Tag Archives: quarks

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.

A Tale of Two Experiments

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Before I begin, two small announcements:

First: I am now on bluesky! Instead of having a separate link in the top menu for each social media account, I’ve changed the format so now there are social media buttons in the right-hand sidebar, right under the “Follow” button. Currently, they cover tumblr, twitter, and bluesky, but there may be more in future.

Second, I’ve put a bit more technical advice on my “Open Source Grant Proposal” post, so people interested in proposing similar research can have some ideas about how best to pitch it.

Now, on to the post:

Gravitational wave telescopes are possibly the most exciting research program in physics right now. Big, expensive machines with more on the way in the coming decades, gravitational wave telescopes need both precise theoretical predictions and high-quality data analysis. For some, gravitational wave telescopes have the potential to reveal genuinely new physics, to probe deviations from general relativity that might be related to phenomena like dark matter, though so far no such deviations have been conclusively observed. In the meantime, they’re teaching us new consequences of known physics. For example, the unusual population of black holes observed by LIGO has motivated those who model star clusters to consider processes in which the motion of three stars or black holes is related to each other, discovering that these processes are more important than expected.

Particle colliders are probably still exciting to the general public, but for many there is a growing sense of fatigue and disillusionment. Current machines like the LHC are big and expensive, and proposed future colliders would be even costlier and take decades to come online, in addition to requiring a huge amount of effort from the community in terms of precise theoretical predictions and data analysis. Some argue that colliders still might uncover genuinely new physics, deviations from the standard model that might explain phenomena like dark matter, but as no such deviations have yet been conclusively observed people are increasingly skeptical. In the meantime, most people working on collider physics are focused on learning new consequences of known physics. For example, by comparing observed results with theoretical approximations, people have found that certain high-energy processes usually left out of calculations are actually needed to get a good agreement with the data, showing that these processes are more important than expected.

…ok, you see what I did there, right? Was that fair?

There are a few key differences, with implications to keep in mind:

First, collider physics is significantly more expensive than gravitational wave physics. LIGO took about $300 million to build and spends about $50 million a year. The LHC took about $5 billion to build and costs $1 billion a year to run. That cost still puts both well below several other government expenses that you probably consider frivolous (please don’t start arguing about which ones in the comments!), but it does mean collider physics demands a bit of a stronger argument.

Second, the theoretical motivation to expect new fundamental physics out of LIGO is generally considered much weaker than for colliders. A large part of the theoretical physics community thought that they had a good argument why they should see something new at the LHC. In contrast, most theorists have been skeptical of the kinds of modified gravity theories that have dramatic enough effects that one could measure them with gravitational wave telescopes, with many of these theories having other pathologies or inconsistencies that made people wary.

Third, the general public finds astrophysics cooler than particle physics. Somehow, telling people “pairs of black holes collide more often than we thought because sometimes a third star in the neighborhood nudges them together” gets people much more excited than “pairs of quarks collide more often than we thought because we need to re-sum large logarithms differently”, even though I don’t think there’s a real “principled” difference between them. Neither reveals new laws of nature, both are upgrades to our ability to model how real physical objects behave, neither is useful to know for anybody living on Earth in the present day.

With all this in mind, my advice to gravitational wave physicists is to try, as much as possible, not to lean on stories about dark matter and modified gravity. You might learn something, and it’s worth occasionally mentioning that. But if you don’t, you run a serious risk of disappointing people. And you have such a big PR advantage if you just lean on new consequences of bog standard GR, that those guys really should get the bulk of the news coverage if you want to keep the public on your side.

Book Review: The Joy of Insight

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There’s something endlessly fascinating about the early days of quantum physics. In a century, we went from a few odd, inexplicable experiments to a practically complete understanding of the fundamental constituents of matter. Along the way the new ideas ended a world war, almost fueled another, and touched almost every field of inquiry. The people lucky enough to be part of this went from familiarly dorky grad students to architects of a new reality. Victor Weisskopf was one of those people, and The Joy of Insight: Passions of a Physicist is his autobiography.

Less well-known today than his contemporaries, Weisskopf made up for it with a front-row seat to basically everything that happened in particle physics. In the late 20’s and early 30’s he went from studying in Göttingen (including a crush on Maria Göppert before a car-owning Joe Mayer snatched her up) to a series of postdoctoral positions that would exhaust even a modern-day physicist, working in Leipzig, Berlin, Copenhagen, Cambridge, Zurich, and Copenhagen again, before fleeing Europe for a faculty position in Rochester, New York. During that time he worked for, studied under, collaborated or partied with basically everyone you might have heard of from that period. As a result, this section of the autobiography was my favorite, chock-full of stories, from the well-known (Pauli’s rudeness and mythical tendency to break experimental equipment) to the less-well known (a lab in Milan planned to prank Pauli with a door that would trigger a fake explosion when opened, which worked every time they tested it…and failed when Pauli showed up), to the more personal (including an in retrospect terrifying visit to the Soviet Union, where they asked him to critique a farming collective!) That era also saw his “almost Nobel”, in his case almost discovering the Lamb Shift.

Despite an “almost Nobel”, Weisskopf was paid pretty poorly when he arrived in Rochester. His story there puts something I’d learned before about another refugee physicist, Hertha Sponer, in a new light. Sponer’s university also didn’t treat her well, and it seemed reminiscent of modern academia. Weisskopf, though, thinks his treatment was tied to his refugee status: that, aware that they had nowhere else to go, universities gave the scientists who fled Europe worse deals than they would have in a Nazi-less world, snapping up talent for cheap. I could imagine this was true for Sponer as well.

Like almost everyone with the relevant expertise, Weisskopf was swept up in the Manhattan project at Los Alamos. There he rose in importance, both in the scientific effort (becoming deputy leader of the theoretical division) and the local community (spending some time on and chairing the project’s “town council”). Like the first sections, this surreal time leads to a wealth of anecdotes, all fascinating. In his descriptions of the life there I can see the beginnings of the kinds of “hiking retreats” physicists would build in later years, like the one at Aspen, that almost seem like attempts to recreate that kind of intense collaboration in an isolated natural place.

After the war, Weisskopf worked at MIT before a stint as director of CERN. He shepherded the facility’s early days, when they were building their first accelerators and deciding what kinds of experiments to pursue. I’d always thought that the “nuclear” in CERN’s name was an artifact of the times, when “nuclear” and “particle” physics were thought of as the same field, but according to Weisskopf the fields were separate and it was already a misnomer when the place was founded. Here the book’s supply of anecdotes becomes a bit more thin, and instead he spends pages on glowing descriptions of people he befriended. The pattern continues after the directorship as his duties get more administrative, spending time as head of the physics department at MIT and working on arms control, some of the latter while a member of the Pontifical Academy of Sciences (which apparently even a Jewish atheist can join). He does work on some science, though, collaborating on the “bag of quarks” model of protons and neutrons. He lives to see the fall of the Berlin wall, and the end of the book has a bit of 90’s optimism to it, the feeling that finally the conflicts of his life would be resolved. Finally, the last chapter abandons chronology altogether, and is mostly a list of his opinions of famous composers, capped off with a Bohr-inspired musing on the complementary nature of science and the arts, humanities, and religion.

One of the things I found most interesting in this book was actually something that went unsaid. Weisskopf’s most famous student was Murray Gell-Mann, a key player in the development of the theory of quarks (including coining the name). Gell-Mann was famously cultured (in contrast to the boorish-almost-as-affectation Feynman) with wide interests in the humanities, and he seems like exactly the sort of person Weisskopf would have gotten along with. Surprisingly though, he gets no anecdotes in this book, and no glowing descriptions: just a few paragraphs, mostly emphasizing how smart he was. I have to wonder if there was some coldness between them. Maybe Weisskopf had difficulty with a student who became so famous in his own right, or maybe they just never connected. Maybe Weisskopf was just trying to be generous: the other anecdotes in that part of the book are of much less famous people, and maybe Weisskopf wanted to prioritize promoting them, feeling that they were underappreciated.

Weisskopf keeps the physics light to try to reach a broad audience. This means he opts for short explanations, and often these are whatever is easiest to reach for. It creates some interesting contradictions: the way he describes his “almost Nobel” work in quantum electrodynamics is very much the way someone would have described it at the time, but very much not how it would be understood later, and by the time he talks about the bag of quarks model his more modern descriptions don’t cleanly link with what he said earlier. Overall, his goal isn’t really to explain the physics, but to explain the physicists. I enjoyed the book for that: people do it far too rarely, and the result was a really fun read.

Congratulations to Syukuro Manabe, Klaus Hasselmann, and Giorgio Parisi!

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The 2021 Nobel Prize in Physics was announced this week, awarded to Syukuro Manabe and Klaus Hasselmann for climate modeling and Giorgio Parisi for understanding a variety of complex physical systems.

Before this year’s prize was announced, I remember a few “water cooler chats” about who might win. No guess came close, though. The Nobel committee seems to have settled in to a strategy of prizes on a loosely linked “basket” of topics, with half the prize going to a prominent theorist and the other half going to two experimental, observational, or (in this case) computational physicists. It’s still unclear why they’re doing this, but regardless it makes it hard to predict what they’ll do next!

When I read the announcement, my first reaction was, “surely it’s not that Parisi?” Giorgio Parisi is known in my field for the Altarelli-Parisi equations (more properly known as the DGLAP equations, the longer acronym because, as is often the case in physics, the Soviets got there first). These equations are in some sense why the scattering amplitudes I study are ever useful at all. I calculate collisions of individual fundamental particles, like quarks and gluons, but a real particle collider like the LHC collides protons. Protons are messy, interacting combinations of quarks and gluons. When they collide you need not merely the equations describing colliding quarks and gluons, but those that describe their messy dynamics inside the proton, and in particular how those dynamics look different for experiments with different energies. The equation that describes that is the DGLAP equation.

As it turns out, Parisi is known for a lot more than the DGLAP equation. He is best known for his work on “spin glasses”, models of materials where quantum spins try to line up with each other, never quite settling down. He also worked on a variety of other complex systems, including flocks of birds!

I don’t know as much about Manabe and Hasselmann’s work. I’ve only seen a few talks on the details of climate modeling. I’ve seen plenty of talks on other types of computer modeling, though, from people who model stars, galaxies, or black holes. And from those, I can appreciate what Manabe and Hasselmann did. Based on those talks, I recognize the importance of those first one-dimensional models, a single column of air, especially back in the 60’s when computer power was limited. Even more, I recognize how impressive it is for someone to stay on the forefront of that kind of field, upgrading models for forty years to stay relevant into the 2000’s, as Manabe did. Those talks also taught me about the challenge of coupling different scales: how small effects in churning fluids can add up and affect the simulation, and how hard it is to model different scales at once. To use these effects to discover which models are reliable, as Hasselmann did, is a major accomplishment.

Alice Through the Parity Glass

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When you look into your mirror in the morning, the face looking back at you isn’t exactly your own. Your mirror image is flipped: left-handed if you’re right-handed, and right-handed if you’re left-handed. Your body is not symmetric in the mirror: we say it does not respect parity symmetry. Zoom in, and many of the molecules in your body also have a “handedness” to them: biology is not the same when flipped in a mirror.

What about physics? At first, you might expect the laws of physics themselves to respect parity symmetry. Newton’s laws are the same when reflected in a mirror, and so are Maxwell’s. But one part of physics breaks this rule: the weak nuclear force, the force that causes nuclear beta decay. The weak nuclear force interacts differently with “right-handed” and “left-handed” particles (shorthand for particles that spin counterclockwise or clockwise with respect to their motion). This came as a surprise to most physicists, but it was predicted by Tsung-Dao Lee and Chen-Ning Yang and demonstrated in 1956 by Chien-Shiung Wu, known in her day as the “Queen of Nuclear Research”. The world really does look different when flipped in a mirror.

I gave a lecture on the weak force for the pedagogy course I took a few weeks back. One piece of feedback I got was that the topic wasn’t very relatable. People wanted to know why they should care about the handedness of the weak force, they wanted to hear about “real-life” applications. Once scientists learned that the weak force didn’t respect parity, what did that let us do?

Thinking about this, I realized this is actually a pretty tricky story to tell. With enough time and background, I could explain that the “handedness” of the Standard Model is a major constraint on attempts to unify physics, ruling out a lot of the simpler options. That’s hard to fit in a short lecture though, and it still isn’t especially close to “real life”.

Then I realized I don’t need to talk about “real life” to give a “real-life example”. People explaining relativity get away with science fiction scenarios, spaceships on voyages to black holes. The key isn’t to be familiar, just relatable. If I can tell a story (with people in it), then maybe I can make this work.

All I need, then, is a person who cares a lot about the world behind a mirror.

Curiouser and curiouser…

When Alice goes through the looking glass in the novel of that name, she enters a world flipped left-to-right, a world with its parity inverted. Following Alice, we have a natural opportunity to explore such a world. Others have used this to explore parity symmetry in biology: for example, a side-plot in Alan Moore’s League of Extraordinary Gentlemen sees Alice come back flipped, and starve when she can’t process mirror-reversed nutrients. I haven’t seen it explored for physics, though.

In order to make this story work, we have to get Alice to care about the weak nuclear force. The most familiar thing the weak force does is cause beta decay. And the most familiar thing that undergoes beta decay is a banana. Bananas contain radioactive potassium, which can transform to calcium by emitting an electron and an anti-electron-neutrino.

The radioactive potassium from a banana doesn’t stay in the body very long, only a few hours at most. But if Alice was especially paranoid about radioactivity, maybe she would want to avoid eating bananas. (We shouldn’t tell her that other foods contain potassium too.) If so, she might view the looking glass as a golden opportunity, a chance to eat as many bananas as she likes without worrying about radiation.

Does this work?

A first problem: can Alice even eat mirror-reversed bananas? I told you many biological molecules have handedness, which led Alan Moore’s version of Alice to starve. If we assume, unlike Moore, that Alice comes back in her original configuration and survives, we should still ask if she gets any benefit out of the bananas in the looking glass.

Researching this, I found that the main thing that makes bananas taste “banana-ish”, isoamyl acetate, does not have handedness: mirror bananas will still taste like bananas. Fructose, a sugar in bananas, does have handedness however: it isn’t the same when flipped in a mirror. Chatting with a chemist, the impression I got was that this isn’t a total loss: often, flipping a sugar results in another, different sugar. A mirror banana might still taste sweet, but less so. Overall, it may still be worth eating.

The next problem is a tougher one: flipping a potassium atom doesn’t actually make it immune to the weak force. The weak force only interacts with left-handed particles and right-handed antiparticles: in beta decay, it transforms a left-handed down quark to a left-handed up quark, producing a left-handed electron and a right-handed anti-neutrino.

Alice would have been fine if all of the quarks in potassium were left-handed, but they aren’t: an equal amount are right-handed, so the mirror weak force will still act on them, and they will still undergo beta decay. Actually, it’s worse than that: quarks, and massive particles in general, don’t actually have a definite handedness. If you speed up enough to catch up to a quark and pass it, then from your perspective it’s now going in the opposite direction, and its handedness is flipped. The only particles with definite handedness are massless particles: those go at the speed of light, so you can never catch up to them. Another way to think about this is that quarks get their mass from the Higgs field, and this happens because the Higgs lets left- and right-handed quarks interact. What we call the quark’s mass is in some sense just left- and right-handed quarks constantly mixing back and forth.

Alice does have the opportunity to do something interesting here, if she can somehow capture the anti-neutrinos from those bananas. Our world appears to only have left-handed neutrinos and right-handed anti-neutrinos. This seemed reasonable when we thought neutrinos were massless, but now we know neutrinos have a (very small) mass. As a result, the hunt is on for right-handed neutrinos or left-handed anti-neutrinos: if we can measure them, we could fix one of the lingering mysteries of the Standard Model. With this in mind, Alice has the potential to really confuse some particle physicists, giving them some left-handed anti-neutrinos from beyond the looking-glass.

It turns out there’s a problem with even this scheme, though. The problem is a much wider one: the whole story is physically inconsistent.

I’d been acting like Alice can pass back and forth through the mirror, carrying all her particles with her. But what are “her particles”? If she carries a banana through the mirror, you might imagine the quarks in the potassium atoms carry over. But those quarks are constantly exchanging other quarks and gluons, as part of the strong force holding them together. They’re also exchanging photons with electrons via the electromagnetic force, and they’re also exchanging W bosons via beta decay. In quantum field theory, all of this is in some sense happening at once, an infinite sum over all possible exchanges. It doesn’t make sense to just carve out one set of particles and plug them in to different fields somewhere else.

If we actually wanted to describe a mirror like Alice’s looking glass in physics, we’d want to do it consistently. This is similar to how physicists think of time travel: you can’t go back in time and murder your grandparents because your whole path in space-time has to stay consistent. You can only go back and do things you “already did”. We treat space in a similar way to time. A mirror like Alice’s imposes a condition, that fields on one side are equal to their mirror image on the other side. Conditions like these get used in string theory on occasion, and they have broad implications for physics on the whole of space-time, not just near the boundary. The upshot is that a world with a mirror like Alice’s in it would be totally different from a world without the looking glass: the weak force as we know it would not exist.

So unfortunately, I still don’t have a good “real life” story for a class about parity symmetry. It’s fun trying to follow Alice through a parity transformation, but there are a few too many problems for the tale to make any real sense. Feel free to suggest improvements!

Electromagnetism Is the Weirdest Force

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For a long time, physicists only knew about two fundamental forces: electromagnetism, and gravity. Physics students follow the same path, studying Newtonian gravity, then E&M, and only later learning about the other fundamental forces. If you’ve just recently heard about the weak nuclear force and the strong nuclear force, it can be tempting to think of them as just slight tweaks on electromagnetism. But while that can be a helpful way to start, in a way it’s precisely backwards. Electromagnetism is simpler than the other forces, that’s true. But because of that simplicity, it’s actually pretty weird as a force.

The weirdness of electromagnetism boils down to one key reason: the electromagnetic field has no charge.

Maybe that sounds weird to you: if you’ve done anything with electromagnetism, you’ve certainly seen charges. But while you’ve calculated the field produced by a charge, the field itself has no charge. You can specify the positions of some electrons and not have to worry that the electric field will introduce new charges you didn’t plan. Mathematically, this means your equations are linear in the field, and thus not all that hard to solve.

The other forces are different. The strong nuclear force has three types of charge, dubbed red, green, and blue. Not just quarks, but the field itself has charges under this system, making the equations that describe it non-linear.

A depiction of a singlet state

Those properties mean that you can’t just think of the strong force as a push or pull between charges, like you could with electromagnetism. The strong force doesn’t just move quarks around, it can change their color, exchanging charge between the quark and the field. That’s one reason why when we’re more careful we refer to it as not the strong force, but the strong interaction.

The weak force also makes more sense when thought of as an interaction. It can change even more properties of particles, turning different flavors of quarks and leptons into each other, resulting in among other phenomena nuclear beta decay. It would be even more like the strong force, but the Higgs field screws that up, stirring together two more fundamental forces and spitting out the weak force and electromagnetism. The result ties them together in weird ways: for example, it means that the weak field can actually have an electric charge.

Interactions like the strong and weak forces are much more “normal” for particle physicists: if you ask us to picture a random fundamental force, chances are it will look like them. It won’t typically look like electromagnetism, the weird “degenerate” case with a field that doesn’t even have a charge. So despite how familiar electromagnetism may be to you, don’t take it as your model of what a fundamental force should look like: of all the forces, it’s the simplest and weirdest.

Theoretical Uncertainty and Uncertain Theory

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Yesterday, Fermilab’s Muon g-2 experiment announced a new measurement of the magnetic moment of the muon, a number which describes how muons interact with magnetic fields. For what might seem like a small technical detail, physicists have been very excited about this measurement because it’s a small technical detail that the Standard Model seems to get wrong, making it a potential hint of new undiscovered particles. Quanta magazine has a great piece on the announcement, which explains more than I will here, but the upshot is that there are two different calculations on the market that attempt to predict the magnetic moment of the muon. One of them, using older methods, disagrees with the experiment. The other, with a new approach, agrees. The question then becomes, which calculation was wrong? And why?

What does it mean for a prediction to match an experimental result? The simple, wrong, answer is that the numbers must be equal: if you predict “3”, the experiment has to measure “3”. The reason why this is wrong is that in practice, every experiment and every prediction has some uncertainty. If you’ve taken a college physics class, you’ve run into this kind of uncertainty in one of its simplest forms, measurement uncertainty. Measure with a ruler, and you can only confidently measure down to the smallest divisions on the ruler. If you measure 3cm, but your ruler has ticks only down to a millimeter, then what you’re measuring might be as large as 3.1cm or as small as 2.9 cm. You just don’t know.

This uncertainty doesn’t mean you throw up your hands and give up. Instead, you estimate the effect it can have. You report, not a measurement of 3cm, but of 3cm plus or minus 1mm. If the prediction was 2.9cm, then you’re fine: it falls within your measurement uncertainty.

Measurements aren’t the only thing that can be uncertain. Predictions have uncertainty too, theoretical uncertainty. Sometimes, this comes from uncertainty on a previous measurement: if you make a prediction based on that experiment that measured 3cm plus or minus 1mm, you have to take that plus or minus into account and estimate its effect (we call this propagation of errors). Sometimes, the uncertainty comes instead from an approximation you’re making. In particle physics, we sometimes approximate interactions between different particles with diagrams, beginning with the simplest diagrams and adding on more complicated ones as we go. To estimate the uncertainty there, we estimate the size of the diagrams we left out, the more complicated ones we haven’t calculated yet. Other times, that approximation doesn’t work, and we need to use a different approximation, treating space and time as a finite grid where we can do computer simulations. In that case, you can estimate your uncertainty based on how small you made your grid. The new approach to predicting the muon magnetic moment uses that kind of approximation.

There’s a common thread in all of these uncertainty estimates: you don’t expect to be too far off on average. Your measurements won’t be perfect, but they won’t all be screwed up in the same way either: chances are, they will randomly be a little below or a little above the truth. Your calculations are similar: whether you’re ignoring complicated particle physics diagrams or the spacing in a simulated grid, you can treat the difference as something small and random. That randomness means you can use statistics to talk about your errors: you have statistical uncertainty. When you have statistical uncertainty, you can estimate, not just how far off you might get, but how likely it is you ended up that far off. In particle physics, we have very strict standards for this kind of thing: to call something new a discovery, we demand that it is so unlikely that it would only show up randomly under the old theory roughly one in a million times. The muon magnetic moment isn’t quite up to our standards for a discovery yet, but the new measurement brought it closer.

The two dueling predictions for the muon’s magnetic moment both estimate some amount of statistical uncertainty. It’s possible that the two calculations just disagree due to chance, and that better measurements or a tighter simulation grid would make them agree. Given their estimates, though, that’s unlikely. That takes us from the realm of theoretical uncertainty, and into uncertainty about the theoretical. The two calculations use very different approaches. The new calculation tries to compute things from first principles, using the Standard Model directly. The risk is that such a calculation needs to make assumptions, ignoring some effects that are too difficult to calculate, and one of those assumptions may be wrong. The older calculation is based more on experimental results, using different experiments to estimate effects that are hard to calculate but that should be similar between different situations. The risk is that the situations may be less similar than expected, their assumptions breaking down in a way that the bottom-up calculation could catch.

None of these risks are easy to estimate. They’re “unknown unknowns”, or rather, “uncertain uncertainties”. And until some of them are resolved, it won’t be clear whether Fermilab’s new measurement is a sign of undiscovered particles, or just a (challenging!) confirmation of the Standard Model.

QCD Meets Gravity 2020, Retrospective

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I was at a Zoomference last week, called QCD Meets Gravity, about the many ways gravity can be thought of as the “square” of other fundamental forces. I didn’t have time to write much about the actual content of the conference, so I figured I’d say a bit more this week.

A big theme of this conference, as in the past few years, was gravitational waves. From LIGO’s first announcement of a successful detection, amplitudeologists have been developing new methods to make predictions for gravitational waves more efficient. It’s a field I’ve dabbled in a bit myself. Last year’s QCD Meets Gravity left me impressed by how much progress had been made, with amplitudeologists already solidly part of the conversation and able to produce competitive results. This year felt like another milestone, in that the amplitudeologists weren’t just catching up with other gravitational wave researchers on the same kinds of problems. Instead, they found new questions that amplitudes are especially well-suited to answer. These included combining two pieces of these calculations (“potential” and “radiation”) that the older community typically has to calculate separately, using an old quantum field theory trick, finding the gravitational wave directly from amplitudes, and finding a few nice calculations that can be used to “generate” the rest.

A large chunk of the talks focused on different “squaring” tricks (or as we actually call them, double-copies). There were double-copies for cosmology and conformal field theory, for the celestial sphere, and even some version of M theory. There were new perspectives on the double-copy, new building blocks and algebraic structures that lie behind it. There were talks on the so-called classical double-copy for space-times, where there have been some strange discoveries (an extra dimension made an appearance) but also a more rigorous picture of where the whole thing comes from, using twistor space. There were not one, but two talks linking the double-copy to the Navier-Stokes equation describing fluids, from two different groups. (I’m really curious whether these perspectives are actually useful for practical calculations about fluids, or just fun to think about.) Finally, while there wasn’t a talk scheduled on this paper, the authors were roped in by popular demand to talk about their work. They claim to have made progress on a longstanding puzzle, how to show that double-copy works at the level of the Lagrangian, and the community was eager to dig into the details.

From there, a grab-bag of talks covered other advancements. There were talks from string theorists and ambitwistor string theorists, from Effective Field Theorists working on gravity and the Standard Model, from calculations in N=4 super Yang-Mills, QCD, and scalar theories. Simon Caron-Huot delved into how causality constrains the theories we can write down, showing an interesting case where the common assumption that all parameters are close to one is actually justified. Nima Arkani-Hamed began his talk by saying he’d surprise us, which he certainly did (and not by keeping on time). It’s tricky to explain why his talk was exciting. Comparing to his earlier discovery of the Amplituhedron, which worked for a toy model, this is a toy calculation in a toy model. While the Amplituhedron wasn’t based on Feynman diagrams, this can’t even be compared with Feynman diagrams. Instead of expanding in a small coupling constant, this expands in a parameter that by all rights should be equal to one. And instead of positivity conditions, there are negativity conditions. All I can say is that with all of that in mind, it looks like real progress on an important and difficult problem from a totally unanticipated direction. In a speech summing up the conference, Zvi Bern mentioned a few exciting words from Nima’s talk: “nonplanar”, “integrated”, “nonperturbative”. I’d add “differential equations” and “infinite sums of ladder diagrams”. Nima and collaborators are trying to figure out what happens when you sum up all of the Feynman diagrams in a theory. I’ve made progress in the past for diagrams with one “direction”, a ladder that grows as you add more loops, but I didn’t know how to add “another direction” to the ladder. In very rough terms, Nima and collaborators figured out how to add that direction.

I’ve probably left things out here, it was a packed conference! It’s been really fun seeing what the community has cooked up, and I can’t wait to see what happens next.

QCD Meets Gravity 2020

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I’m at another Zoom conference this week, QCD Meets Gravity. This year it’s hosted by Northwestern.

The view of the campus from wonder.me

QCD Meets Gravity is a conference series focused on the often-surprising links between quantum chromodynamics on the one hand and gravity on the other. By thinking of gravity as the “square” of forces like the strong nuclear force, researchers have unlocked new calculation techniques and deep insights.

Last year’s conference was very focused on one particular topic, trying to predict the gravitational waves observed by LIGO and VIRGO. That’s still a core topic of the conference, but it feels like there is a bit more diversity in topics this year. We’ve seen a variety of talks on different “squares”: new theories that square to other theories, and new calculations that benefit from “squaring” (even surprising applications to the Navier-Stokes equation!) There are talks on subjects from String Theory to Effective Field Theory, and even a talk on a very different way that “QCD meets gravity”, in collisions of neutron stars.

With still a few more talks to go, expect me to say a bit more next week, probably discussing a few in more detail. (Several people presented exciting work in progress!) Until then, I should get back to watching!

QCD Meets Gravity 2019

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I’m at UCLA this week for QCD Meets Gravity, a conference about the surprising ways that gravity is “QCD squared”.

When I attended this conference two years ago, the community was branching out into a new direction: using tools from particle physics to understand the gravitational waves observed at LIGO.

At this year’s conference, gravitational waves have grown from a promising new direction to a large fraction of the talks. While there were still the usual talks about quantum field theory and string theory (everything from bootstrap methods to a surprising application of double field theory), gravitational waves have clearly become a major focus of this community.

This was highlighted before the first talk, when Zvi Bern brought up a recent paper by Thibault Damour. Bern and collaborators had recently used particle physics methods to push beyond the state of the art in gravitational wave calculations. Damour, an expert in the older methods, claims that Bern et al’s result is wrong, and in doing so also questions an earlier result by Amati, Ciafaloni, and Veneziano. More than that, Damour argued that the whole approach of using these kinds of particle physics tools for gravitational waves is misguided.

There was a lot of good-natured ribbing of Damour in the rest of the conference, as well as some serious attempts to confront his points. Damour’s argument so far is somewhat indirect, so there is hope that a more direct calculation (which Damour is currently pursuing) will resolve the matter. In the meantime, Julio Parra-Martinez described a reproduction of the older Amati/Ciafaloni/Veneziano result with more Damour-approved techniques, as well as additional indirect arguments that Bern et al got things right.

Before the QCD Meets Gravity community worked on gravitational waves, other groups had already built a strong track record in the area. One encouraging thing about this conference was how much the two communities are talking to each other. Several speakers came from the older community, and there were a lot of references in both groups’ talks to the other group’s work. This, more than even the content of the talks, felt like the strongest sign that something productive is happening here.

Many talks began by trying to motivate these gravitational calculations, usually to address the mysteries of astrophysics. Two talks were more direct, with Ramy Brustein and Pierre Vanhove speculating about new fundamental physics that could be uncovered by these calculations. I’m not the kind of physicist who does this kind of speculation, and I confess both talks struck me as rather strange. Vanhove in particular explicitly rejects the popular criterion of “naturalness”, making me wonder if his work is the kind of thing critics of naturalness have in mind.