Tag Archives: science communication

Gateway Hobbies

When biologists tell stories of their childhoods, they’re full of trails of ants and fireflies in jars. Lots of writers start young, telling stories on the playground and making skits with their friends. And the mere existence of “chemistry sets” tells you exactly how many chemists get started. Many fields have these “gateway hobbies”, like gateway drugs for careers, ways that children and teenagers get hooked and gain experience.

Physics is a little different, though. While kids can play with magnets and electricity, there aren’t a whole lot of other “physics hobbies”, especially for esoteric corners like particle physics. Instead, the “gateway hobbies” of physics are more varied, drawing from many different fields.

First, of course, even if a child can’t “do physics”, they can always read about it. Kids will memorize the names of quarks, read about black holes, or watch documentaries about string theory. I’m not counting this as a “physics hobby” because it isn’t really: physics isn’t a collection of isolated facts, but of equations: frameworks you can use to make predictions. Reading about the Big Bang is a good way to get motivated and excited, it’s a great thing to do…but it doesn’t prepare you for the “science part” of the science.

A few efforts at physics popularization get a bit more hands-on. Many come in the form of video games. You can get experience with relativity through Velocity Raptor, quantum mechanics through Quantum Chess, or orbital mechanics through Kerbal Space Program. All of these get just another bit closer to “doing physics” rather than merely reading about it.

One can always gain experience in other fields, and that can be surprisingly relevant. Playing around with a chemistry set gives first-hand experience of the kinds of things that motivated quantum mechanics, and some things that still motivate condensed matter research. Circuits are physics, more directly, even if they’re also engineering: and for some physicists, designing electronic sensors is a huge part of what they do.

Astronomy has a special place, both in the history of physics and the pantheon of hobbies. There’s a huge amateur astronomy community, one that both makes real discoveries and reaches out to kids of all ages. Many physicists got their start looking at the heavens, using it like Newton’s contemporaries as a first glimpse into the mechanisms of nature.

More and more research in physics involves at least some programming, and programming is another activity kids have access to in spades, from Logo to robotics competitions. Learning how to program isn’t just an important skill: it’s also a way for young people to experience a world bound by clear laws and logic, another motivation to study physics.

Of course, if you’re interested in rules and logic, why not go all the way? Plenty of physicists grew up doing math competitions. I have fond memories of Oregon’s Pentagames, and the more “serious” activities go all the way up to the famously challenging Putnam Competition.

Finally, there are physics competitions too, at least in the form of the International Physics Olympiad, where high school students compete in physics prowess.

Not every physicist did these sorts of things, of course: some got hooked later. Others did more than one. A friend of mine who’s always been “Mr. Science” got almost the whole package, with a youth spent exploring the wild west of the early internet, working at a planetarium, and discovering just how easy it is to get legal access to dangerous and radioactive chemicals. There are many paths in to physics, so even if kids can’t “do physics” the same way they “do chemistry”, there’s still plenty to do!

Keeping It Colloquial

In the corners of academia where I hang out, a colloquium is a special kind of talk. Most talks we give are part of weekly seminars for specific groups. For example, the theoretical particle physicists here have a seminar. Each week we invite a speaker, who gives a talk on their recent work. Since they expect an audience of theoretical particle physicists, they can go into more detail.

A colloquium isn’t like that. Colloquia are talks for the whole department: theorists and experimentalists, particle physicists and biophysicists. They’re more prestigious, for big famous professors (or sometimes, for professors interviewing for jobs…). The different audience, and different context, means that the talk plays by different rules.

Recently, I saw a conference full of “colloquium-style” talks, trying to play by these rules. Some succeeded, some didn’t…and I think I now have a better idea of how those rules work.

First, in a colloquium, you’re not just speaking for yourself. You’re an ambassador for your field. For some of the audience, this might be the first time they’ve heard a talk by someone who does your kind of research. You want to give them a good impression, not just about you, but about the whole topic. So while you definitely want to mention your own work, you want to tell a full story, one that gives more than a glimpse of what others are doing as well.

Second, you want to connect to something the audience already knows. With an audience of physicists, you can assume a certain baseline, but not much more than that. You need to make the beginning accessible and start with something familiar. For the conference I mentioned, a talk that did this well was the talk on exoplanets, which started with the familiar planets of the solar system, classifying them in order to show what you might expect exoplanets to look like. In contrast, t’Hooft’s talk did this poorly. His work is exploiting a loophole in a quantum-mechanical argument called Bell’s theorem, which most physicists have heard of. Instead of mentioning Bell’s theorem, he referred vaguely to “criteria from philosophers”, and only even mentioned that near the end of the talk, instead starting with properties of quantum mechanics his audience was much less familiar with.

Moving on, then, you want to present a mystery. So far, everything in the talk has made sense, and your audience feels like they understand. Now, you show them something that doesn’t fit, something their familiar model can’t accommodate. This activates your audience’s scientist instincts: they’re curious now, they want to know the answer. A good example from the conference was a talk on chemistry in space. The speaker emphasized that we can see evidence of complex molecules in space, but that space dust is so absurdly dilute that it seems impossible such molecules could form: two atoms could go a billion years without meeting each other.

You can’t just leave your audience mystified, though. You next have to solve the mystery. Ideally, your solution will be something smart, but simple: something your audience can intuitively understand. This has two benefits. First, it makes you look smart: you described a mysterious problem, and then you show how to solve it! Second, it makes the audience feel smart: they felt the problem was hard, but now they understand how to solve it too. The audience will have good feelings about you as a result, and good feelings about the topic: in some sense, you’ve tied a piece of their self-esteem to knowing the solution to your problem. This was well-done by the speaker discussing space chemistry, who explained that the solution was chemistry on surfaces: if two atoms are on the surface of a dust grain or meteorite, they’re much more likely to react. It was also well-done by a speaker discussing models of diseases like diabetes: he explained the challenge of controlling processes with cells, when cells replicate exponentially, and showed one way they could be controlled, when the immune system kills off any cells that replicate much faster than their neighbors. (He also played the guitar to immune system-themed songs…also a good colloquium strategy for those who can pull it off!)

Finally, a picture is worth a thousand wordsas long as it’s a clear one. For an audience that won’t follow most of your equations, it’s crucial to show them something visual: graphics, puns, pictures of equipment or graphs. Crucially, though, your graphics should be something the audience can understand. If you put up a graph with a lot of incomprehensible detail: parameters you haven’t explained, or just set up in a way your audience doesn’t get, then your audience gets stuck. Much like an unfamiliar word, a mysterious graph will have members of the audience scratching their heads, trying to figure out what it means. They’ll be so busy trying, they’ll miss what you say next, and you’ll lose them! So yes, put in graphs, put in pictures: but make sure that the ones you use, you have time to explain.

Answering Questions: Virtue or Compulsion?

I was talking to a colleague about this blog. I mentioned worries I’ve had about email conversations with readers: worries about whether I’m communicating well, whether the readers are really understanding. For the colleague though, something else stood out:

“You sure are generous with your time.”

Am I?

I’d never really thought about it that way before. It’s not like I drop everything to respond to a comment, or a message. I leave myself a reminder, and get to it when I have time. To the extent that I have a time budget, I don’t spend it freely, I prioritize work before chatting with my readers, as nice as you folks are.

At the same time, though, I think my colleague was getting at a real difference there. It’s true that I don’t answer questions right away. But I do answer them eventually. I can’t imagine being asked a question, and just never answering it.

There are exceptions, of course. If you’re obviously just trolling, just insulting me or messing with me or asking the same question over and over, yeah I’ll skip your question. And if I don’t understand what you’re asking, there’s only so much effort I’m going to put in to try to decipher it. Even in those cases, though, I have a certain amount of regret. I have to take a deep breath and tell myself no, I can really skip this one.

On the one hand, this feels like a moral obligation, a kind of intellectual virtue. If knowledge, truth, information are good regardless of anything else, then answering questions is just straightforwardly good. People ought to know more, asking questions is how you learn, and that can’t work unless we’re willing to teach. Even if there’s something you need to keep secret, you can at least say something, if only to explain why you can’t answer. Just leaving a question hanging feels like something bad people do.

On the other hand, I think this might just be a compulsion, a weird quirk of my personality. It may even be more bad than good, an urge that makes me “waste my time”, or makes me too preoccupied with what others say, drafting responses in my head until I find release by writing them down. I think others are much more comfortable just letting a question lie, and moving on. It feels a bit like the urge to have the last word in a conversation, just more specific: if someone asks me to have the last word, I feel like I have to oblige!

I know this has to have its limits. The more famous bloggers get so many questions they can’t possibly respond to all of them. I’ve seen how people like Neil Gaiman describe responding to questions on tumblr, just opening a giant pile of unread messages, picking a few near the top, and then going back to their day. I can barely stand leaving unread messages in my email. If I got that famous, I don’t know how I’d deal with that. But I’d probably figure something out.

Am I too generous with you guys? Should people always answer questions? And does the fact that I ended this post with questions mean I’ll get more comments?

Of Snowmass and SAGEX

arXiv-watchers might have noticed an avalanche of papers with the word Snowmass in the title. (I contributed to one of them.)

Snowmass is a place, an area in Colorado known for its skiing. It’s also an event in that place, the Snowmass Community Planning Exercise for the American Physical Society’s Division of Particles and Fields. In plain terms, it’s what happens when particle physicists from across the US get together in a ski resort to plan their future.

Usually someone like me wouldn’t be involved in that. (And not because it’s a ski resort.) In the past, these meetings focused on plans for new colliders and detectors. They got contributions from experimentalists, and a few theorists heavily focused on their work, but not the more “formal” theorists beyond.

This Snowmass is different. It’s different because of Corona, which changed it from a big meeting in a resort to a spread-out series of meetings and online activities. It’s also different because they invited theorists to contribute, and not just those interested in particle colliders. The theorists involved study everything from black holes and quantum gravity to supersymmetry and the mathematics of quantum field theory. Groups focused on each topic submit “white papers” summarizing the state of their area. These white papers in turn get organized and summarized into a few subfields, which in turn contribute to the planning exercise. No-one I’ve talked to is entirely clear on how this works, how much the white papers will actually be taken into account or by whom. But it seems like a good chance to influence US funding agencies, like the Department of Energy, and see if we can get them to prioritize our type of research.

Europe has something similar to Snowmass, called the European Strategy for Particle Physics. It also has smaller-scale groups, with their own purposes, goals, and funding sources. One such group is called SAGEX: Scattering Amplitudes: from Geometry to EXperiment. SAGEX is an Innovative Training Network, an organization funded by the EU to train young researchers, in this case in scattering amplitudes. Its fifteen students are finishing their PhDs and ready to take the field by storm. Along the way, they spent a little time in industry internships (mostly at Maple and Mathematica), and quite a bit of time working on outreach.

They have now summed up that outreach work in an online exhibition. I’ve had fun exploring it over the last couple days. They’ve got a lot of good content there, from basic explanations of relativity and quantum mechanics, to detailed games involving Feynman diagrams and associahedra, to a section that uses solitons as a gentle introduction to integrability. If you’re in the target audience, you should check it out!

The Only Speed of Light That Matters

A couple weeks back, someone asked me about a Veritasium video with the provocative title “Why No One Has Measured The Speed Of Light”. Veritasium is a science popularization youtube channel, and usually a fairly good one…so it was a bit surprising to see it make a claim usually reserved for crackpots. Many, many people have measured the speed of light, including Ole Rømer all the way back in 1676. To argue otherwise seems like it demands a massive conspiracy.

Veritasium wasn’t proposing a conspiracy, though, just a technical point. Yes, many experiments have measured the speed of light. However, the speed they measure is in fact a “two-way speed”, the speed that light takes to go somewhere and then come back. They leave open the possibility that light travels differently in different directions, and only has the measured speed on average: that there are different “one-way speeds” of light.

The loophole is clearest using some of the more vivid measurements of the speed of light, timing how long it takes to bounce off a mirror and return. It’s less clear using other measurements of the speed of light, like Rømer’s. Rømer measured the speed of light using the moons of Jupiter, noticing that the time they took to orbit appeared to change based on whether Jupiter was moving towards or away from the Earth. For this measurement Rømer didn’t send any light to Jupiter…but he did have to make assumptions about Jupiter’s rotation, using it like a distant clock. Those assumptions also leave the door open to a loophole, one where the different one-way speeds of light are compensated by different speeds for distant clocks. You can watch the Veritasium video for more details about how this works, or see the wikipedia page for the mathematical details.

When we think of the speed of light as the same in all directions, in some sense we’re making a choice. We’ve chosen a convention, called the Einstein synchronization convention, that lines up distant clocks in a particular way. We didn’t have to choose that convention, though we prefer to (the math gets quite a bit more complicated if we don’t). And crucially for any such choice, it is impossible for any experiment to tell the difference.

So far, Veritasium is doing fine here. But if the video was totally fine, I wouldn’t have written this post. The technical argument is fine, but the video screws up its implications.

Near the end of the video, the host speculates whether this ambiguity is a clue. What if a deeper theory of physics could explain why we can’t tell the difference between different synchronizations? Maybe that would hint at something important.

Well, it does hint at something important, but not something new. What it hints at is that “one-way speeds” don’t matter. Not for light, or really for anything else.

Think about measuring the speed of something, anything. There are two ways to do it. One is to time it against something else, like the signal in a wire, and assume we know that speed. Veritasium shows an example of this, measuring the speed of a baseball that hits a target and sends a signal back. The other way is to send it somewhere with a clock we trust, and compare it to our clock. Each of these requires that something goes back and forth, even if it’s not the same thing each time. We can’t measure the one-way speed of anything because we’re never in two places at once. Everything we measure, every conclusion we come to about the world, rests on something “two-way”: our actions go out, our perceptions go in. Even our depth perception is an inference from our ancestors, whose experience seeing food and traveling to it calibrated our notion of distance.

Synchronization of clocks is a convention because the external world is a convention. What we have really, objectively, truly, are our perceptions and our memories. Everything else is a model we build to fill the gaps in between. Some features of that model are essential: if you change them, you no longer match our perceptions. Other features, though, are just convenience: ways we arrange the model to make it easier to use, to make it not “sound dumb”, to tell a coherent story. Synchronization is one of those things: the notion that you can compare times in distant places is convenient, but as relativity already tells us in other contexts, not necessary. It’s part of our storytelling, not an essential part of our model.

Book Review: The Joy of Insight

There’s something endlessly fascinating about the early days of quantum physics. In a century, we went from a few odd, inexplicable experiments to a practically complete understanding of the fundamental constituents of matter. Along the way the new ideas ended a world war, almost fueled another, and touched almost every field of inquiry. The people lucky enough to be part of this went from familiarly dorky grad students to architects of a new reality. Victor Weisskopf was one of those people, and The Joy of Insight: Passions of a Physicist is his autobiography.

Less well-known today than his contemporaries, Weisskopf made up for it with a front-row seat to basically everything that happened in particle physics. In the late 20’s and early 30’s he went from studying in Göttingen (including a crush on Maria Göppert before a car-owning Joe Mayer snatched her up) to a series of postdoctoral positions that would exhaust even a modern-day physicist, working in Leipzig, Berlin, Copenhagen, Cambridge, Zurich, and Copenhagen again, before fleeing Europe for a faculty position in Rochester, New York. During that time he worked for, studied under, collaborated or partied with basically everyone you might have heard of from that period. As a result, this section of the autobiography was my favorite, chock-full of stories, from the well-known (Pauli’s rudeness and mythical tendency to break experimental equipment) to the less-well known (a lab in Milan planned to prank Pauli with a door that would trigger a fake explosion when opened, which worked every time they tested it…and failed when Pauli showed up), to the more personal (including an in retrospect terrifying visit to the Soviet Union, where they asked him to critique a farming collective!) That era also saw his “almost Nobel”, in his case almost discovering the Lamb Shift.

Despite an “almost Nobel”, Weisskopf was paid pretty poorly when he arrived in Rochester. His story there puts something I’d learned before about another refugee physicist, Hertha Sponer, in a new light. Sponer’s university also didn’t treat her well, and it seemed reminiscent of modern academia. Weisskopf, though, thinks his treatment was tied to his refugee status: that, aware that they had nowhere else to go, universities gave the scientists who fled Europe worse deals than they would have in a Nazi-less world, snapping up talent for cheap. I could imagine this was true for Sponer as well.

Like almost everyone with the relevant expertise, Weisskopf was swept up in the Manhattan project at Los Alamos. There he rose in importance, both in the scientific effort (becoming deputy leader of the theoretical division) and the local community (spending some time on and chairing the project’s “town council”). Like the first sections, this surreal time leads to a wealth of anecdotes, all fascinating. In his descriptions of the life there I can see the beginnings of the kinds of “hiking retreats” physicists would build in later years, like the one at Aspen, that almost seem like attempts to recreate that kind of intense collaboration in an isolated natural place.

After the war, Weisskopf worked at MIT before a stint as director of CERN. He shepherded the facility’s early days, when they were building their first accelerators and deciding what kinds of experiments to pursue. I’d always thought that the “nuclear” in CERN’s name was an artifact of the times, when “nuclear” and “particle” physics were thought of as the same field, but according to Weisskopf the fields were separate and it was already a misnomer when the place was founded. Here the book’s supply of anecdotes becomes a bit more thin, and instead he spends pages on glowing descriptions of people he befriended. The pattern continues after the directorship as his duties get more administrative, spending time as head of the physics department at MIT and working on arms control, some of the latter while a member of the Pontifical Academy of Sciences (which apparently even a Jewish atheist can join). He does work on some science, though, collaborating on the “bag of quarks” model of protons and neutrons. He lives to see the fall of the Berlin wall, and the end of the book has a bit of 90’s optimism to it, the feeling that finally the conflicts of his life would be resolved. Finally, the last chapter abandons chronology altogether, and is mostly a list of his opinions of famous composers, capped off with a Bohr-inspired musing on the complementary nature of science and the arts, humanities, and religion.

One of the things I found most interesting in this book was actually something that went unsaid. Weisskopf’s most famous student was Murray Gell-Mann, a key player in the development of the theory of quarks (including coining the name). Gell-Mann was famously cultured (in contrast to the boorish-almost-as-affectation Feynman) with wide interests in the humanities, and he seems like exactly the sort of person Weisskopf would have gotten along with. Surprisingly though, he gets no anecdotes in this book, and no glowing descriptions: just a few paragraphs, mostly emphasizing how smart he was. I have to wonder if there was some coldness between them. Maybe Weisskopf had difficulty with a student who became so famous in his own right, or maybe they just never connected. Maybe Weisskopf was just trying to be generous: the other anecdotes in that part of the book are of much less famous people, and maybe Weisskopf wanted to prioritize promoting them, feeling that they were underappreciated.

Weisskopf keeps the physics light to try to reach a broad audience. This means he opts for short explanations, and often these are whatever is easiest to reach for. It creates some interesting contradictions: the way he describes his “almost Nobel” work in quantum electrodynamics is very much the way someone would have described it at the time, but very much not how it would be understood later, and by the time he talks about the bag of quarks model his more modern descriptions don’t cleanly link with what he said earlier. Overall, his goal isn’t really to explain the physics, but to explain the physicists. I enjoyed the book for that: people do it far too rarely, and the result was a really fun read.

What Are Students? We Just Don’t Know

I’m taking a pedagogy course at the moment, a term-long follow-up to the one-week intro course I took in the spring. The course begins with yet another pedagogical innovation, a “pre-project”. Before the course has really properly started, we get assembled into groups and told to investigate our students. We are supposed to do interviews on a few chosen themes, all with the objective of getting to know our students better. I’m guessing the point is to sharpen our goals, so that when we start learning pedagogy we’ll have a clearer idea of what problems we’d like to solve.

The more I think about this the more I’m looking forward to it. When I TAed in the past, some of the students were always a bit of a mystery. They sat in the back, skipped assignments, and gradually I saw less and less of them. They didn’t go to office hours or the help room, and I always wondered what happened. When in the course did they “turn off”, when did we lose them? They seemed like a kind of pedagogical dark matter, observable only by their presence on the rosters. I’m hoping to detect a little of that dark matter here.

As it’s a group project, we came up with a theme as a group, and questions to support that theme (in particular, we’re focusing on the different experiences between Danes and international students). Since the topic is on my mind in general though, I thought it would be fun to reach out to you guys. Educators in the comments: if you could ask your students one question, what would it be? Students, what is one thing you think your teachers are missing?

The arXiv SciComm Challenge

Fellow science communicators, think you can explain everything that goes on in your field? If so, I have a challenge for you. Pick a day, and go through all the new papers on arXiv.org in a single area. For each one, try to give a general-audience explanation of what the paper is about. To make it easier, you can ignore cross-listed papers. If your field doesn’t use arXiv, consider if you can do the challenge with another appropriate site.

I’ll start. I’m looking at papers in the “High Energy Physics – Theory” area, announced 6 Jan, 2022. I’ll warn you in advance that I haven’t read these papers, just their abstracts, so apologies if I get your paper wrong!

arXiv:2201.01303 : Holographic State Complexity from Group Cohomology

This paper says it is a contribution to a Proceedings. That means it is based on a talk given at a conference. In my field, a talk like this usually won’t be presenting new results, but instead summarizes results in a previous paper. So keep that in mind.

There is an idea in physics called holography, where two theories are secretly the same even though they describe the world with different numbers of dimensions. Usually this involves a gravitational theory in a “box”, and a theory without gravity that describes the sides of the box. The sides turn out to fully describe the inside of the box, much like a hologram looks 3D but can be printed on a flat sheet of paper. Using this idea, physicists have connected some properties of gravity to properties of the theory on the sides of the box. One of those properties is complexity: the complexity of the theory on the sides of the box says something about gravity inside the box, in particular about the size of wormholes. The trouble is, “complexity” is a bit subjective: it’s not clear how to give a good definition for it for this type of theory. In this paper, the author studies a theory with a precise mathematical definition, called a topological theory. This theory turns out to have mathematical properties that suggest a well-defined notion of complexity for it.

arXiv:2201.01393 : Nonrelativistic effective field theories with enhanced symmetries and soft behavior

We sometimes describe quantum field theory as quantum mechanics plus relativity. That’s not quite true though, because it is possible to define a quantum field theory that doesn’t obey special relativity, a non-relativistic theory. Physicists do this if they want to describe a system moving much slower than the speed of light: it gets used sometimes for nuclear physics, and sometimes for modeling colliding black holes.

In particle physics, a “soft” particle is one with almost no momentum. We can classify theories based on how they behave when a particle becomes more and more soft. In normal quantum field theories, if they have special behavior when a particle becomes soft it’s often due to a symmetry of the theory, where the theory looks the same even if something changes. This paper shows that this is not true for non-relativistic theories: they have more requirements to have special soft behavior, not just symmetry. They “bootstrap” a few theories, using some general restrictions to find them without first knowing how they work (“pulling them up by their own bootstraps”), and show that the theories they find are in a certain sense unique, the only theories of that kind.

arXiv:2201.01552 : Transmutation operators and expansions for 1-loop Feynman integrands

In recent years, physicists in my sub-field have found new ways to calculate the probability that particles collide. One of these methods describes ordinary particles in a way resembling string theory, and from this discovered a whole “web” of theories that were linked together by small modifications of the method. This method originally worked only for the simplest Feynman diagrams, the “tree” diagrams that correspond to classical physics, but was extended to the next-simplest diagrams, diagrams with one “loop” that start incorporating quantum effects.

This paper concerns a particular spinoff of this method, that can find relationships between certain one-loop calculations in a particularly efficient way. It lets you express calculations of particle collisions in a variety of theories in terms of collisions in a very simple theory. Unlike the original method, it doesn’t rely on any particular picture of how these collisions work, either Feynman diagrams or strings.

arXiv:2201.01624 : Moduli and Hidden Matter in Heterotic M-Theory with an Anomalous U(1) Hidden Sector

In string theory (and its more sophisticated cousin M theory), our four-dimensional world is described as a world with more dimensions, where the extra dimensions are twisted up so that they cannot be detected. The shape of the extra dimensions influences the kinds of particles we can observe in our world. That shape is described by variables called “moduli”. If those moduli are stable, then the properties of particles we observe would be fixed, otherwise they would not be. In general it is a challenge in string theory to stabilize these moduli and get a world like what we observe.

This paper discusses shapes that give rise to a “hidden sector”, a set of particles that are disconnected from the particles we know so that they are hard to observe. Such particles are often proposed as a possible explanation for dark matter. This paper calculates, for a particular kind of shape, what the masses of different particles are, as well as how different kinds of particles can decay into each other. For example, a particle that causes inflation (the accelerating expansion of the universe) can decay into effects on the moduli and dark matter. The paper also shows how some of the moduli are made stable in this picture.

arXiv:2201.01630 : Chaos in Celestial CFT

One variant of the holography idea I mentioned earlier is called “celestial” holography. In this picture, the sides of the box are an infinite distance away: a “celestial sphere” depicting the angles particles go after they collide, in the same way a star chart depicts the angles between stars. Recent work has shown that there is something like a sensible theory that describes physics on this celestial sphere, that contains all the information about what happens inside.

This paper shows that the celestial theory has a property called quantum chaos. In physics, a theory is said to be chaotic if it depends very precisely on its initial conditions, so that even a small change will result in a large change later (the usual metaphor is a butterfly flapping its wings and causing a hurricane). This kind of behavior appears to be present in this theory.

arXiv:2201.01657 : Calculations of Delbrück scattering to all orders in αZ

Delbrück scattering is an effect where the nuclei of heavy elements like lead can deflect high-energy photons, as a consequence of quantum field theory. This effect is apparently tricky to calculate, and previous calculations have involved approximations. This paper finds a way to calculate the effect without those approximations, which should let it match better with experiments.

(As an aside, I’m a little confused by the claim that they’re going to all orders in αZ when it looks like they just consider one-loop diagrams…but this is probably just my ignorance, this is a corner of the field quite distant from my own.)

arXiv:2201.01674 : On Unfolded Approach To Off-Shell Supersymmetric Models

Supersymmetry is a relationship between two types of particles: fermions, which typically make up matter, and bosons, which are usually associated with forces. In realistic theories this relationship is “broken” and the two types of particles have different properties, but theoretical physicists often study models where supersymmetry is “unbroken” and the two types of particles have the same mass and charge. This paper finds a new way of describing some theories of this kind that reorganizes them in an interesting way, using an “unfolded” approach in which aspects of the particles that would normally be combined are given their own separate variables.

(This is another one I don’t know much about, this is the first time I’d heard of the unfolded approach.)

arXiv:2201.01679 : Geometric Flow of Bubbles

String theorists have conjectured that only some types of theories can be consistently combined with a full theory of quantum gravity, others live in a “swampland” of non-viable theories. One set of conjectures characterizes this swampland in terms of “flows” in which theories with different geometry can flow in to each other. The properties of these flows are supposed to be related to which theories are or are not in the swampland.

This paper writes down equations describing these flows, and applies them to some toy model “bubble” universes.

arXiv:2201.01697 : Graviton scattering amplitudes in first quantisation

This paper is a pedagogical one, introducing graduate students to a topic rather than presenting new research.

Usually in quantum field theory we do something called “second quantization”, thinking about the world not in terms of particles but in terms of fields that fill all of space and time. However, sometimes one can instead use “first quantization”, which is much more similar to ordinary quantum mechanics. There you think of a single particle traveling along a “world-line”, and calculate the probability it interacts with other particles in particular ways. This approach has recently been used to calculate interactions of gravitons, particles related to the gravitational field in the same way photons are related to the electromagnetic field. The approach has some advantages in terms of simplifying the results, which are described in this paper.

Facts About Math Are Facts About Us

Each year, the Niels Bohr International Academy has a series of public talks. Part of Copenhagen’s Folkeuniversitet (“people’s university”), they attract a mix of older people who want to keep up with modern developments and young students looking for inspiration. I gave a talk a few days ago, as part of this year’s program. The last time I participated, back in 2017, I covered a topic that comes up a lot on this blog: “The Quest for Quantum Gravity”. This year, I was asked to cover something more unusual: “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”.

Some of you might notice that title is already taken: it’s a famous lecture by the physicist Wigner, from 1959. Wigner posed an interesting question: why is advanced mathematics so useful in physics? Time and time again, mathematicians develop an idea purely for its own sake, only for physicists to find it absolutely indispensable to describe some part of the physical world. Should we be surprised that this keeps working? Suspicious?

I talked a bit about this: some of the answers people have suggested over the years, and my own opinion. But like most public talks, the premise was mostly a vehicle for cool examples: physicists through history bringing in new math, and surprising mathematical facts like the ones I talked about a few weeks back at Culture Night. Because of that, I was actually a bit unprepared to dive into the philosophical side of the topic (despite it being in principle a very philosophical topic!) When one of the audience members brought up mathematical Platonism, I floundered a bit, not wanting to say something that was too philosophically naive.

Well, if there’s anywhere I can be naive, it’s my own blog. I even have a label for Amateur Philosophy posts. So let’s do one.

Mathematical Platonism is the idea that mathematical truths “exist”: that they’re somewhere “out there” being discovered. On the other side, one might believe that mathematics is not discovered, but invented. For some reason, a lot of people with the latter opinion seem to think this has something to do with describing nature (for example, an essay a few years back by Lee Smolin defines mathematics as “the study of systems of evoked relationships inspired by observations of nature”).

I’m not a mathematical Platonist. I don’t even like to talk about which things do or don’t “exist”. But I also think that describing mathematics in terms of nature is missing the point. Mathematicians aren’t physicists. While there may have been a time when geometers argued over lines in the sand, these days mathematicians’ inspiration isn’t usually the natural world, at least not in the normal sense.

Instead, I think you can’t describe mathematics without describing mathematicians. A mathematical fact is, deep down, something a mathematician can say without other mathematicians shouting them down. It’s an allowed move in what my hazy secondhand memory of Wittgenstein wants to call a “language game”: something that gets its truth from a context of people interpreting and reacting to it, in the same way a move in chess matters only when everyone is playing by its rules.

This makes mathematics sound very subjective, and we’re used to the opposite: the idea that a mathematical fact is as objective as they come. The important thing to remember is that even with this kind of description, mathematics still ends up vastly less subjective than any other field. We care about subjectivity between different people: if a fact is “true” for Brits and “false” for Germans, then it’s a pretty limited fact. Mathematics is special because the “rules of its game” aren’t rules of one group or another. They’re rules that are in some sense our birthright. Any human who can read and write, or even just act and perceive, can act as a Turing Machine, a universal computer. With enough patience and paper, anything that you can prove to one person you can prove to another: you just have to give them the rules and let them follow them. It doesn’t matter how smart you are, or what you care about most: if something is mathematically true for others, it is mathematically true for you.

Some would argue that this is evidence for mathematical Platonism, that if something is a universal truth it should “exist”. Even if it does, though, I don’t think it’s useful to think of it in that way. Once you believe that mathematical truth is “out there”, you want to try to characterize it, to say something about it besides that it’s “out there”. You’ll be tempted to have an opinion on the Axiom of Choice, or the Continuum Hypothesis. And the whole point is that those aren’t sensible things to have opinions on, that having an opinion about them means denying the mathematical proofs that they are, in the “standard” axioms, undecidable. Whatever is “out there”, it has to include everything you can prove with every axiom system, whichever non-standard ones you can cook up, because mathematicians will happily work on any of them. The whole point of mathematics, the thing that makes it as close to objective as anything can be, is that openness: the idea that as long as an argument is good enough, as long as it can convince anyone prepared to wade through the pages, then it is mathematics. Nothing, so long as it can convince in the long-run, is excluded.

If we take this definition seriously, there are some awkward consequences. You could imagine a future in which every mind, everyone you might be able to do mathematics with, is crushed under some tyrant, forced to agree to something false. A real philosopher would dig in to this corner case, try to salvage the definition or throw it out. I’m not a real philosopher though. So all I can say is that while I don’t think that tyrant gets to define mathematics, I also don’t think there are good alternatives to my argument. Our only access to mathematics, and to truth in general, is through the people who pursue it. I don’t think we can define one without the other.

Outreach Talk on Math’s Role in Physics

Tonight is “Culture Night” in Copenhagen, the night when the city throws open its doors and lets the public in. Museums and hospitals, government buildings and even the Freemasons, all have public events. The Niels Bohr Institute does too, of course: an evening of physics exhibits and demos, capped off with a public lecture by Denmark’s favorite bow-tie wearing weirder-than-usual string theorist, Holger Bech Nielsen. In between, there are a number of short talks by various folks at the institute, including yours truly.

In my talk, I’m going to try and motivate the audience to care about math. Math is dry of course, and difficult for some, but we physicists need it to do our jobs. If you want to be precise about a claim in physics, you need math simply to say what you want clearly enough.

Since you guys likely don’t overlap with my audience tonight, it should be safe to give a little preview. I’ll be using a few examples, but this one is the most complicated:

I’ll be telling a story I stole from chapter seven of the web serial Almost Nowhere. (That link is to the first chapter, by the way, in case you want to read the series without spoilers. It’s very strange, very unique, and at least in my view quite worth reading.) You follow a warrior carrying a spear around a globe in two different paths. The warrior tries to always point in the same direction, but finds that the two different paths result in different spears when they meet. The story illustrates that such a simple concept as “what direction you are pointing” isn’t actually so simple: if you want to think about directions in curved space (like the surface of the Earth, but also, like curved space-time in general relativity) then you need more sophisticated mathematics (a notion called parallel transport) to make sense of it.

It’s kind of an advanced concept for a public talk. But seeing it show up in Almost Nowhere inspired me to try to get it across. I’ll let you know how it goes!

By the way, if you are interested in learning the kinds of mathematics you need for theoretical physics, and you happen to be a Bachelor’s student planning to pursue a PhD, then consider the Perimeter Scholars International Master’s Program! It’s a one-year intensive at the Perimeter Institute in Waterloo, Ontario, in Canada. In a year it gives you a crash course in theoretical physics, giving you tools that will set you ahead of other beginning PhD students. I’ve witnessed it in action, and it’s really remarkable how much the students learn in a year, and what they go on to do with it. Their early registration deadline is on November 15, just a month away, so if you’re interested you may want to start thinking about it.