Lawrence Krauss - The Greatest Story Ever Told--So Far

by Why Are We Here (pdf)

  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

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  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

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  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.

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  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

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  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

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  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.

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  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.

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  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

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  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