We have conquered the easiest challenges in fundamental physics, says Nima Arkani-Hamed. The case for building the next major collider is now more compelling than ever.

How do you view the status of particle physics?

There has never been a better time to be a physicist. The questions on the table today are not about this-or-that detail, but profound ones about the very structure of the laws of nature. The ancients could (and did) wonder about the nature of space and time and the vastness of the cosmos, but the job of a professional scientist isn’t to gape in awe at grand, vague questions – it is to work on the next question. Having ploughed through all the “easier” questions for four centuries, these very deep questions finally confront us: what are space and time? What is the origin and fate of our enormous universe? We are extremely fortunate to live in the era when human beings first get to meaningfully attack these questions. I just wish I could adjust when I was born so that I could be starting as a grad student today! But not everybody shares my enthusiasm. There is cognitive dissonance. Some people are walking around with their heads hanging low, complaining about being disappointed or even depressed that we’ve “only discovered the Higgs and nothing else”.

So who is right?

It boils down to what you think particle physics is really about, and what motivates you to get into this business. One view is that particle physics is the study of the building blocks of matter, in which “new physics” means “new particles”. This is certainly the picture of the 1960s leading to the development of the Standard Model, but it’s not what drew me to the subject. To me, “particle physics” is the study of the fundamental laws of nature, governed by the still mysterious union of space–time and quantum mechanics. Indeed, from the deepest theoretical perspective, the very definition of what a particle is invokes both quantum mechanics and relativity in a crucial way. So if the biggest excitement for you is a cross-section plot with a huge bump in it, possibly with a ticket to Stockholm attached, then, after the discovery of the Higgs, it makes perfect sense to take your ball and go home, since we can make no guarantees of this sort whatsoever. We’re in this business for the long haul of decades and centuries, and if you don’t have the stomach for it, you’d better do something else with your life!

Isn’t the Standard Model a perfect example of the scientific method?

Sure, but part of the reason for the rapid progress in the 1960s is that the intellectual structure of relativity and quantum mechanics was already sitting there to be explored and filled in. But these more revolutionary discoveries took much longer, involving a wide range of theoretical and experimental results far beyond “bump plots”. So “new physics” is much more deeply about “new phenomena” and “new principles”. The discovery of the Higgs particle – especially with nothing else accompanying it so far – is unlike anything we have seen in any state of nature, and is profoundly “new physics” in this sense. The same is true of the other dramatic experimental discovery in the past few decades: that of the accelerating universe. Both discoveries are easily accommodated in our equations, but theoretical attempts to compute the vacuum energy and the scale of the Higgs mass pose gigantic, and perhaps interrelated, theoretical challenges. While we continue to scratch our heads as theorists, the most important path forward for experimentalists is completely clear: measure the hell out of these crazy phenomena! From many points of view, the Higgs is the most important actor in this story amenable to experimental study, so I just can’t stand all the talk of being disappointed by seeing nothing but the Higgs; it’s completely backwards. I find that the physicists who worry about not being able to convince politicians are (more or less secretly) not able to convince themselves that it is worth building the next collider. Fortunately, we do have a critical mass of fantastic young experimentalists who believe it is worth studying the Higgs to death, while also exploring whatever might be at the energy frontier, with no preconceptions about what they might find.

What makes the Higgs boson such a rich target for a future collider?

It is the first example we’ve seen of the simplest possible type of elementary particle. It has no spin, no charge, only mass, and this extreme simplicity makes it theoretically perplexing. There is a striking difference between massive and massless particles that have spin. For instance, a photon is a massless particle of spin one; because it moves at the speed of light, we can’t “catch up” with it, and so we only see it have two “polarisations”, or ways it can spin. By contrast the Z boson, which also has spin one, is massive; since you can catch up with it, you can see it spinning in any of three directions. This “two not equal to three” business is quite profound. As we collide particles at ever increasing energies, we might think that their masses are irrelevant tiny perturbations to their energies, but this is wrong, since something must account for the extra degrees of freedom.

The whole story of the Higgs is about accounting for this “two not equal to three” issue, to explain the extra spin states needed for massive W and Z particles mediating the weak interactions. And this also gives us a good understanding of why the masses of the elementary particles should be pegged to that of the Higgs. But the huge irony is that we don’t have any good understanding for what can explain the mass of the Higgs itself. That’s because there is no difference in the number of degrees of freedom between massive and massless spin-zero particles, and related to this, simple estimates for the Higgs mass from its interactions with virtual particles in the vacuum are wildly wrong. There are also good theoretical arguments, amply confirmed in analogous condensed-matter systems and elsewhere in particle physics, for why we shouldn’t have expected to see such a beast lonely, unaccompanied by other particles. And yet here we are. Nature clearly has other ideas for what the Higgs is about than theorists do.

Is supersymmetry still a motivation for a new collider?

Nobody who is making the case for future colliders is invoking, as a driving motivation, supersymmetry, extra dimensions or any of the other ideas that have been developed over the past 40 years for physics beyond the Standard Model. Certainly many of the versions of these ideas, which were popular in the 1980s and 1990s, are either dead or on life support given the LHC data, but others proposed in the early 2000s are alive and well. The fact that the LHC has ruled out some of the most popular pictures is a fantastic gift to us as theorists. It shows that understanding the origin of the Higgs mass must involve an even larger paradigm change than many had previously imagined. Ironically, had the LHC discovered supersymmetric particles, the case for the next circular collider would be somewhat weaker than it is now, because that would (indirectly) support a picture of a desert between the electroweak and Planck scales. In this picture of the world, most people wanted a linear electron–positron collider to measure the superpartner couplings in detail. It’s a picture people very much loved in the 1990s, and a picture that appears to be wrong. Fine. But when theorists are more confused, it’s the time for more, not less experiments.

What definitive answers will a future high-energy collider give us?

First and foremost, we go to high energies because it’s the frontier, and we look around for new things. While there is absolutely no guarantee we will produce new particles, we will definitely stress test our existing laws in the most extreme environments we have ever probed. Measuring the properties of the Higgs, however, is guaranteed to answer some burning questions. All the drama revolving around the existence of the Higgs would go away if we saw that it had substructure of any sort. But from the LHC, we have only a fuzzy picture of how point-like the Higgs is. A Higgs factory will decisively answer this question via precision measurements of the coupling of the Higgs to a slew of other particles in a very clean experimental environment. After that the ultimate question is whether or not the Higgs looks point-like even when interacting with itself. The simplest possible interaction between elementary particles is when three particles meet at a space–time point. But we have actually never seen any single elementary particle enjoy this simplest possible interaction. For good reasons going back to the basics of relativity and quantum mechanics, there is always some quantum number that must change in this interaction – either spin or charge quantum numbers change. The Higgs is the only known elementary particle allowed to have this most basic process as its dominant self-interaction. A 100 TeV collider producing billions of Higgs particles will not only detect the self-interaction, but will be able to measure it to an accuracy of a few per cent. Just thinking about the first-ever probe of this simplest possible interaction in nature gives me goosebumps.

What are the prospects for future dark-matter searches?

Beyond the measurements of the Higgs properties, there are all sorts of exciting signals of new particles that can be looked for at both Higgs factories and 100 TeV colliders. One I find especially important is WIMP dark matter. There is a funny perception, somewhat paralleling the absence of supersymmetry at the LHC, that the simple paradigm of WIMP dark matter has been ruled out by direct-detection experiments. Nope! In fact, the very simplest models of WIMP dark matter are perfectly alive and well. Once the electroweak quantum numbers of the dark-matter particles are specified, you can unambiguously compute what mass an electroweak charged dark-matter particle should have so that its thermal relic abundance is correct. You get a number between 1–3 TeV, far too heavy to be produced in any sizeable numbers at the LHC. Furthermore, they happen to have miniscule interaction cross sections for direct detection. So these very simplest theories of WIMP dark matter are inaccessible to the LHC and direct-detection experiments. But a 100 TeV collider has just enough juice to either see these particles, or rule out this simplest WIMP picture.

What is the cultural value of a 100 km supercollider?

Both the depth and visceral joy of experiments in particle physics is revealed in how simple it is to explain: we smash things together with the largest machines that have ever been built, to probe the fundamental laws of nature at the tiniest distances we’ve ever seen. But it goes beyond that to something more important about our self-conception as people capable of doing great things. The world has all kinds of long-term problems, some of which might seem impossible to solve. So it’s important to have a group of people who, over centuries, give a concrete template for how to go about grappling with and ultimately conquering seemingly impossible problems, driven by a calling far larger than themselves. Furthermore, suppose it’s 200 years from now, and there are no big colliders on the planet. How can humans be sure that the Higgs or top particles exist? Because it says so in dusty old books? There is an argument to be made that as we advance we should be able to do the things we did in the past. After all, the last time that fundamental knowledge was shoved in old dusty books was in the dark ages, and that didn’t go very well for the West.

What about justifying the cost of the next collider?

There are a number of projects and costs we could be talking about, but let’s call it $5–25 billion. Sounds like a lot, right? But the global economy is growing, not shrinking, and the cost of accelerators as a fraction of GDP has barely changed over the past 40 years – even a 100 TeV collider is in this same ballpark. Meanwhile the scientific issues at stake are more profound than they have been for many decades, so we certainly have an honest science case to make that we need to keep going.

People sometimes say that if we don’t spend billions of dollars on colliders, then we can do all sorts of other experiments instead. I am a huge fan of small-scale experiments, but this argument is silly because science funding is infamously not a zero-sum game. So, it’s not a question of, “do we want to spend tens of billions on collider physics or something else instead”, it is rather “do we want to spend tens of billions on fundamental physics experiments at all”.

Another argument is that we should wait until some breakthrough in accelerator technology, rather than just building bigger machines. This is naïve. Of course miracles can always happen, but we can’t plan doing science around miracles. Similar arguments were made around the time of the cancellation of the Superconducting Super Collider (SSC) 30 years ago, with prominent condensed-matter physicists saying that the SSC should wait for the development of high-temperature superconductors that would dramatically lower the cost. Of course those dreamed-of practical superconductors never materialised, while particle physics continued from strength to strength with the best technology available.

What do you make of claims that colliders are no longer productive?

It would be only to the good to have a no-holds barred, public discussion about the pros and cons of future colliders, led by people with a deep understanding of the relevant technical and scientific issues. It’s funny that non-experts don’t even make the best arguments for not building colliders; I could do a much better job than they do! I can point you to an awesomely fierce debate about future colliders that already took place in China two years ago: (Int. J. Mod. Phys. A 31 1630053 and 1630054). C N Yang, who is one of the greatest physicists of the 20th century and enormously influential in China, came out with a strong attack on colliders, not only in China but more broadly. I was delighted. Having a serious attack meant there could be a serious response, masterfully provided by David Gross. It was the King Kong vs Godzilla of fundamental physics, played out on the pages of major newspapers in China, fantastic!

What are you working on now?

About a decade ago, after a few years of thinking about the cosmology of “eternal inflation” in connection with solutions to the cosmological constant and hierarchy problems, I concluded that these mysteries can’t be understood without reconceptualising what space–time and quantum mechanics are really about. I decided to warm up by trying to understand the dynamics of particle scattering, like collisions at the LHC, from a new starting point, seeing space-time and quantum mechanics as being derived from more primitive notions. This has turned out to be a fascinating adventure, and we are seeing more and more examples of rather magical new mathematical structures, which surprisingly appear to underlie the physics of particle scattering in a wide variety of theories, some close to the real world. I am also turning my attention back to the goal that motivated the warm-up, trying to understand cosmology, as well as possible theories for the origin of the Higgs mass and cosmological constant, from this new point of view. In all my endeavours I continue to be driven, first and foremost, by the desire to connect deep theoretical ideas to experiments and the real world.