Got Branes on the Brain?

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You’ve probably heard it said that string theory contains two types of strings: open, and closed. Closed strings are closed loops, like rubber bands. They give rise to gravity, and in superstring theories to supergravity. Open strings have loose ends, like a rubber band cut in half. They give us Yang-Mills forces, and super Yang-Mills for superstrings.

String theory has more than just strings, though. It also has branes.

Branes, short for membranes, are objects like strings but in other dimensions. The simplest to imagine is a two-dimensional membrane, like a sheet of paper. A three-dimensional membrane would fill all of 3D space, like an infinite cube of jello. Higher dimensional membranes also exist, up to string theory’s limit of nine spatial dimensions.

But you can keep imagining them as sheets of paper if you’d like.

So where did these branes come from? Why doesn’t string theory just have strings?

You might think we’re just trying to be as general as possible, including every possible dimension of object. Strangely enough, this isn’t actually what’s going on! As it turns out, branes can be in lower dimensions too: there are zero-dimensional branes that behave like particles, and one-dimensional branes that are similar to, but crucially not the same thing as, the strings we started out with! If we were just trying to get an object for every dimension we wouldn’t need one-dimensional branes, we’d already have strings!

(By the way, there are also “-1” dimensional branes, but that’s a somewhat more advanced topic.)

Instead, branes come from some strange properties of open strings.

I told you that the ends of open strings are “loose”, but that’s just loose language on my part. Mathematically, there are two options: the ends can be free to wander, or they can be fixed in place. If they’re free, they can move wherever they like with no resistance. If they’re fixed, any attempt to move them will just set them vibrating.

The thing is, you choose between these two options not just once, but once per dimension. You could have the end of the string free to move in two dimensions, but fixed in another, like a magnet was sticking it to some sort of 2D surface…like a brane.

Brane-worlds are dangerous places to live.

In mathematics, the fixed dimensions of end of the string are said to have Dirichlet boundary conditions, which is why this type of branes are called Dirichlet branes, or D-branes. In general, D-branes are things strings can end on. That’s why you can have D1-branes, that despite their string-like shape are different from actual strings: rather, they’re things strings can end on.

You might wonder whether we really need these things. Sure, they’re allowed mathematically, but is that really a good enough reason?

As it turns out, D-branes are not merely allowed in string theory, they are required, due to something called T-duality. I’ve talked about dualities before: they’re relationships between different theories that secretly compute the same thing. T-duality was one of the first-discovered dualities in string theory, and it involves relationships between strings wrapped around circular dimensions.

If a dimension is circular, then closed strings can either move around the circle, or wrap around it instead. As it turns out, a string moving around a small circle has the same energy as a string wrapped around a big circle, where here “small” and “big” are comparisons to the length of the string. It’s not just the energy, though: for every physical quantity, the two descriptions (big circle with strings traveling along it, small circle with strings wrapped around it) give the same answer: the two theories are dual.

If it works with closed strings, what about open strings?

Here something weird happens: if you perform the T-duality operation (switch between the small circle and the big one), then the ends of open strings switch from being free to being fixed! This means that even if we start out with no D-branes at all, our theory was equivalent to one with D-branes all along! No matter what we do, we can’t write down a theory that doesn’t have D-branes!

As it turns out, we could have seen this coming even without string theory, just by looking at (super)gravity.

Long before people saw astrophysical evidence for black holes, before they even figured out that stars could collapse, they worked out the black hole solution in general relativity. Without knowing anything about the sort of matter that could form a black hole, they could nevertheless calculate what space-time would look like around one.

In ten dimensional supergravity, you can do these same sorts of calculations. Instead of getting black holes, though, you get black branes. Rather than showing what space-time looks like around a high-mass point, they showed what it would look like around a higher dimensional, membrane-shaped object. And miraculously, they corresponded exactly to the D-branes that are supposed to be part of string theory!

So if we want string theory, or even supergravity, we’re stuck with D-branes. It’s a good thing we are, too, because D-branes are very useful. In the past, I’ve talked about how most of the fundamental forces of nature have multiple types of charge. One way for string theory to reproduce these multiple types of charge is with D-branes. If each open string is connected to two D-branes, it can behave like gluons, carrying a pair of charges. Since each end of the string is stuck to its respective brane, the charge corresponding to each brane must be conserved, just like charges in the real world.

D-branes aren’t one of the original assumptions of string theory, but they’re a large part of what makes string theory tick. M theory, string theory’s big brother, doesn’t have strings at all: just two- and five-dimensional branes. So be grateful for branes: they make the world a much more interesting place.

Science Never Forgets

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I’ll just be doing a short post this week, I’ve been busy at a workshop on Flux Tubes here at Perimeter.

If you’ve ever heard someone tell the history of string theory, you’ve probably heard that it was first proposed not as a quantum theory of gravity, but as a way to describe the strong nuclear force. Colliders of the time had discovered particles, called mesons, that seemed to have a key role in the strong nuclear force that held protons and neutrons together. These mesons had an unusual property: the faster they spun, the higher their mass, following a very simple and regular pattern known as a Regge trajectory. Researchers found that they could predict this kind of behavior if, rather than particles, these mesons were short lengths of “string”, and with this discovery they invented string theory.

As it turned out, these early researchers were wrong. Mesons are not lengths of string, rather, they are pairs of quarks. The discovery of quarks explained how the strong force acted on protons and neutrons, each made of three quarks, and it also explained why mesons acted a bit like strings: in each meson, the two quarks are linked by a flux tube, a roughly cylindrical area filled with the gluons that carry the strong nuclear force. So rather than strings, mesons turned out to be more like bolas.

Leonin sold separately.

If you’ve heard this story before, you probably think it’s ancient history. We know about quarks and gluons now, and string theory has moved on to bigger and better things. You might be surprised to hear that at this week’s workshop, several presenters have been talking about modeling flux tubes between quarks in terms of string theory!

The thing is, science never forgets a good idea. String theory was superseded by quarks in describing the strong force, but it was only proposed in the first place because it matched the data fairly well. Now, with string theory-inspired techniques, people are calculating the first corrections to the string-like behavior of these flux tubes, comparing them with simulations of quarks and gluons, and finding surprisingly good agreement!

Science isn’t a linear story, where the past falls away to the shiny new theories of the future. It’s a marketplace. Some ideas are traded more widely, some less…but if a product works, even only sometimes, chances are someone out there will have a reason to buy it.

No-One Can Tell You What They Don’t Understand

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On Wednesday, Amanda Peet gave a Public Lecture at Perimeter on string theory and black holes, while I and other Perimeter-folk manned the online chat. If you missed it, it’s recorded online here.

We get a lot of questions in the online chat. Some are quite insightful, some are basic, and some…well, some are kind of strange. Like the person who asked us how holography could be compatible with irrational numbers.

In physics, holography is the idea that you can encode the physics of a wider space using only information on its boundary. If you remember the 90’s or read Buzzfeed a lot, you might remember holograms: weird rainbow-colored images that looked 3d when you turned your head.

On a computer screen, they instead just look awkward.

Holograms in physics are a lot like that, but rather than a 2d image looking like a 3d object, they can be other combinations of dimensions as well. The most famous, AdS/CFT, relates a ten-dimensional space full of strings to a four-dimensional space on its boundary, where the four-dimensional space contains everybody’s favorite theory, N=4 super Yang-Mills.

So from this explanation, it’s probably not obvious what holography has to do with irrational numbers. That’s because there is no connection: holography has nothing to do with irrational numbers.

Naturally, we were all a bit confused, so one of us asked this person what they meant. They responded by asking if we knew what holograms and irrational numbers were. After all, the problem should be obvious then, right?

In this sort of situation, it’s tempting to assume you’re being trolled. In reality, though, the problem was one of the most common in science communication: people can’t tell you what they don’t understand, because they don’t understand it.

When a teacher asks “any questions?”, they’re assuming students will know what they’re missing. But a deep enough misunderstanding doesn’t show itself that way. Misunderstand things enough, and you won’t know you’re missing anything. That’s why it takes real insight to communicate science: you have to anticipate ways that people might misunderstand you.

In this situation, I thought about what associations people have with holograms. While some might remember the rainbow holograms of old, there are other famous holograms that might catch peoples’ attention.

Please state the nature of the medical emergency.

In science fiction, holograms are 3d projections, ways that computers can create objects out of thin air. The connection to a 2d image isn’t immediately apparent, but the idea that holograms are digital images is central.

Digital images are the key, here. A computer has to express everything in a finite number of bits. It can’t express an irrational number, a number with a decimal expansion that goes on to infinity, at least not without tricks. So if you think that holography is about reality being digital, rather than lower-dimensional, then the question makes perfect sense: how could a digital reality contain irrational numbers?

This is the sort of thing we have to keep in mind when communicating science. It’s easy to misunderstand, to take some aspect of what someone said and read it through a different lens. We have to think about how others will read our words, we have to be willing to poke and prod until we root out the source of the confusion. Because nobody is just going to tell us what they don’t get.

Outreach as the End Product of Science

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Sabine Hossenfelder recently wrote a blog post about physics outreach. In it, she identifies two goals: inspiration, and education.

Inspiration outreach is all about making science seem cool. It’s the IFLScience side of things, stoking the science fandom and getting people excited.

Education outreach, by contrast, is about making sure peoples’ beliefs are accurate. It teaches the audience something about the world around them, giving them a better understanding of how the world works.

In both cases, though, Sabine finds it hard to convince other scientists that outreach is valuable. Maybe inspiration helps increase grant funding, maybe education makes people vote better on scientific issues like climate change…but there isn’t a lot of research that shows that outreach really accomplishes either.

Sabine has a number of good suggestions in her post for how to make outreach more effective, but I’d like to take a step back and suggest that maybe we as a community are thinking about outreach in the wrong way. And in order to do that, I’m going to do a little outreach myself, and talk about black holes.

The black hole of physics outreach.

Black holes are collapsed stars, crushed in on themselves by their own gravity so much that one you get close enough (past the event horizon) not even light can escape. This means that if you sent an astronaut past the event horizon, there would be no way for them to communicate with you: any way they might try to get information to you would travel, at most, at the speed of light.

Einstein’s equations keep working fine past the event horizon, but despite that there are some people who view any prediction of what happens inside to be outside the scope of science. If there’s no way to report back, then how could we ever test our predictions? And if we can’t test our predictions, aren’t we missing the cornerstone of science itself?

In a rather entertaining textbook, physicists Edwin F. Taylor and John Archibald Wheeler suggest a way around this: instead of sending just one astronaut, send multiple! Send a whole community! That way, while we might not be able to test our predictions about the inside of the event horizon, the scientific community that falls in certainly can. For them, those predictions aren’t just meaningless speculation, but testable science.

If something seems unsatisfying about this, congratulations: you now understand the purpose of outreach.

As long as scientific advances never get beyond a small community, we’re like Taylor and Wheeler’s astronauts inside the black hole. We can test our predictions among each other, verify them to our heart’s content…but if they never reach the wider mass of humanity, then what have we really accomplished? Have we really created knowledge, when only a few people will ever know it?

In my Who Am I? post, I express the hope that one day the science I blog about will be as well known as electrons and protons. That might sound farfetched, but I really do think it’s possible. In one hundred years, electrons and protons went from esoteric discoveries of a few specialists to something children learn about in grade school. If science is going to live up to its purpose, if we’re going to escape the black hole of our discipline, then in another hundred years quantum field theory needs to do the same. And by doing outreach work, each of us is taking steps in that direction.

String Theorists Who Don’t Touch Strings

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This week I’ve been busy, attending a workshop here at Perimeter on Superstring Perturbation Theory.

Superstrings are the supersymmetric strings that string theorists use to describe fundamental particles, while perturbation theory is the trick, common in almost every area of physics, of solving a problem by a series of increasingly precise approximations.

Based on that description, you’d think that superstring perturbation theory would be a central topic in string theory research. You wouldn’t expect it to be the sort of thing only a few people at the top of the field dabble in. You definitely wouldn’t expect one of the speakers at the workshop to mention that this might be the first conference on superstring perturbation theory he’s been to since the 1980’s.

String perturbation theory is an important subject, but it’s not one many string theorists use. And the reason why is that, oddly enough, very few string theorists actually use strings.

Looking at arXiv as I’m writing this, I can see only one paper in the theoretical physics section that directly uses strings. Most of them use something else: either older concepts like black holes, quantum field theory, and supergravity, or newer ones like d-branes. If you talked to the people who wrote those papers, though, most of them would describe themselves as string theorists.

The reason for the disconnect is that string theory as a field is much more than just the study of strings. String theory is a ten-dimensional universe (or eleven with M theory), where different ways of twisting up some of the dimensions result in different apparent physics in the remaining ones. It’s got strings, but also higher-dimensional membranes (and in the eleven dimensions of M theory it only has membranes, not strings). It’s the recipe for a long list of exotic quantum field theories, and a list of possible relations between them. It’s a new way to look at geometry, to think about the intersection of the nature of space and the dynamics of what inhabits it.

If string theory were really just about strings, it likely wouldn’t have grown any bigger than its quantum gravity rivals, like Loop Quantum Gravity. String theory grew because it inspired research directions that went far afield, and far beyond its conceptual core.

That’s part of why most string theorists will be baffled if you insist that string theory needs proof, or that it’s not the right approach to quantum gravity. For most string theorists, it doesn’t matter whether we live in a stringy world, whether gravity might eventually be described by another model. For most string theorists, string theory is a tool, one that opened up fields of inquiry that don’t have much to do with predicting the output of the LHC or describing the early universe. Or, in many cases, actually using strings.

Who Plagiarizes an Acknowledgements Section?

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I’ve got plagiarists on the brain.

Maybe it was running into this interesting discussion about a plagiarized application for the National Science Foundation’s prestigious Graduate Research Fellowship Program. Maybe it’s due to the talk Paul Ginsparg, founder of arXiv, gave this week about, among other things, detecting plagiarism.

Using arXiv’s repository of every paper someone in physics thought was worth posting, Ginsparg has been using statistical techniques to sift out cases of plagiarism. Probably the funniest cases involved people copying a chunk of their thesis acknowledgements section, as excerpted here. Compare:

“I cannot describe how indebted I am to my wonderful girlfriend, Amanda, whose love and encouragement will always motivate me to achieve all that I can. I could not have written this thesis without her support; in particular, my peculiar working hours and erratic behaviour towards the end could not have been easy to deal with!”

“I cannot describe how indebted I am to my wonderful wife, Renata, whose love and encouragement will always motivate me to achieve all that I can. I could not have written this thesis without her support; in particular, my peculiar working hours and erratic behaviour towards the end could not have been easy to deal with!”

Why would someone do this? Copying the scientific part of a thesis makes sense, in a twisted way: science is hard! But why would someone copy the fluff at the end, the easy part that’s supposed to be a genuine take on your emotions?

The thing is, the acknowledgements section of a thesis isn’t exactly genuine. It’s very formal: a required section of the thesis, with tacit expectations about what’s appropriate to include and what isn’t. It’s also the sort of thing you only write once in your life: while published papers also have acknowledgements sections, they’re typically much shorter, and have different conventions.

If you ever were forced to write thank-you notes as a kid, you know where I’m going with this.

It’s not that you don’t feel grateful, you do! But when you feel grateful, you express it by saying “thank you” and moving on. Writing a note about it isn’t very intuitive, it’s not a way you’re used to expressing gratitude, so the whole experience feels like you’re just following a template.

Literally in some cases.

That sort of situation: where it doesn’t matter how strongly you feel something, only whether you express it in the right way, is a breeding ground for plagiarism. Aunt Mildred isn’t going to care what you write in your thank-you note, and Amanda/Renata isn’t going to be moved by your acknowledgements section. It’s so easy to decide, in that kind of situation, that it’s better to just grab whatever appropriate text you can than to teach yourself a new style of writing.

In general, plagiarism happens because there’s a disconnect between incentives and what they’re meant to be for. In a world where very few beginning graduate students actually have a solid research plan, the NSF’s fellowship application feels like a demand for creative lying, not an honest way to judge scientific potential. In countries eager for highly-cited faculty but low on preexisting experts able to judge scientific merit, tenure becomes easier to get by faking a series of papers than by doing the actual work.

If we want to get rid of plagiarism, we need to make sure our incentives match our intent. We need a system in which people succeed when they do real work, get fellowships when they honestly have talent, and where we care about whether someone was grateful, not how they express it. If we can’t do that, then there will always be people trying to sneak through the cracks.

What’s the Matter with Dark Matter, Matt?

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It’s very rare that I disagree with Matt Strassler. That said, I can’t help but think that, when he criticizes the press for focusing their LHC stories on dark matter, he’s missing an important element.

From his perspective, when the media says that the goal of the new run of the LHC is to detect dark matter, they’re just being lazy. People have heard of dark matter. They might have read that it makes up 23% of the universe, more than regular matter at 4%. So when an LHC physicist wants to explain what they’re working on to a journalist, the easiest way is to talk about dark matter. And when the journalist wants to explain the LHC to the public, they do the same thing.

This explanation makes sense, but it’s a little glib. What Matt Strassler is missing is that, from the public’s perspective, dark matter really is a central part of the LHC’s justification.

Now, I’m not saying that the LHC’s main goal is to detect dark matter! Directly detecting dark matter is pretty low on the LHC’s list of priorities. Even if it detects a new particle with the right properties to be dark matter, it still wouldn’t be able to confirm that it really is dark matter without help from another experiment that actually observes some consequence of the new particle among the stars. I agree with Matt when he writes that the LHC’s priorities for the next run are

studying the newly discovered Higgs particle in great detail, checking its properties very carefully against the predictions of the “Standard Model” (the equations that describe the known apparently-elementary particles and forces) to see whether our current understanding of the Higgs field is complete and correct, and
trying to find particles or other phenomena that might resolve the naturalness puzzle of the Standard Model, a puzzle which makes many particle physicists suspicious that we are missing an important part of the story, and
seeking either dark matter particles or particles that may be shown someday to be “associated” with dark matter.

Here’s the thing, though:

From the public’s perspective, why do we need to study the properties of the Higgs? Because we think it might be different than the Standard Model predicts.

Why do we think it might be different than the Standard Model predicts? More generally, why do we expect the world to be different from the Standard Model at all? Well there are a few reasons, but they generally boil down to two things: the naturalness puzzle, and the fact that the Standard Model doesn’t have anything that could account for dark matter.

Naturalness is a powerful motivation, but it’s hard to sell to the general public. Does the universe appear fine-tuned? Then maybe it just is fine-tuned! Maybe someone fine-tuned it!

These arguments miss the real problem with fine-tuning, but they’re hard to correct in a short article. Getting the public worried about naturalness is tough, tough enough that I don’t think we can demand it of the average journalist, or accuse them of being lazy if they fail to do it.

That leaves dark matter. And for all that naturalness is philosophically murky, dark matter is remarkably clear. We don’t know what 96% of the universe is made of! That’s huge, and not just in a “gee-whiz-cool” way. It shows, directly and intuitively, that physics still has something it needs to solve, that we still have particles to find. Unless you are a fan of (increasingly dubious) modifications to gravity like MOND, dark matter is the strongest possible justification for machines like the LHC.

The LHC won’t confirm dark matter on its own. It might not directly detect it, that’s still quite up-in-the-air. And even if it finds deviations from the Standard Model, it’s not likely they’ll be directly caused by dark matter, at least not in a simple way.

But the reason that the press is describing the LHC’s mission in terms of dark matter isn’t just laziness. It’s because, from the public’s perspective, dark matter is the only vaguely plausible reason to spend billions of dollars searching for new particles, especially when we’ve already found the Higgs. We’re lucky it’s such a good reason.

Want to Make Something New? Just Turn on the Lights.

Only the Boring Kind of Parallel Universes

What Counts as a Fundamental Force?

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I’m giving a presentation next Wednesday for Learning Unlimited, an organization that presents educational talks to seniors in Woodstock, Ontario. The talk introduces the fundamental forces and talks about Yang and Mills before moving on to introduce my work.

While practicing the talk today, someone from Perimeter’s outreach department pointed out a rather surprising missing element: I never mention gravity!

Most people know that there are four fundamental forces of nature. There’s Electromagnetism, there’s Gravity, there’s the Weak Nuclear Force, and there’s the Strong Nuclear Force.

Listed here by their most significant uses.

What ties these things together, though? What makes them all “fundamental forces”?

Mathematically, gravity is the odd one out here. Electromagnetism, the Weak Force, and the Strong Force all share a common description: they’re Yang-Mills forces. Gravity isn’t. While you can sort of think of it as a Yang-Mills force “squared”, it’s quite a bit more complicated than the Yang-Mills forces.

You might be objecting that the common trait of the fundamental forces is obvious: they’re forces! And indeed, you can write down a force law for gravity, and a force law for E&M, and umm…

[Mumble Mumble]

Ok, it’s not quite as bad as xkcd would have us believe. You can actually write down a force law for the weak force, if you really want to, and it’s at least sort of possible to talk about the force exerted by the strong interaction.

All that said, though, why are we thinking about this in terms of forces? Forces are a concept from classical mechanics. For a beginning physics student, they come up again and again, in free-body diagram after free-body diagram. But by the time a student learns quantum mechanics, and quantum field theory, they’ve already learned other ways of framing things where forces aren’t mentioned at all. So while forces are kind of familiar to people starting out, they don’t really match onto anything that most quantum field theorists work with, and it’s a bit weird to classify things that only really appear in quantum field theory (the Weak Nuclear Force, the Strong Nuclear Force) based on whether or not they’re forces.

Isn’t there some connection, though? After all, gravity, electromagnetism, the strong force, and the weak force may be different mathematically, but at least they all involve bosons.

Well, yes. And so does the Higgs.

The Higgs is usually left out of listings of the fundamental forces, because it’s not really a “force”. It doesn’t have a direction, instead it works equally at every point in space. But if you include spin 2 gravity and spin 1 Yang-Mills forces, why not also include the spin 0 Higgs?

Well, if you’re doing that, why not include fermions as well? People often think of fermions as “matter” and bosons as “energy”, but in fact both have energy, and neither is made of it. Electrons and quarks are just as fundamental as photons and gluons and gravitons, just as central a part of how the universe works.

I’m still trying to decide whether my presentation about Yang-Mills forces should also include gravity. On the one hand, it would make everything more familiar. On the other…pretty much this entire post.

4 gravitons

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