Quantum Man: Richard Feynman's Life in Science

by Lawrence M. Krauss

But Feynman also took seriously his own mission of helping to rejuvenate physics in Brazil. He taught courses at the Centro Brasileiro de Pesquisas Fisícas and chastised the Brazilian authorities for teaching students to memorize names and formulas but not to think about what they were doing. He complained they were learning how to explain words in terms of other words, but actually understood nothing and had no feel for the actual phenomena they were supposedly studying. For Feynman, understanding meant being able to take one’s knowledge and apply it to new situations.

  As brilliant as Feynman was, though, the isolation in Brazil kept him from keeping up with the forefront of the field at the time. He managed to independently reproduce results that had already been derived, but did not push the emerging field of particle physics forward. Instead, he had a cultural awakening and a sexual feast.

  First, music. Feynman claimed he was tone-deaf, but there is no doubt, even if he marched to the beat of a different drummer, that he was born with rhythm. All those who were close to him knew that he was constantly drumming with his fingers whenever he worked, on paper, on walls, on anything that was convenient. In Rio, Feynman found the perfect music for his psyche—samba, a hot, rhythmic, and unpretentious hybrid of Latin and African traditions. He joined a samba school and began drumming in samba bands. He even got paid for his efforts. The peak occurred during the annual Carnaval, a debauched street festival, where he could carouse with abandon. And carouse he did. (Purely by coincidence I am writing this as I stare out from a hotel at Copacabana beach.)

  It is easy to understand the fascination Rio had for Feynman. The city is breathtakingly beautiful, surrounded by gorgeous mountain and ocean scenery, and vibrant with the Rio cariocas, locals occupied with partying, arguing, playing soccer, and flirting on the beach. The full spectrum of human activity is almost always on display. The city is seedy, sexy, intense, scary, friendly, and relaxed, all at the same time. There Feynman could escape the confinement of a university town, where one could never quite get away from colleagues or students. Moreover, the Brazilians are a warm, friendly, and accepting people. Feynman could blend in. His own intense enthusiasm, never far from the surface, must have resonated with everyone around him—physicists, local cariocas, and, naturally, women.

  Feynman lived at the Miramar Palace Hotel on Copacabana beach, where he descended into his lonely orgy of drinking (until he frightened himself enough to swear off alcohol for good) and sex. He picked up women on the beach and in clubs and at the hotel’s patio bar, whose proximity to the action of Copacabana was, and still is, addictive. For a while he specialized in stewardesses who stayed at the hotel, and as he famously described over and over again, he enjoyed outsmarting the local women he met in bars. He convinced one of them not only to sleep with him, but also to repay him for the food he had bought her at the bar.

  As often happens, however, this anonymous sex, while diverting, only reinforced his detached loneliness, and perhaps that is why he committed an utterly ridiculous and out-of-character act. He proposed, by letter, to a woman in Ithaca he had known and dated, a woman so different from the rest, and so different from Feynman, that perhaps he convinced himself she was the perfect complement.

  Many of his previous girlfriends realized that the mutual enjoyment they thought they were sharing with Feynman was not being fully reciprocated. Feynman could concentrate completely on a woman he was with, in a way that was utterly captivating. But at the same time, as intense as his physical participation might have seemed, he was really alone with his thoughts. Mary Louise Bell, not savvy to this flaw, apparently pursued him from Ithaca to Pasadena. A platinum blonde with a penchant for high heels and tight clothes, she somehow thought that with Feynman she had the scaffolding from which she could fashion a final structure to her liking, one with a more polished exterior and a better appreciation of the arts, and one who wouldn’t hang around with so many scientists.

  They married in 1952. With hindsight some have said that divorce was inevitable, but there are no real rules from which one can make accurate predictions in matters of the heart. Nevertheless, one of the items brought up in the divorce proceedings was telling. She reported, “He begins working calculus problems in his head as soon as he awakens. He did calculus while driving his car, while sitting in the living room and while lying in bed at night.”

  During the first years together, as he settled into Pasadena following his wild year in Brazil, and his domestic bliss slowly turned into another private hell, he began to think he had made a mistake not only in choice of companion, but in choice of locale. He even wrote to Hans Bethe to discuss moving back to Cornell. But Caltech’s lure was greater than Mary Louise’s, and four years after their marriage, in 1956, he and Mary Louise parted ways, but he remained in Pasadena.

  His new university was quickly growing to become a rival to his own eastern alma mater, MIT. It was an institution that, with its growing experimental and theoretical prominence in fields ranging from astrophysics to biochemistry and genetics, combined with the practical leanings of an engineering school, seemed like a perfect fit. It was. He would stay for the rest of his life.

  Physics was experiencing a period of turmoil at the same time as Feynman’s personal upheavals. Newly discovered elementary particles, mesons and the like, were proliferating madly in the newly built particle accelerators. The elementary particle physics zoo was becoming embarrassingly crowded, so crowded in fact that it wasn’t clear which of the new blips on chart recorders and new tracks in bubble chambers might really represent new elementary particles and which were simply rearrangements of existing ones.

  While Feynman had dabbled early on in the theory of mesons when he was perfecting his understanding of QED, he was also smart enough and realistic enough to know that his new diagrammatic methods were inappropriate to the task at hand. Not only were many of the experiments inconclusive, but the interactions between particles were generally so strong that the systematic effort to use Feynman diagrams to calculate small quantum corrections to processes seemed misplaced. He wrote to Enrico Fermi from Brazil: “Don’t believe any calculation in meson theory that uses a Feynman diagram!” Elsewhere he referred to the field of meson physics by saying, “Perhaps there aren’t enough clues for even a human mind to figure out what is the pattern.”

  I suspect that, in his view, the experimental world of mesons wasn’t yet ready for interpretation, and he had a desire to strike out in a new intellectual direction, one that wasn’t governed so much by attempting to unravel the mathematical intricacies of the quantum world as much as directly trying to puzzle out its physical consequences. He wanted to think about something he could feel and play with, and not something he could only see in his mind. Thus, shortly after arriving at Caltech, Feynman turned to a completely different problem in a different area of physics. He began to explore not the quantum world of the very small, but the very cold.

  The Dutch physicist Kamerlingh Onnes, who worked during the end of the nineteenth and early twentieth centuries, devoted his entire professional life to the physics of the very cold, cooling down systems closer and closer to absolute zero, the temperature where, classically at least, all internal motions of atoms would stop. In so doing, he made a miraculous discovery in 1911. At a temperature of 4 degrees above absolute zero (Onnes eventually got to less than 1 degree above absolute zero, reaching the coldest temperature ever achieved on earth up to that time), he witnessed a spectacular transition in mercury, in which electrical currents suddenly appeared to flow without any resistance at all.

  It had been speculated that electrical resistance would decrease at very low temperatures, based on the simple observation that such a decrease was also observed at higher temperatures. Onnes himself speculated that the resistance would drop to zero at absolute zero, a temperature that can never be obtained directly in the laboratory. However, his amazing result was that the resistance abruptly dropped to exactly zero at a
finite small, but nonzero, temperature. In such a state, an electric current, once started, would never stop. Onnes had discovered the phenomenon he called superconductivity.

  Interestingly, when Onnes won the Nobel Prize two years later, he did not win it explicitly for this discovery, but rather for his general “investigations on the properties of matter at low temperatures which led, inter alia, to the production of liquid helium.” The prize showed unusual prescience (actually dumb luck) on the part of the Nobel Committee because it turned out, for reasons no one could have suspected in 1913, that liquid helium itself had properties at least as fascinating as those related to the conductivity of mercury and other metals at low temperatures. In 1938 it was discovered that liquid helium, when cooled sufficiently, exhibits a phenomenon known as superfluidity, which on its surface seems even stranger than superconductivity. Again, equally remarkably, Onnes probably cooled liquid helium to temperatures where it was superfluid, but didn’t remark on this otherwise remarkable phenomenon.

  In its superfluid phase, helium flows with no friction whatsoever. Put it in a container, and it will spontaneously flow in a thin film up over its edges. No matter how small a crack, it will flow through it. Unlike superconductivity, where the magic is hidden behind resistance and current measurements, with superfluidity it is on full display before our eyes.

  As late as the early 1950s neither of these remarkable phenomena had yet been explained in terms of a microscopic atomic theory. As Feynman put it, they were like “two cities under siege . . . completely surrounded by knowledge although they themselves remained isolated and unassailable.” At the same time, he was enamored with all of the fascinating new phenomena that nature revealed at low temperatures, and said, “I imagine experimental physicists must often look with envy at men like Kamerlingh Onnes, who discovered a field like low temperature, which seems to be bottomless and in which one can go down and down.” Feynman was fascinated by all of these phenomena, but he turned his attention primarily to the mysteries of liquid helium, although he continued to struggle, ultimately unsuccessfully, to unravel the origin of superconductivity.

  While at the time the field of what was eventually to become known as condensed matter physics was small, it is still hard to overemphasize the dramatic jump that Feynman had decided to take. Although the problems of superconductivity and superfluidity had not yet been solved, the people working in the field included some of the best minds in physics, and they had been thinking about the problems for some time.

  Feynman clearly thought a fresh approach was needed, however, and among all of his research efforts, perhaps none better demonstrated how his remarkable physical intuition, combined with his mathematical prowess, could go around, rather than break down, preexisting barriers to understanding. The physical picture he ultimately derived achieved all of his goals for understanding superfluidity and, after the fact, seems remarkably simple—so simple that one wonders why no one else had thought of it. But that was a characteristic of Feynman’s work. Beforehand everything was mired in mist, but after he had shown the way, everything seemed so clear as to be almost obvious.

  Besides his general fascination with interesting phenomena in physics, one might wonder what it was about the problems of liquid helium in particular, and the applications of quantum mechanics to the properties of materials in general, that caused him to shift his focus to this area. I suspect that once again, the motivation might have come from his early efforts to understand the properties of the new strongly interacting elementary particles, mesons. Whereas he realized that Feynman diagrams were not likely to help unravel the thoroughly confusing experimental situation associated with the plethora of new strongly interacting particles emerging from accelerators, he nevertheless was interested in other physical ways that one might quantitatively understand the relevant physics that governed other strongly interacting systems.

  The properties of electrons and atoms in dense materials provided for him precisely a similar problem, but one in which the experimental situation was much cleaner and the theoretical landscape at the time much less crowded. Indeed, until Feynman approached the problem, no one had attempted to use quantum mechanics at a microscopic level to directly derive the general properties of the transition of liquid helium from a normal state to a superfluid state.

  That quantum mechanics played a key role in superfluidity was clear early on. In the first place, the only systems known in nature that behaved in a similar way, with no dissipation and no loss of energy, were atoms. According to the laws of classical electromagnetism, electrons orbiting in circles around protons should lose energy by radiation, so that the electrons would quickly spiral in to the nucleus. However, Niels Bohr postulated, and Erwin Schrödinger eventually demonstrated with his wave equation, that electrons could exist in stable energy levels where their properties would remain fixed in time, with no dissipation in energy.

  So much for individual electrons or atoms, but could a whole macroscopic system like a visible amount of liquid helium exist in a single quantum state? Here there was another clue quantum mechanics was important. Classically, absolute zero is defined as the temperature where all motion ceases. No heat energy exists for atoms to vibrate or jostle one another, as in a standard gas or liquid, or even a solid. Moreover, assuming separate helium atoms had some small residual attraction with each other, which is required so a liquid simply doesn’t fall apart into a gas of individual atoms, then at absolute zero, or near it, helium liquid should instead freeze into a rigid solid, with atoms held in place by their mutual attraction and no heat energy to move them around.

  However, this isn’t the case. As cold as anyone can make it, down well below 1 degree above absolute zero, as even Onnes showed, helium doesn’t solidify. Quantum mechanics is once again the culprit. Even the lowest energy state in any quantum system always has a nonzero energy, associated with quantum fluctuations. Thus, even at absolute zero, helium atoms would still jiggle around. Helium is very light while at the same time the attraction between helium atoms is small enough so that the quantum ground-state energy of the atoms is sufficient enough to cause them to overcome this attraction and move about in a liquid form, rather than freezing in a lattice like a solid. Hydrogen atoms, which are even lighter, would exhibit the same phenomenon, except that hydrogen atoms are much more strongly attracted to each other, so their ground-state energy at low temperatures is not sufficient to break apart the bonds of a solid, and hydrogen freezes.

  Helium is therefore unique in remaining a liquid at low temperatures, and its uniqueness is inherently quantum mechanical in origin. Thus, it makes sense that quantum mechanics also governs the transition that turns helium from a normal liquid to a superfluid at about 2 degrees above absolute zero.

  As early as 1938, the physicist Fritz London had suggested that the transition to superfluidity might be a macroscopic example of a phenomenon that Einstein and the Indian physicist Satyendra Bose had predicted in an ideal gas of bosons—that is, particles with integer values of spin. Unlike fermions, which, as I have described, are subject to the Pauli exclusion principle, and cannot be in the same state at the same time and place, bosons behave precisely the opposite. As Bose and Einstein predicted, a gas of bosons can, at sufficiently low temperature, condense into a single macroscopic quantum state, where all of the particles are in precisely the same quantum state, and the macroscopic configuration would behave as a quantum mechanical and not a classical object. (In a classical object the individual particles have probability amplitudes that are completely uncorrelated with those of their neighbors. As a result, any fancy quantum interference between particles, which comes about by exact cancellations of different probability amplitudes, and which produces many of the strange aspects of the quantum world, is lost.)

  The problem, however, is that Bose-Einstein condensation, as it is called, occurs for an ideal gas, in which the individual particles have no interactions wit
h each other. Helium atoms, however, have weak attraction at a distance, and strong repulsion when they are very close. Was it possible that such a system could still have a Bose-Einstein–like condensation transition? This was one of the problems that drew Feynman’s interest.

  He not only was interested but also had developed the tool that allowed him an intuitive understanding of quantum mechanical effects. His method of recasting quantum mechanics as a sum over paths, with each path weighted by its action, provided, he believed, the perfect framework for picturing the microscopic phenomena that governed liquid helium at low temperatures.

  As Feynman began to think about the sum over paths for each particle in the quantum liquid, two key factors guided him. First, since the helium atoms are bosons, the quantum mechanical amplitude describing their configuration is independent of which boson is where—it remains unchanged if the positions of any two helium atoms are exchanged. This means that paths dominating the path integral (that is, those with the smallest action), in which individual particles returned to their same position, had to be treated as identical to paths where the final positions of all of the particles resembled the initial configuration, while some of the particles had interchanged positions with one another. On the surface this may seem like an irrelevant mathematical subtlety, but it turns out to profoundly affect the physics.

  The second factor focused on the action associated with the motion of any one helium atom in the background of all of its neighbors. Remember that the classical action associated with any trajectory involves summing up the differences between the kinetic and potential energies at all points along the path. Feynman reasoned that as any helium atom moved along at some velocity, it could reach any other point without getting close to another helium atom and experiencing a large repulsive potential (which would increase the action of the path) as long as the neighboring helium atoms simply rearranged themselves to make room for the helium atom as it moved from one place to another. If the atom was moving slowly, then the neighboring atoms would only have to move slowly to get out of the way. In the process of moving out of the way, these helium atoms would gain kinetic energy that would contribute to the action, but their kinetic energy would depend on the speed, and hence the kinetic energy, of the first helium atom.