Tag Archives: particle physics

Reminder to Physics Popularizers: “Discover” Is a Technical Term

C. N. Yang, Dead at 103

I don’t usually do obituaries here, but sometimes I have something worth saying.

Chen Ning Yang, a towering figure in particle physics, died last week.

Picture from 1957, when he received his Nobel

I never met him. By the time I started my PhD at Stony Brook, Yang was long-retired, and hadn’t visited the Yang Institute for Theoretical Physics in quite some time.

(Though there was still an office door, tucked behind the institute’s admin staff, that bore his name.)

The Nobel Prize doesn’t always honor the most important theoretical physicists. In order to get a Nobel Prize, you need to discover something that gets confirmed by experiment. Generally, it has to be a very crisp, clear statement about reality. New calculation methods and broader new understandings are on shakier ground, and theorists who propose them tend to be left out, or at best combined together into lists of partial prizes long after the fact.

Yang was lucky. With T. D. Lee, he had made that crisp, clear statement. He claimed that the laws of physics, counter to everyone’s expectations, are not the same when reflected in a mirror. In 1956, Wu confirmed the prediction, and Lee and Yang got the prize the year after.

That’s a huge, fundamental discovery about the natural world. But as a theorist, I don’t think that was Yang’s greatest accomplishment.

Yang contributed to other fields. Practicing theorists have seen his name strewn across concepts, formalisms, and theorems. I didn’t have space to talk about him in my article on integrability for Quanta Magazine, but only just barely: another paragraph or two, and he would have been there.

But his most influential contribution is something even more fundamental. And long-time readers of this blog should already know what it is.

Yang, along with Robert Mills, proposed Yang-Mills Theory.

There isn’t a Nobel prize for Yang-Mills theory. In 1953, when Yang and Mills proposed the theory, it was obviously wrong, a theory that couldn’t explain anything in the natural world, mercilessly mocked by famous bullshit opponent Wolfgang Pauli. Not even an ambitious idea that seemed outlandish (like plate tectonics), it was a theory with such an obvious missing piece that, for someone who prioritized experiment like the Nobel committee does, it seemed pointless to consider.

All it had going for it was that it was a clear generalization, an obvious next step. If there are forces like electromagnetism, with one type of charge going from plus to minus, why not a theory with multiple, interacting types of charge?

Nothing about Yang-Mills theory was impossible, or contradictory. Mathematically, it was fine. It obeyed all the rules of quantum mechanics. It simply didn’t appear to match anything in the real world.

But, as theorists learn, nature doesn’t let a good idea go to waste.

Of the four fundamental forces of nature, as it would happen, half are Yang-Mills theories. Gravity is different, electromagnetism is simpler, and could be understood without Yang and Mills’ insights. But the weak nuclear force, that’s a Yang-Mills theory. It wasn’t obvious in 1953 because it wasn’t clear how the massless, photon-like particles in Yang-Mills theory could have mass, and it wouldn’t become clear until the work of Peter Higgs over a decade later. And the strong nuclear force, that’s also a Yang-Mills theory, missed because of the ability of such a strong force to “confine” charges, hiding them away.

So Yang got a Nobel, not for understanding half of nature’s forces before anyone else had, but from a quirky question of symmetry.

In practice, Yang was known for all of this, and more. He was enormously influential. I’ve heard it claimed that he personally kept China from investing in a new particle collider, the strength of his reputation the most powerful force on that side of the debate, as he argued that a developing country like China should be investing in science with more short-term industrial impact, like condensed matter and atomic physics. I wonder if the debate will shift with his death, and what commitments the next Chinese five-year plan will make.

Ultimately, Yang is an example of what a theorist can be, a mix of solid work, counterintuitive realizations, and the thought-through generalizations that nature always seems to make use of in the end. If you’re not clear on what a theoretical physicist is, or what one can do, let Yang’s story be your guide.

The Rocks in the Ground Era of Fundamental Physics

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It’s no secret that the early twentieth century was a great time to make progress in fundamental physics. On one level, it was an era when huge swaths of our understanding of the world were being rewritten, with relativity and quantum mechanics just being explored. It was a time when a bright student could guide the emergence of whole new branches of scholarship, and recently discovered physical laws could influence world events on a massive scale.

Put that way, it sounds like it was a time of low-hanging fruit, the early days of a field when great strides can be made before the easy problems are all solved and only the hard ones are left. And that’s part of it, certainly: the fields sprung from that era have gotten more complex and challenging over time, requiring more specialized knowledge to make any kind of progress. But there is also a physical reason why physicists had such an enormous impact back then.

The early twentieth century was the last time that you could dig up a rock out of the ground, do some chemistry, and end up with a discovery about the fundamental laws of physics.

When scientists like Curie and Becquerel were working with uranium, they didn’t yet understand the nature of atoms. The distinctions between elements were described in qualitative terms, but only just beginning to be physically understood. That meant that a weird object in nature, “a weird rock”, could do quite a lot of interesting things.

And once you find a rock that does something physically unexpected, you can scale up. From the chemistry experiments of a single scientist’s lab, countries can build industrial processes to multiply the effect. Nuclear power and the bomb were such radical changes because they represented the end effect of understanding the nature of atoms, and atoms are something people could build factories to manipulate.

Scientists went on to push that understanding further. They wanted to know what the smallest pieces of matter were composed of, to learn the laws behind the most fundamental laws they knew. And with relativity and quantum mechanics, they could begin to do so systematically.

US particle physics has a nice bit of branding. They talk about three frontiers: the Energy Frontier, the Intensity Frontier, and the Cosmic Frontier.

Some things we can’t yet test in physics are gated by energy. If we haven’t discovered a particle, it may be because it’s unstable, decaying quickly into lighter particles so we can’t observe it in everyday life. If these particles interact appreciably with particles of everyday matter like protons and electrons, then we can try to make them in particle colliders. These end up creating pretty much everything up to a certain mass, due to a combination of the tendency in quantum mechanics for everything that can happen to happen, and relativity’s $E=mc^2$ . In the mid-20th century these particle colliders were serious pieces of machinery, but still small enough to make industrial: now, there are so-called medical accelerators in many hospitals based on their designs. But current particle accelerators are a different beast, massive facilities built by international collaborations. This is the Energy Frontier.

Some things in physics are gated by how rare they are. Some particles interact only very faintly with other particles, so to detect them, physicists have to scan a huge chunk of matter, a giant tank of argon or a kilometer of antarctic ice, looking for deviations from the norm. Over time, these experiments have gotten bigger, looking for more and more subtle effects. A few weird ones still fit on tabletops, but only because they have the tools to measure incredibly small variations. Most are gigantic. This is the Intensity Frontier.

Finally, the Cosmic Frontier looks for the unknown behind both kinds of gates, using the wider universe to look at events with extremely high energy or size.

Pushing these frontiers has meant cleaning up our understanding of the fundamental laws of physics up to these frontiers. It means that whatever is still hiding, it either requires huge amounts of energy to produce, or is an extremely rare, subtle effect.

That means that you shouldn’t expect another nuclear bomb out of fundamental physics. Physics experiments are already working on vast scales, to the extent that a secret government project would have to be smaller than publicly known experiments, in physical size, energy use, and budget. And you shouldn’t expect another nuclear power plant, either: we’ve long passed the kinds of things you could devise a clever industrial process to take advantage of at scale.

Instead, new fundamental physics will only be directly useful once we’re the kind of civilization that operates on a much greater scale than we do today. That means larger than the solar system: there wouldn’t be much advantage, at this point, of putting a particle physics experiment on the edge of the Sun. It means the kind of civilization that tosses galaxies around.

It means that right now, you won’t see militaries or companies pushing the frontiers of fundamental physics, unlike the way they might have wanted to at the dawn of the twentieth century. By the time fundamental physics is useful in that way, all of these actors will likely be radically different: companies, governments, and in all likelihood human beings themselves. Instead, supporting fundamental physics right now is an act of philanthropy, maintaining a practice because it maintains good habits of thought and produces powerful ideas, the same reasons organizations support mathematics or poetry. That’s not nothing, and fundamental physics is still often affordable as philanthropy goes. But it’s not changing the world, not the way physicists did in the early twentieth century.

Some Dumb AI Ideas

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Sometimes, when I write a post about AI, I’ve been sitting on an idea for a long time. I’ve talked to experts, I’ve tried to understand the math, I’ve honed my points and cleared away clutter.

This is not one of those times. The ideas in this post almost certainly have something deeply wrong with them. But hopefully they’re interesting food for thought.

My first dumb idea: instruction tuning was a mistake.

I’m drawing the seeds of this one from a tumblr post by nostalgebraist, someone known for making a popular bot trained on his tumblr posts in the early days before GPT became ChatGPT.

AIs like ChatGPT are based on Large Language Models, insanely complicated mathematical formulas that predict, given part of a text, what the rest of that text is likely to look like. In the early days, this was largely how they were used. Loosely described nostalgebraist’s bot, called nostalgebraist-autoresponder, began with a list of tumblr posts and asks and determines what additional posts would best fit in.

If you think about it, though, ChatGPT doesn’t really work like that. ChatGPT has conversations: you send it messages, it sends you responses. The text it creates is a dialogue, with you supplying half the input. But most texts aren’t dialogues, and ChatGPT draws on a lot of non-dialogue texts to make its dialogue-like responses.

The reason it does this is something called instruction tuning. ChatGPT has been intentionally biased, not to give the most likely completion to a task in general, but to give completions that fit this dialogue genre. What I didn’t know until I read nostalgebraist’s post was that this genre was defined artificially: AI researchers made up fake dialogues with AI, cheesy sci-fi conversations imagining how an AI might respond to instructions from a user, and then biased the Large Language Model so that rather than giving the most likely text in general, it gives a text that is more likely to look like these cheesy sci-fi conversations. It’s why ChatGPT sounds kind of like a fictional robot: not because sci-fi writers accurately predicted what AI would sound like, but because AI was created based on sci-fi texts.

For nostalgebraist, this leads into an interesting reflection of how a sci-fi AI should behave, how being warped around a made-up genre without history or depth creates characters which act according to simple narratives and express surprising anxiety.

For myself, though, I can’t help but wonder if the goal of dialogue itself is the problem. Dialogue is clearly important commercially: people use ChatGPT because they can chat with it. But Large Language Models aren’t inherently chatbots: they produce plausible texts, of any sort you could imagine. People seem to want a machine that can, for example, answer scientific questions as part of a conversation. But most competent answers to scientific questions aren’t conversations, they’re papers. If people stuck with the “raw” model, producing excerpts of nonexistent papers rather than imitating a dialogue with a non-existent expert, wouldn’t you expect the answers to be more accurate, with the model no longer biased by an irrelevant goal? Is the need to make a sell-able chatbot making these AIs worse at everything else people are trying to use them for?

I’m imagining a world where, instead of a chatbot, OpenAI built an “alternate universe simulator”. You give it some context, some texts or parts of texts from a universe you made up, and it completes them in a plausible way. By imagining different universes, you can use it to answer different questions. Such a gimmick would get fewer customers, and fewer investors, it would probably do worse. But I have to wonder if the actual technology might have been more useful.

My second idea is dumber, to the point where I mostly know why it doesn’t work. But thinking about it might help clarify how things work for people unused to AI.

I saw someone point out that, unlike something like Wikipedia, AI doesn’t give you context. You shouldn’t trust Wikipedia, or a source you find on Google, blindly. If you want to, you can look through the edit history on Wikipedia, or figure out who wrote a page you found on Google and how. If ChatGPT tells you something, by default you don’t know where that knowledge came from. You can tell it to search, and then you’ll get links, but that’s because it’s using Google or the like behind the scenes anyway. You don’t know where the model is getting its ideas.

Why couldn’t we get that context, though?

Every text produced by a Large Language Model is causally dependent on its training data. Different data, different model, different text. That doesn’t mean that each text draws from one source, or just a few sources: ChatGPT isn’t copying the training data, at least not so literally.

But it does mean that, if ChatGPT says something is true, you should in principle be able to ask which data was most important in making it say that. If you leave a piece of data out of the training, and get similar answers, you can infer that the response you got doesn’t have much to do with that piece of data. But if you leave out a text in training, and now ChatGPT gives totally different responses to the same question…then there’s a pretty meaningful sense that it got the information from that source.

If this were the type of non-AI statistical model people use in physics, this would be straightforward. Researchers do this all the time: take one experiment out of the data, see how their analysis changes, and thereby figure out which experiments are most important to check. One can even sometimes calculate, given a model, where you should look.

Unfortunately, you can’t do this with ChatGPT. The model is just too big. You can’t calculate anything explicitly about it, the giant mathematical formulas behind it are so complicated that the most you can do is get probabilities out case by case, you can’t “unwind” them and see where the numbers come from. And you can’t just take out sources one by one, and train the model again: not when training takes months of expensive computer time.

So unlike with the previous idea, I understand even on a technical level why you can’t do this. But it helped me to be able to think about what I would like to do, if it were possible. Maybe it helps you too!

Did the South Pole Telescope Just Rule Out Neutrino Masses? Not Exactly, Followed by My Speculations

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Recently, the South Pole Telescope’s SPT-3G collaboration released new measurements of the cosmic microwave background, the leftover light from the formation of the first atoms. By measuring this light, cosmologists can infer the early universe’s “shape”: how it rippled on different scales as it expanded into the universe we know today. They compare this shape to mathematical models, equations and simulations which tie together everything we know about gravity and matter, and try to see what it implies for those models’ biggest unknowns.

Some of the most interesting such unknowns are neutrino masses. We know that neutrinos have mass because they transform as they move, from one type of neutrino to another. Those transformations let physicists measure the differences between neutrino masses, but but themselves, they don’t say what the actual masses are. All we know from particle physics, at this point, is a minimum: in order for the neutrinos to differ in mass enough to transform in the way they do, the total mass of the three flavors of neutrino must be at least 0.06 electron-Volts.

(Divided by the speed of light squared to get the right units, if you’re picky about that sort of thing. Physicists aren’t.)

Neutrinos also influenced the early universe, shaping it in a noticeably different way than heavier particles that bind together into atoms, like electrons and protons, did. That effect, observed in the cosmic microwave background and in the distribution of galaxies in the universe today, lets cosmologists calculate a maximum: if neutrinos are more massive than a certain threshold, they could not have the effects cosmologists observe.

Over time as measurements improved, this maximum has decreased. Now, the South Pole Telescope has added more data to the pool, and combining it with prior measurements…well, I’ll quote their paper:

Ok, it’s probably pretty hard to understand what that means if you’re not a physicist. To explain:

There are two different hypotheses for how neutrino masses work, called “hierarchies”. In the “normal” hierarchy, the neutrinos go in the same order as the particles they interact with with the weak nuclear force: electron-neutrinos are lighter than muon neutrinos, which are lighter than tau neutrinos. In the “inverted” hierarchy, they come in the opposite order, and the electron neutrino is the heaviest. Both of these are consistent with the particle-physics data.
Confidence is a statistics thing, which could take a lot of unpacking to define correctly. To give a short but likely tortured-sounding explanation: when you rule out a hypothesis with a certain confidence level, you’re saying that, if that hypothesis was true, there would only be a 100%-minus-that-chance chance that you would see what you actually observed.

So, what are the folks at the South Pole Telescope saying? They’re saying that if you put all the evidence together (that’s roughly what that pile of acroynms at the beginning means), then the result would be incredibly uncharacteristic for either hypothesis for neutrino masses. If you had “normal” neutrino masses, you’d only see these cosmological observations 2.1% of the time. And if you had inverted neutrino masses instead, you’d only see these observations 0.01% of the time!

That sure makes it sound like neither hypothesis is correct, right? Does it actually mean that?

I mean, it could! But I don’t think so. Here I’ll start speculating on the possibilities, from least likely in my opinion to most likely. This is mostly my bias talking, and shouldn’t be taken too seriously.

5. Neutrinos are actually massless

This one is really unlikely. The evidence from particle physics isn’t just quantitative, but qualitative. I don’t know if it’s possible to write down a model that reproduces the results of neutrino oscillation experiments without massive neutrinos, and if it is it would be a very bizarre model that would almost certainly break something else. This is essentially a non-starter.

4. This is a sign of interesting new physics

I mean, it would be nice, right? I’m sure there are many proposals at this point, tweaks that add a few extra fields with some hard-to-notice effects to explain the inconsistency. I can’t rule this out, and unlike the last point there isn’t anything about it that seems impossible. But we’ve had a lot of odd observations, and so far this hasn’t happened.

3. Someone did statistics wrong

This happens more often. Any argument like this is a statistical argument, and while physicists keep getting better at statistics, they’re not professional statisticians. Sometimes there’s a genuine misunderstanding that goes in to testing a model, and once it gets resolved the problem goes away.

2. The issue will go away with more data

The problem could also just…go away. 97.9% confidence sounds huge…but in physics, the standards are higher: you need 99.99994% to announce a new discovery. Physicists do a lot of experiments and observations, and sometimes, they see weird things! As the measurements get more precise, we may well see the disagreement melt away, and cosmology and particle physics both point to the same range for neutrino masses. It’s happened to many other measurements before.

1. We’re reaching the limits of our current approach to cosmology

This is probably not actually the most likely possibility, but it’s my list, what are you going to do?

There are basic assumptions behind how most theoretical physicists do cosmology. These assumptions are reasonably plausible, and seem to be needed to do anything at all. But they can be relaxed. Our universe looks like it’s homogeneous on the largest scales: the same density on average, in every direction you look. But the way that gets enforced in the mathematical models is very direct, and it may be that a different, more indirect, approach has more flexibility. I’ll probably be writing about this more in future, hopefully somewhere journalistic. But there are some very cool ideas floating around, gradually getting fleshed out more and more. It may be that the answer to many of the mysteries of cosmology right now is not new physics, but new mathematics: a new approach to modeling the universe.

Bonus Info on the LHC and Beyond

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Three of my science journalism pieces went up last week!

(This is a total coincidence. One piece was a general explainer “held in reserve” for a nice slot in the schedule, one was a piece I drafted in February, while the third I worked on in May. In journalism, things take as long as they take.)

The shortest piece, at Quanta Magazine, was an explainer about the two types of particles in physics: bosons, and fermions.

I don’t have a ton of bonus info here, because of how tidy the topic is, so just two quick observations.

First, I have the vague impression that Bose, bosons’ namesake, is “claimed” by both modern-day Bangladesh and India. I had friends in grad school who were proud of their fellow physicist from Bangladesh, but while he did his most famous work in Dhaka, he was born and died in Calcutta. Since both were under British India for most of his life, these things likely get complicated.

Second, at the end of the piece I mention a “world on a wire” where fermions and bosons are the same. One example of such a “wire” is a string, like in string theory. One thing all young string theorists learn is “bosonization”: the idea that, in a 1+1-dimensional world like a string, you can re-write any theory with fermions as a theory with bosons, as well as vice versa. This has important implications for how string theory is set up.

Next, in Ars Technica, I had a piece about how LHC physicists are using machine learning to untangle the implications of quantum interference.

As a journalist, it’s really easy to fall into a trap where you give the main person you interview too much credit: after all, you’re approaching the story from their perspective. I tried to be cautious about this, only to be stymied when literally everyone else I interviewed praised Aishik Ghosh to the skies and credited him with being the core motivating force behind the project. So I shrugged my shoulders and followed suit. My understanding is that he has been appropriately rewarded and will soon be a professor at Georgia Tech.

I didn’t list the inventors of the NSBI method that Ghosh and co. used, but names like Kyle Cranmer and Johann Brehmer tend to get bandied about. It’s a method that was originally explored for a more general goal, trying to characterize what the Standard Model might be missing, while the work I talk about in the piece takes it in a new direction, closer to the typical things the ATLAS collaboration looks for.

I also did not say nearly as much as I was tempted to about how the ATLAS collaboration publishes papers, which was honestly one of the most intriguing parts of the story for me. There is a huge amount of review that goes on inside ATLAS before one of their papers reaches the outside world, way more than there ever is in a journal’s peer review process. This is especially true for “physics papers”, where ATLAS is announcing a new conclusion about the physical world, as ATLAS’s reputation stands on those conclusions being reliable. That means starting with an “internal note” that’s hundreds of pages long (and sometimes over a thousand), an editorial board that manages the editing process, disseminating the paper to the entire collaboration for comment, and getting specific experts and institute groups within the collaboration to read through the paper in detail. The process is a bit less onerous for “technical papers”, which describe a new method, not a new conclusion about the world. Still, it’s cumbersome enough that for those papers, often scientists don’t publish them “within ATLAS” at all, instead releasing them independently. The results I reported on are special because they involved a physics paper and a technical paper, both within the ATLAS collaboration process. Instead of just working with partial or simplified data, they wanted to demonstrate the method on a “full analysis”, with all the computation and human coordination that requires. Normally, ATLAS wouldn’t go through the whole process of publishing a physics paper without basing it on new data, but this was different: the method had the potential to be so powerful that the more precise results would be worth stating as physics results alone.

(Also, for the people in the comments worried about training a model on old data: that’s not what they did. In physics, they don’t try to train a neural network model to predict the results of colliders, such a model wouldn’t tell us anything useful. They run colliders to tell us whether what they see matches the analytic, Standard, model. The neural network is trained to predict not what the experiment will say, but what the Standard Model will say, as we can usually only figure that out through time-consuming simulations. So it’s trained on (new) simulations, not on experimental data.)

Finally, on Friday I had a piece in Physics Today about the European Strategy for Particle Physics (or ESPP), and in particular, plans for the next big collider.

Before I even started working on this piece, I saw a thread by Patrick Koppenburg on some of the 263 documents submitted for the ESPP update. While my piece ended up mostly focused on the big circular collider plan that most of the field is converging on (the future circular collider, or FCC), Koppenburg’s thread was more wide-ranging, meant to illustrate the breadth of ideas under discussion. Some of that discussion is about the LHC’s current plans, like its “high-luminosity” upgrade that will see it gather data at much higher rates up until 2040. Some of it is assessing broader concerns, which it may surprise some of you to learn includes sustainability: yes, there are more or less sustainable ways to build giant colliders.

The most fun part of the discussion, though, concerns all of the other collider proposals.

Some report progress on new technologies. Muon colliders are the most famous of these, but there are other proposals that would specifically help with a linear collider. I never did end up understanding what Cooled Copper Colliders are all about, beyond that they let you get more energy in a smaller machine without super-cooling. If you know about them, chime in in the comments! Meanwhile, plasma wakefield acceleration could accelerate electrons on a wave of plasma. This has the disadvantage that you want to collide electrons and positrons, and if you try to stick a positron in plasma it will happily annihilate with the first electron it meets. So what do you do? You go half-and-half, with the HALHF project: speed up the electron with a plasma wakefield, accelerate the positron normally, and have them meet in the middle.

Others are backup plans, or “budget options”, where CERN could get a bit better measurements on some parameters if they can’t stir up the funding to measure the things they really want. They could put electrons and positrons into the LHC tunnel instead of building a new one, for a weaker machine that could still study the Higgs boson to some extent. They could use a similar experiment to produce Z bosons instead, which could serve as a bridge to a different collider project. Or, they could collider the LHC’s proton beam with an electron beam, for an experiment that mixes advantages and disadvantages of some of the other approaches.

While working on the piece, one resource I found invaluable was this colloquium talk by Tristan du Pree, where he goes through the 263 submissions and digs up a lot of interesting numbers and commentary. Read the slides for quotes from the different national inputs and “solo inputs” with comments from particular senior scientists. I used that talk to get a broad impression of what the community was feeling, and it was interesting how well it was reflected in the people I interviewed. The physicist based in Switzerland felt the most urgency for the FCC plan, while the Dutch sources were more cautious, with other Europeans firmly in the middle.

Going over the FCC report itself, one thing I decided to leave out of the discussion was the cost-benefit analysis. There’s the potential for a cute sound-bite there, “see, the collider is net positive!”, but I’m pretty skeptical of the kind of analysis they’re doing there, even if it is standard practice for government projects. Between the biggest benefits listed being industrial benefits to suppliers and early-career researcher training (is a collider unusually good for either of those things, compared to other ways we spend money?) and the fact that about 10% of the benefit is the science itself (where could one possibly get a number like that?), it feels like whatever reasoning is behind this is probably the kind of thing that makes rigor-minded economists wince. I wasn’t able to track down the full calculation though, so I really don’t know, maybe this makes more sense than it looks.

I think a stronger argument than anything along those lines is a much more basic point, about expertise. Right now, we have a community of people trying to do something that is not merely difficult, but fundamental. This isn’t like sending people to space, where many of the engineering concerns will go away when we can send robots instead. This is fundamental engineering progress in how to manipulate the forces of nature (extremely powerful magnets, high voltages) and process huge streams of data. Pushing those technologies to the limit seems like it’s going to be relevant, almost no matter what we end up doing. That’s still not putting the science first and foremost, but it feels a bit closer to an honest appraisal of what good projects like this do for the world.

Why Solving the Muon Puzzle Doesn’t Solve the Puzzle

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You may have heard that the muon g-2 problem has been solved.

Muons are electrons’ heavier cousins. As spinning charged particles, they are magnetic, the strength of that magnetism characterized by a number denoted “g”. If you were to guess this number from classical physics alone, you’d conclude it should be 2, but quantum mechanics tweaks it. The leftover part, “g-2”, can be measured, and predicted, with extraordinary precision, which ought to make it an ideal test: if our current understanding of the particle physics, called the Standard Model, is subtly wrong, the difference might be noticeable there.

And for a while, it looked like such a difference was indeed noticeable. Extremely precise experiments over the last thirty years have consistently found a number slightly different from the extremely precise calculations, different enough that it seemed quite unlikely to be due to chance.

Now, the headlines are singing a different tune.

What changed?

That headline might make you think the change was an experimental result, a new measurement that changed the story. It wasn’t, though. There is a new, more precise measurement, but it agrees with the old measurements.

So the change has to be in the calculations, right? They did a new calculation, corrected a mistake or just pushed up their precision, and found that the Standard Model matches the experiment after all?

…sort of, but again, not really. The group of theoretical physicists associated with the experiment did release new, more accurate calculations. But it wasn’t the new calculations, by themselves, that made a difference. Instead, it was a shift in what kind of calculations they used…or even more specifically, what kind of calculations they trusted.

Parts of the calculation of g-2 can be done with Feynman diagrams, those photogenic squiggles you see on physicists’ blackboards. That part is very precise, and not especially controversial. However, Feynman diagrams only work well when forces between particles are comparatively weak. They’re great for electromagnetism, even better for the weak nuclear force. But for the strong nuclear force, the one that holds protons and neutrons together, you often need a different method.

For g-2, that used to be done via a “data-driven” method. Physicists measured different things, particles affected by the strong nuclear force in different ways, and used that to infer how the strong force would affect g-2. By getting a consistent picture from different experiments, they were reasonably confident that they had the right numbers.

Back in 2020, though, a challenger came to the scene, with another method. Called lattice QCD, this method involves building gigantic computer simulations of the effect of the strong force. People have been doing lattice QCD since the 1970’s, and the simulations have been getting better and better, until in 2020, a group managed to calculate the piece of the g-2 calculation that had until then been done by the data-driven method.

The lattice group found a very different result than what had been found previously. Instead of a wild disagreement with experiment, their calculation agreed. According to them, everything was fine, the muon g-2 was behaving exactly as the Standard Model predicted.

For some of us, that’s where the mystery ended. Clearly, something must be wrong with the data-driven method, not with the Standard Model. No more muon puzzle.

But the data-driven method wasn’t just a guess, it was being used for a reason. A significant group of physicists found the arguments behind it convincing. Now, there was a new puzzle: figuring out why the data-driven method and lattice QCD disagree.

Five years later, has that mystery been solved? Is that, finally, what the headlines are about?

Again, not really, no.

The theorists associated with the experiment have decided to trust lattice QCD, not the data-driven method. But they don’t know what went wrong, exactly.

Instead, they’ve highlighted cracks in the data-driven method. The way the data-driven method works, it brings together different experiments to try to get a shared picture. But that shared picture has started to fall apart. A new measurement by a different experiment doesn’t fit into the system: the data-driven method now “has tensions”, as physicists say. It’s no longer possible to combine all experiments into a shared picture they way they used to. Meanwhile, lattice QCD has gotten even better, reaching even higher precision. From the perspective of the theorists associated with the muon g-2 experiment, switching methods is now clearly the right call.

But does that mean they solved the puzzle?

If you were confident that lattice QCD is the right approach, then the puzzle was already solved in 2020. All that changed was the official collaboration finally acknowledging that.

And if you were confident that the data-driven method was the right approach, then the puzzle is even worse. Now, there are tensions within the method itself…but still no explanation of what went wrong! If you had good reasons to think the method should work, you still have those good reasons. Now you’re just…more puzzled.

I am reminded of another mystery, a few years back, when an old experiment announced a dramatically different measurement for the mass of the W boson. Then, I argued the big mystery was not how the W boson’s mass had changed (it hadn’t), but how they came to be so confident in a result so different from what others, also confidently, had found. In physics, our confidence is encoded in numbers, estimated and measured and tested and computed. If we’re not estimating that confidence correctly…then that’s the real mystery, the real puzzle. One much more important to solve.

Also, I had two more pieces out this week! In Quanta I have a short explainer about bosons and fermions, while at Ars Technica I have a piece about machine learning at the LHC. I may have a “bonus info” post on the latter at some point, I have to think about whether I have enough material for it.

Amplitudes 2025 This Week

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Summer is conference season for academics, and this week held my old sub-field’s big yearly conference, called Amplitudes. This year, it was in Seoul at Seoul National University, the first time the conference has been in Asia.

(I wasn’t there, I don’t go to these anymore. But I’ve been skimming slides in my free time, to give you folks the updates you crave. Be forewarned that conference posts like these get technical fast, I’ll be back to my usual accessible self next week.)

There isn’t a huge amplitudes community in Korea, but it’s bigger than it was back when I got started in the field. Of the organizers, Kanghoon Lee of the Asia Pacific Center for Theoretical Physics and Sangmin Lee of Seoul National University have what I think of as “core amplitudes interests”, like recursion relations and the double-copy. The other Korean organizers are from adjacent areas, work that overlaps with amplitudes but doesn’t show up at the conference each year. There was also a sizeable group of organizers from Taiwan, where there has been a significant amplitudes presence for some time now. I do wonder if Korea was chosen as a compromise between a conference hosted in Taiwan or in mainland China, where there is also quite a substantial amplitudes community.

One thing that impresses me every year is how big, and how sophisticated, the gravitational-wave community in amplitudes has grown. Federico Buccioni’s talk began with a plot that illustrates this well (though that wasn’t his goal):

At the conference Amplitudes, dedicated to the topic of scattering amplitudes, there were almost as many talks with the phrase “black hole” in the title as there were with “scattering” or “amplitudes”! This is for a topic that did not even exist in the subfield when I got my PhD eleven years ago.

With that said, gravitational wave astronomy wasn’t quite as dominant at the conference as Buccioni’s bar chart suggests. There were a few talks each day on the topic: I counted seven in total, excluding any short talks on the subject in the gong show. Spinning black holes were a significant focus, central to Jung-Wook Kim’s, Andres Luna’s and Mao Zeng’s talks (the latter two showing some interesting links between the amplitudes story and classic ideas in classical mechanics) and relevant in several others, with Riccardo Gonzo, Miguel Correia, Ira Rothstein, and Enrico Herrmann’s talks showing not just a wide range of approaches, but an increasing depth of research in this area.

Herrmann’s talk in particular dealt with detector event shapes, a framework that lets physicists think more directly about what a specific particle detector or observer can see. He applied the idea not just to gravitational waves but to quantum gravity and collider physics as well. The latter is historically where this idea has been applied the most thoroughly, as highlighted in Hua Xing Zhu’s talk, where he used them to pick out particular phenomena of interest in QCD.

QCD is, of course, always of interest in the amplitudes field. Buccioni’s talk dealt with the theory’s behavior at high-energies, with a nice example of the “maximal transcendentality principle” where some quantities in QCD are identical to quantities in N=4 super Yang-Mills in the “most transcendental” pieces (loosely, those with the highest powers of pi). Andrea Guerreri’s talk also dealt with high-energy behavior in QCD, trying to address an experimental puzzle where QCD results appeared to violate a fundamental bound all sensible theories were expected to obey. By using S-matrix bootstrap techniques, they clarify the nature of the bound, finding that QCD still obeys it once correctly understood, and conjecture a weird theory that should be possible to frame right on the edge of the bound. The S-matrix bootstrap was also used by Alexandre Homrich, who talked about getting the framework to work for multi-particle scattering.

Heribertus Bayu Hartanto is another recent addition to Korea’s amplitudes community. He talked about a concrete calculation, two-loop five-particle scattering including top quarks, a tricky case that includes elliptic curves.

When amplitudes lead to integrals involving elliptic curves, many standard methods fail. Jake Bourjaily’s talk raised a question he has brought up again and again: what does it mean to do an integral for a new type of function? One possible answer is that it depends on what kind of numerics you can do, and since more general numerical methods can be cumbersome one often needs to understand the new type of function in more detail. In light of that, Stephen Jones’ talk was interesting in taking a common problem often cited with generic approaches (that they have trouble with the complex numbers introduced by Minkowski space) and finding a more natural way in a particular generic approach (sector decomposition) to take them into account. Giulio Salvatori talked about a much less conventional numerical method, linked to the latest trend in Nima-ology, surfaceology. One of the big selling points of the surface integral framework promoted by people like Salvatori and Nima Arkani-Hamed is that it’s supposed to give a clear integral to do for each scattering amplitude, one which should be amenable to a numerical treatment recently developed by Michael Borinsky. Salvatori can currently apply the method only to a toy model (up to ten loops!), but he has some ideas for how to generalize it, which will require handling divergences and numerators.

Other approaches to the “problem of integration” included Anna-Laura Sattelberger’s talk that presented a method to find differential equations for the kind of integrals that show up in amplitudes using the mathematical software Macaulay2, including presenting a package. Matthias Wilhelm talked about the work I did with him, using machine learning to find better methods for solving integrals with integration-by-parts, an area where two other groups have now also published. Pierpaolo Mastrolia talked about integration-by-parts’ up-and-coming contender, intersection theory, a method which appears to be delving into more mathematical tools in an effort to catch up with its competitor.

Sometimes, one is more specifically interested in the singularities of integrals than their numerics more generally. Felix Tellander talked about a geometric method to pin these down which largely went over my head, but he did have a very nice short description of the approach: “Describe the singularities of the integrand. Find a map representing integration. Map the singularities of the integrand onto the singularities of the integral.”

While QCD and gravity are the applications of choice, amplitudes methods germinate in N=4 super Yang-Mills. Ruth Britto’s talk opened the conference with an overview of progress along those lines before going into her own recent work with one-loop integrals and interesting implications of ideas from cluster algebras. Cluster algebras made appearances in several other talks, including Anastasia Volovich’s talk which discussed how ideas from that corner called flag cluster algebras may give insights into QCD amplitudes, though some symbol letters still seem to be hard to track down. Matteo Parisi covered another idea, cluster promotion maps, which he thinks may help pin down algebraic symbol letters.

The link between cluster algebras and symbol letters is an ongoing mystery where the field is seeing progress. Another symbol letter mystery is antipodal duality, where flipping an amplitude like a palindrome somehow gives another valid amplitude. Lance Dixon has made progress in understanding where this duality comes from, finding a toy model where it can be understood and proved.

Others pushed the boundaries of methods specific to N=4 super Yang-Mills, looking for novel structures. Song He’s talk pushes an older approach by Bourjaily and collaborators up to twelve loops, finding new patterns and connections to other theories and observables. Qinglin Yang bootstraps Wilson loops with a Lagrangian insertion, adding a side to the polygon used in previous efforts and finding that, much like when you add particles to amplitudes in a bootstrap, the method gets stricter and more powerful. Jaroslav Trnka talked about work he has been doing with “negative geometries”, an odd method descended from the amplituhedron that looks at amplitudes from a totally different perspective, probing a bit of their non-perturbative data. He’s finding more parts of that setup that can be accessed and re-summed, finding interestingly that multiple-zeta-values show up in quantities where we know they ultimately cancel out. Livia Ferro also talked about a descendant of the amplituhedron, this time for cosmology, getting differential equations for cosmological observables in a particular theory from a combinatorial approach.

Outside of everybody’s favorite theories, some speakers talked about more general approaches to understanding the differences between theories. Andreas Helset covered work on the geometry of the space of quantum fields in a theory, applying the method to a general framework for characterizing deviations from the standard model called the SMEFT. Jasper Roosmale Nepveu also talked about a general space of theories, thinking about how positivity (a trait linked to fundamental constraints like causality and unitarity) gets tangled up with loop effects, and the implications this has for renormalization.

Soft theorems, universal behavior of amplitudes when a particle has low energy, continue to be a trendy topic, with Silvia Nagy showing how the story continues to higher orders and Sangmin Choi investigating loop effects. Callum Jones talks about one of the more powerful results from the soft limit, Weinberg’s theorem showing the uniqueness of gravity. Weinberg’s proof was set up in Minkowski space, but we may ultimately live in curved, de Sitter space. Jones showed how the ideas Weinberg explored generalize in de Sitter, using some tools from the soft-theorem-inspired field of dS/CFT. Julio Parra-Martinez, meanwhile, tied soft theorems to another trendy topic, higher symmetries, a more general notion of the usual types of symmetries that physicists have explored in the past. Lucia Cordova reported work that was not particularly connected to soft theorems but was connected to these higher symmetries, showing how they interact with crossing symmetry and the S-matrix bootstrap.

Finally, a surprisingly large number of talks linked to Kevin Costello and Natalie Paquette’s work with self-dual gauge theories, where they found exact solutions from a fairly mathy angle. Paquette gave an update on her work on the topic, while Alfredo Guevara talked about applications to black holes, comparing the power of expanding around a self-dual gauge theory to that of working with supersymmetry. Atul Sharma looked at scattering in self-dual backgrounds in work that merges older twistor space ideas with the new approach, while Roland Bittelson talked about calculating around an instanton background.

Also, I had another piece up this week at FirstPrinciples, based on an interview with the (outgoing) president of the Sloan Foundation. I won’t have a “bonus info” post for this one, as most of what I learned went into the piece. But if you don’t know what the Sloan Foundation does, take a look! I hadn’t known they funded Jupyter notebooks and Hidden Figures, or that they introduced Kahneman and Tversky.

In Scientific American, With a Piece on Vacuum Decay

Experiments Should Be Surprising, but Not Too Surprising

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People are talking about colliders again.

This year, the European particle physics community is updating its shared plan for the future, the European Strategy for Particle Physics. A raft of proposals at the end of March stirred up a tail of public debate, focused on asking what sort of new particle collider should be built, and discussing potential reasons why.

That discussion, in turn, has got me thinking about experiments, and how they’re justified.

The purpose of experiments, and of science in general, is to learn something new. The more sure we are of something, the less reason there is to test it. Scientists don’t check whether the Sun rises every day. Like everyone else, they assume it will rise, and use that knowledge to learn other things.

You want your experiment to surprise you. But to design an experiment to surprise you, you run into a contradiction.

Suppose that every morning, you check whether the Sun rises. If it doesn’t, you will really be surprised! You’ll have made the discovery of the century! That’s a really exciting payoff, grant agencies should be lining up to pay for…

Well, is that actually likely to happen, though?

The same reasons it would be surprising if the Sun stopped rising are reasons why we shouldn’t expect the Sun to stop rising. A sunrise-checking observatory has incredibly high potential scientific reward…but an absurdly low chance of giving that reward.

Ok, so you can re-frame your experiment. You’re not hoping the Sun won’t rise, you’re observing the sunrise. You expect it to rise, almost guaranteed, so your experiment has an almost guaranteed payoff.

But what a small payoff! You saw exactly what you expected, there’s no science in that!

By either criterion, the “does the Sun rise” observatory is a stupid experiment. Real experiments operate in between the two extremes. They also mix motivations. Together, that leads to some interesting tensions.

What was the purpose of the Large Hadron Collider?

There were a few things physicists were pretty sure of, when they planned the LHC. Previous colliders had measured W bosons and Z bosons, and their properties made it clear that something was missing. If you could collide protons with enough energy, physicists were pretty sure you’d see the missing piece. Physicists had a reasonably plausible story for that missing piece, in the form of the Higgs boson. So physicists could be pretty sure they’d see something, and reasonably sure it would be the Higgs boson.

If physicists expected the Higgs boson, what was the point of the experiment?

First, physicists expected to see the Higgs boson, but they didn’t expect it to have the mass that it did. In fact, they didn’t know anything about the particle’s mass, besides that it should be low enough that the collider could produce it, and high enough that it hadn’t been detected before. The specific number? That was a surprise, and an almost-inevitable one. A rare creature, an almost-guaranteed scientific payoff.

I say almost, because there was a second point. The Higgs boson didn’t have to be there. In fact, it didn’t have to exist at all. There was a much bigger potential payoff, of noticing something very strange, something much more complicated than the straightforward theory most physicists had expected.

(Many people also argued for another almost-guaranteed payoff, and that got a lot more press. People talked about finding the origin of dark matter by discovering supersymmetric particles, which they argued was almost guaranteed due to a principle called naturalness. This is very important for understanding the history…but it’s an argument that many people feel has failed, and that isn’t showing up much anymore. So for this post, I’ll leave it to the side.)

This mix, of a guaranteed small surprise and the potential for a very large surprise, was a big part of what made the LHC make sense. The mix has changed a bit for people considering a new collider, and it’s making for a rougher conversation.

Like the LHC, most of the new collider proposals have a guaranteed payoff. The LHC could measure the mass of the Higgs, these new colliders will measure its “couplings”: how strongly it influences other particles and forces.

Unlike the LHC, though, this guarantee is not a guaranteed surprise. Before building the LHC, we did not know the mass of the Higgs, and we could not predict it. On the other hand, now we absolutely can predict the couplings of the Higgs. We have quite precise numbers, our expectation for what they should be based on a theory that so far has proven quite successful.

We aren’t certain, of course, just like physicists weren’t certain before. The Higgs boson might have many surprising properties, things that contradict our current best theory and usher in something new. These surprises could genuinely tell us something about some of the big questions, from the nature of dark matter to the universe’s balance of matter and antimatter to the stability of the laws of physics.

But of course, they also might not. We no longer have that rare creature, a guaranteed mild surprise, to hedge in case the big surprises fail. We have guaranteed observations, and experimenters will happily tell you about them…but no guaranteed surprises.

That’s a strange position to be in. And I’m not sure physicists have figured out what to do about it.

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Stories about physics from someone who's been there