Tag Archives: theoretical physics

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!

Small Shifts for Specificity

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Cosmologists are annoyed at a recent spate of news articles claiming the universe is 26.7 billion years old (rather than 13.8 billion as based on the current best measurements). To some of the science-reading public, the news sounds like a confirmation of hints they’d already heard: about an ancient “Methuselah” star that seemed to be older than the universe (later estimates put it younger), and recent observations from the James Webb Space Telescope of early galaxies that look older than they ought.

“The news doesn’t come from a telescope, though, or a new observation of the sky. Instead, it comes from this press release from the University of Ottawa: “Reinventing cosmology: uOttawa research puts age of universe at 26.7 — not 13.7 — billion years”.

(If you look, you’ll find many websites copying this press release almost word-for-word. This is pretty common in science news, where some websites simply aggregate press releases and others base most of their science news on them rather than paying enough for actual journalism.)

The press release, in turn, is talking about a theory, not an observation. The theorist, Rajendra Gupta, was motivated by examples like the early galaxies observed by JWST and the Methuselah star. Since the 13.8 billion year age of the universe is based on a mathematical model, he tried to find a different mathematical model that led to an older universe. Eventually, by hypothesizing what seems like every unproven physics effect he could think of, he found one that gives a different estimate, 26.7 billion. He probably wasn’t the first person to do this, because coming up with different models to explain odd observations is a standard thing cosmologists do all the time, and until one of the models is shown to explain a wider range of observations (because our best theories explain a lot, so they’re hard to replace), they’re just treated as speculation, not newsworthy science.

This is a pretty clear case of hype, and as such most of the discussion has been about what went wrong. Should we blame the theorist? The university? The journalists? Elon Musk?

Rather than blame, I think it’s more productive to offer advice. And in this situation, the person I think could use some advice is the person who wrote the press release.

So suppose you work for a university, writing their press releases. One day, you hear that one of your professors has done something very cool, something worthy of a press release: they’ve found a new estimate for the age of the universe. What do you do?

One thing you absolutely shouldn’t do is question the science. That just isn’t your job, and even if it were you don’t have the expertise to do that. Anyone who’s hoping that you will only write articles about good science and not bad science is being unrealistic, that’s just not an option.

If you can’t be more accurate, though, you can still be more precise. You can write your article, and in particular your headline, so that you express what you do know as clearly and specifically as possible.

(I’m assuming here you write your own headlines. This is not normal in journalism, where most headlines are written by an editor, not by the writer of a piece. But university press offices are small enough that I’m assuming, perhaps incorrectly, that you can choose how to title your piece.)

Let’s take a look at the title, “Reinventing cosmology: uOttawa research puts age of universe at 26.7 — not 13.7 — billion years”, and see if we can make some small changes to improve it.

One very general word in that title is “research”. Lots of people do research: astronomers do research when they collect observations, theorists do research when they make new models. If you say “research”, some people will think you’re reporting a new observation, a new measurement that gives a radically different age for the universe.

But you know that’s not true, it’s not what the scientist you’re talking to is telling you. So to avoid the misunderstanding, you can get a bit more specific, and replace the word “research” with a more precise one: “Reinventing cosmology: uOttawa theory puts age of universe at 26.7 — not 13.7 — billion years”.

“Theory” is just as familiar a word as “research”. You won’t lose clicks, you won’t confuse people. But now, you’ve closed off a big potential misunderstanding. By a small shift, you’ve gotten a lot clearer. And you didn’t need to question the science to do it!

You can do more small shifts, if you understand a bit more of the science. “Puts” is kind of ambiguous: a theory could put an age somewhere because it computes it from first principles, or because it dialed some parameter to get there. Here, the theory was intentionally chosen to give an older universe, so the title should hint at this in some way. Instead of “puts”, then, you can use “allows”: “Reinventing cosmology: uOttawa theory allows age of universe to be 26.7 — not 13.7 — billion years”.

These kinds of little tricks can be very helpful. If you’re trying to avoid being misunderstood, then it’s good to be as specific as you can, given what you understand. If you do it carefully, you don’t have to question your scientists’ ideas or downplay their contributions. You can do your job, promote your scientists, and still contribute to responsible journalism.

What RIBs Could Look Like

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The journal Nature recently published an opinion piece about a new concept for science funding called Research Impact Bonds (or RIBs).

Normally, when a government funds something, they can’t be sure it will work. They pay in advance, and have to guess whether a program will do what they expect, or whether a project will finish on time. Impact bonds are a way for them to pay afterwards, so they only pay for projects that actually deliver. Instead, the projects are funded by private investors, who buy “impact bonds” that guarantee them a share of government funding if the project is successful. Here’s an example given in the Nature piece:

For instance, say the Swiss government promises to pay up to one million Swiss francs (US$1.1 million) to service providers that achieve a measurable outcome, such as reducing illiteracy in a certain population by 5%, within a specified number of years. A broker finds one or more service providers that think they can achieve this at a cost of, say, 900,000 francs, as well as investors who agree to pay these costs up front — thus taking on the risk of the project — for a potential 10% gain if successful. If the providers achieve their goals, the government pays 990,000 francs: 900,000 francs for the work and a 90,000-franc investment return. If the project does not succeed, the investors lose their money, but the government does not.

The author of the piece, Michael Hill, thinks that this could be a new way for governments to fund science. In his model, scientists would apply to the government to propose new RIBs. The projects would have to have specific goals and time-frames: “measure the power of this cancer treatment to this accuracy in five years”, for example. If the government thinks the goal is valuable, they commit to paying some amount of money if the goal is reached. Then investors can decide whether the investment is worthwhile. The projects they expect to work get investor money, and if they do end up working the investors get government money. The government only has to pay if the projects work, but the scientists get paid regardless.

Ok, what’s the catch?

One criticism I’ve seen is that this kind of model could only work for very predictable research, maybe even just for applied research. While the author admits RIBs would only be suitable for certain sorts of projects, I think the range is wider than you might think. The project just has to have a measurable goal by a specified end date. Many particle physics experiments work that way: a dark matter detector, for instance, is trying to either rule out or detect dark matter to a certain level of statistical power within a certain run time. Even “discovery” machines, that we build to try to discover the unexpected, usually have this kind of goal: a bigger version of the LHC, for instance, might try to measure the coupling of Higgs bosons to a certain accuracy.

There are a few bigger issues with this model, though. If you go through the math in Hill’s example, you’ll notice that if the project works, the government ends up paying one million Swiss francs for a service that only cost the provider 900,000 Swiss francs. Under a normal system, the government would only have had to pay 900,000. This gets compensated by the fact that not every project works, so the government only pays for some projects and not others. But investors will be aware of this, and that means the government can’t offer too many unrealistic RIBs: the greater the risk investors are going to take, the more return they’ll expect. On average then, the government would have to pay about as much as they would normally: the cost of the projects that succeed, plus enough money to cover the risk that some fail. (In fact, they’d probably pay a bit more, to give the investors a return on the investment.)

So the government typically won’t save money, at least not if they want to fund the same amount of research. Instead, the idea is that they will avoid risk. But it’s not at all clear to me that the type of risk they avoid is one they want to.

RIBs might appeal to voters: it might sound only fair that a government only funds the research that actually works. That’s not really a problem for the government itself, though: because governments usually pay for many small projects, they still get roughly as much success overall as they want, they just don’t get to pick where. Instead, RIBS put the government agency in a much bigger risk, the risk of unexpected success. As part of offering RIBs, the government would have to estimate how much money they would be able to pay when the projects end. They would want to fund enough projects so that, on average, they pay that amount of money. (Otherwise, they’d end up funding science much less than they do now!) But if the projects work out better than expected, then they’d have to pay much more than they planned. And government science agencies usually can’t do this. In many countries, they can’t plan far in advance at all: their budgets get decided by legislators year to year, and delays in decisions mean delays in funding. If an agency offered RIBs that were more successful than expected, they’d either have to cut funding somewhere else (probably firing a lot of people), or just default on their RIBs, weakening the concept for the next time they used them. These risks, unlike the risk of individual experiments not working, are risks that can really hurt government agencies.

Impact bonds typically have another advantage, in that they spread out decision-making. The Swiss government in Hill’s example doesn’t have to figure out which service providers can increase literacy, or how much it will cost them: it just puts up a budget, and lets investors and service providers figure out if they can make it work. This also serves as a hedge against corruption. If the government made the decisions, they might distribute funding for unrelated political reasons or even out of straight-up bribery. They’d also have to pay evaluators to figure things out. Investors won’t take bribes to lose money, so in theory would be better at choosing projects that will actually work, and would have a vested interest in paying for a good investigation.

This advantage doesn’t apply to Hill’s model of RIBs, though. In Hill’s model, scientists still need to apply to the government to decide which of their projects get offered as RIBs, so the government still needs to decide which projects are worth investing in. Then the scientists or the government need to take another step, and convince investors. The scientists in this equation effectively have to apply twice, which anyone who has applied for a government grant will realize is quite a lot of extra time and effort.

So overall, I don’t think Hills’ model of RIBs is useful, even for the purpose he imagines. It’s too risky for government science agencies to commit to payments like that, and it generates more, not less, work for scientists and the agency.

Hill’s model, though, isn’t the only way RIBs can work. And “avoiding risk” isn’t the only reason we might want them. There are two other reasons one might want RIBs, with very different-sounding motivations.

First, you might be pessimistic about mainstream science. Maybe you think scientists are making bad decisions, choosing ideas that either won’t pan out or won’t have sufficient impact, based more on fashion than on careful thought. You want to incentivize them to do better, to try to work out what impact they might have with some actual numbers and stand by their judgement. If that’s your perspective, you might be interested in RIBs for the same reason other people are interested in prediction markets: by getting investors involved, you have people willing to pay for an accurate estimate.

Second, you might instead be optimistic about mainstream science. You think scientists are doing great work, work that could have an enormous impact, but they don’t get to “capture that value”. Some projects might be essential to important, well-funded goals, but languish unrewarded. Others won’t see their value until long in the future, or will do so in unexpected ways. If scientists could fund projects based on their future impact, with RIBs, maybe they could fund more of this kind of work.

(I first started thinking about this perspective due to a talk by Sabrina Pasterski. The talk itself offended a lot of people, and had some pretty impractical ideas, like selling NFTs of important physics papers. But I think one part of the perspective, that scientists have more impact than we think, is worth holding on to.)

If you have either of those motivations, Hill’s model won’t help. But another kind of model perhaps could. Unlike Hill’s, it could fund much more speculative research, ideas where we don’t know the impact until decades down the line. To demonstrate, I’ll show how it could fund some very speculative research: the work of Peter van Nieuwenhuizen.

Peter van Nieuwenhuizen is one of the pioneers of the theory of supergravity, a theory that augments gravity with supersymmetric partner particles. From its beginnings in the 1970’s, the theory ended up having a major impact on string theory, and today they are largely thought of as part of the same picture of how the universe might work.

His work has, over time, had more practical consequences though. In the 2000’s, researchers working with supergravity noticed a calculational shortcut: they could do a complicated supergravity calculation as the “square” of a much simpler calculation in another theory, called Yang-Mills. Over time, they realized the shortcut worked not just for supergravity, but for ordinary gravity as well, and not just for particle physics calculations but for gravitational wave calculations. Now, their method may make an important contribution to calculations for future gravitational wave telescopes like the Einstein telescope, letting them measure properties of neutron stars.

With that in mind, imagine the following:

In 1967, Jocelyn Bell Burnell and Antony Hewish detected a pulsar, in one of the first direct pieces of evidence for the existence of neutron stars. Suppose that in the early 1970’s NASA decided to announce a future purchase of RIBs: in 2050, they would pay a certain amount to whoever was responsible for finding the equation of state of a neutron star, the formula that describes how its matter moves under pressure. They compute based on estimates of economic growth and inflation, and arrive at some suitably substantial number.

At the same time, but unrelatedly, van Nieuwenhuizen and collaborators sell RIBs. Maybe they use the proceeds to buy more computer time for their calculations, or to refund travel so they can more easily meet and discuss. They tell the buyers that, if some government later decides to reward their discoveries, the holders of the RIB would get a predetermined cut of the rewards.

The years roll by, and barring some unexpected medical advances the discoverers of supergravity die. In the meantime, researchers use their discovery to figure out how to make accurate predictions of gravitational waves from merging neutron stars. When the Einstein telescope turns out, it detects such a merger, and the accurate predictions let them compute the neutron star’s equation of state.

In 2050, then, NASA looks back. They make a list of everyone who contributed to the discovery of the neutron star’s equation of state, every result that was needed for the discovery, and try to estimate how important each contribution was. Then they spend the money they promised buying RIBs, up to the value for each contributor. This includes RIBs originally held by the investors in van Nieuwenhuizen and collaborators. Their current holders make some money, justifying whatever value they paid from their previous owners.

Imagine a world in which government agencies do this kind of thing all the time. Scientists could sell RIBs in their projects, without knowing exactly which agency would ultimately pay for them. Rather than long grant applications, they could write short summaries for investors, guessing at the range of their potential impact, and it would be up to the investors to decide whether the estimate made sense. Scientists could get some of the value of their discoveries, even when that value is quite unpredictable. And they would be incentivized to pick discoveries that could have high impact, and to put a bit of thought and math into what kind of impact that could be.

(Should I still be calling these things bonds, when the buyers don’t know how much they’ll be worth at the end? Probably not. These are more like research impact shares, on a research impact stock market.)

Are there problems with this model, then? Oh sure, loads!

I already mentioned that it’s hard for government agencies to commit to spending money five years down the line. A seventy-year commitment, from that perspective, sounds completely ridiculous.

But we don’t actually need that in the model. All we need is a good reason for investors to think that, eventually, NASA will buy some research impact shares. If government agencies do this regularly, then they would have that reason. They could buy a variety of theoretical developments, a diversified pool to make it more likely some government agency would reward them. This version of the model would be riskier, though, so they’d want more return in exchange.

Another problem is the decision-making aspect. Government agencies wouldn’t have to predict the future, but they would have to accurately assess the past, fairly estimating who contributed to a project, and they would have to do it predictably enough that it could give rise to worthwhile investments. This is itself both controversial and a lot of work. If we figure out the neutron star equation of state, I’m not sure I trust NASA to reward van Nieuwenhuizen’s contribution to it.

This leads to the last modification of the model, and the most speculative one. Over time, government agencies will get better and better at assigning credit. Maybe they’ll have better models of how scientific progress works, maybe they’ll even have advanced AI. A future government (or benevolent AI, if you’re into that) might decide to buy research impact shares in order to validate important past work.

If you believe that might happen, then you don’t need a track record of government agencies buying research impact shares. As a scientist, you can find a sufficiently futuristically inclined investor, and tell them this story. You can sell them some shares, and tell them that, when the AI comes, they will have the right to whatever benefit it bestows upon your research.

I could imagine some people doing this. If you have an image of your work saving humanity in the distant future, you should be able to use that image to sell something to investors. It would be insanely speculative, a giant pile of what-ifs with no guarantee of any of it cashing out. But at least it’s better than NFTs.

Not Made of Photons Either

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If you know a bit about quantum physics, you might have heard that everything is made out of particles. Mass comes from Higgs particles, gravity from graviton particles, and light and electricity and magnetism from photon particles. The particles are the “quanta”, the smallest possible units of stuff.

This is not really how quantum physics works.

You might have heard (instead, or in addition), that light is both particle and wave. Maybe you’ve heard it said that it is both at the same time, or that it is one or the other, depending on how you look at it.

This is also not really how quantum physics works.

If you think that light is both a particle and a wave, you might get the impression there are only two options. This is better than thinking there is only one option, but still not really the truth. The truth is there are many options. It all depends on what you measure.

Suppose you have a particle collider, like the Large Hadron Collider at CERN. Sometimes, the particles you collide release photons. You surround the collision with particle detectors. When a photon hits them, these particle detectors amplify it, turning it into an electrical signal in a computer.

If you want to predict what those particle detectors see, you might put together a theory of photons. You’ll try to calculate the chance that you see some specific photon with some specific energy to some reasonable approximation…and you’ll get infinity.

You might think you’ve heard this story before. Maybe you’ve heard people talk about calculations in quantum field theory that give infinity, with buzzwords like divergences and renormalization. You may remember them saying that this is a sign that our theories are incomplete, that there are parameters we can’t predict or that the theory is just a low-energy approximation to a deeper theory.

This is not that story. That story is about “ultraviolet divergences”, infinities that come from high-energy particles. This story is about “infrared divergences” from low-energy particles. Infrared divergences don’t mean our theory is incomplete. Our theory is fine. We’re just using it wrong.

The problem is that I lied to you a little bit, earlier. I told you that your particle detectors can detect photons, so you might have imagined they can detect any photon you like. But that is impossible. A photon’s energy is determined by its wavelength: X-rays have more energy than UV light, which has more energy than IR light, which has more energy than microwaves. No matter how you build your particle detector, there will be some energy low enough that it cannot detect, a wavelength of photons that gives no response at all.

When you think you’re detecting just one photon, then, you’re not actually detecting just one photon. You’re detecting one photon, plus some huge number of undetectable photons that are too low-energy to see. We call these soft photons. You don’t know how many soft photons you generate, because you can’t detect them. Thus, as always in quantum mechanics, you have to add up every possibility.

That adding up is crucial, because it makes the infinite results go away. The different infinities pair up, negative and positive, at each order of approximation. Those pesky infrared divergences aren’t really a problem, provided you’re honest about what you’re actually detecting.

But while infrared divergences aren’t really a problem, they do say something about your model. You were modeling particles as single photons, and that made your calculations complicated, with a lot of un-physical infinite results. But you could, instead, have made another model. You could have modeled particles as dressed photons: one photon, plus a cloud of soft photons.

For a particle physicists, these dressed photons have advantages and disadvantages. They aren’t always the best tool, and can be complicated to use. But one thing they definitely do is avoid infinite results. You can interpret them a little more easily.

That ease, though, raises a question. You started out with a model in which each particle you detect was a photon. You could have imagined it as a model of reality, one in which every electromagnetic field was made up of photons.

But then you found another model, one which sometimes makes more sense. And in that model, instead, you model your particles as dressed photons. You could then once again imagine a model of reality, now with every electromagnetic field made up of dressed photons, not the ordinary ones.

So now it looks like you have three options. Are electromagnetic fields made out of waves, or particles…or dressed particles?

That’s a trick question. It was always a trick question, and will always be a trick question.

Ancient Greek philosophers argued about whether everything was made of water, or fire, or innumerable other things. Now, we teach children that science has found the answer: a world made of atoms, or protons, or quarks.

But scientists are actually answering a different, and much more important, question. “What is everything really made of?” is still a question for philosophers. We scientists want to know what we will observe. We want a model that makes predictions, that tells us what actions we can do and what results we should expect, that lets us develop technology and improve our lives.

And if we want to make those predictions, then our models can make different choices. We can arrange things in different ways, grouping the fluid possibilities of reality into different concrete “stuff”. We can choose what to measure, and how best to describe it. We don’t end up with one “what everything is made of”, but more than one, different stories for different contexts. As long as those models make the right predictions, we’ve done the only job we ever needed to do.

Cabinet of Curiosities: The Deluxe Train Set

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I’ve got a new paper out this week with Andrew McLeod. I’m thinking of it as another entry in this year’s “cabinet of curiosities”, interesting Feynman diagrams with unusual properties. Although this one might be hard to fit into a cabinet.

Over the past few years, I’ve been finding Feynman diagrams with interesting connections to Calabi-Yau manifolds, the spaces originally studied by string theorists to roll up their extra dimensions. With Andrew and other collaborators, I found an interesting family of these diagrams called traintracks, which involve higher-and-higher dimensional manifolds as they get longer and longer.

This time, we started hooking up our traintracks together.

We call diagrams like these traintrack network diagrams, or traintrack networks for short. The original traintracks just went “one way”: one family, going higher in Calabi-Yau dimension the longer they got. These networks branch out, one traintrack leading to another and another.

In principle, these are much more complicated diagrams. But we find we can work with them in almost the same way. We can find the same “starting point” we had for the original traintracks, the set of integrals used to find the Calabi-Yau manifold. We’ve even got more reliable tricks, a method recently honed by some friends of ours that consistently find a Calabi-Yau manifold inside the original traintracks.

Surprisingly, though, this isn’t enough.

It works for one type of traintrack network, a so-called “cross diagram” like this:

But for other diagrams, if the network branches any more, the trick stops working. We still get an answer, but that answer is some more general space, not just a Calabi-Yau manifold.

That doesn’t mean that these general traintrack networks don’t involve Calabi-Yaus at all, mind you: it just means this method doesn’t tell us one way or the other. It’s also possible that simpler versions of these diagrams, involving fewer particles, will once again involve Calabi-Yaus. This is the case for some similar diagrams in two dimensions. But it’s starting to raise a question: how special are the Calabi-Yau related diagrams? How general do we expect them to be?

Another fun thing we noticed has to do with differential equations. There are equations that relate one diagram to another simpler one. We’ve used them in the past to build up “ladders” of diagrams, relating each picture to one with one of its boxes “deleted”. We noticed, playing with these traintrack networks, that these equations do a bit more than we thought. “Deleting” a box can make a traintrack short, but it can also chop a traintrack in half, leaving two “dangling” pieces, one on either side.

This reminded me of an important point, one we occasionally lose track of. The best-studied diagrams related to Calabi-Yaus are called “sunrise” diagrams. If you squish together a loop in one of those diagrams, the whole diagram squishes together, becoming much simpler. Because of that, we’re used to thinking of these as diagrams with a single “geometry”, one that shows up when you don’t “squish” anything.

Traintracks, and traintrack networks, are different. “Squishing” the diagram, or “deleting” a box, gives you a simpler diagram, but not much simpler. In particular, the new diagram will still contain traintracks, and traintrack networks. That means that we really should think of each traintrack network not just as one “top geometry”, but of a collection of geometries, different Calabi-Yaus that break into different combinations of Calabi-Yaus in different ways. It’s something we probably should have anticipated, but the form these networks take is a good reminder, one that points out that we still have a lot to do if we want to understand these diagrams.