Ken Wilson, dead at 77

Wilson was a hero to many, many theoretical physicists, including me. Wilson's father did his PhD with Linus Pauling, Wilson with Murray Gell-Mann, both at Caltech (see Defining Merit). To Wilson we owe much of our modern understanding of renormalization, effective field theory, phase transitions, lattice quantum field theory, and, of course, the renormalization group.

NYTimes: ... His colleagues hailed Dr. Wilson as a legend who had changed how theoretical physicists went about their work, especially in particle physics, the study of the elementary and fundamental constituents of nature. He was also a pioneer in using computers and then supercomputers to study the properties of quarks, the building blocks of protons and neutrons.

“He’s a giant in theoretical physics,” said Frank Wilczek, a Nobelist at the Massachusetts Institute of Technology, calling his work “quite profound.”

Steven Weinberg, a Nobel winner at the University of Texas at Austin, said, “Ken Wilson was one of a very small number of physicists who changed the way we all think, not just about specific phenomena, but about a vast range of different phenomena.”

Kenneth Geddes Wilson was born on June 8, 1936, in Waltham, Mass., the first of three children of Edgar and Emily Buckingham Wilson. His father was a chemist at Harvard. His mother had been a physics graduate student before marrying. One grandfather was an engineering professor at M.I.T. and the other the speaker of the Tennessee House of Representatives.

Kenneth Wilson entered Harvard at 16, majored in math and was the Ivy League mile champion. He obtained his Ph.D. at the California Institute of Technology under the legendary theorist Murray Gell-Mann, then did postdoctoral studies at Harvard as a junior fellow that included a year at CERN, the European nuclear research organization in Geneva. He joined Cornell as a physics professor in 1963.

... From the start, Dr. Wilson was drawn to difficult problems that could take years to solve, said Kurt Gottfried, a Cornell colleague. One such problem was phase transitions, the passage from water to steam or atoms lining up to make a magnet. At the critical point — the temperature at which the change happens — orderly behavior breaks down, but theorists had few clues to how to calculate what was happening.

Dr. Wilson realized that the key to the problem was that fluctuations were happening on all scales at once — from the jostling and zooming of individual atoms to the oscillations of the entire system — something conventional theory could not handle.

At the heart of Dr. Wilson’s work was an abstruse mathematical apparatus known as the renormalization group, which had been conceived by his thesis adviser, Dr. Gell-Mann, and Francis Low in 1951. They had pointed out that fundamental properties of particles and forces varied depending on the scale over which they are measured.

Dr. Wilson realized that such “scaling” was intrinsic to the problems in phase transitions. In a series of papers in the early 1970s, building on the work of Michael Fisher and Benjamin Widom at Cornell and Leo Kadanoff, then at the University of Chicago, he applied the renormalization idea to show how the critical phenomena could be solved by dividing the problem up into simpler pieces, so that what was happening at the melting point, for example, could be considered on one scale at a time.

The results showed that many seemingly unrelated systems — from magnets to liquids — could exhibit the same characteristic behavior as they approached the critical point. The concept proved to be of wide relevance in physics and was cited by the Royal Swedish Academy of Sciences in presenting the Nobel.

Dr. Wilson went on to apply the same divide-and-conquer strategy to quantum field theory, the mathematical language that underlies the study of the most elementary particles and fundamental forces in nature. The theory was plagued by such vexing issues as infinities and other mathematical absurdities when physicists tried to calculate something like the mass of an electron. A method had been developed to work around these anomalies, but many physicists worried that they were just sweeping a fatal flaw in physics under the rug and that, in the words of Dr. Wilczek, “quantum field theory was doomed.”

Dr. Wilson’s new technique banished the infinities for good, putting the theory on a sounder footing. As the Caltech physicist John Preskill put it in a blog post, “Wilson changed that.”

Dr. Wilson’s ideas played a major role in the development of quantum chromodynamics, the branch of quantum theory that describes the behavior of quarks and the gluons that stick them together to form protons and neutrons. In 1974, in order to solve the equations of this theory numerically and gain a more precise understanding of this process, he invented a digitized version of the theory called lattice gauge theory, in which space is imagined as a kind of finely resolved jungle gym where every intersection of the bars represents a point in space-time.

From Wilson's 1982 Nobel Lecture:

... When I entered graduate school at California Institute of Technology, in 1956, the default for the most promising students was to enter elementary particle theory, the field in which Murray Gell-Mann, Richard Feynman, and Jon Mathews were all engaged. I rebelled briefly against this default, spending a summer at the General Atomic Corp. working for Marshall Rosenbluth on plasma physics and talking with S. Chandresekhar who was also at General Atomic for the summer. After about a month of work I was ordered to write up my results, as a result of which I swore to myself that I would choose a subject for research where it would take at least five years before I had anything worth writing about. Elementary particle theory seemed to offer the best prospects of meeting this criterion and I asked Murray for a problem to work on.

... In 1960 I turned in a thesis to Cal Tech containing a mish-mash of curious calculations. I was already a Junior Fellow at Harvard. In 1962 I went to CERN for a year. ... By 1963 it was clear that the only subject I wanted to pursue was quantum field theory applied to strong interactions. I rejected S matrix theory because the equations of S matrix theory, even if one could write them down, were too complicated and inelegant to be a theory; in contrast the existence of a strong coupling approximation as well as a weak coupling approximation to fixed source meson theory helped me believe that quantum field theory might make sense. As far as strong interactions were concerned, all that one could say was that the theories one could write down, such as pseudoscalar meson theory, were obviously wrong. No one had any idea of a theory that could be correct. One could make these statements even though no one had the foggiest notion how to solve these theories in the strong coupling domain.

... When I entered graduate school, I had carried out the instructions given to me by my father and had knocked on both Murray Gell-Mann’s and Feynman’s doors, and asked them what they were currently doing. Murray wrote down the partition function for the three dimensional Ising model and said it would be nice if I could solve it (at least that is how I remember the conversation). Feynman’s answer was “nothing”.

... My very strong desire to work in quantum field did not seem likely to lead to quick publications; but I had already found out that I seemed to be able to get jobs even if I didn’t publish anything so I did not worry about ‘publish or perish’ questions.

... This work showed me that a renormalization group transformation, whose purpose was to eliminate an energy scale or a length scale or whatever from a problem, could produce an effective interaction with arbitrarily many coupling constants, without being a disaster. The renormalization group formalism based on fixed points could still be correct, and furthermore one could hope that only a small finite number of these couplings would be important for the qualitative behavior of the transformations, with the remaining couplings being important only for quantitative computations. In other words the couplings should have an order of importance, and for any desired but given degree of accuracy only a finite subset of the couplings would be needed. In my model the order of importance was determined by orders in the expansion in powers of l/L. ...

From Wilson's Nobel biographical entry:

... My schooling took place in Wellesley, Woods Hole, Massachusetts (second, third/fourth grades in two years), Shady Hill School in Cambridge, Mass. (from fifth to eighth grade), ninth grade at the Magdalen College School in Oxford, England, and tenth and twelfth grades (skipping the eleventh) at the George School in eastern Pennsylvania. Before the year in England I had read about mathematics and physics in books supplied by my father and his friends. I learned the basic principle of calculus from Mathematics and Imagination by Kasner and Newman, and went of to work through a calculus text, until I got stuck in a chapter on involutes and evolutes. Around this time I decided to become a physicist. Later (before entering college) I remember working on symbolic logic with my father; he also tried, unsuccessfully, to teach me group theory. I found high school dull. In 1952 I entered Harvard. I majored in mathematics, but studied physics (both by intent), participated in the Putnam Mathematics competition, and ran the mile for the track team (and crosscountry as well). I began research, working summers at the Woods Hole Oceanographic Institution, especially for Arnold Arons (then based at Amherst).

My graduate studies were carried out at the California Institute of Technology. I spent two years in the Kellogg Laboratory of nuclear physics, gaining experimental experience while taking theory courses; I then worked on a thesis for Murray Gell-Mann. While at Cal Tech I talked a lot with Jon Mathews, then a junior faculty member; he taught me how to use the Institute's computer; we also went on hikes together. I spent a summer at the General Atomic Company in San Diego working with Marshall Rosenbluth in plasma physics. Another summer Donald Groom (then a fellow graduate student) and I hiked the John Muir Trail in the Sierra Nevada from Yosemite Park to Mt. Whitney. After my third year I went off to Harvard to be a Junior Fellow while Gell-Mann went off to Paris. During the first year of the fellowship I went back to Cal Tech for a few months to finish my thesis. There was relatively little theoretical activity at Harvard at the time; I went often to M.I.T. to use their computer and eat lunch with the M.I.T. theory group, led by Francis Low.

IIRC Gell-Mann was twice nominated for the Society of Fellows and twice rejected! Was there ever a bigger mistake in personnel selection? :-) On the other hand, John Bardeen (JF '35) twice won the Nobel Prize in physics (once for the transistor, once for superconductivity), so the selection process must have something going for it! See these slides from a talk by Howard Georgi for some more details about theoretical physics at Harvard in the 1970s.