Tag Archives: quantum field theory

Generalized Unitarity: The Frankenstein Method for Amplitudes

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This is going to be a bit more technical than my usual, but you were warned.

There are a few things you’ll need to know to understand this post.

First, you should know that when we calculate probabilities of things happening in particle physics, we can do it by drawing Feynman diagrams, pictures of particles traveling and interacting. These diagrams can have loops, and the particle in the loop can have any momentum, from zero on up to infinity: you have to add up all the possibilities to get whatever you’re trying to calculate.

Second, you should understand that the “particles” in these loops aren’t really particles. They’re “virtual particles”, better understood as disturbances in quantum fields. Matt Strassler has a very nice article about this. In particular, these “particles” don’t have to obey E=mc^2 (or rather, if we include kinetic energy, E^2=p^2 c^2+m^2 c^4, where p is the momentum).

You can imagine a space that the momentum and energy “live in”. It’s got three dimensions for the three directions momentum can have, and one more dimension for the energy. Virtual particles can live anywhere in this four-dimensional space, but real particles have to live on a “shell” of points that obey E^2=p^2 c^2+m^2 c^4. If you’ve heard physicists say “on-shell” or “off-shell”, they’re referring to whether a particle is virtual, a quantum mechanical disturbance (and thus lives anywhere in the space) or a real classical particle (living on this “shell”).

Third, you should appreciate that in quantum physics, in Scott Aaronson’s words, we put complex numbers in our ontologies. Often, quantum weirdness shows itself when we look at our calculations as functions of complex numbers.

Let’s say I’m calculating an amplitude with one loop, and I draw a diagram like this:

NiceBox.png

Unitarity is how particle physicists say “all probabilities have to add up to one”. Since we have complex numbers in our ontologies, this statement is more complicated than it looks. One thing it ends up implying is that if I calculate an amplitude from the one-loop diagram above, its imaginary part will be given by multiplying together two simpler amplitudes:

CutBox.png

Here you can imagine that I took a pair of scissors and “cut” the diagram in two along the dashed line. Now that the diagram has been “cut”, the particles I cut through are no longer part of a loop, so they’re no longer virtual: they’re real, on-shell particles.

If I wanted, I could keep “cutting” the diagram, generalizing this implication of unitarity. (For those who know some complex analysis, this involves taking residues.) I could cut all of the lines in the loop, like this:

MaxCutBox

Now something interesting happens. Here I’ve forced all four of the particles in the loop to be “on-shell”, to obey E^2=p^2 c^2+m^2 c^4. Previously, the momentum and energy in the loop was entirely free, living in its four-dimensional space. Now, though, it must obey four equations. And for those who’ve seen some algebra, four independent equations and four unknowns gives us one solution. By cutting all of these particles, we’ve killed all of the freedom that the loop momentum had. Instead of the living, quantum amplitude we had, we’ve cut it up into a bunch of dead, classical parts.

Why do this?

Well, suppose we have a guess for what the full amplitude should be. We’ve still got some uncertainty in our guess: it’s an ansatz.

If we wanted to check our guess, to fix the uncertainty in our ansatz, we could compare it to the full amplitude. But then we’d have to calculate the full quantum amplitude, and that’s hard.

It’s a lot easier, though, to calculate those “dead” classical amplitudes.

That’s the method we call “generalized unitarity”. We stitch together these easier-to-calculate, “dead” amplitudes. Enough different stitching patterns, and we can fix all the uncertainty in our ansatz, ending up with a unique correct answer without ever doing the full quantum calculation. Like Frankenstein, from dead parts we’ve assembled a living thing.

frankenstein27s_monster_28boris_karloff29

It’s off-shell!

How well does this work?

That depends on how good the ansatz is. The ansatze for one loop are very well understood, and for two loops the community is getting there. For higher loops, you have to be either smart or lucky. I happen to know some people who are both, I’ll be talking about them next week.

Poll Results, and What’s Next

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I’ll leave last week’s poll up a while longer as more votes trickle in, but the overall pattern (beyond “Zipf–like“) is pretty clear.

From pretty early on, most requests were for more explanations of QFT, gravity, and string theory concepts, with amplitudes content a clear second. This is something I can definitely do more of: I haven’t had much inspiration for interesting pieces of this sort recently, but it’s something I can ramp up in future.

I suspect that many of the people voting for more QFT and more amplitudes content were also interested in something else, though: more physics news. Xezlec mentioned that with Résonaances and Of Particular Significance quiet, there’s an open niche for vaguely reasonable people blogging about physics.

The truth is, I didn’t think of adding a “more physics news” option to the poll. I’m not a great source of news: not being a phenomenologist, I don’t keep up with the latest experimental results, and since my sub-field is small and insular I’m not always aware of the latest thing Witten or Maldacena is working on.

For an example of the former: recently, various LHC teams presented results at the Moriond and Aspen conferences, with no new evidence of supersymmetry in the data they’ve gathered thus far. This triggered concessions on several bets about SUSY (including an amusingly awkward conversation about how to pay one of them).

And I only know about that because other bloggers talked about it.

So I’m not going to be a reliable source of physics news.

With that said, knowing there’s a sizable number of people interested in this kind of thing is helpful. I’ve definitely had times when I saw something I found interesting, but wasn’t sure if my audience would care. (For example, recently there’s been some substantial progress on the problem that gave this blog its name.) Now that I know some of you are interested, I’ll err on the side of posting about these kinds of things.

“What’s it like to be a physicist” and science popularization were both consistently third and fourth in the poll, switching back and forth as more votes came in. This tells me that while many of you want more technical content, there are still people interested in pieces aimed to a broader audience, so I won’t abandon those.

The other topics were fairly close together, with the more “news-y” ones (astrophysics/cosmology and criticism of bad science coverage) beating the less “news-y” ones. This also supports my guess that people were looking for a “more physics news” option. A few people even voted for “more arguments”, which was really more of a joke topic: getting into arguments with other bloggers tends to bring in readers, but it’s not something I ever plan to do intentionally.

So, what’s next? I’ll explain more quantum field theory, talk more about interesting progress in amplitudes, and mention news when I come across it, trusting you guys to find it interesting. I’ll keep up with the low-level stuff, and with trying to humanize physics, to get the public to understand what being a physicist is all about. And I’ll think about some of the specific suggestions you gave: I’m always looking for good post ideas.

The Way to a Mathematician’s Heart Is through a Pi

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Want to win over a mathematician? Bake them a pi.

Of course, presentation counts. You can’t just pour a spew of digits.

1200px-pi_tau_digit_runs-svg

If you have to, at least season it with 9’s

Ideally, you’ve baked your pi at home, in a comfortable physical theory. You lay out a graph to give it structure, then wrap it in algebraic curves before baking under an integration.

(Sometimes you can skip this part. My mathematician will happily eat graphs and ignore the pi.)

At this point, if your motives are pure (or at least mixed Tate), you have your pi. To make it more interesting, be sure to pair with a well-aged Riemann zeta value. With the right preparation, you can achieve a truly cosmic pi.

whirled-pies-54

Fine, that last joke was a bit of a stretch. Hope you had a fun pi day!

Popularization as News, Popularization as Signpost

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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.

south_falls_silver_falls_state_park

Example:

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?

wonder_mountain_dry_backside_waterfall

Like so:

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.

Hexagon Functions Meet the Amplituhedron: Thinking Positive

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I finished a new paper recently, it’s up on arXiv now.

This time, we’re collaborating with Jaroslav Trnka, of Amplituhedron fame, to investigate connections between the Amplituhedron and our hexagon function approach.

The Amplituhedron is a way to think about scattering amplitudes in our favorite toy model theory, N=4 super Yang-Mills. Specifically, it describes amplitudes as the “volume” of some geometric space.

Here’s something you might expect: if something is a volume, it should be positive, right? You can’t have a negative amount of space. So you’d naturally guess that these scattering amplitudes, if they’re really the “volume” of something, should be positive.

“Volume” is in quotation marks there for a reason, though, because the real story is a bit more complicated. The Amplituhedron isn’t literally the volume of some space, there are a bunch of other mathematical steps between the geometric story of the Amplituhedron on the one end and the final amplitude on the other. If it was literally a volume, calculating it would be quite a bit easier: mathematicians have gotten very talented at calculating volumes. But if it was literally a volume, it would have to be positive.

What our paper demonstrates is that, in the right regions (selected by the structure of the Amplituhedron), the amplitudes we’ve calculated so far are in fact positive. That first, basic requirement for the amplitude to actually literally be a volume is satisfied.

Of course, this doesn’t prove anything. There’s still a lot of work to do to actually find the thing the amplitude is the volume of, and this isn’t even proof that such a thing exists. It’s another, small piece of evidence. But it’s a reassuring one, and it’s nice to begin to link our approach with the Amplituhedron folks.

This week was the 75th birthday of John Schwarz, one of the founders of string theory and a discoverer of N=4 super Yang-Mills. We’ve dedicated the paper to him. His influence on the field, like the amplitudes of N=4 themselves, has been consistently positive.

The Parable of the Entanglers and the Bootstrappers

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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.

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

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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?

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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.

Hexagon Functions IV: Steinmann Harder

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It’s paper season! I’ve got another paper out this week, this one a continuation of the hexagon function story.

The story so far:

My collaborators and I have been calculating “six-particle” (two particles collide, four come out, or three collide, three come out…) scattering amplitudes (probabilities that particles scatter) in N=4 super Yang-Mills. We calculate them starting with an ansatz (a guess, basically) made up of a type of functions called hexagon functions: “hexagon” because they’re the right functions for six-particle scattering. We then narrow down our guess by bringing in other information: for example, if two particles are close to lining up, our answer needs to match the one calculated with something called the POPE, so we can throw out guesses that don’t match that. In the end, only one guess survives, and we can check that it’s the right answer.

So what’s new this time?

More loops:

In quantum field theory, most of our calculations are approximate, and we measure the precision in something called loops. The more loops, the closer we are to the exact result, and the more complicated the calculation becomes.

This time, we’re at five loops of precision. To give you an idea of how complicated that is: I store these functions in text files. We’ve got a new, more efficient notation for them. With that, the two-loop functions fit into files around 20KB. Three loops, 500KB. Four, 15MB. And five? 300MB.

So if you want to imagine five loops, think about something that needs to be stored in a 300MB text file.

More insight:

We started out having noticed some weird new symmetries of our old results, so we brought in Simon Caron-Huot, expert on weird new symmetries. He couldn’t figure out that one…but he did notice an entirely different symmetry, one that turned out to have been first noticed in the 60’s, called the Steinmann relations.

The core idea of the Steinmann relations goes back to the old method of calculating amplitudes, with Feynman diagrams. In Feynman diagrams, lines represent particles traveling from one part of the diagram to the other. In a simplified form, the Steinmann conditions are telling us that diagrams can’t take two mutually exclusive shapes at the same time. If three particles are going one way, they can’t also be going another way.

steinmann2

With the Steinmann relations, things suddenly became a whole lot easier. Calculations that we had taken months to do, Simon was now doing in a week. Finally we could narrow things down and get the full answer, and we could do it with clear, physics-based rules.

More bootstrap:

In physics, when we call something a “bootstrap” it’s in reference to the phrase “pull yourself up by your own boostraps”. That impossible task, lifting yourself  with no outside support, is essentially what we do when we “bootstrap”: we do a calculation with no external input, simply by applying general rules.

In the past, our hexagon function calculations always had some sort of external data. For the first time, with the Steinmann conditions, we don’t need that. Every constraint, everything we do to narrow down our guess, is either a general rule or comes out of our lower-loop results. We never need detailed information from anywhere else.

This is big, because it might allow us to avoid loops altogether. Normally, each loop is an approximation, narrowed down using similar approximations from others. If we don’t need the approximations from others, though, then we might not need any approximations at all. For this particular theory, for this toy model, we might be able to actually calculate scattering amplitudes exactly, for any strength of forces and any energy. Nobody’s been able to do that for this kind of theory before.

We’re already making progress. We’ve got some test cases, simpler quantities that we can understand with no approximations. We’re starting to understand the tools we need, the pieces of our bootstrap. We’ve got a real chance, now, of doing something really fundamentally new.

So keep watching this blog, keep your eyes on arXiv: big things are coming.

Physics Is about Legos

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There’s a summer camp going on at Waterloo’s Institute for Quantum Computing called QCSYS, the Quantum Cryptography School for Young Students. A lot of these kids are interested in physics in general, not just quantum computing, so they give them a tour of Perimeter. While they’re here, they get a talk from a local postdoc, and this year that postdoc was me.

There’s an image that Perimeter has tossed around a lot recently, All Known Physics in One Equation. This article has an example from a talk given by Neil Turok. I thought it would be fun to explain that equation in terms a (bright, recently taught about quantum mechanics) high school student could understand. To do that, I’d have to explain what the equation is made of: spinors and vectors and tensors and the like.

The last time I had to explain that kind of thing here, I used a video game metaphor. For this talk, I came up with a better metaphor: legos.

Vectors are legos. Spinors are legos. Tensors are legos. They’re legos because they can be connected up together, but only in certain ways. Their “bumps” have to line up properly. And their nature as legos determines what you can build with them.

If you’re interested, here’s my presentation. Experts be warned: there’s a handwaving warning early in this talk, and it applies to a lot of it. In particular, the discussion of gauge group indices leaves out a lot. My goal in this talk was to give a vague idea of what the Standard Model Lagrangian is “made of”, and from the questions I got I think I succeeded.

Most of String Theory Is Not String Pheno

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Last week, Sabine Hossenfelder wrote a post entitled “Why not string theory?” In it, she argued that string theory has a much more dominant position in physics than it ought to: that it’s crowding out alternative theories like Loop Quantum Gravity and hogging much more funding than it actually merits.

If you follow the string wars at all, you’ve heard these sorts of arguments before. There’s not really anything new here.

That said, there were a few sentences in Hossenfelder’s post that got my attention, and inspired me to write this post.

So far, string theory has scored in two areas. First, it has proved interesting for mathematicians. But I’m not one to easily get floored by pretty theorems – I care about math only to the extent that it’s useful to explain the world. Second, string theory has shown to be useful to push ahead with the lesser understood aspects of quantum field theories. This seems a fruitful avenue and is certainly something to continue. However, this has nothing to do with string theory as a theory of quantum gravity and a unification of the fundamental interactions.

(Bolding mine)

Here, Hossenfelder explicitly leaves out string theorists who work on “lesser understood aspects of quantum field theories” from her critique. They’re not the big, dominant program she’s worried about.

What Hossenfelder doesn’t seem to realize is that right now, it is precisely the “aspects of quantum field theories” crowd that is big and dominant. The communities of string theorists working on something else, and especially those making bold pronouncements about the nature of the real world, are much, much smaller.

Let’s define some terms:

Phenomenology (or pheno for short) is the part of theoretical physics that attempts to make predictions that can be tested in experiments. String pheno, then, covers attempts to use string theory to make predictions. In practice, though, it’s broader than that: while some people do attempt to predict the results of experiments, more work on figuring out how models constructed by other phenomenologists can make sense in string theory. This still attempts to test string theory in some sense: if a phenomenologist’s model turns out to be true but it can’t be replicated in string theory then string theory would be falsified. That said, it’s more indirect. In parallel to string phenomenology, there is also the related field of string cosmology, which has a similar relationship with cosmology.

If other string theorists aren’t trying to make predictions, what exactly are they doing? Well, a large number of them are studying quantum field theories. Quantum field theories are currently our most powerful theories of nature, but there are many aspects of them that we don’t yet understand. For a large proportion of string theorists, string theory is useful because it provides a new way to understand these theories in terms of different configurations of string theory, which often uncovers novel and unexpected properties. This is still physics, not mathematics: the goal, in the end, is to understand theories that govern the real world. But it doesn’t involve the same sort of direct statements about the world as string phenomenology or string cosmology: crucially, it doesn’t depend on whether string theory is true.

Last week, I said that before replying to Hossenfelder’s post I’d have to gather some numbers. I was hoping to find some statistics on how many people work on each of these fields, or on their funding. Unfortunately, nobody seems to collect statistics broken down by sub-field like this.

As a proxy, though, we can look at conferences. Strings is the premier conference in string theory. If something has high status in the string community, it will probably get a talk at Strings. So to investigate, I took a look at the talks given last year, at Strings 2015, and broke them down by sub-field.

strings2015topics

Here I’ve left out the historical overview talks, since they don’t say much about current research.

“QFT” is for talks about lesser understood aspects of quantum field theories. Amplitudes, my own sub-field, should be part of this: I’ve separated it out to show what a typical sub-field of the QFT block might look like.

“Formal Strings” refers to research into the fundamentals of how to do calculations in string theory: in principle, both the QFT folks and the string pheno folks find it useful.

“Holography” is a sub-topic of string theory in which string theory in some space is equivalent to a quantum field theory on the boundary of that space. Some people study this because they want to learn about quantum field theory from string theory, others because they want to learn about quantum gravity from quantum field theory. Since the field can’t be cleanly divided into quantum gravity and quantum field theory research, I’ve given it its own category.

While all string theory research is in principle about quantum gravity, the “Quantum Gravity” section refers to people focused on the sorts of topics that interest non-string quantum gravity theorists, like black hole entropy.

Finally, we have String Cosmology and String Phenomenology, which I’ve already defined.

Don’t take the exact numbers here too seriously: not every talk fit cleanly into a category, so there were some judgement calls on my part. Nonetheless, this should give you a decent idea of the makeup of the string theory community.

The biggest wedge in the diagram by far, taking up a majority of the talks, is QFT. Throwing in Amplitudes (part of QFT) and Formal Strings (useful to both), and you’ve got two thirds of the conference. Even if you believe Hossenfelder’s tale of the failures of string theory, then, that only matters to a third of this diagram. And once you take into account that many of the Holography and Quantum Gravity people are interested in aspects of QFT as well, you’re looking at an even smaller group. Really, Hossenfelder’s criticism is aimed at two small slices on the chart: String Pheno, and String Cosmo.

Of course, string phenomenologists also have their own conference. It’s called String Pheno, and last year it had 130 participants. In contrast, LOOPS’ 2015, the conference for string theory’s most famous “rival”, had…190 participants. The fields are really pretty comparable.

Now, I have a lot more sympathy for the string phenomenologists and string cosmologists than I do for loop quantum gravity. If other string theorists felt the same way, then maybe that would cause the sort of sociological effect that Hossenfelder is worried about.

But in practice, I don’t think this happens. I’ve met string theorists who didn’t even know that people still did string phenomenology. The two communities are almost entirely disjoint: string phenomenologists and string cosmologists interact much more with other phenomenologists and cosmologists than they do with other string theorists.

You want to talk about sociology? Sociologically, people choose careers and fund research because they expect something to happen soon. People don’t want to be left high and dry by a dearth of experiments, don’t feel comfortable working on something that may only be vindicated long after they’re dead. Most people choose the safe option, the one that, even if it’s still aimed at a distant goal, is also producing interesting results now (aspects of quantum field theories, for example).

The people that don’t? Tend to form small, tight-knit, passionate communities. They carve out a few havens of like-minded people, and they think big thoughts while the world around them seems to only care about their careers.

If you’re a loop quantum gravity theorist, or a quantum gravity phenomenologist like Hossenfelder, and you see some of your struggles in that paragraph, please realize that string phenomenology is like that too.

I feel like Hossenfelder imagines a world in which string theory is struck from its high place, and alternative theories of quantum gravity are of comparable size and power. But from where I’m sitting, it doesn’t look like it would work out that way. Instead, you’d have alternatives grow to the same size as similarly risky parts of string theory, like string phenomenology. And surprise, surprise: they’re already that size.

In certain corners of the internet, people like to argue about “punching up” and “punching down”. Hossenfelder seems to think she’s “punching up”, giving the big dominant group a taste of its own medicine. But by leaving out string theorists who study QFTs, she’s really “punching down”, or at least sideways, and calling out a sub-group that doesn’t have much more power than her own.