Monthly Archives: February 2020

These Ain’t Democritus’s Particles

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Physicists talk a lot about fundamental particles. But what do we mean by fundamental?

The Ancient Greek philosopher Democritus thought the world was composed of fundamental indivisible objects, constantly in motion. He called these objects “atoms”, and believed they could never be created or destroyed, with every other phenomenon explained by different types of interlocking atoms.

The things we call atoms today aren’t really like this, as you probably know. Atoms aren’t indivisible: their electrons can be split from their nuclei, and with more energy their nuclei can be split into protons and neutrons. More energy yet, and protons and neutrons can in turn be split into quarks. Still, at this point you might wonder: could quarks be Democritus’s atoms?

In a word, no. Nonetheless, quarks are, as far as we know, fundamental particles. As it turns out, our “fundamental” is very different from Democritus’s. Our fundamental particles can transform.

Think about beta decay. You might be used to thinking of it in terms of protons and neutrons: an unstable neutron decays, becoming a proton, an electron, and an (electron-anti-)neutrino. You might think that when the neutron decays, it literally “decays”, falling apart into smaller pieces.

But when you look at the quarks, the neutron’s smallest pieces, that isn’t the picture at all. In beta decay, a down quark in the neutron changes, turning into an up quark and an unstable W boson. The W boson then decays into an electron and a neutrino, while the up quark becomes part of the new proton. Even looking at the most fundamental particles we know, Democritus’s picture of unchanging atoms just isn’t true.

Could there be some even lower level of reality that works the way Democritus imagined? It’s not impossible. But the key insight of modern particle physics is that there doesn’t need to be.

As far as we know, up quarks and down quarks are both fundamental. Neither is “made of” the other, or “made of” anything else. But they also aren’t little round indestructible balls. They’re manifestations of quantum fields, “ripples” that slosh from one sort to another in complicated ways.

When we ask which particles are fundamental, we’re asking what quantum fields we need to describe reality. We’re asking for the simplest explanation, the simplest mathematical model, that’s consistent with everything we could observe. So “fundamental” doesn’t end up meaning indivisible, or unchanging. It’s fundamental like an axiom: used to derive the rest.

Understanding Is Translation

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Kernighan’s Law states, “Debugging is twice as hard as writing the code in the first place. Therefore, if you write the code as cleverly as possible, you are, by definition, not smart enough to debug it.” People sometimes make a similar argument about philosophy of mind: “The attempt of the mind to analyze itself [is] an effort analogous to one who would lift himself by his own bootstraps.”

Both points operate on a shared kind of logic. They picture understanding something as modeling it in your mind, with every detail clear. If you’ve already used all your mind’s power to design code, you won’t be able to model when it goes wrong. And modeling your own mind is clearly nonsense, you would need an even larger mind to hold the model.

The trouble is, this isn’t really how understanding works. To understand something, you don’t need to hold a perfect model of it in your head. Instead, you translate it into something you can more easily work with. Like explanations, these translations can be different for different people.

To understand something, I need to know the algorithm behind it. I want to know how to calculate it, the pieces that go in and where they come from. I want to code it up, to test it out on odd cases and see how it behaves, to get a feel for what it can do.

Others need a more physical picture. They need to know where the particles are going, or how energy and momentum are conserved. They want entropy to be increased, action to be minimized, scales to make sense dimensionally.

Others in turn are more mathematical. They want to start with definitions and axioms. To understand something, they want to see it as an example of a broader class of thing, groups or algebras or categories, to fit it into a bigger picture.

Each of these are a kind of translation, turning something into code-speak or physics-speak or math-speak. They don’t require modeling every detail, but when done well they can still explain every detail.

So while yes, it is good practice not to write code that is too “smart”, and too hard to debug…it’s not impossible to debug your smartest code. And while you can’t hold an entire mind inside of yours, you don’t actually need to do that to understand the brain. In both cases, all you need is a translation.

Valentine’s Day Physics Poem 2020

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It’s Valentine’s Day, time for my traditional physics poem. I’m trying a new format this year, let me know what you think!

Cherish the Effective

Self-styled wise men waste away, pining for the Ultimate Theory.
I tell you now: spurn their fate.
Scorn the Ultimate.
Cherish the Effective.
 
When you dream of an Ultimate Theory, what do you see?
An answer to your every question?
Every worry,
Every weakness,
Resolved?
A thing of beauty?
A thing of
       your notion
              and only your notion
of beauty?
 
Nature, she has her own worries.
Science, she never stops asking.
Your fairytale ending?
You won’t get it.
And you’ll hurt, and be hurt, in the trying.
 
You need a theory that isn’t an ending.
A theory you
              only
                   start
                          understanding
But can always discover.
No rigid, final truth,
But gentle corrections.
And as you push
                The scale
                           The energy
Your theory always has room for something new.
 
A theory like that, we call Effective.
A theory you can live
                      your
                           life
                                with.
It’s worth more than you think.

You Can’t Anticipate a Breakthrough

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As a scientist, you’re surrounded by puzzles. For every test and every answer, ten new questions pop up. You can spend a lifetime on question after question, never getting bored.

But which questions matter? If you want to change the world, if you want to discover something deep, which questions should you focus on? And which should you ignore?

Last year, my collaborators and I completed a long, complicated project. We were calculating the chance fundamental particles bounce off each other in a toy model of nuclear forces, pushing to very high levels of precision. We managed to figure out a lot, but as always, there were many questions left unanswered in the end.

The deepest of these questions came from number theory. We had noticed surprising patterns in the numbers that showed up in our calculation, reminiscent of the fancifully-named Cosmic Galois Theory. Certain kinds of numbers never showed up, while others appeared again and again. In order to see these patterns, though, we needed an unusual fudge factor: an unexplained number multiplying our result. It was clear that there was some principle at work, a part of the physics intimately tied to particular types of numbers.

There were also questions that seemed less deep. In order to compute our result, we compared to predictions from other methods: specific situations where the question becomes simpler and there are other ways of calculating the answer. As we finished writing the paper, we realized we could do more with some of these predictions. There were situations we didn’t use that nonetheless simplified things, and more predictions that it looked like we could make. By the time we saw these, we were quite close to publishing, so most of us didn’t have the patience to follow these new leads. We just wanted to get the paper out.

At the time, I expected the new predictions would lead, at best, to more efficiency. Maybe we could have gotten our result faster, or cleaned it up a bit. They didn’t seem essential, and they didn’t seem deep.

Fast forward to this year, and some of my collaborators (specifically, Lance Dixon and Georgios Papathanasiou, along with Benjamin Basso) have a new paper up: “The Origin of the Six-Gluon Amplitude in Planar N=4 SYM”. The “origin” in their title refers to one of those situations: when the variables in the problem are small, and you’re close to the “origin” of a plot in those variables. But the paper also sheds light on the origin of our calculation’s mysterious “Cosmic Galois” behavior.

It turns out that the origin (of the plot) can be related to another situation, when the paths of two particles in our calculation almost line up. There, the calculation can be done with another method, called the Pentagon Operator Product Expansion, or POPE. By relating the two, Basso, Dixon, and Papathanasiou were able to predict not only how our result should have behaved near the origin, but how more complicated as-yet un-calculated results should behave.

The biggest surprise, though, lurked in the details. Building their predictions from the POPE method, they found their calculation separated into two pieces: one which described the physics of the particles involved, and a “normalization”. This normalization, predicted by the POPE method, involved some rather special numbers…the same as the “fudge factor” we had introduced earlier! Somehow, the POPE’s physics-based setup “knows” about Cosmic Galois Theory!

It seems that, by studying predictions in this specific situation, Basso, Dixon, and Papathanasiou have accomplished something much deeper: a strong hint of where our mysterious number patterns come from. It’s rather humbling to realize that, were I in their place, I never would have found this: I had assumed “the origin” was just a leftover detail, perhaps useful but not deep.

I’m still digesting their result. For now, it’s a reminder that I shouldn’t try to pre-judge questions. If you want to learn something deep, it isn’t enough to sit thinking about it, just focusing on that one problem. You have to follow every lead you have, work on every problem you can, do solid calculation after solid calculation. Sometimes, you’ll just make incremental progress, just fill in the details. But occasionally, you’ll have a breakthrough, something that justifies the whole adventure and opens your door to something strange and new. And I’m starting to think that when it comes to breakthroughs, that’s always been the only way there.