Tag Archives: Nima Arkani-Hamed

When It Rains It Amplitudes

The last few weeks have seen a rain of amplitudes papers on arXiv, including quite a few interesting ones.

rainydays

As well as a fair amount of actual rain in Copenhagen

Over the last year Nima Arkani-Hamed has been talking up four or five really interesting results, and not actually publishing any of them. This has understandably frustrated pretty much everybody. In the last week he published two of them, Cosmological Polytopes and the Wavefunction of the Universe with Paolo Benincasa and Alexander Postnikov and Scattering Amplitudes For All Masses and Spins with Tzu-Chen Huang and Yu-tin Huang. So while I’ll have to wait on the others (I’m particularly looking forward to seeing what he’s been working on with Ellis Yuan) this can at least tide me over.

Cosmological Polytopes and the Wavefunction of the Universe is Nima & co.’s attempt to get a geometrical picture for cosmological correlators, analogous to the Ampituhedron. Cosmological correlators ask questions about the overall behavior of the visible universe: how likely is one clump of matter to be some distance from another? What sorts of patterns might we see in the Cosmic Microwave Background? This is the sort of thing that can be used for “cosmological collider physics”, an idea I mention briefly here.

Paolo Benincasa was visiting Perimeter near the end of my time there, so I got a few chances to chat with him about this. One thing he mentioned, but that didn’t register fully at the time, was Postnikov’s involvement. I had expected that even if Nima and Paolo found something interesting that it wouldn’t lead to particularly deep mathematics. Unlike the N=4 super Yang-Mills theory that generates the Amplituhedron, the theories involved in these cosmological correlators aren’t particularly unique, they’re just a particular class of models cosmologists use that happen to work well with Nima’s methods. Given that, it’s really surprising that they found something mathematically interesting enough to interest Postnikov, a mathematician who was involved in the early days of the Amplituhedron’s predecessor, the Positive Grassmannian. If there’s something that mathematically worthwhile in such a seemingly arbitrary theory then perhaps some of the beauty of the Amplithedron are much more general than I had thought.

Scattering Amplitudes For All Masses and Spins is on some level a byproduct of Nima and Yu-tin’s investigations of whether string theory is unique. Still, it’s a useful byproduct. Many of the tricks we use in scattering amplitudes are at their best for theories with massless particles. Once the particles have masses our notation gets a lot messier, and we often have to rely on older methods. What Nima, Yu-tin, and Tzu-Chen have done here is to build a notation similar to what we use for massless particle, but for massive ones.

The advantage of doing this isn’t just clean-looking papers: using this notation makes it a lot easier to see what kinds of theories make sense. There are a variety of old theorems that restrict what sorts of theories you can write down: photons can’t interact directly with each other, there can only be one “gravitational force”, particles with spins greater than two shouldn’t be massless, etc. The original theorems were often fairly involved, but for massless particles there were usually nice ways to prove them in modern amplitudes notation. Yu-tin in particular has a lot of experience finding these kinds of proofs. What the new notation does is make these nice simple proofs possible for massive particles as well. For example, you can try to use the new notation to write down an interaction between a massive particle with spin greater than two and gravity, and what you find is that any expression you write breaks down: it works fine at low energies, but once you’re looking at particles with energies much higher than their mass you start predicting probabilities greater than one. This suggests that particles with higher spins shouldn’t be “fundamental”, they should be explained in terms of other particles at higher energies. The only way around this turns out to be an infinite series of particles to cancel problems from the previous ones, the sort of structure that higher vibrations have in string theory. I often don’t appreciate papers that others claim are a pleasure to read, but this one really was a pleasure to read: there’s something viscerally satisfying about seeing so many important constraints manifest so cleanly.

I’ve talked before about the difference between planar and non-planar theories. Planar theories end up being simpler, and in the case of N=4 super Yang-Mills this results in powerful symmetries that let us do much more complicated calculations. Non-planar theories are more complicated, but necessary for understanding gravity. Dual Conformal Symmetry, Integration-by-Parts Reduction, Differential Equations and the Nonplanar Sector, a new paper by Zvi Bern, Michael Enciso, Harald Ita, and Mao Zeng, works on bridging the gap between these two worlds.

Most of the paper is concerned with using some of the symmetries of N=4 super Yang-Mills in other, more realistic (but still planar) theories. The idea is that even if those symmetries don’t hold one can still use techniques that respect those symmetries, and those techniques can often be a lot cleaner than techniques that don’t. This is probably the most practically useful part of the paper, but the part I was most curious about is in the last few sections, where they discuss non-planar theories. For a while now I’ve been interested in ways to treat a non-planar theory as if it were planar, to try to leverage the powerful symmetries we have in planar N=4 super Yang-Mills elsewhere. Their trick is surprisingly simple: they just cut the diagram open! Oddly enough, they really do end up with similar symmetries using this method. I still need to read this in more detail to understand its limitations, since deep down it feels like something this simple couldn’t possibly work. Still, if anything like the symmetries of planar N=4 holds in the non-planar case there’s a lot we could do with it.

There are a bunch of other interesting recent papers that I haven’t had time to read. Some look like they might relate to weird properties of N=4 super Yang-Mills, others say interesting things about the interconnected web of theories tied together by their behavior when a particle becomes “soft”. Another presents a method for dealing with elliptic functions, one of the main obstructions to applying my hexagon function technique to more situations. And of course I shouldn’t fail to mention a paper by my colleague Carlos Cardona, applying amplitudes techniques to AdS/CFT. Overall, a lot of interesting stuff in a short span of time. I should probably get back to reading it!

Advertisements

KITP Conference Retrospective

I’m back from the conference in Santa Barbara, and I thought I’d share a few things I found interesting. (For my non-physicist readers: I know it’s been a bit more technical than usual recently, I promise I’ll get back to some general audience stuff soon!)

James Drummond talked about efforts to extend the hexagon function method I work on to amplitudes with seven (or more) particles. In general, the method involves starting with a guess for what an amplitude should look like, and honing that guess based on behavior in special cases where it’s easier to calculate. In one of those special cases (called the multi-Regge limit), I had thought it would be quite difficult to calculate for more than six particles, but James clarified for me that there’s really only one additional piece needed, and they’re pretty close to having a complete understanding of it.

There were a few talks about ways to think about amplitudes in quantum field theory as the output of a string theory-like setup. There’s been progress pushing to higher quantum-ness, and in understanding the weird web of interconnected theories this setup gives rise to. In the comments, Thoglu asked about one part of this web of theories called Z theory.

Z theory is weird. Most of the theories that come out of this “web” come from a consistent sort of logic: just like you can “square” Yang-Mills to get gravity, you can “square” other theories to get more unusual things. In possibly the oldest known example, you can “square” the part of string theory that looks like Yang-Mills at low energy (open strings) to get the part that looks like gravity (closed strings). Z theory asks: could the open string also come from “multiplying” two theories together? Weirdly enough, the answer is yes: it comes from “multiplying” normal Yang-Mills with a part that takes care of the “stringiness”, a part which Oliver Schlotterer is calling “Z theory”. It’s not clear whether this Z theory makes sense as a theory on its own (for the experts: it may not even be unitary) but it is somewhat surprising that you can isolate a “building block” that just takes care of stringiness.

Peter Young in the comments asked about the Correlahedron. Scattering amplitudes ask a specific sort of question: if some particles come in from very far away, what’s the chance they scatter off each other and some other particles end up very far away? Correlators ask a more general question, about the relationships of quantum fields at different places and times, of which amplitudes are a special case. Just as the Amplituhedron is a geometrical object that specifies scattering amplitudes (in a particular theory), the Correlahedron is supposed to represent correlators (in the same theory). In some sense (different from the sense above) it’s the “square” of the Amplituhedron, and the process that gets you from it to the Amplituhedron is a geometrical version of the process that gets you from the correlator to the amplitude.

For the Amplituhedron, there’s a reasonably smooth story of how to get the amplitude. News articles tended to say the amplitude was the “volume” of the Amplituhedron, but that’s not quite correct. In fact, to find the amplitude you need to add up, not the inside of the Amplituhedron, but something that goes infinite at the Amplituhedron’s boundaries. Finding this “something” can be done on a case by case basis, but it get tricky in more complicated cases.

For the Correlahedron, this part of the story is missing: they don’t know how to define this “something”, the old recipe doesn’t work. Oddly enough, this actually makes me optimistic. This part of the story is something that people working on the Amplituhedron have been trying to avoid for a while, to find a shape where they can more honestly just take the volume. The fact that the old story doesn’t work for the Correlahedron suggests that it might provide some insight into how to build the Amplituhedron in a different way, that bypasses this problem.

There were several more talks by mathematicians trying to understand various aspects of the Amplituhedron. One of them was by Hugh Thomas, who as a fun coincidence actually went to high school with Nima Arkani-Hamed, one of the Amplituhedron’s inventors. He’s now teamed up with Nima and Jaroslav Trnka to try to understand what it means to be inside the Amplituhedron. In the original setup, they had a recipe to generate points inside the Amplituhedron, but they didn’t have a fully geometrical picture of what put them “inside”. Unlike with a normal shape, with the Amplituhedron you can’t just check which side of the wall you’re on. Instead, they can flatten the Amplituhedron, and observe that for points “inside” the Amplituhedron winds around them a specific number of times (hence “Unwinding the Amplituhedron“). Flatten it down to a line and you can read this off from the list of flips over your point, an on-off sequence like binary. If you’ve ever heard the buzzword “scattering amplitudes as binary code”, this is where that comes from.

They also have a better understanding of how supersymmetry shows up in the Amplituhedron, which Song He talked about in his talk. Previously, supersymmetry looked to be quite central, part of the basic geometric shape. Now, they can instead understand it in a different way, with the supersymmetric part coming from derivatives (for the specialists: differential forms) of the part in normal space and time. The encouraging thing is that you can include these sorts of derivatives even if your theory isn’t supersymmetric, to keep track of the various types of particles, and Song provided a few examples in his talk. This is important, because it opens up the possibility that something Amplituhedron-like could be found for a non-supersymmetric theory. Along those lines, Nima talked about ways that aspects of the “nice” description of space and time we use for the Amplituhedron can be generalized to other messier theories.

While he didn’t talk about it at the conference, Jake Bourjaily has a new paper out about a refinement of the generalized unitarity technique I talked about a few weeks back. Generalized unitarity involves matching a “cut up” version of an amplitude to a guess. What Jake is proposing is that in at least some cases you can start with a guess that’s as easy to work with as possible, where each piece of the guess matches up to just one of the “cuts” that you’re checking.  Think about it like a game of twenty questions where you’ve divided all possible answers into twenty individual boxes: for each box, you can just ask “is it in this box”?

Finally, I’ve already talked about the highlight of the conference, so I can direct you to that post for more details. I’ll just mention here that there’s still a fair bit of work to do for Zvi Bern and collaborators to get their result into a form they can check, since the initial output of their setup is quite messy. It’s led to worries about whether they’ll have enough computer power at higher loops, but I’m confident that they still have a few tricks up their sleeves.

What Space Can Tell Us about Fundamental Physics

Back when LIGO announced its detection of gravitational waves, there was one question people kept asking me: “what does this say about quantum gravity?”

The answer, each time, was “nothing”. LIGO’s success told us nothing about quantum gravity, and very likely LIGO will never tell us anything about quantum gravity.

The sheer volume of questions made me think, though. Astronomy, astrophysics, and cosmology fascinate people. They capture the public’s imagination in a way that makes them expect breakthroughs about fundamental questions. Especially now, with the LHC so far seeing nothing new since the Higgs, people are turning to space for answers.

Is that a fair expectation? Well, yes and no.

Most astrophysicists aren’t concerned with finding new fundamental laws of nature. They’re interested in big systems like stars and galaxies, where we know most of the basic rules but can’t possibly calculate all their consequences. Like most physicists, they’re doing the vital work of “physics of decimals”.

At the same time, there’s a decent chunk of astrophysics and cosmology that does matter for fundamental physics. Just not all of it. Here are some of the key areas where space has something important to say about the fundamental rules that govern our world:

 

1. Dark Matter:

Galaxies rotate at different speeds than their stars would alone. Clusters of galaxies bend light that passes by, and do so more than their visible mass would suggest. And when scientists try to model the evolution of the universe, from early images to its current form, the models require an additional piece: extra matter that cannot interact with light. All of this suggests that there is some extra “dark” matter in the universe, not described by our standard model of particle physics.

If we want to understand this dark matter, we need to know more about its properties, and much of that can be learned from astronomy. If it turns out dark matter isn’t really matter after all, if it can be explained by a modification of gravity or better calculations of gravity’s effects, then it still will have important implications for fundamental physics, and astronomical evidence will still be key to finding those implications.

2. Dark Energy (/Cosmological Constant/Inflation/…):

The universe is expanding, and its expansion appears to be accelerating. It also seems more smooth and uniform than expected, suggesting that it had a period of much greater acceleration early on. Both of these suggest some extra quantity: a changing acceleration, a “dark energy”, the sort of thing that can often be explained by a new scalar field like the Higgs.

Again, the specifics: how (and perhaps if) the universe is expanding now, what kinds of early expansion (if any) the shape of the universe suggests, these will almost certainly have implications for fundamental physics.

3. Limits on stable stuff:

Let’s say you have a new proposal for particle physics. You’ve predicted a new particle, but it can’t interact with anything else, or interacts so weakly we’d never detect it. If your new particle is stable, then you can still say something about it, because its mass would have an effect on the early universe. Too many such particles and they would throw off cosmologists’ models, ruling them out.

Alternatively, you might predict something that could be detected, but hasn’t, like a magnetic monopole. Then cosmologists can tell you how many such particles would have been produced in the early universe, and thus how likely we would be to detect them today. If you predict too many particles and we don’t see them, then that becomes evidence against your proposal.

4. “Cosmological Collider Physics”:

A few years back, Nima Arkani-Hamed and Juan Maldacena suggested that the early universe could be viewed as an extremely high energy particle collider. While this collider performed only one experiment, the results from that experiment are spread across the sky, and observed patterns in the early universe should tell us something about the particles produced by the cosmic collider.

People are still teasing out the implications of this idea, but it looks promising, and could mean we have a lot more to learn from examining the structure of the universe.

5. Big Weird Space Stuff:

If you suspect we live in a multiverse, you might want to look for signs of other universes brushing up against our own. If your model of the early universe predicts vast cosmic strings, maybe a gravitational wave detector like LIGO will be able to see them.

6. Unexpected weirdness:

In all likelihood, nothing visibly “quantum” happens at the event horizons of astrophysical black holes. If you think there’s something to see though, the Event Horizon Telescope might be able to see it. There’s a grab bag of other predictions like this: situations where we probably won’t see anything, but where at least one person thinks there’s a question worth asking.

 

I’ve probably left something out here, but this should give you a general idea. There is a lot that fundamental physics can learn from astronomy, from the overall structure and origins of the universe to unexplained phenomena like dark matter. But not everything in astronomy has these sorts of implications: for the most part, astronomy is interesting not because it tells us something about the fundamental laws of nature, but because it tells us how the vast space above us actually happens to work.

Four Gravitons in China

I’m in China this week, at the School and Workshop on Amplitudes in Beijing 2016.

img_20161018_085714

It’s a little chilly this time of year, so the dragons have accessorized

A few years back, I mentioned that there didn’t seem to be many amplitudeologists in Asia. That’s changed quite a lot over just the last few years. Song He and Yu-tin Huang went from postdocs in the west to faculty positions in China and Taiwan, respectively, while Bo Feng’s group in China has expanded. As a consequence, there’s now a substantial community here. This is the third “Amplitudes in Asia” conference, with past years meeting in Hong Kong and Taipei.

The “school” part of the conference was last week. I wasn’t here, but the students here seem to have enjoyed it a lot. This week is the “workshop” part, and there have been talks on a variety of parts of amplitudes. Nima showed up on Wednesday and managed to talk for his usual impressively long amount of time, finishing with a public lecture about the future of physics. The talk was ostensibly about why China should build the next big collider, but for the most part it ended up as a more general talk about exciting open questions in high energy physics. The talks were recorded, so they should be online at some point.

So You Want to Prove String Theory, Part II: How Can QCD Be a String Theory?

A couple weeks back, I had a post about Nima Arkani-Hamed’s talk at Strings 2016. Nima and his collaborators were trying to find what sorts of scattering amplitudes (formulas that calculate the chance that particles scatter off each other) are allowed in a theory of quantum gravity. Their goal was to show that, with certain assumptions, string theory gives the only consistent answer.

At the time, my old advisor Michael Douglas suggested that I might find Zohar Komargodski’s talk more interesting. Now that I’ve finally gotten around to watching it, I agree. The story is cleaner, more conclusive…and it gives me an excuse to say something else I’ve been meaning to talk about.

Zohar Komargodski has a track record of deriving interesting results that are true not just for the sorts of toy models we like to work with but for realistic theories as well. He’s collaborating with amplitudes miracle-worker Simon Caron-Huot (who I’ve collaborated with recently), Amit Sever (one of the integrability wizards who came up with the POPE program) and Alexander Zhiboedov, whose name seems to show up all over the place. Overall, the team is 100% hot young talent, which tends to be a recipe for success.

While Nima’s calculation focuses on gravity, Zohar and company are asking a broader question. They’re looking at any theory with particles of high spin and nonzero mass. Like Nima, they’re looking at scattering amplitudes, in the limit that the forces involved are weak. Unlike Nima, they’re focusing on a particular limit: rather than trying to fix the full form of the amplitude, they’re interested in how it behaves for extreme, unphysical values for the particles’ momenta. Despite being unphysical, this limit can reveal something about how the theory works.

What they figured out is that, for the sorts of theories they’re looking at, the amplitude has to take a particular form in their unphysical limit. In particular, it takes a form that indicates the presence of strings.

What sort of theories are they looking at? What theories have “particles of high spin and nonzero mass”? Well, some are string theories. Others are Yang-Mills theories … theories similar to QCD.

For the experts, I encourage you to watch Zohar’s talk or read the paper for more detail. It’s a fun story that showcases how very general constraints on scattering amplitudes can translate into quite specific statements.

For the non-experts, though, there’s something that may already be confusing. When I’ve talked about Yang-Mills theories before, I’ve talked about them in terms of particles of spin 1. Where did these “higher spin” particles come from? And where are the strings? How can there be strings in a theory that I’ve described as “similar to QCD”?

If I just stuck to the higher spin particles, things could almost stay familiar. The fundamental particles of Yang-Mills theories have spin 1, but these particles can combine into composite particles, which can have higher spin and higher mass. That should be intuitive: in some sense, it’s just like protons, neutrons, and electrons combining to form atoms.

What about the strings? I’ve actually talked about that before, but I’d like to try out a new analogy. Have you ever heard of Conway’s Game of Life?

pic288405_md

Not this one!

gospers_glider_gun

This one!

Conway’s Game of Life starts with a grid of black and white squares, and evolves in steps, with each square’s color determined by the color of adjacent squares in the last step. “Fundamentally”, the game is just those rules. In practice, though, structure can emerge: a zoo of self-propagating creatures that dance across the screen.

The strings that can show up in Yang-Mills theories are like this. They aren’t introduced directly in the definition of the theory. Instead, they’re consequences: structures that form when you let the rules evolve and see what they create. They’re another description of the theory, one with its own advantages.

When I tell people I’m a theoretical physicist, they inevitably ask me “Have any of your theories been tested?” They’re operating from one idea of what a theoretical physicist does: propose new theories to describe the world, based on available evidence. Lots of theorists do that, they’re called phenomenologists, but it’s not what I do, or what most theorists I interact with day-to-day do.

So I describe what I do, how I test new mathematical techniques to make particle physics calculations faster. And in general, that’s pretty easy for people to understand. Just as they can imagine people out there testing theories, they can imagine people who work to support the others, making tools to make their work easier. But while that’s what I do, it’s not the best description of what most of my colleagues do.

What most theorists I know do is like finding new animals in Conway’s game of life. They start with theories for which we know the rules: well-tested theories like QCD, or well-studied proposals like string theory. They ask themselves, not how they can change the rules, but what results the rules have. They look for structures, and in doing so find new perspectives, learning to see the animals that live on Conway’s black and white grid. (This is something I’ve gestured at before, but this seems like a cleaner framing.)

Doing that, theorists have seen strings in the structure of QCD-like theories. And now Zohar and collaborators have a clean argument that the structures others have seen should show up, not only there, but in a broader class of theories.

This isn’t about whether the world is fundamentally described by string theory, ten dimensions and all. That’s an entirely different topic. What it is is a question about what sorts of structures emerge when we try to describe the world. What it does is show that strings are, in some sense (and, as for Nima, [with some conditions]) inevitable, that they come out of our rules even if we don’t expect them to.

So You Want to Prove String Theory (Or: Nima Did Something Cool Again)

Nima Arkani-Hamed, of Amplituhedron fame, has been making noises recently about proving string theory.

Now, I can already hear the smartarses in the comments correcting me here. You can’t prove a scientific theory, you can only provide evidence for it.

Well, in this case I don’t mean “provide evidence”. (Direct evidence for string theory is quite unlikely at the moment given the high energies at which it becomes relevant and large number of consistent solutions, but an indirect approach might yet work.) I actually mean “prove”.

See, there are two ways to think about the problem of quantum gravity. One is as an experimental problem: at high enough energies for quantum gravity to be relevant, what actually happens? Since it’s going to be a very long time before we can probe those energies, though, in practice we instead have a technical problem: can we write down a theory that looks like gravity in familiar situations, while avoiding the pesky infinities that come with naive attempts at quantum gravity?

If you can prove that string theory is the only theory that does that, then you’ve proven string theory. If you can prove that string theory is the only theory that does that [with certain conditions] then you’ve proven string theory [with certain conditions].

That, in broad terms, is what Nima has been edging towards. At this year’s Strings conference, he unveiled some progress towards that goal. And since I just recently got around to watching his talk, you get to hear my take on it.

 Nima has been working with Yu-tin Huang, an amplitudeologist who tends to show up everywhere, and one of his students. Working in parallel, an all-star cast has been doing a similar calculation for Yang-Mills theory. The Yang-Mills story is cool, and probably worth a post in its own right, but I think you guys are more interested in the quantum gravity one.

What is Nima doing here?

Nima is looking at scattering amplitudes, probabilities for particles to scatter off of each other. In this case, the particles are gravitons, the particle form of gravitational waves.

Normally, the problems with quantum gravity show up when your scattering amplitudes have loops. Here, Nima is looking at amplitudes without loops, the most important contributions when the force in question is weak (the “weakly coupled” in Nima’s title).

Even for these amplitudes you can gain insight into quantum gravity by seeing what happens at high energies (the “UV” in the title). String amplitudes have nice behavior at high energies, naive gravity amplitudes do not. The question then becomes, are there other amplitudes that preserve this nice behavior, while still obeying the rules of physics? Or is string theory truly unique, the only theory that can do this?

The team that asked a similar question about Yang-Mills theory found that string theory was unique, that every theory that obeyed their conditions was in some sense “stringy”. That makes it even more surprising that, for quantum gravity, the answer was no: the string theory amplitude is not unique. In fact, Nima and his collaborators found an infinite set of amplitudes that met their conditions, related by a parameter they could vary freely.

What are these other amplitudes, then?

Nima thinks they can’t be part of a consistent theory, and he’s probably right. They have a number of tests they haven’t done: in particular, they’ve only been looking at amplitudes involving two gravitons scattering off each other, but a real theory should have consistent answers for any number of gravitons interacting, and it’s doesn’t look like these “alternate” amplitudes can be generalized to work for that.

That said, at this point it’s still possible that these other amplitudes are part of some sort of sensible theory. And that would be incredibly interesting, because we’ve never seen anything like that before.

There are approaches to quantum gravity besides string theory, sure. But common to all of them is an inability to actually calculate scattering amplitudes. If there really were a theory that generated these “alternate” amplitudes, it wouldn’t correspond to any existing quantum gravity proposal.

(Incidentally, this is also why this sort of “proof” of string theory might not convince everyone. Non-string quantum gravity approaches tend to talk about things fairly far removed from scattering amplitudes, so some would see this kind of thing as apples and oranges.)

I’d be fascinated to see where this goes. Either we have a new set of gravity scattering amplitudes to work with, or string theory turns out to be unique in a more rigorous and specific way than we’ve previously known. No matter what, something interesting is going to happen.

After the talk David Gross drew on his experience of the origin of string theory to question whether this work is just retreading the path to an old dead end. String theory arose from an attempt to find a scattering amplitude with nice properties, but it was only by understanding this amplitude physically in terms of vibrating strings that it was able to make real progress.

I generally agree with Nima’s answer, but to re-frame it in my own words: in the amplitudes sub-field, there’s something of a cycle. We try to impose general rules, until by using those rules we have a new calculation technique. We then do a bunch of calculations with the new technique. Finally, we look at the results of those calculations, try to find new general rules, and start the cycle again.

String theory is the result of people applying general rules to scattering amplitudes and learning enough to discover not just a new calculation technique, but a new physical theory. Now, we’ve done quite a lot of string theory calculations, and quite a lot more quantum field theory calculations as well. We have a lot of “data”.

And when you have a lot of data, it becomes much more productive to look for patterns. Now, if we start trying to apply general rules, we have a much better idea of what we’re looking for. This lets us get a lot further than people did the first time through the cycle. It’s what let Nima find the Amplituhedron, and it’s something Yu-tin has a pretty good track record of as well.

So in general, I’m optimistic. As a community, we’re poised to find out some very interesting things about what gravity scattering amplitudes can look like. Maybe, we’ll even prove string theory. [With certain conditions, of course. 😉 ]

Where do you get all those mathematical toys?

I’m at a conference at Caltech this week, so it’s going to be a shorter post than usual.

The conference is on something call the Positive Grassmannian, a precursor to Nima Arkani-Hamed’s much-hyped Amplituhedron. Both are variants of a central idea: take complicated calculations in physics and express them in terms of clean, well-defined mathematical objects.

Because of this, this conference is attended not just by physicists, but by mathematicians as well, and it’s been interesting watching how the two groups interact.

From a physics perspective, mathematicians are great because they give us so many useful tools! Many significant advances in my field happened because a physicist talked to a mathematician and learned that a problem that had stymied the physics world had already been solved in the math community.

This tends to lead to certain expectations among physicists. If a mathematician gives a talk at a physics conference, we expect them to present something we can use. Our ideal math talk is like when Q presents the gadgets at the beginning of a Bond movie: a ton of new toys with just enough explanation for us to use them to save the day in the second act.

Pictured: Mathematicians, through Physicist eyes

You may see the beginning of a problem here, once you realize that physicists are the James Bond in this analogy.

Physicists like to see themselves as the protagonists of their own stories. That’s true of every field, though, to some degree or another. And it’s certainly true of mathematicians.

Mathematicians don’t go to physics conferences just to be someone’s supporting cast. They do it because physics problems are interesting to them: by hearing what physicists are working on they hope to get inspiration for new mathematical structures, concepts jury-rigged together by physicists that represent corners that mathematics hasn’t yet explored. Their goal is to take home an idea that they can turn into something productive, gaining glory among their fellow mathematicians. And if that sounds familiar…

Pictured: Physicists, through Mathematician eyes

While it’s amusing to watch the different expectations go head-to-head, the best collaborations between physicists and mathematicians are those where both sides respect that the other is the protagonist of their own story. Allow for give-and-take, paying attention not just to what you find interesting but to what the other person does, without assuming a tired old movie script, and it’s possible to make great progress.

Of course, that’s true of life in general as well.