Kenneth Wilson 1936-2013

Kenneth Wilson died this past weekend, in Maine at the age of 77. Some obituaries can be found here, here, here, and here.

Wilson won the Nobel prize in 1982 for his work on critical phenomena and phase transitions, but his influence on particle theory was arguably even greater than on condensed matter physics. Unfortunately I never got a chance to meet him, but a large part of what I was learning about quantum field theory back in my days as a graduate student came either directly or indirectly from him.

Soon after the discovery of asymptotic freedom in 1973, he started work on developing lattice methods for studying gauge theories non-perturbatively with a fixed cut-off. This founded the whole field of lattice gauge theory, which remains a major and active part of HEP theory. Not many people have a whole section of the arXiv they’re responsible for. For his story of how this came about, see his 2004 The Origins of Lattice Gauge Theory.

The reason Wilson was well-placed to quickly get lattice gauge theory off the ground in 1973-4 was that he was one of very few theorists who had been thinking hard and fruitfully about the meaning of non-perturbative quantum field theory. After getting an undergraduate degree in math from Harvard in 1956, he did his thesis work under Gell-Mann at Caltech, finishing in 1961 and developing an interest in the renormalization group. From 1963 on he was focusing his research on strong interactions and the high energy behavior of quantum field theory. This was a time when QFT had fallen out of favor, with S-matrix theory considered the cutting edge. One reason others weren’t thinking about this was that the problem was very hard. It was also perhaps the deepest problem around: how do you make sense of quantum field theory? What is QFT, really, outside of the approximation method of perturbation theory?

By the early 1970s, Wilson had developed the ideas about the renormalization group and QFT that now form the foundation of how we think about non-perturbative QFTs. The first applications of this actually were to problems about critical phenomena, and it was for this work that he won the Nobel prize. With the arrival of QCD, these ideas became central to the whole field of particle theory, with much of the 1970s and early 80s devoted to investigations that relied heavily on them. If you were a graduate student then, you certainly were reading his papers.

For more from Wilson himself about his life and work, see his 1983 Nobel Prize lecture and a long interview from 2002 here, here and here.

John Preskill has a wonderful posting up about Wilson, with the title We are all Wilsonians now. He ends it by explaining Wilson’s early role in the debate about “naturalness”. Wilson was well aware of the quadratic sensitivity of elementary scalars to the cut-off and had argued that this meant that you didn’t expect to see elementary scalars at low masses. This argument was developed here by Susskind as a motivation for technicolor. Preskill doesn’t mention though that Wilson later referred to this as a “blunder”. In 2004 he had this to say:

The final blunder was a claim that scalar elementary particles were unlikely to occur in elementary particle physics at currently measurable energies unless they were associated with some kind of broken symmetry [23]. The claim was that, otherwise, their masses were likely to be far higher than could be detected. The claim was that it would be unnatural for such particles to have masses small enough to be detectable soon. But this claim makes no sense when one becomes familiar with the history of physics. There have been a number of cases where numbers arose that were unexpectedly small or large. An early example was the very large distance to the nearest star as compared to the distance to the Sun, as needed by Copernicus, because otherwise the nearest stars would have exhibited measurable parallax as the Earth moved around the Sun. Within elementary particle physics, one has unexpectedly large ratios of masses, such as the large ratio of the muon mass to the electron mass. There is also the very small value of the weak coupling constant. In the time since my paper was written, another set of unexpectedly small masses was discovered: the neutrino masses. There is also the riddle of dark energy in cosmology, with its implication of possibly an extremely small value for the cosmological constant in Einstein’s theory of general relativity.

This blunder was potentially more serious, if it caused any subsequent researchers to dismiss possibilities for very large or very small values for parameters that now must be taken seriously…

He then goes on to argue at length that the lesson of the history of science is that often what seemed like unlikely possibilities turned out to be the right ones, with the argument for unlikeliness just a reflection of the fact that people had been making assumptions that weren’t true and/or they didn’t understand the possibilities as well as they thought they did.

Wilson may be no longer with us, but his ideas certainly are, and they’re very relevant to the biggest controversies of the day.

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17 Responses to Kenneth Wilson 1936-2013

  1. Igor Khavkine says:

    Peter, that’s a great quote from Wilson. It’s great to see such a “radically conservative” position from the man himself. I wonder how it would play with the current mainstream opinion, if it were better known. 😉

    Looking at the list of his achievements, it’s hard not to find them impressive. However, it is sad to see that part of his legacy is a wide spread conflation of two distinct concepts: perturbative renormalization in QFT and a lift of classical scaling transformations to quantum theory (aka the renormalization group). Moreover, the idea that some (or all) field theories must be defined with an explicit cutoff (in addition to not having any empirical evidence for the existence of any such fundamental cutoff in our world) is tantamount to forsaking the hope of answering the mathematical question of whether renormalized continuum QFTs can be defined on their own terms, independent of any particular choice of regulator. I don’t know of any other, similarly important mathematical question, where the widespread opinion is to simply give up looking for an answer.

    I hope that in the future Wilson is remembered more for his important work on the analysis of scaling transformations in QFT (both lattice and continuum), his work on operator product expansions, his work on lattice field theory itself and his work on critical phenomena in condensed matter systems (where explicit cutoffs do actually exist).

  2. Peter Woit says:


    I think that the issue of regulators is only one of many where there’s a conventional wisdom among particle theorists that keeps people from working in other directions. Unfortunately, we don’t know which of these pieces of conventional wisdom are wrong and will someday be seen as what was keeping people from making progress. It does though look like “naturalness” is a good candidate…

  3. meet says:

    Even if you had met Ken Wilson in person, it is unlikely that you would have gotten anything much out of it. He was a brilliant and very nice person but very, very shy. Perhaps if you had been his student or postdoc … but he accepted very few graduate students. Michael Peskin is perhaps his most famous graduate student. Paul Ginsparg was also his student. It is well known that as an assistant professor at Cornell, Wilson published maybe six papers in five years. But when the time came for tenure, Hans Bethe, who was the Grand Old Man of Cornell Physics in those days, protected Wilson (“This man is deep.”) and insisted that Wilson be granted tenure. The next year or so, Wilson’s groundbreaking papers on the renormalization group were published, and the rest is history. At the Cornell press conference for Wilson’s Nobel Prize, Bethe sat next to Wilson at the table and preened himself like a mother hen. Bethe had a smile six inches across from end to end.

  4. gs says:


    During roughly the same time frame in which Wilson was doing his scaling-based work, Mandelbrot was formulating (and popularizing) fractals.

    In my amateur opinion each was uninfluenced by, and possibly unaware of, the other’s progress. but in a sense they approached the same monolith from very different directions.

  5. King Ray says:

    Lightspeed, Kenneth Wilson.

  6. Blake says:

    Offtopic: Is John Ellis for real saying that the LHC results are actually “encouraging” for SUSY? Are SUSY proponents becoming divorced from reality, or am I missing something.

  7. Peter Woit says:

    Blake, I had the Google+ hangout thing on in a window for a while, and did hear Ellis going on about the situation of SUSY being encouraging. This is pretty delusional, but it’s also not really news that SUSY proponents aren’t willing to admit the situation they’re in. So, unless there’s something really surprising, best to avoid yet more of the same discussion about SUSY here, where it’s off-topic.

  8. MathPhys says:

    K Wilson was a scientific and an intellectual hero to many of us who learnt quantum field theory in the late 1970’s and early 1980’s. The fact that he wrote one very deep physics paper per year from the late 1960’s to the mid 1970’s, before he eventually turned his attention to computing, set him apart as a great scientist and a profound thinker who did things his own way, and that we looked up to, but had no way to emulate.

    I met him in 1982. He was quiet, reticent, reserved but also very polite. For someone who ran the mile in less than 4 minutes as a young man, he was quite out of shape in his 40’s. Listening to his lecture, then asking him questions, I was struck by how he gave very simple arguments that were natural and totally convincing when he said them, but difficult to reproduce after the discussion. His mind worked differently from most other people. RIP.

  9. q&a says:

    The legend was that Ken Wilson didn’t answer the question you asked, but the question you should have asked.

  10. Jeff M says:

    OK, if you get far enough into “The Origins of Lattice Gauge Theory” you find Wilson discussing a bizarre episode from the early 70s of someone who read a paper of his and called him to set up a meeting in Ithaca. At the meeting the person gradually explained to Wilson that his work agreed with this person’s idea that the world was a computer simulation (if fact, a chain of computer simulations). Of course, this is now discussed seriously in many circles, but wow, to have come up with that given what computers were like in the early 70s!! No doubt chemicals were involved…

  11. MathPhys says:

    It’s not clear to me why he wrote “I kept listening. But then he asserted that eventually one comes to a computer simulation run by a Supreme Being. At that point I managed to terminate the conversation.” My understanding is that Wilson held religious beliefs.

  12. Peter Woit says:


    Maybe his religious beliefs included a Supreme Being that didn’t do silly things like run computer simulations…

  13. Peter Shor says:

    If a Supreme Being is omnipotent, why would he choose to simulate a world rather than actually creating one? Would you expect your Supreme Being to do shoddy work? (Of course, computer scientists and physicists may disagree about whether simulating a world is the inferior method …)

  14. MathPhys says:

    I personally think that to think of the universe as a computer simulation is just as good as any other image that one can come up with to put metaphysical concepts into words.

    More interestingly (to me) is the fact that I have always remembered that Wilson was a Quaker. I’m not so sure how I knew this, but the last time that I have thought of this cannot be long after meeting him in 1982 or 1983, so it may have been Wilson himself who mentioned it, though that seems unlikely.

    He was intellectually miles ahead of anyone else around him, but treated everyone from the most pretentious professor (there were many) to the lowliest graduate students (there was only one) on equal footing and equally seriously. When someone mentioned running the mile in 4 minutes, he smiled and said “That was a long time ago”.

  15. hari says:

    Is this the last talk delivered by Wilson?
    Only abstract seems to be available.

  16. Anonyrat says:

    MathPhys, this database of people does list Wilson as a Quaker.

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