Tag Archives: particle physics

Why Journals Are Sticky

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An older professor in my field has a quirk: every time he organizes a conference, he publishes all the talks in a conference proceeding.

In some fields, this would be quite normal. In computer science, where progress flows like a torrent, new developments are announced at conferences long before they have the time to be written up carefully as a published paper. Conference proceedings are summaries of what was presented at the conference, published so that anyone can catch up on the new developments.

In my field, this is rarer. A few results at each conference will be genuinely new, never-before-published discoveries. Most, though, are talks on older results, results already available online. Writing them up again in summarized form as a conference proceeding seems like a massive waste of time.

The cynical explanation is that this professor is doing this for the citations. Each conference proceeding one of his students publishes is another publication on their CV, another work that they can demand people cite whenever someone uses their ideas or software, something that puts them above others’ students without actually doing any extra scientific work.

I don’t think that’s how this professor thinks about it, though. He certainly cares about his students’ careers, and will fight for them to get cited as much as possible. But he asks everyone at the conference to publish a proceeding, not just his students. I think he’d argue that proceedings are helpful, that they can summarize papers in new ways and make them more accessible. And if they give everyone involved a bit more glory, if they let them add new entries to their CV and get fancy books on their shelves, so much the better for everyone.

My guess is, he really believes something like that. And I’m fairly sure he’s wrong.

The occasional conference proceeding helps, but only because it makes us more flexible. Sometimes, it’s important to let others know about a new result that hasn’t been published yet, and we let conference proceedings go into less detail than a full published paper, so this can speed things up. Sometimes, an old result can benefit from a new, clearer explanation, which normally couldn’t be published without it being a new result (or lecture notes). It’s good to have the option of a conference proceeding.

But there is absolutely no reason to have one for every single talk at a conference.

Between the cynical reason and the explicit reason, there’s the banal one. This guy insists on conference proceedings because they were more useful in the past, because they’re useful in other fields, and because he’s been doing them himself for years. He insists on them because to him, they’re a part of what it means to be a responsible scientist.

And people go along with it. Because they don’t want to get into a fight with this guy, certainly. But also because it’s a bit of extra work that could give a bit of a career boost, so what’s the harm?

I think something similar to this is why academic journals still work the way they do.

In the past, journals were the way physicists heard about new discoveries. They would get each edition in the mail, and read up on new developments. The journal needed to pay professional copyeditors and printers, so they needed money, and they got that money from investors by being part of for-profit companies that sold shares.

Now, though, physicists in my field don’t read journals. We publish our new discoveries online on a non-profit website, formatting them ourselves with software that uses the same programming skills we use in the rest of our professional lives. We then discuss the papers in email threads and journal club meetings. When a paper is wrong, or missing something important, we tell the author, and they fix it.

Oh, and then after that we submit the papers to the same for-profit journals and the same review process that we used to use before we did all this, listing the journals that finally accept the papers on our CVs.

Why do we still do that?

Again, you can be cynical. You can accuse the journals of mafia-ish behavior, you can tie things back to the desperate need to publish in high-ranked journals to get hired. But I think the real answer is a bit more innocent, and human, than that.

Imagine that you’re a senior person in the field. You may remember the time before we had all of these nice web-based publishing options, when journals were the best way to hear about new developments. More importantly than that, though, you’ve worked with these journals. You’ve certainly reviewed papers for them, everyone in the field does that, but you may have also served as an editor, tracking down reviewers and handling communication between the authors and the journal. You’ve seen plenty of cases where the journal mattered, where tracking down the right reviewers caught a mistake or shot down a crackpot’s ambitions, where the editing cleaned something up or made a work more appear more professional. You think of the journals as having high standards, standards you have helped to uphold: when choosing between candidates for a job, you notice that one has several papers in Physical Review Letters, and remember papers you’ve rejected for not meeting what you intuited were that journal’s standards. To you, journals are a key part of being a responsible scientist.

Does any of that make journals worth it, though?

Well, that depends on costs. It depends on alternatives. It depends not merely on what the journals catch, but on how often they do it, and how much would have been caught on its own. It depends on whether the high standards you want to apply to job applicants are already being applied by the people who write their recommendation letters and establish their reputations.

And you’re not in a position to evaluate any of that, of course. Few people are, who don’t spend a ton of time thinking about scientific publishing.

And thus, for the non-senior people, there’s not much reason to push back. One hears a few lofty speeches about Elsevier’s profits, and dreams about the end of the big for-profit journals. But most people aren’t cut out to be crusaders or reformers, especially when they signed up to be scientists. Most people are content not to annoy the most respected people in their field by telling them that something they’ve spent an enormous amount of time on is now pointless. Most people want to be seen as helpful by these people, to not slack off on work like reviewing that they argue needs doing.

And most of us have no reason to think we know that much better, anyway. Again, we’re scientists, not scientific publishing experts.

I don’t think it’s good practice to accuse people of cognitive biases. Everyone thinks they have good reasons to believe what they believe, and the only way to convince them is to address those reasons.

But the way we use journals in physics these days is genuinely baffling. It’s hard to explain, it’s the kind of thing people have been looking quizzically at for years. And this kind of explanation is the only one I’ve found that matches what I’ve seen. Between the cynical explanation and the literal arguments, there’s the basic human desire to do what seems like the responsible thing. That tends to explain a lot.

The Machine Learning for Physics Recipe

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Last week, I went to a conference on machine learning for physics. Machine learning covers a huge variety of methods and ideas, several of which were on full display. But again and again, I noticed a pattern. The people who seemed to be making the best use of machine learning, the ones who were the most confident in their conclusions and getting the most impressive results, the ones who felt like they had a whole assembly line instead of just a prototype, all of them were doing essentially the same thing.

This post is about that thing. If you want to do machine learning in physics, these are the situations where you’re most likely to see a benefit. You can do other things, and they may work too. But this recipe seems to work over and over again.

First, you need simulations, and you need an experiment.

Your experiment gives you data, and that data isn’t easy to interpret. Maybe you’ve embedded a bunch of cameras in the antarctic ice, and your data tells you when they trigger and how bright the light is. Maybe you’ve surrounded a particle collision with layers silicon, and your data tells you how much electric charge the different layers absorb. Maybe you’ve got an array of telescopes focused on a black hole far far away, and your data are pixels gathered from each telescope.

You want to infer, from your data, what happened physically. Your cameras in the ice saw signs of a neutrino, you want to know how much energy it had and where it was coming from. Your silicon is absorbing particles, what kind are they and what processes did they come from? The black hole might have the rings predicted by general relativity, but it might have weirder rings from a variant theory.

In each case, you can’t just calculate the answer you need. The neutrino streams past, interacting with the ice and camera positions in unpredictable ways. People can write down clean approximations for particles in the highest-energy part of a collision, but once they start cooling down the process becomes so messy that no straightforward formula describes them. Your array of telescopes fuzz and pixellate and have to be assembled together in a complicated way, so that there is no one guaranteed answer you can find to establish what they saw.

In each case, though, you can use simulations. If you specify in advance the energy and path of the neutrino, you can use a computer to predict how much light your cameras should see. If you know what particles you started with, you can run sophisticated particle physics code to see what “showers” of particles you eventually find. If you have the original black hole image, you can fuzz and pixellate and take it apart to match what your array of telescopes will do.

The problem is, for the experiments, you can’t anticipate, and you don’t know in advance. And simulations, while cheaper than experiments, aren’t cheap. You can’t run a simulation for every possible input and then check them against the experiments. You need to fill in the gaps, run some simulations and then use some theory, some statistical method or human-tweaked guess, to figure out how to interpret your experiments.

Or, you can use Machine Learning. You train a machine learning model, one well-suited the task (anything from the old standby of boosted decision trees to an old fad of normalizing flows to the latest hotness of graph neural networks). You run a bunch of simulations, as many as you can reasonably afford, and you use that data for training, making a program that matches the input data you want to find with its simulated results. This program will be less reliable than your simulations, but it will run much faster. If it’s reliable enough, you can use it instead of the old human-made guesses and tweaks. You now have an efficient, reliable way to go from your raw experiment data to the physical questions you actually care about.

Crucially, each of the elements in this recipe is essential.

You need a simulation. If you just have an experiment with no simulation, then you don’t have a way to interpret the results, and training a machine to reproduce the experiment won’t tell you anything new.

You need an experiment. If you just have simulations, training a machine to reproduce them also doesn’t tell you anything new. You need some reason to want to predict the results of the simulations, beyond just seeing what happens in between which the machine can’t tell you.

And you need to not have anything better than the simulation. If you have a theory where you can write out formulas for what happens then you don’t need machine learning, you can interpret the experiments more easily without it. This applies if you’ve carefully designed your experiment to measure something easy to interpret, like the ratio of rates of two processes that should be exactly the same.

These aren’t the only things you need. You also need to do the whole thing carefully enough that you understand well your uncertainties, not just what the machine predicts but how often it gets it wrong, and whether it’s likely to do something strange when you use it on the actual experiment. But if you can do that, you have a reliable recipe, one many people have followed successfully before. You have a good chance of making things work.

This isn’t the only way physicists can use machine learning. There are people looking into something more akin to what’s called unsupervised learning, where you look for strange events in your data as clues for what to investigate further. And there are people like me, trying to use machine learning on the mathematical side, to guess new formulas and new heuristics. There is likely promise in many of these approaches. But for now, they aren’t a recipe.

HAMLET-Physics 2024

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Back in January, I announced I was leaving France and leaving academia. Since then, it hasn’t made much sense for me to go to conferences, even the big conference of my sub-field or the conference I organized.

I did go to a conference this week, though. I had two excuses:

  1. The conference was here in Copenhagen, so no travel required.
  2. The conference was about machine learning.

HAMLET-Physics, or How to Apply Machine Learning to Experimental and Theoretical Physics, had the additional advantage of having an amusing acronym. Thanks to generous support by Carlsberg and the Danish Data Science Academy, they could back up their choice by taking everyone on a tour of Kronborg (better known in the English-speaking world as Elsinore).

This conference’s purpose was to bring together physicists who use machine learning, machine learning-ists who might have something useful to say to those physicists, and other physicists who don’t use machine learning yet but have a sneaking suspicion they might have to at some point. As a result, the conference was super-interdisciplinary, with talks by people addressing very different problems with very different methods.

Interdisciplinary conferences are tricky. It’s easy for the different groups of people to just talk past each other: everyone shows up, gives the same talk they always do, socializes with the same friends they always meet, then leaves.

There were a few talks that hit that mold, and were so technical only a few people understood. But most were better. The majority of the speakers did really well at presenting their work in a way that would be understandable and even exciting to people outside their field, while still having enough detail that we all learned something. I was particularly impressed by Thea Aarestad’s keynote talk on Tuesday, a really engaging view of how machine learning can be used under the extremely tight time constraints LHC experiments need to decide whether to record incoming data.

For the social aspect, the organizers had a cute/gimmicky/machine-learning-themed solution. Based on short descriptions and our public research profiles, they clustered attendees, plotting the connections between them. They then used ChatGPT to write conversation prompts between any two people on the basis of their shared interests. In practice, this turned out to be amusing but totally unnecessary. We were drawn to speak to each other not by conversation prompts, but by a drive to learn from each other. “Why do you do it that way?” was a powerful conversation-starter, as was “what’s the best way to do this?” Despite the different fields, the shared methodologies gave us strong reasons to talk, and meant that people were very rarely motivated to pick one of ChatGPT’s “suggestions”.

Overall, I got a better feeling for how machine learning is useful in physics (and am planning a post on that in future). I also got some fresh ideas for what to do myself, and a bit of a picture of what the future holds in store.

At Quanta This Week, With a Piece on Vacuum Decay

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I have a short piece at Quanta Magazine this week, about a physics-y end of the world as we know it called vacuum decay.

For science-minded folks who want to learn a bit more: I have a sentence in the article mentioning other uncertainties. In case you’re curious what those uncertainties are:

Gamma (\gamma) here is the decay rate, its inverse gives the time it takes for a cubic gigaparsec of space to experience vacuum decay. The three uncertainties are from experiments, the uncertainties of our current knowledge of the Higgs mass, top quark mass, and the strength of the strong force.

Occasionally, you see futurology-types mention “uncertainties in the exponent” to argue that some prediction (say, how long it will take till we have human-level AI) is so uncertain that estimates barely even make sense: it might be 10 years, or 1000 years. I find it fun that for vacuum decay, because of that \log_{10}, there is actually uncertainty in the exponent! Vacuum decay might happen in as few as 10^{411} years or as many as 10^{1333} years, and that’s the result of an actual, reasonable calculation!

For physicist readers, I should mention that I got a lot out of reading some slides from a 2016 talk by Matthew Schwartz. Not many details of the calculation made it into the piece, but the slides were helpful in dispelling a few misconceptions that could have gotten into the piece. There’s an instinct to think about the situation in terms of the energy, to think about how difficult it is for quantum uncertainty to get you over the energy barrier to the next vacuum. There are methods that sort of look like that, if you squint, but that’s not really how you do the calculation, and there end up being a lot of interesting subtleties in the actual story. There were also a few numbers that it was tempting to put on the plots in the article, but turn out to be gauge dependent!

Another thing I learned from those slides how far you can actually take the uncertainties mentioned above. The higher-energy Higgs vacuum is pretty dang high-energy, to the point where quantum gravity effects could potentially matter. And at that point, all bets are off. The calculation, with all those nice uncertainties, is a calculation within the framework of the Standard Model. All of the things we don’t yet know about high-energy physics, especially quantum gravity, could freely mess with this. The universe as we know it could still be long-lived, but it could be a lot shorter-lived as well. That in turns makes this calculation a lot more of a practice-ground to hone techniques, rather than an actual estimate you can rely on.

Rube Goldberg Reality

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Quantum mechanics is famously unintuitive, but the most intuitive way to think about it is probably the path integral. In the path integral formulation, to find the chance a particle goes from point A to point B, you look at every path you can draw from one place to another. For each path you calculate a complex number, a “weight” for that path. Most of these weights cancel out, leaving the path the particle would travel under classical physics with the biggest contribution. They don’t perfectly cancel out, though, so the other paths still matter. In the end, the way the particle behaves depends on all of these possible paths.

If you’ve heard this story, it might make you feel like you have some intuition for how quantum physics works. With each path getting less likely as it strays from the classical, you might have a picture of a nice orderly set of options, with physicists able to pick out the chance of any given thing happening based on the path.

In a world with just one particle swimming along, this might not be too hard. But our world doesn’t run on the quantum mechanics of individual particles. It runs on quantum field theory. And there, things stop being so intuitive.

First, the paths aren’t “paths”. For particles, you can imagine something in one place, traveling along. But particles are just ripples in quantum fields, which can grow, shrink, or change. For quantum fields instead of quantum particles, the path integral isn’t a sum over paths of a single particle, but a sum over paths traveled by fields. The fields start out in some configuration (which may look like a particle at point A) and then end up in a different configuration (which may look like a particle at point B). You have to add up weights, not for every path a single particle could travel, but every different set of ways the fields could have been in between configuration A and configuration B.

More importantly, though, there is more than one field! Maybe you’ve heard about electric and magnetic fields shifting back and forth in a wave of light, one generating the other. Other fields interact like this, including the fields behind things you might think of as particles like electrons. For any two fields that can affect each other, a disturbance in one can lead to a disturbance in the other. An electromagnetic field can disturb the electron field, which can disturb the Higgs field, and so on.

The path integral formulation tells you that all of these paths matter. Not just the path of one particle or one field chugging along by itself, but the path where the electromagnetic field kicks off a Higgs field disturbance down the line, only to become a disturbance in the electromagnetic field again. Reality is all of these paths at once, a Rube Goldberg machine of a universe.

In such a universe, intuition is a fool’s errand. Mathematics fares a bit better, but is still difficult. While physicists sometimes have shortcuts, most of the time these calculations have to be done piece by piece, breaking the paths down into simpler stories that approximate the true answer.

In the path integral formulation of quantum physics, everything happens at once. And “everything” may be quite a bit larger than you expect.

Amplitudes 2024, Continued

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I’ve now had time to look over the rest of the slides from the Amplitudes 2024 conference, so I can say something about Thursday and Friday’s talks.

Thursday was gravity-focused. Zvi Bern’s review talk was actually a review, a tour of the state of the art in using amplitudes techniques to make predictions for gravitational wave physics. Bern emphasized that future experiments will require much more precision: two more orders of magnitude, which in our lingo amounts to two more “loops”. The current state of the art is three loops, but they’ve been hacking away at four, doing things piece by piece in a way that cleverly also yields publications (for example, they can do just the integrals needed for supergravity, which are simpler). Four loops here is the first time that the Feynman diagrams involve Calabi-Yau manifolds, so they will likely need techniques from some of the folks I talked about last week. Once they have four loops, they’ll want to go to five, since that is the level of precision you need to learn something about the material in neutron stars. The talk covered a variety of other developments, some of which were talked about later on Thursday and some of which were only mentioned here.

Of that day’s other speakers, Stefano De Angelis, Lucile Cangemi, Mikhail Ivanov, and Alessandra Buonanno also focused on gravitational waves. De Angelis talked about the subtleties that show up when you try to calculate gravitational waveforms directly with amplitudes methods, showcasing various improvements to the pipeline there. Cangemi talked about a recurring question with its own list of subtleties, namely how the Kerr metric for spinning black holes emerges from the math of amplitudes of spinning particles. Gravitational waves were the focus of only the second half of Ivanov’s talk, where he talked about how amplitudes methods can clear up some of the subtler effects people try to take into account. The first half was about another gravitational application, that of using amplitudes methods to compute the correlations of galaxy structures in the sky, a field where it looks like a lot of progress can be made. Finally, Buonanno gave the kind of talk she’s given a few times at these conferences, a talk that puts these methods in context, explaining how amplitudes results are packaged with other types of calculations into the Effective-One-Body framework which then is more directly used at LIGO. This year’s talk went into more detail about what the predictions are actually used for, which I appreciated. I hadn’t realized that there have been a handful of black hole collisions discovered by other groups from LIGO’s data, a win for open science! Her slides had a nice diagram explaining what data from the gravitational wave is used to infer what black hole properties, quite a bit more organized than the statistical template-matching I was imagining. She explained the logic behind Bern’s statement that gravitational wave telescopes will need two more orders of magnitude, pointing out that that kind of precision is necessary to be sure that something that might appear to be a deviation from Einstein’s theory of gravity is not actually a subtle effect of known physics. Her method typically is adjusted to fit numerical simulations, but she shows that even without that adjustment they now fit the numerics quite well, thanks in part to contributions from amplitudes calculations.

Of the other talks that day, David Kosower’s was the only one that didn’t explicitly involve gravity. Instead, his talk focused on a more general question, namely how to find a well-defined basis of integrals for Feynman diagrams, which turns out to involve some rather subtle mathematics and geometry. This is a topic that my former boss Jake Bourjaily worked on in a different context for some time, and I’m curious whether there is any connection between the two approaches. Oliver Schlotterer gave the day’s second review talk, once again of the “actually a review” kind, covering a variety of recent developments in string theory amplitudes. These include some new pictures of how string theory amplitudes that correspond to Yang-Mills theories “square” to amplitudes involving gravity at higher loops and progress towards going past two loops, the current state of the art for most string amplitude calculations. (For the experts: this does not involve taking the final integral over the moduli space, which is still a big unsolved problem.) He also talked about progress by Sebastian Mizera and collaborators in understanding how the integrals that show up in string theory make sense in the complex plane. This is a problem that people had mostly managed to avoid dealing with because of certain simplifications in the calculations people typically did (no moduli space integration, expansion in the string length), but taking things seriously means confronting it, and Mizera and collaborators found a novel solution to the problem that has already passed a lot of checks. Finally, Tobias Hansen’s talk also related to string theory, specifically in anti-de-Sitter space, where the duality between string theory and N=4 super Yang-Mills lets him and his collaborators do Yang-Mills calculations and see markedly stringy-looking behavior.

Friday began with Kevin Costello, whose not-really-a-review talk dealt with his work with Natalie Paquette showing that one can use an exactly-solvable system to learn something about QCD. This only works for certain rather specific combinations of particles: for example, in order to have three colors of quarks, they need to do the calculation for nine flavors. Still, they managed to do a calculation with this method that had not previously been done with more traditional means, and to me it’s impressive that anything like this works for a theory without supersymmetry. Mina Himwich and Diksha Jain both had talks related to a topic of current interest, “celestial” conformal field theory, a picture that tries to apply ideas from holography in which a theory on the boundary of a space fully describes the interior, to the “boundary” of flat space, infinitely far away. Himwich talked about a symmetry observed in that research program, and how that symmetry can be seen using more normal methods, which also lead to some suggestions of how the idea might be generalized. Jain likewise covered a different approach, one in which one sets artificial boundaries in flat space and sees what happens when those boundaries move.

Yifei He described progress in the modern S-matrix bootstrap approach. Previously, this approach had gotten quite general constraints on amplitudes. She tries to do something more specific, and predict the S-matrix for scattering of pions in the real world. By imposing compatibility with knowledge from low energies and high energies, she was able to find a much more restricted space of consistent S-matrices, and these turn out to actually match pretty well to experimental results. Mathieu Giroux addresses an important question for a variety of parts of amplitudes research, how to predict the singularities of Feynman diagrams. He explored a recursive approach to solving Landau’s equations for these singularities, one which seems impressively powerful, in one case being able to find a solution that in text form is approximately the length of Harry Potter. Finally, Juan Maldacena closed the conference by talking about some progress he’s made towards an old idea, that of defining M theory in terms of a theory involving actual matrices. This is a very challenging thing to do, but he is at least able to tackle the simplest possible case, involving correlations between three observations. This had a known answer, so his work serves mostly as a confirmation that the original idea makes sense at at least this level.

(Not At) Amplitudes 2024 at the IAS

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For over a decade, I studied scattering amplitudes, the formulas particle physicists use to find the probability that particles collide, or scatter, in different ways. I went to Amplitudes, the field’s big yearly conference, every year from 2015 to 2023.

This year is different. I’m on the way out of the field, looking for my next steps. Meanwhile, Amplitudes 2024 is going full speed ahead at the Institute for Advanced Study in Princeton.

With poster art that is, as the kids probably don’t say anymore, “on fleek”

The talks aren’t live-streamed this year, but they are posting slides, and they will be posting recordings. Since a few of my readers are interested in new amplitudes developments, I’ve been paging through the posted slides looking for interesting highlights. So far, I’ve only seen slides from the first few days: I will probably write about the later talks in a future post.

Each day of Amplitudes this year has two 45-minute “review talks”, one first thing in the morning and the other first thing after lunch. I put “review talks” in quotes because they vary a lot, between talks that try to introduce a topic for the rest of the conference to talks that mostly focus on the speaker’s own research. Lorenzo Tancredi’s talk was of the former type, an introduction to the many steps that go into making predictions for the LHC, with a focus on those topics where amplitudeologists have made progress. The talk opens with the type of motivation I’d been writing in grant and job applications over the last few years (we don’t know most of the properties of the Higgs yet! To measure them, we’ll need to calculate amplitudes with massive particles to high precision!), before moving into a review of the challenges and approaches in different steps of these calculations. While Tancredi apologizes in advance that the talk may be biased, I found it surprisingly complete: if you want to get an idea of the current state of the “LHC amplitudes pipeline”, his slides are a good place to start.

Tancredi’s talk serves as introduction for a variety of LHC-focused talks, some later that day and some later in the week. Federica Devoto discussed high-energy quarks while Chiara Signorile-Signorile and George Sterman showed advances in handling of low-energy particles. Xiaofeng Xu has a program that helps predict symbol letters, the building-blocks of scattering amplitudes that can be used to reconstruct or build up the whole thing, while Samuel Abreu talked about a tricky state-of-the-art case where Xu’s program misses part of the answer.

Later Monday morning veered away from the LHC to focus on more toy-model theories. Renata Kallosh’s talk in particular caught my attention. This blog is named after a long-standing question in amplitudes: will the four-graviton amplitude in N=8 supergravity diverge at seven loops in four dimensions? This seemingly arcane question is deep down a question about what is actually required for a successful theory of quantum gravity, and in particular whether some of the virtues of string theory can be captured by a simpler theory instead. Answering the question requires a prodigious calculation, and the more “loops” are involved the more difficult it is. Six years ago, the calculation got to five loops, and it hasn’t passed that mark since then. That five-loop calculation gave some reason for pessimism, a nice pattern at lower loops that stopped applying at five.

Kallosh thinks she has an idea of what to expect. She’s noticed a symmetry in supergravity, one that hadn’t previously been taken into account. She thinks that symmetry should keep N=8 supergravity from diverging on schedule…but only in exactly four dimensions. All of the lower-loop calculations in N=8 supergravity diverged in higher dimensions than four, and it seems like with this new symmetry she understands why. Her suggestion is to focus on other four-dimensional calculations. If seven loops is still too hard, then dialing back the amount of supersymmetry from N=8 to something lower should let her confirm her suspicions. Already a while back N=5 supergravity was found to diverge later than expected in four dimensions. She wants to know whether that pattern continues.

(Her backup slides also have a fun historical point: in dimensions greater than four, you can’t get elliptical planetary orbits. So four dimensions is special for our style of life.)

Other talks on Monday included a talk by Zahra Zahraee on progress towards “solving” the field’s favorite toy model, N=4 super Yang-Mills. Christian Copetti talked about the work I mentioned here, while Meta employee François Charlton’s “review talk” dealt with his work applying machine learning techniques to “translate” between questions in mathematics and their answers. In particular, he reported progress with my current boss Matthias Wilhelm and frequent collaborator and mentor Lance Dixon on using transformers to guess high-loop formulas in N=4 super Yang-Mills. They have an interesting proof of principle now, but it will probably still be a while until they can use the method to predict something beyond the state of the art.

In the meantime at least they have some hilarious AI-generated images

Tuesday’s review by Ian Moult was genuinely a review, but of a topic not otherwise covered at the conference, that of “detector observables”. The idea is that rather than talking about which individual particles are detected, one can ask questions that make more sense in terms of the experimental setup, like asking about the amounts of energy deposited in different detectors. This type of story has gone from an idle observation by theorists to a full research program, with theorists and experimentalists in active dialogue.

Natalia Toro brought up that, while we say each particle has a definite spin, that may not actually be the case. Particles with so-called “continuous spins” can masquerade as particles with a definite integer spin at lower energies. Toro and Schuster promoted this view of particles ten years ago, but now can make a bit more sense of it, including understanding how continuous-spin particles can interact.

The rest of Tuesday continued to be a bit of a grab-bag. Yael Shadmi talked about applying amplitudes techniques to Effective Field Theory calculations, while Franziska Porkert talked about a Feynman diagram involving two different elliptic curves. Interestingly (well, to me at least), the curves never appear “together”, you can represent the diagram as a sum of terms involving one curve and terms involving the other, much simpler than it could have been!

Tuesday afternoon’s review talk by Iain Stewart was one of those “guest from an adjacent field” talks, in this case from an approach called SCET, and at first glance didn’t seem to do much to reach out to the non-SCET people in the audience. Frequent past collaborator of mine Andrew McLeod showed off a new set of relations between singularities of amplitudes, found by digging in to the structure of the equations discovered by Landau that control this behavior. He and his collaborators are proposing a new way to keep track of these things involving “minimal cuts”, a clear pun on the “maximal cuts” that have been of great use to other parts of the community. Whether this has more or less staying power than “negative geometries” remains to be seen.

Closing Tuesday, Shruti Paranjape showed there was more to discover about the simplest amplitudes, called “tree amplitudes”. By asking why these amplitudes are sometimes equal to zero, she was able to draw a connection to the “double-copy” structure that links the theory of the strong force and the theory of gravity. Johannes Henn’s talk noticed an intriguing pattern. A while back, I had looked into under which circumstances amplitudes were positive. Henn found that “positive” is an understatement. In a certain region, the amplitudes we were looking at turn out to not just be positive, but also always decreasing, and also with second derivative always positive. In fact, the derivatives appear to alternate, always with one sign or the other as one takes more derivatives. Henn is calling this unusual property “completely monotonous”, and trying to figure out how widely it holds.

Wednesday had a more mathematical theme. Bernd Sturmfels began with a “review talk” that largely focused on his own work on the space of curves with marked points, including a surprising analogy between amplitudes and the likelihood functions one needs to minimize in machine learning. Lauren Williams was the other “actual mathematician” of the day, and covered her work on various topics related to the amplituhedron.

The remaining talks on Wednesday were not literally by mathematicians, but were “mathematically informed”. Carolina Figueiredo and Hayden Lee talked about work with Nima Arkani-Hamed on different projects. Figueiredo’s talk covered recent developments in the “curve integral formalism”, a recent step in Nima’s quest to geometrize everything in sight, this time in the context of more realistic theories. The talk, which like those Nima gives used tablet-written slides, described new insights one can gain from this picture, including new pictures of how more complicated amplitudes can be built up of simpler ones. If you want to understand the curve integral formalism further, I’d actually suggest instead looking at Mark Spradlin’s slides from later that day. The second part of Spradlin’s talk dealt with an area Figueiredo marked for future research, including fermions in the curve integral picture. I confess I’m still not entirely sure what the curve integral formalism is good for, but Spradlin’s talk gave me a better idea of what it’s doing. (The first part of his talk was on a different topic, exploring the space of string-like amplitudes to figure out which ones are actually consistent.)

Hayden Lee’s talk mentions the emergence of time, but the actual story is a bit more technical. Lee and collaborators are looking at cosmological correlators, observables like scattering amplitudes but for cosmology. Evaluating these is challenging with standard techniques, but can be approached with some novel diagram-based rules which let the results be described in terms of the measurable quantities at the end in a kind of “amplituhedron-esque” way.

Aidan Herderschee and Mariana Carrillo González had talks on Wednesday on ways of dealing with curved space. Herderschee talked about how various amplitudes techniques need to be changed to deal with amplitudes in anti-de-Sitter space, with difference equations replacing differential equations and sum-by-parts relations replacing integration-by-parts relations. Carrillo González looked at curved space through the lens of a special kind of toy model theory called a self-dual theory, which allowed her to do cosmology-related calculations using a double-copy technique.

Finally, Stephen Sharpe had the second review talk on Wednesday. This was another “outside guest” talk, a discussion from someone who does Lattice QCD about how they have been using their methods to calculate scattering amplitudes. They seem to count the number of particles a bit differently than we do, I’m curious whether this came up in the question session.

At Quanta This Week, and Some Bonus Material

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When I moved back to Denmark, I mentioned that I was planning to do more science journalism work. The first fruit of that plan is up this week: I have a piece at Quanta Magazine about a perennially trendy topic in physics, the S-matrix.

It’s been great working with Quanta again. They’ve been thorough, attentive to the science, and patient with my still-uncertain life situation. I’m quite likely to have more pieces there in future, and I’ve got ideas cooking with other outlets as well, so stay tuned!

My piece with Quanta is relatively short, the kind of thing they used to label a “blog” rather than say a “feature”. Since the S-matrix is a pretty broad topic, there were a few things I couldn’t cover there, so I thought it would be nice to discuss them here. You can think of this as a kind of “bonus material” section for the piece. So before reading on, read my piece at Quanta first!

Welcome back!

At Quanta I wrote a kind of cartoon of the S-matrix, asking you to think about it as a matrix of probabilities, with rows for input particles and columns for output particles. There are a couple different simplifications I snuck in there, the pop physicist’s “lies to children“. One, I already flag in the piece: the entries aren’t really probabilities, they’re complex numbers, probability amplitudes.

There’s another simplification that I didn’t have space to flag. The rows and columns aren’t just lists of particles, they’re lists of particles in particular states.

What do I mean by states? A state is a complete description of a particle. A particle’s state includes its energy and momentum, including the direction it’s traveling in. It includes its spin, and the direction of its spin: for example, clockwise or counterclockwise? It also includes any charges, from the familiar electric charge to the color of a quark.

This makes the matrix even bigger than you might have thought. I was already describing an infinite matrix, one where you can have as many columns and rows as you can imagine numbers of colliding particles. But the number of rows and columns isn’t just infinite, but uncountable, as many rows and columns as there are different numbers you can use for energy and momentum.

For some of you, an uncountably infinite matrix doesn’t sound much like a matrix. But for mathematicians familiar with vector spaces, this is totally reasonable. Even if your matrix is infinite, or even uncountably infinite, it can still be useful to think about it as a matrix.

Another subtlety, which I’m sure physicists will be howling at me about: the Higgs boson is not supposed to be in the S-matrix!

In the article, I alluded to the idea that the S-matrix lets you “hide” particles that only exist momentarily inside of a particle collision. The Higgs is precisely that sort of particle, an unstable particle. And normally, the S-matrix is supposed to only describe interactions between stable particles, particles that can survive all the way to infinity.

In my defense, if you want a nice table of probabilities to put in an article, you need an unstable particle: interactions between stable particles depend on their energy and momentum, sometimes in complicated ways, while a single unstable particle will decay into a reliable set of options.

More technically, there are also contexts in which it’s totally fine to think about an S-matrix between unstable particles, even if it’s not usually how we use the idea.

My piece also didn’t have a lot of room to discuss new developments. I thought at minimum I’d say a bit more about the work of the young people I mentioned. You can think of this as an appetizer: there are a lot of people working on different aspects of this subject these days.

Part of the initial inspiration for the piece was when an editor at Quanta noticed a recent paper by Christian Copetti, Lucía Cordova, and Shota Komatsu. The paper shows an interesting case, where one of the “logical” conditions imposed in the original S-matrix bootstrap doesn’t actually apply. It ended up being too technical for the Quanta piece, but I thought I could say a bit about it, and related questions, here.

Some of the conditions imposed by the original bootstrappers seem unavoidable. Quantum mechanics makes no sense if doesn’t compute probabilities, and probabilities can’t be negative, or larger than one, so we’d better have an S-matrix that obeys those rules. Causality is another big one: we probably shouldn’t have an S-matrix that lets us send messages back in time and change the past.

Other conditions came from a mixture of intuition and observation. Crossing is a big one here. Crossing tells you that you can take an S-matrix entry with in-coming particles, and relate it to a different S-matrix entry with out-going anti-particles, using techniques from the calculus of complex numbers.

Crossing may seem quite obscure, but after some experience with S-matrices it feels obvious and intuitive. That’s why for an expert, results like the paper by Copetti, Cordova, and Komatsu seem so surprising. What they found was that a particularly exotic type of symmetry, called a non-invertible symmetry, was incompatible with crossing symmetry. They could find consistent S-matrices for theories with these strange non-invertible symmetries, but only if they threw out one of the basic assumptions of the bootstrap.

This was weird, but upon reflection not too weird. In theories with non-invertible symmetries, the behaviors of different particles are correlated together. One can’t treat far away particles as separate, the way one usually does with the S-matrix. So trying to “cross” a particle from one side of a process to another changes more than it usually would, and you need a more sophisticated approach to keep track of it. When I talked to Cordova and Komatsu, they related this to another concept called soft theorems, aspects of which have been getting a lot of attention and funding of late.

In the meantime, others have been trying to figure out where the crossing rules come from in the first place.

There were attempts in the 1970’s to understand crossing in terms of other fundamental principles. They slowed in part because, as the original S-matrix bootstrap was overtaken by QCD, there was less motivation to do this type of work anymore. But they also ran into a weird puzzle. When they tried to use the rules of crossing more broadly, only some of the things they found looked like S-matrices. Others looked like stranger, meaningless calculations.

A recent paper by Simon Caron-Huot, Mathieu Giroux, Holmfridur Hannesdottir, and Sebastian Mizera revisited these meaningless calculations, and showed that they aren’t so meaningless after all. In particular, some of them match well to the kinds of calculations people wanted to do to predict gravitational waves from colliding black holes.

Imagine a pair of black holes passing close to each other, then scattering away in different directions. Unlike particles in a collider, we have no hope of catching the black holes themselves. They’re big classical objects, and they will continue far away from us. We do catch gravitational waves, emitted from the interaction of the black holes.

This different setup turns out to give the problem a very different character. It ends up meaning that instead of the S-matrix, you want a subtly different mathematical object, one related to the original S-matrix by crossing relations. Using crossing, Caron-Huot, Giroux, Hannesdottir and Mizera found many different quantities one could observe in different situations, linked by the same rules that the original S-matrix bootstrappers used to relate S-matrix entries.

The work of these two groups is just some of the work done in the new S-matrix program, but it’s typical of where the focus is going. People are trying to understand the general rules found in the past. They want to know where they came from, and as a consequence, when they can go wrong. They have a lot to learn from the older papers, and a lot of new insights come from diligent reading. But they also have a lot of new insights to discover, based on the new tools and perspectives of the modern day. For the most part, they don’t expect to find a new unified theory of physics from bootstrapping alone. But by learning how S-matrices work in general, they expect to find valuable knowledge no matter how the future goes.

Getting It Right vs Getting It Done

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With all the hype around machine learning, I occasionally get asked if it could be used to make predictions for particle colliders, like the LHC.

Physicists do use machine learning these days, to be clear. There are tricks and heuristics, ways to quickly classify different particle collisions and speed up computation. But if you’re imagining something that replaces particle physics calculations entirely, or even replace the LHC itself, then you’re misunderstanding what particle physics calculations are for.

Why do physicists try to predict the results of particle collisions? Why not just observe what happens?

Physicists make predictions not in order to know what will happen in advance, but to compare those predictions to experimental results. If the predictions match the experiments, that supports existing theories like the Standard Model. If they don’t, then a new theory might be needed.

Those predictions certainly don’t need to be made by humans: most of the calculations are done by computers anyway. And they don’t need to be perfectly accurate: in particle physics, every calculation is an approximation. But the approximations used in particle physics are controlled approximations. Physicists keep track of what assumptions they make, and how they might go wrong. That’s not something you can typically do in machine learning, where you might train a neural network with millions of parameters. The whole point is to be able to check experiments against a known theory, and we can’t do that if we don’t know whether our calculation actually respects the theory.

That difference, between caring about the result and caring about how you got there, is a useful guide. If you want to predict how a protein folds in order to understand what it does in a cell, then you will find AlphaFold useful. If you want to confirm your theory of how protein folding happens, it will be less useful.

Some industries just want the final result, and can benefit from machine learning. If you want to know what your customers will buy, or which suppliers are cheating you, or whether your warehouse is moldy, then machine learning can be really helpful.

Other industries are trying, like particle physicists, to confirm that a theory is true. If you’re running a clinical trial, you want to be crystal clear about how the trial data turn into statistics. You, and the regulators, care about how you got there, not just about what answer you got. The same can be true for banks: if laws tell you you aren’t allowed to discriminate against certain kinds of customers for loans, you need to use a method where you know what traits you’re actually discriminating against.

So will physicists use machine learning? Yes, and more of it over time. But will they use it to replace normal calculations, or replace the LHC? No, that would be missing the point.

The Hidden Higgs

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Peter Higgs, the theoretical physicist whose name graces the Higgs boson, died this week.

Peter Higgs, after the Higgs boson discovery was confirmed

This post isn’t an obituary: you can find plenty of those online, and I don’t have anything special to say that others haven’t. Reading the obituaries, you’ll notice they summarize Higgs’s contribution in different ways. Higgs was one of the people who proposed what today is known as the Higgs mechanism, the principle by which most (perhaps all) elementary particles gain their mass. He wasn’t the only one: Robert Brout and François Englert proposed essentially the same idea in a paper that was published two months earlier, in August 1964. Two other teams came up with the idea slightly later than that: Gerald Guralnik, Carl Richard Hagen, and Tom Kibble were published one month after Higgs, while Alexander Migdal and Alexander Polyakov found the idea independently in 1965 but couldn’t get it published till 1966.

Higgs did, however, do something that Brout and Englert didn’t. His paper doesn’t just propose a mechanism, involving a field which gives particles mass. It also proposes a particle one could discover as a result. Read the more detailed obituaries, and you’ll discover that this particle was not in the original paper: Higgs’s paper was rejected at first, and he added the discussion of the particle to make it more interesting.

At this point, I bet some of you are wondering what the big deal was. You’ve heard me say that particles are ripples in quantum fields. So shouldn’t we expect every field to have a particle?

Tell that to the other three Higgs bosons.

Electromagnetism has one type of charge, with two signs: plus, and minus. There are electrons, with negative charge, and their anti-particles, positrons, with positive charge.

Quarks have three types of charge, called colors: red, green, and blue. Each of these also has two “signs”: red and anti-red, green and anti-green, and blue and anti-blue. So for each type of quark (like an up quark), there are six different versions: red, green, and blue, and anti-quarks with anti-red, anti-green, and anti-blue.

Diagram of the colors of quarks

When we talk about quarks, we say that the force under which they are charged, the strong nuclear force, is an “SU(3)” force. The “S” and “U” there are shorthand for mathematical properties that are a bit too complicated to explain here, but the “(3)” is quite simple: it means there are three colors.

The Higgs boson’s primary role is to make the weak nuclear force weak, by making the particles that carry it from place to place massive. (That way, it takes too much energy for them to go anywhere, a feeling I think we can all relate to.) The weak nuclear force is an “SU(2)” force. So there should be two “colors” of particles that interact with the weak nuclear force…which includes Higgs bosons. For each, there should also be an anti-color, just like the quarks had anti-red, anti-green, and anti-blue. So we need two “colors” of Higgs bosons, and two “anti-colors”, for a total of four!

But the Higgs boson discovered at the LHC was a neutral particle. It didn’t have any electric charge, or any color. There was only one, not four. So what happened to the other three Higgs bosons?

The real answer is subtle, one of those physics things that’s tricky to concisely explain. But a partial answer is that they’re indistinguishable from the W and Z bosons.

Normally, the fundamental forces have transverse waves, with two polarizations. Light can wiggle along its path back and forth, or up and down, but it can’t wiggle forward and backward. A fundamental force with massive particles is different, because they can have longitudinal waves: they have an extra direction in which they can wiggle. There are two W bosons (plus and minus) and one Z boson, and they all get one more polarization when they become massive due to the Higgs.

That’s three new ways the W and Z bosons can wiggle. That’s the same number as the number of Higgs bosons that went away, and that’s no coincidence. We physicist like to say that the W and Z bosons “ate” the extra Higgs, which is evocative but may sound mysterious. Instead, you can think of it as the two wiggles being secretly the same, mixing together in a way that makes them impossible to tell apart.

The “count”, of how many wiggles exist, stays the same. You start with four Higgs wiggles, and two wiggles each for the precursors of the W+, W-, and Z bosons, giving ten. You end up with one Higgs wiggle, and three wiggles each for the W+, W-, and Z bosons, which still adds up to ten. But which fields match with which wiggles, and thus which particles we can detect, changes. It takes some thought to look at the whole system and figure out, for each field, what kind of particle you might find.

Higgs did that work. And now, we call it the Higgs boson.