Tag Archives: theoretical physics

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.

Cause and Effect and Stories

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You can think of cause and effect as the ultimate story. The world is filled with one damn thing happening after another, but to make sense of it we organize it into a narrative: this happened first, and it caused that, which caused that. We tie this to “what if” stories, stories about things that didn’t happen: if this hadn’t happened, then it wouldn’t have caused that, so that wouldn’t have happened.

We also tell stories about cause and effect. Physicists use cause and effect as a tool, a criterion to make sense of new theories: does this theory respect cause and effect, or not? And just like everything else in science, there is more than one story they tell about it.

As a physicist, how would you think about cause and effect?

The simplest, and most obvious requirement, is that effects should follow their causes. Cause and effect shouldn’t go backwards in time, the cause should come before the effect.

This all sounds sensible, until you remember that in physics “before” and “after” are relative. If you try to describe the order of two distant events, your description will be different than someone moving with a different velocity. You might think two things happened at the same time, while they think one happened first, and someone else thinks the other happened first.

You’d think this makes a total mess of cause and effect, but actually everything remains fine, as long nothing goes faster than the speed of light. If someone could travel between two events slower than the speed of light, then everybody will agree on their order, and so everyone can agree on which one caused the other. Cause and effect only get screwed up if they can happen faster than light.

(If the two events are two different times you observed something, then cause and effect will always be fine, since you yourself can’t go faster than the speed of light. So nobody will contradict what you observe, they just might interpret it differently.)

So if you want to make sure that your theory respects cause and effect, you’d better be sure that nothing goes faster than light. It turns out, this is not automatic! In general relativity, an effect called Shapiro time delay makes light take longer to pass a heavy object than to go through empty space. If you modify general relativity, you can accidentally get a theory with a Shapiro time advance, where light arrives sooner than it would through empty space. In such a theory, at least some observers will see effects happen before their causes!

Once you know how to check this, as a physicist, there are two kinds of stories you can tell. I’ve heard different people in the field tell both.

First, you can say that cause and effect should be a basic physical principle. Using this principle, you can derive other restrictions, demands on what properties matter and energy can have. You can carve away theories that violate these rules, making sure that we’re testing for theories that actually make sense.

On the other hand, there are a lot of stories about time travel. Time travel screws up cause and effect in a very direct way. When Harry Potter and Hermione travel back in time at the end of Harry Potter and the Prisoner of Azkaban, they cause the event that saves Harry’s life earlier in the book. Science fiction and fantasy are full of stories like this, and many of them are perfectly consistent. How can we be so sure that we don’t live in such a world?

The other type of story positions the physics of cause and effect as a search for evidence. We’re looking for physics that violates cause and effect, because if it exists, then on some small level it should be possible to travel back in time. By writing down the consequences of cause and effect, we get to describe what evidence we’d need to see it breaking down, and if we see it whole new possibilities open up.

These are both good stories! And like all other stories in science, they only capture part of what the scientists are up to. Some people stick to one or the other, some go between them, driven by the actual research, not the story itself. Like cause and effect itself, the story is just one way to describe the world around us.

Stories Backwards and Forwards

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You can always start with “once upon a time”…

I come up with tricks to make calculations in particle physics easier. That’s my one-sentence story, or my most common one. If I want to tell a longer story, I have more options.

Here’s one longer story:

I want to figure out what Nature is telling us. I want to take all the data we have access to that has anything to say about fundamental physics, every collider and gravitational wave telescope and ripple in the overall structure of the universe, and squeeze it as hard as I can until something comes out. I want to make sure we understand the implications of our current best theories as well as we can, to as high precision as we can, because I want to know whether they match what we see.

To do that, I am starting with a type of calculation I know how to do best. That’s both because I can make progress with it, and because it will be important for making these inferences, for testing our theories. I am following a hint in a theory that definitely does not describe the real world, one that is both simpler to work with and surprisingly complex, one that has a good track record, both for me and others, for advancing these calculations. And at the end of the day, I’ll make our ability to infer things from Nature that much better.

Here’s another:

Physicists, unknowing, proposed a kind of toy model, one often simpler to work with but not necessarily simpler to describe. Using this model, they pursued increasingly elaborate calculations, and time and time again, those calculations surprised them. The results were not random, not a disorderly mess of everything they could plausibly have gotten. Instead, they had structure, symmetries and patterns and mathematical properties that the physicists can’t seem to explain. If we can explain them, we will advance our knowledge of models and theories and ideas, geometry and combinatorics, learning more about the unexpected consequences of the rules we invent.

We can also help the physicists advance physics, of course. That’s a happy accident, but one that justifies the money and time, showing the rest of the world that understanding consequences of rules is still important and valuable.

These seem like very different stories, but they’re not so different. They change in order, physics then math or math then physics, backwards and forwards. By doing that, they change in emphasis, in where they’re putting glory and how they’re catching your attention. But at the end of the day, I’m investigating mathematical mysteries, and I’m advancing our ability to do precision physics.

(Maybe you think that my motivation must lie with one of these stories and not the other. One is “what I’m really doing”, the other is a lie made up for grant agencies.
Increasingly, I don’t think people work like that. If we are at heart stories, we’re retroactive stories. Our motivation day to day doesn’t follow one neat story or another. We move forward, we maybe have deep values underneath, but our accounts of “why” can and will change depending on context. We’re human, and thus as messy as that word should entail.)

I can tell more than two stories if I want to. I won’t here. But this is largely what I’m working on at the moment. In applying for grants, I need to get the details right, to sprinkle the right references and the right scientific arguments, but the broad story is equally important. I keep shuffling that story, a pile of not-quite-literal index cards, finding different orders and seeing how they sound, imagining my audience and thinking about what stories would work for them.

Amplitudes 2023 Retrospective

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I’m back from CERN this week, with a bit more time to write, so I thought I’d share some thoughts about last week’s Amplitudes conference.

One thing I got wrong in last week’s post: I’ve now been told only 213 people actually showed up in person, as opposed to the 250-ish estimate I had last week. This may seem fewer than Amplitudes in Prague had, but it seems likely they had a few fewer show up than appeared on the website. Overall, the field is at least holding steady from year to year, and definitely has grown since the pandemic (when 2019’s 175 was already a very big attendance).

It was cool having a conference in CERN proper, surrounded by the history of European particle physics. The lecture hall had an abstract particle collision carved into the wood, and the visitor center would in principle have had Standard Model coffee mugs were they not sold out until next May. (There was still enough other particle physics swag, Swiss chocolate, and Swiss chocolate that was also particle physics swag.) I’d planned to stay on-site at the CERN hostel, but I ended up appreciated not doing that: the folks who did seemed to end up a bit cooped up by the end of the conference, even with the conference dinner as a chance to get out.

Past Amplitudes conferences have had associated public lectures. This time we had a not-supposed-to-be-public lecture, a discussion between Nima Arkani-Hamed and Beate Heinemann about the future of particle physics. Nima, prominent as an amplitudeologist, also has a long track record of reasoning about what might lie beyond the Standard Model. Beate Heinemann is an experimentalist, one who has risen through the ranks of a variety of different particle physics experiments, ending up well-positioned to take a broad view of all of them.

It would have been fun if the discussion erupted into an argument, but despite some attempts at provocative questions from the audience that was not going to happen, as Beate and Nima have been friends for a long time. Instead, they exchanged perspectives: on what’s coming up experimentally, and what theories could explain it. Both argued that it was best to have many different directions, a variety of experiments covering a variety of approaches. (There wasn’t any evangelism for particular experiments, besides a joking sotto voce mention of a muon collider.) Nima in particular advocated that, whether theorist or experimentalist, you have to have some belief that what you’re doing could lead to a huge breakthrough. If you think of yourself as just a “foot soldier”, covering one set of checks among many, then you’ll lose motivation. I think Nima would agree that this optimism is irrational, but necessary, sort of like how one hears (maybe inaccurately) that most new businesses fail, but someone still needs to start businesses.

Michelangelo Mangano’s talk on Thursday covered similar ground, but with different emphasis. He agrees that there are still things out there worth discovering: that our current model of the Higgs, for instance, is in some ways just a guess: a simplest-possible answer that doesn’t explain as much as we’d like. But he also emphasized that Standard Model physics can be “new physics” too. Just because we know the model doesn’t mean we can calculate its consequences, and there are a wealth of results from the LHC that improve our models of protons, nuclei, and the types of physical situations they partake in, without changing the Standard Model.

We saw an impressive example of this in Gregory Korchemsky’s talk on Wednesday. He presented an experimental mystery, an odd behavior in the correlation of energies of jets of particles at the LHC. These jets can include a very large number of particles, enough to make it very hard to understand them from first principles. Instead, Korchemsky tried out our field’s favorite toy model, where such calculations are easier. By modeling the situation in the limit of a very large number of particles, he was able to reproduce the behavior of the experiment. The result was a reminder of what particle physics was like before the Standard Model, and what it might become again: partial models to explain odd observations, a quest to use the tools of physics to understand things we can’t just a priori compute.

On the other hand, amplitudes does do a priori computations pretty well as well. Fabrizio Caola’s talk opened the conference by reminding us just how much our precise calculations can do. He pointed out that the LHC has only gathered 5% of its planned data, and already it is able to rule out certain types of new physics to fairly high energies (by ruling out indirect effects, that would show up in high-precision calculations). One of those precise calculations featured in the next talk, by Guilio Gambuti. (A FORM user, his diagrams were the basis for the header image of my Quanta article last winter.) Tiziano Peraro followed up with a technique meant to speed up these kinds of calculations, a trick to simplify one of the more computationally intensive steps in intersection theory.

The rest of Monday was more mathematical, with talks by Zeno Capatti, Jaroslav Trnka, Chia-Kai Kuo, Anastasia Volovich, Francis Brown, Michael Borinsky, and Anna-Laura Sattelberger. Borinksy’s talk felt the most practical, a refinement of his numerical methods complete with some actual claims about computational efficiency. Francis Brown discussed an impressively powerful result, a set of formulas that manages to unite a variety of invariants of Feynman diagrams under a shared explanation.

Tuesday began with what I might call “visitors”: people from adjacent fields with an interest in amplitudes. Alday described how the duality between string theory in AdS space and super Yang-Mills on the boundary can be used to get quite concrete information about string theory, calculating how the theory’s amplitudes are corrected by the curvature of AdS space using a kind of “bootstrap” method that felt nicely familiar. Tim Cohen talked about a kind of geometric picture of theories that extend the Standard Model, including an interesting discussion of whether it’s really “geometric”. Marko Simonovic explained how the integration techniques we develop in scattering amplitudes can also be relevant in cosmology, especially for the next generation of “sky mappers” like the Euclid telescope. This talk was especially interesting to me since this sort of cosmology has a significant presence at CEA Paris-Saclay. Along those lines an interesting paper, “Cosmology meets cohomology”, showed up during the conference. I haven’t had a chance to read it yet!

Just before lunch, we had David Broadhurst give one of his inimitable talks, complete with number theory, extremely precise numerics, and literary and historical references (apparently, Källén died flying his own plane). He also remedied a gap in our whimsically biological diagram naming conventions, renaming the pedestrian “double-box” as a (in this context, Orwellian) lobster. Karol Kampf described unusual structures in a particular Effective Field Theory, while Henriette Elvang’s talk addressed what would become a meaningful subtheme of the conference, where methods from the mathematical field of optimization help amplitudes researchers constrain the space of possible theories. Giulia Isabella covered another topic on this theme later in the day, though one of her group’s selling points is managing to avoid quite so heavy-duty computations.

The other three talks on Tuesday dealt with amplitudes techniques for gravitational wave calculations, as did the first talk on Wednesday. Several of the calculations only dealt with scattering black holes, instead of colliding ones. While some of the results can be used indirectly to understand the colliding case too, a method to directly calculate behavior of colliding black holes came up again and again as an important missing piece.

The talks on Wednesday had to start late, owing to a rather bizarre power outage (the lights in the room worked fine, but not the projector). Since Wednesday was the free afternoon (home of quickly sold-out CERN tours), this meant there were only three talks: Veneziano’s talk on gravitational scattering, Korchemsky’s talk, and Nima’s talk. Nima famously never finishes on time, and this time attempted to control his timing via the surprising method of presenting, rather than one topic, five “abstracts” on recent work that he had not yet published. Even more surprisingly, this almost worked, and he didn’t run too ridiculously over time, while still managing to hint at a variety of ways that the combinatorial lessons behind the amplituhedron are gradually yielding useful perspectives on more general realistic theories.

Thursday, Andrea Puhm began with a survey of celestial amplitudes, a topic that tries to build the same sort of powerful duality used in AdS/CFT but for flat space instead. They’re gradually tackling the weird, sort-of-theory they find on the boundary of flat space. The two next talks, by Lorenz Eberhardt and Hofie Hannesdottir, shared a collaborator in common, namely Sebastian Mizera. They also shared a common theme, taking a problem most people would have assumed was solved and showing that approaching it carefully reveals extensive structure and new insights.

Cristian Vergu, in turn, delved deep into the literature to build up a novel and unusual integration method. We’ve chatted quite a bit about it at the Niels Bohr Institute, so it was nice to see it get some attention on the big stage. We then had an afternoon of trips beyond polylogarithms, with talks by Anne Spiering, Christoph Nega, and Martijn Hidding, each pushing the boundaries of what we can do with our hardest-to-understand integrals. Einan Gardi and Ruth Britto finished the day, with a deeper understanding of the behavior of high-energy particles and a new more mathematically compatible way of thinking about “cut” diagrams, respectively.

On Friday, João Penedones gave us an update on a technique with some links to the effective field theory-optimization ideas that came up earlier, one that “bootstraps” whole non-perturbative amplitudes. Shota Komatsu talked about an intriguing variant of the “planar” limit, one involving large numbers of particles and a slick re-writing of infinite sums of Feynman diagrams. Grant Remmen and Cliff Cheung gave a two-parter on a bewildering variety of things that are both surprisingly like, and surprisingly unlike, string theory: important progress towards answering the question “is string theory unique?”

Friday afternoon brought the last three talks of the conference. James Drummond had more progress trying to understand the symbol letters of supersymmetric Yang-Mills, while Callum Jones showed how Feynman diagrams can apply to yet another unfamiliar field, the study of vortices and their dynamics. Lance Dixon closed the conference without any Greta Thunberg references, but with a result that explains last year’s mystery of antipodal duality. The explanation involves an even more mysterious property called antipodal self-duality, so we’re not out of work yet!