Steven Weinberg talks to CERN Courier about his seminal 1967 work and discusses where next for particle physics following the discovery of the Higgs boson.
Steven Weinberg was 34 when he produced his iconic “Model of Leptons”. The paper marked a moment of clarity in the history of particle physics and gave rise to the electroweak Standard Model, but it was also exceptional in inspiring one of the biggest experimental programmes science has ever seen. Flushing out and measuring its predicted W, Z and Higgs bosons took a multi-billion Swiss-franc effort in Europe that spanned four major projects – Gargamelle, the SPS, LEP and the LHC – and defined CERN’s research programme, keeping experimentalists in gainful employment for at least four decades. Not bad for a theory that, as Weinberg wrote at the time, “has too many arbitrary features for [its] predictions to be taken very seriously”.
Needless to say, Weinberg is delighted to have been able to witness the validation of the Standard Model (SM) over the decades. “I mean, it’s what keeps you going as a theoretical physicist to hope that one of your squiggles will turn out to describe reality,” he says. “I wouldn’t have been surprised or even very chagrined that, although the general idea was right, this particular model didn’t describe nature.”
Today, 50 years after his 1967 insight, Weinberg protests the notion that he is retired. The US has laws against discrimination on the basis of age, he says dryly. “I tell the people here that I plan to retire shortly after I die.” He is currently teaching a course in astrophysics at the University of Texas at Austin, his base for the past 35 years, and has two books and a new cosmology paper in the pipeline. Weinberg spoke to the Courier by phone in September from his home, reflecting on the state of high-energy physics following the Higgs boson discovery and on where the best hopes for new physics might lie. He began by recounting the thought processes that led him to his seminal 1967 work – many of which took place in children’s playgrounds.
“It was a complicated time of my life because my family had moved to Cambridge from Berkeley while my wife was studying at Harvard for her law degree. I had all the responsibility of taking care of our four-year old daughter, including taking her to nursery school, and a lot of my thinking was done while sitting on park benches and watching my daughter play,” he says.
Weinberg did not set out to unify the forces. He had been applying his ideas about symmetries, specifically the structure SU(2)×SU(2), to the strong interaction but it implied that the rho meson would be massless, contrary to experiment. “When I had the idea that the massless rho meson might really be the photon, it became natural to me that the rest of this gauge theory, suitably modified, could only be a theory of weak forces.” The work went quickly once he realised what he was doing. “You take the left-handed electron plus neutrino doublet and right-handed electron and ask what the most general possible symmetry group is, which turns out to be SU(2)×U(1)×U(1). Then you throw one U(1) away because if that was an unbroken gauge symmetry, you would have long-range forces among electrons which you don’t observe. So you’re led almost inevitably towards SU(2)×U(1). Indeed, though at first I didn’t know it, the same group had been used in a different way earlier by Glashow and by Salam and Ward.”
The paper was published without fanfare in Physical Review Letters on 20 November within a month of its submission. Weinberg doesn’t recall any talk he gave before the publication. He mentioned it in a side comment at the Solvay conference around that time (see “Birth of a symmetry”), but it didn’t arouse tremendous excitement.
In many ways, the paper was uncharacteristic of Weinberg. His tendency was to write general papers without worrying too much about their specific realisation in nature, he says, but in this one he was more specific. “Of course, experimentalists don’t test general ideas, so I was delighted when they showed that my theory was the right one. And then, after the neutral-currents discovery, the W and Z were discovered directly at CERN 10 years later and measured in detail at LEP and SLAC.”
It was not the specific model of leptons that excited him, though. Since his graduate days at Princeton, Weinberg has been hooked on the possibility of having a deductive basis for a physical theory following from the principles of symmetry and, in particular, renormalisability. “Symmetry is not enough by itself. In electromagnetism, for example, if you write down all the symmetries we know, such as Lorentz invariance and gauge invariance, you don’t get a unique theory that predicts the magnetic moment of the electron. The only way to do that is to add the principle of renormalisability – which dictates a high degree of simplicity in the theory and excludes these additional terms that would have changed the magnetic moment of the electron from the value Schwinger calculated in 1948.”
Renormalisability was the technique that connected quantum field theory to reality, offering a scientifically sound way to deal with the infinities that arise in calculations. Back when his paper was published, however, Weinberg did not know if his theory was renormalisable. That was probably why nobody took much notice of it, he says. “Remember: when we’re talking about renormalisability, it’s not just something theorists do to get rid of infinities. It was a criterion that was the sort you look for in theoretical physics, that defines a certain type of simplicity in your theories which otherwise would be arbitrary. We’re talking about whether we can have a theory of the weak interaction in which we can calculate beyond the lowest order in perturbation theory.” Weinberg strongly suspected his might be such a theory because before spontaneous symmetry breaking is taken into account, it has the same form as QED and it had already been proved that non-spontaneously broken Yang–Mills theories were renormalisable. “Salam and I weren’t sure but we didn’t think spontaneous symmetry breaking would affect the renormalisability because if you go to very high energies (much larger than the W or Z mass), the fact the symmetry is broken is no longer significant.” Had he not thought the model renormalisable, he might not have published. “The prospect of issuing an erratum was too much!”
In 1971, Weinberg began to realise that his paper was “hot stuff”, following the critical breakthrough by ’t Hooft and Veltman proving that the theory was renormalisable, although whether or not his particular model of leptons was correct was a still matter for experiment. The same year, he also tried to extend his ideas to the strong interactions using the quark model, in which there was little confidence at the time. The reality of quarks became clear with the discovery by Gross and Wilczek and Politzer in 1973 of the asymptotic freedom of some gauge theories, and the subsequent development of quantum chromodynamics, to which Weinberg, along with Gross and Wilczek, contributed the idea that it is impossible to isolate coloured particles such as quarks and gluons.
“It’s funny you know, people look back at the 1970s as one of the most miserable peacetime decades in the 20th century, as there was lots of unemployment and high inflation, in the US at least,” he muses. “But for us physicists it was a great time: everything was coming together, and experimentalists and theorists were talking to each other in lots of ways. Things are much harder today.”
The Higgs nightmare
The discovery of the Higgs boson by the ATLAS and CMS experiments at CERN five years ago was the capstone in Weinberg’s model. Until then, no one knew for sure how the electroweak symmetry gets broken to give elementary particles their masses – it was still possible that the Higgs mechanism was correct but that it does not involve a Higgs boson, for instance, or that the “Higgs” is a composite particle bound by new strong forces that lead to a dynamical breakdown of the symmetry. Precisely such a model, called technicolour, was proposed by Weinberg and Susskind in 1979. Back in 1967, though, Weinberg took the simplest possibility: a doublet of scalars. It was the only kind of elementary field that could not only give mass to the W and the Z but also the electron, he reasoned, and it would lead to the necessary existence of a leftover scalar particle that was not eliminated by the Higgs mechanism and became known as the Higgs boson. “The discovery of the Higgs boson was very important because it confirmed the very simple early picture of spontaneous symmetry breaking, which we couldn’t have known was correct because there were alternatives,” he says.
So did Weinberg’s 1967 paper also predict the Higgs boson? “It depends, as Bill Clinton might say, what is meant by the word ‘the’,” he laughs. “Is it the Higgs boson? Well, the existence of these particles in the general class of spontaneously broken gauge theories was predicted by Higgs and so on, and if you included theories that are non-gauge invariant then even earlier by Goldstone. But if by ‘the’ you mean the particle discovered, then that was predicted in my paper. The first paper that made a specific prediction of a single neutral particle whose coupling to leptons and later also to quarks was proportional to their masses was the 1967 model of leptons. The others also had a scalar particle but they were not developing a theory of weak interactions, they were considering several classes of theories with leftover scalars with unknown properties.”
Weinberg thinks the Nobel-prize committee made an “excellent job” in deciding who would share in the 2013 prize for the discovery (François Englert and Peter Higgs). “It isn’t a prize for predicting the Higgs boson, it is a prize for the theoretical discovery of the Higgs mechanism, which is exactly right because that is what was proposed by those 1964 papers. I rediscovered it in 1967 because I was working on spontaneously broken SU(2)×SU(2) gauge theory for the strong interaction, but I take no credit for it because it was already in the literature for three years. The actual Higgs boson, I think that was an experimental achievement.”
Unlike many particle physicists on the day of the Higgs announcement on 4 July 2012, Weinberg doesn’t recall exactly what he was doing when he heard the news. What he is sure of is that we are entering what he described several years ago as the “nightmare scenario” of having found a SM Higgs boson and nothing else. He says we’ve gotten ourselves into a rather unfortunate situation because the SM describes all the physics that can be addressed experimentally except things outside the SM like gravity and the neutrino masses. “It’s nobody’s fault. It is not an intellectual failure. It’s just a fix we’ve got into.” He doesn’t hold out too much hope in mainstream theoretical arguments for the existence of physics beyond the SM at the energies currently being probed at the LHC – i.e. that new heavy particles must exist to cancel out quantum contributions to the Higgs mass that would cause it to spiral to infinity. The fact that we now know that an elementary Higgs scalar exists makes this “hierarchy problem” somewhat harder, Weinberg concedes, but he points out that we’ve been living with the problem already for 40 years. So far the LHC has not found evidence for physics beyond the SM, including the most popular solution to shield the Higgs from getting additional mass: supersymmetry (SUSY). “Worse, there isn’t any one completely satisfactory SUSY model. Every SUSY model has things in it that are troublesome,” says Weinberg.
He thinks we might have to find other explanations for this and other absurdly fine-tuned parameters in the universe, such as the very small value of the vacuum energy or cosmological constant, or even abandon traditional explanations altogether.
“No one has come up with a plausible suggestion there except for the somewhat desperate suggestion that it is anthropic – that you have a multiverse and by accident there are occasional sub-universes where the vacuum energy is small and it’s only those in which galaxies can form – and people have suggested similar anthropic arguments for the smallness of the Higgs mass and the quark-mass hierarchy,” says Weinberg, who himself used anthropic reasoning in the 1980s to estimate, correctly, the approximate value of the cosmological constant a decade before it was inferred observationally from the velocities of distant supernovae. It’s a depressing kind of solution to the problem, he accepts. “But as I’ve said: there are many conditions that we impose on the laws of nature such as logical consistency, but we don’t have the right to impose the condition that the laws should be such that they make us happy!”
Weinberg’s outlook on the field today is pretty much as it was in 1979 when he gave his Nobel-prize lecture. The only big difference would be string theory, he says, which hadn’t yet come along as a possible theory of everything. “Apart from that, I said about the future beyond the SM that I think it’s unfortunate that there isn’t a clear idea to break into it.” Even the discovery of neutrino masses, inferred from the observation of neutrino oscillations 20 years ago, does not threaten the SM, he says. On the contrary: neutrino masses are what you expect.
Neutrinos and new physics
By the time Weinberg received his Nobel prize in late 1979, he had arrived at a more nuanced interpretation of field theory and described it in a paper titled “Phenomenological Lagrangians”. Building on the work of others, such as Schwinger, it presented the SM as the leading term in an “effective” field theory that is merely a low-energy manifestation of a deeper microscopic theory that we are yet to uncover. In this more modern view, field theories don’t have to be renormalisable to be logically consistent but can contain, in addition to the renormalisable terms, a slew of non-renormalisable terms that are suppressed by negative powers of some very large mass (corresponding to the scale at which the true theory applies).
For neutrinos, treating the SM as an effective field theory has major implications. Whereas simply inserting neutrino masses into the theory would violate the SU(2)×U(1) symmetry, Weinberg realised that there is an interaction between leptons and the Higgs doublet that avoids this. Crucially, since the interaction is non-renormalisable, it is suppressed by a very large-mass denominator – explaining both the existence of neutrino masses and their smallnesses and giving rise to what is more generally called the seesaw mechanism.
“In a sense it is beyond the SM, but I would rather say it is beyond the leading terms – the renormalisable, unsuppressed part of the SM,” says Weinberg. “But hell – so is gravity! The symmetries of general relativity don’t allow any renormalisable interactions of massless spin-2 particles called gravitons. We know about gravity even though it’s incredibly strongly suppressed only because it has this property of adding up: every atom in the Earth attracts a falling body, always pulling in the same direction. If it wasn’t for that fact, we wouldn’t know about its existence from experiments – certainly not at experiments at the LHC.” Of course, neutrinos were still thought massless back in 1979. Weinberg does not take credit for predicting neutrino masses, but he thinks it’s the right interpretation. What’s more, he says, the non-renormalisable interaction that produces the neutrino masses is probably also accompanied with non-renormalisable interactions that produce proton decay and other things that haven’t been observed, such as violation of baryon-number conservations. “We don’t know anything about the details of those terms, but I’ll swear they are there.”
As to what is the true high-energy theory of elementary particles, Weinberg says string theory is still the best hope we have. “I am glad people are working on string theory and trying to explore it, although I notice that the smart guys such as Witten seem to have turned their attention to solid-state physics lately. Maybe that’s a sign that they are giving up, but I hope not.” Weinberg worked on strings himself in the late 1980s, writing a couple of papers “of stunning unimportance”, but decided not to devote his career to it. As is documented in his 1992 book Dreams of a Final Theory, and much earlier in his Nobel lecture, he has his own hunch about an ultimate microscopic theory of nature, rooted in an idea called “asymptotic safety”. Weinberg also still holds hope that one day a paper posted in the arXiv preprint server by some previously unknown graduate student will turn the SM on its head – a 21st century model of particles “that incorporates dark matter and dark energy and has all the hallmarks of being a correct theory, using ideas no one had thought of before”.
Until that day comes, particle physicists have to be content with scouring the TeV energy scale at the LHC for new particles and with subjecting the SM to increasingly precise tests – not just at the LHC but at numerous other experiments at CERN and beyond. The field also faces a critical decision in the next few years as to what the next big-ticket collider experiment should be: an electron–positron collider, which potentially comes in straight or circular varieties, or a more energetic hadron collider. Most of the options on the table have precision measurements of the Higgs boson as part of their physics cases.
Next steps for the field
Weinberg says he doesn’t have an educated opinion on which machine should come next. “It hinges partly on what the experimentalists can actually accomplish, and I’m not equipped to judge that. And it hinges also on what the new physics is, and I’m not equipped to judge that!” he says. “If I had a very specific proposal for beyond-the-SM then it might indicate in which of these directions we should go, but I don’t know of any proposal that is attractive enough to go one way or the other.” Although he would like to see the Higgs, the first scalar particle discovered, measured in more detail, he fears that it will just confirm the simplest picture of the Higgs mechanism. “Because that’s what you get if you insist on a renormalisable theory, and I think it’s correct to do so for reasons I was beginning to understand in 1979.”
He is glad that CERN is continuing with the LHC, and that the US is doing neutrino-oscillation experiments, “which seems to now be the American style having given up on the SSC”. Another topic he thinks should be pushed more is the search for baryon non-conservation (proton decay) on Earth. But the most promising arena for progress these days is astronomy, he says. After all, otherwise we wouldn’t even dream of the existence of dark matter and dark energy, and it’s an area where experiment is still very fruitful – as evidenced by the recent discovery of gravitational waves. “My goodness, that’s the most exciting thing – studying gravitational radiation not just for its own sake but opening up a whole area of astronomy.” Cosmology, along with the foundational issues of quantum mechanics, is the subject of Weinberg’s own recent work, and he is currently putting together a paper with co-worker Raphael Flaugera on the effect of the intergalactic medium on gravitational waves from distance sources.
Reflecting on physics
It is beyond doubt that Weinberg’s 1967 paper was game-changing, but does he himself rate it as his most important contribution to physics? “Oh I don’t know. I don’t like praising my own papers. The 1967 paper was part of a programme of many decades – a concern with symmetries, especially broken ones – which went back to the early 1960s, at least to my paper with Goldstone and Salam raising the issue of massless Goldstone bosons, after which Higgs et al. showed us how to avoid them. I guess mine was a key paper in that department, but I had been working on broken symmetries in the context of strong interactions for a decade. Then there is the development of effective theories, which is not so much a theory but a point of view.” What he prizes above all else, however, is not embodied in any single paper or certainly not in any single model: it is about changing the point of view of physicists.
“I prized the 1967 paper programmatically because it exemplified the need to look for a renormalisable theory based on symmetries that are spontaneously broken, and by god it turned out to be the right model!” From the start, he knew his model of leptons was the kind of theory that looked right, but it doesn’t just take a certain mind to be able to see such truths, he explains. It takes a lot of minds over a long period. Weinberg illustrates the process with the example of chicken sexing. It is important in the poultry business to be able to determine the sex of newborn chicks, he says, and there was a school that taught the science of chicken sexing by giving people a newborn chick and asking them to say whether it was male of female: if they guessed wrong, they would receive some sort of punishment, while if they guessed right they got some kind of reward. After repeating the process hundreds of times, people began to guess correctly. “We’ve learned that, just as feeling the underside of a newborn chicken you might learn what distinguishes a male from a female, science is not the experience of just one scientist but of the whole community extending back to antiquity, which has gradually beaten into us which theory is beautiful and which is likely to be right.”
Asked what single mystery, if he could choose, he would like to see solved in his lifetime, Weinberg doesn’t have to think for long: he wants to be able to explain the observed pattern of quark and lepton masses. In the summer of 1972, when the SM was coming together, he set himself the task of figuring it out but couldn’t come up with anything. “It was the worst summer of my life! I mean, obviously there are broader questions such as: why is there something rather than nothing? But if you ask for a very specific question, that’s the one. And I’m no closer now to answering it than I was in the summer of 1972,” he says, still audibly irritated. He also doesn’t want to die without knowing what dark matter is. There are all kinds of frustrations, he says. “But how could it be otherwise? I am enjoying what I am doing and I have had a good run, and I have a few more years. We’re having a total eclipse here in April 2024 and I look forward to seeing that.”
Forty years after the publication of his famous book The First Three Minutes, which has been translated into 22 languages and for which he still receives royalty cheques, he intends to go on writing. He has a contract with Cambridge University Press to publish a new book called Lectures on Astrophysics based on his current teaching activities and is bringing out a third collection of popular essays with Harvard University Press, with a fourth planned.
The last three minutes
Steven Weinberg’s career – from his undergraduate days at Cornell, graduate studies in Princeton, and subsequent positions at Columbia, Berkeley, Harvard, MIT and Texas – is one that any physicist would aspire to. His name will always be associated with our fundamental understanding of the universe, and you get the feeling that none of it ever felt much like “work” in the usual sense. “The physics career, quite apart from what you do in physics day to day, has given me the opportunity to know a lot of interesting people and to visit different countries not as a tourist but as a co-worker,” he says. “It’s such a delight to talk to fellow physicists and to work-up a paper based on a common understanding, and to at the same time transcend national boundaries. I like that so much.” Not that he has collaborated that much: as with “A Model of Leptons”, most of his 350 or so papers have been “one-man jobs”.
Yet Weinberg is not your stereotypical lost-in-his-work genius who locks himself away for long periods to work on a problem. His best ideas don’t come to him while he’s working at all. He recalls one day he came out of the shower and exclaimed to his wife that he had figured out why the cosmological constant is so small (at a time before he had started thinking about anthropic explanations). “Then the next day I came out and I said [deep voice] ‘no’! So ideas come to you all the time and most of them are no good, and every once in a while you find one that is good and you have fun working at your desk. Getting good ideas isn’t something you get by trying hard, but by thinking a lot about what problems bother you. But that doesn’t always work either – just think of my ruined summer in 1972!”
He never works in his office. His research work has always been done at home, where he and his wife have separate offices down the hall from one another and interrupt one another frequently. “I’m not hard to interrupt. I have a television set on my desk which I keep on while I work, typically watching an old movie, because I find work in theoretical physics so far removed from normal affairs.” Doesn’t it distract him? “But I need the distraction to keep at my desk because the actual work is so, well…it’s so chillingly non-human. I need to feel that I am still part of the human race while I’m doing it.”