Quantum Man: Richard Feynman's Life in Science (27 page)

Feynman’s methods for understanding quantized Yang-Mills theories turned out to be of crucial importance for the major developments in physics at the end of the decade. First, Steven Weinberg rediscovered Glashow’s model for
electroweak unification
, as it was called, in the context of a specific and more realistic Yang-Mills theory where the weak bosons could, in principle, start out with zero mass—preserving the gauge symmetry—and their mass could arise later, spontaneously, due to the dynamics of the theory.

This was a beautiful potential solution to the problem of finding a theory of the weak interaction. But there remained a problem. Was the theory “renormalizable”? Namely, could one show, as Feynman, Schwinger, and Tomonaga did in QED, that all of the infinities can be efficiently removed in the prediction of physical quantities? In 1972, a young Dutch graduate student, Gerardus ’t Hooft and his supervisor, Martinus Veltman, building on Feynman’s methods for quantizing these theories, provided the answer: yes. Suddenly the Glashow-Weinberg theory became interesting! Within the next five years experiments began to provide evidence that the theory was correct, including the need for three new heavy-gauge bosons, and in 1984 at CERN the heavy bosons themselves were discovered. All of these developments produced a field day of Nobel Prizes: for Glashow, Weinberg, and Abdus Salam, who had done work similar to theirs, and for ’t Hooft and Veltman and the experimentalists who discovered the weak bosons.

Now theorists had wonderful and fundamental theories of the weak and electromagnetic interactions, but the strong interaction remained puzzling. A more complicated Yang-Mills theory, associated with the same symmetry group that Gell-Mann had used to classify quarks, SU(3), seemed promising. In this case the “3” did not correspond to different “flavors” of quarks—that is, up, down, and strange—but rather to some new internal quantum number which became called
color
. This theory seemed to be able to describe the phenomenological features of the way quarks might combine together to form hadrons. In analogy to QED, it was called
quantum chromodynamics
, or
QCD
. However, once again the strong interaction was short range, seeming to require massive bosons.

But more important, how could a strong new force explain the fact that the objects inside protons, whether one called them partons or quarks, act as if they are not interacting? The solution came within a year, and it hearkened back to Gell-Mann and Low’s results about the strengthening of the effective value of the electric charge on electrons at small scales.

In 1973, at a time when the stock in quantum field theory seemed to be rising, following the progress in the electroweak theory, a young theorist at Princeton who had been weaned at Berkeley on the nuclear democracy models, which argued that particles and fields were the wrong way to approach the strong interactions, decided to kill the only remaining theory that still had any hope of explaining the strong interaction. David Gross and his brilliant student Frank Wilczek decided to examine the short-distance behavior of Yang-Mills theories, and QCD in particular, with the aim of showing that the effective magnitude of the “color charges” in QCD would, as in QED, appear to increase at short distances due to screening by virtual particles at longer ones. If this were the case there was no hope for such a QCD theory explaining the SLAC scaling results exposed by Feynman and Bjorken. For different reasons, a Harvard graduate student of Sidney Coleman’s, David Politzer, was also independently investigating the scaling properties of QCD.

To the surprise of all three scientists, precisely the opposite behavior from what was expected was observed in the resulting equations (once various crucial sign errors were checked and corrected), but only for Yang-Mills theories such as QCD. The effective “color charge” of quarks would not get larger at short distances, but smaller. The theorists dubbed this remarkable and unexpected property, asymptotic freedom. Gross and Wilczek and then Politzer followed up on this discovery with a series of papers in which they adopted precisely the formulation Feynman had developed for making comparisons with the results of the scaling experiments at SLAC. They discovered that not only could QCD explain the scaling, but also, due to the fact that the interactions between quarks were not zero but were nevertheless weaker than they would be without asymptotic freedom, it was possible to calculate corrections to the scaling behavior, which should be observable.

Meanwhile Feynman remained skeptical of all of the excitement about the new results. He had seen theorists get carried away too many times with new grand ideas to jump on any bandwagons. What was particularly interesting was that his skepticism persisted
in spite
of the fact that these new results arose from exploiting the very techniques that he had pioneered, both for understanding scaling experiments and for dealing with Yang-Mills theories.

Eventually—by the mid-1970s—Feynman had become convinced that there was enough merit in these ideas that he began to follow up on them in detail, and with great zest and energy. With a postdoctoral researcher, Rick Field, Feynman calculated a host of potentially physically observable effects in QCD, helping spearhead a new and exciting era of close mutual contact between experiment and theory. It was hard work. The energy scale at which QCD interactions became weak enough that the calculations of the theorists were reliable was somewhat higher than the experimentalists were able to achieve. Therefore, even though tentative confirmation of the predictions of asymptotic freedom were coming in, it took at least another decade—until the mid-1980s, close to the time of Feynman’s death—before the theory was fully confirmed. And it took another twenty years before Gross, Wilczek, and Politzer were awarded the Nobel Prize for their work on asymptotic freedom.

During his last years, as much as Feynman remained fascinated with QCD, a part of him continued to resist fully buying into the theory. For while the theory seemed to do a wonderful job explaining the SLAC scaling—and while the subsequent predicted scaling deviations were also observed and indeed all measurements of the strength of the QCD interaction showed it getting weaker at short distances and high energies—on the opposite long-distance scale the theory became unwieldy. This prevented any theoretical test of what would have been the gold standard for Feynman: an explanation of why we don’t see any free quarks in nature.

The conventional wisdom is that QCD gets so strong at large distances that the force between quarks remains constant with distance, and therefore it would take, in principle, an infinite amount of energy to pull two quarks fully apart. This expectation has been supported by complex computer calculations, calculations of the type spearheaded by Feynman when he was working on the Connection Machine for Hillis in Boston.

But a computer result was, to Feynman, merely an invitation to understand the physics. As he had learned at the feet of Bethe so many years ago, until he had an analytical understanding of why something happened such that it could produce numbers comparable with experimental data, he didn’t trust the equations. And he didn’t have that. Until he did, he wasn’t willing to lay down his sword.

This was when I first met Richard Feynman, as I described at the beginning of this book. He came to Vancouver and lectured with great excitement on an idea he thought could prove that QCD would be
confining
, as the problem of the “non-observation” of isolated free quarks was called. The problem was too difficult to treat in three dimensions, but he was pretty sure that in two dimensions he could develop an analytical approach that would finally settle the matter in a way that would satisfy him.

F
EYNMAN CONTINUED TO
press on hard, through his battle with cancer, first treated in 1979 and then reappearing in 1987, and through the increasing distractions associated with his growing fame, from activities surrounding his best-selling autobiographical books to his stint on the
Challenger
commission (where he personally helped uncover the reason for the tragic space shuttle explosion). But he never lived to see his goal realized. To this very day, while computer calculations have improved tremendously, giving more and more support to the notion of confinement, and while a host of new theoretical techniques have allowed sophisticated new ways of dealing with Yang-Mills theories, no one has come up with a simple and elegant proof that the theory must confine quarks. No one doubts the theory, but the “Feynman test,” if one might call it that, has not yet been met.

Feynman’s legacy lives on, however, every single day. The only truly efficient and productive techniques for dealing with both Yang-Mills gauge theories and gravity involve Feynman’s path-integral formalism. Essentially no other formulation of quantum field theory is used by modern physicists. But more important, the results of path integrals, asymptotic freedom, and the renormalizability of the strong and weak interactions have pointed physicists in a new direction, giving a new understanding of scientific truth in a way that should have made Feynman finally feel proud of the work he did on QED, instead of feeling that he had merely found an elegant way to sweep problems under the rug.

Feynman’s path-integral methodology allowed physicists to systematically examine how the predictions of the theory change as one changes the distance scale at which one chooses to alter the theory to remove the effects of higher- and higher-energy virtual particles in order to renormalize the theory. Because in his language quantum theories are formulated by explicitly examining space-time paths, one can “integrate out” (that is, average over) the very small wiggles in paths appropriate to these scales, and thereby consider only paths that no longer have such wiggles.

The physicist Kenneth Wilson, who later won a Nobel Prize, demonstrated that this integrating out means that the resulting theory, the finite theory, is really only an “effective theory,” one that is appropriate to describe nature on scales larger than the cutoff scale where small wiggles in paths are integrated out.

Feynman’s technique of getting rid of infinities then was not an artificial kluge, but rather physically essential. This is because we now realize we should no longer expect a theory to hold, unaltered, at all energy and distance scales. No one expects QED, the best-tested and most-beloved theory in physics, to remain the appropriate description of nature as the scales get smaller and smaller. Indeed, as Glashow, Weinberg, and Salam demonstrated, at a sufficiently high-energy scale QED merges with the weak interaction to form a new unified theory.

We now understand that
all
physical theories are merely effective theories that describe nature on a certain range of scales. There is no such thing yet as absolute scientific truth, if by that we mean a theory that is valid at all scales at all times. The physical need for renormalization is then simple: the infinite theory—namely, the one where we extrapolate our theory down to arbitrarily small distance scales—is
not
the right theory and the infinities are the sign of this. If we choose to so extrapolate the theory, we are doing so beyond its domain of validity. By cutting off the theory at some small scale, we are simply ignoring the unknown new physics which would inevitably change the theory at these scales. The finite answers we get are meaningful precisely because if we wish to probe phenomena at large distance scales, we
can
ignore this unknown new physics at tiny scales. Sensible, renormalizable theories like QED are insensitive to new physics at distance scales well below those scales where we perform experiments to test the theories.

Feynman’s hope that somehow we would be able to solve the infinity problem in QED without renormalization was therefore a misplaced hope. We now know that his picture, which allows us to systematically see how to ignore the things we do not understand, is as good a one as we are likely to get. In short, Feynman did as much as was possible, and far from hiding the problems of field theory, his mathematical fix was much more than that. It truly demonstrated new physical principles that he had always hoped he would one day be responsible for discovering.

This new understanding would have pleased Feynman, not just because it gives new significance to his own early work but because it keeps the mysteries fresh. No currently known theory is the final answer. He would have liked that. As he once said, “People say to me, ‘Are you looking for the ultimate laws of physics?’ No, I’m not. I’m just looking to find out more about the world. If it turns out there is a simple, ultimate law which explains everything, so be it; that would be very nice to discover. If it turns out it’s like an onion, with millions of layers, and we’re sick and tired of looking at the layers, then that’s the way it is. But whatever way it comes out, it’s nature, and she’s going to come out the way she is.”

At the same time, the remarkable developments of the 1970s made possible by building on Feynman’s work led many physicists to strike out in another direction. After the success of electroweak unification and asymptotic freedom, a new possibility arose. After all, as Gell-Mann and Low showed, QED gets stronger at small scales. And as Gross, Wilczek, and Politzer demonstrated, QCD gets weaker at small scales. Maybe if we went to a very small scale, which we estimate might be sixteen orders of magnitude smaller than the size of a proton, and some twelve orders of magnitude smaller than the best current accelerators can probe, all the known forces might become unified in a single theory, with a single strength. This possibility, which Glashow dubbed
grand unification
, became the driving force for particle physics in much of the 1980s, subsumed by an even grander goal when string theory was discovered to allow a possible unification of the three nongravitational forces with gravity.

Feynman, however, remained suspicious. All his life he had fought against reading too much into data, and he had witnessed a host of brilliant, elegant theories fall by the wayside. Moreover, he knew that unless theorists are willing and able to continue to test their ideas against the cold light of experimentation, the possibility for self-delusion remains great. He knew, as he often said, that the easiest person to fool is yourself.