Journalists Are Terrible at Quasiparticles

No, they haven’t, and no, that’s not what they found, and no, that doesn’t make sense.

Quantum field theory is how we understand particle physics. Each fundamental particle comes from a quantum field, a law of nature in its own right extending across space and time. That’s why it’s so momentous when we detect a fundamental particle, like the Higgs, for the first time, why it’s not just like discovering a new species of plant.

That’s not the only thing quantum field theory is used for, though. Quantum field theory is also enormously important in condensed matter and solid state physics, the study of properties of materials.

When studying materials, you generally don’t want to start with fundamental particles. Instead, you usually want to think about overall properties, ways the whole material can move and change overall. If you want to understand the quantum properties of these changes, you end up describing them the same way particle physicists talk about fundamental fields: you use quantum field theory.

In particle physics, particles come from vibrations in fields. In condensed matter, your fields are general properties of the material, but they can also vibrate, and these vibrations give rise to quasiparticles.

Probably the simplest examples of quasiparticles are the “holes” in semiconductors. Semiconductors are materials used to make transistors. They can be “doped” with extra slots for electrons. Electrons in the semiconductor will move around from slot to slot. When an electron moves, though, you can just as easily think about it as a “hole”, an empty slot, that “moved” backwards. As it turns out, thinking about electrons and holes independently makes understanding semiconductors a lot easier, and the same applies to other types of quasiparticles in other materials.

Unfortunately, the article I linked above is pretty impressively terrible, and communicates precisely none of that.

The problem starts in the headline:

Scientists have finally discovered massless particles, and they could revolutionise electronics

Scientists have finally discovered massless particles, eh? So we haven’t seen any massless particles before? You can’t think of even one?

After 85 years of searching, researchers have confirmed the existence of a massless particle called the Weyl fermion for the first time ever. With the unique ability to behave as both matter and anti-matter inside a crystal, this strange particle can create electrons that have no mass.

Ah, so it’s a massless fermion, I see. Well indeed, there are no known fundamental massless fermions, not since we discovered neutrinos have mass anyway. The statement that these things “create electrons” of any sort is utter nonsense, however, let alone that they create electrons that themselves have no mass.

Electrons are the backbone of today’s electronics, and while they carry charge pretty well, they also have the tendency to bounce into each other and scatter, losing energy and producing heat. But back in 1929, a German physicist called Hermann Weyl theorised that a massless fermion must exist, that could carry charge far more efficiently than regular electrons.

Ok, no. Just no.

The problem here is that this particular journalist doesn’t understand the difference between pure theory and phenomenology. Weyl didn’t theorize that a massless fermion “must exist”, nor did he say anything about their ability to carry charge. Weyl described, mathematically, how a massless fermion could behave. Weyl fermions aren’t some proposed new fundamental particle, like the Higgs boson: they’re a general type of particle. For a while, people thought that neutrinos were Weyl fermions, before it was discovered that they had mass. What we’re seeing here isn’t some ultimate experimental vindication of Weyl, it’s just an old mathematical structure that’s been duplicated in a new material.

What’s particularly cool about the discovery is that the researchers found the Weyl fermion in a synthetic crystal in the lab, unlike most other particle discoveries, such as the famous Higgs boson, which are only observed in the aftermath of particle collisions. This means that the research is easily reproducible, and scientists will be able to immediately begin figuring out how to use the Weyl fermion in electronics.

Arrgh!

Fundamental particles from particle physics, like the Higgs boson, and quasiparticles, like this particular Weyl fermion, are completely different things! Comparing them like this, as if this is some new efficient trick that could have been used to discover the Higgs, just needlessly confuses people.

Weyl fermions are what’s known as quasiparticles, which means they can only exist in a solid such as a crystal, and not as standalone particles. But further research will help scientists work out just how useful they could be. “The physics of the Weyl fermion are so strange, there could be many things that arise from this particle that we’re just not capable of imagining now,” said Hasan.

In the very last paragraph, the author finally mentions quasiparticles. There’s no mention of the fact that they’re more like waves in the material than like fundamental particles, though. From this description, it makes it sound like they’re just particles that happen to chill inside crystals, like they’re agoraphobic or something.

What the scientists involved here actually discovered is probably quite interesting. They’ve discovered a new sort of ripple in the material they studied. The ripple can carry charge, and because it can behave like a massless particle it can carry charge much faster than electrons can. (To get a basic idea as to how this works, think about waves in the ocean. You can have a wave that goes much faster than the ocean’s current. As the wave travels, no actual water molecules travel from one side to the other. Instead, it is the motion that travels, the energy pushing the wave up and down being transferred along.)

There’s no reason to compare this to particle physics, to make it sound like another Higgs boson. This sort of thing dilutes the excitement of actual particle discoveries, perpetuating the misconception of particles as just more species to find and catalog. Furthermore, it’s just completely unnecessary: condensed matter is a very exciting field, one that the majority of physicists work on. It doesn’t need to ride on the coat-tails of particle physics rhetoric in order to capture peoples’ attention. I’ve seen journalists do this kind of thing before, comparing new quasiparticles and composite particles with fundamental particles like the Higgs, and every time I cringe. Don’t you have any respect for the subject you’re writing about?

Pentaquarks!

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Earlier this week, the LHCb experiment at the Large Hadron Collider announced that, after painstakingly analyzing the data from earlier runs, they have decisive evidence of a previously unobserved particle: the pentaquark.

What’s a pentaquark? In simple terms, it’s five quarks stuck together. Stick two up quarks and a down quark together, and you get a proton. Stick two quarks together, you get a meson of some sort. Five, you get a pentaquark.

(In this case, if you’re curious: two up quarks, one down quark, one charm quark and one anti-charm quark.)

Artist’s Conception

Crucially, this means pentaquarks are not fundamental particles. Fundamental particles aren’t like species, but composite particles like pentaquarks are: they’re examples of a dizzying variety of combinations of an already-known set of basic building blocks.

So why is this discovery exciting? If we already knew that quarks existed, and we already knew the forces between them, shouldn’t we already know all about pentaquarks?

Well, not really. People definitely expected pentaquarks to exist, they were predicted fifty years ago. But their exact properties, or how likely they were to show up? Largely unknown.

Quantum field theory is hard, and this is especially true of QCD, the theory of quarks and gluons. We know the basic rules, but calculating their large-scale consequences, which composite particles we’re going to detect and which we won’t, is still largely out of our reach. We have to supplement first-principles calculations with experimental data, to take bits and pieces and approximations until we get something reasonably sensible.

This is an important point in general, not just for pentaquarks. Often, people get very excited about the idea of a “theory of everything”. At best, such a theory would tell us the fundamental rules that govern the universe. The thing is, we already know many of these rules, even if we don’t yet know all of them. What we can’t do, in general, is predict their full consequences. Most of physics, most of science in general, is about investigating these consequences, coming up with models for things we can’t dream of calculating from first principles, and it really does start as early as “what composite particles can you make out of quarks?”

Pentaquarks have been a long time coming, long enough that someone occasionally proposed a model that explained that they didn’t exist. There are still other exotic states of quarks and gluons out there, like glueballs, that have been predicted but not yet observed. It’s going to take time, effort, and data before we fully understand composite particles, even though we know the rules of QCD.

What Do You Get When You Put 136 Amplitudeologists into One Room? Amplitudes 2015!

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I’m at Amplitudes this week, my subfield’s big yearly conference, located this year in sweltering but otherwise lovely Zurich.

A typical inhabitant of Zurich.

I gave a talk on Tuesday. They’ve posted the slides online, and I think they’re going to post the talk itself at some point.

This is the first year I’ve been to Amplitudes, and it’s remarkable seeing the breadth of the field. We’ve got everything from people focused heavily on the needs of experimentalists, trying to perfect calculations that will reduce the error on measurements coming out of the LHC, to people primarily interested in some of the more esoteric aspects of string theory. Putting everyone into the same room definitely helps emphasize just how many different approaches there are under the amplitudes umbrella. It’s the first time I’ve really appreciated just how “big” the field is, how much it’s grown to encompass.

Where Do the Experts Go When They Need an Expert?

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If your game crashes, or Windows keeps spitting out bizarre error messages, you google the problem. Chances are, you find someone on a help forum who had the same problem, and hopefully someone else posted the answer.

(If your preferred strategy is to ask a younger relative, then I’m sorry, but nine times out of ten they’re just doing that.)

What do scientists do, though? We’re at the cutting-edge of knowledge. When we have a problem, who do we turn to?

Typically, Stack Exchange.

The thing is, when we’re really confused about something, most of the time it’s not really a physics problem. We get mystified by the intricacies of Mathematica, or we need some quality trick from numerical methods. And while I haven’t done much with them yet, there are communities dedicated to answering actual physics questions, like Physics Overflow.

The idea I was working on last week? That came from a poster on the Mathematica Stack Exchange, who mentioned a handy little function called Association that I hadn’t heard of before. (It worked, by the way.)

Science is a collaborative process. Sometimes that means actual collaborators, but sometimes we need a little help from folks online, just like everyone else.

Why I Spent Convergence Working

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Convergence is basically Perimeter Institute Christmas.

This week, the building was dressed up in festive posters and elaborate chalk art, and filled with Perimeter’s many distant relations. Convergence is like a hybrid of an alumni reunion and a conference, where Perimeter’s former students and close collaborators come to hear talks about the glory of Perimeter and the marvels of its research.

Lewis Carroll, Anti-String Theorist?

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You all know the real meaning of Alice in Wonderland, right?

No, I’m not talking about drugs, or darker things. I’m talking about math!

The 19th century was a time of great changes in mathematics, and Charles Dodgson, pen name Lewis Carroll, was opposed to almost all of it. A very traditional mathematician, Dodgson thought of Euclid’s Elements as the pinnacle of mathematical reasoning. Non-Euclidean geometry, symbolic algebra, complex numbers, all of these were viewed by Dodgson as nonsense, perverting students away from the study of Euclidean geometry and arithmetic, subjects that actually described the real world.

Scholars of Dodgson/Carroll’s writing have posited that the craziness of Wonderland was intended to parody the craziness Dodgson saw in mathematics. When Alice encounters the Caterpillar, she grows and shrinks non-uniformly as the Caterpillar advises her to “keep her temper”. “Temper” here refers not to anger, but to ratios between different parts: something preserved in Euclidean geometry but potentially violated by symbolic algebra. Similarly, the frantic rotations around the table by the Mad Hatter and his tea party are thought to represent imaginary numbers and quaternions, concepts used to understand rotation which had to postulate extra dimensions to do so.

Dodgson was on the wrong side of history, and today mathematics deals with even more abstract concepts. What amuses me, though, is how well Dodgson’s parodies match certain criticisms of string theory.

String theorists often study theories with two properties not found in the real world: conformal symmetry and supersymmetry.

In a theory with conformal symmetry, distances aren’t fixed. Different parts of objects can grow and shrink different amounts, and the theory will still predict the same physical behavior. The only restriction is that angles need to be preserved: two lines that meet at a given angle must meet at the same angle after transformation. In other words, keep your temper.

Alice, undergoing a conformal transformation.

I’ve talked about supersymmetry before. A supersymmetric theory can be “turned” in certain ways, related to exchanging different types of particles. If you “turn” the theory twice in the same “direction”, you get back to where you started, sort of like how if you square the imaginary number i you get back to the real number -1. Supersymmetry sees a group of particles and declares that “it’s time to change places!”

I thought the string theory skeptics among my readers might find the parallels here amusing. With parody, if not always with science, the best work was often done long, long ago.

Yo Dawg, I Heard You Liked Quantum Field Theory so I Made You a String Theory

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String theory may sound strange and exotic, with its extra dimensions and loops of string. Deep down, though, string theory is by far the most conservative attempt at a theory of quantum gravity. It just takes the tools of quantum field theory, and applies them all over again.

Picture a loop of string, traveling through space. From one moment to the next, the loop occupies a loop-shaped region. Now imagine joining all those regions together, forming a tunnel: the space swept out by the string over its entire existence. As the string joins other strings, merging and dividing, the result is a complicated surface. In string theory, we call this surface the worldsheet.

Yes, it looks like Yog-Sothoth. It always looks like Yog-Sothoth.

Imagine what it’s like to live on this two-dimensional surface. You don’t know where the string is in the space around it, because you can’t see off the surface. You can learn something about it, though, because making the worldsheet bend takes energy. I’ve talked about this kind of situation before, and the result is that your world contains a scalar field.

Living on the two-dimensional surface, then, you can describe your world with two-dimensional quantum field theory. Your two-dimensional theory, reinterpreted, then tells you the position of the string in higher-dimensional space. If we were just doing normal particle physics, we’d use quantum field theory to describe the particles. Now that we’ve replaced particles with strings, our quantum field theory describes things that are the result of another quantum field theory.

Xzibit would be proud.

If you understand this aspect of string theory, everything else makes a lot more sense. If you’re just imagining lengths of string, it’s hard to understand how strings can have supersymmetry. In these terms, though, it’s simple: instead of just scalar fields, supersymmetric strings also have fermions (fields with spin 1/2) as part of their two-dimensional quantum field theory.

It’s also deeply related to all those weird extra dimensions. As it turns out, two-dimensional quantum field theories are much more restricted than their cousins in our four (three space plus one time)-dimensional world. In order for a theory with only scalars (like the worldsheet of a moving loop of string) to make sense, there have to be twenty-six scalars. Each scalar is a direction in which the worldsheet can bend, so if you just have scalars you’re looking at a 26-dimensional world. Supersymmetry changes this calculation by adding fermions: with fermions and scalars, you need ten scalars to make your theory mathematically consistent, which is why superstring theory lives in ten dimensions.

This also gives you yet another way to think about branes. Strings come from two-dimensional quantum field theories, while branes come from quantum field theories in other dimensions.

Sticking a quantum field theory inside a quantum field theory is the most straightforward way to move forward. Fundamentally, it’s just using tools we already know work. That doesn’t mean it’s the right solution, or that it describes reality: that’s for the future to establish. But I hope I’ve made it a bit clearer why it’s by far the most popular option.

Physics Is a Small World

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Earlier this week, Vilhelm Bohr gave a talk at Perimeter about the life of his grandfather, the famous physicist Niels Bohr. The video of the talk doesn’t appear to be up on the Perimeter site yet, but it should be soon.

Until then, here is a picture of some eyebrows.

This was especially special for me, because my family has a longstanding connection to the Bohrs. My great grandfather worked at the Niels Bohr Institute in the mid-1930’s, and his children became good friends with Bohr’s grandchildren, often visiting each other even after my family relocated to the US.

These kinds of connections are more common in physics than you might think. Time and again I’m surprised by how closely linked people are in this field. There’s a guy here at Perimeter who went to school with Jaroslav Trnka, and a bunch of Israelis at nearby institutions all know each other from college. In my case, I went to high school with an unusually large number of mathematicians.

While it’s fun to see familiar faces, there’s a dark side to the connected nature of physics. So much of what it takes to succeed in academia involves knowing unwritten rules, as well as a wealth of other information that just isn’t widely known. Many people don’t even know it’s possible to have a career in physics, and I’ve met many who didn’t know that science grad schools pay your tuition. Academic families, and academic communities, have an enormous leg up on this kind of knowledge, so it’s not surprising that so many physicists come from so few sources.

Artificially limiting the pool of people who become physicists is bound to hurt us in the long run. Great insights often come from outsiders, like Hooke in the 17th century and Noether in the early 20th. If we can expand the reach of physics, make the unwritten rules written and the secret tricks revealed, if we work to make physics available to anyone who might be suited for it, then we can make sure that physics doesn’t end up a hereditary institution, with all the problems that entails.

Calculus Is About Pokemon

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Occasionally, people tell me that calculus was when they really gave up on math. It’s a pity, because for me calculus was the first time math really started to become fun. After all, it’s when math introduces the Pokemon.

What Pokemon? Why, the special functions of course.

By special functions I mean things like $\sin x$ , $\cos x$ , $e^x$ , and $\ln x$ . Like Pokemon, these guys come in a bewildering variety. And in calculus, you learn that they, like Pokemon, can evolve.

$x$ integrates into $\frac{1}{2}x^2$ !

$\frac{1}{x}$ integrates into $\ln x$ !

$\sin x$ integrates into $-\cos x$ , and $\cos x$ integrates into… $\sin x$ .

Ok, the analogy isn’t perfect. Pokemon don’t evolve back into themselves. But the same things that make Pokemon so appealing are precisely why calculus was such a breath of fresh air. Suddenly, there was a grand diversity of new things, and those new things were related.

College gave me new Pokemon, in the form of the Bessel functions. Nowadays, I work with a group of functions called Polylogarithms, and they’re even more like Pokemon. Logarithms are like the baby Pokemon of the Polylogarithms, integrating into Dilogarithms. Dilogarithms integrate into Trilogarithms, and so on.

Polylogarithms, in turn, evolve into Poliwrath

To this day, the talks I enjoy the most are those that show me new special functions, or new relations between old ones. If a talk shows me a new use of multiple zeta values, or new types of Polylogarithm, it’s not just teaching me new physics or mathematics: it’s expanding my Pokemon collection.

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.

4 gravitons

Stories about physics from someone who's been there

Journalists Are Terrible at Quasiparticles

Pentaquarks!

What Do You Get When You Put 136 Amplitudeologists into One Room? Amplitudes 2015!

Where Do the Experts Go When They Need an Expert?

Why I Spent Convergence Working

Lewis Carroll, Anti-String Theorist?

Yo Dawg, I Heard You Liked Quantum Field Theory so I Made You a String Theory

Physics Is a Small World

Calculus Is About Pokemon

Got Branes on the Brain?