at a distance the physical effects of the initial negative charge are
reduced.
This meant, according to Landau, that the closer you get to an
electron, the larger its actual charge will appear. If we measure the
electron charge to be some specific value at large distances, as we do,
that would mean that the “bare” charge on the electron—namely the
charge on the fundamental particle considered without all the
infinite dressing by particle-antiparticle pairs surrounding it on ever-
smaller scales—would have to be infinite. Clearly something was
rotten with this picture.
Gross was influenced not only by his supervisor, but also by the
prevailing sentiments of the time, mostly arguments by Gell-Mann,
who dominated theoretical particle physics in the late fifties and
early sixties. Gell-Mann advocated using algebraic relations that
arise from thinking about field theories, then keeping the relations
and throwing away the field theory. In a particularly Gell-Mann-
esque description, he stated, “We may compare this process to a
method sometimes employed in French cuisine: a piece of pheasant
meat is cooked between two slices of veal, which are then discarded.”
Thus one could abstract out properties of quarks that might be
useful for predictions, but then ignore the actual possible existence
of quarks. However, Gross began to be disenchanted by just using
͜͞͡
ideas associated with global symmetries and algebras and longed to
explore dynamics that might actually describe the physical processes
that were occurring inside strongly interacting particles. Gross and
his collaborator Curtis Callan built upon earlier work by James
Bjorken to show that the charged particle apparently located inside
protons and neutrons had to have spin ½, identical to that of
electrons. Later, with other collaborators, Gross showed that a
similar analysis of neutrino scattering off protons and neutrons as
measured at CERN revealed that the components looked just like the
quarks that Gell-Mann had proposed.
If it quacks like a duck and walks like a duck, it is probably a duck.
Thus, for Gross, and others, the reality of quarks was now
convincing.
But as convinced as many such as Gross were by the reality of
quarks, they were equally convinced that this implied that field
theory could not possibly be the correct way to describe the strong
interaction. The results of the experiment required the constituents
to be essentially noninteracting, not strongly interacting.
In 1969 Gross’s colleagues at Princeton Curtis Callan and Kurt
Symanzik rediscovered a set of equations explored by Landau, and
then Gell-Mann and Francis Low, that described how quantities in
quantum field theory might evolve with scale. If the partons inferred
by the SLAC experiments had any interactions at all—as quarks
must have—then measurable departures from the scaling that
Bjorken had derived would occur, and the results that Gross and his
collaborators had also derived when comparing theory and the
SLAC experiments would also have to be modified.
Over the next two years, with the results of ’t Hooft and Veltman,
and the growing success of the predictions of the theory of the weak
and electromagnetic interactions, more people began to turn their
attention once again to quantum field theory. Gross decided to
͞͡͝
prove in great generality that no sensible quantum field theory could
possibly reproduce the experimental results about the nature of
protons and neutrons observed at SLAC. Thus he hoped to kill this
whole approach to attempting to understand the strong interaction.
First, he would prove that the only way to explain the SLAC results
was if somehow, at short distances, the strength of the quantum field
interactions would have to go to zero, i.e., the fields would essentially
become noninteracting at short distances. Then, after that, he would
show that no quantum field theory had this property.
Recall that Landau had shown that quantum electrodynamics, the
prototypical consistent quantum field theory, has precisely the
opposite behavior. The strength of electric charges becomes larger as
the scale at which you probe particles (such as electrons) gets smaller
due to the cloud of virtual particles and antiparticles surrounding
them.
Early in 1973 Gross and his collaborator Giorgio Parisi had
completed the first part of the proof, namely that scaling as observed
at SLAC implied the strong interactions of the proton’s constituents
must go to zero at small-distance scales if the strong nuclear force
was to be described by any fundamental quantum field theory.
Next, Gross attempted to show that no field theories actually had
this behavior—the strength of interactions going to zero at small-
distance scales—which he dubbed asymptotic freedom. With help
from Harvard’s Sidney Coleman, who was visiting Princeton at the
time, Gross was able to complete this proof for all sensible quantum
field theories, except for Yang-Mills-type gauge theories.
Gross now took on a new graduate student, twenty-one-year-old
Frank Wilczek, who had come to Princeton from the University of
Chicago planning to study mathematics, but who switched to
physics after taking Gross’s graduate class in field theory.
͞͡͞
Gross was either lucky or astute because he served as the graduate
supervisor of probably the two most remarkable intellects among
physicists in my generation, Wilczek and Edward Witten, who
helped lead the string theory revolution in the 1980s and ’90s and
who is the only physicist ever to win the prestigious Fields Medal,
the highest award given to mathematicians. Wilczek is probably one
of the few true physics polymaths. Frank and I became frequent
collaborators and friends in the early 1980s, and he is not only one of
the most creative physicists I have ever worked with, he also has an
encyclopedic knowledge of the field. He has read almost every
physics text ever written, and he has assimilated the information. In
the intervening years, he has made numerous fundamental
contributions not only to particle physics, but to cosmology and also
the physics of materials.
Gross assigned Wilczek to explore with him the one remaining
loophole in Gross’s previous proof—determining how the strength
of the interaction in Yang-Mills theories changed as one went to
shorter-distance scales—to prove that these theories too could not
exhibit asymptotic freedom. They decided to directly and explicitly
calculate the behavior of the interactions in the theories at shorter
and shorter-distance scales.
This was a formidable task. Since that time tools have been
developed for doing the calculation as a homework problem in a
graduate course. Moreover, things are always easier to calculate
when you know what the answer will be, as we now do. After several
hectic months, with numerous false starts and
numerical errors, in
February of 1973 they completed their calculations and discovered,
to Gross’s great surprise, that in fact Yang-Mills theories are
asymptotically free—the interaction strength in these theories does
approach zero as interacting particles get closer together. As Gross
later put it, in his Nobel address, “For me the discovery of asymptotic
͟͞͡
freedom was totally unexpected. Like an atheist who has just
received a message from a burning bush, I became an immediate
true believer.”
Sidney Coleman had assigned his own graduate student David
Politzer to do a similar calculation, and his independent result
agreed with Gross and Wilczek’s and was obtained at about the same
time. That the results agreed gave both groups greater confidence in
them.
Not only can Yang-Mills theories be asymptotically free, they are
the only field theories that are. This led Gross and Wilczek to
suggest, in the opening of their landmark paper, that because of this
uniqueness, and because asymptotic freedom seemed to be required
for any theory of the strong interaction given the 1968 SLAC
experimental results, perhaps a Yang-Mills theory could explain the
strong interaction.
Which Yang-Mills theory was the right one needed to be
determined, and also why the massless gauge particles that are the
hallmark of Yang-Mills theories had not been seen. And related to
this, perhaps the most important long-standing question remained:
Where were the quarks?
But before I address these questions, you might be wondering
why Yang-Mills theories have such a different behavior from their
simpler cousin quantum electrodynamics, where Landau had shown
the strength of the interaction between electric charges gets larger
on small-distance scales.
The key is somewhat subtle and lies in the nature of the massless
gauge particles in Yang-Mills theory. Unlike photons in QED, which
have no electric charge, the gluons that were predicted to mediate
the strong interaction possess Yang-Mills charges, and therefore
gluons interact with each other. But because Yang-Mills theories are
more complicated than QED, the charges on gluons are also more
͞͡͠
complicated than the simple electric charges on electrons. Each
gluon not only looks like a charged particle, but also like a little
charged magnet.
If you bring a small magnet near some iron, the iron gets
magnetized and you end up with a more powerful magnet.
Something similar happens with Yang-Mills theories. If I have some
particle with a Yang-Mills charge, say, a quark, then quarks and
antiquarks can pop out of the vacuum around the charge and screen
it, as happens in electromagnetism. But gluons can also pop out of
the vacuum, and since they act like little magnets, they tend to align
themselves along the direction of the field produced by the original
quark. This increases the strength of the field, which in turn induces
more gluons to pop out of the vacuum, which further increases the
field, and so on.
As a result, the deeper into the virtual gluon cloud you penetrate
—i.e., the closer you get to the quark—the weaker the field will look.
Ultimately, as you bring two quarks closer together, the interaction
will get so weak that they will begin to act as if they are not
interacting at all, the characteristic of asymptotic freedom.
I used gluons and quarks as labels here, but the discovery of
asymptotic freedom did not point uniquely to any specific Yang-
Mills theory. However, Gross and Wilczek recognized the natural
candidate was the Yang-Mills theory that Greenberg and others had
posited was necessary for Gell-Mann’s quark hypothesis to explain
the observed nature of elementary particles. In this theory each
quark carries one of three different types of charges, which are
labeled, for lack of better names, by colors, say, red, green, or blue.
Because of this nomenclature Gell-Mann coined a name for this
Yang-Mills theory: quantum chromodynamics (QCD), the quantum
theory of colored charges, in analogy to quantum electrodynamics,
the quantum theory of electric charges.
͞͡͡
Gross and Wilczek posited, based on the observational arguments
in favor of such a symmetry associated with quarks, that quantum
chromodynamics was the correct gauge theory of the strong
interaction of quarks.
The remarkable idea of asymptotic freedom got an equally
remarkable experimental boost within a year or so of these
theoretical developments. Experiments at SLAC and at another
accelerator in Brookhaven, Long Island, made the striking and
unexpected discovery of a new massive elementary particle that
appeared as if it might be made up of a new quark—indeed, the so-
called charmed quark that had been predicted by Glashow and
friends four years earlier.
But this new discovery was peculiar, because the new particle
lived far longer than one might imagine based on the measured
lifetime of unstable lighter strongly interacting particles. As the
experimentalists who discovered this new particle said, observing it
was like wandering in the jungle and finding a new species of
humans who lived not up to one hundred, but up to ten thousand
years.
Had the discovery been made even five years earlier, it would
have seemed inexplicable. But in this case, fortune favored the
prepared mind. Tom Appelquist and David Politzer, both at Harvard
at the time, quickly realized that if asymptotic freedom was indeed a
property of the strong interaction, then one could show that the
interactions governing more massive quarks would be less strong
than the interactions governing the lighter, more familiar quarks.
Interactions that are less strong would mean particles decay less
quickly. What would otherwise have been a mystery was in this case
a verification of the new idea of asymptotic freedom. Everything
seemed to be fitting into place.
͢͞͡
Except for one pretty big thing. If the theory of quantum
chromodynamics was a theory of the interactions of quarks and
gluons, where were the quarks and gluons? How come none had ever
been seen in an experiment?
Asymptotic freedom provides a key clue. If the strength of the
strong interaction gets weaker the closer one gets to a quark, then
conversely it should get stronger and stronger the farther one is away
from the quark. Imagine, then, what happens if I have a quark and an
antiquark that are bound together by the strong interaction and I try
to pull them apart. As I try to pull them apart, I need more and more
energy because the strength of the attraction between them grows
with distance. Eventually so much energy becomes stored in the
fields surrounding the quarks that it becomes energetically favorable
instead for a new quark-antiquark pair to pop out of the vacuum and
then for each to become bound to one of the original particles. T
he
process is shown schematically below.
It would be like stretching a rubber band. Eventually the band will
snap into two pieces instead of stretching forever. Each piece in this
case would then represent a new bound quark-antiquark pair.
What would this mean for experiments? Well, if I accelerate a
particle such as an electron and it collides with a quark inside a
proton, it will kick the quark out of the proton. But as the quark
begins to exit the proton, the interactions of the quark with the
remaining quarks will increase, and it will eventually be energetically
ͣ͞͡
favored for virtual quark-antiquark pairs to pop out of the vacuum
and bind to both the ejected quark and the other quarks as well. This
means that one will create a shower of strongly interacting particles,
such as protons or neutrons or pions or so on, moving along the
direction of the original ejected quark, and similarly a shower of
strongly interacting particles recoiling in the direction of motion of
the original remaining quarks left over from the proton. One will
never see the quarks themselves.
Similarly, if a particle collides with a quark, in recoiling
sometimes the quark will emit a gluon before it binds with an
antiquark popping out of the vacuum. Then since gluons interact
with each other as well as with quarks, the new gluon might emit
more gluons. The gluons in turn will be surrounded by new quarks
that pop out of the vacuum, creating new strongly interacting
particles moving along the direction of each original gluon. In this
case one would expect in some cases to see not a single shower
moving in the direction of the original quark, but several showers,
corresponding to each new gluon that is emitted along the way.
Because quantum chromodynamics is a specific, well-defined
theory, one can predict the rate at which quarks will emit gluons,
and the rate at which one would see a single shower, or jet as it is
called, kicked out when an electron collides with a proton or
neutron, and the rate at which one would see two showers, and so
on. Eventually, when accelerators became powerful enough to
observe all these processes, the observed rates agreed well with the
predictions of the theory.
There is every reason to believe that this picture of free quarks
and gluons quickly getting bound to new quarks and antiquarks so
Lawrence Krauss - The Greatest Story Ever Told--So Far Page 27