Monthly Archives: January 2018

The Rippling Pond Universe

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[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.

Water Drop

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.

Tutoring at GGI

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I’m still at the Galileo Galilei Institute this week, tutoring at the winter school.

At GGI’s winter school, each week is featuring a pair of lecturers. This week, the lectures alternate between Lance Dixon covering the basics of amplitudeology and Csaba Csaki, discussing ways in which the Higgs could be a composite made up of new fundamental particles.

Most of the students at this school are phenomenologists, physicists who make predictions for particle physics. I’m an amplitudeologist, I study the calculation tools behind those predictions. You’d think these would be very close areas, but it’s been interesting seeing how different our approaches really are.

Some of the difference is apparent just from watching the board. In Csaki’s lectures, the equations that show up are short, a few terms long at most. When amplitudes show up, it’s for their general properties: how many factors of the coupling constant, or the multipliers that show up with loops. There aren’t any long technical calculations, and in general they aren’t needed: he’s arguing about the kinds of physics that can show up, not the specifics of how they give rise to precise numbers.

In contrast, Lance’s board filled up with longer calculations, each with many moving parts. Even things that seem simple from our perspective take a decent amount of board space to derive, and involve no small amount of technical symbol-shuffling. For most of the students, working out an amplitude this complicated was an unfamiliar experience. There are a few applications for which you need the kind of power that amplitudeology provides, and a few students were working on them. For the rest, it was a bit like learning about a foreign culture, an exercise in understanding what other people are doing rather than picking up a new skill themselves. Still, they made a strong go at it, and it was enlightening to see the pieces that ended up mattering to them, and to hear the kinds of questions they asked.

At the GGI Lectures on the Theory of Fundamental Interactions

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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.

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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.

Proofs and Insight

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Hearing us talking about the Amplituhedron, the professor across the table chimed in.

“The problem with you amplitudes people, I never know what’s a conjecture and what’s proven. The Amplituhedron, is that still a conjecture?”

The Amplituhedron, indeed, is still a conjecture (although a pretty well-supported one at this point). After clearing that up, we got to talking about the role proofs play in theoretical physics.

The professor was worried that we weren’t being direct enough in stating which ideas in amplitudes had been proven. While I agreed that we should be clearer, one of his points stood out to me: he argued that one benefit of clearly labeling conjectures is that it motivates people to go back and prove things. That’s a good thing to do in general, to be sure that your conjecture is really true, but often it has an added benefit: even if you’re pretty sure your conjecture is true, proving it can show you why it’s true, leading to new and valuable insight.

There’s a long history of important physics only becoming clear when someone took the time to work out a proof. But in amplitudes right now, I don’t think our lack of proofs is leading to a lack of insight. That’s because the kinds of things we’d like to prove often require novel insight themselves.

It’s not clear what it would take to prove the Amplituhedron. Even if you’ve got a perfectly clear, mathematically nice definition for it, you’d still need to prove that it does what it’s supposed to do: that it really calculates scattering amplitudes in N=4 super Yang-Mills. In order to do that, you’d need a very complete understanding of how those calculations work. You’d need to be able to see how known methods give rise to something like the Amplituhedron, or to find the Amplituhedron buried deep in the structure of the theory.

If you had that kind of insight? Then yeah, you could prove the Amplituhedron, and accomplish remarkable things along the way. But more than that, if you had that sort of insight, you would prove the Amplituhedron. Even if you didn’t know about the Amplituhedron to begin with, or weren’t sure whether or not it was a conjecture, once you had that kind of insight proving something like the Amplituhedron would be the inevitable next step. The signpost, “this is a conjecture” is helpful for other reasons, but it doesn’t change circumstances here: either you have what you need, or you don’t.

This contrasts with how progress works in other parts of physics, and how it has worked at other times. Sometimes, a field is moving so fast that conjectures get left by the wayside, even when they’re provable. You get situations where everyone busily assumes something is true and builds off it, and no-one takes the time to work out why. In that sort of field, it can be really valuable to clearly point out conjectures, so that someone gets motivated to work out the proof (and to hopefully discover something along the way).

I don’t think amplitudes is in that position though. It’s still worthwhile to signal our conjectures, to make clear what needs a proof and what doesn’t. But our big conjectures, like the Amplituhedron, aren’t the kind of thing someone can prove just by taking some time off and working on it. They require new, powerful insight. Because of that, our time is typically best served looking for that insight, finding novel examples and unusual perspectives that clear up what’s really going on. That’s a fair bit broader an activity than just working out a proof.