In science, every project is different. Sometimes, my collaborators and I have a clear enough goal, and a clear enough way to get there. There are always surprises along the way, of course, but nonetheless we keep a certain amount of structure. That can mean dividing tasks (“you find the basis, I’ll find the constraints”), or it can mean everyone doing the same work in parallel, like a group of students helping each other with homework.
Recently, I’ve experienced a different kind of collaboration. The goals are less clear, and the methods are more…playful.
A big task improves with collaboration: you can divide it up. A delicate task improves with collaboration: you can check each other’s work. An unclear task also improves with collaboration: you can explore more ground.
Picture a bunch of children playing in a sandbox. The children start out sitting by themselves, each digging in the sand. Some are building castles, others dig moats, or search for buried treasure, or dinosaur bones. As the children play, their games link up: the moat protects the castle, the knights leave for treasure, the dinosaur awakens and attacks. The stories feed back on one another, and the game grows.
The project I’m working on now is a bit like that sandbox. Each of us has our own ideas about what we’d like to build, and each experiments with them. We see what works and what doesn’t, which castles hold and which fall over. We keep an eye on what each other are doing, and adjust: if that castle is close to done, maybe a moat would improve the view. Piece by piece, the unclear task becomes clearer. Our individual goals draw us in different directions, but what we discover in the end brings us back together, richer for our distant discoveries.
Working this way requires a lot of communication! In the past, I was mystified when I saw other physicists spend hours talking at a blackboard. I thought that must be a waste of time: surely they’d get more done if they sat at their desks and worked things out, rather than having to talk through every step. Now I realize they were likely part of a different kind of collaboration: not dividing tasks or working in parallel on a clear calculation, but exploring different approaches. In these collaborations, those long chats are a kind of calibration: by explaining what you’re trying to do, you see whether it makes sense to your collaborators. You can drop the parts that don’t make sense and build in some of your collaborators’ ideas. In the end you begin to converge, to something that everyone can endorse. Your sandcastles meet up, your stories become one story. When everything looks good, you’re ready to call over your mom (or in this case, the arXiv) and show it off.
Now that I’ve rested up after this year’s Amplitudes, I’ll give a few of my impressions.
Overall, I think the conference went pretty well. People seemed amused by the digital Niels Bohr, even if he looked a bit like a puppet (Lance compared him to Yoda in his final speech, which was…apt). We used Gather.town, originally just for the poster session and a “virtual reception”, but later we also encouraged people to meet up in it during breaks. That in particular was a big hit: I think people really liked the ability to just move around and chat in impromptu groups, and while nobody seemed to use the “virtual bar”, the “virtual beach” had a lively crowd. Time zones were inevitably rough, but I think we ended up with a good compromise where everyone could still see a meaningful chunk of the conference.
A few things didn’t work as well. For those planning conferences, I would strongly suggest not making a brand new gmail account to send out conference announcements: for a lot of people the emails went straight to spam. Zulip was a bust: I’m not sure if people found it more confusing than last year’s Slack or didn’t notice it due to the spam issue, but almost no-one posted in it. YouTube was complicated: the stream went down a few times and I could never figure out exactly why, it may have just been internet issues here at the Niels Bohr Institute (we did have a power outage one night and had to scramble to get internet access back the next morning). As far as I could tell YouTube wouldn’t let me re-open the previous stream so each time I had to post a new link, which probably was frustrating for those following along there.
That said, this was less of a problem than it might have been, because attendance/”viewership” as a whole was lower than expected. Zoomplitudes last year had massive numbers of people join in both on Zoom and via YouTube. We had a lot fewer: out of over 500 registered participants, we had fewer than 200 on Zoom at any one time, and at most 30 or so on YouTube. Confusion around the conference email might have played a role here, but I suspect part of the difference is simple fatigue: after over a year of this pandemic, online conferences no longer feel like an exciting new experience.
The actual content of the conference ranged pretty widely. Some people reviewed earlier work, others presented recent papers or even work-in-progress. As in recent years, a meaningful chunk of the conference focused on applications of amplitudes techniques to gravitational wave physics. This included a talk by Thibault Damour, who has by now mostly made his peace with the field after his early doubts were sorted out. He still suspected that the mismatch of scales (weak coupling on the one hand, classical scattering on the other) would cause problems in future, but after his work withLaporta and Mastrolia even he had to acknowledge that amplitudes techniques were useful.
In the past I would have put the double-copy and gravitational wave researchers under the same heading, but this year they were quite distinct. While a few of the gravitational wave talks mentioned the double-copy, most of those who brought it up were doing something quite a bit more abstract than gravitational wave physics. Indeed, several people were pushing the boundaries of what it means to double-copy. There were modified KLT kernels, different versions of color-kinematics duality, and explorations of what kinds of massive particles can and (arguably more interestingly) cannot be compatible with a double-copy framework. The sheer range of different generalizations had me briefly wondering whether the double-copy could be “too flexible to be meaningful”, whether the right definitions would let you double-copy anything out of anything. I was reassured by the points where each talk argued that certain things didn’t work: it suggests that wherever this mysterious structure comes from, its powers are limited enough to make it meaningful.
A fair number of talks dealt with what has always been our main application, collider physics. There the context shifted, but the message stayed consistent: for a “clean” enough process two or three-loop calculations can make a big difference, taking a prediction that would be completely off from experiment and bringing it into line. These are more useful the more that can be varied about the calculation: functions are more useful than numbers, for example. I was gratified to hear confirmation that a particular kind of process, where two massless particles like quarks become three massive particles like W or Z bosons, is one of these “clean enough” examples: it means someone will need to compute my “tardigrade” diagram eventually.
If collider physics is our main application, N=4 super Yang-Mills has always been our main toy model. Jaroslav Trnka gave us the details behind Nima’s exciting talk from last year, and Nima had a whole new exciting talk this year with promised connections to category theory (connections he didn’t quite reach after speaking for two and a half hours). Anastasia Volovich presented two distinct methods for predicting square-root symbol letters, while my colleague Chi Zhang showed some exciting progress with the elliptic double-box, realizing the several-year dream of representing it in a useful basis of integrals and showcasing several interesting properties. Anne Spiering came over from the integrability side to show us just how special the “planar” version of the theory really is: by increasing the number of colors of gluons, she showed that one could smoothly go between an “integrability-esque” spectrum and a “chaotic” spectrum. Finally, Lance Dixon mentioned his progress with form-factors in his talk at the end of the conference, showing off some statistics of coefficients of different functions and speculating that machine learning might be able to predict them.
On the more mathematical side, Francis Brown showed us a new way to get numbers out of graphs, one distinct but related to our usual interpretation in terms of Feynman diagrams. I’m still unsure what it will be used for, but the fact that it maps every graph to something finite probably has some interesting implications. Albrecht Klemm and Claude Duhr talked about two sides of the same story, their recent work on integrals involving Calabi-Yau manifolds. They focused on a particular nice set of integrals, and time will tell whether the methods work more broadly, but there are some exciting suggestions that at least parts will.
There’s been a resurgence of the old dream of the S-matrix community, constraining amplitudes via “general constraints” alone, and several talks dealt with those ideas. Sebastian Mizera went the other direction, and tried to test one of those “general constraints”, seeing under which circumstances he could prove that you can swap a particle going in with an antiparticle going out. Others went out to infinity, trying to understand amplitudes from the perspective of the so-called “celestial sphere” where they appear to be governed by conformal field theories of some sort. A few talks dealt with amplitudes in string theory itself: Yvonne Geyer built them out of field-theory amplitudes, while Ashoke Sen explained how to include D-instantons in them.
We also had three “special talks” in the evenings. I’ve mentioned Nima’s already. Zvi Bern gave a retrospective talk that I somewhat cheesily describe as “good for the soul”: a look to the early days of the field that reminded us of why we are who we are. Lance Dixon closed the conference with a light-hearted summary and a look to the future. That future includes next year’s Amplitudes, which after a hasty discussion during this year’s conference has now localized to Prague. Let’s hope it’s in person!
I’m busy this week with Amplitudes 2021. Being behind the “organizer’s desk” for one of these conferences is an entirely different experience. There’s a lot to keep track of, keeping the Zoom going smoothly, the website up to date, and the YouTube stream running. Luckily we have good help, a team of students handling a lot of the more finicky details. I think we’ve been putting on a good conference, but there are definitely lessons I’ve learned for the next time I host something.
The content has been interesting too of course, and despite being busy I’ve still gotten to watch the talks. I’ll say more about this after the conference, there have been quite a few interesting developments in the past year.
In my line of work, I spend a lot of time explaining physics. I write posts here of course, and give the occasional public lecture. I also explain physics when I supervise Master’s students, and in a broader sense whenever I chat with my collaborators or write papers. I’ll explain physics even more when I start teaching. But of all the ways to explain physics, there’s one that has always been my favorite: the one-on-one conversation.
Talking science one-on-one is validating in a uniquely satisfying way. You get instant feedback, questions when you’re unclear and comprehension when you’re close. There’s a kind of puzzle to it, discovering what you need to fill in the gaps in one particular person’s understanding. As a kid, I’d chase this feeling with imaginary conversations: I’d plot out a chat with Democritus or Newton, trying to explain physics or evolution or democracy. It was a game, seeing how I could ground our modern understanding in concepts someone from history already knew.
I’ll never get a chance in real life to explain physics to a Democritus or a Newton, to bridge a gap quite that large. But, as I’ve discovered over the years, everyone has bits and pieces they don’t yet understand. Even focused on the most popular topics, like black holes or elementary particles, everyone has gaps in what they’ve managed to pick up. I do too! So any conversation can be its own kind of adventure, discovering what that one person knows, what they don’t, and how to connect the two.
Of course, there’s fun in writing and public speaking too (not to mention, of course, research). Still, I sometimes wonder if there’s a career out there in just the part I like best: just one conversation after another, delving deep into one person’s understanding, making real progress, then moving on to the next. It wouldn’t be efficient by any means, but it sure sounds fun.
The scientific method, as we usually learn it, starts with a hypothesis. The scientist begins with a guess, and asks a question with a clear answer: true, or false? That guess lets them design an experiment, observe the consequences, and improve our knowledge of the world.
But where did the scientist get the hypothesis in the first place? Often, through some form of exploratory research.
Exploratory research is research done, not to answer a precise question, but to find interesting questions to ask. Each field has their own approach to exploration. A psychologist might start with interviews, asking broad questions to find narrower questions for a future survey. An ecologist might film an animal, looking for changes in its behavior. A chemist might measure many properties of a new material, seeing if any stand out. Each approach is like digging for treasure, not sure of exactly what you will find.
Mathematicians and theoretical physicists don’t do experiments, but we still need hypotheses. We need an idea of what we plan to prove, or what kind of theory we want to build: like other scientists, we want to ask a question with a clear, true/false answer. And to find those questions, we still do exploratory research.
What does exploratory research look like, in the theoretical world? Often, it begins with examples and calculations. We can start with a known method, or a guess at a new one, a recipe for doing some specific kind of calculation. Recipe in hand, we proceed to do the same kind of calculation for a few different examples, covering different sorts of situation. Along the way, we notice patterns: maybe the same steps happen over and over, or the result always has some feature.
We can then ask, do those same steps always happen? Does the result really always have that feature? We have our guess, our hypothesis, and our attempt to prove it is much like an experiment. If we find a proof, our hypothesis was true. On the other hand, we might not be able to find a proof. Instead, exploring, we might find a counterexample – one where the steps don’t occur, the feature doesn’t show up. That’s one way to learn that our hypothesis was false.
This kind of exploration is essential to discovery. As scientists, we all have to eventually ask clear yes/no questions, to submit our beliefs to clear tests. But we can’t start with those questions. We have to dig around first, to observe the world without a clear plan, to get to a point where we have a good question to ask.
A couple different things that some of you might like to know about:
Are you an amateur with an idea you think might revolutionize all of physics? If so, absolutely do not contact me about it. Instead, you can talk to these people. Sabine Hossenfelder runs a service that will hook you up with a scientist who will patiently listen to your idea and help you learn what you need to develop it further. They do charge for that service, and they aren’t cheap, so only do this if you can comfortably afford it. If you can’t, then I have some advice in a post here. Try to contact people who are experts in the specific topic you’re working on, ask concrete questions that you expect to give useful answers, and be prepared to do some background reading.
Are you an undergraduate student planning for a career in theoretical physics? If so, consider the Perimeter Scholars International (PSI) master’s program. Located at the Perimeter Institute in Waterloo, Canada, PSI is an intense one-year boot-camp in theoretical physics, teaching the foundational ideas you’ll need for the rest of your career. It’s something I wish I was aware of when I was applying for schools at that age. Theoretical physics is a hard field, and a big part of what makes it hard is all the background knowledge one needs to take part in it. Starting work on a PhD with that background knowledge already in place can be a tremendous advantage. There are other programs with similar concepts, but I’ve gotten a really good impression of PSI specifically so it’s them I would recommend. Note that applications for the new year aren’t open yet: I always plan to advertise them when they open, and I always forget. So consider this an extremely-early warning.
Are you an amplitudeologist? Registration for Amplitudes 2021 is now live! We’re doing an online conference this year, co-hosted by the Niels Bohr Institute and Penn State. We’ll be doing a virtual poster session, so if you want to contribute to that please include a title and abstract when you register. We also plan to stream on YouTube, and will have a fun online surprise closer to the conference date.
I’ve found that when it comes to reading papers, there are two distinct things I look for.
Sometimes, I read a paper looking for an answer. Typically, this is a “how to” kind of answer: I’m trying to do something, and the paper I’m reading is supposed to explain how. More rarely, I’m directly using a result: the paper proved a theorem or compute a formula, and I just take it as written and use it to calculate something else. Either way, I’m seeking out the paper with a specific goal in mind, which typically means I’m reading it long after it came out.
Other times, I read a paper looking for a question. Specifically, I look for the questions the author couldn’t answer. Sometimes these are things they point out, limitations of their result or opportunities for further study. Sometimes, these are things they don’t notice, holes or patterns in their results that make me wonder “what if?” Either can be the seed of a new line of research, a problem I can solve with a new project. If I read a paper in this way, typically it just came out, and this is the first time I’ve read it. When that isn’t the case, it’s because I start out with another reason to read it: often I’m looking for an answer, only to realize the answer I need isn’t there. The missing answer then becomes my new question.
I’m curious about the balance of these two behaviors in different fields. My guess is that some fields read papers more for their answers, while others read them more for their questions. If you’re working in another field, let me know what you do in the comments!
A reader pointed me to Stephen Wolfram’s one-year update of his proposal for a unified theory of physics. I was pretty squeamish about it one year ago, and now I’m even less interested in wading in to the topic. But I thought it would be worth saying something, and rather than say something specific, I realized I could say something general. I thought I’d talk a bit about how we judge good and bad research in theoretical physics.
In science, there are two things we want out of a new result: we want it to be true, and we want it to be surprising. The first condition should be obvious, but the second is also important. There’s no reason to do an experiment or calculation if it will just tell us something we already know. We do science in the hope of learning something new, and that means that the best results are the ones we didn’t expect.
(What about replications? We’ll get there.)
If you’re judging an experiment, you can measure both of these things with statistics. Statistics lets you estimate how likely an experiment’s conclusion is to be true: was there a large enough sample? Strong enough evidence? It also lets you judge how surprising the experiment is, by estimating how likely it would be to happen given what was known beforehand. Did existing theories and earlier experiments make the result seem likely, or unlikely? While you might not have considered replications surprising, from this perspective they can be: if a prior experiment seems unreliable, successfully replicating it can itself be a surprising result.
If instead you’re judging a theoretical result, these measures get more subtle. There aren’t always good statistical tools to test them. Nonetheless, you don’t have to rely on vague intuitions either. You can be fairly precise, both about how true a result is and how surprising it is.
We get our results in theoretical physics through mathematical methods. Sometimes, this is an actual mathematical proof: guaranteed to be true, no statistics needed. Sometimes, it resembles a proof, but falls short: vague definitions and unstated assumptions mar the argument, making it less likely to be true. Sometimes, the result uses an approximation. In those cases we do get to use some statistics, estimating how good the approximation may be. Finally, a result can’t be true if it contradicts something we already know. This could be a logical contradiction in the result itself, but if the result is meant to describe reality (note: not always the case), it might contradict the results of a prior experiment.
What makes a theoretical result surprising? And how precise can we be about that surprise?
Theoretical results can be surprising in the light of earlier theory. Sometimes, this gets made precise by a no-go theorem, a proof that some kind of theoretical result is impossible to obtain. If a result finds a loophole in a no-go theorem, that can be quite surprising. Other times, a result is surprising because it’s something no-one else was able to do. To be precise about that kind of surprise, you need to show that the result is something others wanted to do, but couldn’t. Maybe someone else made a conjecture, and only you were able to prove it. Maybe others did approximate calculations, and now you can do them more precisely. Maybe a question was controversial, with different people arguing for different sides, and you have a more conclusive argument. This is one of the better reasons to include a long list of references in a paper: not to pad your friends’ citation counts, but to show that your accomplishment is surprising: that others might have wanted to achieve it, but had to settle for something lesser.
In general, this means that showing whether a theoretical result is good: not merely true, but surprising and new, links you up to the rest of the theoretical community. You can put in all the work you like on a theory of everything, and make it as rigorous as possible, but if all you did was reproduce a sub-case of someone else’s theory then you haven’t accomplished all that much. If you put your work in context, compare and contrast to what others have done before, then we can start getting precise about how much we should be surprised, and get an idea of what your result is really worth.
There are theoretical physicists who can do everything they do with a pencil and a piece of paper. I’m not one of them. The calculations I do are long, complicated, or tedious enough that they’re often best done with a computer. For a calculation like that, I can’t just use existing software “out of the box”: I need to program special-purpose tools to do the kind of calculation I need. This means each project has its own kind of learning curve. If I already have the right code, or almost the right code, things go very smoothly: with a few tweaks I can do a lot of interesting calculations. If I don’t have the right code yet, things go much more slowly: I have to build up my technology, figuring out what I need piece by piece until I’m back up to my usual speed.
I don’t always need to use computers to do my calculations. Sometimes my work hinges on something more conceptual: understanding a mathematical proof, or the arguments from another physicist’s paper. While this seems different on the surface, I’ve found that it has the same kinds of learning curves. If I know the right papers and mathematical methods, I can go pretty quickly. If I don’t, I have to “build up my technology”, reading and practicing, a slow build-up to my goal.
The times when I have to “build my technology” are always a bit frustrating. I don’t work as fast as I’d like, and I get tripped up by dumb mistakes. I keep having to go back, almost to the beginning, realizing that some aspect of how I set things up needs to be changed to make the rest work. As I go, though, the work gets more and more satisfying. I find pieces (of the code, of my understanding) that become solid, that I can rely on. I build my technology, and I can do more and more, and feel better about myself in the bargain. Eventually, I get back up to my full abilities, my technology set up, and a wide variety of calculations become possible.
Yesterday, Fermilab’s Muon g-2 experiment announced a new measurement of the magnetic moment of the muon, a number which describes how muons interact with magnetic fields. For what might seem like a small technical detail, physicists have been very excited about this measurement because it’s a small technical detail that the Standard Model seems to get wrong, making it a potential hint of new undiscovered particles. Quanta magazine has a great piece on the announcement, which explains more than I will here, but the upshot is that there are two different calculations on the market that attempt to predict the magnetic moment of the muon. One of them, using older methods, disagrees with the experiment. The other, with a new approach, agrees. The question then becomes, which calculation was wrong? And why?
What does it mean for a prediction to match an experimental result? The simple, wrong, answer is that the numbers must be equal: if you predict “3”, the experiment has to measure “3”. The reason why this is wrong is that in practice, every experiment and every prediction has some uncertainty. If you’ve taken a college physics class, you’ve run into this kind of uncertainty in one of its simplest forms, measurement uncertainty. Measure with a ruler, and you can only confidently measure down to the smallest divisions on the ruler. If you measure 3cm, but your ruler has ticks only down to a millimeter, then what you’re measuring might be as large as 3.1cm or as small as 2.9 cm. You just don’t know.
This uncertainty doesn’t mean you throw up your hands and give up. Instead, you estimate the effect it can have. You report, not a measurement of 3cm, but of 3cm plus or minus 1mm. If the prediction was 2.9cm, then you’re fine: it falls within your measurement uncertainty.
There’s a common thread in all of these uncertainty estimates: you don’t expect to be too far off on average. Your measurements won’t be perfect, but they won’t all be screwed up in the same way either: chances are, they will randomly be a little below or a little above the truth. Your calculations are similar: whether you’re ignoring complicated particle physics diagrams or the spacing in a simulated grid, you can treat the difference as something small and random. That randomness means you can use statistics to talk about your errors: you have statistical uncertainty. When you have statistical uncertainty, you can estimate, not just how far off you might get, but how likely it is you ended up that far off. In particle physics, we have very strict standards for this kind of thing: to call something new a discovery, we demand that it is so unlikely that it would only show up randomly under the old theory roughly one in a million times. The muon magnetic moment isn’t quite up to our standards for a discovery yet, but the new measurement brought it closer.
The two dueling predictions for the muon’s magnetic moment both estimate some amount of statistical uncertainty. It’s possible that the two calculations just disagree due to chance, and that better measurements or a tighter simulation grid would make them agree. Given their estimates, though, that’s unlikely. That takes us from the realm of theoretical uncertainty, and into uncertainty about the theoretical. The two calculations use very different approaches. The new calculation tries to compute things from first principles, using the Standard Model directly. The risk is that such a calculation needs to make assumptions, ignoring some effects that are too difficult to calculate, and one of those assumptions may be wrong. The older calculation is based more on experimental results, using different experiments to estimate effects that are hard to calculate but that should be similar between different situations. The risk is that the situations may be less similar than expected, their assumptions breaking down in a way that the bottom-up calculation could catch.
None of these risks are easy to estimate. They’re “unknown unknowns”, or rather, “uncertain uncertainties”. And until some of them are resolved, it won’t be clear whether Fermilab’s new measurement is a sign of undiscovered particles, or just a (challenging!) confirmation of the Standard Model.