I watched Hamilton on Disney+ recently. With GIFs and songs from the show all over social media for the last few years, there weren’t many surprises. One thing that nonetheless struck me was the focus on historical evidence. The musical Hamilton is based on Ron Chernow’s biography of Alexander Hamilton, and it preserves a surprising amount of the historian’s care for how we know what we know, hidden within the show’s other themes. From the refrain of “who tells your story”, to the importance of Eliza burning her letters with Hamilton (not just the emotional gesture but the “gap in the narrative” it created for historians), to the song “The Room Where It Happens” (which looked from GIFsets like it was about Burr’s desire for power, but is mostly about how much of history is hidden in conversations we can only partly reconstruct), the show keeps the puzzle of reasoning from incomplete evidence front-and-center.
Any time we try to reason about the past, we are faced with these kinds of questions. They don’t just apply to history, but to the so-called historical sciences as well, sciences that study the past. Instead of asking “who” told the story, such scientists must keep in mind “what” is telling the story. For example, paleontologists reason from fossils, and thus are limited by what does and doesn’t get preserved. As a result after a century of studying dinosaurs, only in the last twenty years did it become clear they had feathers.
Astronomy, too, is a historical science. Whenever astronomers look out at distant stars, they are looking at the past. And just like historians and paleontologists, they are limited by what evidence happened to be preserved, and what part of that evidence they can access.
Try to reason about the whole universe, and you end up asking similar questions. When we see the movement of “standard candle” stars, is that because the universe’s expansion is accelerating, or are the stars moving as a group?
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 dabbledin 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.
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!
Two big physics experiments consistently make the news. The Large Hadron Collider, or LHC, and the Laser Interferometer Gravitational-Wave Observatory, or LIGO. One collides protons, the other watches colliding black holes and neutron stars. But while this may make the experiments sound quite similar, their goals couldn’t be more different.
The goal of the LHC, put simply, is to discover the rules that govern reality. Should the LHC find a new fundamental particle, it will tell us something we didn’t know about the laws of physics, a newly discovered fact that holds true everywhere in the universe. So far, it has discovered the Higgs boson, and while that particular rule was expected we didn’t know the details until they were tested. Now physicists hope to find something more, a deviation from the Standard Model that hints at a new law of nature altogether.
LIGO, in contrast, isn’t really for discovering the rules of the universe. Instead, it discovers the consequences of those rules, on a grand scale. Even if we knew the laws of physics completely, we can’t calculate everything from those first principles. We can simulate some things, and approximate others, but we need experiments to tweak those simulations and test those approximations. LIGO fills that role. We can try to estimate how common black holes are, and how large, but LIGO’s results were still a surprise, suggesting medium-sized black holes are more common than researchers expected. In the future, gravitational wave telescopes might discover more of these kinds of consequences, from the shape of neutron stars to the aftermath of cosmic inflation.
There are a few exceptions for both experiments. The LHC can also discover the consequences of the laws of physics, especially when those consequences are very difficult to calculate, finding complicated arrangements of known particles, like pentaquarks and glueballs. And it’s possible, though perhaps not likely, that LIGO could discover something about quantum gravity. Quantum gravity’s effects are expected to be so small that these experiments won’t see them, but some have speculated that an unusually large effect could be detected by a gravitational wave telescope.
As scientists, we want to know everything we can about everything we find. We want to know the basic laws that govern the universe, but we also want to know the consequences of those laws, the story of how our particular universe came to be the way it is today. And luckily, we have experiments for both.
During Zoomplitudes (my field’s big yearly conference, this year on Zoom) I didn’t have time to write a long blog post. I said a bit about the format, but didn’t get a chance to talk about the science. I figured this week I’d go back and give a few more of my impressions. As always, conference posts are a bit more technical than my usual posts, so regulars be warned!
The conference opened with a talk by Gavin Salam, there as an ambassador for LHC physics. Salam pointed out that, while a decent proportion of speakers at Amplitudes mention the LHC in their papers, that fraction has fallen over the years. (Another speaker jokingly wondered which of those mentions were just in the paper’s introduction.) He argued that there is still useful work for us, LHC measurements that will require serious amplitudes calculations to understand. He also brought up what seems like the most credible argument for a new, higher-energy collider: that there are important properties of the Higgs, in particular its interactions, that we still have not observed.
The next few talks hopefully warmed Salam’s heart, as they featured calculations for real-world particle physics. Nathaniel Craig and Yael Shadmi in particular covered the link between amplitudes and Standard Model Effective Field Theory (SMEFT), a method to systematically characterize corrections beyond the Standard Model. Shadmi’s talk struck me because the kind of work she described (building the SMEFT “amplitudes-style”, directly from observable information rather than more complicated proxies) is something I’d seen people speculate about for a while, but which hadn’t been done until quite recently. Now, several groups have managed it, and look like they’ve gotten essentially “all the way there”, rather than just partial results that only manage to replicate part of the SMEFT. Overall it’s much faster progress than I would have expected.
After Shadmi’s talk was a brace of talks on N=4 super Yang-Mills, featuring cosmic Galois theory and an impressively groan-worthy “origin story” joke. The final talk of the day, by Hofie Hannesdottir, covered work with some of my colleagues at the NBI. Due to coronavirus I hadn’t gotten to hear about this in person, so it was good to hear a talk on it, a blend of old methods and new priorities to better understand some old discoveries.
The next day focused on a topic that has grown in importance in our community, calculations for gravitational wave telescopes like LIGO. Several speakers focused on new methods for collisions of spinning objects, where a few different approaches are making good progress (Radu Roiban’s proposal to use higher-spin field theory was particularly interesting) but things still aren’t quite “production-ready”. The older, post-Newtonian method is still very much production-ready, as evidenced by Michele Levi’s talk that covered, among other topics, our recentcollaboration. Julio Parra-Martinez discussed some interesting behavior shared by both supersymmetric and non-supersymmetric gravity theories. Thibault Damour had previously expressed doubts about use of amplitudes methods to answer this kind of question, and part of Parra-Martinez’s aim was to confirm the calculation with methods Damour would consider more reliable. Damour (who was actually in the audience, which I suspect would not have happened at an in-person conference) had already recanted some related doubts, but it’s not clear to me whether that extended to the results Parra-Martinez discussed (or whether Damour has stated the problem with his old analysis).
There were a few talks that day that didn’t relate to gravitational waves, though this might have been an accident, since both speakers also work on that topic. Zvi Bern’s talk linked to the previous day’s SMEFT discussion, with a calculation using amplitudes methods of direct relevance to SMEFT researchers. Clifford Cheung’s talk proposed a rather strange/fun idea, conformal symmetry in negative dimensions!
Wednesday was “amplituhedron day”, with a variety of talks on positive geometries and cluster algebras. Featured in several talks was “tropicalization“, a mathematical procedure that can simplify complicated geometries while still preserving essential features. Here, it was used to trim down infinite “alphabets” conjectured for some calculations into a finite set, and in doing so understand the origin of “square root letters”. The day ended with a talk by Nima Arkani-Hamed, who despite offering to bet that he could finish his talk within the half-hour slot took almost twice that. The organizers seemed to have planned for this, since there was one fewer talk that day, and as such the day ended at roughly the usual time regardless.
We also took probably the most unique conference photo I will ever appear in.
For lack of a better name, I’ll call Thursday’s theme “celestial”. The day included talks by cosmologists (including approaches using amplitudes-ish methods from Daniel Baumann and Charlotte Sleight, and a curiously un-amplitudes-related talk from Daniel Green), talks on “celestial amplitudes” (amplitudes viewed from the surface of an infinitely distant sphere), and various talks with some link to string theory. I’m including in that last category intersection theory, which has really become its own thing. This included a talk by Simon Caron-Huot about using intersection theory more directly in understanding Feynman integrals, and a talk by Sebastian Mizera using intersection theory to investigate how gravity is Yang-Mills squared. Both gave me a much better idea of the speakers’ goals. In Mizera’s case he’s aiming for something very ambitious. He wants to use intersection theory to figure out when and how one can “double-copy” theories, and might figure out why the procedure “got stuck” at five loops. The day ended with a talk by Pedro Vieira, who gave an extremely lucid and well-presented “blackboard-style” talk on bootstrapping amplitudes.
Friday was a grab-bag of topics. Samuel Abreu discussed an interesting calculation using the numerical unitarity method. It was notable in part because renormalization played a bigger role than it does in most amplitudes work, and in part because they now have a cool logo for their group’s software, Caravel. Claude Duhr and Ruth Britto gave a two-part talk on their work on a Feynman integral coaction. I’d had doubts about the diagrammatic coaction they had worked on in the past because it felt a bit ad-hoc. Now, they’re using intersection theory, and have a clean story that seems to tie everything together. Andrew McLeod talked about our work on a Feynman diagram Calabi-Yau “bestiary”, while Cristian Vergu had a more rigorous understanding of our “traintrack” integrals.
There are two key elements of a conference that are tricky to do on Zoom. You can’t do a conference dinner, so you can’t do the traditional joke-filled conference dinner speech. The end of the conference is also tricky: traditionally, this is when everyone applauds the organizers and the secretaries are given flowers. As chair for the last session, Lance Dixon stepped up to fill both gaps, with a closing speech that was both a touching tribute to the hard work of organizing the conference and a hilarious pile of in-jokes, including a participation award to Arkani-Hamed for his (unprecedented, as far as I’m aware) perfect attendance.
Two weeks ago, I told you that Andrew and Michèle and I had written a paper, predicting what gravitational wave telescopes like LIGO see when black holes collide. You may remember that LIGO doesn’t just see colliding black holes: it sees colliding neutron stars too. So why didn’t we predict what happens when neutron stars collide?
Actually, we did. Our calculation doesn’t just apply to black holes. It applies to neutron stars too. And not just neutron stars: it applies to anything of roughly the right size and shape. Black holes, neutron stars, very large grapefruits…
LIGO’s next big discovery
That’s the magic of Effective Field Theory, the “zoom lens” of particle physics. Zoom out far enough, and any big, round object starts looking like a particle. Black holes, neutron stars, grapefruits, we can describe them all using the same math.
Ok, so we can describe both black holes and neutron stars. Can we tell the difference between them?
In our last calculation, no. In this one, yes!
Effective Field Theory isn’t just a zoom lens, it’s a controlled approximation. That means that when we “zoom out” we don’t just throw out anything “too small to see”. Instead, we approximate it, estimating how big of an effect it can have. Depending on how precise we want to be, we can include more and more of these approximated effects. If our estimates are good, we’ll include everything that matters, and get a good approximation for what we’re trying to observe.
At the precision of our last calculation, a black hole and a neutron star still look exactly the same. Our new calculation aims for a bit higher precision though. (For the experts: we’re at a higher order in spin.) The higher precision means that we can actually see the difference: our result changes for two colliding black holes versus two colliding grapefruits.
So does that mean I can tell you what happens when two neutron stars collide, according to our calculation? Actually, no. That’s not because we screwed up the calculation: it’s because some of the properties of neutron stars are unknown.
The Effective Field Theory of neutron stars has what we call “free parameters”, unknown variables. People have tried to estimate some of these (called “Love numbers” after the mathematician A. E. H. Love), but they depend on the details of how neutron stars work: what stuff they contain, how that stuff is shaped, and how it can move. To find them out, we probably can’t just calculate: we’ll have to measure, observe an actual neutron star collision and see what the numbers actually are.
That’s one of the purposes of gravitational wave telescopes. It’s not (as far as I know) something LIGO can measure. But future telescopes, with more precision, should be able to. By watching two colliding neutron stars and comparing to a high-precision calculation, physicists will better understand what those neutron stars are made of. In order to do that, they will need someone to do that high-precision calculation. And that’s why people like me are involved.
I had a new paper up last Friday with Michèle Levi and Andrew McLeod, on a topic I hadn’t worked on before: colliding black holes.
I am an “amplitudeologist”. I work on particle physics calculations, computing “scattering amplitudes” to find the probability that fundamental particles bounce off each other. This sounds like the farthest thing possible from black holes. Nevertheless, the two are tightly linked, through the magic of something called Effective Field Theory.
Effective Field Theory is a kind of “zoom knob” for particle physics. You “zoom out” to some chosen scale, and write down a theory that describes physics at that scale. Your theory won’t be a complete description: you’re ignoring everything that’s “too small to see”. It will, however, be an effective description: one that, at the scale you’re interested in, is effectively true.
Particle physicists usually use Effective Field Theory to go between different theories of particle physics, to zoom out from strings to quarks to protons and neutrons. But you can zoom out even further, all the way out to astronomical distances. Zoom out far enough, and even something as massive as a black hole looks like just another particle.
Just click the “zoom X10” button fifteen times, and you’re there!
In this picture, the force of gravity between black holes looks like particles (specifically, gravitons) going back and forth. With this picture, physicists can calculate what happens when two black holes collide with each other, making predictions that can be checked with new gravitational wave telescopes like LIGO.
Researchers have pushed this technique quite far. As the calculations get more and more precise (more and more “loops”), they have gotten more and more challenging. This is particularly true when the black holes are spinning, an extra wrinkle in the calculation that adds a surprising amount of complexity.
That’s where I came in. I can’t compete with the experts on black holes, but I certainly know a thing or two about complicated particle physics calculations. Amplitudeologists, like Andrew McLeod and me, have a grab-bag of tricks that make these kinds of calculations a lot easier. With Michèle Levi’s expertise working with spinning black holes in Effective Field Theory, we were able to combine our knowledge to push beyond the state of the art, to a new level of precision.
This project has been quite exciting for me, for a number of reasons. For one, it’s my first time working with gravitons: despite this blog’s name, I’d never published a paper on gravity before. For another, as my brother quipped when he heard about it, this is by far the most “applied” paper I’ve ever written. I mostly work with a theory called N=4 super Yang-Mills, a toy model we use to develop new techniques. This paper isn’t a toy model: the calculation we did should describe black holes out there in the sky, in the real world. There’s a decent chance someone will use this calculation to compare with actual data, from LIGO or a future telescope. That, in particular, is an absurdly exciting prospect.
Because this was such an applied calculation, it was an opportunity to explore the more applied part of my own field. We ended up using well-known techniques from that corner, but I look forward to doing something more inventive in future.
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 pushbeyond 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.
The things one learns from Wikipedia. For example, today I learned that the country song “The Gambler” was selected for preservation by the US Library of Congress as being “culturally, historically, or artistically significant.”
You’ve got to know when to hold ’em, know when to fold ’em,
Know when to walk away, know when to run.
Knowing when to “hold ’em” or “fold ’em” is important in life in general, but it’s particularly important in science.
And not just on poker night
As scientists, we’re often trying to do something no-one else has done before. That’s exciting, but it’s risky too: sometimes whatever we’re trying simply doesn’t work. In those situations, it’s important to recognize when we aren’t making progress, and change tactics. The trick is, we can’t give up too early either: science is genuinely hard, and sometimes when we feel stuck we’re actually close to the finish line. Knowing which is which, when to “hold” and when to “fold”, is an essential skill, and a hard one to learn.
Sometimes, we can figure this out mathematically. Computational complexity theory classifies calculations by how difficult they are, including how long they take. If you can estimate how much time you should take to do a calculation, you can decide whether you’ll finish it in a reasonable amount of time. If you just want a rough guess, you can do a simpler version of the calculation, and see how long that takes, then estimate how much longer the full one will. If you figure out you’re doomed, then it’s time to switch to a more efficient algorithm, or a different question entirely.
Sometimes, we don’t just have to consider time, but money as well. If you’re doing an experiment, you have to estimate how much the equipment will cost, and how much it will cost to run it. Experimenters get pretty good at estimating these things, but they still screw up sometimes and run over budget. Occasionally this is fine: LIGO didn’t detect anything in its first eight-year run, but they upgraded the machines and tried again, and won a Nobel prize. Other times it’s a disaster, and money keeps being funneled into a project that never works. Telling the difference is crucial, and it’s something we as a community are still not so good at.
Sometimes we just have to follow our instincts. This is dangerous, because we have a bias (the “sunk cost fallacy”) to stick with something if we’ve already spent a lot of time or money on it. To counteract that, it’s good to cultivate a bias in the opposite direction, which you might call “scientific impatience”. Getting frustrated with slow progress may not seem productive, but it keeps you motivated to search for a better way. Experienced scientists get used to how long certain types of project take. Too little progress, and they look for another option. This can fail, killing a project that was going to succeed, but it can also prevent over-investment in a failing idea. Only a mix of instincts keeps the field moving.
In the end, science is a gamble. Like the song, we have to know when to hold ’em and fold ’em, when to walk away, and when to run an idea as far as it will go. Sometimes it works, and sometimes it doesn’t. That’s science.
The Breakthrough Prize was designed to complement the Nobel Prize, rewarding deserving researchers who wouldn’t otherwise get the Nobel. The Nobel Prize is only awarded to theoretical physicists when they predict something that is later observed in an experiment. Many theorists are instead renowned for their mathematical inventions, concepts that other theorists build on and use but that do not by themselves make testable predictions. The Breakthrough Prize celebrates these theorists, and while it has also been awarded to others who the Nobel committee could not or did not recognize (various large experimental collaborations, Jocelyn Bell Burnell), this has always been the physics prize’s primary focus.
The Breakthrough Prize website describes supergravity as a theory that combines gravity with particle physics. That’s a bit misleading: while the theory does treat gravity in a “particle physics” way, unlike string theory it doesn’t solve the famous problems with combining quantum mechanics and gravity. (At least, as far as we know.)
It’s better to say that supergravity is a theory that links gravity to other parts of particle physics, via supersymmetry. Supersymmetry is a relationship between two types of particles: bosons, like photons, gravitons, or the Higgs, and fermions, like electrons or quarks. In supersymmetry, each type of boson has a fermion “partner”, and vice versa. In supergravity, gravity itself gets a partner, called the gravitino. Supersymmetry links the properties of particles and their partners together: both must have the same mass and the same charge. In a sense, it can unify different types of particles, explaining both under the same set of rules.
In the real world, we don’t see bosons and fermions with the same mass and charge. If gravitinos exist, then supersymmetry would have to be “broken”, giving them a high mass that makes them hard to find. Some hoped that the Large Hadron Collider could find these particles, but now it looks like it won’t, so there is no evidence for supergravity at the moment.
Instead, supergravity’s success has been as a tool to understand other theories of gravity. When the theory was proposed in the 1970’s, it was thought of as a rival to string theory. Instead, over the years it consistently managed to point out aspects of string theory that the string theorists themselves had missed, for example noticing that the theory needed not just strings but higher-dimensional objects called “branes”. Now, supergravity is understood as one part of a broader string theory picture.
The discovery of supergravity by Ferrara, Freedman, and van Nieuwenhuizen is exactly the kind of work the Breakthrough Prize was created to reward. Supergravity is a theory with deep mathematics, rich structure, and wide applicability. There is of course no guarantee that such a theory describes the real world. What is guaranteed, though, is that someone will find it useful.
