The Quote Of The Week - Higgs On Anderson's Role In The Higgs Mechanism
    By Tommaso Dorigo | December 5th 2013 07:50 AM | 13 comments | Print | E-mail | Track Comments
    About Tommaso

    I am an experimental particle physicist working with the CMS experiment at CERN. In my spare time I play chess, abuse the piano, and aim my dobson...

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    "During the years 1962 to 1964 a debate developed about whether the Goldstone theorem could be evaded. Anderson pointed out that in a superconductor the Goldstone mode becomes a massive plasmon mode due to its electromagnetic interaction, and that this mode is just the longitudinal partner of transversely polarized electromagnetic modes, which also are massive (the Meissner effect!). Ths was the first description of what has become known as the Higgs mechanism.
    Anderson remarked that "the Goldstone zero-mass difficulty is not a serious one, because we can probably cancel it off against an equal Yang-Mills zero-mass problem". However, since he had neither found an error in the proof of the Goldstone theorem nor discussed explicitly any relativistic model, Anderson's remark was disbelieved at the time by those particle theorists who read it, myself included!"

    (Peter Higgs, in "The Rise of the Standard Model, ed. L.Hoddeson, L.Brown, M.Riordan, M.Dresden)

    I believe the above quote is of interest to a reader of this blog, who recently questioned the role of Anderson in the construction of the spontaneous symmetry breaking mechanism that gives rise to the Higgs boson and mass to the vector bosons of electroweak theory...
    For those who are left wondering: the Goldstone theorem states that the spontaneous breaking of a continuous symmetry creates zero-mass bosons - which do not exist in nature, thus making the idea of spontaneously breaking electroweak theory unappealing in the early 60's.


    Touche, Tommaso, touche...

    Yeah, thought so ;-)
    I was very very disappointed that Anderson did not get the nobel in connection with the discovery of the Higgs. He did everything in his power to *prevent* its discovery, so giving it to him would have been intensely embarrassing for the sour old bastard.

    Vladimir Kalitvianski
    P. Anderson did his best for the US.

    What he failed in is convincing particle physicists that particles are quasi-particles, collective motion modes in complex systems.
    I don't really care one way or the other, but in the quote "the Goldstone zero-mass difficulty is not a serious one, because we can probably cancel it off against an equal Yang-Mills zero-mass problem" the word "probably" is interesting.

    Anderson made a suggestion that "probably" would solve a problem, but he didn't offer a solution himself. Now imagine a mathematician A who writes about an unproven theorem that the proof "probably" could be found because of X, Y and Z. Imagine a second mathematician B who proves the theorem and proves at the same time that the suggestion of A was correct. Could one honestly say that A proved the theorem? Sure, A "played a role" in the proof, but so did countless other mathematicians - after all, the theorem didn't come out of thin air, nor did the first attempts to prove it etc.

    I also found a remarkable quote on Peter Woit's blog.

    "(...) the “Anderson model”. The latter describes the behavior of a magnetic impurity in a metallic host. The model was mathematically described and solved (within a mean-field approximation) by Anderson in Phys. Rev. 124, 41–53 (1961).

    It might be not known to many in the HEP community, but the mechanism that the model captures had been described much earlier (with words, but in detail) by Jaques Friedel in Can. J. Phys 34, p. 1190 (1956). It is hard to believe that Anderson was not aware of Friedel’s work since, at the time, the number of Physicists working on Solid State problems was rather small and they met regularly. But to his own merit, Anderson was the first to formulate these ideas mathematically, thus lying the foundations of fields such like the so-called Kondo problem (...)"

    Another case of someone who had the right ideas but didn't write down the mathematical details. How would you describe the role of Friedel in the work of Anderson? It's an interesting question. One could say with hindsight that the work of Anderson in this case was difficult and the work of Brout, Englert, Higgs etc. comparatively easy. I don't know if that's true, but if it were, then it's even more remarkable that Anderson didn't work out the mathematical details of the Higgs mechanism in particle physics himself.

    Hi exsci,

    if your handle means something you certainly appreciate that the scientific contribution
    of a researcher is measured mainly through his published papers, and that quotes and
    verbal suggestions almost never play a role. So I think that has to be kept in mind one
    way or another in the case you discuss.

    As for his "probably", for a mathematician or a theoretical physicist that word is loaded
    with meaning IMO. I read it is a classic understatement, like "I can't prove it to you
    straight away, but I'd bet one testicle on it."

    Vladimir Kalitvianski
    "As for his "probably", ..."

    I think you are right. P. Anderson knew how to write it down, but it was not his direct business. In addition, one should give a physical interpretation to this "Higgs field" which was probably not clear to him what picture to advance, so he advised others as far as he could, but abstained himself.

    I guess the physical nature of the Higgs field is still unknown to HEP physicists.

    Your first paragraph makes the point I was trying to make. As far as I know (but correct me if I'm wrong) Brout, Englert and Higgs were the first to give a mathematical description of the Higgs mechanism and publish it.

    It's interesting that Anderson had the right idea. Nobody I know denies it. But it's unclear to me how one should evaluate his "role" in the discovery of the Higgs mechanism. The quote by Higgs you offer, doesn't make me wiser.

    (Btw, note that Jaques Friedel apparently published his ideas, albeit in a verbal version).

    Luis Gonzalez-Mestres
    At that time, the Ginzburg-Landau theory of superconductivity already existed :

    V.L. Ginzburg and L.D. Landau, Zh. Eksp. Teor. Fiz. 20, 1064 (1950)

    and also the BCS theory :

    L. N. Cooper, "Bound Electron Pairs in a Degenerate Fermi Gas", Phys. Rev 104, 1189 - 1190 (1956).
    J. Bardeen, L. N. Cooper, and J. R. Schrieffer, "Microscopic Theory of Superconductivity", Phys. Rev. 106, 162 - 164 (1957).
    J. Bardeen, L. N. Cooper, and J. R. Schrieffer, "Theory of Superconductivity", Phys. Rev. 108, 1175 (1957

    You can even find both in Wikipedia :

    In the Ginzburg-Landau approach, there is no Goldstone problem. The mass of the electromagnetic vector field is the inverse of the penetration length. This corresponds to what Anderson said.

    Thirty years ago, I used to teach the standard model of Particle Physics starting from the Ginzburg-Landau lagrangian for superconductivity. This was in Grenoble, where condensed matter Physics is strong, and students seemed to like it a lot. It was easy to understand that the difference between the Ginzburg-Landau lagrangian and that of the standard model is just :
    - the symmetry group (non-abelian in the case of the standard model)
    - the presence of fermions as matter fields in the standard model
    - the quantum character of particle fields
    - the physical vacuum has to be dealt with similarly to the ground state of the superconductor
    In going from the Ginzburg-Landau lagrangian to that of the standard model, there was no hard conceptual difficulty. Basically, technical problems to solve. This may explain Anderson's attitude.

    You can also look at the Nobel Prize lecture of Yoichiro Nambu :

    They all got the Nobel Prize :

    - Landau, in 1962
    - Ginzburg, in 2003
    - Bardeen, Cooper and Schrieffer, in 1972
    - Anderson, in 1977
    - Nambu, in 2008

    Best regards
    Hello Luis,

    thanks for your input and your useful links !
    The situation of Anderson - having the right idea but not publishing a detailed calculation - is not unique.
    Gerard 't Hooft discovered asymptotic freedom and mentioned it at a conference in 1972.But he didn't publish and Politzer, Gross and Wilczek got the Nobel in 2004. 't Hooft won a Nobel in 1999. Should the Swedish Academy have given a second Nobel to 't Hooft?

    "In going from the Ginzburg-Landau lagrangian to that of the standard model, there was no hard conceptual difficulty. Basically, technical problems to solve. This may explain Anderson's attitude."

    Perhaps that may explain Anderson's attitude. But if the 't Hooft story is correct, there weren't many "technical problems" left in the case of confinement. He had already done the calculations. One could also argue that Cabbibo should have received a Nobel. He discovered the idea of a mixing angle for a two generation model of the weak interaction. Some people claim that the extension by Kobayashi and Maskawa to three generations was just a technicality.

    Who is right? I don't know. But by giving a second Nobel to Anderson, the Swedish Academy would have opened a can of worms (the biggest worm probably being Ernst Stueckelberg ...)

    It would appear that the field of quantum field theory and its application was ripe for discovery in the 50-60's. In attributing who discovered what it seems the deciding factor is who published the idea first. How is this treated today? Is posting on arxiv considered published?

    Yes, a preprint is sufficient to determine who did something first. But it somehow depends
    on the context.