Quantum Man: Richard Feynman's Life in Science

by Lawrence M. Krauss

  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.

  FEYNMAN 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 a
t 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.

  When he railed against pseudo-scientists, alien-abduction “experts,” astrologers, and quacks, he tried to remind us that we seem to be hard wired to find that what happens to each of us naturally appears to take on a special significance and meaning, even if it is an accident. We have to guard against this, and the only way to do so is by adhering to the straitjacket of empirical reality. So, when faced with claims that the end of physics was near and the ultimate laws of physics were right around the corner, Feynman simply uttered, with the wisdom of age, “I’ve had a lifetime of that . . . a lifetime of people who believe that the answer is just around the corner.”

  If the remarkable professional life of one of the most remarkable scientists of the twentieth century is to teach us anything, it is that the excitement and hubris that naturally follow from the rare privilege of uncovering even a small slice of nature’s hidden mysteries need to be tempered by the realization that however much we have learned, more surprises are in store for us, if we are willing to carry on searching. For a fearless and brilliant adventurer like Richard Feynman, this was the reason for living.

  EPILOGUE

  Character Is Destiny

  The way I think of what we’re doing is, we’re exploring—we’re trying to find out as much as we can about the world . . . my interest in science is to simply find out more about the world, and the more I find out, the better it is.

  —RICHARD FEYNMAN

  Richard Feynman died shortly before midnight on Februrary 15, 1988, at the age of sixty-nine. In those few years he had managed to change not only the world, or at least our understanding of it, but also the lives of everyone he met. No one who had the privilege of knowing him was untouched. There was something so unique about him that it was impossible to view him as one viewed others. If it is true that character is destiny, he then seemed born to discover great things, even as his discoveries were the product of unbelievably hard work, boundless energy, and a rigid integrity aligned with a brilliant mind.

  It may also be true that as much as he achieved, he could have accomplished much more had he been more willing to listen and learn from those around him, and insist less on discovering absolutely everything for himself. But accomplishment was not his purpose. It was learning about the world. He felt the fun lay in discovering something, for himself, even if everyone else in the world already knew it. Time after time, when he found out that someone else had scooped him in a discovery, his reaction was not one of despair, but rather, “Hey, isn’t that great that we got it right?”

  Perhaps we can learn the most about a person by the collective reactions of those around him, and so to complete the picture of Richard Feynman, I decided to include some of these reactions that did not make it into the preceding pages, but that might illuminate more fully the remarkable experience of knowing the man, and one or two stories that, for me, capture his essence.

  First, consider the experience of a young student, Richard Sherman, who was fortunate enough to spend an afternoon in Feynman’s office:

  I can recall one episode that I found particularly awesome. Midway through my first year I was doing research on superconductivity, and one afternoon I went into his office to discuss the results. . . . I started to write equations on the blackboard, and he began to analyze them very rapidly. We were interrupted by a phone call. . . . Feynman immediately switched from superconductivity to some problem in high-energy-particle physics, into the middle of an incredibly complicated calculation that was being performed by somebody else. . . . He talked with that person for maybe five or ten minutes. When he was through, he hung up and continued the discussion on my particular calculations, at exactly the point he had left off. . . . The phone range again. This time it was somebody in theoretical solid-state physics, completely unrelated to anything we had been speaking about. But there he was, telling them, “No. No, that’s not the way to do it. . . . You need to do it this way. . . .” . . . This sort of thing went on over about three hours—different sorts of technical telephone calls, each time in a completely different field, and involving different types of calculations. . . . It was staggering. I have never seen this kind of thing again.

  Or a not-too-different experience related by Danny Hillis, after Feynman started his summer job at Thinking Machines:

  Often, when one of us asked him for advice, he would gruffly refuse with, “That’s not my department.” I could never figure out just what his department was, but it didn’t matter anyway, because he spent most of his time working on these “not my department” problems. . . . More often than not he would come back a few days after his refusal and remark, “I’ve been thinking about what you asked the other day and
it seems to me . . .” . . . But what Richard hated, or at least pretended to hate, was being asked to give advice. So why were people always asking him for it? Because even when Richard didn’t understand, he always seemed to understand better than the rest of us. And whatever he understood, he could make others understand as well. Richard made people feel like children do when a grown-up first treats them as adults. He was never afraid to tell the truth.

  Solving problems was not a choice for Feynman, it was a necessity, as his college chum Ted Welton realized early on. Feynman couldn’t have stopped if he tried, and he didn’t try because he was so good at it. Not even a fatal illness could stop him. Consider a story his Caltech colleague David Goodstein told to the filmmaker Christopher Sykes:

  One day Feynman’s secretary Helen Tuck called me up to tell me quietly that Dick had cancer and that he would be going into the hospital for an operation the following Friday. . . . This particular Friday, a week before the operation . . . I told him that somebody had found an apparent error in a calculation that we had done . . . and I didn’t know what the error was. Would he be willing to spend some time with me to look for it? And he said, “Sure.” . . . On Monday morning we met in my office and he sat down and started working. . . . Most of the time I just sat there looking at him, and thinking to myself, “Look at this man. He faces the abyss. He doesn’t know whether he is going to live through this week, and here is this really unimportant problem in two-dimensional elastic theory.” But he was consumed by it, and he worked on it all day long. . . . Finally, at six o’clock in the evening, we decided that the problem was intractable . . . so we gave up and went home. . . . Two hours later, he called me at home to say that he had solved the problem. He hadn’t been able to stop working on it, and finally he had found the solution to this utterly obscure problem . . . he was exhilarated, absolutely walking on air. . . . This was four days before the operation. I think that tells you a little bit about what drove the man to do what he did.