# Things I’d Like to Know More About

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.

# Don’t Marry Your Arbitrary

This fall, I’m TAing a course on General Relativity. I haven’t taught in a while, so it’s been a good opportunity to reconnect with how students think.

This week, one problem left several students confused. The problem involved Christoffel symbols, the bane of many a physics grad student, but the trick that they had to use was in the end quite simple. It’s an example of a broader trick, a way of thinking about problems that comes up all across physics.

To see a simplified version of the problem, imagine you start with this sum:

$g(j)=\Sigma_{i=0}^n ( f(i,j)-f(j,i) )$

Now, imagine you want to sum the function $g(j)$ over $j$. You can write:

$\Sigma_{j=0}^n g(j) = \Sigma_{j=0}^n \Sigma_{i=0}^n ( f(i,j)-f(j,i) )$

Let’s break this up into two terms, for later convenience:

$\Sigma_{j=0}^n g(j) = \Sigma_{j=0}^n \Sigma_{i=0}^n f(i,j) - \Sigma_{j=0}^n \Sigma_{i=0}^n f(j,i)$

Without telling you anything about $f(i,j)$, what do you know about this sum?

Well, one thing you know is that $i$ and $j$ are arbitrary.

$i$ and $j$ are letters you happened to use. You could have used different letters, $x$ and $y$, or $\alpha$ and $\beta$. You could even use different letters in each term, if you wanted to. You could even just pick one term, and swap $i$ and $j$.

$\Sigma_{j=0}^n g(j) = \Sigma_{j=0}^n \Sigma_{i=0}^n f(i,j) - \Sigma_{i=0}^n \Sigma_{j=0}^n f(i,j) = 0$

And now, without knowing anything about $f(i,j)$, you know that $\Sigma_{j=0}^n g(j)$ is zero.

In physics, it’s extremely important to keep track of what could be really physical, and what is merely your arbitrary choice. In general relativity, your choice of polar versus spherical coordinates shouldn’t affect your calculation. In quantum field theory, your choice of gauge shouldn’t matter, and neither should your scheme for regularizing divergences.

Ideally, you’d do your calculation without making any of those arbitrary choices: no coordinates, no choice of gauge, no regularization scheme. In practice, sometimes you can do this, sometimes you can’t. When you can’t, you need to keep that arbitrariness in the back of your mind, and not get stuck assuming your choice was the only one. If you’re careful with arbitrariness, it can be one of the most powerful tools in physics. If you’re not, you can stare at a mess of Christoffel symbols for hours, and nobody wants that.

# Current Themes 2018

I’m at Current Themes in High Energy Physics and Cosmology this week, the yearly conference of the Niels Bohr International Academy. (I talked about their trademark eclectic mix of topics last year.)

This year, the “current theme” was broadly gravitational (though with plenty of exceptions!).

For example, almost getting kicked out of the Botanical Garden

There were talks on phenomena we observe gravitationally, like dark matter. There were talks on calculating amplitudes in gravity theories, both classical and quantum. There were talks about black holes, and the overall shape of the universe. Subir Sarkar talked about his suspicion that the expansion of the universe isn’t actually accelerating, and while I still think the news coverage of it was overblown I sympathize a bit more with his point. He’s got a fairly specific worry, that we’re in a region that’s moving unusually with respect to the surrounding universe, that hasn’t really been investigated in much detail before. I don’t think he’s found anything definitive yet, but it will be interesting as more data accumulates to see what happens.

Of course, current themes can’t stick to just one theme, so there were non-gravitational talks as well. Nima Arkani-Hamed’s talk covered some results he’s talked about in the past, a geometric picture for constraining various theories, but with an interesting new development: while most of the constraints he found restrict things to be positive, one type of constraint he investigated allowed for a very small negative region, around thirty orders of magnitude smaller than the positive part. The extremely small size of the negative region was the most surprising part of the story, as it’s quite hard to get that kind of extremely small scale out of the math we typically invoke in physics (a similar sense of surprise motivates the idea of “naturalness” in particle physics).

There were other interesting talks, which I might talk about later. They should have slides up online soon in case any of you want to have a look.

# Bubbles of Nothing

I recently learned about a very cool concept, called a bubble of nothing.

Read about physics long enough, and you’ll hear all sorts of cosmic disaster scenarios. If the Higgs vacuum decays, and the Higgs field switches to a different value, then the masses of most fundamental particles would change. It would be the end of physics, and life, as we know it.

A bubble of nothing is even more extreme. In a bubble of nothing, space itself ceases to exist.

The idea was first explored by Witten in 1982. Witten started with a simple model, a world with our four familiar dimensions of space and time, plus one curled-up extra dimension. What he found was that this simple world is unstable: quantum mechanics (and, as was later found, thermodynamics) lets it “tunnel” to another world, one that contains a small “bubble”, a sphere in which nothing at all exists.

Except perhaps the Nowhere Man

A bubble of nothing might sound like a black hole, but it’s quite different. Throw a particle into a black hole and it will fall in, never to return. Throw it into a bubble of nothing, though, and something more interesting happens. As you get closer, the extra dimension of space gets smaller and smaller. Eventually, it stops, smoothly closing off. The particle you threw in will just bounce back, smoothly, off the outside of the bubble. Essentially, it reached the edge of the universe.

The bubble starts out small, comparable to the size of the curled-up dimension. But it doesn’t stay that way. In Witten’s setup, the bubble grows, faster and faster, until it’s moving at the speed of light, erasing the rest of the universe from existence.

You probably shouldn’t worry about this happening to us. As far as I’m aware, nobody has written down a realistic model that can transform into a bubble of nothing.

Still, it’s an evocative concept, and one I’m surprised isn’t used more often in science fiction. I could see writers using a bubble of nothing as a risk from an experimental FTL drive, or using a stable (or slowly growing) bubble as the relic of some catastrophic alien war. The idea of a bubble of literal nothing is haunting enough that it ought to be put to good use.

# We Didn’t Deserve Hawking

I don’t usually do obituaries. I didn’t do one when Joseph Polchinksi died, though his textbook is sitting an arm’s reach from me right now. I never collaborated with Polchinski, I never met him, and others were much better at telling his story.

I never met Stephen Hawking, either. When I was at Perimeter, I’d often get asked if I had. Visitors would see his name on the Perimeter website, and I’d have to disappoint them by explaining that he hadn’t visited the institute in quite some time. His health, while exceptional for a septuagenarian with ALS, wasn’t up to the travel.

Was his work especially relevant to mine? Only because of its relevance to everyone who does gravitational physics. The universality of singularities in general relativity, black hole thermodynamics and Hawking radiation, these sharpened the questions around quantum gravity. Without his work, string theory wouldn’t have tried to answer the questions Hawking posed, and it wouldn’t have become the field it is today.

Hawking was unique, though, not necessarily because of his work, but because of his recognizability. Those visitors to Perimeter were a cross-section of the Canadian public. Some of them didn’t know the name of the speaker for the lecture they came to see. Some, arriving after reading Lee Smolin’s book, could only refer to him as “that older fellow who thinks about quantum gravity”. But Hawking? They knew Hawking. Without exception, they knew Hawking.

Who was the last physicist the public knew, like that? Feynman, at the height of his popularity, might have been close. You’d have to go back to Einstein to find someone who was really solidly known like that, who you could mention in homes across the world and expect recognition. And who else has that kind of status? Bohr might have it in Denmark. Go further back, and you’ll find people know Newton, they know Gaileo.

Einstein changed our picture of space and time irrevocably. Newton invented physics as we know it. Galileo and Copernicus pointed up to the sky and shouted that the Earth moves!

Hawking asked questions. He told us what did and didn’t make sense, he showed what we had to take into account. He laid the rules of engagement, and the rest of quantum gravity came and asked alongside him.

We live in an age of questions now. We’re starting to glimpse the answers, we have candidates and frameworks and tools, and if we’re feeling very optimistic we might already be sitting on a theory of everything. But we haven’t turned that corner yet, from asking questions to changing the world.

These ages don’t usually get a household name. Normally, you need an Einstein, a Newton, a Galileo, you need to shake the foundations of the world.

Somehow, Hawking gave us one anyway. Somehow, in our age of questions, we put a face in everyone’s mind, a figure huddled in a wheelchair with a snarky, computer-generated voice. Somehow Hawking reached out and reminded the world that there were people out there asking, that there was a big beautiful puzzle that our field was trying to solve.

Deep down, I’m not sure we deserved that. I hope we deserve it soon.

# The Rippling Pond Universe

[Background: Someone told me they couldn’t imagine popularizing Quantum Field Theory in the same flashy way people popularize String Theory. Naturally I took this as a challenge. Please don’t take any statements about what “really exists” here too seriously, this isn’t intended as metaphysics, just metaphor.]

You probably learned about atoms in school.

Your teacher would have explained that these aren’t the same atoms the ancient Greeks imagined. Democritus thought of atoms as indivisible, unchanging spheres, the fundamental constituents of matter. We know, though, that atoms aren’t indivisible. They’re clouds of electrons, buzzing in their orbits around a nucleus of protons and neutrons. Chemists can divide the electrons from the rest, nuclear physicists can break the nucleus. The atom is not indivisible.

And perhaps your teacher remarked on how amazing it is, that the nucleus is such a tiny part of the atom, that the atom, and thus all solid matter, is mostly empty space.

You might have learned that protons and neutrons, too, are not indivisible. That each proton, and each neutron, is composed of three particles called quarks, particles which can be briefly freed by powerful particle colliders.

And you might have wondered, then, even if you didn’t think to ask: are quarks atoms? The real atoms, the Greek atoms, solid indestructible balls of fundamental matter?

They aren’t, by the way.

You might have gotten an inkling of this, learning about beta decay. In beta decay, a neutron transforms, becoming a proton, an electron, and a neutrino. Look for an electron inside a neutron, and you won’t find one. Even if you look at the quarks, you see the same transformation: a down quark becomes an up quark, plus an electron, plus a neutrino. If quarks were atoms, indivisible and unchanging, this couldn’t happen. There’s nowhere for the electron to hide.

In fact, there are no atoms, not the way the Greeks imagined. Just ripples.

Picture the universe as a pond. This isn’t a still pond: something has disturbed it, setting ripples and whirlpools in motion. These ripples and whirlpools skim along the surface of the pond, eddying together and scattering apart.

Our universe is not a simple pond, and so these are not simple ripples. They shine and shimmer, each with their own bright hue, colors beyond our ordinary experience that mix in unfamiliar ways. The different-colored ripples interact, merge and split, and the pond glows with their light.

Stand back far enough, and you notice patterns. See that red ripple, that stays together and keeps its shape, that meets other ripples and interacts in predictable ways. You might imagine the red ripple is an atom, truly indivisible…until it splits, transforms, into ripples of new colors. The quark has changed, down to up, an electron and a neutrino rippling away.

All of our world is encoded in the colors of these ripples, each kind of charge its own kind of hue. With a wink (like your teacher’s, telling you of empty atoms), I can tell you that distance itself is just a kind of ripple, one that links other ripples together. The pond’s very nature as a place is defined by the ripples on it.

This is Quantum Field Theory, the universe of ripples. Democritus said that in truth there are only atoms and the void, but he was wrong. There are no atoms. There is only the void. It ripples and shimmers, and each of us lives as a collection of whirlpools, skimming the surface, seeming concrete and real and vital…until the ripples dissolve, and a new pattern comes.

# At the GGI Lectures on the Theory of Fundamental Interactions

I’m at the Galileo Galilei Institute for Theoretical Physics in Florence at their winter school, the GGI Lectures on the Theory of Fundamental Interactions. Next week I’ll be helping Lance Dixon teach Amplitudeology, this week, I’m catching the tail end of Ira Rothstein’s lectures.

The Galileo Galilei Institute, at the end of a long, winding road filled with small, speedy cars and motorcycles, in classic Italian fashion

Rothstein has been heavily involved in doing gravitational wave calculations using tools from quantum field theory, something that has recently captured a lot of interest from amplitudes people. Specifically, he uses Effective Field Theory, theories that are “effectively” true at some scale but hide away higher-energy physics. In the case of gravitational waves, these theories are a powerful way to calculate the waves that LIGO and VIRGO can observe without using the full machinery of general relativity.

After seeing Rothstein’s lectures, I’m reminded of something he pointed out at the QCD Meets Gravity conference in December. He emphasized then that even if amplitudes people get very good at drawing diagrams for classical general relativity, that won’t be the whole story: there’s a series of corrections needed to “match” between the quantities LIGO is able to see and the ones we’re able to calculate. Different methods incorporate these corrections in different ways, and the most intuitive approach for us amplitudes folks may still end up cumbersome once all the corrections are included. In typical amplitudes fashion, this just makes me wonder if there’s a shortcut: some way to compute, not just a piece that gets plugged in to an Effective Field Theory story, but the waves LIGO sees in one fell swoop (or at least, the part where gravity is weak enough that our methods are still useful). That’s probably a bit naive of me, though.