My Life as a Quant (8 page)

I spent my second and third years at Columbia taking the myriad of required courses, all the while continuing my quest for a particle physics thesis advisor. Finally, in early 1969 I reached an agreement to work for Norman Christ. He was the most recent in the long line of T. D.'s
wunderkinder
, a polite and enthusiastically perky young man who was just about my age, but who had received his PhD under T. D.'s tutelage in record time two years earlier, before I had even arrived at Columbia. After two years as a postdoc at the Institute for Advanced Study in Princeton, he had returned to Columbia as a tenured associate professor. In terms of a career, he seemed to have everything one could hope for. It must have been a heavy burden, however, to carry the weight of so many expectations of precociousness. I was relieved, many years later, to hear him uncharacteristically comment that a physicist spends about half of his or her time enthralled and the other half in depression, an observation that corresponded closely to my own experience.

I was Norman's first PhD student and, perhaps because he had been a student so recently himself, our relations were stilted. During the four years I worked for him he never succeeded in finding a comfortable mode of addressing me. I suppose that the difficulty arose from the tension between the parity of our ages and the disparity of our relative positions. He could not bring himself to simply call me “Emanuel” and so he eventually resorted to addressing me as “Mr. Derman,” uttered between invisible quote marks in a manner intended to imply ironic jocosity. I, in turn, could never manage to call him “Norman.” It was only with my father- and mother-in-law that I ever again experienced a similar sort of naming difficulty: The first names they told me to use seemed to connote too much familiarity, “Dr.” and “Mrs.” seemed too formal, and the Slovak analogs of “Mom” and “Dad” that my wife used were too unnatural. In the end, with them though not with Norman, first names prevailed.

In the fall of 1968, I moved out of I. House to share an apartment with a friend on Amsterdam Avenue and 120th Street, just across the street from where I now teach financial engineering. With most of my foreign friends from the previous two years back in their home countries, I spent much time alone. One evening I experienced my first mugging at the hands of a group of teenagers, with two more muggings to follow over the next few years. But, on the plus side, sometime in the spring of 1969, I noticed a new and exotic foreign female student in the physics department library. Since women in physics were rare, a new arrival attracted everyone's attention. Though I hadn't yet contrived to meet her, I watched from a distance her laughter-filled gesticulating conversations with some of the other graduate students. Then, one Saturday evening, I saw her at a fellow student's party on 119th Street. I approached her and learned that her name was Eva. She had left Czechoslovakia for a summer job in Germany during the Prague Spring of 1968 and, after the Russian invasion, had not returned. Her English was charmingly limited; I felt sad to see the skimpy physics lecture notes she had jotted down in Slovak during physics classes that were delivered in English. When I walked her home from the party we discovered that we both lived in the same apartment building on 120th Street. Soon we were spending much of our time together.

I spent the summer of 1969 at a particle physics summer school at Brookhaven National Laboratories in Upton, Long Island. Most weekends I headed back into the city to see Eva; sometimes she came out to Brookhaven to visit me. We went swimming in the rough surf off Smith Point, in Atlantic Ocean waves of a size I hadn't seen since I had left Cape Town. But mostly the summer weeks dragged by slowly and yet unquietly on dreary Long Island, until finally, at summer's end, I went home to Cape Town to visit my family.

I was restless there, too. Three years had passed since I had left, and one day, confused about my future on all fronts, I visited an Afrikaner psychiatrist named Jannie Louw at the recommendation of my elder sister. He listened to my account of distant loneliness and uncertainty, and then half-pleased and half-displeased me by avoiding specific advice and instead suggesting a philosophical approach to my suffering. I went to see him once more, and when I left, he recommended that I read two books: Victor Frankl's
Man's Search for Meaning
and Rudolf Steiner's
Knowledge of the Higher Worlds
. I found some solace in Frankl, but never bothered with Steiner until years later.

One person who made a strong impression on me during that Brookhaven summer was Mike Green, a graduate student in particle physics at Cambridge. Mike was far ahead of me academically, already working on research for his thesis. Everything went enviably faster in British graduate schools. In subsequent years I ran into him regularly at summer research institutes in Aspen and Stanford, and at university seminars at Oxford and Cambridge. Always, he was single-mindedly working away on his beloved string theory, a model that treats elementary particles as tiny, one-dimensional, rubber-band-like, vibrating strings that wiggle and move at relativistic speeds. I always admired Mike's tenacity, his capacity for banging away at the same problem for years until it yielded. Fifteen years later, when I had already left physics, Mike became famous for proving that string theories could be mathematically consistent only if the universe had either 10 or 26 dimensions. Uncharacteristically, I didn't feel the smallest pinch of envy or competition at his deserved success. Like the Kaluza-Klein theories I had studied as an undergraduate, Mike's model of particles was viable only in a large-dimensioned universe, which could be mapped to our apparently four-dimensional universe only if its extent in each of those extra dimensions was so small as to be unobservable. String theory is so arcane that physicists sometimes describe it as “a little bit of twenty-first–century physics that accidentally fell into the twentieth century.”

The physics department was home to more passionate clashes. Several professors, among them Leon Lederman, Malvin Ruderman, and Richard Garwin, worked part-time for the Jason Division of the Institute for Defense Analysis, a group of elite scientists from elite universities who studied defense-related problems. Norman Christ, my young PhD advisor, was a member, too. During the height of the Vietnam protests, Columbia antiwar student groups picketed these professors at their homes and in their seminars. Though the contents of the Jason reports were presumably secret, the antiwar activists circulated their titles. I recall one, “Interdiction of Trucks by Night,” which we assumed to be about methods of bombing the Ho Chi Minh trail. One fall we heard that antiwar protesters had picketed Ruderman's home in his suburban neighborhood on the eve of Yom Kippur, pointing out the conflict they perceived between observing the Jewish day of atonement and writing military-related advisory papers. I recall Ruderman responding with great and somewhat disingenuous indignation at the invasion of his personal life. I was most impressed by Richard Garwin. Whereas most of the other professors tried to dodge the moral responsibilities of their military-related activities with a mixture of righteous outrage, wry charm, and vague ramblings about working from within the system, Garwin simply asserted that there was a role for force in the world, and that he believed in what he was doing.

Jason still exists, though a March 23, 2002,
New York Times
article reported that the Pentagon has withdrawn its budgetary support. Jason, the article jokingly noted, is rumored to be an acronym for Junior Achiever, Somewhat Older Now—English for
ex-wunderkind
, I guess.

In late 1969 I finally began my PhD thesis. Just at that time, the particle physics world I was entering was agog over two momentous new developments. First, experimentalists were discovering the earliest hints of the actual existence of quarks, and second, theorists were beginning to understand the origin of the subtle similarity between the weak and electromagnetic forces.

Gell-Mann's version of the Eightfold Way had predicted that the proton, the neutron, and all the other thus-far observed strongly interacting particles could in principle be made out of three smaller subparticles called quarks. Quarks, if they existed, had to be almost unbelievably peculiar; they had to carry a fractional electric charge of either one-third or two-thirds the charge of the proton, but no one had
ever
seen a particle of fractional charge. Although the Eightfold Way implied their existence, physicists were reluctant to take them seriously. Instead, avoiding the reality behind their mathematics, they had come to think of quarks as mathematically consistent but fictitious components that could never be observed. It was as though the only coins you had ever seen in circulation were nickels, dimes, and quarters, and you had concluded that somewhere there had to be a one-cent coin.

If a proton really contained three hard little quarks deep inside it, one should be able to “see” them experimentally by shooting a fast electron at a proton and observing it recoil sharply when it struck a quark head-on. The method is a little like looking for bits of eggshell in a sponge cake—once in a while, as you chew, you hear a sharp crack as your teeth hit a fragment of shell.

Robert Hofstadter, my cousin's City College friend of the 1930s, had observed no such sharp recoils, and everyone had concluded that the proton was pure sponge and no eggshell. Hofstadter's experiments, however, were limited. He had kept an eye only on the so-called
elastic
collisions, those in which the target proton remained intact as it recoiled like a struck billiard ball. Now, in the late 1960s, a later generation of physicists at the Stanford Linear Accelerator Center (SLAC) began to watch so-called
inelastic
electron-proton collisions in which the proton disintegrated rather than recoiled after being struck. Amazingly, in these collisions, many of the electrons did in fact recoil sharply, as though they had struck something very hard and small. Somewhere deep inside there truly were bits of eggshell.

Feynman, from his base at Caltech in Pasadena, had developed a simple phenomenological picture of the proton as a closed bag of hard little quark-like constituents which he called its “partons.” In Feynman's picture, the energetic electrons that scattered off the protons at SLAC provided a metaphorical X-ray view of the partons inside the proton, much as an ordinary X-ray or a CAT scan uses high-frequency radiation to provide a view of our internal organs. Using the information from the SLAC X-ray of the partons, one could calculate many other properties of the proton itself.

More and more, we began to believe that protons, long thought of as unsplittable, might be composite—they might contain quarks. But this was not all that excited us; we were also increasingly becoming aware of the similarity between the weak and electromagnetic forces. Since the 1930s, physicists had been aware of an intriguing analogy between Maxwell's 1873 theory of electricity and magnetism and Fermi's 1934 theory of the weak force. However, no one had yet been able to extend this analogy into a consistent theory of the two forces. Then, in the 1960s, Glashow, Weinberg, and Salam, all working independently, accomplished this unification by creating what is now called the “standard model.” They based their theory on Yang's symmetry principle of local gauge invariance.

The standard model related nature's forces to each other much like Mendeleyev's periodic table had connected the diverse chemical elements. Mendeleyev had detected a hint of order in the properties of elements and then deduced the existence of other as yet-undiscovered elements necessary to complete the pattern. Similarly, Glashow, Weinberg, and Salam had detected a pattern in both the weak and electromagnetic forces, and then deduced the existence of other previously undiscovered weak forces necessary to complete their picture. The sum total of all these forces comprised the standard model. It was an ambitious but compelling theory; when it was verified, its creators won the Nobel Prize. Much of theoretical particle physics works in this way: You hear a few isolated bars of a beautiful song and try to figure out the whole piece by generalizing the pattern in the fragments.

My thesis work over the next three years employed both the theory of quarks and the Weinberg-Salam standard model which predicted new weak forces between electrons and quarks. One of these new forces, the so-called
weak neutral current
, would cause a small violation of parity in the collisions of electrons and quarks. If protons were bags of quarks, one should also be able to observe a small violation of parity in electron-proton collisions. The effect would be small and subtle, for the most part masked by the much stronger electromagnetic force between electrons and quarks.

In my thesis I proposed a new test of the standard model. In particular I suggested that experimentalists at SLAC try to observe the effects of the standard model's parity-violating weak force in the inelastic collisions of electrons with protons. In order to estimate the size of the signal, I made use of many of the skills I had gained during the past few years. I employed Lee and Yang's framework for analyzing parity violation and I used Feynman's parton-model description of the proton as a bag of quarks. In this way I calculated how much of a parity-violating asymmetry would be seen if the standard model were indeed correct.

I began my research in 1970. Slowly, I read the multitude of papers that explained how to use the parton model, repeating their published calculations on my own and checking that I could reproduce their results. Step by step, I learned the mechanics of the model and how to use it. Then I began my own work.

My first task was to carry out the long mathematical calculations that predicted the distribution of electrons recoiling after a collision with a quark. I did each calculation using “Feynman diagrams,” the cartoon-like representation invented by Feynman to systematize the ways in which particles interacted during collisions. I drew all the possible diagrams that could occur in a theory, and then, using Feynman's rules, translated each picture into a mathematical formula and evaluated it. The calculations, carried out with pen and paper, took up tens of pages. I repeated each calculation at least twice to check for consistency. When successive calculations didn't match, I searched each one for errors and eliminated them until I found agreement. Today, however, much of the repetitive algebraic manipulation would be done with symbolic mathematical programs like Mathematica™.