Quantum Man: Richard Feynman's Life in Science (8 page)

This was Feynman’s first experience with the realization, which would reoccur many times over his subsequent career, that while he loved theoretical calculations, he didn’t really trust them until they were put to experimental tests. As daunting as it was to try to understand nature at the edges of knowledge, it was equally daunting to be responsible for decisions based on his calculations that would ultimately have an immediate impact on the largest industrial project ever carried out by one country.

In the end, Wilson’s proposed device for isotope separation was not chosen. What was selected for major production of U235 were the processes known as electromagnetic separation and gaseous diffusion.

Feynman’s thesis supervisor, John Wheeler, did not abandon him during this period. Wheeler had left Princeton to work with Enrico Fermi on building the first nuclear reactor at the University of Chicago—where they would test the principle of controlled chain reactions as a first step toward the uncontrolled chain reactions that would be required to build a nuclear bomb. But Wheeler was aware of what Feynman was working on, and in the spring of 1942 he decided enough was enough. He and Wigner felt that Feynman’s thesis work was close enough to completion to be written up, and he told him so, in no uncertain terms.

Feynman proceeded to do just that. He was aware of what he had achieved. He had re-derived quantum mechanics in terms of an action principle involving a sum (or rather, in the language of mathematics, an integral) over different paths. This allowed a generalization to situations where the standard Schrödinger approach would not work—in particular the absorber theory that he and Wheeler had worked out for electromagnetism. This is what interested him—his real step forward, he thought—and the new method he had invented for deriving quantum mechanics was primarily a means toward this end.

But he was more concerned about what he hadn’t yet achieved, and he devoted the final section of his thesis to describing the limitations of his work thus far. First and foremost, his thesis did not contain any comparison with experiments, which he regarded as the real test of the worth of any theoretical idea. Part of the problem was that while he had reformulated purely nonrelativistic quantum mechanics, he was acutely aware that in order to address real experiments involving charges and radiation, the appropriate theory—quantum electrodynamics—was needed so as to incorporate relativity, which involved addressing a host of problems he had not yet dealt with.

Finally, Feynman was concerned with the physical interpretation of his new viewpoint for dealing with the quantum world—in particular, the issue of making a connection between the temporally spread-out paths and probability amplitudes inherent in his new formulation, and the possibility of making real physical measurements at any specific time. The problem of measurement was not new or unique to Feynman’s thesis. His work merely appeared to exacerbate it. The world of measurements lies within the classical world of our experience, where weird quantum paradoxes don’t ever seem to arise. How does a “measurement” ensure that the underlying quantum universe ends up appearing sensible to our eyes?

The first person to comprehensively attempt to quantitatively discuss this measurement problem in the context of quantum mechanics was John von Neumann, at Princeton, whom Feynman had the opportunity to interact and disagree with. Anyone who has heard anything about quantum mechanics often hears that one cannot separate the observer from that which is being observed. But in practice this is exactly what is required in order to make predictions and compare them with experimental data. Feynman was particularly concerned about this key question of how to separate the measuring apparatus and the system being observed in the context of the specific quantum mechanical calculations he wanted to perform.

The conventional verbiage goes as follows: When we make a measurement, we “collapse the wave function.” In other words, we suddenly reduce the probability amplitude to be zero in every state but one. Therefore, the system has a 100 percent probability of being in only one configuration, and different possible configurations do not interfere with each other, as in the examples discussed in the last chapter. But this simply begs the questions: How does a measurement collapse the wave function, and what is so special about such a measurement? Is a human being needed to make the observation?

New-age hucksters aside, consciousness is not the key. Rather, Feynman argued that we must consider the system plus the observer together as a single quantum system (which is fundamentally true, after all). If the observing apparatus is “large”—that is, it has many internal degrees of freedom—then we can show that such a large system behaves classically—interference between different possible macroscopic quantum states of the apparatus becomes infinitesimally small, so small as to be irrelevant for all practical purposes.

By the act of measurement, we somehow produce an interaction between this “large” observing system and a “small” quantum system, and these become correlated. This correlation ultimately fixes the small quantum mechanical system to also exist in a single well-defined state, the state we then “measure” the system to be in. In this sense, we say the wave function of the small system has
collapsed
(meaning the probability amplitude of being in any state other than the one we measure is now zero). Humans have nothing to do with it. The observing system simply has to be large and classical and correlated with the quantum system via a measurement.

This still does not fully resolve the question, which then becomes: how do we determine what comprises the large classical observing part of the combined system and what comprises the quantum part? Feynman spent considerable time discussing this issue with von Neumann. He was not satisfied with von Neumann’s argument that someone had to decide, in some sense arbitrarily, where to make the cut between classical observer and observed. That sounded like a philosophical cop-out. Feynman believed that since quantum mechanics underlies reality, it should be consistently incorporated throughout instead of making ad hoc separations between an observer and the observed. In fact, he worked hard to define measurements purely in terms of correlations between different subsystems and letting the size of one of them go to infinity. If nonzero and finite correlations remained in this limit, Feynman labeled this a “measurement” of the smaller subsystem, which could be made arbitrarily accurate as the size of the “measuring” part of the system grew to be larger and larger. As he colorfully put it in a note he wrote to himself, regarding the example of a spot on a photographic plate that somehow recorded an event involving a single atom,

What can we expect to end with if we say we can’t see many things about one atom precisely, what in fact can we see. Proposal: Only those properties of a single atom can be measured which can be correlated (with finite probability) (by various experimental arrangements) with an unlimited number of atoms. (i.e. the photographic spot is “real” because it can be enlarged and projected on screens, or affect large vats of chemicals, or big brains etc etc—it can be made to affect ever increasing sizes of things—it can determine whether a train goes from N.Y. to Chicago—or an atom bomb explodes—etc).

Measurement theory still remains the bugaboo of quantum mechanics. While great progress has been made, it is still fair to say that a complete description of how the classical world of our experience results from an underlying quantum reality has not been developed, at least to the satisfaction of all physicists.

This example of Feynman’s focus when finishing his thesis is important because it demonstrates the sophisticated issues this mere graduate student in physics insisted on wrestling with as he worked. In addition, Feynman’s “path-integral formalism” made it possible to separate systems into pieces, which seems central to the idea of measurement in quantum mechanics, allowing one to isolate parts of a system one either does not or cannot measure and to separate these clearly from those parts one wishes to focus on. This is generally not possible in standard formulations of quantum mechanics.

The idea is really relatively straightforward. We sum all those weights corresponding to the action associated with those paths or parts of paths we wish to ignore the specific details of, for example, summing up the effect of having small circular loops—so small we could never measure them—swirling around the more normal straight trajectories between two points. The effect of these additions may be to change, by a small calculable amount, what would be the action associated with a straight trajectory without the loops. After having done the summation (or in the case of an infinite number of such additional paths, the integral), we can then forget about such extra loop trajectories and focus on only trajectories that are more straight, as long as we use the new, altered action for this trajectory in our calculations. This process is called
integrating out
parts of the system.

This may seem, at first sight, like a technical detail not worth mentioning. However, as we will see later, it ultimately would allow almost all of the most important theoretical advances in fundamental physics in the twentieth century to occur, and it would allow us to totally quantitatively revolutionize what are otherwise such vague notions as scientific truth.

But for the moment, in 1942 as he completed this thesis, titled “The Principle of Least Action in Quantum Mechanics,” Feynman had other things on his mind. Preparing to graduate that June, he had received word that he was to move to Los Alamos to focus on the actual building of the atomic bomb. He was also busy planning for his long hoped-for marriage following his graduation. He thus had to put his immediate physics concerns to rest and focus on sorting out the rest of his life. Perhaps all of the diversions explain why, even as he acknowledged Professor Wheeler for his advice and encouragement, he never took the opportunity to add what surely would have been a far more poetic acknowledgment to the connection made between the subject of the thesis (and ultimately the work that would win him the Nobel Prize) and that fateful afternoon in his high school physics class when Mr. Bader awakened his mind to the subtle beauties of theoretical physics.

Three years and what undoubtedly seemed like a lifetime later, the war had ended and he finally got around to writing up his thesis for publication. He still did not make this connection. Instead he was able to clearly enunciate what undoubtedly had been the very same hopes he carried with him as he left Princeton, and which had continued to buoy him through the various immediate insanities of the world of human affairs over which he had so little control, until the day he was finally free to explore full-time the more intoxicating insanities of the quantum universe, which he felt much more confident he could conquer:

The formulation is mathematically equivalent to the more usual formulations. There are therefore no fundamentally new results. However there is pleasure in recognizing old things from a new viewpoint. Also there are problems for which the new viewpoint offers a distinct advantage. . . . In addition, there is always the hope that the new point of view will inspire an idea for the modification of present theories, a modification necessary to encompass present experiments.

CHAPTER
6

Loss of Innocence

He’s another Dirac. Only this time human.

—E
UGENE
W
IGNER, SPEAKING
ABOUT
R
ICHARD
F
EYNMAN

R
ichard Feynman graduated with a PhD from Princeton in 1942 as a relatively naive and hopeful young man, known to his fellow students and professors as a brilliant and brash intellect, but largely unknown outside the university. He emerged three years later, from Los Alamos, as a well-tested physicist highly regarded by most of the major players in physics around the world, and a somewhat jaded and world-weary adult. Along the way, he experienced incredible personal loss, as well as the loss of intellectual and moral innocence that is the inevitable by-product of war.

T
HE INK HAD
barely dried on Feynman’s diploma when he began to execute his decision, outlined in that dispassionate letter to his mother, to marry Arline. The opposition by his parents and Arline’s, who were more concerned about his health and Arline’s than about their mutual love, was futile. Both he and Arline felt the other was a bastion against any onslaught from the rest of the world. Together anything was possible, and they refused to be pessimistic about the future. As Arline wrote to Richard shortly after he had moved into a new flat in Princeton and made final arrangements for the ceremony, “We’re not little people—we’re giants. . . . I know we both have a future ahead of us—with a world of happiness—now and forever.”

Every aspect of their brief lives together is, in retrospect, heart wrenching. On what would be their wedding day, Richard borrowed a station wagon from a friend, which he outfitted with mattresses so Arline could lie down. Then he drove from Princeton to her parents’ home and picked her up in her wedding dress, and together they drove to Staten Island for a wedding ceremony with no family or acquaintances, and from there to what would become Arline’s temporary new home, a charity hospital in New Jersey.

Shortly thereafter, without any fanfare or honeymoon, Feynman returned to work at Princeton, except there was nothing to do. The project with Wilson had been closed down and the team was waiting for new orders. Since the main activity at the time was taking place in Chicago, where Enrico Fermi and Wheeler were working on building a nuclear reactor, Feynman was sent to Chicago to learn what was going on there.

His trip in 1943 began what would be a succession of opportunities to ultimately meet and impress his peers and his bosses. While the war disrupted all lives, in at least two senses it provided Feynman with incredible opportunities he would not otherwise have had.

First, since the best and brightest minds were being gathered to spend two years in close quarters, Feynman was given a chance to shine in front of individuals he would have otherwise had to travel around the world to meet. He had already, through his attendance since 1942 at periodic group meetings in New York and at the MIT Radiation Laboratory in Massachusetts, impressed the brilliant, if troubled, physicist Robert Oppenheimer, who would shortly be chosen to lead the entire atomic bomb project. In Chicago, while carrying out his job of gathering information, he blew away members of the theory group there when he was able to perform a calculation that had eluded them for over a month.

Following his return to and debriefing at Princeton, he didn’t have to wait long before learning what was to come next. Oppenheimer had been chosen to lead the bomb project, and shortly after that he picked Los Alamos, New Mexico—a remote and starkly beautiful countryside where he had previously roamed as a younger man, and which also fit the army’s requirements of isolation and safety—as the site of what would soon become the most advanced laboratory in the world, with the highest concentration of brilliant scientists ever seen per square mile (even allowing, as John F. Kennedy once did, for those days when Thomas Jefferson dined alone in the White House).

Oppenheimer was a brilliant scientist, but more important for the success of the atomic bomb project, he was an equally brilliant judge of talent in others. He quickly began to recruit and amass a team of outstanding colleagues to relocate to Los Alamos even before the laboratory and associated housing had been completed. Needless to say, he sought out Feynman, and did whatever he could to convince him to move to New Mexico with the first wave of scientists, at the end of March in 1943.

Oppenheimer’s offer led to the other fortuitious impact that the war effort had on the married couple. Arline’s illness was progressing. She would live only two years following their marriage. The first years of any marriage should be a time, if there is ever going to be a time, of romance and adventure. Had the war not turned the world topsy-turvy, Feynman undoubtedly would have taken longer to finish his doctorate, he and Arline would have continued their strained existence in Princeton as her health deteriorated, and then, before she died, he might have proceeded to an assistant professorship in some place not that different than Princeton. Instead, his decision to move to the wild and unknown Southwest would give the young couple, especially Arline, the chance for a morsel of the romance and adventure that they had been longing for and that she otherwise would never have been able to enjoy.

Feynman was touched by Oppenheimer’s concern and consideration. “Oppie,” as he was known to his colleagues, seemed to be the perfect leader for this group of independent-minded scientists. He commanded their respect—as Feynman later said, “We could discuss everything technically because he understood it all.” At the same time he showed uncommon concern about the well-being of each and every person he had recruited for this task. Again, as Feynman remembered it, “Oppenheimer was extremely human. When he was recruiting all these people to go to Los Alamos . . . he still worried about all the details. For example, when he asked me to come I told him I had this problem—that my wife had tuberculosis. He himself found a hospital and called me up to say they had found somewhere that would take care of her. I was only one of all the many people he was recruiting, but this was the way he always was, concerned with people’s individual problems.” Oppenheimer’s call from Chicago about finding a hospital for Arline was the first telephone call Feynman had received from so far away, perhaps one of the reasons he was so touched. In any case, after some negotiations with the army authorities, Arline and Richard were set to board the Santa Fe “Chief” from Chicago on March 30. Arline was beside herself with joy and excitement:

Dearest Rich—if you only knew how happy you’ve made me with this train trip of ours—it’s all I’ve wanted and dreamed about since we’ve been married . . . with only one day left—I’m so excited and happy and bursting with joy—I think, eat, and sleep “you”—our life, our love, our marriage—the great future we are building. . . . If only tomorrow would hurry and come.

At Arline’s urging, the two of them purchased a ticket for a private room, then they boarded the train and headed west. Ultimately, after exploring several possibilities, Arline was placed in a sanatorium in Albuquerque, one hundred miles from the laboratory site (there was no laboratory there yet), and Richard somehow made the trip to see her once a week.

In one sense, Richard Feynman had been preparing for this experience his whole life. All of his talents were to be exploited during the next two years: his lightning computational abilities, his mathematical wizardry, his physical intuition, his clear appreciation for experiment, his disrespect for authority, his breadth of physics knowledge from nuclear physics to the physics of materials (shortly after arriving he became ill, and in a letter to his mother reported reading a chemical engineering textbook with topics ranging from “Transportation of Fluids” to “Distillation” while in the infirmary for three days), and his fascination with computing machines.

The physics work was quite different from his academic work. It was easier than pushing the forefront into the unknown laws, but a lot dirtier than working on pristine single electrons in hydrogen atoms. Aside from his contributions to the development of the bomb, Feynman left little permanent scientific legacy from his work during this time. (There is a formula for the efficiency of a nuclear weapon, called the Bethe-Feynman formula, that is still used today, but that is about it.)

Nevertheless, Los Alamos had a profound influence on Feynman’s career, and it all began by accident, as so many things do. Again, in his words: “Most of the big shots were out of town for one reason or the other, getting their furniture transferred or something. Except for Hans Bethe. It seems that when he was working on an idea he always liked to discuss it with someone. He couldn’t find anybody around, so he came down to my office . . . and he started to explain what he was thinking. When it comes to physics I forget exactly who I’m talking to, so I was saying, ‘No, no! That’s crazy!’ and so on. Whenever I objected, I was always wrong, but nevertheless that’s what he wanted.” As Bethe remembers it, “I knew nothing about him. . . . He had only recently got his Ph.D. from Wheeler, at Princeton. We got to talking, and he obviously was very bright. At the meetings and seminars he always asked questions which seemed particularly intelligent and penetrating. We began to collaborate together.” And in another reminiscence, “He was very lively from the beginning. . . . I realized very quickly that he was something phenomenal. . . . I thought Feynman perhaps the most ingenious man in the whole division, so we worked a great deal together.”

The opportunity to work with Bethe at Los Alamos was fateful in the extreme. They complemented each other in remarkable ways, sharing uncanny physical intuition, mental stamina, and calculational ability. But Bethe was, in several other senses, everything that Feynman was not. He was calm and deliberate, and unlike the excitable Feynman, Bethe was “unflappable.” This was also reflected in their mathematical styles. Bethe began a calculation at the beginning, and ended at the end, no matter how long or difficult the road between was. Feynman, on the other hand, was as likely to begin in the middle or at the end, and jump back and forth until he had convinced himself he was right (or wrong). In other areas, Bethe served as a remarkable role model. Feynman loved his humor, his unaffected manner, and his straightforward and collegial way of dealing with others. And whereas Wheeler helped free up Feynman’s enthusiasm and creativity, he was not the physicist that Bethe was. If Feynman was to rise to new, and higher levels, he needed someone he could go head to head with. Bethe was the man.

By the time Bethe had moved to Los Alamos, he had resolved one of the most important and vexing questions in astrophysics: how does the sun shine? For over a century scientists had wondered what energy process powers the sun so it has been able to shine with its observed luminosity for over 4 billion years. The earliest estimate, by a German doctor in the early eighteenth century, suggested that if the sun were a big ball of burning coal, it could burn with its observed brightness for about 10,000 years, which happened to be in nice accord with some biblical estimates of the age of the universe. Later in the century, two famous physicists, Heinrich Helmholtz and Lord Kelvin, estimated that the sun could be powered by the energy released during gravitational contraction, and this energy source could power the sun for perhaps 100 million years. However, even this estimate was far too low to explain what was by then the inferred age of the solar system—namely, billions, not hundreds of millions, of years.

The mystery persisted through the 1920s, when the famous British astrophysicist Sir Arthur Stanley Eddington argued that there must be some unknown source of energy powering the solar interior. The problem was that model calculations of the sun’s profile suggested that the interior was no more than 10 million degrees in temperature, which is hot, but not that hot. In other words, the physical processes associated with the energies available at these temperatures were thought to be fairly well understood, with no room for new exotic physics. As a result, Eddington’s assertion was met with skepticism, leading him to utter his famous rebuke: “To those that think the temperature in the center of the Sun is not hot enough for some new physical process to take place, I say: Go and find a hotter place!”

Bethe, who had studied with the greatest theoretical physicists in Europe, including Arnold Sommerfeld, Paul Dirac, and Enrico Fermi, had, by the early 1930s, established himself as perhaps the world’s foremost authority on the emerging field of nuclear physics. He wrote the definitive set of reviews in this field, which Feynman had studied while an undergraduate. If anyone was prepared to find the new process that powered the sun, it was Bethe, and in 1939 he made his great discovery. He realized that newly discovered nuclear reactions (similar in spirit to those later exploited in building the fission bomb, but instead of being based on breaking up heavy nuclei such as uranium and plutonium, these involved fusing light nuclei such as hydrogen into heavier nuclei) provided the key to releasing tremendous amounts of energy. Moreover, he showed that there was a series of reactions starting with protons, which make up the nuclei of hydrogen, and ultimately producing the nuclei of the next lightest element, helium, that would release more than twenty million times as much energy as comparable chemical reactions between hydrogen would release. While at a temperature of only 10 million degrees the average hydrogen nucleus might take over a billion years to experience a collision energetic enough to initiate such a reaction, over a hundred thousand tons of hydrogen could nevertheless convert to helium each second, providing enough energy to power the sun at its current luminosity for about 10 billion years.

For this important theoretical discovery, Bethe was awarded the Nobel Prize in Physics in 1969, four years after Feynman would share the prize for his own work on quantum electrodynamics (QED). And the nuclear “fusion” reactions Bethe exploited in his explanation of the workings of the sun would be re-created seven years after the end of World War II, in the development of “thermonuclear explosives,” otherwise known as hydrogen bombs.