We’ve had talks from a variety of corners of amplitudes, with major themes including the web of theories that can sort of be described by string theory-esque models, the amplituhedron, and theories you can “square” to get other theories. I’m excited about Zvi Bern’s talk at the end of the conference, which will describe the progress I talked about last week. There’s also been recent progress on understanding the amplituhedron, which I will likely post about in the near future.
Do the same thing you would with any other theory, and you get infinity. You get repeated infinities, an infinity of infinities. And while you could fix one or two infinities, fixing an infinite number requires giving up an infinity of possible predictions, so in the end your theory predicts nothing.
String theory fixes this with its own infinity, the infinite number of ways a string can vibrate. Because this infinity is organized and structured and well-understood, you’re left with a theory that is still at least capable of making predictions.
(Note that this is an independent question from whether string theory can make predictions for experiments in the real world. This is a much more “in-principle” statement: if we knew everything we might want to about physics, all the fields and particles and shapes of the extra dimensions, we could use string theory to make predictions. Even if we knew all of that, we still couldn’t make predictions from naive quantum gravity.)
Are there ways to fix the problem that don’t involve an infinity of vibrations? Or at least, to fix part of the problem?
That’s what Zvi Bern, John Joseph Carrasco, Henrik Johansson, and a growing cast of collaborators have been trying to find out.
They’re investigating N=8 supergravity, a theory that takes gravity and adds on a host of related particles. It’s one of the easiest theories to get from string theory, by curling up extra dimensions in a particularly simple way and ignoring higher-energy vibrations.
Bern, along with Lance Dixon and David Kosower, invented the generalized unitarity technique I talked about last week. Along with Carrasco and Johansson, he figured out another important trick: the idea that you can do calculations in gravity by squaring the appropriate part of calculations in Yang-Mills theory. For N=8 supergravity, the theory you need to square is my favorite theory, N=4 super Yang-Mills.
Using this, they started pushing forward, calculating approximations to greater and greater precision (more and more loops).
What they found, at each step, was that N=8 supergravity behaved better than expected. In fact, it behaved like N=4 super Yang-Mills.
N=4 super Yang-Mills is special, because in four dimensions (three space and one time, the dimensions we’re used to in daily life) there are no infinities to fix. In a world with more dimensions, though, you start getting infinities, and with more and more loops you need fewer and fewer dimensions to see them.
N=8 supergravity, unexpectedly, was giving infinities in the same dimensions that N=4 super Yang-Mills did (and no earlier). If it kept doing that, you might guess that it also had no infinities in four dimensions. You might wonder if, at least loop by loop, N=8 supergravity could be a way to fix quantum gravity without string theory.
Of course, you’d only really know if you could check in four dimensions.
If you want to check in four dimensions, though, you run into a problem. The fewer dimensions you’re looking at, the more loops you need before N=8 supergravity could possibly give infinity. In four dimensions, you need a forbidding seven loops of precision.
Still, Bern, Carrasco, and Johansson were up to the challenge. Along with Lance Dixon, David Kosower, and Radu Roiban, they looked at three loops, calculating an interaction of four gravitons, and the pattern continued. Four loops, and it was still going strong.
At around this time, I had just started grad school. My first project was a cumbersome numerical calculation. To keep me motivated, my advisor mentioned that the work I was doing would be good preparation for a much grander project: the calculation of whether the four-graviton interaction in N=8 supergravity diverges at seven loops. All I’d have to do was wait for Bern and collaborators to get there.
I named this blog “4 gravitons and a grad student”, and hoped I would get a chance to contribute.
And then something unexpected happened. They got stuck at five loops.
The method they were using, generalized unitarity, is an ansatz-based method. You start with a guess, then refine it. As such, the method is ultimately only as good as your guess.
Their guesses, in general, were pretty good. The trick they were using, squaring N=4 to get N=8, requires a certain type of guess: one in which the pieces they square have similar relationships to the different types of charge in Yang-Mills theory. There’s still an infinite number of guesses that can obey this, so they applied more restrictions, expectations based on other calculations, to get something more manageable. This worked at three loops, and worked (with a little extra thought) at four loops.
But at five loops they were stuck. They couldn’t find anything, with their restrictions, that gave the correct answer when “cut up” by generalized unitarity. And while they could drop some restrictions, if they dropped too many they’d end up with far too general a guess, something that could take months of computer time to solve.
So they stopped.
They did quite a bit of interesting work in the meantime. They found more theories they could square to get gravity theories, of more and more unusual types. They calculated infinities in other theories, and found surprises there too, other cases where infinities didn’t show up when they were “supposed” to. But for some time, the N=8 supergravity calculation was stalled.
And in the meantime, I went off in another direction, which long-time readers of this blog already know about.
Recently, though, they’ve broken the stall.
What they realized is that the condition on their guess, that the parts they square be related like Yang-Mills charges, wasn’t entirely necessary. Instead, they could start with a “bad” guess, and modify it, using the failure of those relations to fill in the missing pieces.
It looks like this is going to work.
We’re all at an amplitudes program right now in Santa Barbara. Walking through the halls of the KITP, I overhear conversations about five loops. They’re paring things down, honing their code, getting rid of the last few bugs, and checking their results.
They’re almost there, and it’s exciting. It looks like finally things are moving again, like the train to seven loops has once again left the station.
Increasingly, they’re beginning to understand the absent infinities, to see that they really are due to something unexpected and new.
N=8 supergravity isn’t going to be the next theory of everything. (For one, you can’t get chiral fermions out of it.) But if it really has no infinities at any loop, that tells us something about what a theory of quantum gravity is allowed to be, about the minimum necessary to at least make sense on a loop-by-loop level.
And that, I think, is worth being excited about.
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.
Lubos Motl has responded to my post from last week about the recent Caltech short, Quantum is Calling. His response is pretty much exactly what you’d expect, including the cameos by Salma Hayek and Kaley Cuoco.
The only surprise was his lack of concern for accuracy. Quantum is Calling got the conjecture it was trying to popularize almost precisely backwards. I was expecting that to bother him, at least a little.
Should it bother you?
That depends on what you think Quantum is Calling is trying to do.
Science popularization, even good science popularization, tends to get things wrong. Some of that is inevitable, a result of translating complex concepts to a wider audience.
Sometimes, though, you can’t really chalk it up to translation. Interstellar had some extremely accurate visualizations of black holes, but it also had an extremely silly love-powered tesseract. That wasn’t their attempt to convey some subtle scientific truth, it was just meant to sound cool.
And the thing is, that’s not a bad thing to do. For a certain kind of piece, sounding cool really is the point.
Imagine being an explorer. You travel out into the wilderness and find a beautiful waterfall.
How do you tell people about it?
One option is the press. The news can cover your travels, so people can stay up to date with the latest in waterfall discoveries. In general, you’d prefer this sort of thing to be fairly accurate: the goal here is to inform people, to give them a better idea of the world around them.
Alternatively, you can advertise. You put signposts up around town pointing toward the waterfall, complete with vivid pictures. Here, accuracy matters a lot less: you’re trying to get people excited, knowing that as they get closer they can get more detailed information.
In science popularization, the “news” here isn’t just news. It’s also blog posts, press releases, and public lectures. It’s the part of science popularization that’s supposed to keep people informed, and it’s one that we hope is mostly accurate, at least as far as possible.
The “signposts”, meanwhile, are things like Interstellar. Their audience is as wide as it can possibly be, and we don’t expect them to get things right. They’re meant to excite people, to get them interested in science. The expectation is that a few students will find the imagery interesting enough to go further, at which point they can learn the full story and clear up any remaining misconceptions.
Quantum is Calling is pretty clearly meant to be a signpost. The inaccuracy is one way to tell, but it should be clear just from the context. We’re talking about a piece with Hollywood stars here. The relative star-dom of Zoe Saldana and Keanu Reeves doesn’t matter, the presence of any mainstream film stars whatsoever means they’re going for the broadest possible audience.
(Of course, the fact that it’s set up to look like an official tie-in to the Star Trek films doesn’t hurt matters either.)
They’re also quite explicit about their goals. The piece’s predecessor has Keanu Reeves send a message back in time, with the goal of inspiring a generation of young scientists to build a future paradise. They’re not subtle about this.
Ok, so what’s the problem? Signposts are allowed to be inaccurate, so the inaccuracy shouldn’t matter. Eventually people will climb up to the waterfall and see it for themselves, right?
What if the waterfall isn’t there?
The evidence for ER=EPR (the conjecture that Quantum is Calling is popularizing) isn’t like seeing a waterfall. It’s more like finding it via surveying. By looking at the slope of nearby terrain and following the rivers, you can get fairly confident that there should be a waterfall there, even if you can’t yet see it over the next ridge. You can then start sending scouts, laying in supplies, and getting ready for a push to the waterfall. You can alert the news, telling journalists of the magnificent waterfall you expect to find, so the public can appreciate the majesty of your achievement.
What you probably shouldn’t do is put up a sign for tourists.
As I hope I made clear in my last post, ER=EPR has some decent evidence. It hasn’t shown that it can handle “foot traffic”, though. The number of researchers working on it is still small. (For a fun but not especially rigorous exercise, try typing “ER=EPR” and “AdS/CFT” into physics database INSPIRE.) Conjectures at this stage are frequently successful, but they often fail, and ER=EPR still has a decent chance of doing so. Tying your inspiring signpost to something that may well not be there risks sending tourists up to an empty waterfall. They won’t come down happy.
As such, I’m fine with “news-style” popularizations of ER=EPR. And I’m fine with “signposts” for conjectures that have shown they can handle some foot traffic. (A piece that sends Zoe Saldana to the holodeck to learn about holography could be fun, for example.) But making this sort of high-profile signpost for ER=EPR feels irresponsible and premature. There will be plenty of time for a Star Trek tie-in to ER=EPR once it’s clear the idea is here to stay.
A few weeks back, Caltech’s Institute of Quantum Information and Matter released a short film titled Quantum is Calling. It’s the second in what looks like will become a series of pieces featuring Hollywood actors popularizing ideas in physics. The first used the game of Quantum Chess to talk about superposition and entanglement. This one, featuring Zoe Saldana, is about a conjecture by Juan Maldacena and Leonard Susskind called ER=EPR. The conjecture speculates that pairs of entangled particles (as investigated by Einstein, Podolsky, and Rosen) are in some sense secretly connected by wormholes (or Einstein-Rosen bridges).
The film is fun, but I’m not sure ER=EPR is established well enough to deserve this kind of treatment.
At this point, some of you are nodding your heads for the wrong reason. You’re thinking I’m saying this because ER=EPR is a conjecture.
I’m not saying that.
The fact of the matter is, conjectures play a very important role in theoretical physics, and “conjecture” covers a wide range. Some conjectures are supported by incredibly strong evidence, just short of mathematical proof. Others are wild speculations, “wouldn’t it be convenient if…” ER=EPR is, well…somewhere in the middle.
Most popularizers don’t spend much effort distinguishing things in this middle ground. I’d like to talk a bit about the different sorts of evidence conjectures can have, using ER=EPR as an example.
The first level of evidence is motivation.
At its weakest, motivation is the “wouldn’t it be convenient if…” line of reasoning. Some conjectures never get past this point. Hawking’s chronology protection conjecture, for instance, points out that physics (and to some extent logic) has a hard time dealing with time travel, and wouldn’t it be convenient if time travel was impossible?
For ER=EPR, this kind of motivation comes from the black hole firewall paradox. Without going into it in detail, arguments suggested that the event horizons of older black holes would resemble walls of fire, incinerating anything that fell in, in contrast with Einstein’s picture in which passing the horizon has no obvious effect at the time. ER=EPR provides one way to avoid this argument, making event horizons subtle and smooth once more.
Motivation isn’t just “wouldn’t it be convenient if…” though. It can also include stronger arguments: suggestive comparisons that, while they could be coincidental, when put together draw a stronger picture.
In ER=EPR, this comes from certain similarities between the type of wormhole Maldacena and Susskind were considering, and pairs of entangled particles. Both connect two different places, but both do so in an unusually limited way. The wormholes of ER=EPR are non-traversable: you cannot travel through them. Entangled particles can’t be traveled through (as you would expect), but more generally can’t be communicated through: there are theorems to prove it. This is the kind of suggestive similarity that can begin to motivate a conjecture.
(Amusingly, the plot of the film breaks this in both directions. Keanu Reeves can neither steal your cat through a wormhole, nor send you coded messages with entangled particles.)
Motivation is a good reason to investigate something, but a bad reason to believe it. Luckily, conjectures can have stronger forms of evidence. Many of the strongest conjectures are correspondences, supported by a wealth of non-trivial examples.
In science, the gold standard has always been experimental evidence. There’s a reason for that: when you do an experiment, you’re taking a risk. Doing an experiment gives reality a chance to prove you wrong. In a good experiment (a non-trivial one) the result isn’t obvious from the beginning, so that success or failure tells you something new about the universe.
In theoretical physics, there are things we can’t test with experiments, either because they’re far beyond our capabilities or because the claims are mathematical. Despite this, the overall philosophy of experiments is still relevant, especially when we’re studying a correspondence.
“Correspondence” is a word we use to refer to situations where two different theories are unexpectedly computing the same thing. Often, these are very different theories, living in different dimensions with different sorts of particles. With the right “dictionary”, though, you can translate between them, doing a calculation in one theory that matches a calculation in the other one.
Even when we can’t do non-trivial experiments, then, we can still have non-trivial examples. When the result of a calculation isn’t obvious from the beginning, showing that it matches on both sides of a correspondence takes the same sort of risk as doing an experiment, and gives the same sort of evidence.
Some of the best-supported conjectures in theoretical physics have this form. AdS/CFT is technically a conjecture: a correspondence between string theory in a hyperbola-shaped space and my favorite theory, N=4 super Yang-Mills. Despite being a conjecture, the wealth of nontrivial examples is so strong that it would be extremely surprising if it turned out to be false.
ER=EPR is also a correspondence, between entangled particles on the one hand and wormholes on the other. Does it have nontrivial examples?
Some, but not enough. Originally, it was based on one core example, an entangled state that could be cleanly matched to the simplest wormhole. Now, new examples have been added, covering wormholes with electric fields and higher spins. The full “dictionary” is still unclear, with some pairs of entangled particles being harder to describe in terms of wormholes. So while this kind of evidence is being built, it isn’t as solid as our best conjectures yet.
I’m fine with people popularizing this kind of conjecture. It deserves blog posts and press articles, and it’s a fine idea to have fun with. I wouldn’t be uncomfortable with the Bohemian Gravity guy doing a piece on it, for example. But for the second installment of a star-studded series like the one Caltech is doing…it’s not really there yet, and putting it there gives people the wrong idea.
I hope I’ve given you a better idea of the different types of conjectures, from the most fuzzy to those just shy of certain. I’d like to do this kind of piece more often, though in future I’ll probably stick with topics in my sub-field (where I actually know what I’m talking about 😉 ). If there’s a particular conjecture you’re curious about, ask in the comments!
There’s been some buzz around a recent Quanta article by K. C. Cole, The Strange Second Life of String Theory. I found it a bit simplistic of a take on the topic, so I thought I’d offer a different one.
String theory has been called the particle physicist’s approach to quantum gravity. Other approaches use the discovery of general relativity as a model: they’re looking for a big conceptual break from older theories. String theory, in contrast, starts out with a technical problem (naive quantum gravity calculations that give infinity) proposes physical objects that could solve the problem (strings, branes), and figures out which theories of these objects are consistent with existing data (originally the five superstring theories, now all understood as parts of M theory).
That approach worked. It didn’t work all the way, because regardless of whether there are indirect tests that can shed light on quantum gravity, particle physics-style tests are far beyond our capabilities. But in some sense, it went as far as it can: we’ve got a potential solution to the problem, and (apart from some controversy about the cosmological constant) it looks consistent with observations. Until actual evidence surfaces, that’s the end of that particular story.
When people talk about the failure of string theory, they’re usually talking about its aspirations as a “theory of everything”. String theory requires the world to have eleven dimensions, with seven curled up small enough that we can’t observe them. Different arrangements of those dimensions lead to different four-dimensional particles. For a time, it was thought that there would be only a few possible arrangements: few enough that people could find the one that describes the world and use it to predict undiscovered particles.
That particular dream didn’t work out. Instead, it became apparent that there were a truly vast number of different arrangements of dimensions, with no unique prediction likely to surface.
By the time I took my first string theory course in grad school, all of this was well established. I was entering a field shaped by these two facts: string theory’s success as a particle-physics style solution to quantum gravity, and its failure as a uniquely predictive theory of everything.
The quirky thing about science: sociologically, success and failure look pretty similar. Either way, it’s time to find a new project.
A colleague of mine recently said that we’re all either entanglers or bootstrappers. It was a joke, based on two massive grants from the Simons Foundation. But it’s also a good way to summarize two different ways string theory has moved on, from its success and from its failure.
The entanglers start from string theory’s success and say, what’s next?
As it turns out, a particle-physics style understanding of quantum gravity doesn’t tell you everything you need to know. Some of the big conceptual questions the more general relativity-esque approaches were interested in are still worth asking. Luckily, string theory provides tools to answer them.
Many of those answers come from AdS/CFT, the discovery that string theory in a particular warped space-time is dual (secretly the same theory) to a more particle-physics style theory on the edge of that space-time. With that discovery, people could start understanding properties of gravity in terms of properties of particle-physics style theories. They could use concepts like information, complexity, and quantum entanglement (hence “entanglers”) to ask deeper questions about the structure of space-time and the nature of black holes.
The bootstrappers, meanwhile, start from string theory’s failure and ask, what can we do with it?
Twisting up the dimensions of string theory yields a vast number of different arrangements of particles. Rather than viewing this as a problem, why not draw on it as a resource?
“Bootstrappers” explore this space of particle-physics style theories, using ones with interesting properties to find powerful calculation tricks. The name comes from the conformal bootstrap, a technique that finds conformal theories (roughly: theories that are the same at every scale) by “pulling itself by its own boostraps”, using nothing but a kind of self-consistency.
Many accounts, including Cole’s, attribute people like the boostrappers to AdS/CFT as well, crediting it with inspiring string theorists to take a closer look at particle physics-style theories. That may be true in some cases, but I don’t think it’s the whole story: my subfield is bootstrappy, and while it has drawn on AdS/CFT that wasn’t what got it started. Overall, I think it’s more the case that the tools of string theory’s “particle physics-esque approach”, like conformal theories and supersymmetry, ended up (perhaps unsurprisingly) useful for understanding particle physics-style theories.
Not everyone is a “boostrapper” or an “entangler”, even in the broad sense I’m using the words. The two groups also sometimes overlap. Nevertheless, it’s a good way to think about what string theorists are doing these days. Both of these groups start out learning string theory: it’s the only way to learn about AdS/CFT, and it introduces the bootstrappers to a bunch of powerful particle physics tools all in one course. Where they go from there varies, and can be more or less “stringy”. But it’s research that wouldn’t have existed without string theory to get it started.
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?
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. 😉 ]