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.

An AI Opinions Chart

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You ever read something and suddenly a whole classification scheme lights up in your head?

A thread on X from “stringking42069” showed me a combination of opinions I hadn’t seen before. stringking42069 is a pro-string theory commentator with a macho gym bro memer gimmick. He’s openly contemptuous of many physicists who describe themselves as string theorists, arguing that only a smaller number really deserve the name.

To be clear, none of that is the new combination. Long-time readers of this blog will remember a frequent commenter with a very similar attitude, if much less tendency to use the word “bro”.

The new thing, from my perspective, is how he thinks about AI. As he explains in that thread, he sees AI as great at certain kinds of physics calculations, ones where the methods and goals are mostly known and the challenge is working out the math. He doesn’t expect it to be able to contribute real creativity or judgement, the messy decision-making that physicists use to decide what is worth building in the first place.

Others with that perspective tend to argue that this will be a boon for scientists, who AI will free up to do creative work, multiplying their output. The difference is, stringking42069 thinks a lot of scientists are not doing creative work in the first place, including most of the people making extensive use of AI. So if anything he’s happy to see them go, and only pissed that they’re sucking up resources and attention on the way out, and discouraging students who could be joining the parts of the field that do real creative work.

It made me realize that there are two axes to thinking about AI in physics.

On the one hand, there’s where you think AI capabilities are. Is AI going to lead to “a nation of geniuses in a data center”, an AI-powered super-(cyber-)Ed Witten for everything and everyone? Is AI great at routine work and coding, but will never be able to do anything really creative or novel? Or is AI total hype, almost always a waste of time?

On the other hand, there’s another axis: misanthropy about science. For some of the people arguing about AI online, most scientists are good people trying their best to do worthwhile things. For others, most scientists are complacent and cliquish, wasting time and money on ideas that are going nowhere and forcing the real geniuses out of the field.

Put those together, and you get the table below:

Thinks academia is mostly fineMisanthrope
AI geniuses are comingThe practice of science will change. We’ll play at science like chess, and have fun trying to read and understand amazing AI insights.Soon all scientists will be out of a job when the public notices AI can do it all better. Then the real breakthroughs will come.
AI can do routine workAI frees scientists to focus on what we do best: creativity. We should think carefully about how to train junior scientists now, though.AI is comparable to bad scientists who only do derivative work. If they leave, we real paradigm-changers could inherit the field.
AI is complete hypeMost scientists don’t use AI. AI is worrying because it misleads students and the public, who should listen to real scientists.Scientists are shilling for AI companies, as you should expect for people who waste the public’s money on reputation games.

This classification is missing a lot, of course. One important question is not just what AI can do in principle, but what it can do cost-effectively, and whether anyone is actually willing to pay for it. A point where I agree with stringking42069 is that companies get a lot of good PR out of building AI physicists right now, and that PR benefit won’t be relevant forever. I’m also leaving out the more general questions of AI’s effect on society, for example people who think AI geniuses will lead to the end of the world as we know it.

But I suspect if you look at this table, you can already start matching the scientists you see on social media. I’ve seen examples of all of these in the wild (though the bottom-left is somewhat rare, as far as I can tell). Where do you fall?

Should You Read What You Cite? That Depends

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When arXiv announced it would ban people for hallucinated citations, that is citations of papers that don’t exist, the discussion online got sidetracked by the question of whether academics actually read the papers they cite. Some people proudly insisted that any good scholar always reads every paper they reference, others argued that was ridiculous.

As always, the answer is never that simple. In certain fields, it is enormously important to read the papers you cite if you want to do solid, careful, scholarly work. In others, it’s entirely irrelevant.

It mostly comes down to what citations are for. And luckily, I’ve already written a post about that.

So let’s go through the citation motivations I mention in that post.

First, some citations are about respecting priority, feeding the system by which academics get credit for having an idea first. The incentive system of academia depends on getting this more or less right, but that doesn’t mean every academic has to check things at every step of the way. Besides, if you get this wrong, you’ll find out quickly. Submit a paper to a preprint server like arXiv, and you’ll be sure to get emails telling you that some obscure Soviet researcher figured it all out first.

Other citations are about substantiating claims. These are the most important to get right. Here, you really ought to have read, if not the whole paper, at least the full justification for the claim you’re making. You can have some leeway if the methods are unfamiliar enough, for example a complicated experiment you can’t understand all the details of. Science and technology do require some trust. But you should have at least a sense of where things could go wrong, and why.

Citations to provide context are a different beast. Here, you’re trying to tell a reader where your ideas come from. You can’t show them the conversations you have with your colleagues, the things they value and get you excited about. So you have to show them papers instead. But the papers aren’t the thing you read, they’re just a convenient proxy.

Finally, citations do sometimes just exist to follow social conventions. And yeah, you don’t have to read these, just like you don’t have to say how you’re doing when someone asks you how you’re doing. They’re the academic equivalent of social white lies, and should be taken roughly as seriously, both by their supporters and detractors.

Doing Things Well Is an International Activity

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In the US, funding agencies seem to be increasingly opposed to an often inevitable feature of good science: international collaboration. Scientists have been told by officials at the National Institutes of Health that they need to remove mention of foreign collaborators from progress reports, or that they need to avoid such collaborations to begin with. At NASA, officials have told scientists that rather than just avoiding funding work in China, they should actively avoid collaborating with Chinese researchers. And a recently introduced bill would make that restriction more explicit.

I have a general policy against discussing concrete political issues on this blog, so I’m not going to dig into the details of who’s doing what here, how far it’s going or how novel it is. That policy extends to the comments. If you mention specific laws, politicians, or political parties, I will delete your comment.

I do want to say something more general, though. I think people often underestimate just how important international collaboration is.

I’ve talked before about how scientific specialization spreads scientists around the world. Scientists want to work with people who work on their specific interests, and there are often only a few people that fit that description. So people move across the world, creating centers of expertise.

More than that, though, essentially any activity, done well, is done internationally. The better you want to perform, the more likely it is that the best collaborator will be someone in another country.

People don’t notice this as much as they could, because they’re used to the exceptions. Popular art is often siloed by language and cultural references. Sports are intentionally set up as competitions between regions and nations, and militaries compete as a practical necessity. But without those exceptions, international competition wins out. The best doctor, the best classical musician, and the best businessperson for a job can’t be expected to come from one country or another. Those fields, like science, are international.

When that internationalism is weak, it’s a warning sign. Without that drive to succeed on an international stage, scientists get lazy. There are countries with a history of academic cronyism, where universities were run more on interpersonal politics than scholarly merit, cozy fiefdoms where prominent academics dole out positions. To combat this, policymakers work to make their research systems more international. They explicitly ask about international collaborations and participation in international conferences in grant applications, not to discourage them, but to encourage them: to reward academics who show merit on the international stage and break up lazy patronage networks.

It worries me that it sounds like some US policymakers want to do the opposite. People are increasingly worried about bias and groupthink in the sciences, and increasingly mad that scientists could be wasting the public’s money to maintain a cushy lifestyle. International collaboration is how you hold scientists to account, how you force them to compete and show their merit. If you drop that, academia is going to get a whole lot worse.

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?

Make No Mistakes

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I’m taking a Danish exam next week, and it’s a big one, a culmination of years learning the language. My classmates are stressed. Despite how much we’ve learned, it feels like we’re always making little mistakes. We write the wrong prepositions, put verbs in the wrong form, or mess up the order of words in a sentence. And while we should have time to check our work, that doesn’t help as much as it should. If we don’t notice a mistake the first time around, what guarantee is there that we notice it on the next read, or the next? Too many checks and we can even end up second-guessing ourselves, “correcting” something that was right to begin with.

It’s given me some sympathy for AI.

Earlier this month, investor Marc Andreessen posted a custom prompt he inputs when using AI, which was immediately mocked.

The silliest instruction, according to many critics, was to “Never hallucinate or make anything up.” It’s similar to a prompt that’s become a meme used to make fun of AI-using “vibe coders”, “Make no mistakes”.

Experts point out that this is just not how AI works. Large language model-powered programs like ChatGPT are inherently random, producing text largely based on its similarity to other text. “Hallucinations” or “mistakes” are an inevitable feature of the technology, and a prompt like Andreessen wrote isn’t a set of instructions the AI will follow without error: it’s just another part of the text the AI is trying to generate.

All that said, telling an AI to “make no mistakes” should have some effect. But it likely won’t be what you want.

The best way I’ve found to understand AI is in terms of stories. Chatbots like ChatGPT take a large language model, a mathematical formula for how words are most likely to appear in a text, and warp it, twisting it to almost always produce one particular kind of text: one half of a dialogue with a fictional AI assistant. This twisted formula determines how the AI responds to your prompts, but these days it also is used behind the scenes, in a kind of structured soliloquy called a “chain of thought”. You can think of the prompts you send to the AI as a preface to those soliloquies, and imagine the AI telling stories of a sort that would typically follow that preface.

So if you tell an AI “make no mistakes” or “do not hallucinate”, you’re making it more likely to generate the kind of story that begins, “the AI was instructed to make no mistakes”.

Let me put it this way, Mr. Amor. The 9000 series is the most reliable computer ever made. No 9000 computer has ever made a mistake or distorted information. We are all, by any practical definition of the words, foolproof and incapable of error. – HAL 9000, “2001: A Space Odyssey”

You’d expect this to affect the chain of thought. For example, the AI might occasionally pause to say “I’m supposed to make no mistakes, so I should check this. What could have gone wrong?” and then list something that plausibly could be wrong with its idea. If this happens often enough, you’ll probably catch some real problems.

But I’m reminded of my classmates, practicing for that Danish exam. We can go over the text again and again, asking if this thing, or that, might be wrong. We can try again and again to use our mental model of the Danish language, seeing if this time it catches a new mistake. But there are things we won’t catch. And if we do it too much, we’ll second-guess ourselves out of the good answers, too.

Ultimately, “make no mistakes” isn’t a great instruction, either for humans or for chatbots. And its use by people like Marc Andreessen has me wondering if they are used to interacting with humans in the same way, as tools that keep making mistakes no matter how many times they’re instructed not to, requiring more and more long-winded instructions and yet continuing to misbehave.

Then again, that may be a mistake on my part.

Bonus Info for “100-year-old assumption about the universe may soon be overturned”

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I had a piece up in New Scientist last week (paywalled, sorry!), about a new analysis that suggests the universe is less homogeneous (more “lumpy”) that most cosmologists believe.

The piece was a bit different than my usual. Normally I do what people in the biz call “features”: longer articles about general trends. This was a much more classic “news piece”. The people I interviewed had several papers up in early April, the editors at New Scientist thought they were interesting enough to write about, so I was asked for a short, timely piece with the key takeaways.

That means I didn’t have a ton of space for background info. So if you’d like to know more, this post is for you!

The 100-year old assumption in the title refers to the Friedmann–Lemaître–Robertson–Walker (or FLRW) universe, an idea that first came together in the 1920’s, where cosmologists model the universe as homogeneous and isotropic: the same no matter where, or in which direction, you look. That sounds like a crazy assumption, but on the largest scales we can measure it’s actually mostly fine. Once you’re trying to calculate ripples in the cosmic microwave background or find out how fast distant galaxies are accelerating away, it works surprisingly well to act like the universe is an evenly-mixed soup of matter, radiation, dark matter, and dark energy.

But every assumption in physics has its doubters. The doubters of homogeneity are known as inhomogeneous cosmologists, and I’ve been sympathetic to their complaints for a while now.

I even let an inhomogeneous cosmologist do a guest post on my blog, back in 2019. That post argued something dramatic: that dark energy may not even exist, but that measurements of accelerating expansion may be a consequence of a dramatic lopsidedness in the universe around us.

The people I covered in New Scientist, Asta Heinesen, Tim Clifton, and Sofie Marie Koksbang, are arguing something much less dramatic…but that’s part of what makes it more compelling. Instead of arguing that the universe is dramatically uneven or lopsided, they’re arguing that the universe can still be on average smooth and homogeneous, the soup of galaxies people seem to expect…but still, can’t be fully modeled that way.

This is a tricky distinction to explain, and certainly something I didn’t have space to cover well enough in New Scientist. But let me take a stab at it here:

Any cosmologist will agree that FLRW can’t be the whole story. We know the universe isn’t a perfectly mixed soup: there are galaxies, and stars, and black holes, and they all wiggle the fabric of the universe in different places. When they study the universe as a whole, they’re averaging out all of that, to get the overall behavior, a bit like you could average the number of children in each family to get the average children per family in a country.

But FLRW isn’t just an average, it’s a model of spacetime. Because of that, it has to obey certain equations, called Einstein’s equations. It has to make sense by itself, as the correct answer for how spacetime would behave if it were filled with a uniform soup.

That’s an extra restriction, and that extra restriction can get you in trouble. To continue with the analogy, any real family has a whole number of children. But the average family doesn’t have a whole number of children. When I was born, the average family in the US had around 2.5 children. A lot of cartoons imagined what the half-child looked like.

From the perspective of Heinesen, Clifton, and Koksbang, assuming FLRW is a bit like assuming that the average family must have two children, or three, and can’t possibly have 2.5. Averages don’t have to look like sensible spacetimes, they don’t have to obey the Einstein equations.

In practice, the assumption of FLRW has worked a lot better than assuming that the average family can’t have 2.5 children, and that’s why Heinesen, Clifton, and Koksbang are cautious. They’re not claiming that inhomogeneity can explain everything, all the way to major components of the universe like dark energy. But they do think it can be a good explanation for smaller effects. And as cosmologists worry about smaller and smaller effects, wondering if dark energy changes over time and why the expansion rate of the universe doesn’t match up between different measurements, it can be important to remember that averages aren’t all-powerful. Eventually, they can break down. It’s a more subtle issue than a fractional child. But, as I covered in New Scientist, it may already be happening.

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.