One Hundred Years of Quantum
PhysicsDaniel Kleppner and Roman Jackiw*
An informed list of the most profound scientific developments of
the 20th century is likely to include general relativity, quantum
mechanics, big bang cosmology, the unraveling of the genetic code,
evolutionary biology, and perhaps a few other topics of the reader's
choice. Among these, quantum mechanics is unique because of its
profoundly radical quality. Quantum mechanics forced physicists to
reshape their ideas of reality, to rethink the nature of things at
the deepest level, and to revise their concepts of position and
speed, as well as their notions of cause and effect.
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 Although quantum mechanics was created to
describe an abstract atomic world far removed from daily experience,
its impact on our daily lives could hardly be greater. The
spectacular advances in chemistry, biology, and medicineand in
essentially every other sciencecould not have occurred without the
tools that quantum mechanics made possible. Without quantum
mechanics there would be no global economy to speak of, because the
electronics revolution that brought us the computer age is a child
of quantum mechanics. So is the photonics revolution that brought us
the Information Age. The creation of quantum physics has transformed
our world, bringing with it all the benefitsand the risksof a
scientific revolution.
Unlike general relativity, which grew out of a brilliant insight
into the connection between gravity and geometry, or the deciphering
of DNA, which unveiled a new world of biology, quantum mechanics did
not spring from a single step. Rather, it was created in one of
those rare concentrations of genius that occur from time to time in
history. For 20 years after their introduction, quantum ideas were
so confused that there was little basis for progress; then a small
group of physicists created quantum mechanics in three tumultuous
years. These scientists were troubled by what they were doing and in
some cases distressed by what they had done.
The unique situation of this crucial yet elusive theory is
perhaps best summarized by the following observation: Quantum theory
is the most precisely tested and most successful theory in the
history of science. Nevertheless, not only was quantum mechanics
deeply disturbing to its founders, today75 years after the theory
was essentially cast in its current formsome of the luminaries of
science remain dissatisfied with its foundations and its
interpretation, even as they acknowledge its stunning power.
This year marks the 100th anniversary of Max Planck's creation of
the quantum concept. In his seminal paper on thermal radiation,
Planck hypothesized that the total energy of a vibrating system
cannot be changed continuously. Instead, the energy must jump from
one value to another in discrete steps, or quanta, of energy. The
idea of energy quanta was so radical that Planck let it lay fallow.
Then, Einstein, in his wonder year of 1905, recognized the
implications of quantization for light. Even then the concept was so
bizarre that there was little basis for progress. Twenty more years
and a fresh generation of physicists were required to create modern
quantum theory.
To understand the revolutionary impact of quantum physics one
need only look at prequantum physics. From 1890 to 1900, physics
journals were filled with papers on atomic spectra and essentially
every other measurable property of matter, such as viscosity,
elasticity, electrical and thermal conductivity, coefficients of
expansion, indices of refraction, and thermoelastic coefficients.
Spurred by the energy of the Victorian work ethic and the
development of ever more ingenious experimental methods, knowledge
accumulated at a prodigious rate.
What is most striking to the contemporary eye, however, is that
the compendious descriptions of the properties of matter were
essentially empirical. Thousands of pages of spectral data listed
precise values for the wavelengths of the elements, but nobody knew
why spectral lines occurred, much less what information they
conveyed. Thermal and electrical conductivities were interpreted by
suggestive models that fitted roughly half of the facts. There were
numerous empirical laws, but they were not satisfying. For instance,
the DulongPetit law established a simple relation between specific
heat and the atomic weight of a material. Much of the time it
worked; sometimes it didn't. The masses of equal volumes of gas were
in the ratios of integersmostly. The Periodic Table, which
provided a key organizing principle for the flourishing science of
chemistry, had absolutely no theoretical basis.
Among the greatest achievements of the revolution is this:
Quantum mechanics has provided a quantitative theory of matter. We
now understand essentially every detail of atomic structure; the
Periodic Table has a simple and natural explanation; and the vast
arrays of spectral data fit into an elegant theoretical framework.
Quantum theory permits the quantitative understanding of molecules,
of solids and liquids, and of conductors and semiconductors. It
explains bizarre phenomena such as superconductivity and
superfluidity, and exotic forms of matter such as the stuff of
neutron stars and BoseEinstein condensates, in which all the atoms
in a gas behave like a single superatom. Quantum mechanics provides
essential tools for all of the sciences and for every advanced
technology.
Quantum physics actually encompasses two entities. The first is
the theory of matter at the atomic level: quantum mechanics. It is
quantum mechanics that allows us to understand and manipulate the
material world. The second is the quantum theory of fields. Quantum
field theory plays a totally different role in science, to which we
shall return later.
Quantum Mechanics The
clue that triggered the quantum revolution came not from studies of
matter but from a problem in radiation. The specific challenge was
to understand the spectrum of light emitted by hot bodies: blackbody
radiation. The phenomenon is familiar to anyone who has stared at a
fire. Hot matter glows, and the hotter it becomes the brighter it
glows. The spectrum of the light is broad, with a peak that shifts
from red to yellow and finally to blue (although we cannot see that)
as the temperature is raised.
It should have been possible to understand the shape of the
spectrum by combining concepts from thermodynamics and
electromagnetic theory, but all attempts failed. However, by
assuming that the energies of the vibrating electrons that radiate
the light are quantized, Planck obtained an expression that agreed
beautifully with experiment. But as he recognized all too well, the
theory was physically absurd, "an act of desperation," as he later
described it.
Planck applied his quantum hypothesis to the energy of the
vibrators in the walls of a radiating body. Quantum physics might
have ended there if in 1905 a noviceAlbert Einsteinhad not
reluctantly concluded that if a vibrator's energy is quantized, then
the energy of the electromagnetic field that it
radiateslightmust also be quantized. Einstein thus imbued light
with particlelike behavior, notwithstanding that James Clerk
Maxwell's theory, and over a century of definitive experiments,
testified to light's wave nature. Experiments on the photoelectric
effect in the following decade revealed that when light is absorbed
its energy actually arrives in discrete bundles, as if carried by a
particle. The dual nature of lightparticlelike or wavelike
depending on what one looks forwas the first example of a vexing
theme that would recur throughout quantum physics. The duality
constituted a theoretical conundrum for the next 20 years.
The first step toward quantum theory had been precipitated by a
dilemma about radiation. The second step was precipitated by a
dilemma about matter. It was known that atoms contain positively and
negatively charged particles. But oppositely charged particles
attract. According to electromagnetic theory, therefore, they should
spiral into each other, radiating light in a broad spectrum until
they collapse.
Once again, the door to progress was opened by a novice: Niels
Bohr. In 1913, Bohr proposed a radical hypothesis: Electrons in an
atom exist only in certain stationary states, including a ground
state. Electrons change their energy by "jumping" between the
stationary states, emitting light whose wavelength depends on the
energy difference. By combining known laws with bizarre assumptions
about quantum behavior, Bohr swept away the problem of atomic
stability. Bohr's theory was full of contradictions, but it provided
a quantitative description of the spectrum of the hydrogen atom. He
recognized both the success and the shortcomings of his model. With
uncanny foresight, he rallied physicists to create a new physics.
His vision was eventually fulfilled, although it took 12 years and a
new generation of young physicists.
At first, attempts to advance Bohr's quantum ideasthe socalled
old quantum theorysuffered one defeat after another. Then a series
of developments totally changed the course of thinking.
In 1923 Louis de Broglie, in his Ph.D. thesis, proposed that the
particle behavior of light should have its counterpart in the wave
behavior of particles. He associated a wavelength with the momentum
of a particle: The higher the momentum the shorter the wavelength.
The idea was intriguing, but no one knew what a particle's wave
nature might signify or how it related to atomic structure.
Nevertheless, de Broglie's hypothesis was an important precursor for
events soon to take place.
In the summer of 1924, there was yet another precursor. Satyendra
N. Bose proposed a totally new way to explain the Planck radiation
law. He treated light as if it were a gas of massless particles (now
called photons) that do not obey the classical laws of Boltzmann
statistics but behave according to a new type of statistics based on
particles' indistinguishable nature. Einstein immediately applied
Bose's reasoning to a real gas of massive particles and obtained a
new lawto become known as the BoseEinstein distributionfor how
energy is shared by the particles in a gas. Under normal
circumstances, however, the new and old theories predicted the same
behavior for atoms in a gas. Einstein took no further interest, and
the result lay undeveloped for more than a decade. Still, its key
idea, the indistinguishability of particles, was about to become
critically important.
Suddenly, a tumultuous series of events occurred, culminating in
a scientific revolution. In the 3year period from January 1925 to
January 1928:
· Wolfgang Pauli proposed the exclusion principle, providing a
theoretical basis for the Periodic Table.
· Werner Heisenberg, with Max Born and Pascual Jordan, discovered
matrix mechanics, the first version of quantum mechanics. The
historical goal of understanding electron motion within atoms was
abandoned in favor of a systematic method for organizing observable
spectral lines.
· Erwin Schrödinger invented wave mechanics, a second form of
quantum mechanics in which the state of a system is described by a
wave function, the solution to Schrödinger's equation. Matrix
mechanics and wave mechanics, apparently incompatible, were shown to
be equivalent.
· Electrons were shown to obey a new type of statistical law,
FermiDirac statistics. It was recognized that all particles obey
either FermiDirac statistics or BoseEinstein statistics, and that
the two classes have fundamentally different properties.
· Heisenberg enunciated the Uncertainty Principle.
· Paul A. M. Dirac developed a relativistic wave equation for the
electron that explained electron spin and predicted antimatter.
· Dirac laid the foundations of quantum field theory by providing
a quantum description of the electromagnetic field.
· Bohr announced the complementarity principle, a philosophical
principle that helped to resolve apparent paradoxes of quantum
theory, particularly waveparticle duality.
The principal players in the creation of quantum theory were
young. In 1925, Pauli was 25 years old, Heisenberg and Enrico Fermi
were 24, and Dirac and Jordan were 23. Schrödinger, at age 36, was a
late bloomer. Born and Bohr were older still, and it is significant
that their contributions were largely interpretative. The profoundly
radical nature of the intellectual achievement is revealed by
Einstein's reaction. Having invented some of the key concepts that
led to quantum theory, Einstein rejected it. His paper on
BoseEinstein statistics was his last contribution to quantum
physics and his last significant contribution to physics.
That a new generation of physicists was needed to create quantum
mechanics is hardly surprising. Lord Kelvin described why in a
letter to Bohr congratulating him on his 1913 paper on hydrogen. He
said that there was much truth in Bohr's paper, but he would never
understand it himself. Kelvin recognized that radically new physics
would need to come from unfettered minds.
In 1928, the revolution was finished and the foundations of
quantum mechanics were essentially complete. The frenetic pace with
which it occurred is revealed by an anecdote recounted by the late
Abraham Pais in Inward Bound. In 1925, the concept of
electron spin had been proposed by Samuel Goudsmit and George
Uhlenbeck. Bohr was deeply skeptical. In December, he traveled to
Leiden, the Netherlands, to attend the jubilee of Hendrik A.
Lorentz's doctorate. Pauli met the train at Hamburg, Germany, to
find out Bohr's opinion about the possibility of electron spin. Bohr
said the proposal was "very, very interesting," his wellknown
putdown phrase. Later at Leiden, Einstein and Paul Ehrenfest met
Bohr's train, also to discuss spin. There, Bohr explained his
objection, but Einstein showed a way around it and converted Bohr
into a supporter. On his return journey, Bohr met with yet more
discussants. When the train passed through Göttingen, Germany,
Heisenberg and Jordan were waiting at the station to ask his
opinion. And at the Berlin station, Pauli was waiting, having
traveled especially from Hamburg. Bohr told them all that the
discovery of electron spin was a great advance.
The creation of quantum mechanics triggered a scientific gold
rush. Among the early achievements were these: Heisenberg laid the
foundations for atomic structure theory by obtaining an approximate
solution to Schrödinger's equation for the helium atom in 1927, and
general techniques for calculating the structures of atoms were
created soon after by John Slater, Douglas Rayner Hartree, and
Vladimir Fock. The structure of the hydrogen molecule was solved by
Fritz London and Walter Heitler; Linus Pauling built on their
results to found theoretical chemistry. Arnold Sommerfeld and Pauli
laid the foundations of the theory of electrons in metals, and Felix
Bloch created band structure theory. Heisenberg explained the origin
of ferromagnetism. The enigma of the random nature of radioactive
decay by alpha particle emission was explained in 1928 by George
Gamow, who showed that it occurs by quantum mechanical tunneling.
In the following years Hans Bethe laid the foundations for nuclear
physics and explained the energy source of stars. With these
developments atomic, molecular, solid state, and nuclear physics
entered the modern age.
Controversy and
Confusion Alongside these advances, however,
fierce debates were taking place on the interpretation and validity
of quantum mechanics. Foremost among the protagonists were Bohr and
Heisenberg, who embraced the new theory, and Einstein and
Schrödinger, who were dissatisfied. To appreciate the reasons for
such turmoil, one needs to understand some of the key features of
quantum theory, which we summarize here. (For simplicity, we
describe the Schrödinger version of quantum mechanics, sometimes
called wave mechanics.)
Fundamental description: the wave function. The behavior
of a system is described by Schrödinger's equation. The solutions to
Schrödinger's equation are known as wave functions. The complete
knowledge of a system is described by its wave function, and from
the wave function one can calculate the possible values of every
observable quantity. The probability of finding an electron in a
given volume of space is proportional to the square of the magnitude
of the wave function. Consequently, the location of the particle is
"spread out" over the volume of the wave function. The momentum of a
particle depends on the slope of the wave function: The greater the
slope, the higher the momentum. Because the slope varies from place
to place, momentum is also "spread out." The need to abandon a
classical picture in which position and velocity can be determined
with arbitrary accuracy in favor of a blurred picture of
probabilities is at the heart of quantum mechanics.
Measurements made on identical systems that are identically
prepared will not yield identical results. Rather, the results will
be scattered over a range described by the wave function.
Consequently, the concept of an electron having a particular
location and a particular momentum loses its foundation. The
Uncertainty Principle quantifies this: To locate a particle
precisely, the wave function must be sharply peaked (that is, not
spread out). However, a sharp peak requires a steep slope, and so
the spread in momentum will be great. Conversely, if the momentum
has a small spread, the slope of the wave function must be small,
which means that it must spread out over a large volume, thereby
portraying the particle's location less exactly.
Waves can interfere. Their heights add or subtract
depending on their relative phase. Where the amplitudes are in
phase, they add; where they are out of phase, they subtract. If a
wave can follow several paths from source to receiver, as a light
wave undergoing twoslit interference, then the illumination will
generally display interference fringes. Particles obeying a wave
equation will do likewise, as in electron diffraction. The analogy
seems reasonable until one inquires about the nature of the wave. A
wave is generally thought of as a disturbance in a medium. In
quantum mechanics there is no medium, and in a sense there is no
wave, as the wave function is fundamentally a statement of our
knowledge of a system.
Symmetry and identity. A helium atom consists of a
nucleus surrounded by two electrons. The wave function of helium
describes the position of each electron. However, there is no way of
distinguishing which electron is which. Consequently, if the
electrons are switched the system must look the same, which is to
say the probability of finding the electrons in given positions is
unchanged. Because the probability depends on the square of
the magnitude of the wave function, the wave function for the system
with the interchanged particles must be related to the original wave
function in one of two ways: Either it is identical to the original
wave function, or its sign is simply reversed, i.e., it is
multiplied by a factor of 1. Which one is it?
One of the astonishing discoveries in quantum mechanics is that
for electrons the wave function always changes sign. The
consequences are dramatic, for if two electrons are in the same
quantum state, then the wave function has to be its negative
opposite. Consequently, the wave function must vanish. Thus, the
probability of finding two electrons in the same state is zero. This
is the Pauli exclusion principle. All particles with halfinteger
spin, including electrons, behave this way and are called fermions.
For particles with integer spin, including photons, the wave
function does not change sign. Such particles are called bosons.
Electrons in an atom arrange themselves in shells because they are
fermions, but light from a laser emerges in a single superintense
beamessentially a single quantum statebecause light is composed
of bosons. Recently, atoms in a gas have been cooled to the quantum
regime where they form a BoseEinstein condensate, in which the
system can emit a superintense matter beamforming an atom laser.
These ideas apply only to identical particles, because if
different particles are interchanged the wave function will
certainly be different. Consequently, particles behave like fermions
or like bosons only if they are totally identical. The
absolute identity of like particles is among the most mysterious
aspects of quantum mechanics. Among the achievements of quantum
field theory is that it can explain this mystery.
What does it mean? Questions such as what a wave
function "really is" and what is meant by "making a measurement"
were intensely debated in the early years. By 1930, however, a more
or less standard interpretation of quantum mechanics had been
developed by Bohr and his colleagues, the socalled Copenhagen
interpretation. The key elements are the probabilistic description
of matter and events, and reconciliation of the wavelike and
particlelike natures of things through Bohr's principle of
complementarity. Einstein never accepted quantum theory. He and Bohr
debated its principles until Einstein's death in 1955.
A central issue in the debates on quantum mechanics was whether
the wave function contains all possible information about a system
or if there might be underlying factorshidden variablesthat
determine the outcome of a particular measurement. In the mid1960s
John S. Bell showed that if hidden variables existed, experimentally
observed probabilities would have to fall below certain limits,
dubbed "Bell's inequalities." Experiments were carried out by a
number of groups, which found that the inequalities were violated.
Their collective data came down decisively against the possibility
of hidden variables. For most scientists, this resolved any doubt
about the validity of quantum mechanics.
Nevertheless, the nature of quantum theory continues to attract
attention because of the fascination with what is sometimes
described as "quantum weirdness." The weird properties of quantum
systems arise from what is known as entanglement. Briefly, a quantum
system, such as an atom, can exist in any one of a number of
stationary states but also in a superpositionor sumof such
states. If one measures some property such as the energy of an atom
in a superposition state, in general the result is sometimes one
value, sometimes another. So far, nothing is weird.
It is also possible, however, to construct a twoatom system in
an entangled state in which the properties of both atoms are shared
with each other. If the atoms are separated, information about one
is shared, or entangled, in the state of the other. The behavior is
unexplainable except in the language of quantum mechanics. The
effects are so surprising that they are the focus of study by a
small but active theoretical and experimental community. The issues
are not limited to questions of principle, as entanglement can be
useful. Entangled states have already been employed in quantum
communication systems, and entanglement underlies all proposals for
quantum computation.
The Second
Revolution During the frenetic years in the
mid1920s when quantum mechanics was being invented, another
revolution was under way. The foundations were being laid for the
second branch of quantum physicsquantum field theory. Unlike
quantum mechanics, which was created in a short flurry of activity
and emerged essentially complete, quantum field theory has a
tortuous history that continues today. In spite of the difficulties,
the predictions of quantum field theory are the most precise in all
of physics, and quantum field theory constitutes a paradigm for some
of the most crucial areas of theoretical inquiry.
The problem that motivated quantum field theory was the question
of how an atom radiates light as its electrons "jump" from excited
states to the ground state. Einstein proposed such a process, called
spontaneous emission, in 1916, but he had no way to calculate its
rate. Solving the problem required developing a fully relativistic
quantum theory of electromagnetic fields, a quantum theory of light.
Quantum mechanics is the theory of matter. Quantum field theory, as
its name suggests, is the theory of fields, not only electromagnetic
fields but other fields that were subsequently discovered.
In 1925 Born, Heisenberg, and Jordan published some initial ideas
for a theory of light, but the seminal steps were taken by Diraca
young and essentially unknown physicist working in isolationwho
presented his field theory in 1926. The theory was full of pitfalls:
formidable calculational complexity, predictions of infinite
quantities, and apparent violations of the correspondence principle.
In the late 1940s a new approach to the quantum theory of fields,
QED (for quantum electrodynamics), was developed by Richard Feynman,
Julian Schwinger, and SinItiro Tomonaga. They sidestepped the
infinities by a procedure, called renormalization, which essentially
subtracts infinite quantities so as to leave finite results. Because
there is no exact solution to the complicated equations of the
theory, an approximate answer is presented as a series of terms that
become more and more difficult to calculate. Although the terms
become successively smaller, at some point they should start to
grow, indicating the breakdown of the approximation. In spite of
these perils, QED ranks among the most brilliant successes in the
history of physics. Its prediction of the interaction strength
between an electron and a magnetic field has been experimentally
confirmed to a precision of two parts in 1,000,000,000,000.
Notwithstanding its fantastic successes, QED harbors enigmas. The
view of empty spacethe vacuumthat the theory provides initially
seems preposterous. It turns out that empty space is not really
empty. Rather, it is filled with small, fluctuating electromagnetic
fields. These vacuum fluctuations are essential for explaining
spontaneous emission. Furthermore, they produce small but measurable
shifts in the energies of atoms and certain properties of particles
such as the electron. Strange as they seem, these effects have been
confirmed by some of the most precise experiments ever carried out.
At the low energies of the world around us, quantum mechanics is
fantastically accurate. But at high energies where relativistic
effects come into play, a more general approach is needed. Quantum
field theory was invented to reconcile quantum mechanics with
special relativity.
The towering role that quantum field theory plays in physics
arises from the answers it provides to some of the most profound
questions about the nature of matter. Quantum field theory explains
why there are two fundamental classes of particlesfermions and
bosonsand how their properties are related to their intrinsic
spin. It describes how particlesnot only photons, but electrons
and positrons (antielectrons)are created and annihilated. It
explains the mysterious nature of identity in quantum mechanicshow
identical particles are absolutely identical because they are
created by the same underlying field. QED describes not only the
electron but the class of particles called leptons that includes the
muon, the tau meson, and their antiparticles.
Because QED is a theory for leptons, however, it cannot describe
more complex particles called hadrons. These include protons,
neutrons, and a wealth of mesons. For hadrons, a new theory had to
be invented, a generalization of QED called quantum chromodynamics,
or QCD. Analogies abound between QED and QCD. Electrons are the
constituents of atoms; quarks are the constituents of hadrons. In
QED the force between charged particles is mediated by the photon;
in QCD the force between quarks is mediated by the gluon. In spite
of the parallels, there is a crucial difference between QED and QCD.
Unlike leptons and photons, quarks and gluons are forever confined
within the hadron. They cannot be liberated and studied in
isolation.
QED and QCD are the cornerstones for a grand synthesis known as
the Standard Model. The Standard Model has successfully accounted
for every particle experiment carried out to date. However, for many
physicists the Standard Model is inadequate, because data on the
masses, charges, and other properties of the fundamental particles
need to be found from experiments. An ideal theory would predict all
of these.
Today, the quest to understand the ultimate nature of matter is
the focus of an intense scientific study that is reminiscent of the
frenzied and miraculous days in which quantum mechanics was created,
and whose outcome may be even more farreaching. The effort is
inextricably bound to the quest for a quantum description of
gravity. The procedure for quantizing the electromagnetic field that
worked so brilliantly in QED has failed to work for gravity, in
spite of a halfcentury of effort. The problem is critical, for if
general relativity and quantum mechanics are both correct, then they
must ultimately provide a consistent description for the same
events. There is no contradiction in the normal world around us,
because gravity is so fantastically weak compared to the electrical
forces in atoms that quantum effects are negligible and a classical
description works beautifully. But for a system such as a black hole
where gravity is incredibly strong, we have no reliable way to
predict quantum behavior.
One century ago our understanding of the physical world was
empirical. Quantum physics gave us a theory of matter and fields,
and that knowledge transformed our world. Looking to the next
century, quantum mechanics will continue to provide fundamental
concepts and essential tools for all of the sciences. We can make
such a prediction confidently because for the world around us
quantum physics provides an exact and complete theory. However,
physics today has this in common with physics in 1900: It remains
ultimately empiricalwe cannot fully predict the properties of the
elementary constituents of matter, we must measure them.
Perhaps string theorya generalization of quantum field theory
that eliminates all infinities by replacing pointlike objects such
as the electron with extended objectsor some theory only now being
conceived, will solve the riddle. Whatever the outcome, the dream of
ultimate understanding will continue to be a driving force for new
knowledge, as it has been since the dawn of science. One century
from now, the consequences of pursuing that dream will belie our
imagination.
Further Reading
B. Bederson, Ed., More Things in Heaven and Earth: A
Celebration of Physics at the Millennium (Springer Verlag, New
York, 1999). J. S. Bell, Speakable and Unspeakable in Quantum
Mechanics: Collected Papers on Quantum Mechanics (reprint
edition) (Cambridge University Press, Cambridge, 1989). L. M.
Brown, A. Pais, B. Pippard, Eds., Twentieth Century Physics
(Institute of Physics, Philadelphia 1995). D. Cassidy,
Uncertainty: The Life and Science of Werner Heisenberg (W.
H. Freeman, New York, 1993). A. Einstein, BornEinstein
Letters, trans. Irene Born (Macmillan, London, 1971). H.
Kragh, Dirac: A Scientific Biography (Cambridge University
Press, Cambridge, 1990). W. Moore, Schrödinger: Life and
Thought (Cambridge University Press, Cambridge, 1989). A.
Pais, Inward Bound: Of Matter and Forces in the Physical
World (Oxford University Press, Oxford, 1986). A. Pais,
Niels Bohr's Times: In Physics, Philosophy, and Polity
(Oxford University Press, Oxford, 1991).
Daniel Kleppner is Lester Wolf Professor of Physics and Acting
Director of the Research Laboratory of Electronics at the
Massachusetts Institute of Technology. His research interests
include atomic physics, quantum optics, ultraprecise spectroscopy,
and BoseEinstein condensation.
Roman Jackiw is Jerrold Jacharias Professor of Physics at MIT.
His research interests include applying quantum field theory to
physical problems, theoretical particle physics, and the search for
unexpected, subtle effects that may apply to particle, condensed
matter, and gravitational physics.
A
Timeline of Quantum Physics 
1800s 
1897 Pieter Zeeman shows that
light is radiated by the motion of charged particles in an
atom, and Joseph John (J. J.) Thomson discovers the
electron. 
1900s 
1900 Max Planck explains blackbody
radiation in the context of quantized energy emission: Quantum
theory is born. 
1905 Albert Einstein proposes that
light, which has wavelike properties, also consists of
discrete, quantized bundles of energy, which are later called
photons. 
1911 Ernest Rutherford proposes
the nuclear model of the atom. 
1913 Niels Bohr proposes his
planetary model of the atom, along with the concept of
stationary energy states, and accounts for the spectrum of
hydrogen. 
1914 James Franck and Gustav Hertz
confirm the existence of stationary states through an electron
scattering experiment. 
1923 Arthur Compton observes that
xrays behave like miniature billiard balls in their
interactions with electrons, thereby providing further
evidence for the particle nature of light. 
1923 Louis de Broglie generalizes
waveparticle duality by suggesting that particles of matter
are also wavelike. 
1924 Satyendra Nath Bose and
Albert Einstein find a new way to count quantum particles,
later called Bose Einstein statistics, and they predict that
extremely cold atoms should condense into a single quantum
state, later known as a BoseEinstein condensate. 
1925 Wolfgang Pauli enunciates the
exclusion principle. 
1925 Werner Heisenberg, Max Born,
and Pascual Jordan develop matrix mechanics, the first version
of quantum mechanics, and make an initial step toward quantum
field theory. 
1926 Erwin Schrödinger develops a
second description of quantum physics, called wave mechanics.
It includes what becomes one of the most famous formulae of
science, which is later known as the Schrödinger
equation. 
1926 Enrico Fermi and Paul A. M.
Dirac find that quantum mechanics requires a second way to
count particles, FermiDirac statistics, opening the way to
solid state physics. 
1926 Dirac publishes a seminal
paper on the quantum theory of light. 
1927 Heisenberg states his
Uncertainty Principle, that it is impossible to exactly
measure the position and momentum of a particle at the same
time. 
1928 Dirac presents a relativistic
theory of the electron that includes the prediction of
antimatter. 
1932 Carl David Anderson discovers
antimatter, an antielectron called the positron. 
1934 Hideki Yukawa proposes that
nuclear forces are mediated by massive particles called
mesons, which are analogous to the photon in mediating
electromagnetic forces. 
194648 Experiments by Isidor I.
Rabi, Willis Lamb, and Polykarp Kusch reveal discrepancies in
the Dirac theory. 
1948 Richard Feynman, Julian
Schwinger, and SinItiro Tomonaga develop the first complete
theory of the interaction of photons and electrons, quantum
electrodynamics, which accounts for the discrepancies in the
Dirac theory. 
1957 John Bardeen, Leon Cooper,
and J. Robert Schrieffer show that electrons can form pairs
whose quantum properties allow them to travel without
resistance, providing an explanation for the zero electrical
resistance of superconductors. 
1959 Yakir Aharonov and David Bohm
predict that a magnetic field affects the quantum properties
of an electron in a way that is forbidden by classical
physics. The AharonovBohm effect is observed in 1960 and
hints at a wealth of unexpected macroscopic effects. 
1960 Building on work by Charles
Townes, Arthur Schawlow, and others, Theodore Maiman builds
the first practical laser. 
1964 John S. Bell proposes an
experimental test, "Bell's inequalities," of whether quantum
mechanics provides the most complete possible description of a
system. 
1970s Foundations are laid for the
Standard Model of Particle Physics, in which matter is said to
be built of quarks and leptons that interact via the four
physical forces. 
1982 Alain Aspect carries out an
experimental test of Bell's inequalities and confirms the
completeness of quantum mechanics. 
1995 Eric Cornell, Carl Wieman,
and Wolfgang Ketterle trap clouds of metallic atoms cooled to
less than a millionth of a degree above absolute zero,
producing BoseEinstein condensates, which were first
predicted 70 years earlier. This accomplishment leads to the
creation of the atom laser and superfluid gases. 
For more extensive
timelines of quantum physics, see two of Abraham Pais's books:
Inward Bound: Of Matter and Forces in the Physical
World and Niels Bohr's Times: In Physics, Philosophy,
and Polity.
Also see timeline.aps.org/APS/index.html 
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Related articles in Science:
 CORRECTIONS AND CLARIFICATIONS.
Science 2000 289: 2052. (in Letters) [Full
Text]
Volume 289,
Number 5481, Issue of 11 Aug 2000, pp. 893898. Copyright © 2000 by The American Association for the
Advancement of Science.
