Intuitive

Concrete

This is how phenomenology works:

Technically, I still had to choose between being a theorist or an experimentalist, but for me, this wasn’t much of a choice.The essence of theoretical physics is the attempt to look at the universe, and then mentally apprehend its structure. If you are right, you emulate Newton and Einstein: You find one of the Ten Commandments. You write down a simple set of laws that, plucked from nowhere, miraculously describes and predicts how God’s world works.This was the struggle to which I aspired. Anything else would have been a compromise that I was not prepared to make.

Even within theoretical particle physics there are further refinements. Pure theory is the search for abstract laws, for a formulation of the divine commandments that rule the world. But, for every Moses descending from the mountain with a valid new law, there are countless well-intentioned prophets whose proposed laws turn out to be wrong. So how does one tell when a theory is right?

Beauty, even mathematical beauty, is not enough. Physicists must test a new theory by elaborating the ways in which it manifests itself in the world. Physicists who do so-called phenomenology work out the detailed and observable consequences of a theory, providing the practical link between principles and experiment, between mind and matter. Phenomenologists elaborate the theory; they create heuristic approximations to engineer the theory into a pragmatic tool; they propose experiments to validate or refute a theory, using the theory itself to compute the expected results. Phenomenologists deal a little more with the ripples on the surface and a little less with the laws beneath it.

Though I wanted to do pure theory, I ultimately ended up spending much of my life in physics as a phenomenologist. Over the long run,this stood me in very good stead. When I moved to Wall Street, I found quantitative finance to resemble phenomenology much more than it resembled pure theory. Quantitative finance is concerned with the techniques that people use to value financial contracts and, given the fluctuations of the human psyche, it is a pragmatic study of surfaces rather than a principled study of depths. Physics, in contrast, is concerned with God’s canons, which seem to be more easily captured in the simple broad statements that characterize profound physical laws.

At the University of Pennsylvania, now without a PhD advisor, I had to take my own road, and so I began to look for something new to work on. I had spent most my graduate student years working on high-energy phenomenology, comparing other people’s theories with other people’s experiments. It was useful and interesting, but not as visionary as the physics I had imagined doing. Trying to be ambitious, I began to study the so-called Lee model, an idealized and therefore analytically soluble theory of particle interactions that was the subject of an early paper by T. D. [Lee] himself. I hoped that it would form the basis for a deeper under-standing of quark forces. I spent most of my first semester at Penn trying vainly to master the field. But I found it difficult to concentrate; I was restless from the lack of friends, tense from the strains of a geographically divided marital life, and tired from all the back-and-forth driving—I would go to New York on Friday nights and return to Philadelphia early on Monday mornings. Some weekends I was just too weary to make the trip and remained alone in Philadelphia, killing time and feeling half-resentful.

Which of these new particles—the hypothetical neutral heavy lepton or the hypothetical charmed quark—was the progenitor of the dimuons? The test would lie in the distribution of their speeds. The relative speeds of the positively and negatively charged muons would depend on whether the heavy lepton or the charmed quark had been their parent. In the former case, both muons arose from the decay of the heavy lepton and, because both had a similar origin, they tended to emerge with similar speeds; in the latter, the positively charged muon arose from the decay of a charmed quark and would have a very different speed. Much as each brand of water gun produces its own characteristic spray of water, so the different particles, when they decay, produce their own characteristic dimuon distribution. Together with my colleagues Lay Nam Chang and John Ng, I began to investigate the properties of the dimuon distribution that resulted from heavy lepton production in order to compare it with the muonspeeds reported by Mann and his collaborators. It was a classic phenomenology problem, the comparison of theory and experiment, closely related to my thesis work, and so I knew how to calculate the distributions of the final speeds and angles of muons. Lay Nam, John, and I checked each other’s analytical calculations, and I wrote the computer program to evaluate the distribution of the muons. Suddenly I was involved again, and it was simply thrilling to be working on something new and relevant in close proximity to the experimentalists. I entered a period of great mental stimulation which resuscitated me. Spontaneously, I began to rise early in the morning; as soon as I awoke I rushed into work to calculate and program. I participated in long, intoxicatingly buoyant arguments and discussions on blackboards, where Lay Nam, John, and I took turns scribbling and talking, one of us seizing the chalk from the other. Rivalries and self-doubt disappeared as we pushed forward, working keenly late into the night. The exact nature of the hypothetical weak force responsible for the decay of the putative heavy lepton was not known—it had to be conjectured, and there were a variety of forms it could reasonably take. LayNam, John, and I calculated the relative speeds of the muons for a wide (but not exhaustive) range of forces. We showed that for all the cases we considered, the predicted disparity between the speeds of the positive and negative muon, when both were produced by the decay of a heavy lepton, was much smaller than the disparity observed by Mann and his collaborators. Therefore, we claimed, it was highly unlikely that the dimuon events signaled the production of a new heavy neutral lepton. We circulated our work as a “preprint,” a mimeographed prepublication report sent out to other physicists in the field, and it drew a gratifying spurt of attention. Now, almost down to the wire, I had completed a piece of research that would get me my next postdoc position, just as my two-year stint at Penn trailed off into its last few months. I sent out my letters of application and, late in the spring of 1975, in the nick of time, I received postdoctoral offers from the University of Wisconsin at Madison and from Oxford University in England. The work we did on heavy leptons was topical and timely, but not quite thorough enough. Though we had shown that it was unlikely that a heavy lepton had produced the dimuons, we had not proved it truly impossible—we had not calculated the asymmetry for every possible form of the hypothetical weak force that caused its decay. A few months later, Bram Pais (one of the few Columbia seminar speakers I had seen stand up to T. D. Lee) and his long-time collaborator, Sam Treiman of Princeton, entered the scene. Both of them old hands at analyzing weak interactions, they derived a very general upper bound to the asymmetry between the speeds of the positive and negative muons produced in the decay of a heavy lepton, no matter what the form of its still unknown weak force. They showed that the maximum value of the asymmetry under any circumstances was smaller than the one observed by Mann and his collaborators, and so truly excluded heavy leptons as a source of the dimuons. What we had shown to be unlikely Pais and Treiman had then demonstrated to be impossible. More experienced and professional than Lay Nam, John, and me, they received the lion’s share of the credit, but we got a little, too; it was more than enough to get me that second postdoc offer from Oxford.

I felt naively proud to be at Oxford. Coming from Anglophile South Africa, I saw Oxford as the epitome of academic life. And doing physics when I got there was suddenly much easier; I had struggled through the valley of the shadow in my first year at Penn, but now I knew how to find suitable problems on which to work. I had learned how to complete a piece of research or, failing that, how to at least salvage something publishable and interesting. I learned to let one piece of work flow into the next. I finally knew how to treat research a little more like a business.

At Oxford I continued working on the theory of dimuon production. Heavy neutral leptons were dead, as my colleagues and I had suggested and as Pais and Treiman had proved. The dimuon events could instead signal the production and subsequent decay of a short-lived charmed quark, an equally interesting possibility. I set about calculating the distribution of dimuons that would correspond to the decay of newly produced charmed quarks. It was useful work, professionally done. I did more theoretical calculations, wrote more FORTRAN programs to compute dimuon distributions, documented the work, circulated the preprints I wrote to other physics departments, and published the papers. I still remember the excitement of working late into the night, hurrying to debug programs and then submit them to the computer center. I recall best the unspoiled joy of spontaneously waking early, tired but driven, and then rushing off to work because I wanted to go to work and couldn’t sleep any more. I was excited to see what came next. … I spent that whole year working on the phenomenology of charm production. It was a good life. I felt adult because I was earning a living, yet I was often fancy-free in the way that I imagined a life spent on acquiring knowledge should be.

From My Life As A Quant by Emanuel Derman

Abstract

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