
av
i
siblesoftMeV
g–r
ayhardm
icrg–r
ayMolecularActiveIrrelevantIrrelevantIrrelevantAtomicFrozenActiveIrrelevantIrrel
evantNuclearFrozenFrozenActiveIrrelevantHadronic
Frozen
Frozen
Frozen
Active
Victor Weisskopf called it. As sum-The “quantum ladder” of water—themarized in
the illustration above,important degrees of freedom changeas we shorten the
wavelength ohttp://www.51wendang.com/doc/f25c1567573777508636613af lightwith the
scale on which it is probed,we increase the energy of lightdescribed here by the
wavelength ofquanta in direct proportion. As welight.
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move from microwaves to visiblelight to Xrays to gamma rays weprobe successively
deeper layers ofthe structure of a water molecule.The appropriate constituent
de-scription depends on the scale of theprobe. At one extreme, we cannothope to
describe the highest energyexcitations of water without know-ing about quarks and
gluons; on theother hand, no one needs quarks andgluons to describe the way water
isheated in a microwave oven.
P
ERHAPSTHEMOSTef-
fective theory of all was theone invented by the nuclearphysicists in the 1940s. It
reigned foronly a few years, before the discov-ery of myriad excited states of
theproton and neutron led to its aban-donment and eventual replacementwith today’s
Standard
Model
ofquarks
and
leptons.
The
nuclear
stan-dard
modhttp://www.51wendang.com/doc/f25c1567573777508636613ael was based on three
con-stituents: the proton (p); the neutron(n); and the electron (e). The neutri-no
(ndecays, and perhaps one should counte) plays a bit part in radioactivethe photon
(g), the quantum of theelectromagnetic field. So the basiclist is three, four, or ?ve,
roughly asshort as Empedocles’ and far more ef-fective at explaining Nature. Most
ofnuclear physics and astrophysics and
BEAM LINE37
There istantalizing
all of atomic, molecular, and con-densed matter physics can be un-derstood in terms
of these few con-stituents. The nuclei of atoms arebuilt up of protons and neutrons
ac-cording to fairly simple empiricalrules. Atoms, in turn, are composedof electrons
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held in orbit around nu-clei by electromagnetism. All the dif-ferent chemical
elements from hy-drogen (the lightest) to uranium (theheaviest naturally occurring)
are
justdifferent
organizations
of
electronsaround
nuclei
with
elechttp://www.51wendang.com/doc/f25c1567573777508636613atriccharge.
different
Even
the
radioactive process-es that transmute one element intoanother are well described in
thepnenegworld.
The nuclear model of the worldwas soon replaced by another. Cer-tain tell-tale
signatures that emergedearly in the 1950s made it
constituentswere
not
so
elementary
after
clear thatthese “elementary”
all.
Thesame
signatures
of
compositenesshave repeated every time one set ofconstituents is replaced by
another:Excitations. If a particle is com-posite, when it is hit hard enough
itscomponent parts will be excited intoa quasi-stable state, which laterdecays by
emitting radiation. The hy-drogen atom provides a classicexample. When hydrogen atoms
areheated so that they collide with oneanother violently, light of character-istic
frequencies is emitted. As soonas it was understood that the lightcomes from the
de-excitation of itsinner workings, hydrogen’s days asan elementary particle were
over.Similarly, during http://www.51wendang.com/doc/f25c1567573777508636613athe
1950s physicistsdiscovered that when a proton orneutron is hit hard enough,
excitedstates are formed and characteristicradiation (of light or other hadrons)38
SUMMER/FALL 2000
evidence that newrelationshipsawait discovery.
is emitted. This suggest that protonsand neutrons, like hydrogen, have in-ner
workings capable of excitationand de-excitation. Of course, if onlyfeeble energies
are available, the in-ternal structure cannot be excited,and it will not be possible
to tellwhether or not the particle is com-posite. So an experimenter needs
ahigh-energy accelerator to probe com-positeness by looking for excitations.Complex
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force laws. We have adeep prejudice that the forces be-tween elementary particles
shouldbe simple, like Coulomb’s law for theelectrostatic force between pointcharges:
F12= q1q2/r21derive from the complex motion of the2. Because theyelectrons within
the
atom,
forces
be-tween
atoms
are
nothttp://www.51wendang.com/doc/f25c1567573777508636613a simple. Nor, itturns out,
are the forces between pro-tons and neutrons. They depend onthe relative orientation
of the parti-cles and their relative velocities; theyare complicated functions of
the dis-tance between them. Nowadays theforces between the proton and neu-tron are
summarized by pages of ta-bles in the Physical Review. We nowunderstand that they
derive from the
complex quark and gluon substruc-ture within protons and neutrons.The complicated
features of forcelaws die away quickly with distance.So if an experimenter looks at
a par-ticle from far away or with lowresolution, it is not possible to tellwhether
it is composite. A high-energy accelerator is needed to probeshort distances and see
the deviationsfrom simple force laws that are tell-tale signs of compositeness.
Form factors. When two struc-tureless particles scatter, the resultsare determined
by
the
simple
forcesbetween
them.
If
one
particleshttp://www.51wendang.com/doc/f25c1567573777508636613ahas
of
the
substructure,
the scattering ismodi?ed. In general the probabilityof the scattered particle
retaining
itsidentity—this
is
known
as
“elasticscattering”—is
reduced,
becausethere is a chance that the particle willbe excited or converted into some-thing
else. The factor by which theelastic scattering probability isdiminished is known
as a “form fac-tor.” Robert Hofstadter ?rst discov-ered that the proton has a form
fac-tor in experiments performed atStanford in the 1950s. This was in-controvertible
evidence that the pro-ton is composite.
If, however, one scatters lightlyfrom a composite particle, nothingnew is excited,
and no form factor isobserved. Once again, a high-energyaccelerator is necessary to
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scatterhard enough to probe a particle’s con-stituents.
Deep inelastic scattering. Thebest proof of compositeness is, ofcourse, to detect
directly the sub-constituents out of which a parti-cle is composed. Rutherford
fhttp://www.51wendang.com/doc/f25c1567573777508636613aoundthe nucleus of the atom
by scatter-ing aparticles from a gold foil and
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