When learning about various ideas in mathematics and physics, I’m always fascinated by the history of these ideas and eagerly read whatever I can find on the subject. Partly this is because my understanding of ideas is often enlightened by finding out where they came from, especially what problems they were invented to solve. It’s also true that the history of these fields is a huge and remarkable story, in many ways far more intricate, subtle and surprising than any novel ever written, and can be appreciated as such. It’s quite possible that I’ve spent more time on this than is healthy, since there are good reasons for the fact that many scientists wait until late in their career to develop serious historical interests. Time spent studying history is not time spent developing new ideas.
One peculiar aspect of the present state of particle theory is that our current best fundamental physical theory, the Standard Model, is getting so old that fewer and fewer active physicists have any first-hand knowledge of its history. To a large degree, this history spans just about exactly a quarter-century, from renormalized QED in 1948 to asymptotic freedom in 1973. Before 1948 all we had were first-order calculations in QED, by 1973 the full Standard Model was in place. Physicists who finished a Ph.D in 1973 are now in their early 60s and soon will be getting to retirement age. First-hand understanding of where the Standard Model came from is now not part of the background of particle physicists in the most active stage of their careers.
One reason I started thinking about this is a recent exchange in the comment section of the last posting, sparked by my referring parenthetically to the fact that Yang and Mills had developed Yang-Mills theory (in 1954) in the context of trying to describe the strong interactions. The SU(2) gauge theory they wrote down didn’t work for this purpose, since what was needed was an SU(3) theory of quark colors, something that had to await at least the discovery of quarks. The SU(2) gauge theory of isotopic spin they were considering ultimately did find a role in the electroweak part of the Standard model, but this idea got started only after the symmetry properties of the weak interactions became clear later in the 1950s. Schwinger and his student Glashow were among the first to work on this idea, with the correct theory not appearing until 1967 after the role of the Higgs mechanism was understood.
Anonymous commenter “H-I-G-G-S” reacted to my allusion to this history as follows:
You said “Actually, Yang-Mills theory was invented to describe part of the standard model (the strong interactions)”
Not true. Go back and read the original paper.
Well, I have read the original paper, as well as a lot of secondary literature about it. The paper begins with a discussion of the symmetry properties of the strong interactions of nucleons and pions, which was the main topic of the day in 1954, due to the large number of strongly interacting states being discovered at accelerators. Nothing about the weak interactions, which was a different topic, with the symmetry properties of such interactions not understood until a few years later.
I devoted a few minutes to Googling “Yang-Mills” and “history”, and turned up quotes from David Gross and Steven Weinberg explicitly stating that the strong interactions were the motivation for Yang and Mills and posted comments with those. It seems though that “H-I-G-G-S” is not satisfied with this, recently responding:
Perhaps Yang and Mills were hoping to develop a theory of the strong interactions. Perhaps not. Where is the evidence that they were? You don’t cite any statements from their actual paper. You don’t direct me to any historical documents where they were interviewed about their thoughts. If you did I would be happy to have a look and I might be convinced that this was indeed their motivation. Instead you argue by appeal to a higher authority, in this case Gross and Weinberg. Of course when they argue about the importance of string theory you do not agree with them, but when they support a point you like they are suddenly experts who cannot be disputed. Gross was 13 years old when the Yang-Mills paper was published. Why do you think he should know what they were thinking?
I had actually cited a relevant statement from the paper, but I’m not sure what if anything could possibly satisfy “H-I-G-G-S”. Perhaps there is a published interview where Yang makes the kind of explicit, unambiguous statement about his motivations that “H-I-G-G-S” requires and maybe someone with enough interest can dig this up. Since “H-I-G-G-S” insists on anonymity, all I know is that he or she is from a major metropolitan area home to major universities, and appears to be a particle theorist who has been around for a while, although not long enough to know much history. Despite this, he/she has rather definite ideas about what this history is, coupled with a steadfast skepticism about any information which might indicate these ideas don’t correspond to historical reality.
I don’t know to what extent the case of “H-I-G-G-S” reflects the general understanding of the historical roots of the Standard Model among active theorists working on trying to extend it. Much effort on this blog has been devoted to trying to puncture the historical narrative that has solidified over the last 25 years about the supposed march forward of such speculative ideas such as extra dimensions, supersymmetry and string theory. Perhaps it would also be a good idea to worry about misconceptions concerning the history of successful parts of the subject, as well as the unwillingness of many particle theorists to give up such misconceptions.
Update: Here are some suggestions for reading about the history of the Standard Model, ordered very roughly from more popular to more technical:
For the early history of gauge theory, there is
This is a great time to be studying history. Besides google, there is scholar.google.com which links to papers that reference the paper you searched for, as does Phys. Rev. And most major journals are online. I can find more articles in one hour online than I used to find in a week at the library.
I’ve been studying history to see where things went wrong. The introduction of quarks met with the same criticism as strings do today. The discussion of EPR through the ages is fascinating.
Some of the most fascinating papers have no citing articles.
Yes, I am in my 60’s, 63 to be precise and without the interruption of the Vietnam tour, I would have had my PhD in 1973. But then I would have been part of the establishment I am now criticizing. I am not a fan of the standard model, I am bothered by the idea that there are conserved quantities which are not defined for all particles and not conserved in all interactions (isospin, strangeness…)
and it is exciting that people long ago had the same reservations.
One of my cousins has a PhD in history and she says “Nothing changes faster that the past” both because scholars keep digging up new material but also because there are some who keep rewriting the past.
The widespread ignorance of the history of the ideas of particle physics is disgusting. The first application of Yang-Mills SU(2) to attempt to deal with weak interactions was by Schwinger and Glashow in 1956, see Glashow’s Nobel Prize lecture here:
‘Schwinger, as early as 1956, believed that the weak and electromagnetic interactions should be combined into a gauge theory. The charged massive vector intermediary and the massless photon were to be the gauge mesons. As his student, I accepted his faith. … We used the original SU(2) gauge interaction of Yang and Mills. Things had to be arranged so that the charged current, but not the neutral (electromagnetic) current, would violate parity and strangeness. Such a theory is technically possible to construct, but it is both ugly and experimentally false [H. Georgi and S. L. Glashow, Physical Review Letters, 28, 1494 (1972)]. We know now that neutral currents do exist and that the electroweak gauge group must be larger than SU(2).
‘Another electroweak synthesis without neutral currents was put forward by Salam and Ward in 1959. Again, they failed to see how to incorporate the experimental fact of parity violation. Incidentally, in a continuation of their work in 1961, they suggested a gauge theory of strong, weak and electromagnetic interactions based on the local symmetry group SU(2) x SU(2) [A. Salam and J. Ward, Nuovo Cimento, 19, 165 (1961)]. This was a remarkable portent of the SU(3) x SU(2) x U(1) model which is accepted today.
‘We come to my own work done in Copenhagen in 1960, and done independently by Salam and Ward. We finally saw that a gauge group larger than SU(2) was necessary to describe the electroweak interactions. Salam and Ward were motivated by the compelling beauty of gauge theory. I thought I saw a way to a renormalizable scheme. I was led to SU(2) x U(1) by analogy with the appropriate isospin-hypercharge group which characterizes strong interactions. In this model there were two electrically neutral intermediaries: the massless photon and a massive neutral vector meson which I called B but which is now known as Z. The weak mixing angle determined to what linear combination of SU(2) x U(1) generators B would correspond. The precise form of the predicted neutral-current interaction has been verified by recent experimental data. …’
Peter, this H-I-G-G-S fellow is a typical internet troll, I wouldn’t waste time on him. Though he did allow you to make a point I suppose…
Thomas R Love, I’m not sure I understand your reservations about the standard model. Isospin and strangeness are approximately conserved quantities (that is, they are not conserved, but they almost are). And surely they are defined for all particles? The strangeness is the number of strange quarks minus anti strange quarks, for example. Or am I mixed up?
big vlad/Thomas Love,
Please stick to the topic of history. Again this is not a forum for people to explain their favorite unconventional ideas to the world.
Peter,
Wasn’t Gross’ remarks made at a celebration of Yang’s 70th birthday — was he present?
Michael,
Yes, that’s true. Almost certainly Yang was there.
I agree that there’s a great deal of interest attached to sorting this out.
I have a general impression (perhaps someone can correct me about this) that in the mid-50’s there was less theoretical urgency felt in moving beyond the four-Fermi theory of weak interactions than in trying to develop the theory of strong interactions. The reason was that the non-renormalizability of the theory was not widely perceived as a fundamental failing (only later did that general sentiment develop), and, given the weakness of the force, the f-F treatment seemed a good start. On the other hand, the strong force was — well, strong, and so worries about finding a consistent way of doing perturbations were much more timely.
Pawl,
I think what’s most relevant is that in the early 1950s there was a huge amount of experimental data coming in about the strong interactions, with all sorts of new particle states being discovered, and hardly any theory at all to account for them. Because of this, just about all theorists those days were focused on the strong interactions. There was much less data concerning weak interactions, and the four-fermi theory accounted for what was known, with the question of higher loop calculations in that case a purely academic one.
Yang and Mills didn’t need to explain in their paper that they were thinking about the strong interactions, that would have been obvious to everyone. If they were thinking at all about the weak interactions, they would have mentioned that explicitly.
Peter,
Thanks. I think we’re saying almost the same thing.
Peter and others , I agree history of physics is a fascinating subject.
In cosmology, history of cosmic inflation is also very interesting
and quite differnent form what appears in textbooks with very important papers by Kazanas, Starobinsky and Sato (and probably others) before
Guth’s paper.
On the question of wether or not is healthy to devote time to study history of physics, i believe that history itself (a “one loop” reflexion:) shows that really deep thinkers like Galileo, Newton, Maxwell or Einstein were quite interested an well informed on that respect. Probably the usefulness of that kind of knowledege depends on what yo do: if you are a problem solver working on a given predetermined conceptual background (a “local thinker”, a man of detail)it is probably OK not to know anything about history, but if you are a big picture “strategic” thinker, you better be aware of your discipline history.
At any rate, any self respecting phys grad student should have some exposure to phys history, at least as an antidote to the dreadful possibility of being some sort of phys “energyzer bunny” stuffed with batteries and set to go in the place and direction of choice of his PhD advisor, as many wannabe string theorists in this days.
I think Abraham Pais’s Inward Bound has something to say on this. In the discussion on page 585 of the introduction of Yang-Mills theory the discussion over the next few pages is exclusively phrased with respect to nucleons and to vector mesons as the exchange particles. This surely gives the context for the discussion above.
Perhaps also reference 172 in that chapter also has something interesting to say – this reference is “C.N. Yang, Selected Papers 1945-1980, p 19, Freeman, San Francisco 1983” where the page reference describes Yangs recollections of a seminar he gave in Princeton where Pauli was very critical and Pais was also present.
This would perhaps give the definitive answer?
that story is so well-known, yet so funny… Pauli was asking Yang about the mass of the intermediate vector mesons (now gluons), probably knowing that they were massless and therefore a killer for the theory (there are no massless hadrons…). Yang responded he wasn’t sure of the answer. Apparently, Pauli was so insistent and hostile with his questions that Yang just sat down at the front row and stopped talking! Then Oppenheimer encouraged him to continue delivering his talk, which he did.
Hi,
Can anybody suggest me a good book on history of particle physics?…..Other than Pais’ “Inward Bound”
Pauli did it first, before Yang-Mills, in some letters to Pais, “Meson Nucleon Interaction and Differential Geometry” (written “to see what it looks like”, in three days in July. See O’Raifeartaigh, “Dawning of Gauge Theory”. Like Gauss, he did not publish.
-drl
Peter,
I have a copy of “Selected Papers by C.N.Yang, 1942-1980”, in which Yang made extensive comments on every paper there, mainly with historical interests. The comments on the Yang-Mills are on p19…Maybe this gentleman H-I-G-G-S can go to the library to find it out.
http://universe-review.ca/R15-21-YangPauli.htm
@Indrajeet: I found ‘Second Creation’ by Robert Crease and Charles Mann to be a very interesting history of particle physics etc. Covers the period from early 20th century to early eighties (only) – very little, if not nothing, about string theory IIRC. Maybe others (physicists in particular) can comment on how good an account of history it is.
Rajagopal
Hi Peter, interesting post.
In the book ‘It Must be Beautiful’ (Granta Books), Christine Sutton has a lovely chapter on Yang-Mills theory, outlining the development of the theory, its initial failure and its modern use in particle physics.
There is also a nice reference to Lochlainn’s book on the history of gauge theory!
Chris Quigg deals with this issue in his “Gauge Theory of the Strong, Weak and Electromagnetic Interactions”, p.55. where he cites the original 1954 paper by Yang and Mills.:
I’l paraphrase his remarks a bit:
“A free nucleon Lagrangian, written in terms of the composite fermion fields for the proton and neutron, has an invariance under global isospin rotation, and the isospin current is conserved. Thus one has complete freedom in naming the proton and the neutron (in the absence of electromagnetism), but only at a single point in space-time. Once freely chosen, the convention must be respected everywhere throughout space-time.
This single restriction may seem, as it did to Yang-Mills, at odds with the idea of a local field theory. Furthermore, we have seen that electromagnetism possesses a local gauge invariance, and that by imposing a local symmetry on a free-particle Lagrangian it is possible to construct a correct theory of electrodynamics. In analogy with electromagnetism we are led to ask whether we can require that the freedom to name the two states of the nucleon be available independently as every space-time point. Can we, in other words, turn the global SU(2) invariance of the free field theory into a mathematically consistent local SU(2) invariance”
He then goes on, following Yang-Mills, to construct the non-Abelian Yang-Mills Lagrangian for the nucleon, pointing out the standard defect, namely that as a consequence of local gauge invariance, the Yang-Mills quanta are massless vector bosons and of infinite range and therefore cannot serve as a successful phenomenological description of the strong nuclear force which involves the exchange of massive particles.
So of course, as you pointed out, Yang-Mills were trying to develop a phenomenological description of strong interactions, specifically a SU(2)-isospin gauge theory, but hit a brick wall once the quanta their theory produced were massless vector bosons.
Lochlainn O’Raifeartaigh (Cormac’s father) in his beautiful monograph “Group Structures of Gauge Theories” also refers to the 1954 paper (p.79)
“It is now generally accepted that Weyl’s gauge principle can be used to describe the strong and weak interactions and well as the EM ones by generalizing U(1) to other compact Lie groups. The first extension of the principle, to the isospin SU(2) group, was made by Yang and Mills (1954)”
Moriyasu’s book “An Elementary Primer for Gauge Theory” is the shortest path to learn the subject that I know of and it nicely outlines the history involved.
Rajagopal,
Thanks a lot. I will have a look at it.
I’ve added to the posting a list of books that I’ve found most useful for learning some of the history of the standard model.
Peter, would you consider adding to your list of books
Constructing Quarks: A Sociological History of Particle Physics
by Andrew Pickering (Chicago 1984)
Tony Smith
Yang-Mills is sometimes called Yang-Mills-Shaw theory on this side of the pond:
http://www.hull.ac.uk/php/masrs/reminiscences.html#Anchor-3.4-55015
Peter and minions,
I may not have been clear, or perhaps you are deliberately misunderstanding me. In either case it might be good if I amplify my remarks. I’m quite aware that isospin is a symmetry of the strong interactions and that Yang and Mills were discussing strongly interacting particles like the neutron, proton, and pion. They were obviously trying to make isospin a local symmetry in the context of the strong interactions. So I’m sure they viewed what they were doing as related to the strong interactions. If that’s all you mean by saying that “Yang-Mills was invented to describe the strong interactions” then I have no quibble with you. But your statement, and the statement in many of the quotes in the comments sound quite a bit stronger. It makes it sound like they were trying to develop a full theory of the strong interactions based on gauging isospin. While this has a certain historical resonance to it since Yang-Mills theory ended up being the basis for QCD, I suspect it overstates the case. For example, at the time the strong interactions were known at large distances to be mediated by pion exchange. Yang and Mills make no attempt to describe the pion or its affects in their theory. They don’t try to describe the neutron or the proton. What they do is to gauge isospin and then speculate that the apparently massless isovector spin one particle they find might acquire mass by some mechanism. So it seems they were trying to describe features of the strong interactions, and perhaps new particles resulting from the strong interactions, but I still see no evidence that they had any reason to think they were developing a full theory of the strong interactions.
What undoubtedly gave their theory a strong boost was the discovery 7 years later of a massive spin one isovector partice, the rho meson, just as predicted except for the awkward question of its mass. This, along with the work of Sakurai around 1960 gave Yang-Mills theory a strong boost, but even then it was used to describe features of the strong interactions such as Vector Meson Dominance and not as a comprehensive attempt to describe the full spectrum and structure of the strong interactions.
In general I suspect that history is often more complicated than the “just so” kind of descriptions that Christine quoted which make it sound like Yang and Mills almost had QCD except for using SU(2) instead of SU(3).
H-I-G-G-S,
The historical record of the context of the Yang-Mills paper is unambiguous: they were hoping to get a theory of the strong interactions with a gauge theory of isospin, which they showed would imply that interactions were due to exchange of isospin 1 vector mesons. This idea doesn’t work, which they clearly realized since they didn’t pursue it after the original paper.
Your comments here about this being “not true”, telling me to go read the paper, that you “don’t believe the claim that they were trying to describe the strong interactions”, that maybe they were not trying to develop a theory of strong interactions, and that Gross might not know what he was talking about since he was only 13 in 1954 are just completely ridiculous. All you are doing is providing an amusing example of how some particle theorists don’t know the history of their field, are quick to accuse others of not knowing what they are talking about, and completely incapable of admitting it when they make a mistake.
No one claims anywhere that Yang and Mills “almost had QCD”, you’re trying to justify your own absurd comments by putting sillier ones in other people’s mouths.
H-I-G-G-S wrote:
In general I suspect that history is often more complicated than the “just so” kind of descriptions that Christine quoted which make it sound like Yang and Mills almost had QCD except for using SU(2) instead of SU(3).
No. I just included some excerpts that I thought being relevant for the discussion, but evidently one should read the book to have the complete outline that Moriyasu offers. In any case, I hope the following excerpts will complement my previous ones:
From my previous quotes and the present ones, I see in no place any claims that you suggest. I agree that Moriyasu’s book is a very concise and elementary treatment of gauge theory but I fail to see where he got history unbalanced. Since I just included excerpts, reading the book is advisable. In any case, Peter has included a nice list of references on the matter.
Thanks,
Christine
I still see no evidence that they had any reason to think they were developing a full theory of the strong interactions.
Cao in his “Conceptual Developments of 20th Century Field Theories” puts the matter under two main motivations (pages 273-274):
Since I am not certain whether this conciliates Peter and H-I-G-G-H’s points of view, I let the matter with you.
Lubos weighs in supporting H-I-G-G-S against Gross and Weinberg here
http://motls.blogspot.com/2009/02/history-of-yang-mills-theory-and.html
According to him, the desire of Yang and Mills to come up with a theory of the strong force had nothing to do with their gauging isospin. He does draw some historical lessons, noting correctly that a theory developed for one purpose may turn out not to work for that, but find use elsewhere. For instance, a theory once thought to be a spaceship capable of giving a TOE may turn out to be a toaster capable of approximately describing the viscosity of a quark-gluon plasma….
Tony,
The list I put up is certainly not exhaustive, and “Constructing Quarks” is also a good history of subject. There are quite a few others, but I’ll leave that list as a personal one of the things I most enjoyed or found useful.
Peter,
Your statement “The historical record of the context of the Yang-Mills paper is unambiguous:” is certainly true, but it is also not what we are talking about. I agree that the context is clear, but the motivation and thoughts of Yang and Mills, which is the topic under discussion, are not.
The historical record is rarely unambiguous on any topic, and you have yet to cite a single iota of primary material, by which I mean statements in the original paper or interviews with Yang and Mills or their colleagues near the time they were doing the work. I’m just as well acquainted with the secondary material as you are, but its not much help in trying to figure out what Yang and Mills were actually thinking at the time.
H-I-G-G-S,
This is just ridiculous. Yang, like almost every other major theorist of the day, at that time was trying to find a theory of the strong interactions. The paper explicitly mentions this context, and every knowledgeable person who discusses it describes it as an effort to come up with a strong interaction theory, except you.
You completely ignored the what I quoted from the paper itself:
“We then propose that all physical processes (not involving the electromagnetic field) be invariant under an isotopic gauge transformation…”
What physical processes do you think he’s talking about? If it’s not the strong interactions, it’s gravity or the weak interactions. If you’re claiming that Yang had the idea of getting a weak interaction theory by gauging the right SU(2) a couple years before Schwinger, that’s a dramatic new advance in the history of the subject. Except I don’t think anyone will believe it except you.
At the end of the paper, they discuss experimental limits on the mass of the vector boson in their theory. They explicitly say it should decay into pions with a lifetime less than 10^-20 seconds. This is a strongly interacting particle.
It’s always astonished me how ignorant people are of physics history, how quick to make pronouncements when it’s patently obvious that they have never bothered to even learn what the papers were, much less read them. This is hardly new – it was true when I was in school 25 years ago.
Of course everything you say about Yang-Mills and their motivation – which had to be enormously strong in the face of Pauli’s criticism (he himself had tried the idea a year or so earlier but did not publish it) – is entirely correct.
-drl
Yang makes a few remarks concerning his motivation in his “Selected Papers (with commentary)” book. He says that as more and more hadrons were discovered there was clearly a need to find a general principle that would constrain the possible interactions, and he was looking at local isospin gauge invariance for this purpose. He also remarks that Pauli’s unpublished note was called “Meson-Nucleon Interaction and Differential Geometry”.
This idea is not totally wrong, by the way (if the Higgs mechanism is added). If the rho meson is a gauge particle, then the rho-pi-pi, rho-N-N, etc couplings are related. These relations are experimentally satisfied to a reasonably good (20%, or so) accuracy (for reasons that are not understood very well).
The idea of gauging isospin and making the rho triplet massive by means of the Higgs mechanism was, I think, what Weinberg had in mind before realizing that it could be applied more successfully to leptons.
In any case, isospin symmetry cannot be spontaneously broken in QCD (like chiral symmetry is), according to a theorem by Vafa and Witten.
Thomas,
The reason for those relations is starting to be understood as a consequence of string dual models of QCD where isospin is in fact a gauge symmetry in the higher-dimensional dual theory.
Peters and others , see these talks at PI which does touch upon some historical aspects.
http://pirsa.org/09020027/
http://pirsa.org/09010009
Hi Peter,
I think the way we study even scientific matters in Italy is different from the way these are studied elsewhere. Maybe this is a hindrance, maybe it is an advantage – but I feel cultured by having studied the Standard Model not as it is now, but how it was developed – and I was 7 years old when the theory was sealed.
During my studies, by no means deeper than those of most of my italian colleagues, I for instance took great pleasure in understanding in deep detail what drove the choice of V-A over S-T, for instance, and the historical developments of the mid fifties.
As for Yang-Mills theory: I have never had any doubt that their aim was understanding strong interactions. I thank Professor Antonio Bassetto for teaching me a thing or two in his powerful course of Quantum Field Theory.
Cheers,
T.
H-I-G-S-S, that’s interesting. Is SU(6) symmetry also a gauge symmetry in the dual model?
Ghame,
Which SU(6) do you mean? The SU(6) of six flavors (u,d,s,c,b,t) or the non-relativistic SU(6) mixing rotations and isospin?
H-I-G-G-S, I meant the nonrelativistic SU(6). The reason why I asked is that the octet meson-octet baryon-decuplet baryon couplings obey SU(6) with pretty good accuracy. So, if the pretty badly broken isospin relation between rho-pi-pi and rho-N-N couplings comes from a gauge symmetry, why not the SU(6) relation for decuplet couplings? Sure, SU(6) is not an internal symmetry so it seems unreasonable for it to be a gauge symmetry but,t what do I know about dual models?