that one would never observe a free quark or gluon is valid. This is
called Confinement because quarks and gluons are always confined
inside strongly interacting particles such as protons and neutrons
ͤ͞͡
and can never break free from them without getting confined in
newly created strongly interacting particles.
Since the actual process by which the quarks get confined occurs
as the forces become stronger and stronger when the quark moves
farther and farther away from its original companions, the standard
calculations of quantum field theory, which are valid when the
interactions are not too strong, break down. So this picture,
validated by experiment, cannot be fully confirmed by tractable
calculations at the moment.
Will we ever derive the necessary mathematical tools to
analytically demonstrate from first principles that confinement is
indeed a mathematical property of quantum chromodynamics? This
is the million-dollar question, literally. The Clay Mathematics
Institute has announced a million-dollar prize for a rigorous
mathematical proof that quantum chromodynamics does not allow
free quarks or gluons to be produced. While no claimants to the
prize have yet come forward, we nevertheless have strong indirect
support of this idea, coming not only from experimental
observations, but also from numerical simulations that closely
approximate
the
complicated
interactions
in
quantum
chromodynamics. This is heartening, if not definitive. We still have
to confirm that it is some property of the theory and not of the
computer simulation. However, for physicists, if not mathematicians,
this seems pretty convincing.
One final bit of direct evidence that QCD is correct came from a
realm where exact calculations can be done. Because quarks are not
completely free at short distances, I earlier mentioned that there
should be calculable corrections to exotic scaling phenomena
observed in the high-energy collisions of electrons off protons and
neutrons, as originally observed at SLAC. Perfect scaling would
require completely noninteracting particles. The corrections that
ͥ͞͡
one could calculate in quantum chromodynamics would only be
observable in experiments that were far more sensitive than those
originally performed at SLAC. It took the development of new,
higher-energy accelerators to probe them. After thirty years or so,
enough evidence was in so that comparison of theoretical
predictions and experiment agreed at the 1 percent level, and
quantum chromodynamics as the theory of the strong interaction
was finally verified in a precise and detailed way.
Gross, Wilczek, and Politzer were finally awarded the Nobel Prize
in 2004 for their discovery of asymptotic freedom. The
experimentalists who had first discovered scaling at SLAC, which
was the key observation that set theorists off in the right direction,
were awarded the Nobel Prize much earlier, in 1990. And the
experimentalists who discovered the charmed quark in 1974 won
the Nobel Prize two years later, in 1976.
But the biggest prize of all, as Richard Feynman has said, is not the
recognition by a medal or a cash award, or even the praise one gets
from colleagues or the public, but the prize of actually learning
something new about nature.
• • •
In this sense the 1970s were perhaps the richest decade in the
twentieth century, if not in the entire history of physics. In 1970 we
understood only one force in nature completely as a quantum
theory, namely quantum electrodynamics. By 1979 we had
developed and experimentally verified perhaps the greatest
theoretical edifice yet created by human minds, the Standard Model
of particle physics, describing precisely three of the four known
forces in nature. The effort spanned the entire history of modern
science, from Galileo’s investigations of the nature of moving bodies,
through Newton’s discovery of the laws of motion, through the
͢͜͞
experimental and theoretical investigations of the nature of
electromagnetism, through Einstein’s unification of space and time,
through the discoveries of the nucleus, quantum mechanics, protons,
neutrons, and the discovery of the weak and strong forces
themselves.
But the most remarkable characteristic of all in this long march
toward the light is how different the fundamental nature of reality is
from the shadows of reality that we experience every day, and in
particular how the fundamental quantities that appear to govern our
existence are not fundamental at all.
Making up the heart of observed matter are particles that had
never been directly observed and, if we are correct, will never be
directly observable—quarks and gluons. The properties of forces that
govern the interactions of these particles—and also the particles that
have formed the basis of modern experimental physics for more
than a century, electrons—are also, on a fundamental level,
completely different from the properties we directly observe and on
which we depend for our existence. The strong interaction between
protons and neutrons is only a long-distance remnant of the
underlying force between quarks, whose fundamental properties are
masked by the complicated interactions within the nucleus. The
weak interaction and the electromagnetic interaction, which could
not be more different on the surface—one is short-range, while the
other is long-range, and one appears thousands of times weaker than
the other—are in fact intimately related and reflect different facets of
a single whole.
That whole is hidden from us because of the accident of nature
we call spontaneous symmetry breaking, which distinguishes the two
weak and electromagnetic interactions in the world of our
experience and hides their true nature. More than that, the
properties of the particles that produce the characteristics of the
͢͞͝
beautiful world we observe around us are only possible because, after
the accident of spontaneous symmetry breaking, just one particle in
nature—the photon—remains massless. If symmetry breaking had
never occurred so that underlying symmetries of the forces
governing matter were manifest—which in turn would mean that
the particles conveying the weak force would also be massless, as
would most of the particles that make us up—essentially nothing we
see in the universe today, from galaxies to stars, to planets, to people,
to birds and bees, to scientists and politicians, would ever have
formed.
Moreover, we have learned that even these particles that make us
up are not all that exist in nature. The observed particles combine in
simple groupings, or families. The up and down quarks make up
protons and neutrons. Along with them one finds the electron, and
its partner, the electron neutrino. Then, f
or reasons we still don’t
understand, there is a heavier family, made up of the charm and
strange quark on the one hand, and the muon and its neutrino on
the other. And finally, as experiments have now confirmed over the
past decade or two, there is a third family, made of two new types of
quarks, called bottom and top, and an accompanying heavy version
of the electron called the tau particle, along with its neutrino.
Beyond these particles, as I shall soon describe, we have every
reason to expect that other elementary particles exist that have never
been observed. While these particles, which we think make up the
mysterious dark matter that dominates the mass of our galaxy and all
observed galaxies, may be invisible to our telescopes, our
observations and theories nevertheless suggest that galaxies and stars
could never have formed without the existence of dark matter.
And at the heart of all of the forces governing the dynamical
behavior of everything we can observe is a beautiful mathematical
framework called gauge symmetry. All of the known forces, strong,
͢͞͞
weak, electromagnetic, and even gravity, possess this mathematical
property, and for the three former examples, it is precisely this
property that ensures that the theories make mathematical sense and
that nasty quantum infinities disappear from all calculations of
quantities that can be compared to experiment.
With the exception of electromagnetism, these other symmetries
remain completely hidden from view. The gauge symmetry of the
strong force is hidden because confinement presumably hides the
fundamental particles that manifest this symmetry. The gauge
symmetry of the weak force is not manifest in the world in which we
live because it is spontaneously broken so that the W and Z particles
become extremely massive.
• • •
The shadows on the wall of everyday life are truly merely shadows.
In this sense, the greatest story every told, so far, has been slowly
playing out over the more than two thousand years since Plato first
imagined it in his analogy of the cave.
But as remarkable as this story is, two elephants remain in the
room. Two protagonists in our tale could until recently have meant
that the key aspects of the story comprised a mere fairy tale invented
by theorists with overactive imaginations.
First, the W and Z particles, postulated in 1960 to explain the
weak interaction, almost one hundred times more massive than
protons and neutrons, were still mere theoretical postulates, even if
the indirect evidence for their existence was overwhelming. More
than this, an invisible field—the Higgs field—was predicted to
permeate all of space, masking the true nature of reality and making
our existence possible because it spontaneously breaks the symmetry
between the weak and the electromagnetic interactions.
͢͟͞
To celebrate a story that claims to describe how it is that we exist,
but that also posits an invisible field permeating all of space, sounds
suspiciously like a religious celebration, and not a scientific one. To
truly ensure that our beliefs conform to the evidence of reality rather
than how we would like reality to be, to keep science worthy of the
name, we had to discover the Higgs field. Only then could we truly
know if the significance of the features of our world that we hold so
dear might be no greater than that of the features of one random ice
crystal on a window. Or, more to the point, perhaps, no greater than
the significance of the superconducting nature of wire in a
laboratory versus the normal resistance of the wires in my computer.
The experimental effort to carry out this task was no easier than
that in developing the theory itself. In many ways it was more
daunting, taking more than fifty years and involving the most
difficult fabrication of technology that humans have ever attempted.
͢͞͠
C h a p t e r 2 0
S PA N K I N G T H E VA C U U M
If anyone slaps you on the right cheek, turn to him the other also.
—MATTHEW 5:39
As the 1970s ended, theorists were on top of the world,
triumphant and exultant. With progress leading to the Standard
Model so swift, what other new worlds were there to conquer?
Dreams of a theory of everything, long dormant, began to rise again
and not just in the dim recesses of the collective subconscious of
theorists.
Still, the W and Z gauge particles had never actually been
observed, and the challenge to directly observe them was pretty
daunting. Their masses were precisely predicted in the theory at
about ninety times the mass of the proton. The challenge to produce
these particles comes from a simple bit of physics.
Einstein’s fundamental equation of relativity, E = mc2, tells us that
we can convert energy into mass by accelerating particles to energies
of many times their rest mass. We can then smash them into targets
to see what comes out.
The problem is that the energy available to produce new particles
by smashing other fast-moving particles into stationary targets is
given by what is called the center-of-mass energy. For those
undaunted by another formula, this turns out to be the square root
of twice the product of the energy of the accelerated particle times
the rest mass energy of the target particle. Imagine accelerating a
particle to one hundred times the rest mass energy of the proton
͢͞͡
(which is about one gigaelectronvolt—GeV). In a collision with
stationary protons in a target, the center-of-mass energy that is
available to create new particles is then only about 14 GeV. This is
just slightly greater than the center-of-mass energy available in the
highest-energy particle accelerator in 1972.
To reach the energies required to produce massive particles such
as the W or Z bosons, two opposing beams of particles must collide.
In this case the total center-of-mass energy is simply twice the
energy of each beam. If each colliding beam of particles has an
energy of one hundred times the rest mass of a proton, this then
yields 200 GeV of energy to be converted into the mass of new
particles.
Why, then, produce accelerators with stationary targets and not
colliders? The answer is quite simple. If I am shooting a bullet at a
barn door, I am more or less guaranteed to hit something. If I shoot
a bullet at another incoming bullet, however, I’d have to be a much
better shot than probably anyone else alive and have a better gun
than any now made to be guaranteed to hit it.
This was the challenge facing experimentalists in 1976, by which
time they took the electroweak model seriously enough that they
thought it worth the time, effort, and money to try to test it.
But no one knew how to build a device with the appropriate
energy. Accelerating individual beams of particles or antiparticles to
high energies had been achieved. By 1976 protons were being
&nb
sp; accelerated to 500 GeV, and electrons up to 50 GeV. At lower
energies, collisions of electrons and their antiparticles had
successfully been carried out, and this is how the new particle
containing the charmed quark and antiquark had been discovered in
1974.
Protons, having greater mass and thus more rest energy initially,
are easier to accelerate to high energies. In 1976 a proton accelerator
͢͢͞
at the European Organization for Nuclear Research (CERN) in
Geneva, the Super Proton Synchrotron (SPS), had just been
commissioned as a conventional fixed-target accelerator operating
with a proton beam at 400 GeV. However, another accelerator at
Fermilab, near Chicago, had already achieved proton beams of 500
GeV by the time the SPS turned on. In June of that year, physicists
Carlo Rubbia, Peter McIntyre, and David Cline made a bold
suggestion at a neutrino conference: converting the SPS at CERN
into a machine that collided protons with their antiparticles—
antiprotons—would allow CERN to potentially produce W’s and Z’s.
Their bold idea was to use the same circular tunnel to accelerate
protons in one direction, and antiprotons in another. Since the two
particles have opposite electric charges, the same accelerating
mechanism would have opposite effects on each particle. So a single
accelerator could in principle produce two high-energy beams
circulating in opposite directions.
The logic of such a proposal was clear, but its implementation
was not. In the first place, given the strength of the weak interaction,
the production of even a few W and Z particles would require the
collision of hundreds of billions of protons and antiprotons. But no
one had ever produced and collected enough antiprotons to make an
accelerator beam.
Next, you might imagine that with two beams traversing the same
tunnel in opposite directions, particles would be colliding all around
the tunnel and not in the detectors designed to measure the products
of the collisions. However, this is far from the case. The cross section
of even a small tunnel compared to the size of the region over which
a proton and an antiproton might collide is so huge that the problem
is quite the opposite. It seemed impossible to produce enough
antiprotons and ensure that both they and the protons in the proton
Lawrence Krauss - The Greatest Story Ever Told--So Far Page 28