Tag Archives: LIGO

Amplitudes 2021 Retrospective

Phew!

The conference photo

Now that I’ve rested up after this year’s Amplitudes, I’ll give a few of my impressions.

Overall, I think the conference went pretty well. People seemed amused by the digital Niels Bohr, even if he looked a bit like a puppet (Lance compared him to Yoda in his final speech, which was…apt). We used Gather.town, originally just for the poster session and a “virtual reception”, but later we also encouraged people to meet up in it during breaks. That in particular was a big hit: I think people really liked the ability to just move around and chat in impromptu groups, and while nobody seemed to use the “virtual bar”, the “virtual beach” had a lively crowd. Time zones were inevitably rough, but I think we ended up with a good compromise where everyone could still see a meaningful chunk of the conference.

A few things didn’t work as well. For those planning conferences, I would strongly suggest not making a brand new gmail account to send out conference announcements: for a lot of people the emails went straight to spam. Zulip was a bust: I’m not sure if people found it more confusing than last year’s Slack or didn’t notice it due to the spam issue, but almost no-one posted in it. YouTube was complicated: the stream went down a few times and I could never figure out exactly why, it may have just been internet issues here at the Niels Bohr Institute (we did have a power outage one night and had to scramble to get internet access back the next morning). As far as I could tell YouTube wouldn’t let me re-open the previous stream so each time I had to post a new link, which probably was frustrating for those following along there.

That said, this was less of a problem than it might have been, because attendance/”viewership” as a whole was lower than expected. Zoomplitudes last year had massive numbers of people join in both on Zoom and via YouTube. We had a lot fewer: out of over 500 registered participants, we had fewer than 200 on Zoom at any one time, and at most 30 or so on YouTube. Confusion around the conference email might have played a role here, but I suspect part of the difference is simple fatigue: after over a year of this pandemic, online conferences no longer feel like an exciting new experience.

The actual content of the conference ranged pretty widely. Some people reviewed earlier work, others presented recent papers or even work-in-progress. As in recent years, a meaningful chunk of the conference focused on applications of amplitudes techniques to gravitational wave physics. This included a talk by Thibault Damour, who has by now mostly made his peace with the field after his early doubts were sorted out. He still suspected that the mismatch of scales (weak coupling on the one hand, classical scattering on the other) would cause problems in future, but after his work with Laporta and Mastrolia even he had to acknowledge that amplitudes techniques were useful.

In the past I would have put the double-copy and gravitational wave researchers under the same heading, but this year they were quite distinct. While a few of the gravitational wave talks mentioned the double-copy, most of those who brought it up were doing something quite a bit more abstract than gravitational wave physics. Indeed, several people were pushing the boundaries of what it means to double-copy. There were modified KLT kernels, different versions of color-kinematics duality, and explorations of what kinds of massive particles can and (arguably more interestingly) cannot be compatible with a double-copy framework. The sheer range of different generalizations had me briefly wondering whether the double-copy could be “too flexible to be meaningful”, whether the right definitions would let you double-copy anything out of anything. I was reassured by the points where each talk argued that certain things didn’t work: it suggests that wherever this mysterious structure comes from, its powers are limited enough to make it meaningful.

A fair number of talks dealt with what has always been our main application, collider physics. There the context shifted, but the message stayed consistent: for a “clean” enough process two or three-loop calculations can make a big difference, taking a prediction that would be completely off from experiment and bringing it into line. These are more useful the more that can be varied about the calculation: functions are more useful than numbers, for example. I was gratified to hear confirmation that a particular kind of process, where two massless particles like quarks become three massive particles like W or Z bosons, is one of these “clean enough” examples: it means someone will need to compute my “tardigrade” diagram eventually.

If collider physics is our main application, N=4 super Yang-Mills has always been our main toy model. Jaroslav Trnka gave us the details behind Nima’s exciting talk from last year, and Nima had a whole new exciting talk this year with promised connections to category theory (connections he didn’t quite reach after speaking for two and a half hours). Anastasia Volovich presented two distinct methods for predicting square-root symbol letters, while my colleague Chi Zhang showed some exciting progress with the elliptic double-box, realizing the several-year dream of representing it in a useful basis of integrals and showcasing several interesting properties. Anne Spiering came over from the integrability side to show us just how special the “planar” version of the theory really is: by increasing the number of colors of gluons, she showed that one could smoothly go between an “integrability-esque” spectrum and a “chaotic” spectrum. Finally, Lance Dixon mentioned his progress with form-factors in his talk at the end of the conference, showing off some statistics of coefficients of different functions and speculating that machine learning might be able to predict them.

On the more mathematical side, Francis Brown showed us a new way to get numbers out of graphs, one distinct but related to our usual interpretation in terms of Feynman diagrams. I’m still unsure what it will be used for, but the fact that it maps every graph to something finite probably has some interesting implications. Albrecht Klemm and Claude Duhr talked about two sides of the same story, their recent work on integrals involving Calabi-Yau manifolds. They focused on a particular nice set of integrals, and time will tell whether the methods work more broadly, but there are some exciting suggestions that at least parts will.

There’s been a resurgence of the old dream of the S-matrix community, constraining amplitudes via “general constraints” alone, and several talks dealt with those ideas. Sebastian Mizera went the other direction, and tried to test one of those “general constraints”, seeing under which circumstances he could prove that you can swap a particle going in with an antiparticle going out. Others went out to infinity, trying to understand amplitudes from the perspective of the so-called “celestial sphere” where they appear to be governed by conformal field theories of some sort. A few talks dealt with amplitudes in string theory itself: Yvonne Geyer built them out of field-theory amplitudes, while Ashoke Sen explained how to include D-instantons in them.

We also had three “special talks” in the evenings. I’ve mentioned Nima’s already. Zvi Bern gave a retrospective talk that I somewhat cheesily describe as “good for the soul”: a look to the early days of the field that reminded us of why we are who we are. Lance Dixon closed the conference with a light-hearted summary and a look to the future. That future includes next year’s Amplitudes, which after a hasty discussion during this year’s conference has now localized to Prague. Let’s hope it’s in person!

Black Holes, Neutron Stars, and the Power of Love

What’s the difference between a black hole and a neutron star?

When a massive star nears the end of its life, it starts running out of nuclear fuel. Without the support of a continuous explosion, the star begins to collapse, crushed under its own weight.

What happens then depends on how much weight that is. The most massive stars collapse completely, into the densest form anything can take: a black hole. Einstein’s equations say a black hole is a single point, infinitely dense: get close enough and nothing, not even light, can escape. A quantum theory of gravity would change this, but not a lot: a quantum black hole would still be as dense as quantum matter can get, still equipped with a similar “point of no return”.

A slightly less massive star collapses, not to a black hole, but to a neutron star. Matter in a neutron star doesn’t collapse to a single point, but it does change dramatically. Each electron in the old star is crushed together with a proton until it becomes a neutron, a forced reversal of the more familiar process of Beta decay. Instead of a ball of hydrogen and helium, the star then ends up like a single atomic nucleus, one roughly the size of a city.

Not kidding about the “city” thing…and remember, this is more massive than the Sun

Now, let me ask a slightly different question: how do you tell the difference between a black hole and a neutron star?

Sometimes, you can tell this through ordinary astronomy. Neutron stars do emit light, unlike black holes, though for most neutron stars this is hard to detect. In the past, astronomers would use other objects instead, looking at light from matter falling in, orbiting, or passing by a black hole or neutron star to estimate its mass and size.

Now they have another tool: gravitational wave telescopes. Maybe you’ve heard of LIGO, or its European cousin Virgo: massive machines that do astronomy not with light but by detecting ripples in space and time. In the future, these will be joined by an even bigger setup in space, called LISA. When two black holes or neutron stars collide they “ring” the fabric of space and time like a bell, sending out waves in every direction. By analyzing the frequency of these waves, scientists can learn something about what made them: in particular, whether the waves were made by black holes or neutron stars.

One big difference between black holes and neutron stars lies in something called their “Love numbers“. From far enough away, you can pretend both black holes and neutron stars are single points, like fundamental particles. Try to get more precise, and this picture starts to fail, but if you’re smart you can include small corrections and keep things working. Some of those corrections, called Love numbers, measure how much one object gets squeezed and stretched by the other’s gravitational field. They’re called Love numbers not because they measure how hug-able a neutron star is, but after the mathematician who first proposed them, A. E. H. Love.

What can we learn from Love numbers? Quite a lot. More impressively, there are several different types of questions Love numbers can answer. There are questions about our theories, questions about the natural world, and questions about fundamental physics.

You might have heard that black holes “have no hair”. A black hole in space can be described by just two numbers: its mass, and how much it spins. A star is much more complicated, with sunspots and solar flares and layers of different gases in different amounts. For a black hole, all of that is compressed down to nothing, reduced to just those two numbers and nothing else.

With that in mind, you might think a black hole should have zero Love numbers: it should be impossible to squeeze it or stretch it. This is fundamentally a question about a theory, Einstein’s theory of relativity. If we took that theory for granted, and didn’t add anything to it, what would the consequences be? Would black holes have zero Love number, or not?

It turns out black holes do have zero Love number, if they aren’t spinning. If they are, things are more complicated: a few calculations made it look like spinning black holes also had zero Love number, but just last year a more detailed proof showed that this doesn’t hold. Somehow, despite having “no hair”, you can actually “squeeze” a spinning black hole.

(EDIT: Folks on twitter pointed out a wrinkle here: more recent papers are arguing that spinning black holes actually do have zero Love number as well, and that the earlier papers confused Love numbers with a different effect. All that is to say this is still very much an active area of research!)

The physics behind neutron stars is in principle known, but in practice hard to understand. When they are formed, almost every type of physics gets involved: gas and dust, neutrino blasts, nuclear physics, and general relativity holding it all together.

Because of all this complexity, the structure of neutron stars can’t be calculated from “first principles” alone. Finding it out isn’t a question about our theories, but a question about the natural world. We need to go out and measure how neutron stars actually behave.

Love numbers are a promising way to do that. Love numbers tell you how an object gets squeezed and stretched in a gravitational field. Learning the Love numbers of neutron stars will tell us something about their structure: namely, how squeezable and stretchable they are. Already, LIGO and Virgo have given us some information about this, and ruled out a few possibilities. In future, the LISA telescope will show much more.

Returning to black holes, you might wonder what happens if we don’t stick to Einstein’s theory of relativity. Physicists expect that relativity has to be modified to account for quantum effects, to make a true theory of quantum gravity. We don’t quite know how to do that yet, but there are a few proposals on the table.

Asking for the true theory of quantum gravity isn’t just a question about some specific part of the natural world, it’s a question about the fundamental laws of physics. Can Love numbers help us answer it?

Maybe. Some theorists think that quantum gravity will change the Love numbers of black holes. Fewer, but still some, think they will change enough to be detectable, with future gravitational wave telescopes like LISA. I get the impression this is controversial, both because of the different proposals involved and the approximations used to understand them. Still, it’s fun that Love numbers can answer so many different types of questions, and teach us so many different things about physics.

Unrelated: For those curious about what I look/sound like, I recently gave a talk of outreach advice for the Max Planck Institute for Physics, and they posted it online here.

Reality as an Algebra of Observables

Listen to a physicist talk about quantum mechanics, and you’ll hear the word “observable”. Observables are, intuitively enough, things that can be observed. They’re properties that, in principle, one could measure in an experiment, like the position of a particle or its momentum. They’re the kinds of things linked by uncertainty principles, where the better you know one, the worse you know the other.

Some physicists get frustrated by this focus on measurements alone. They think we ought to treat quantum mechanics, not like a black box that produces results, but as information about some underlying reality. Instead of just observables, they want us to look for “beables“: not just things that can be observed, but things that something can be. From their perspective, the way other physicists focus on observables feels like giving up, like those physicists are abandoning their sacred duty to understand the world. Others, like the Quantum Bayesians or QBists, disagree, arguing that quantum mechanics really is, and ought to be, a theory of how individuals get evidence about the world.

I’m not really going to weigh in on that debate, I still don’t feel like I know enough to even write a decent summary. But I do think that one of the instincts on the “beables” side is wrong. If we focus on observables in quantum mechanics, I don’t think we’re doing anything all that unusual. Even in other parts of physics, we can think about reality purely in terms of observations. Doing so isn’t a dereliction of duty: often, it’s the most useful way to understand the world.

When we try to comprehend the world, we always start alone. From our time in the womb, we have only our senses and emotions to go on. With a combination of instinct and inference we start assembling a consistent picture of reality. Philosophers called phenomenologists (not to be confused with the physicists called phenomenologists) study this process in detail, trying to characterize how different things present themselves to an individual consciousness.

For my point here, these details don’t matter so much. That’s because in practice, we aren’t alone in understanding the world. Based on what others say about the world, we conclude they perceive much like we do, and we learn by their observations just as we learn by our own. We can make things abstract: instead of the specifics of how individuals perceive, we think about groups of scientists making measurements. At the end of this train lie observables: things that we as a community could in principle learn, and share with each other, ignoring the details of how exactly we measure them.

If each of these observables was unrelated, just scattered points of data, then we couldn’t learn much. Luckily, they are related. In quantum mechanics, some of these relationships are the uncertainty principles I mentioned earlier. Others relate measurements at different places, or at different times. The fancy way to refer to all these relationships is as an algebra: loosely, it’s something you can “do algebra with”, like you did with numbers and variables in high school. When physicists and mathematicians want to do quantum mechanics or quantum field theory seriously, they often talk about an “algebra of observables”, a formal way of thinking about all of these relationships.

Focusing on those two things, observables and how they are related, isn’t just useful in the quantum world. It’s an important way to think in other areas of physics too. If you’ve heard people talk about relativity, the focus on measurement screams out, in thought experiments full of abstract clocks and abstract yardsticks. Without this discipline, you find paradoxes, only to resolve them when you carefully track what each person can observe. More recently, physicists in my field have had success computing the chance particles collide by focusing on the end result, the actual measurements people can make, ignoring what might happen in between to cause that measurement. We can then break measurements down into simpler measurements, or use the structure of simpler measurements to guess more complicated ones. While we typically have done this in quantum theories, that’s not really a limitation: the same techniques make sense for problems in classical physics, like computing the gravitational waves emitted by colliding black holes.

With this in mind, we really can think of reality in those terms: not as a set of beable objects, but as a set of observable facts, linked together in an algebra of observables. Paring things down to what we can know in this way is more honest, and it’s also more powerful and useful. Far from a betrayal of physics, it’s the best advantage we physicists have in our quest to understand the world.

What Tells Your Story

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.

These limitations lead to mysteries, and often controversies. Before LIGO, astronomers had an idea of what the typical mass of a black hole was. After LIGO, a new slate of black holes has been observed, with much higher mass. It’s still unclear why.

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?

Push far enough back and the evidence doesn’t just lead to controversy, but to hard limits on what we can know. No matter how good our telescopes are, we won’t see light older than the cosmic microwave background: before that background was emitted the universe was filled with plasma, which would have absorbed any earlier light, erasing anything we could learn from it. Gravitational waves may one day let us probe earlier, and make discoveries as surprising as feathered dinosaurs. But there is yet a stronger limit to how far back we can go, beyond which any evidence has been so diluted that it is indistinguishable from random noise. We can never quite see into “the room where it happened”.

It’s gratifying to see questions of historical evidence in a Broadway musical, in the same way it was gratifying to hear fractals mentioned in a Disney movie. It’s important to think about who, and what, is telling the stories we learn. Spreading that lesson helps all of us reason better.

QCD Meets Gravity 2020, Retrospective

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

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!

Discovering the Rules, Discovering the Consequences

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.

Zoomplitudes Retrospective

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 recent collaboration. 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.

4gravitons, Spinning Up

I had a new paper out last week, with Michèle Levi and Andrew McLeod. But to explain it, I’ll need to clarify something about our last paper.

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.

4gravitons Exchanges a Graviton

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.