Tag Archives: theoretical physics

At Quanta This Week, and Some Bonus Material

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When I moved back to Denmark, I mentioned that I was planning to do more science journalism work. The first fruit of that plan is up this week: I have a piece at Quanta Magazine about a perennially trendy topic in physics, the S-matrix.

It’s been great working with Quanta again. They’ve been thorough, attentive to the science, and patient with my still-uncertain life situation. I’m quite likely to have more pieces there in future, and I’ve got ideas cooking with other outlets as well, so stay tuned!

My piece with Quanta is relatively short, the kind of thing they used to label a “blog” rather than say a “feature”. Since the S-matrix is a pretty broad topic, there were a few things I couldn’t cover there, so I thought it would be nice to discuss them here. You can think of this as a kind of “bonus material” section for the piece. So before reading on, read my piece at Quanta first!

Welcome back!

At Quanta I wrote a kind of cartoon of the S-matrix, asking you to think about it as a matrix of probabilities, with rows for input particles and columns for output particles. There are a couple different simplifications I snuck in there, the pop physicist’s “lies to children“. One, I already flag in the piece: the entries aren’t really probabilities, they’re complex numbers, probability amplitudes.

There’s another simplification that I didn’t have space to flag. The rows and columns aren’t just lists of particles, they’re lists of particles in particular states.

What do I mean by states? A state is a complete description of a particle. A particle’s state includes its energy and momentum, including the direction it’s traveling in. It includes its spin, and the direction of its spin: for example, clockwise or counterclockwise? It also includes any charges, from the familiar electric charge to the color of a quark.

This makes the matrix even bigger than you might have thought. I was already describing an infinite matrix, one where you can have as many columns and rows as you can imagine numbers of colliding particles. But the number of rows and columns isn’t just infinite, but uncountable, as many rows and columns as there are different numbers you can use for energy and momentum.

For some of you, an uncountably infinite matrix doesn’t sound much like a matrix. But for mathematicians familiar with vector spaces, this is totally reasonable. Even if your matrix is infinite, or even uncountably infinite, it can still be useful to think about it as a matrix.

Another subtlety, which I’m sure physicists will be howling at me about: the Higgs boson is not supposed to be in the S-matrix!

In the article, I alluded to the idea that the S-matrix lets you “hide” particles that only exist momentarily inside of a particle collision. The Higgs is precisely that sort of particle, an unstable particle. And normally, the S-matrix is supposed to only describe interactions between stable particles, particles that can survive all the way to infinity.

In my defense, if you want a nice table of probabilities to put in an article, you need an unstable particle: interactions between stable particles depend on their energy and momentum, sometimes in complicated ways, while a single unstable particle will decay into a reliable set of options.

More technically, there are also contexts in which it’s totally fine to think about an S-matrix between unstable particles, even if it’s not usually how we use the idea.

My piece also didn’t have a lot of room to discuss new developments. I thought at minimum I’d say a bit more about the work of the young people I mentioned. You can think of this as an appetizer: there are a lot of people working on different aspects of this subject these days.

Part of the initial inspiration for the piece was when an editor at Quanta noticed a recent paper by Christian Copetti, Lucía Cordova, and Shota Komatsu. The paper shows an interesting case, where one of the “logical” conditions imposed in the original S-matrix bootstrap doesn’t actually apply. It ended up being too technical for the Quanta piece, but I thought I could say a bit about it, and related questions, here.

Some of the conditions imposed by the original bootstrappers seem unavoidable. Quantum mechanics makes no sense if doesn’t compute probabilities, and probabilities can’t be negative, or larger than one, so we’d better have an S-matrix that obeys those rules. Causality is another big one: we probably shouldn’t have an S-matrix that lets us send messages back in time and change the past.

Other conditions came from a mixture of intuition and observation. Crossing is a big one here. Crossing tells you that you can take an S-matrix entry with in-coming particles, and relate it to a different S-matrix entry with out-going anti-particles, using techniques from the calculus of complex numbers.

Crossing may seem quite obscure, but after some experience with S-matrices it feels obvious and intuitive. That’s why for an expert, results like the paper by Copetti, Cordova, and Komatsu seem so surprising. What they found was that a particularly exotic type of symmetry, called a non-invertible symmetry, was incompatible with crossing symmetry. They could find consistent S-matrices for theories with these strange non-invertible symmetries, but only if they threw out one of the basic assumptions of the bootstrap.

This was weird, but upon reflection not too weird. In theories with non-invertible symmetries, the behaviors of different particles are correlated together. One can’t treat far away particles as separate, the way one usually does with the S-matrix. So trying to “cross” a particle from one side of a process to another changes more than it usually would, and you need a more sophisticated approach to keep track of it. When I talked to Cordova and Komatsu, they related this to another concept called soft theorems, aspects of which have been getting a lot of attention and funding of late.

In the meantime, others have been trying to figure out where the crossing rules come from in the first place.

There were attempts in the 1970’s to understand crossing in terms of other fundamental principles. They slowed in part because, as the original S-matrix bootstrap was overtaken by QCD, there was less motivation to do this type of work anymore. But they also ran into a weird puzzle. When they tried to use the rules of crossing more broadly, only some of the things they found looked like S-matrices. Others looked like stranger, meaningless calculations.

A recent paper by Simon Caron-Huot, Mathieu Giroux, Holmfridur Hannesdottir, and Sebastian Mizera revisited these meaningless calculations, and showed that they aren’t so meaningless after all. In particular, some of them match well to the kinds of calculations people wanted to do to predict gravitational waves from colliding black holes.

Imagine a pair of black holes passing close to each other, then scattering away in different directions. Unlike particles in a collider, we have no hope of catching the black holes themselves. They’re big classical objects, and they will continue far away from us. We do catch gravitational waves, emitted from the interaction of the black holes.

This different setup turns out to give the problem a very different character. It ends up meaning that instead of the S-matrix, you want a subtly different mathematical object, one related to the original S-matrix by crossing relations. Using crossing, Caron-Huot, Giroux, Hannesdottir and Mizera found many different quantities one could observe in different situations, linked by the same rules that the original S-matrix bootstrappers used to relate S-matrix entries.

The work of these two groups is just some of the work done in the new S-matrix program, but it’s typical of where the focus is going. People are trying to understand the general rules found in the past. They want to know where they came from, and as a consequence, when they can go wrong. They have a lot to learn from the older papers, and a lot of new insights come from diligent reading. But they also have a lot of new insights to discover, based on the new tools and perspectives of the modern day. For the most part, they don’t expect to find a new unified theory of physics from bootstrapping alone. But by learning how S-matrices work in general, they expect to find valuable knowledge no matter how the future goes.

The Impact of Jim Simons

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The obituaries have been weirdly relevant lately.

First, a couple weeks back, Daniel Dennett died. Dennett was someone who could have had a huge impact on my life. Growing up combatively atheist in the early 2000’s, Dennett seemed to be exploring every question that mattered: how the semblance of consciousness could come from non-conscious matter, how evolution gives rise to complexity, how to raise a new generation to grow beyond religion and think seriously about the world around them. I went to Tufts to get my bachelor’s degree based on a glowing description he wrote in the acknowledgements of one of his books, and after getting there, I asked him to be my advisor.

(One of three, because the US education system, like all good games, can be min-maxed.)

I then proceeded to be far too intimidated to have a conversation with him more meaningful than “can you please sign my registration form?”

I heard a few good stories about Dennett while I was there, and I saw him debate once. I went into physics for my PhD, not philosophy.

Jim Simons died on May 10. I never spoke to him at all, not even to ask him to sign something. But he had a much bigger impact on my life.

I began my PhD at SUNY Stony Brook with a small scholarship from the Simons Foundation. The university’s Simons Center for Geometry and Physics had just opened, a shining edifice of modern glass next to the concrete blocks of the physics and math departments.

For a student aspiring to theoretical physics, the Simons Center virtually shouted a message. It taught me that physics, and especially theoretical physics, was something prestigious, something special. That if I kept going down that path I could stay in that world of shiny new buildings and daily cookie breaks with the occasional fancy jar-based desserts, of talks by artists and a café with twenty-dollar lunches (half-price once a week for students, the only time we could afford it, and still about twice what we paid elsewhere on campus). There would be garden parties with sushi buffets and late conference dinners with cauliflower steaks and watermelon salads. If I was smart enough (and I longed to be smart enough), that would be my future.

Simons and his foundation clearly wanted to say something along those lines, if not quite as filtered by the stars in a student’s eyes. He thought that theoretical physics, and research more broadly, should be something prestigious. That his favored scholars deserved more, and should demand more.

This did have weird consequences sometimes. One year, the university charged us an extra “academic excellence fee”. The story we heard was that Simons had demanded Stony Brook increase its tuition in order to accept his donations, so that it would charge more similarly to more prestigious places. As a state university, Stony Brook couldn’t do that…but it could add an extra fee. And since PhD students got their tuition, but not fees, paid by the department, we were left with an extra dent in our budgets.

The Simons Foundation created Quanta Magazine. If the Simons Center used food to tell me physics mattered, Quanta delivered the same message to professors through journalism. Suddenly, someone was writing about us, not just copying press releases but with the research and care of an investigative reporter. And they wrote about everything: not just sci-fi stories and cancer cures but abstract mathematics and the space of quantum field theories. Professors who had spent their lives straining to capture the public’s interest suddenly were shown an audience that actually wanted the real story.

In practice, the Simons Foundation made its decisions through the usual experts and grant committees. But the way we thought about it, the decisions always had a Jim Simons flavor. When others in my field applied for funding from the Foundation, they debated what Simons would want: would he support research on predictions for the LHC and LIGO? Or would he favor links to pure mathematics, or hints towards quantum gravity? Simons Collaboration Grants have an enormous impact on theoretical physics, dwarfing many other sources of funding. A grant funds an army of postdocs across the US, shifting the priorities of the field for years at a time.

Denmark has big foundations that have an outsize impact on science. Carlsberg, Villum, and the bigger-than-Denmark’s GDP Novo Nordisk have foundations with a major influence on scientific priorities. But Denmark is a country of six million. It’s much harder to have that influence on a country of three hundred million. Despite that, Simons came surprisingly close.

While we did like to think of the Foundation’s priorities as Simons’, I suspect that it will continue largely on the same track without him. Quanta Magazine is editorially independent, and clearly puts its trust in the journalists that made it what it is today.

I didn’t know Simons, I don’t think I even ever smelled one of his famous cigars. Usually, that would be enough to keep me from writing a post like this. But, through the Foundation, and now through Quanta, he’s been there with me the last fourteen years. That’s worth a reflection, at the very least.

Generalizing a Black Box Theory

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In physics and in machine learning, we have different ways of thinking about models.

A model in physics, like the Standard Model, is a tool to make predictions. Using statistics and a whole lot of data (from particle physics experiments), we fix the model’s free parameters (like the mass of the Higgs boson). The model then lets us predict what we’ll see next: when we turn on the Large Hadron Collider, what will the data look like? In physics, when a model works well, we think that model is true, that it describes the real way the world works. The Standard Model isn’t the ultimate truth: we expect that a better model exists that makes better predictions. But it is still true, in an in-between kind of way. There really are Higgs bosons, even if they’re a result of some more mysterious process underneath, just like there really are atoms, even if they’re made out of protons, neutrons, and electrons.

A model in machine learning, like the Large Language Model that fuels ChatGPT, is also a tool to make predictions. Using statistics and a whole lot of data (from text on the internet, or images, or databases of proteins, or games of chess…) we fix the model’s free parameters (called weights, numbers for the strengths of connections between metaphorical neurons). The model then lets us predict what we’ll see next: when a text begins “Q: How do I report a stolen card? A:”, how does it end?

So far, that sounds a lot like physics. But in machine learning, we don’t generally think these models are true, at least not in the same way. The thing producing language isn’t really a neural network like a Large Language Model. It’s the sum of many human brains, many internet users, spread over many different circumstances. Each brain might be sort of like a neural network, but they’re not like the neural networks sitting on OpenAI’s servers. A Large Language Model isn’t true in some in-between kind of way, like atoms or Higgs bosons. It just isn’t true. It’s a black box, a machine that makes predictions, and nothing more.

But here’s the rub: what do we mean by true?

I want to be a pragmatist here. I don’t want to get stuck in a philosophical rabbit-hole, arguing with metaphysicists about what “really exists”. A true theory should be one that makes good predictions, that lets each of us know, based on our actions, what we should expect to see. That’s why science leads to technology, why governments and companies pay people to do it: because the truth lets us know what will happen, and make better choices. So if Large Language Models and the Standard Model both make good predictions, why is only one of them true?

Recently, I saw Dan Elton of More is Different make the point that there is a practical reason to prefer the “true” explanations: they generalize. A Large Language Model might predict what words come next in a text. But it doesn’t predict what happens when you crack someone’s brain open and see how the neurons connect to each other, even if that person is the one who made the text. A good explanation, a true model, can be used elsewhere. The Standard Model tells you what data from the Large Hadron Collider will look like, but it also tells you what data from the muon g-2 experiment will look like. It also, in principle, tells you things far away from particle physics: what stars look like, what atoms look like, what the inside of a nuclear reactor looks like. A black box can’t do that, even if it makes great predictions.

It’s a good point. But thinking about it, I realized things are a little murkier.

You can’t generalize a Large Language Model to tell you how human neurons are connected. But you can generalize it in other ways, and people do. There’s a huge industry in trying to figure out what GPT and its relatives “know”. How much math can they do? How much do they know about geography? Can they predict the future?

These generalizations don’t work the way that they do in physics, or the rest of science, though. When we generalize the Standard Model, we aren’t taking a machine that makes particle physics predictions and trying to see what those particle physics predictions can tell us. We’re taking something “inside” the machine, the fields and particles, and generalizing that, seeing how the things around us could be made of those fields and those particles. In contrast, when people generalize GPT, they typically don’t look inside the “black box”. They use the Large Language Model to make predictions, and see what those predictions “know about”.

On the other hand, we do sometimes generalize scientific models that way too.

If you’re simulating the climate, or a baby star, or a colony of bacteria, you typically aren’t using your simulation like a prediction machine. You don’t plug in exactly what is going on in reality, then ask what happens next. Instead, you run many simulations with different conditions, and look for patterns. You see how a cloud of sulfur might cool down the Earth, or how baby stars often form in groups, leading them to grow up into systems of orbiting black holes. Your simulation is kind of like a black box, one that you try out in different ways until you uncover some explainable principle, something your simulation “knows” that you can generalize.

And isn’t nature that kind of black box, too? When we do an experiment, aren’t we just doing what the Large Language Models are doing, prompting the black box in different ways to get an idea of what it knows? Are scientists who do experiments that picky about finding out what’s “really going on”, or do they just want a model that works?

We want our models to be general, and to be usable. Building a black box can’t be the whole story, because a black box, by itself, isn’t general. But it can certainly be part of the story. Going from the black box of nature to the black box of a machine lets you run tests you couldn’t previously do, lets you investigate faster and ask stranger questions. With a simulation, you can blow up stars. With a Large Language Model, you can ask, for a million social media comments, whether the average internet user would call them positive or negative. And if you make sure to generalize, and try to make better decisions, then it won’t be just the machine learning. You’ll be learning too.

What Are Particles? The Gentle Introduction

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On this blog, I write about particle physics for the general public. I try to make things as simple as possible, but I do have to assume some things. In particular, I usually assume you know what particles are!

This time, I won’t do that. I know some people out there don’t know what a particle is, or what particle physicists do. If you’re a person like that, this post is for you! I’m going to give a gentle introduction to what particle physics is all about.

Let’s start with atoms.

Every object and substance around you, everything you can touch or lift or walk on, the water you drink and the air you breathe, all of these are made up of atoms. Some are simple: an iron bar is made of Iron atoms, aluminum foil is mostly Aluminum atoms. Some are made of combinations of atoms into molecules, like water’s famous H2O: each molecule has two Hydrogen atoms and one Oxygen atom. Some are made of more complicated mixtures: air is mostly pairs of Nitrogen atoms, with a healthy amount of pairs of Oxygen, some Carbon Dioxide (CO2), and many other things, while the concrete sidewalks you walk on have Calcium, Silicon, Aluminum, Iron, and Oxygen, all combined in various ways.

There is a dizzying array of different types of atoms, called chemical elements. Most occur in nature, but some are man-made, created by cutting-edge nuclear physics. They can all be organized in the periodic table of elements, which you’ve probably seen on a classroom wall.

The periodic table

The periodic table is called the periodic table because it repeats, periodically. Each element is different, but their properties resemble each other. Oxygen is a gas, Sulfur a yellow powder, Polonium an extremely radioactive metal…but just as you can find H2O, you can make H2S, and even H2Po. The elements get heavier as you go down the table, and more metal-like, but their chemical properties, the kinds of molecules you can make with them, repeat.

Around 1900, physicists started figuring out why the elements repeat. What they discovered is that each atom is made of smaller building-blocks, called sub-atomic particles. (“Sub-atomic” because they’re smaller than atoms!) Each atom has electrons on the outside, and on the inside has a nucleus made of protons and neutrons. Atoms of different elements have different numbers of protons and electrons, which explains their different properties.

Different atoms with different numbers of protons, neutrons, and electrons

Around the same time, other physicists studied electricity, magnetism, and light. These things aren’t made up of atoms, but it was discovered that they are all aspects of the same force, the electromagnetic force. And starting with Einstein, physicists figured out that this force has particles too. A beam of light is made up of another type of sub-atomic particle, called a photon.

For a little while then, it seemed that the universe was beautifully simple. All of matter was made of electrons, protons, and neutrons, while light was made of photons.

(There’s also gravity, of course. That’s more complicated, in this post I’ll leave it out.)

Soon, though, nuclear physicists started noticing stranger things. In the 1930’s, as they tried to understand the physics behind radioactivity and mapped out rays from outer space, they found particles that didn’t fit the recipe. Over the next forty years, theoretical physicists puzzled over their equations, while experimental physicists built machines to slam protons and electrons together, all trying to figure out how they work.

Finally, in the 1970’s, physicists had a theory they thought they could trust. They called this theory the Standard Model. It organized their discoveries, and gave them equations that could predict what future experiments would see.

In the Standard Model, there are two new forces, the weak nuclear force and the strong nuclear force. Just like photons for the electromagnetic force, each of these new forces has a particle. The general word for these particles is bosons, named after Satyendra Nath Bose, a collaborator of Einstein who figured out the right equations for this type of particle. The weak force has bosons called W and Z, while the strong force has bosons called gluons. A final type of boson, called the Higgs boson after a theorist who suggested it, rounds out the picture.

The Standard Model also has new types of matter particles. Neutrinos interact with the weak nuclear force, and are so light and hard to catch that they pass through nearly everything. Quarks are inside protons and neutrons: a proton contains one one down quark and two up quarks, while a neutron contains two down quarks and one up quark. The quarks explained all of the other strange particles found in nuclear physics.

Finally, the Standard Model, like the periodic table, repeats. There are three generations of particles. The first, with electrons, up quarks, down quarks, and one type of neutrino, show up in ordinary matter. The other generations are heavier, and not usually found in nature except in extreme conditions. The second generation has muons (similar to electrons), strange quarks, charm quarks, and a new type of neutrino called a muon-neutrino. The third generation has tauons, bottom quarks, top quarks, and tau-neutrinos.

(You can call these last quarks “truth quarks” and “beauty quarks” instead, if you like.)

Physicists had the equations, but the equations still had some unknowns. They didn’t know how heavy the new particles were, for example. Finding those unknowns took more experiments, over the next forty years. Finally, in 2012, the last unknown was found when a massive machine called the Large Hadron Collider was used to measure the Higgs boson.

The Standard Model

We think that these particles are all elementary particles. Unlike protons and neutrons, which are both made of up quarks and down quarks, we think that the particles of the Standard Model are not made up of anything else, that they really are elementary building-blocks of the universe.

We have the equations, and we’ve found all the unknowns, but there is still more to discover. We haven’t seen everything the Standard Model can do: to see some properties of the particles and check they match, we’d need a new machine, one even bigger than the Large Hadron Collider. We also know that the Standard Model is incomplete. There is at least one new particle, called dark matter, that can’t be any of the known particles. Mysteries involving the neutrinos imply another type of unknown particle. We’re also missing deeper things. There are patterns in the table, like the generations, that we can’t explain.

We don’t know if any one experiment will work, or if any one theory will prove true. So particle physicists keep working, trying to find new tricks and make new discoveries.

Models, Large Language and Otherwise

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In particle physics, our best model goes under the unimaginative name “Standard Model“. The Standard Model models the world in terms of interactions of different particles, or more properly quantum fields. The fields have different masses and interact with different strengths, and each mass and interaction strength is a parameter: a “free” number in the model, one we have to fix based on data. There are nineteen parameters in the Standard Model (not counting the parameters for massive neutrinos, which were discovered later).

In principle, we could propose a model with more parameters that fit the data better. With enough parameters, one can fit almost anything. That’s cheating, though, and it’s a type of cheating we know how to catch. We have statistical tests that let us estimate how impressed we should be when a model matches the data. If a model is just getting ahead on extra parameters without capturing something real, we can spot that, because it gets a worse score on those tests. A model with a bad score might match the data you used to fix its parameters, but it won’t predict future data, so it isn’t actually useful. Right now the Standard Model (plus neutrino masses) gets the best score on those tests, when fitted to all the data we have access to, so we think of it as our best and most useful model. If someone proposed a model that got a better score, we’d switch: but so far, no-one has managed.

Physicists care about this not just because a good model is useful. We think that the best model is, in some sense, how things really work. The fact that the Standard Model fits the data best doesn’t just mean we can use it to predict more data in the future: it means that somehow, deep down, that the world is made up of quantum fields the way the Standard Model describes.

If you’ve been following developments in machine learning, or AI, you might have heard the word “model” slung around. For example, GPT is a Large Language Model, or LLM for short.

Large Language Models are more like the Standard Model than you might think. Just as the Standard Model models the world in terms of interacting quantum fields, Large Language Models model the world in terms of a network of connections between artificial “neurons”. Just as particles have different interaction strengths, pairs of neurons have different connection weights. Those connection weights are the parameters of a Large Language Model, in the same way that the masses and interaction strengths of particles are the parameters of the Standard Model. The parameters for a Large Language Model are fixed by a giant corpus of text data, almost the whole internet reduced to a string of bytes that the LLM needs to match, in the same way the Standard Model needs to match data from particle collider experiments. The Standard Model has nineteen parameters, Large Language Models have billions.

Increasingly, machine learning models seem to capture things better than other types of models. If you want to know how a protein is going to fold, you can try to make a simplified model of how its atoms and molecules interact with each other…but instead, you can make your model a neural network. And that turns out to work better. If you’re a bank and you want to know how many of your clients will default on their loans, you could ask an economist to make a macroeconomic model…or, you can just make your model a neural network too.

In physics, we think that the best model is the model that is closest to reality. Clearly, though, this can’t be what’s going on here. Real proteins don’t fold based on neural networks, and neither do real economies. Both economies and folding proteins are very complicated, so any model we can use right now won’t be what’s “really going on”, unlike the comparatively simple world of particle physics. Still, it seems weird that, compared to the simplified economic or chemical models, neural networks can work better, even if they’re very obviously not really what’s going on. Is there another way to think about them?

I used to get annoyed at people using the word “AI” to refer to machine learning models. In my mind, AI was the thing that shows up in science fiction, machines that can think as well or better than humans. (The actual term of art for this is AGI, artificial general intelligence.) Machine learning, and LLMs in particular, felt like a meaningful step towards that kind of AI, but they clearly aren’t there yet.

Since then, I’ve been convinced that the term isn’t quite so annoying. The AI field isn’t called AI because they’re creating a human-equivalent sci-fi intelligence. They’re called AI because the things they build are inspired by how human intelligence works.

As humans, we model things with mathematics, but we also model them with our own brains. Consciously, we might think about objects and their places in space, about people and their motivations and actions, about canonical texts and their contents. But all of those things cash out in our neurons. Anything we think, anything we believe, any model we can actually apply by ourselves in our own lives, is a model embedded in a neural network. It’s quite a bit more complicated neural network than an LLM, but it’s very much still a kind of neural network.

Because humans are alright at modeling a variety of things, because we can see and navigate the world and persuade and manipulate each other, we know that neural networks can do these things. A human brain may not be the best model for any given phenomenon: an engineer can model the flight of a baseball with math much better than the best baseball player can with their unaided brain. But human brains still tend to be fairly good models for a wide variety of things. Evolution has selected them to be.

So with that in mind, it shouldn’t be too surprising that neural networks can model things like protein folding. Even if proteins don’t fold based on neural networks, even if the success of AlphaFold isn’t capturing the actual details of the real world the way the Standard Model does, the model is capturing something. It’s loosely capturing the way a human would think about the problem, if you gave that human all the data they needed. And humans are, and remain, pretty good at thinking! So we have reason, not rigorous, but at least intuitive reason, to think that neural networks will actually be good models of things.

What Referees Are For

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This week, we had a colloquium talk by the managing editor of the Open Journal of Astrophysics.

The Open Journal of Astrophysics is an example of an arXiv overlay journal. In the old days, journals shouldered the difficult task of compiling scientists’ work into a readable format and sending them to university libraries all over the world so people could stay up to date with the work of distant colleagues. They used to charge libraries for the journals, now some instead charge authors per paper they want to publish.

Now, most of that is unnecessary due to online resources, in my field the arXiv. We prepare our papers using free tools like LaTeX, then upload them to arXiv.org, a website that makes the papers freely accessible for everybody. I don’t think I’ve ever read a paper in a physical journal in my field, and I only check journal websites if I think there’s a mistake in the arXiv version. The rest of the time, I just use the arXiv.

Still, journals do one thing the arXiv doesn’t do, and that’s refereeing. Each paper a journal receives is sent out to a few expert referees. The referees read the paper, and either reject it, accept it as-is, or demand changes before they can accept it. The journal then publishes accepted papers only.

The goal of arXiv overlay journals is to make this feature of journals also unnecessary. To do this, they notice that if every paper is already on arXiv, they don’t need to host papers or print them or typeset them. They just need to find suitable referees, and announce which papers passed.

The Open Journal of Astrophysics is a relatively small arXiv overlay journal. They operate quite cheaply, in part because the people running it can handle most of it as a minor distraction from their day job. SciPost is much bigger, and has to spend more per paper to operate. Still, it spends a lot less than journals charge authors.

We had a spirited discussion after the talk, and someone brought up an interesting point: why do we need to announce which papers passed? Can’t we just publish everything?

What, in the end, are the referees actually for? Why do we need them?

One function of referees is to check for mistakes. This is most important in mathematics, where referees might spend years making sure every step in a proof works as intended. Other fields vary, from theoretical physics (where we can check some things sometimes, but often have to make do with spotting poorly explained parts of a calculation), to fields that do experiments in the real world (where referees can look for warning signs and shady statistics, but won’t actually reproduce the experiment). A mistake found by a referee can be a boon to not just the wider scientific community, but to the author as well. Most scientists would prefer their papers to be correct, so we’re often happy to hear about a genuine mistake.

If this was all referees were for, though, then you don’t actually need to reject any papers. As a colleague of mine suggested, you just need the referees to publish their reports. Then the papers could be published along with comments from the referees, and possibly also responses from the author. Readers could see any mistakes the referees found, and judge for themselves what they show about the result.

Referees already publish their reports in SciPost much of the time, though not currently in the Open Journal of Astrophysics. Both journals still reject some papers, though. In part, that’s because they serve another function: referees are supposed to tell us which papers are “good”.

Some journals are more prestigious and fancy than others. Nature and Science are the most famous, though people in my field almost never bother to publish in either. Still, we have a hierarchy in mind, with Physical Review Letters on the high end and JHEP on the lower one. Publishing in a fancier and more prestigious journal is supposed to say something about you as a scientist, to say that your work is fancier and more prestigious. If you can’t publish in any journal at all, then your work wasn’t interesting enough to merit getting credit for it, and maybe you should have worked harder.

What does that credit buy you? Ostensibly, everything. Jobs are more likely to hire you if you’ve published in more prestigious places, and grant agencies will be more likely to give you money.

In practice, though, this depends a lot on who’s making the decisions. Some people will weigh these kinds of things highly, especially if they aren’t familiar with a candidate’s work. Others will be able to rely on other things, from numbers of papers and citations to informal assessments of a scientist’s impact. I genuinely don’t know whether the journals I published in made any impact at all when I was hired, and I’m a bit afraid to ask. I haven’t yet sat on the kind of committee that makes these decisions, so I don’t know what things look like from the other side either.

But I do know that, on a certain level, journals and publications can’t matter quite as much as we think. As I mentioned, my field doesn’t use Nature or Science, while others do. A grant agency or hiring committee comparing two scientists would have to take that into account, just as they have to take into account the thousands of authors on every single paper by the ATLAS and CMS experiments. If a field started publishing every paper regardless of quality, they’d have to adapt there too, and find a new way to judge people compatible with that.

Can we just publish everything, papers and referee letters and responses and letters and reviews? Maybe. I think there are fields where this could really work well, and fields where it would collapse into the invective of a YouTube comments section. I’m not sure where my own field sits. Theoretical particle physics is relatively small and close-knit, but it’s also cool and popular, with many strong and dumb opinions floating around. I’d like to believe we could handle it, that we could prune back the professional cruft and turn our field into a real conversation between scholars. But I don’t know.

IPhT-60 Retrospective

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Last week, my institute had its 60th anniversary party, which like every party in academia takes the form of a conference.

For unclear reasons, this one also included a physics-themed arcade game machine.

Going in, I knew very little about the history of the Institute of Theoretical Physics, of the CEA it’s part of (Commissariat of Atomic Energy, now Atomic and Alternative Energy), or of French physics in general, so I found the first few talks very interesting. I learned that in France in the early 1950’s, theoretical physics was quite neglected. Key developments, like relativity and statistical mechanics, were seen as “too German” due to their origins with Einstein and Boltzmann (nevermind that this was precisely why the Nazis thought they were “not German enough”), while de Broglie suppressed investigation of quantum mechanics. It took French people educated abroad to come back and jumpstart progress.

The CEA is, in a sense, the French equivalent of the some of the US’s national labs, and like them got its start as part of a national push towards nuclear weapons and nuclear power.

(Unlike the US’s national labs, the CEA is technically a private company. It’s not even a non-profit: there are for-profit components that sell services and technology to the energy industry. Never fear, my work remains strictly useless.)

My official title is Ingénieur Chercheur, research engineer. In the early days, that title was more literal. Most of the CEA’s first permanent employees didn’t have PhDs, but were hired straight out of undergraduate studies. The director, Claude Bloch, was in his 40’s, but most of the others were in their 20’s. There was apparently quite a bit of imposter syndrome back then, with very young people struggling to catch up to the global state of the art.

They did manage to catch up, though, and even excel. In the 60’s and 70’s, researchers at the institute laid the groundwork for a lot of ideas that are popular in my field at the moment. Stora’s work established a new way to think about symmetry that became the textbook approach we all learn in school, while Froissart figured out a consistency condition for high-energy physics whose consequences we’re still teasing out. Pham was another major figure at the institute in that era. With my rudimentary French I started reading his work back in Copenhagen, looking for new insights. I didn’t go nearly as fast as my partner in the reading group though, whose mastery of French and mathematics has seen him use Pham’s work in surprising new ways.

Hearing about my institute’s past, I felt a bit of pride in the physicists of the era, not just for the science they accomplished but for the tools they built to do it. This was the era of preprints, first as physical papers, orange folders mailed to lists around the world, and later online as the arXiv. Physicists here were early adopters of some aspects, though late adopters of others (they were still mailing orange folders a ways into the 90’s). They also adopted computation, with giant punch-card reading, sheets-of-output-producing computers staffed at all hours of the night. A few physicists dove deep into the new machines, and guided the others as capabilities changed and evolved, while others were mostly just annoyed by the noise!

When the institute began, scientific papers were still typed on actual typewriters, with equations handwritten in or typeset in ingenious ways. A pool of secretaries handled much of the typing, many of whom were able to come to the conference! I wonder what they felt, seeing what the institute has become since.

I also got to learn a bit about the institute’s present, and by implication its future. I saw talks covering different areas, from multiple angles on mathematical physics to simulations of large numbers of particles, quantum computing, and machine learning. I even learned a bit from talks on my own area of high-energy physics, highlighting how much one can learn from talking to new people.

IPhT’s 60-Year Anniversary

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This year is the 60th anniversary of my new employer, the Institut de Physique Théorique of CEA Paris-Saclay (or IPhT for short). In celebration, they’re holding a short conference, with a variety of festivities. They’ve been rushing to complete a film about the institute, and I hear there’s even a vintage arcade game decorated with Feynman diagrams. For me, it will be a chance to learn a bit more about the history of this place, which I currently know shamefully little about.

(For example, despite having his textbook on my shelf, I don’t know much about what our Auditorium’s namesake Claude Itzykson was known for.)

Since I’m busy with the conference this week, I won’t have time for a long blog post. Next week I’ll be able to say more, and tell you what I learned!

Theorems About Reductionism

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A reductionist would say that the behavior of the big is due to the behavior of the small. Big things are made up of small things, so anything the big things do must be explicable in terms of what the small things are doing. It may be very hard to explain things this way: you wouldn’t want to describe the economy in terms of motion of carbon atoms. But in principle, if you could calculate everything, you’d find the small things are enough: there are no fundamental “new rules” that only apply to big things.

A physicist reductionist would have to amend this story. Zoom in far enough, and it doesn’t really make sense to talk about “small things”, “big things”, or even “things” at all. The world is governed by interactions of quantum fields, ripples spreading and colliding and changing form. Some of these ripples (like the ones we call “protons”) are made up of smaller things…but ultimately most aren’t. They just are what they are.

Still, a physicist can rescue the idea of reductionism by thinking about renormalization. If you’ve heard of renormalization, you probably think of it as a trick physicists use to hide inconvenient infinite results in their calculations. But an arguably better way to think about it is as a kind of “zoom” dial for quantum field theories. Starting with a theory, we can use renormalization to “zoom out”, ignoring the smallest details and seeing what picture emerges. As we “zoom”, different forces will seem to get stronger or weaker: electromagnetism matters less when we zoom out, the strong nuclear force matters more.

(Why then, is electromagnetism so much more important in everyday life? The strong force gets so strong as we zoom out that we stop seeing individual particles, and only see them bound into protons and neutrons. Electromagnetism is like this too, binding electrons and protons into neutral atoms. In both cases, it can be better, once we’ve zoomed out, to use a new description: you don’t want to do chemistry keeping track of the quarks and gluons.)

A physicists reductionist then, would expect renormalization to always go “one way”. As we “zoom out”, we should find that our theories in a meaningful sense get simpler and simpler. Maybe they’re still hard to work with: it’s easier to think about gluons and quarks when zoomed in than the zoo of different nuclear particles we need to consider when zoomed out. But at each step, we’re ignoring some details. And if you’re a reductionist, you shouldn’t expect “zooming out” to show you anything truly fundamentally new.

Can you prove that, though?

Surprisingly, yes!

In 2011, Zohar Komargodski and Adam Schwimmer proved a result called the a-theorem. “The a-theorem” is probably the least google-able theorem in the universe, which has probably made it hard to popularize. It is named after a quantity, labeled “a”, that gives a particular way to add up energy in a quantum field theory. Komargodski and Schwimmer proved that, when you do the renormalization procedure and “zoom out”, then this quantity “a” will always get smaller.

Why does this say anything about reductionism?

Suppose you have a theory that violates reductionism. You zoom out, and see something genuinely new: a fact about big things that isn’t due to facts about small things. If you had a theory like that, then you could imagine “zooming in” again, and using your new fact about big things to predict something about the small things that you couldn’t before. You’d find that renormalization doesn’t just go “one way”: with new facts able to show up at every scale, zooming out isn’t necessarily ignoring more and zooming in isn’t necessarily ignoring less. It would depend on the situation which way the renormalization procedure would go.

The a-theorem puts a stop to this. It says that, when you “zoom out”, there is a number that always gets smaller. In some ways it doesn’t matter what that number is (as long as you’re not cheating and using the scale directly). In this case, it is a number that loosely counts “how much is going on” in a given space. And because it always decreases when you do renormalization, it means that renormalization can never “go backwards”. You can never renormalize back from your “zoomed out” theory to the “zoomed in” one.

The a-theorem, like every theorem, is based on assumptions. Here, the assumptions are mostly that quantum field theory works in the normal way, that the theory we’re dealing with is not a totally new type of theory instead. One assumption I find interesting is the assumption of locality, that no signals can travel faster than the speed of light. On a naive level, this makes a lot of sense to me. If you can send signals faster than light, then you can’t control your “zoom lens”. Physics in a small area might be changed by something happening very far away, so you can’t “zoom in” in a way that lets you keep including everything that could possibly be relevant. If you have signals that go faster than light, you could transmit information between different parts of big things without them having to “go through” small things first. You’d screw up reductionism, and have surprises show up on every scale.

Personally, I find it really cool that it’s possible to prove a theorem that says something about a seemingly philosophical topic like reductionism. Even with assumptions (and even with the above speculations about the speed of light), it’s quite interesting that one can say anything at all about this kind of thing from a physics perspective. I hope you find it interesting too!

Academic Hiring: My Field vs. Bret’s

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Bret Deveraux is a historian and history-blogger who’s had a rough time on the academic job market. He recently had a post about how academic hiring works, at least in his corner of academia. Since we probably have some overlap in audience (and should have more, if you’re at all interested in ancient history he’s got some great posts), I figured I’d make a post of my own pointing out how my field, and fields nearby, do things differently.

First, there’s a big difference in context. The way Bret describes things, it sounds like he’s applying only to jobs in the US (maybe also Canada?). In my field, you can do that (the US is one of a few countries big enough to do that), but in practice most searches are at least somewhat international. If you look at the Rumor Mill, you’ll see a fair bit of overlap between US searches and UK searches, for example.

Which brings up another difference: rumor mills! It can be hard for applicants to get a clear picture of what’s going on. Universities sometimes forget to let applicants know they weren’t shortlisted, or even that someone else was hired. Rumor mills are an informal way to counteract this. They’re websites where people post which jobs are advertised in a given year, who got shortlisted, and who eventually got offered the job. There’s a rumor mill for the US market (including some UK jobs anyway), a UK rumor mill, a German/Nordic rumor mill (which also has a bunch of Italian jobs on it, to the seeming annoyance of the organizers), and various ones that I haven’t used but are linked on the US one’s page.

Bret describes a seasonal market with two stages: a first stage aimed at permanent positions, and a second stage for temporary adjunct teaching positions. My field doesn’t typically do adjuncts, so we just have the first stage. This is usually, like Bret’s field, something that happens in the Fall through Winter, but in Europe institutional funding decisions can get made later in the year, so I’ve seen new permanent positions get advertised even into the early Spring.

(Our temporary positions are research-focused, and advertised at basically the same time of year as the faculty positions, with the caveat that there is a special rule for postdocs. Due to a widely signed agreement, we in high-energy theory have agreed to not require postdocs to make a decision about whether they will accept a position until Feb 15 at the earliest. This stopped what used to be an arms race, with positions requiring postdocs to decide earlier and earlier in order to snatch the good ones before other places could make offers. The deadline was recently pushed a bit later yet, to lower administrative load during the Christmas break.)

Bret also describes two stages of interviews, a long-list interviewed on Zoom (that used to be interviewed at an important conference) and a short-list interviewed on campus. We just have the latter: while there are sometimes long-lists, they’re usually an internal affair, and I can’t think of a conference you could expect everyone to go to for interviews anyway. Our short-lists are also longer than his: I was among eight candidates when I interviewed for my position, which is a little high but not unheard of, five is quite typical.

His description of the actual campus visit matches my experience pretty well. There’s a dedicated talk, and something that resembles a “normal job interview”, but the rest, conversations from the drive in to the dinners if they organize them, are all interviews on some level too.

(I would add though, that while everyone there is trying to sort out if you’d be a good fit for them, you should also try to sort out if they’d be a good fit for you. I’ll write more about this another time, but I’m increasingly convinced that a key element in my landing a permanent position was the realization that, rather than just trying for every position I where I plausibly had a chance, I should focus on positions where I would actually be excited to collaborate with folks there.)

Bret’s field, as mentioned, has a “second round” of interviews for temporary positions, including adjuncts and postdocs. We don’t have adjuncts, but we do have postdocs, and they mostly interview at the same time the faculty do. For Bret, this wouldn’t make any sense, because anyone applying for postdocs is also applying for faculty positions, but in my field there’s less overlap. For one, very few people apply for faculty positions right out of their PhD: almost everyone, except those viewed as exceptional superstars, does at least one postdoc first. After that, you can certainly have collisions, with someone taking a postdoc and then getting a faculty job. The few times I’ve broached this possibility with people, they were flexible: most people have no hard feelings if a postdoc accepts a position and then changes their mind when they get a faculty job, and many faculty jobs let people defer a year, so they can do their postdoc and then start their faculty job afterwards.

(It helps that my field never seems to have all that much pressure to fill teaching roles. I’m not sure why (giant lecture courses using fewer profs? more research funding meaning we don’t have to justify ourselves with more undergrad majors?), but it’s probably part of why we don’t seem to hire adjuncts very often.)

Much like in Bret’s field, we usually need to submit a cover letter, CV, research statement, and letters of recommendation. Usually we submit a teaching statement, not a portfolio: some countries (Denmark) have been introducing portfolios but for now they’re not common. Diversity statements are broadly speaking a US and Canada thing: you will almost always need to submit one for a job in those places (one memorable job I looked at asserted that Italian-American counted as diversity), and sometimes in the UK, but much more rarely elsewhere in Europe (I can think of only one example). You never need to submit transcripts except if you’re applying to some unusually bureaucracy-obsessed country. “Writing samples” sometimes take the form of requests for a few important published papers: most places don’t ask for this, though. Our cover letters are less fixed (I’ve never heard a two-page limit, and various jobs actually asked for quite different things). While most jobs require three letters of recommendation, I was surprised to learn (several years in to applying…) that one sometimes can submit more, with three just being a minimum.

Just like Bret’s field, these statements all need to be tailored to the job to some extent (something I once again appreciated more a few years in). That does mean a lot of work, because much like Bret’s field there are often only a few reasonable permanent jobs one can apply for worldwide each year (maybe more than 6-12, but that depends on what you’re looking for), and they essentially all have hundreds of applicants. I won’t comment as much on how hiring decisions get made, except to say that my field seems a little less dysfunctional than Bret’s with “just out of PhD” hires quite rare and most people doing a few postdocs before finding a position. Still, there is a noticeable bias towards comparatively fresh PhDs, and this is reinforced by the European grant system: the ERC Starting Grant is a huge sum of money compared to many other national grants, and you can only apply for it within seven years from your PhD. The ERC Consolidator Grant can be applied for later (twelve years from PhD), but has higher standards (I’m working on an application for it this year). If you aren’t able to apply for either of those, then a lot of European institutions won’t consider you.