LHC Black Hole Reassurance: The Professional Version

Leave a reply

A while back I wrote a post trying to reassure you that the Large Hadron Collider cannot create a black hole that could destroy the Earth. If you’re the kind of person who is worried about this kind of thing, you’ve probably heard a variety of arguments: that it hasn’t happened yet, despite the LHC running for quite some time, that it didn’t happen before the LHC with cosmic rays of comparable energy, and that a black hole that small would quickly decay due to Hawking radiation. I thought it would be nice to give a different sort of argument, a back-of-the-envelope calculation you can try out yourself, showing that even if a black hole was produced using all of the LHC’s energy and fell directly into the center of the Earth, and even if Hawking radiation didn’t exist, it would still take longer than the lifetime of the universe to cause any detectable damage. Modeling the black hole as falling through the Earth and just slurping up everything that falls into its event horizon, it wouldn’t even double in size before the stars burn out.

That calculation was extremely simple by physics standards. As it turns out, it was too simple. A friend of mine started thinking harder about the problem, and dug up this paper from 2008: Astrophysical implications of hypothetical stable TeV-scale black holes.

Before the LHC even turned on, the experts were hard at work studying precisely this question. The paper has two authors, Steve Giddings and Michelangelo Mangano. Giddings is an expert on the problem of quantum gravity, while Mangano is an expert on LHC physics, so the two are exactly the dream team you’d ask for to answer this question. Like me, they pretend that black holes don’t decay due to Hawking radiation, and pretend that one falls to straight from the LHC to the center of the Earth, for the most pessimistic possible scenario.

Unlike me, but like my friend, they point out that the Earth is not actually a uniform sphere of matter. It’s made up of particles: quarks arranged into nucleons arranged into nuclei arranged into atoms. And a black hole that hits a nucleus will probably not just slurp up an event horizon-sized chunk of the nucleus: it will slurp up the whole nucleus.

This in turn means that the black hole starts out growing much more fast. Eventually, it slows down again: once it’s bigger than an atom, it starts gobbling up atoms a few at a time until eventually it is back to slurping up a cylinder of the Earth’s material as it passes through.

But an atom-sized black hole will grow faster than an LHC-energy-sized black hole. How much faster is estimated in the Giddings and Mangano paper, and it depends on the number of dimensions. For eight dimensions, we’re safe. For fewer, they need new arguments.

Wait a minute, you might ask, aren’t there only four dimensions? Is this some string theory nonsense?

Kind of, yes. In order for the LHC to produce black holes, gravity would need to have a much stronger effect than we expect on subatomic particles. That requires something weird, and the most plausible such weirdness people considered at the time were extra dimensions. With extra dimensions of the right size, the LHC might have produced black holes. It’s that kind of scenario that Giddings and Mangano are checking: they don’t know of a plausible way for black holes to be produced at the LHC if there are just four dimensions.

For fewer than eight dimensions, though, they have a problem: the back-of-the-envelope calculation suggests black holes could actually grow fast enough to cause real damage. Here, they fall back on the other type of argument: if this could happen, would it have happened already? They argue that, if the LHC could produce black holes in this way, then cosmic rays could produce black holes when they hit super-dense astronomical objects, such as white dwarfs and neutron stars. Those black holes would eat up the white dwarfs and neutron stars, in the same way one might be worried they could eat up the Earth. But we can observe that white dwarfs and neutron stars do in fact exist, and typically live much longer than they would if they were constantly being eaten by miniature black holes. So we can conclude that any black holes like this don’t exist, and we’re safe.

If you’ve got a smattering of physics knowledge, I encourage you to read through the paper. They consider a lot of different scenarios, much more than I can summarize in a post. I don’t know if you’ll find it reassuring, since they may not cover whatever you happen to be worried about. But it’s a lot of fun seeing how the experts handle the problem.

Models, Large Language and Otherwise

5 Replies

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.

Newtonmas Pageants

Leave a reply

Newtonmas: because if you’re going to celebrate someone supposedly born on December 25, you might as well pick someone whose actual birthday was within two weeks of that.

My past Newtonmas posts have tended to be about gifts, which is a pretty easy theme. But Christmas, for some, isn’t just about Santa Claus delivering gifts, but about someone’s birth. Children put on plays acting out different characters. In Mexico, they include little devils, who try to tempt the shepherds away from visiting Jesus.

Could we do this kind of thing for Newtonmas? A Newtonmas Pageant?

The miraculous child

Historians do know a bit about Newton’s birth. His father (also named Isaac Newton) died two months before he was born. Newton was born prematurely, his mother apparently claimed he could fit inside a quart mug.

The mug may be surprising (it comes in quarts?), but there isn’t really enough material for a proper story here. That said, it would be kind of beside the point if there were. If we’re celebrating science, maybe the story of one particular child is not the story we should be telling.

Instead, we can tell stories about scientific ideas. These often have quite dramatic stories. Instead of running from inn to inn looking for rooms, scientists run from journal to journal trying to publish. Instead of frankincense, myrrh, and gold, there are Nobel prizes. Instead of devils tempting the shepherds away, you have tempting but unproductive ideas. For example, Newton battled ideas from Descartes and Liebniz that suggested gravity could be caused by a vortex of fluid. The idea was popular because it was mechanical-sounding: no invisible force of gravity needed. But it didn’t work, and Newton spent half of the Principia where he wrote down his new science building a theory of fluids so he could say it didn’t work.

So for this Newtonmas, tell the story of a scientific idea: one that had a difficult birth but that, eventually brought pilgrims and gifts from miles around.

Merry Newtonmas, everyone!

If That Measures the Quantum Vacuum, Anything Does

8 Replies

Sabine Hossenfelder has gradually transitioned from critical written content about physics to YouTube videos, mostly short science news clips with the occasional longer piece. Luckily for us in the unable-to-listen-to-podcasts demographic, the transcripts of these videos are occasionally published on her organization’s Substack.

Unluckily, it feels like the short news format is leading to some lazy metaphors. There are stories science journalists sometimes tell because they’re easy and familiar, even if they don’t really make sense. Scientists often tell them too, for the same reason. But the more careful voices avoid them.

Hossenfelder has been that careful before, but one of her recent pieces falls short. The piece is titled “This Experiment Will Measure Nothing, But Very Precisely”.

The “nothing” in the title is the oft-mythologized quantum vacuum. The story goes that in quantum theory, empty space isn’t really empty. It’s full of “virtual” particles, that pop in and out of existence, jostling things around.

This…is not a good way to think about it. Really, it’s not. If you want to understand what’s going on physically, it’s best to think about measurements, and measurements involve particles: you can’t measure anything in pure empty space, you don’t have anything to measure with. Instead, every story you can tell about the “quantum vacuum” and virtual particles, you can tell about interactions between particles that actually exist.

(That post I link above, by the way, was partially inspired by a more careful post by Hossenfelder. She does know this stuff. She just doesn’t always use it.)

Let me tell the story Hossenfelder’s piece is telling, in a less silly way:

In the earliest physics classes, you learn that light does not affect other light. Shine two flashlight beams across each other, and they’ll pass right through. You can trace the rays of each source, independently, keeping track of how they travel and bounce around the room.

In quantum theory, that’s not quite true. Light can interact with light, through subtle quantum effects. This effect is tiny, so tiny it hasn’t been measured before. But with ingenious tricks involving tuning three different lasers in exactly the right way, a team of physicists in Dresden has figured out how it could be done.

And see, that’s already cool, right? It’s cool when people figure out how to see things that have never been seen before, full stop.

But the way Hossenfelder presents it, the cool thing about this is that they are “measuring nothing”. That they’re measuring “the quantum vacuum”, really precisely.

And I mean, you can say that, I guess. But it’s equally true of every subtle quantum effect.

In classical physics, electrons should have a very specific behavior in a magnetic field, called their magnetic moment. Quantum theory changes this: electrons have a slightly different magnetic moment, an anomalous magnetic moment. And people have measured this subtle effect: it’s famously the most precisely confirmed prediction in all of science.

That effect can equally well be described as an effect of the quantum vacuum. You can draw the same pictures, if you really want to, with virtual particles popping in and out of the vacuum. One effect (light bouncing off light) doesn’t exist at all in classical physics, while the other (electrons moving in a magnetic field) exists, but is subtly different. But both, in exactly the same sense, are “measurements of nothing”.

So if you really want to stick on the idea that, whenever you measure any subtle quantum effect, you measure “the quantum vacuum”…then we’re already doing that, all the time. Using it to popularize some stuff (say, this experiment) and not other stuff (the LHC is also measuring the quantum vacuum) is just inconsistent.

Better, in my view, to skip the silly talk about nothing. Talk about what we actually measure. It’s cool enough that way.

What’s in a Subfield?

Leave a reply

A while back, someone asked me what my subfield, amplitudeology, is really about. I wrote an answer to that here, a short-term and long-term perspective that line up with the stories we often tell about the field. I talked about how we try to figure out ways to calculate probabilities faster, first for understanding the output of particle colliders like the LHC, then more recently for gravitational wave telescopes. I talked about how the philosophy we use for that carries us farther, how focusing on the minimal information we need to make a prediction gives us hope that we can generalize and even propose totally new theories.

The world doesn’t follow stories, though, not quite so neatly. Try to define something as simple as the word “game” and you run into trouble. Some games have a winner and a loser, some games everyone is on one team, and some games don’t have winners or losers at all. Games can involve physical exercise, computers, boards and dice, or just people telling stories. They can be played for fun, or for money, silly or deadly serious. Most have rules, but some don’t even have that. Instead, games are linked by history: a series of resemblances, people saying that “this” is a game because it’s kind of like “that”.

A subfield isn’t just a word, it’s a group of people. So subfields aren’t defined just by resemblance. Instead, they’re defined by practicality.

To ask what amplitudeology is really about, think about why you might want to call yourself an amplitudeologist. It could be a question of goals, certainly: you might care a lot about making better predictions for the LHC, or you could have some other grand story in mind about how amplitudes will save the world. Instead, though, it could be a matter of training: you learned certain methods, certain mathematics, a certain perspective, and now you apply it to your research, even if it goes further afield from what was considered “amplitudeology” before. It could even be a matter of community, joining with others who you think do cool stuff, even if you don’t share exactly the same goals or the same methods.

Calling yourself an amplitudeologist means you go to their conferences and listen to their talks, means you look to them to collaborate and pay attention to their papers. Those kinds of things define a subfield: not some grand mission statement, but practical questions of interest, what people work on and know and where they’re going with that. Instead of one story, like every other word, amplitudeology has a practical meaning that shifts and changes with time. That’s the way subfields should be: useful to the people who practice them.

What Referees Are For

2 Replies

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.

A Significant Calculation

7 Replies

Particle physicists have a weird relationship to journals. We publish all our results for free on a website called the arXiv, and when we need to read a paper that’s the first place we look. But we still submit our work to journals, because we need some way to vouch that we’re doing good work. Explicit numbers (h-index, impact factor) are falling out of favor, but we still need to demonstrate that we get published in good journals, that we do enough work, and that work has an impact on others. We need it to get jobs, to get grants to fund research at those jobs, and to get future jobs for the students and postdocs we hire with those grants. Our employers need it to justify their own funding, to summarize their progress so governments and administrators can decide who gets what.

This can create weird tensions. When people love a topic, they want to talk about it with each other. They want to say all sorts of things, big and small, to contribute new ideas and correct others and move things forward. But as professional physicists, we also have to publish papers. We can publish some “notes”, little statements on the arXiv that we don’t plan to make into a paper, but we don’t really get “credit” for those. So in practice, we try to force anything we want to say into a paper-sized chunk.

That wouldn’t be a problem if paper-sized chunks were flexible, and you can see when journals historically tried to make them that way. Some journals publish “letters”, short pieces a few pages long, to contrast with their usual papers that can run from twenty to a few hundred pages. These “letters” tend to be viewed as prestigious, though, so they end up being judged on roughly the same standards as the normal papers, if not more strictly.

What standards are those? For each journal, you can find an official list. The Journal of High-Energy Physics, for example, instructs reviewers to look for “high scientific
quality, originality and relevance”. That rules out papers that just reproduce old results, but otherwise is frustratingly vague. What constitutes high scientific quality? Relevant to whom?

In practice, reviewers use a much fuzzier criterion: is this “paper-like”? Does this look like other things that get published, or not?

Each field will assess that differently. It’s a criterion of familiarity, of whether a paper looks like what people in the field generally publish. In my field, one rule of thumb is that a paper must contain a significant calculation.

A “significant calculation” is still quite fuzzy, but the idea is to make sure that a paper requires some amount of actual work. Someone has to do something challenging, and the work shouldn’t be half-done: as much as feasible, they should finish, and calculate something new. Ideally, this should be something that nobody had calculated before, but if the perspective is new enough it can be something old. It should “look hard”, though.

That’s a fine way to judge whether someone is working hard, which is something we sometimes want to judge. But since we’re incentivized to make everything into a paper, this means that every time we want to say something, we want to accompany it with some “significant calculation”, some concrete time-consuming work. This can happen even if we want to say something that’s quite direct and simple, a fact that can be quickly justified but nonetheless has been ignored by the field. If we don’t want it to be “just” an un-credited note, we have to find some way to turn it into a “significant calculation”. We do extra work, sometimes pointless work, in order to make something “paper-sized”.

I like to think about what academia would be like without the need to fill out a career. The model I keep imagining is that of a web forum or a blogging platform. There would be the big projects, the in-depth guides and effortposts. But there would also be shorter contributions, people building off each other, comments on longer pieces and quick alerts pinned to the top of the page. We’d have a shared record of knowledge, where everyone contributes what they want to whatever level of detail they want.

I think math is a bit closer to this ideal. Despite their higher standards for review, checking the logic of every paper to make sure it makes sense to publish, math papers can sometimes be very short, or on apparently trivial things. Physics doesn’t quite work this way, and I suspect part of it is our funding sources. If you’re mostly paid to teach, like many mathematicians, your research is more flexible. If you’re paid to research, like many physicists, then people want to make sure your research is productive, and that tends to cram it into measurable boxes.

In today’s world, I don’t think physics can shift cultures that drastically. Even as we build new structures to rival the journals, the career incentives remain. Physics couldn’t become math unless it shed most of the world’s physicists.

In the long run, though…well, we may one day find ourselves in a world where we don’t have to work all our days to keep each other alive. And if we do, hopefully we’ll change how scientists publish.

IPhT-60 Retrospective

Leave a reply

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

Leave a reply

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

10 Replies

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!