Tag Archives: particle physics

Data Comes From Papers

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There’s a lovely resource that I suspect most non-physicists don’t know about. It’s called the Particle Data Group, and its interactive site PDGLive.

If you want to know the most up-to-date information on a subatomic particle, PDGLive has your back. From their home page, you can click on familiar particles like photons (\gamma), electrons (e) or gluons and find the best info experiments have provided on properties like their mass and charge. It’s a great place to get an authoritative number for any particle physics property you’re interested in.

Of course, scientists don’t just accept one authoritative answer for anything, even whether Pluto is a planet. That’s why each measurement in PDGLive comes with an arrow you can expand to see a table of past measurements, which you can compare to.

Each measurement comes with a link to a source. And each source is not an experiment webpage, or some entry in a database. It’s a document, a publication, a paper.

In fact, PDGLive itself is just a website version of a paper, the Particle Data Group’s “Review of Particle Physics”. Click enough times, and you’ll find sections of a pdf on the site, explaining their reasoning for picking this experiment over that, emphasizing this or the other thing.

People talk about papers as how academics persuade one another, or how they show off and establish credit. But papers are also just a way to organize data. Each time an experiment figures something out, all of their reasoning and procedures are summarized together with the numbers they got. And anyone who reports those numbers to you will include a link, so you can go back, and check where the number came from.

It probably feels a bit weird, all of these numbers and technical details bottoming out in an archaic practice of writing down words for other human beings. But it means that all of the richness of the process is there somewhere, linked together and collated by the same social forces that keep track of credit, all in one navigable whole.

So when you run into a number, spare some thought for where it came from. You can probably find out.

Better Bounds

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I swear this isn’t turning into an AI blog. But did you see the one about the Riemann hypothesis?

Someone at Anthropic did something I’m sure they’re all tempted to do, and tried to use an internal version of their Claude AI system to prove the most famous open conjecture in mathematics. It didn’t work, to be clear, and I get the impression they didn’t expect it to. But out of six hundred or so fruitless tries, one attempt did prove a new bound. Previously, mathematicians had been able to prove that at least 41.6% of the zeroes of the Riemann zeta function satisfied the Riemann hypothesis. Now, the new proof shows that at least 67.2% satisfy it.

Anthropic’s press release is impressively careful. As someone who’s had to think about how to write content that both excites the public and doesn’t piss off experts too much, they do an admirable job walking that line. They even say, straight-out, “We don’t expect that the techniques Claude used will lead to proving the Riemann hypothesis.”

Bounds are like that, sometimes.

I should know. Physicists also find bounds.

Physics has its own conjectures with the fame of the Riemann hypothesis. Dark matter might be made of detectable particles. Protons could decay. There might be extra dimensions, or magnetic monopoles, or cosmic strings. General relativity might be subtly wrong.

It would be an amazing achievement to demonstrate any of these things. But most physicists won’t manage that. Instead, they bound them.

Physicists compete to get better bounds, excluding unusual possibilities with greater and greater care. They find evidence that dark matter can’t be of a specific mass with a specific charge, so the next experiment has to look somewhere else, or find evidence that general relativity holds to even greater precision, so any deviation must be even smaller. Some work to improve experiments with better and better bounds. Others analyze data from older experiments, or find under-appreciated consequences of known facts, and can get even better bounds.

Bounds aren’t typically newsworthy (though occasionally they make it through), so most people don’t hear about them. If you read the news, you hear about positive claims much more often than negative ones: evidence for something new, not evidence that our current knowledge holds. But the nature of physics is that most work supports the status quo. Most work improves bounds.

Do bounds lead, with time, to the positive claims? Sometimes, but not always. Often, bounds are just bounds. They’re attempts to use the methods physicists have to learn something new about the world. Even if the new fact is just “don’t look here”.

Bonus Info on Dark Energy and Muons

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I had two pieces up this month, one in New Scientist and one in Quanta. I figured I’d give a bit of “bonus info” for both here.

The New Scientist piece covered a paper arguing that, according to the supernova evidence, there is no need for dark energy, because the universe isn’t speeding up after all. That’s a pretty dramatic claim, and it’s one the majority of cosmologists don’t agree with. But a small group has been hammering at the consensus.

Long-time followers of this blog have already heard of these folks. I criticized news coverage around a paper with one of the authors, Subir Sarkar, back in 2016, when he was only arguing that the supernova evidence was insufficient to establish dark energy, not that it was literally the wrong way around. He and his co-authors wanted an opportunity to state their case, so I posted their response a few weeks later. Later, I got to know Rameez, another author on the new paper. He ended up doing a guest post in 2019, on the next step in the story.

That story went from a statistical critique to an active proposal for something outside the consensus, in the form of inhomogeneous cosmology, the idea that the universe may be lumpier than typically assumed, with flowing currents that explain things otherwise attributed to exotic physics. That’s another topic I’ve covered before, but in this article I didn’t have the space to go into it.

Sarkar and Rameez are claiming something much more radical than most proponents of inhomogeneous cosmology, arguing against dark energy as a whole, not just more subtle effects. They told me a lot about their reasoning, most of which also didn’t make it into the piece.

It’s largely not going to make it here, either. Not due to space limitations: I’ve been pushing the blog post lengths you folks tolerate for a long time, no reason to stop now. Rather, it’s because I genuinely don’t feel qualified to judge this.

The issue is, cosmology is messy.

How do you figure out how the universe is expanding? You can look at supernovae, and use how dim they are to estimate how far away they are. The issue is, supernovae vary, even famous “standard candles”: they move in different ways, they shine differently depending on different things. Simulations aren’t nearly advanced enough to tell you all this from first principles, and so there are a wash of different corrections based largely on empirical observations, taking this or that correlation seriously and factoring them out of the measurement, while disregarding other correlations as spurious. Which of these combinations of corrections you trust determines whether the universe seems to be accelerating or decelerating.

It makes me glad I went into particle physics instead of cosmology, where you can mostly model everything from first-principles, and compare to your models.

Of course, even that can get you into trouble.

Take that Quanta piece. I wrote an update of the muon g-2 measurement. In some ways, this is an issue that many think of as already solved, by precisely that kind of first-principles modeling. Muons seemed to be violating the Standard Model, according to a calculation based in part on empirical formulas. Lattice QCD researchers figured out how to do that part of the prediction via a first-principles simulation instead, with enough accuracy that it could substitute for the empirical formulas. And lo and behold, the new prediction agreed with the experiment. Eventually, the experts accepted it, and all was well.

Except, as I commented at the time, not really. Because the empirical formulas were based on other experiments, colliding electrons and positrons. And as I now understand in much more detail, the disagreement between those electron-positron experiments is worryingly large.

So nobody is resting on their laurels. The lattice folks improved their calculation, with a result published in Nature this year that prompted Quanta to ask me to report on it. The people using the empirical method are still trying to sort out what happened. And the experimentalists are busy scrutinizing how they analyze their data, and collecting and analyzing more.

A few details that didn’t make it into the piece:

First: it goes beyond the level I was aiming for in the piece, but I really do want to emphasize the role of error estimates. Ultimately, every step in the story was not just one where experiments and predictions disagree, but one where they disagree past their reported error. The problem with disagreement between the new experiments isn’t that they disagree, it’s that they disagree so badly that they’re straining the statistical methods the people using the empirical method use to combine results together, so badly that if taken seriously, those methods would have to throw away ten years of progress of increasing precision. I don’t expect it, but I really hope for a postmortem in which we learn how to better estimate the kinds of experimental errors that can cause this. I haven’t seen that kind of postmortem for other results, so I don’t expect one here. But I have to believe that in the background someone is learning something, and getting better at this.

Second: one interesting question my editors raised was whether it was possible to do a first-principles calculation to compare with the electron-positron experiments. The answer is yes, but with some caveats. One will be recognizable to physicists: lattice QCD can only compute energy-integrated cross-sections, not measurements at particular energies like experiments find. But they can compute integrals with a modulating function…such as one strongly peaked at a particular energy. It’s a familiar type of trick for a quantum field theorist, though in this case it’s trickier than it sounds. I actually misunderstood, and thought that the same people I was talking to about the muon g-2 calculation had done that, and found it agreed with one of the electron-positron experiments over another. That’s not true: their comparisons were more indirect, while other groups attempting more direct comparisons haven’t quite gotten something good enough to do more than gesture at an agreement. So while the direction was correct, there are indeed lattice-based suggestions that favor one experiment over the others, the piece phrased things much too definitely. There’ll be a correction fixing this.

In Defense of Reductionist Chauvinism

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I don’t think people who argue about reductionism are really arguing about reductionism.

Reductionism is the idea that the behavior of big, complicated things (people, economies, ecosystems) boils down to the behavior of their smallest constituents (molecules, atoms, subatomic particles). It’s often contrasted with emergence, the idea that new rules emerge in those big, complicated systems that are more than just the rules that govern the smallest scales.

Emergence can be divided into two kinds: weak and strong. In strong emergence, the big, complicated things have their own causal powers that aren’t due to smaller things at all. This tends to get mystical, with ideas like “lifeforce” and “consciousness”. Weak emergence is much milder, and while the big complicated things are best described by their own laws, in weak emergence they are in principle still caused by laws on smaller scales.

In practice, basically no-one believes in strong emergence: it seems way too much like magic for most scientists. And basically everyone believes in weak emergence: it would be nuts to insist that economists and biologists aren’t discovering important rules that would be almost impossible to find for someone who just had physics and chemistry to work with.

So if everyone agrees, what do people argue about?

Arguments about reductionism are really arguments about attitudes. If you position yourself as a reductionist, or an emergentist, you’re defending a particular way of thinking about the world, one that privileges one scale over another. When people argue for emergence, what they really seem to be doing is opposing a kind of “reductionist chauvinism”, where people like physicists insist that their perspective is the most valuable one.

And that’s understandable, because physicists can definitely be jerks sometimes. Let it be known I am no fan of jerks.

But I think it’s worth defending reductionism, not as a philosophy, but as an attitude or perspective. Worth arguing not about whether things in practice reduce or not, but about whether reduction is a good goal, about whether science that reduces more successfully is healthier science.

Because I think it is. And the reason boils down to agreement.

Simpler systems are less controversial systems. When we write down the laws that govern subatomic particles, they’re more definite: less heuristic, more precisely specified, with fewer exceptions. That isn’t to say there’s zero controversy in these subjects, there’s even controversy between mathematicians. But the more thoroughly you can boil something down to simple rules, the easier time you have of convincing others you’re right.

In contrast, the laws of the largest scales, like psychology and biology, are deeply heuristic. They thrive on exceptions and guidelines, general tendencies without clearly defined limits. And the problem with such laws is that they can lead to intractable arguments. Different schools of thought in psychology may simply never be able to convince each other, and may just have to wait for one to die off, the aesthetic feel of one set of ideas falling out of fashion as people become preoccupied with different sorts of problems.

Every time you can reduce, you avoid those insoluble disagreements. The simpler a system you can invoke, the more you can cooperate and build off each other’s work, the less time you have to waste disagreeing, the more you can accept people with different aesthetic and philosophical preferences as just different perspectives on what are ultimately the same facts. Reductionism is a technology for peace, and one of the most powerful we have.

So yeah, I’m a bit of a chauvinist about reductionism. That’s typical of an ex-physicist, sure. But it comes from a place of concern. I want a peaceful world, where we can learn from each other and find ways to agree. And reductionism is how I get there.

Amplitudes 2026

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This week was Amplitudes, my old subfield’s big yearly conference. This year, it’s at Queen Mary University of London.

I’m too busy to attend these days, now that nobody is paying me a salary to do that sort of thing. But it’s still a good chance to keep up with the field, which helps me find stories. And I know I have a few readers who are interested. So I read the slides when I can, and fill you all in.

As of writing this, I’ve read through slides from the first few days of talks. I’ll likely post on the rest next week. As usual when I’m conference-blogging, this post will be quite a bit more technical than my average post, so readers beware: I’ll be mentioning a lot of amplitude-ish ideas without much explanation. I’m happy to explain in the comments if you’re curious, though!

Before I launch into talking about the content, I should mention something I’ve heard about the venue. Apparently this year registration filled up surprisingly quickly. The rumor is that the folks at Queen Mary weren’t able to find a venue with enough space to host the full community, leading to a smaller conference than usual. As the Amplitudes subfield grows, I suspect this will be more and more of a challenge. I remember back when I was organizing in 2021, rooms that could hold enough people were shockingly expensive to book. I wouldn’t be surprised if this becomes more of an issue going forward.

David Kosower opened the conference with a review of the state of the art in amplitudes for gravitational waves. I enjoyed an early slide showing how LIGO has increased in precision over the last ten years, which really helped illustrate the value that good theoretical predictions can bring as the experiment gets better. I also appreciated his attempt to get people to stop saying “post-Minkowskian” and start using a more normal term like Relativistic Perturbation Theory, though based on the other talks it doesn’t look like it’s catching on. After covering the overall state of the art (currently around four loops) he talked about his own work looking for ways to more directly get waveforms for orbiting black holes out of an amplitudes-style calculation, a theme his collaborator Donal O’Connell covered in more detail later that day. (The trick, apparently, is background fields!) Other gravitational wave-related talks came from Gustav Jakobsen, who covered four-loop results using the worldline method, Graham Brown, who explained how to calculate the Magnusian Jakobsen mentioned (it’s the log of the amplitude, basically), Canxin Shi, who talked about how a concept called Stratonovich-Weyl quantization helps explain structures that keep showing up in classical observables, Giulia Isabella, who covered a way to get six-loop contributions to gravitational waves via a wave equation, Lara Bohnenblust, who showed how to get strong-field information from a shockwave limit, and Gang Chen, whose slides were brief enough that I didn’t really get a clear idea of what he was up to. Rounding out the day were two talks that didn’t involve gravitational waves: Zihan Zhou, reporting on work with Nima on a water wave polytope called the hydrotope that they found a general formula for with help from Claude (the AI, not Duhr, to steal a recurring joke from Lancefest), and Michael Ruf, who probably snuck in due to the fact that he has done a lot of work with gravitational waves, but was reporting on a QCD calculation using a tool called Scorpio.

Tuesday had more of a QCD theme. Thomas Gehrmann gave the day’s opening review talk, where he pointed out that to get 1% precision for predictions for the LHC, we’ll likely need three-loop calculations. He pointed out the important role IR real emission calculations and improvements in parton distribution functions need to play, and pointed out that collider physics isn’t just the LHC: between reanalyses of older electron-positron collider data and the upcoming electron-ion collider and FCC, there are even more contexts where high-precision QCD will matter. Simone Zoia talked about one aspect of the current state of the art, five-particle processes involving massive particles, where the functions get strange and elliptical and one has to think hard about the methods one uses (for example, do you want canonical differential equations, or almost-canonical? Bulirsch-Stoer or AMFlow for numerics?) He also included an excellent Laplace quote, “Nature Laughs at the Difficulties of Integration”. Yang Zhang talked about a different calculational frontier, covering progress in the planar limit and with no masses, but for two-loop six-particle and three-loop five-particle scattering. The talk included some nice branding, like an “epsilon collaboration” proposing an algorithm to find epsilon forms for any Feynman integral and a program called Effortless to find symbol letters. Yang Zhang is also a skilled amateur photographer, and he mentions taking the conference photo for Amplitudes five times before. Personally, I’m surprised it’s only been five times! Dmitry Chicherin presented results bootstrapping QCD amplitudes. This was a dream of mine back in my hexagon function days, and while they aren’t quite at the point of being useful (my understanding is they’re still only getting the leading transcendentality, and none of the amplitudes they’re finding are new) it’s still pretty cool that this is even possible now. Bo Feng proposed what he claims is a general algorithm to find generating functions for IBP reduction. It’s not clear to me whether his setup bypasses the computational difficulties in existing methods (mostly involving solving large systems of equations), or whether it shifts the issue elsewhere, though. Pierre Vanhove’s talk also involved QCD, though at an effective field theory mediated step removed, with chiral perturbation theory, a theory of low-energy QCD that he used to shore up the lower energy ranges of lattice calculations for contributions to the muon anomalous magnetic moment (a natural calculation to involve him due to the presence of novel elliptic integrals). Overall, the QCD talks impressed me with the wide range of software packages mentioned, some of which already existed when I was in the field but many of which are new. I do wonder if this is just a result of many research paths maturing at the same time, or if people are finding it easier to write packages with tools like Claude Code.

The remaining three Tuesday talks were more mathematical or theoretical in focus. Henrik Johansson talked about black hole Compton scattering in N=8 supergravity, where it’s possible to use the wave equation to extract all-loop results. Cristian Vergu reported on his progress with Landau analysis. It’s been really fun watching this grow from a small reading group at NBI to what appears to be at this point quite a deep understanding, including a picture of how to understand amplitude singularities with quite a lot of breadth and detail, and the persistent hope that this could allow one to manipulate singular quantities without needing dimensional regularization. Michael Borinsky gave an update on tropicalization, where he showcased a theorem he proved demonstrating a way to compute certain classes of amplitudes in polynomial time in the loop order, even when the number of Feynman diagrams increases factorially. The examples he talked through were impressive, but I’m still a bit skeptical this could work for the Standard Model. I’d want to talk to him about it to figure it out, anyway!

Wednesday was a short day, as is tradition, to give people some time for tourism in the afternoon. Alexander Zhiboedov began the day with a talk on energy correlators in N=4 super Yang-Mills at finite coupling, where he is now able to do a bootstrap with two-sided bounds to hone in on the actual quantity even outside of the planar limit. Arthur Lipstein and Daniel Baumann both talked about cosmological correlators, the former with amplitudeologists’ favorite toy model of the conformally coupled scalar and the latter with Yang-Mills and gravity in de Sitter space. Dave Dunbar closed the day with a historical talk, walking through the milestone amplitudes papers before the Amplitudes conference existed. It’s the kind of talk he could have given at Lancefest the week before if others hadn’t already covered the material!

I’ll cover the rest of the conference (Thursday and Friday) in next week’s post, so see you then!

At Lancefest

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It’s been a while since I’ve said this: I’m at a conference this week!

Specifically, I’m at Lancefest, which is not just any old conference, but a birthday conference for Lance Dixon. When a renowned academic turns 60 or so, their students and collaborators hold a birthday party-flavored conference for them. The conferences are usually a mix of academic talks and reminiscences, with the occasional roast thrown in.

I went to my advisor’s birthday conference four years ago. Lance wasn’t my advisor, but in many ways he might as well have been. When my advisor took a sabbatical in the middle of my PhD, he sent me to work with Lance. It was my first real experience doing research in a team, not just puzzling away by myself with occasional feedback. And I was hooked: I spent the rest of my academic career in Lance’s field. We collaborated time after time, and even when I started to branch out he remained a frequent presence.

In part, that’s because Lance’s field was really Lance’s field. Amplitudeology has grown a lot since I started out, with several hundred people going to the field’s big yearly conference and subfields like Elliptics having their own yearly conferences. In such a world, it’s tough for anyone to feel like a truly central figure. But Lance tends to. He’s been able to keep up with that growing world, to keep finding important problems and keep understanding others’ ideas. While some have specialized, or stepped back, Lance seems to somehow manage to be a father figure for the whole field all at once. It’s a capability his advisor Jeff Harvey might have predicted, he mentioned in his talk that Lance’s interests were always broad. Over the years the young students I met who joined when the amplitudes field was already large saw Lance as a kind of mysterious titan, and were occasionally awed that I had worked with him. “What was that like?”

Well, it was like working with Lance. Lance isn’t a manager at heart, like some senior academics end up. He wants to understand everything he works on, and will happily dive in, Maple subscription in hand, and try to figure things out for himself. He wants you to keep up with him, understanding on your own terms, to keep him honest, to provide an independent check. But that often wasn’t possible, because the man is just so damn fast. He’d be miles ahead of me, with his Maple and his laptop, while I was churning overnight Mathematica runs on a twenty-machine cluster.

(Was the difference due to our taste in software? Partly. I did learn to use Maple later, it genuinely is faster at some things. But Lance is faster at almost everything.)

And he cared so damn much sometimes. About getting things right, like a scientist should. About making things nice, too: finding a pretty basis of functions, a better notation for the paper, something that might jostle out the next big insight. Working with him, you could feel like that one paper was the most important thing in the universe.

Others at the event have had similar stories. Fernando Febres Cordero remembers noticing a potential issue, emailing Lance about it, and in a few minutes hearing back with a potential explanation.

Lance is someone who became a leader without really being a politician. He doesn’t have the legions of students in tenured positions that some do. I trimmed that count by one, and it wasn’t huge to begin with. But for someone who isn’t “everywhere” in that sense, he manages to be “everywhere” all the same.

So Lance, happy birthday! You’re really the only person who could have had a birthday conference quite like this, a cross-section of the field, all with something kind to say. Thanks for putting up with any embarrassment associated with having this much attention for three days, and I wish you many Maple-fueled mysteries to come.

Radiation Radiates

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I recently finished reading The Orphan Master’s Son, a (Pulitzer-winning, apparently) novel set in 2000’s-era North Korea. In one plot point, Kim Jong Il has agents steal a Japanese telescope designed to measure the cosmic microwave background radiation, under the mistaken impression that it will help him find uranium.

The novel plays it for (horrified) laughs, but I’ve seen this kind of misunderstanding crop up in the real world too. Sure, most people would realize that a telescope probably won’t help you find something buried under a mountain of rock. But there’s a deeper misunderstanding here. Ask yourself: what does “radiation” mean?

We talk about radioactive elements like uranium releasing radiation. We talk about electromagnetic radiation, including everything from gamma rays to visible light to the 5G of your cell phone. We talk about cosmic radiation coming in from space, and about the cosmic background radiation that originated in the early universe. For someone who doesn’t know much about physics, it probably sounds like all of these are the same kind of thing.

But they’re not!

It’s helpful to break things down in terms of particles. Radioactive elements release three main types of radiation: alpha, beta, and gamma. Alpha radiation consists of helium nuclei: two protons stuck together with two neutrons. Beta radiation consists of electrons. Gamma radiation is a type of electromagnetic radiation, and consists of photons: particles of light.

Anything we call electromagnetic radiation is a wave in the electromagnetic field, a ripple that moves through space. That’s different from other shapes of electromagnetic fields, like a magnetic field that stays in place. From a particle perspective, an electromagnetic wave is made up of photons, and physicists will often describe all such waves as light. Some of that light is the familiar rainbow of visible light, while some has lower-energy photons, like microwaves and radio waves, or higher-energy photons, like gamma rays or X-rays.

Cosmic radiation (more often called cosmic rays), like radiation from radioactive elements, can be many types of particles again. Most of it consists of protons, while some consist of various nuclei, or electrons. A smaller fraction are antimatter, like antiprotons or positrons. Sometimes, physicists include neutrinos when they talk about cosmic rays, while sometimes they include gamma rays.

The cosmic background radiation is once again different. This is an overall hum of microwaves, electromagnetic radiation from the early universe that has gotten fainter and more diffuse over time. Cosmologists will sometimes talk about when the universe was “radiation-dominated” versus “matter-dominated”. They’re referring to times when most of the energy of the universe was in electromagnetic radiation, versus when it was mostly in other particles.

The only thing that ties all of these meanings together is the word’s literal meaning: radiation radiates. It starts in one place and travels outwards, having an effect at a distance. For the first scientists to observe phenomena like X-rays, this was almost all they knew about them, so they tossed them together in one category. Now, we know much more, but the names stuck.

So if you hear a physicist use the word “radiation”, try to avoid making any assumptions. You can’t know, just from that word, what they mean.

And please, don’t steal any Japanese space telescopes.

ArXiv Will Ban You for Hallucinated References

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Thomas Dietterich, Chair of the Computer Science section of the preprint server arXiv.org, recently clarified the site’s policies towards “hallucinated” citations and other signs of careless use of AI in a post on X. If your paper contains a citation to a paper that doesn’t actually exist, or has other signs you didn’t read it before posting like leftover commentary (the example he gave was “here is a 200 word summary; would you like me to make any changes?”), then you can get banned from the arXiv for one year. Even after that year you’d be on a kind of “probation”, and would need to show that your next few papers had been accepted by peer-reviewed journals first before posting them.

At the risk of saying the obvious, this is a good idea! arXiv isn’t peer review, it isn’t meant to judge the value of the papers it hosts. But it still needs to be a useful place for scientists to post their papers, which is why they try to keep spam and irrelevant content to a minimum. If you don’t actually endorse the content of a paper, you shouldn’t post it in the first place.

That said, the whole existence of hallucinated citations on arXiv feels a little silly. It makes sense for academic journals and preprint servers in other fields. But arXiv was the first site of its kind for a reason. Its users, physicists, mathematicians, and computer scientists, don’t need much hand-holding when it comes to computers. Papers submitted to arXiv aren’t typically written in Word, they’re written in a document-writing language called LaTeX, that lets users make decently-formatted papers without help from a journal. Physicist-written code may be terrible by any reasonable criteria…but it exists, much more universally than for example biologist-written code.

This extends to citations. In my old field, there is a database called INSPIRE that updates automatically from arXiv. Click on a paper, and a handy “cite” link gives you standardized citations in several formats, ready to copy and paste into your LaTeX code. Nearly every citation in my papers is copied from there. The ones that aren’t are either from other fields where I didn’t know of that style of database, or things that haven’t been published (this can be manuscripts in preparation, or personal communications).

All of this, though, feels like a lot less than what the field could be doing. In a world where almost everyone posts their papers to the same website, and almost everyone has at least a rudimentary understanding of programming…why are people still writing citations in free-form text in the first place? Why aren’t citations built in to the submitted papers on arXiv, automatically linked to the papers they cite? Why don’t we have a setup where, except for a small number of “special” citations, every citation is built so that it automatically goes to a real paper, and gives a clear error message if it doesn’t? In short, why are hallucinated citations even possible?

Look, I’m naive, I get that. I believe in automation, not in the modern context of LLMs and other heuristics, but in setting clear procedures and building clear rules. The world doesn’t work that way! The clear rules are always more contentious than you expect, the fuzzy human-led version always the only choice people can agree on.

But still. Citations. There has to be a better system, right?

Breakthrough Prize 2026

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Because of last week’s “bonus info” post, I’m only now getting around to commenting on this year’s Breakthrough Prizes in Fundamental Physics. While I don’t comment on them every year, I know enough about several of this year’s winners that I figured a post would be helpful.

For those who haven’t heard of it, the Breakthrough Prizes are a bit like the Nobel, if it was created by a 21st century rich person instead of a 19th century one. They give out more money, and instead of an organization like the Swedish Academy of Sciences they pick winners via a committee of past winners. They’re more flexible in structure than the Nobel, with extra prizes for early-career researchers and a tendency to reward accomplishments that are either entirely theoretical or solid experimental work that doesn’t show a new discovery, both of which are things the Nobel Prize is structured to avoid. They’ve also shown willingness to reward large collaborations, rather than following the Nobel’s informal rule to only give the award to three people at a time.

This last was on display this year in their main award in physics this year, for the muon g-2 collaborations. The award is going to collaborations of scientists and engineers at three different particle colliders, for work done over a span of over fifty years to measure the magnetic properties of the muon. These measurements have shown a tantalizing discrepancy with predictions that inspired many to conjecture new physics. However, in the last few years it’s looked more and more like the discrepancy was due to an imprecise prediction, and better methods seem to be converging to the experimental value. At this point, smart money is that there is no disagreement with the Standard Model here, but as always in science there’s a chance some mystery remains.

The Breakthrough Prize also offered a special, out-of-schedule prize to David Gross. Already a Nobel laureate, Gross had a crucial role in our understanding of the force of quantum chromodynamics that binds protons and neutrons together. He was also a major founding figure in string theory, and since the Breakthrough Prize is more comfortable recognizing theoretical contributions they get to mention this as well. Gross is also known in the community for his personality, which tends to fill up any room he’s in. I can only imagine the conversations that led to Breakthrough’s decision to add a special prize for him this year.

Breakthrough is also adding a new recurring prize, the Vera Rubin New Frontiers Prize, honoring women who make important contributions to physics within two years of their PhD. The prize is a bit smaller than the exiting early-career New Horizons in Physics Prizes, presumably because it goes to even younger researchers. This year’s winner is from my old field, scattering amplitudes. Carolina Figueiredo is part of the latest evolution of the research program behind the amplituhedron. The new framework of “surfaceology” seems like a promising geometry-flavored way to understand particle physics calculations in more realistic theories, and unlike its predecessors may have some practical value eventually as well. Congrats Carolina!

Finally, the New Horizons in Physics Prizes are for impressive early-career researchers. I don’t know much about the first recipient, Benjamin Safdi, who works on searches for axions and axion-like particles, today’s most trendy dark matter candidate. I know a bit more about the work done by Clay Córdova, Thomas Dumitrescu, Shu-Heng Shao, and Yifan Wang, having met several of them in my physics career. They work on what are called generalized symmetries, concepts which go beyond the usual idea of how symmetry is supposed to work by involving more complicated tensors. I saw these crop up a fair bit in talks, but they were distant enough from my area that I never had a particularly clear grasp of what people were doing with them. I know even less about the work of the last three, Dillon Brout, J. Colin Hill, Mathew Madhavacheril, Maria Vincenzi, Daniel Scolnic, and W. L. Kimmy Wu, on cosmological measurements, but I was friends with Mathew in grad school and am impressed that he’s now working on cosmology given how little cosmology research there was at Stony Brook at the time.

A Window on Absolutely Everything

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It’s often said that in quantum physics, everything that can happen will happen.

One way this comes up is in something called a path integral, used to calculate the probabilities of quantum events. If you want to find what happens to a particle traveling from point A to point B, you have to add up a contribution for every path, no matter how windy, that goes between A and B. These contributions mostly cancel out, and matter less the further they are from a straight line, so the straight-line path is, for the most part, a good description of what happens. But in principle, all of the other paths matter too.

The same thing happens in quantum field theory, in more elaborate form. Instead of a path from one place to another, the paths are from one configuration of quantum fields to another, via all the different ways fields can in principle interact. We are almost never able to take account of all these possibilities mathematically, so we have to approximate, organizing the interactions into more and more complicated pictures called Feynman diagrams, each with a smaller and smaller effect.

In principle, these diagrams need to contain every single combination of interactions that might result in the end-state we’re interested in. These combinations can have a Rube Goldberg flavor, with one field activating another, which activates another, only to all cancel out in the end. Because of this, any field that exists, any particle no matter how rare, can matter, if only a little.

And from that, physicists can learn something.

Because absolutely everything matters, physicists get to reason about absolutely everything that exists.

The best example involves something called an anomaly. These aren’t the anomalies of experimental physics, unexpected results that have a tendency to go away with better measurements. Instead of something unexpected, a theorist’s anomaly is something impossible.

Anomalies are combinations of particles that, if they were to show up together in a sum of Feynman diagrams, would break the rules that the theory was made with in the first place. If they show up, they’re a sign of an inconsistent theory, one that doesn’t obey its own rules and thus doesn’t make sense.

In order to have a theory without anomalies, different calculations involving different particles need to cancel. For example, it might be that the charge of different particles has to add up to zero. This means that if you’ve only discovered a few particles, and their charges don’t add up to zero, then you know you’re missing one. There is an extra particle there, which you haven’t observed, that together makes charge add up to zero.

This logic actually works! It was used to predict the top quark. Before the top quark was discovered, the list of quarks, electrons, and neutrinos had electric charges that didn’t add up to zero. One particle was missing, with the same charge as the up quark and charm quark. It was found in 1995, after being proposed almost 20 years earlier.