Thus, even as scientist-philosophers of the twentieth century had stumbled—often by a convoluted and dimly lit path—outside our cave of shadows to glimpse the otherwise hidden reality beneath the surface, one more force relevant to understanding the fundamental structure of matter was conspicuously missing from the beautiful emerging tapestry of nature.
Chapter 19
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FREE AT LAST
Let my people go.
—EXODUS 9:1
The long road that led to electroweak unification was a tour de force of intellectual perseverance and ingenuity. But it was also a detour de force. Almost all of the major ideas introduced by Yang, Mills, Yukawa, Higgs, and others that led to this theory were developed in the apparently unsuccessful struggle to understand the strongest force in nature, the strong nuclear force. Recall that this force, and the strongly interacting particles that manifested it, had so bedeviled physicists that in the 1960s many of them had given up hope of ever explaining it via the techniques of quantum field theory that had so successfully now described both electromagnetism and the weak interaction.
There had been one success, centered on Gell-Mann and Zweig’s proposal that all the strongly interacting particles that had been observed, including the proton and the neutron, could be understood as being made up of more fundamental objects, which, as I have described, Gell-Mann called quarks. All the known strongly interacting particles, and at the time undiscovered particles, could be classified assuming they were made of quarks. Moreover, the symmetry arguments that led Gell-Mann in particular to come up with his model served as the basis for making some sense of the otherwise confusing data associated with the reactions of strongly interacting matter.
Nevertheless, Gell-Mann had allowed that his scheme might merely be a mathematical construct, useful for classification, and that quarks might not represent real particles. After all, no free quarks had ever been observed in accelerators or cosmic-ray experiments. He was also probably influenced by the popular idea that quantum field theory, and hence the notion of elementary particles themselves, broke down on nuclear scales. Even as late as 1972 Gell-Mann stated, “Let us end by emphasizing our main point, that it may well be possible to construct an explicit theory of hadrons, based on quarks and some kind of glue. . . . Since the entities we start with are fictitious, there is no need for any conflict with the bootstrap . . . point of view.”
Viewed in this context, the effort to describe the strong interaction by a Yang-Mills gauge quantum field theory, with real gauge particles mediating the force, would be misplaced. It also seemed impossible. The strong force appeared to operate only on nuclear scales, so if it was to be described by a gauge theory, the photonlike particles that would convey the force would have to be heavy. But there was also no evidence of a Higgs mechanism, with massive strongly interacting Higgs-like particles, which experiments could have easily detected. Compounding this, the force was simply so strong that even if it was described by a gauge theory, then all of the quantum field theory techniques developed for deriving predictions—which worked so well for the other forces—would have broken down if applied to the strong force. This is why Gell-Mann in his quote referred to the “bootstrap”—the Zen-like idea that no particles were truly fundamental. The sound of no hands clapping, if you will.
Whenever theory faces an impasse like this, it sure helps to have experiment as a guide, and that is exactly what happened, in 1968. A series of pivotal experiments, performed by Henry Kendall, Jerry Friedman, and Richard Taylor, using the newly built SLAC accelerator to scatter high-energy electrons off protons and neutrons, revealed something remarkable. Protons and neutrons did appear to have some substructure, but it was strange. The collisions had properties no one had expected. Was the signal due to quarks?
Theorists were quick to come to the rescue. James Bjorken demonstrated that the phenomena observed by the experimentalists, called scaling, could be understood if protons and neutrons were composed of virtually noninteracting pointlike particles. Feynman then interpreted these objects as real particles, which he dubbed partons, and suggested they could be identified with Gell-Mann’s quarks.
This picture had a big problem, however. If all strongly interacting particles were composed of quarks, then quarks should surely be strongly interacting themselves. Why should they appear to be almost free inside protons and neutrons and not be interacting strongly with each other?
Moreover, in 1965, Nambu, Moo-Young Han, and Oscar Greenberg had convincingly argued that, if strongly interacting particles were composed of quarks and if they were fermions, like electrons, then Gell-Mann’s classification of known particles by various combinations of quarks would only be consistent if quarks possessed some new kind of internal charge, a new Yang-Mills gauge charge. This would imply that they interacted strongly via a new set of gauge bosons, which were then called gluons. But where were the gluons, and where were the quarks, and why was there no evidence of quarks interacting strongly inside protons and neutrons if they were really to be identified with Feynman’s partons?
In yet another problem with quarks, protons and neutrons have weak interactions, and if these particles were made up of quarks, then the quarks would also have to have weak interactions in addition to strong interactions. Gell-Mann had identified three different types of quarks as comprising all known strongly interacting particles at the time. Mesons could be comprised of quark-antiquark pairs. Protons and neutrons could be made up of three fractionally charged quarks, which Gell-Mann called up (u) and down (d) quarks. The proton would be made of two up quarks and one down quark, while the neutron would be made of two down quarks and one up quark. In addition to these two types of quarks, one additional type of quark, a heavier version of the down quark, was required to make up exotic new elementary particles. Gell-Mann called this the strange (s) quark, and particles containing s quarks were dubbed to possess “strangeness.”
When neutral currents were first proposed as part of the weak interaction, this created a problem. If quarks interacted with the Z particles, then u, d, and s quarks could remain u, d, and s quarks before and after the neutral current interaction, just as electrons remained electrons before and after the interaction. However, because the d and s quarks had precisely the same electric and isotopic spin charges, nothing would prevent an s quark from converting into a d quark when it interacted with a Z particle. This would allow particles containing s quarks to decay into particles containing d quarks. But no such “strangeness-changing decays” were observed, with high sensitivity in experiments. Something was wrong.
This absence of “strangeness-changing neutral currents” was explained brilliantly, at least in principle, by Sheldon Glashow, along with collaborators John Iliopoulos and Luciano Maiani, in 1970. They took the quark model seriously and suggested that if a fourth quark, dubbed a charm (c) quark, existed, which had the same charge as the u quark, then a remarkable mathematical cancellation could occur in the calculated transformation rate for an s quark into a d quark, and strangeness-changing neutral currents would be suppressed, in agreement with experiments.
Moreover, this scheme began to suggest a nice symmetry between quarks and particles such as electrons and muons, all of which could exist in pairs associated with the weak force. The electron would be paired with its own neutrino, as would the muon. The up and down quarks would form one pair, and the charm and the strange quark another pair. W particles interacting with one particle in each pair would turn it into the other particle in the pair.
None of these arguments addressed the central problems of the strong interaction between quarks, however. Why had no one ever observed a quark? And, if the strong interaction was described by a gauge theory with gluons as the gauge particles, how come no one had ever observed a gluon? And if the gluons were massless, how come the strong force was short-range?
These problems continued to suggest to some that quantum field theory was the wrong approach for understanding the
strong force. Freeman Dyson, who had played such an important role in the development of the first successful quantum field theory, quantum electrodynamics, asserted, when describing the strong interaction, “The correct theory will not be found in the next hundred years.”
One of those who were convinced that quantum field theory was doomed was a brilliant young theorist, David Gross. Trained under Geoffrey Chew, the inventor of the bootstrap picture of nuclear democracy, in which elementary particles were an illusion masking a structure in which only symmetries and not particles were real, Gross was well primed to try to kill quantum field theory for good.
Recall that even as late as 1965, when Richard Feynman received his Nobel Prize, it was still felt that the procedure he and others had developed for getting rid of infinities in quantum field theory was a trick—that something was fundamentally wrong at small scales with the picture that quantum field theory presented.
Russian physicist Lev Landau had shown in the 1950s that the electric charge on an electron depends on the scale at which you measure it. Virtual particles pop out of empty space, and electrons and all other elementary particles are surrounded by a cloud of virtual particle-antiparticle pairs. These pairs screen the charge, just as a charge in a dielectric material gets screened. Positively charged virtual particles tend to closely surround the negative charge, and so 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 asymptoti
c 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.
The Greatest Story Ever Told—So Far Page 22