Tag Archives: quantum gravity

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.

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.

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

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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.

A Non-Amplitudish Solution to an Amplitudish Problem

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There was an interesting paper last week, claiming to solve a long-standing problem in my subfield.

I calculate what are called scattering amplitudes, formulas that tell us the chance that two particles scatter off each other. Formulas like these exist for theories like the strong nuclear force, called Yang-Mills theories, they also exist for the hypothetical graviton particles of gravity. One of the biggest insights in scattering amplitude research in the last few decades is that these two types of formulas are tied together: as we like to say, gravity is Yang-Mills squared.

A huge chunk of my subfield grew out of that insight. For one, it’s why some of us think we have something useful to say about colliding black holes. But while it’s been used in a dozen different ways, an important element was missing: the principle was never actually proven (at least, not in the way it’s been used).

Now, a group in the UK and the Czech Republic claims to have proven it.

I say “claims” not because I’m skeptical, but because without a fair bit more reading I don’t think I can judge this one. That’s because the group, and the approach they use, isn’t “amplitudish”. They aren’t doing what amplitudes researchers would do.

In the amplitudes subfield, we like to write things as much as possible in terms of measurable, “on-shell” particles. This is in contrast to the older approach that writes things instead in terms of more general quantum fields, with formulas called Lagrangians to describe theories. In part, we avoid the older Lagrangian framing to avoid redundancy: there are many different ways to write a Lagrangian for the exact same physics. We have another reason though, which might seem contradictory: we avoid Lagrangians to stay flexible. There are many ways to rewrite scattering amplitudes that make different properties manifest, and some of the strangest ones don’t seem to correspond to any Lagrangian at all.

If you’d asked me before last week, I’d say that “gravity is Yang-Mills squared” was in that category: something you couldn’t make manifest fully with just a Lagrangian, that you’d need some stranger magic to prove. If this paper is right, then that’s wrong: if you’re careful enough you can prove “gravity is Yang-Mills squared” in the old-school, Lagrangian way.

I’m curious how this is going to develop: what amplitudes people will think about it, what will happen as the experts chime in. For now, as mentioned, I’m reserving judgement, except to say “interesting if true”.

4gravitons Exchanges a Graviton

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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.

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.

Breakthrough Prize for Supergravity

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This week, $3 Million was awarded by the Breakthrough Prize to Sergio Ferrara, Daniel Z. Freedman and Peter van Nieuwenhuizen, the discoverers of the theory of supergravity, part of a special award separate from their yearly Fundamental Physics Prize. There’s a nice interview with Peter van Nieuwenhuizen on the Stony Brook University website, about his reaction to the award.

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.

In my corner of physics, we try to find shortcuts for complicated calculations. We benefit a lot from toy models: simpler, unrealistic theories that let us test our ideas before applying them to the real world. Supergravity is one of the best toy models we’ve got, a theory that makes gravity simple enough that we can start to make progress. Right now, colleagues of mine are developing new techniques for calculations at LIGO, the gravitational wave telescope. If they hadn’t worked with supergravity first, they would never have discovered these techniques.

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.

Why I Wasn’t Bothered by the “Science” in Avengers: Endgame

Things I’d Like to Know More About

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This is an accountability post, of sorts.

As a kid, I wanted to know everything. Eventually, I realized this was a little unrealistic. Doomed to know some things and not others, I picked physics as a kind of triage. Other fields I could learn as an outsider: not well enough to compete with the experts, but enough to at least appreciate what they were doing. After watching a few string theory documentaries, I realized this wasn’t the case for physics: if I was going to ever understand what those string theorists were up to, I would have to go to grad school in string theory.

Over time, this goal lost focus. I’ve become a very specialized creature, an “amplitudeologist”. I didn’t have time or energy for my old questions. In an irony that will surprise no-one, a career as a physicist doesn’t leave much time for curiosity about physics.

One of the great things about this blog is how you guys remind me of those old questions, bringing me out of my overspecialized comfort zone. In that spirit, in this post I’m going to list a few things in physics that I really want to understand better. The idea is to make a public commitment: within a year, I want to understand one of these topics at least well enough to write a decent blog post on it.

Wilsonian Quantum Field Theory:

When you first learn quantum field theory as a physicist, you learn how unsightly infinite results get covered up via an ad-hoc-looking process called renormalization. Eventually you learn a more modern perspective, that these infinite results show up because we’re ignorant of the complete theory at high energies. You learn that you can think of theories at a particular scale, and characterize them by what happens when you “zoom” in and out, in an approach codified by the physicist Kenneth Wilson.

While I understand the basics of Wilson’s approach, the courses I took in grad school skipped the deeper implications. This includes the idea of theories that are defined at all energies, “flowing” from an otherwise scale-invariant theory perturbed with extra pieces. Other physicists are much more comfortable thinking in these terms, and the topic is important for quite a few deep questions, including what it means to properly define a theory and where laws of nature “live”. If I’m going to have an informed opinion on any of those topics, I’ll need to go back and learn the Wilsonian approach properly.

Wormholes:

If you’re a fan of science fiction, you probably know that wormholes are the most realistic option for faster-than-light travel, something that is at least allowed by the equations of general relativity. “Most realistic” isn’t the same as “realistic”, though. Opening a wormhole and keeping it stable requires some kind of “exotic matter”, and that matter needs to violate a set of restrictions, called “energy conditions”, that normal matter obeys. Some of these energy conditions are just conjectures, some we even know how to violate, while others are proven to hold for certain types of theories. Some energy conditions don’t rule out wormholes, but instead restrict their usefulness: you can have non-traversable wormholes (basically, two inescapable black holes that happen to meet in the middle), or traversable wormholes where the distance through the wormhole is always longer than the distance outside.

I’ve seen a few talks on this topic, but I’m still confused about the big picture: which conditions have been proven, what assumptions were needed, and what do they all imply? I haven’t found a publicly-accessible account that covers everything. I owe it to myself as a kid, not to mention everyone who’s a kid now, to get a satisfactory answer.

Quantum Foundations:

Quantum Foundations is a field that many physicists think is a waste of time. It deals with the questions that troubled Einstein and Bohr, questions about what quantum mechanics really means, or why the rules of quantum mechanics are the way they are. These tend to be quite philosophical questions, where it’s hard to tell if people are making progress or just arguing in circles.

I’m more optimistic about philosophy than most physicists, at least when it’s pursued with enough analytic rigor. I’d like to at least understand the leading arguments for different interpretations, what the constraints on interpretations are and the main loopholes. That way, if I end up concluding the field is a waste of time at least I’d be making an informed decision.

4 gravitons

The trials and tribulations of four gravitons and a postdoc