Quantum Man: Richard Feynman's Life in Science Page 17

  Feynman missed out on solving some of them, but the influence of his ideas was unmistakable. Take the “one that got away,” superconductivity. Feynman never succeeded in obtaining the physical breakthrough that the physicists John Bardeen, Leon Cooper, and Robert Schrieffer did to explain this phenomenon—largely because Feynman did not attempt to fully follow previous work in the field, a nagging characteristic that would cause him to miss out on a number of key discoveries—but their approach borrowed heavily from the ideas he introduced to study the properties of materials in general, and specifically the ideas he developed to explain superfluidity. Feynman’s first paper applying his space-time approach to understanding the properties of electrons in materials detailed the importance of the electron coupling to vibrational modes in the material. This coupling turned out to be of crucial importance in understanding the interactions that allow electron pairs to bind together and condense in a superconductor. Indeed, a year before he and his colleagues finally cracked the problem that led to their own Nobel Prize, Schrieffer was in the audience listening to Feynman talk about both superfluidity and superconductivity, and was fascinated to hear Feynman talk in great detail about his own ideas about superconductivity that went wrong. Their own approach to understanding superconductivity was to figure out, just as Feynman had, how a Bose-Einstein–like condensate could form, in this case for particles like electrons that were not bosons. Equally important was demonstrating, as Feynman had demonstrated, that there was an energy gap between the ground state and the excited states, so that at low energies, collisions which otherwise produce excitations that dissipate energy could not occur.

  Feynman’s ideas about how angular momentum would be introduced into a superfluid that was forced to rotate, through the formation of vortices, was also remarkably prescient. A precisely similar phenomenon occurs in superconductors. Here, a superconductor will normally not allow a magnetic field to exist inside of it, just as a superfluid will tend not to move in circular eddies. However, as Feynman showed, if the fluid is forced to rotate (say, by putting it under high pressure and freezing it, and then rotating it and allowing it to melt), the circulation will occur by the production of vortices. Alexei Abrikosov later showed that one can force magnetic field lines through a superconductor, but they too will permeate the superconductor in thin vortex lines. He won the Nobel Prize for his work and said, in his Nobel address, that he put his original proposal in a drawer because Landau didn’t think much of it. It was only after learning about Feynman’s thoughts about rotational vortices in superfluids that Abrikosov had the courage to publish his ideas on magnetic vortices. Feynman’s foray into condensed matter physics was thus remarkable, not just for the manner in which his intuition led to key insights, but by the way in which, in the course of less than a half-dozen pieces of work, his imprint on the field was demonstrable.

  During this period, Feynman enjoyed reaching out to a new community of physicists, but he also suffered the anxieties that occur when entering a field outside one’s expertise. Sometimes you get stepped on. For example, after Feynman surprised Onsager’s students with his predictions of vortices at a conference to which he was invited to speak, he had occasion to meet Onsager at a condensed matter physics meeting. At dinner before Feynman gave a talk, Onsager asked him, “So you think you have a theory of liquid helium?” Feynman answered, “Yes, I do.” Onsager merely replied, “Hmpf,” leading Feynman to think that Onsager didn’t expect much from him.

  The next day, however, when Feynman said there was one aspect of the phase transition he didn’t understand, Onsager spoke up right away, saying, “Mr. Feynman is new in our field, and there is evidently something he doesn’t know about it, and we ought to educate him.” Feynman was petrified, but Onsager continued by saying that the thing that Feynman didn’t understand about helium was not understood for any material, and “therefore the fact that he cannot do it for He II is no reflection at all on the value of his contribution to understanding the rest of the phenomena.”

  Feynman was so taken by this show of warmth that he and Onsager continued to meet and discuss things, even though Feynman did most of the talking. Onsager was not one of Garrison Keillor’s Norwegian bachelor farmers from Minnesota, but he came from the same Norwegian stock, and spoke only rarely, when he felt there was something he really had to say.

  And while Feynman may have missed out on a few extra prizes, the biggest one for him was always in understanding the physics. If he ever felt jealousy or regret because of a lost prize, or misplaced credit, he didn’t show it. Numerous examples abound where he had worked something out to his own satisfaction, but had not felt the need to write up a paper, only to have someone else gain attention for the same idea. Likewise, if he discovered that someone else had a similar idea, he often referenced their own work rather than his own. For example, perhaps in response to Onsager’s show of intellectual generosity at their first meeting, he always credited Onsager with the idea of vortices, even though he discovered Onsager’s work long after he had derived his own results.

  One of the best examples of Feynman’s magnanimity in this regard occurred twenty years after he first started thinking about liquid helium and vortices. When thinking about two-dimensional systems like thin films of liquid helium Feynman realized that the possible appearance of vortices could dramatically change their properties, resulting in a type of phase transition that apparently violated a famous mathematical theorem about the behavior of such two-dimensional systems. He even wrote a paper on the subject. However, he discovered that two young, and then unknown physicists, John Kosterlitz and David Thouless, had just produced a similar paper on the same idea. Rather than swamp them, or scoop them, Feynman decided not to submit his paper for publication, being content on simply having solved the problem himself. The remarkable phase transition has become known as the Kosterlitz-Thouless transition.

  But, much as Feynman enjoyed this respite from the unsettled experimental and theoretical terrain of particle physics, he still yearned to discover a new law of nature, and fundamental physics at the cutting edge was the best possibility. Thus, even as he was working on liquid helium, he was trying to keep up with what was going on in his home territory. Dirac had had his equation. Feynman didn’t yet have his.

  CHAPTER 13

  Hiding in the Mirror

  That was a moment when I knew how nature worked.

  —RICHARD FEYNMAN

  The same mesons that had begun to invade Richard Feynman’s world in 1950 had turned every particle physicists’ world upside down by 1956. New particles kept being discovered, and each one was stranger than the one before. Particles were produced strongly in cosmic rays, but the same physics that produced them should have caused them to quickly decay. Instead, they lasted as long as a hundred-millionth of a second, which doesn’t sound too long, but is millions of times longer than one would predict on the basis of first principles.

  By 1956, Feynman’s fame among physicists was secure. Feynman diagrams had become a part of the standard toolbox of the physics community, and anyone who was passing through Caltech would make every effort to pay homage. Everyone wanted to talk to Feynman because they wanted to talk about their own physics problems. The very same characteristic that made him so irresistible to women worked wonders on scientists as well. It was a characteristic he shared with the remarkable Italian physicist Enrico Fermi, the Nobel laureate who helped lead the Manhattan Project to build the first controlled nuclear reactor at the University of Chicago, and the last nuclear or particle physicist who was equally adept at theory as at experimentation. Fermi had developed a simple theory that described the nuclear process associated with the decay of the neutron into a proton (and an electron and ultimately a new particle that Fermi had dubbed a neutrino—Italian for “little neutron”), so-called beta decay, one of the essential processes that formed a part of the reactions that led to both the atomic bomb and, later, the
rmonuclear weapons.

  Since the neutron lived almost ten minutes before decaying, a virtual eternity compared to the lifetimes of the unstable strongly interacting mesons that were being discovered in the 1950s, it was recognized that the forces at work governing its decay must be very weak. The interaction that Fermi developed a model for in beta decay was therefore called the weak interaction. By the mid-1950s it had become clear that the weak interaction was a wholly distinct force in nature, separate from the strong interactions that were producing all of the new particles being observed in accelerators, and that the weak force was likely to be responsible for the decays of all of the particles with anomalously long lifetimes. But while Fermi’s model for beta decay was simple, there was no underlying theory that connected all of the interactions that were being observed and ascribed to this new force.

  Fermi had built the University of Chicago theory group into an international powerhouse. Everyone wanted to be there, to share not just in the excitement of the physics but also in the excitement of working with Fermi. He had a highly unusual characteristic—one he and Feynman shared: When they listened, they actually listened! They focused all of their attention on what was being talked about, and tried to understand the ideas being expressed, and if possible, tried to help improve upon them.

  Unfortunately, Fermi died in 1954 of cancer, probably induced by careless handling of radioactive materials at a time when the dangers involved were not understood. His death was a blow both to physics and to Chicago, where he had helped train young theorists and experimentalists who would come to dominate the entire field for the next generation.

  After Fermi’s death, young theorists began to be drawn to Feynman’s magnetism. Unlike Fermi, he did not have the character or patience to diligently help train scientists. Yet, there was nothing so flattering as having Feynman direct all of his attention at their ideas. For once Feynman latched on to a problem, he would not rest until he had either solved it or decided it was unsolvable. Many young physicists would mistake his interest in their problems for an interest in them. The result was seductive in the extreme.

  One man who was attracted from Chicago to Feynman’s light was a twenty-five-year-old wunderkind named Murray Gell-Mann. If Feynman dominated particle physics in the immediate postwar era, Gell-Mann would do so in the decade that followed. As Feynman would later describe, in one of his characteristic displays of praise for the work of others, “Our knowledge of fundamental physics contains not one fruitful idea that does not carry the name of Murray Gell-Mann.”

  There is little hyperbole here. Gell-Mann’s talents provided a perfect match to the problems of the time, and he left an indelible mark on the field, not just through exotic language like strangeness and quarks, but through his ideas, which, like Feynman’s, continue to color discussions at the forefront of physics today.

  Gell-Mann was nevertheless in many ways the opposite of Feynman. Like Julian Schwinger, he was a child prodigy. Graduating from high school at the age of fifteen, he received his best offer from Yale, which disappointed him, but he went anyway. At nineteen he graduated and moved to MIT, where he received his PhD at the age of twenty-one. He once told me that he could have graduated in a single year if he hadn’t wasted time trying to perfect the subject of his thesis.

  Gell-Mann not only had mastered physics by the age of twenty-one, he had mastered everything. Most notable was his fascination with languages, their etymology, pronunciation, and relationships. It is hard to find anyone who knows Murray who hasn’t listened to him correct the pronunciation of their own name.

  But Gell-Mann bore a distinct difference from Schwinger that led to his attraction to Feynman. He had no patience with those who couched their often-marginal efforts in fancy formalism. Gell-Mann could see right through the ruse, and there were few physicists who could be so dismissive of the work of others as he could be. But Gell-Mann knew from Feynman’s work, and from listening to him talk, that when he was doing physics, there was no bullshit, no pretense, nothing but the physics. Moreover, Feynman’s solutions actually mattered. As Gell-Mann put it, “What I always liked about Richard’s style was the lack of pomposity in his presentation. I was tired of theorists who dressed up their work in fancy mathematical language or invented pretentious frameworks for their sometimes rather modest contributions. Richard’s ideas, often powerful, ingenious, and original, were presented in a straightforward manner that I found refreshing.”

  There was another facet of Feynman’s character, the showman, that appealed to Gell-Mann much less. As he later described it, he “spent a great deal of time and energy generating anecdotes about himself.” But while this feature would later grate on Gell-Mann’s nerves, following Fermi’s death in 1954, as he considered where he might want to work if he left Chicago, and with whom he might want to work, the choice seemed clear.

  Gell-Mann, along with the theoretical physicist Francis Low, had done a remarkable early calculation in 1954 using Feynman’s QED that sought to address the question of what precisely would happen to the theory as one explored smaller and smaller scales—exactly the traditionally unobservable regime where Feynman’s prescription for removing infinities involved artificially altering the theory. The result was surprising, and while technical and difficult to follow at the time, it eventually laid the basis for many of the developments in particle physics in the 1970s.

  They found that due to the effects of virtual particle-antiparticle pairs that had to be incorporated when considering quantum mechanical effects in QED, physically measurable quantities like the electric charge on an electron depend on the scale at which they are measured. In the case of QED, in fact, the effective charge on the electron, and hence the strength of the electromagnetic interaction, would appear to increase as one penetrated the cloud of virtual electron-positron pairs that would be surrounding each particle.

  Feynman, who was famous for ignoring the papers of others as he independently tried to derive, or more often re-derive, all physics results, nevertheless was very impressed with the paper by Gell-Mann and Low, and he told Gell-Mann so when he first visited Caltech. In fact, Feynman said it was the only QED calculation he knew of that he had not independently derived on his own. In retrospect, this was somewhat surprising because the effect of the Gell-Mann–Low approach was to lead to a totally different interpretation of removing infinities in quantum field theory than Feynman continued to express for some time. It suggests, as you will see, that Feynman’s approach to renormalization, which he had always thought was just an artificial kluge that one day would be replaced by a true fundamental understanding of QED, instead reflected an underlying physical reality that is central to the way nature works on its smallest scales.

  When Gell-Mann arrived at Caltech, it was clear to him, and to much of the rest of the physics community, that perhaps the two greatest physics minds in a generation were now located in a single institution. Everyone was prepared for spontaneous combustion.

  While it is inevitably unfair to choose a single quality to characterize the work of such a deep and inventive mind, Gell-Mann had already begun to make his mark on physics, and would continue to do so, by uncovering new symmetries of nature on its smallest scales. Symmetry is central to our current understanding of nature, but its significance is vastly misunderstood in the public consciousness, in part because things that have more symmetry in physics are perceived to be less interesting in an artistic sense. Traditionally the more ornate the symmetries of a piece of artwork, the more it is appreciated. Thus, a beautiful chandelier with many identical curved pieces is treasured. The artwork of M. C. Escher, in which many copies of a fish or other animal are embedded within a drawing, is another example. But in physics, the symmetries that are most treasured are those that make nature the least ornate. A boring sphere is far more symmetric than a tetrahedron, for example.

  This is because symmetries in physics tell us that objects or sy
stems do not change when we change our perspective. Thus, for example, when we rotate a tetrahedron by 60 degrees along any of its sides, it looks identical. A sphere, however, has much more symmetry because when we rotate a sphere by any angle, no matter how small or large, it looks the same. Recognizing the fact that symmetries imply that something doesn’t change as we change our perspective makes the significance of symmetries in physics, in retrospect, seem almost obvious. But it was not until the young German mathematician Emmy Noether unveiled what is now called Noether’s theorem in 1918 that the ultimate mathematical implications of symmetries for physics became manifest.

  What Noether—who was originally unable to get a university position because she was a woman—demonstrated was that for each symmetry that exists in nature, there must also exist a quantity that is conserved—namely, one that does not change with time. The most famous examples are the conservation of energy and the conservation of momentum. Often in school students learn that these quantities are conserved, but they are taught this as if it is an act of faith. However, Noether’s theorem tells us that the conservation of energy arises because the laws of physics do not change with time—they were the same yesterday as they are today—and that the conservation of momentum arises because the laws of physics do not vary from point to point—they will be the same if we do experiments in London or New York.

  The attempt to use the symmetries of nature to constrain or govern the fundamental laws of physics became more common in the early 1950s as the plethora of new elementary particles appearing in accelerators forced physicists to seek out some order amid the apparent chaos. The effort focused on the search for quantities that did not appear to change when one particle decayed into other particles, for example. The hope was that such conserved quantities would allow one to work backward to find out the underlying symmetries of nature, and that these would then govern the mathematical form of the equations that would describe the relevant physics. That hope has been realized.