There's a new fermion, you guys
July 23, 2015 9:26 AM   Subscribe

Princeton researchers have discovered a long-theorized, never-observed variety of massless (quasi)-particle called the Weyl fermion. Exciting things to come maybe! (Bat-signal: expert.)

Drumroll for breathless speculation: Could Majorana fermions be next?
posted by Zerowensboring (25 comments total) 13 users marked this as a favorite
In space, no one can hear you speculate. Snark aside: fascinating. /Spock eyebrow
posted by y2karl at 10:03 AM on July 23, 2015

If this is true (and that's the biggest if I've iffed this year) then that right there is your 2018 Nobel Prize in Physics, give or take a year.
posted by eriko at 10:32 AM on July 23, 2015 [1 favorite]

The part recounting the moment of discovery is particlarly exciting:

That night, in the mid-watch when the old man -- as his wont at intervals -- stepped forth from the scuttle in which he leaned, and went to his pivot-hole, he suddenly thrust out his face fiercely, snuffing up the sea air as a sagacious ship’s dog will, in drawing nigh to some barbarous isle. He declared that a weyl must be near. Soon that peculiar odor, sometimes to a great distance given forth by the living fermion, was palpable to all the watch; nor was any mariner surprised when, after inspecting the compass, and then the dog-vane, and then ascertaining the precise bearing of the odor as nearly as possible, Ahab rapidly ordered the ship’s course to be slightly altered, and the sail to be shortened.
posted by Sunburnt at 10:56 AM on July 23, 2015 [7 favorites]

Is Weyl pronounced "whale" or "vile"? I mean, there's a rich harvest of puns in either direction, but it would be good to know which are technically correct.
posted by yoink at 11:22 AM on July 23, 2015

My takeaway from the gizmag article is sci-fi technology powered by crystals which is a wonderful (if likely not entirely correct) image. Kind of blows my mind that a simple material is the key to harnessing these weird fermions that produce massless electrons, it's like real life handwavium.
posted by jason_steakums at 11:23 AM on July 23, 2015

metafilter: it's like real life handwavium
posted by lalochezia at 11:31 AM on July 23, 2015 [3 favorites]

> Is Weyl pronounced "whale" or "vile"?

Hermann Weyl was German, so [vaɪl] ("vile").
posted by languagehat at 11:39 AM on July 23, 2015

"Could Majorana fermions be next?"

Didn't they already legalize Majorana in Colorado?
posted by I-baLL at 12:10 PM on July 23, 2015 [3 favorites]

I hate to rain on everyone's parade, but the key words in the Science abstract are "emergent quasiparticle". In other words, this is not a fundamentally new particle; this is a collection of neutrons, protons, and electrons that these physicists have (very cleverly) managed to get to behave as though it had Weyl fermions running around inside it. It's like when "magnetic monopoles" were discovered in a similar sold-state experiment a few years back.
posted by Johnny Assay at 12:10 PM on July 23, 2015 [2 favorites]

Weyl fermion
Fermi arc
pseudogap state
Fermi surface
reciprocal lattice
momentum space
Brillouin zone

Not weyls, but olyfaunts; and maybe all the way down.
posted by the Real Dan at 12:18 PM on July 23, 2015

I'm struggling to get to grips with what these things are. Most articles either have extremely hard maths or are clearly a journalist being told "try and make sense of this" and failing.

Ok, so they're massless - that's fine, we've got other things that are massless like the photon. But these have a charge, a bit like an electron. And they've got spin like other quantum objects and I assume stuff like charge-parity. But can only be found inside a solid? Ok, I sort of get that - we've seen stuff in superconductors which might be axions which are very nearly massless (but they do have some mass so these aren't the same thing).

"The researchers also found that Weyl fermions can be used to create massless electron"
* There's no such thing as a massless electron. If it's an electron, it'll have a mass of 512MeV. I'm pretty sure the article is just restating that there are Weyl particles.

I'm thoroughly confused by what these things are and how they could perform in interactions - could you start with an electron and somehow get a Weyl particle with the same charge but a "something else" with no charge but has mass? If they're actually fundamental then we should be able to get some data out of a particle accelerator or positron collider.
posted by BigCalm at 12:59 PM on July 23, 2015

Yeah but man those vile gypsum hippies have knowed about crystal power for a long time, dude. Some things in description give me an oddball lift. This is one of them.
posted by Oyéah at 1:51 PM on July 23, 2015

Ummm... PhysicsMatt?

The press-release from Princton is weird. It keeps referring to the lab's findings as Fermions, but the paper in Science only references them being manifest as emergent quasiparticles. It seems more accurate to say "we've discovered/developed a semi-metal material that allows us to demonstrate engery changes in spectroscopy that may be consistent with mathmatical predictions of a (very) hypothetical fermion(?)"

Also, I understand it important to find some plausible technological application for press releases or funding grants. But it's almost comical how often the press release repeats the very specifc application in electronics for a particle that up until now existed only as a place holder in a set of equations proposed by a theoritical physicist in 1929.

But, yeah, my qualifications for commenting on this FPP are undergrad courses in modern physics/ linear algebra, and fitfull trolling of StackExchange forums... soooo..... yeah....
posted by midmarch snowman at 4:12 PM on July 23, 2015

> Hermann Weyl was German, so [vaɪl] ("vile").

"Is it possible his middle name was Mel?" said Sunburnt, desperate to save the joke.
posted by Sunburnt at 4:15 PM on July 23, 2015 [2 favorites]

physicsmatt physicsmatt physicsmatt
posted by lalochezia at 8:11 PM on July 23, 2015 [1 favorite]

physicsmatt has left the building.
posted by jamjam at 8:29 PM on July 23, 2015

let me just say "Weyl to go!!!"
posted by oneswellfoop at 9:10 PM on July 23, 2015

Would you like fries with that ?
posted by y2karl at 8:40 AM on July 24, 2015

posted by fermion at 11:37 AM on July 24, 2015

Note that this Weyl fermion is a quasiparticle like a phonon or hole, not a fundamental physical particle like an electron or proton.
posted by foobaz at 12:36 PM on July 24, 2015

OK, so this isn’t a new particle-particle, like a new electron or new quark or new photon or new Higgs boson or something. It isn’t a fundamental particle that is part of the Standard Model of particle physics or extensions thereof (the known fundamental particles are three copies of spin-1/2 quarks and leptons with each copy containing an “up-like” and “down-like” quark, a charged electron-analog, and a neutrino; the gauge boson force carriers, the photon, W boson, Z boson, and gluon; the scalar Higgs boson; and the not-directly-seen-but-inferred spin-2 graviton). What this is is a “quasi-particle,” which is to say a quantum excitation of a field that was constructed in a very particular material. This is the domain of condensed matter physics, and in fact much of the extremely interesting work —both experimental and theoretical — in quantum field theory (QFT) occurs in condensed matter systems. This is because as a physicist who studies the Standard Model and Beyond the Standard Model physics, I “care” about exactly one set of particles and fields: the ones that we know exist. I might postulate all sorts of other mathematically interesting fields and field theories, ones with nice symmetries and unique bizarre properties, but if the Universe chose for whatever reason not to realize such theories, then it is of limited use to me. Right now, a lot of the interesting ideas that string theorists and their intellectual descendants are working on are applicable or might be applicable in condensed matter systems. You want to realize a conformally symmetric system? Well the real world isn’t one, but the CMX people might be able to build you an approximation of one, and then fiddle with the system so that you can actually futz with “fundamental” parameters and see your theory change.

I’m not a condensed matter physicist, either experimental or theoretical, so I’m not the best person to discuss the possible applications of this result. Maybe none, and frankly the pop-sci write-ups linked here were incoherent to me on that point. I can’t even tell you what knobs you turn to mess with the physical system to realize these constructed field theories. I’m a theorist, so to me most experimental set-ups are Things That I Should Stay Away From. (as a particle theorist I have a non-zero Pauli charge, meaning experiments fail when I get near them)

I’m actually working on a blog post about how to think about particles in QFTs now, though it might take a while to get done. I’ll leave that to be described later, as I think some pictures will help. Suffice to say, for any system described by a field theory, what you have is some physical parameter that can be defined in many places (the field). This might be the height of water in the ocean, or the displacement of a guitar string, or the strength of the electromagnetic field, or the density of electrons which are “free-floating” a the lattice of atoms in many solid-state materials like metals. The key point is that, when you perturb that field at one place, it effects the field nearby, so that displacements or overdensities or whatever can propagate. For water waves, this is due to the interaction of polar water molecules (the same thing that makes a “skin” of surface tension in water. Water is weird you guys). For guitar strings it’s because the atoms at one place are locked in bonds with atoms next to them, so moving the string sideways pulls the atoms next to them. For EM fields, propagation is a result of Maxwell’s equations, and is an example of a “fundamental” field; the photon field. The laws of Nature are such that the EM field perturbed at one point in the right fashion can propagate that perturbation over distances and time; a wave.

Fortunately, as it turns out the free-wave equation is one thing we can solve exactly. The joke in QFT is that we can solve this equation and nothing else. We can’t actually solve interacting fields evolution analytically in most cases, at least not using the basic techniques. Now, if you’re just looking at a field theory, you are doing classical mechanics, and you look at waves moving. Adding the quantum part means that you find that the excitations must come in discrete packets, obtained by “quantizing” the wave-equation. This causes a great deal of confusion to the public, since then people start saying things like “is it a particle or a wave? AAAAAHHHHHH” A quantum particle is an excitation of a quantum field. That’s it. It acts exactly like an excitation of a quantum field, no more, no less. In fact, the laws of Nature governing the behavior of QFTs are the same in general form as classical mechanics (though not the formulation in terms of forces that you learn in Physics 101; you want Lagrangians and Hamiltonian mechanics instead). It’s all perfectly understandable, as long as you stop asking “is this a wave or a particle” and just understand “it’s a quantum field.” Then you realize that instead the real question is why don’t our “particles” here in the macro-scale act like quantum field excitations, since “macrophysics” is just the application of QFTs on a large scale. (the answer is the Planck’s constant is a small quantity compared to the relevant actions at our scales)

So in a quasiparticle system, you’re overlaying a constructed set of fields built in some controlled way so you can get interesting, unique excitations. These fields are built of course from electron fields and quark fields, and so on, in the same way that the “water field” of the ocean is built from electron fields and quark fields, or that protons are built from quark fields. Just on a smaller scale and more finely controlled. The best known quasiparticles are “phonons,” which are quantum excitations of the atomic lattice in metals or other materials. What this means is that it’s a quantum sound wave; like photons or other quantum fields, the vibrational energy, the disturbance in the field, propagates “like a wave” but arrives “like a particle” (to use the usual analogy. Again, this is just standard QFT mechanics).

Ok, so what’s the big deal? The discovery is of a quasiparticle that acts like a “Majorana” fermion. A fermion is a particle that obeys Fermi-Dirac statistics, as opposed to a boson that obeys Bose-Einstein statistics. This means two fermions cannot occupy the same quantum state; the famous Pauli exclusion principle. “Matter” fields are all fermions: electrons, quarks, and the composite protons and neutrons. It’s why we have chemistry: if electrons were bosons, which can occupy the same states as each other, every atom would have all their boson-electrons in the ground state, which is bad for interesting things like life to occur.

Now, it turns out that you can prove mathematically that all fermions in a relativistic QFT are half-integer spin particles, and all bosons are integer spin. I cannot explain this to you, I wish I could. It is true: the electrons and quarks are spin-1/2 (in units of Planck’s constant), the photon, W, Z, and gluon are bosons with spin-1, and the Higgs is a scalar boson with spin-0. Interestingly, in condensed matter systems you can build quasiparticles that have different statistics than either of these; called “anyons.” (Get it?) These require 2-D field theories, which occur in graphene, for example.

We care here about fermions, spin-1/2 fermions actually, which we refer to as “spinors.” Now, the prototypical fermion is the electron, as it is a fundamental (as far as we know) particle, unlike the composite proton made of quarks. The electron has an anti-partner, the positron, with the same mass but opposite “quantum numbers,” including charge (the electron is charge -1, the positron +1, and if only Ben Franklin had picked a different sign in his electrical experiments I wouldn’t have that extra minus sign around and everything would be slightly more sensible). Now, you might call these two different particles, and in fact they are, but the way to split the states of the electron/positron pair are not the way you’d think.

See, one of the oddities of quantum mechanics is that if you measure the spin of a fermion along any axis, you’ll either find the spin aligned with that axis or anti-aligned (the “direction” of a spinning object like a wheel can be obtained as follows: take a wheel, take your right hand and curve your fingers in the spinward direction of the rim. The direction of your thumb is “the spin direction.” It’s an arbitrary choice but once we make it we all can agree. Except, you’ll note, those bastards living in the mirror-world who can’t agree with you about which is the “right hand.” Isn’t that Interesting… ).

We can use the direction of motion of a particle as “the axis” for specificity, and then talk about “left-handed” particles (LH) with spin aligned opposite the direction of travel and “right-handed” particles (RH) with spin pointed in the direction of travel. For the electron/positron pair, there are now 4 possible states: particle LH, particle RH, antiparticle LH, and antiparticle RH. You might want to group them as two particles thusly:
( particle LH, particle RH ) and ( antiparticle LH, antiparticle RH ).

Instead, group them like this:
( particle LH, antiparticle RH ) and ( antiparticle LH, particle RH ).

These two sets of particles each have the minimum number of states you need to describe a quantum spin-1/2 particle. Each is what is known as a “Weyl” fermion. The particle and antiparticle in each Weyl fermion have opposite quantum numbers from each other. For technical reasons, as someone who deals with a theory called “supersymmetry” a lot, I like to deal exclusively with “left-handed” fields, so I call the first Weyl fermion for the electron “e_L” and the 2nd “e_R bar” (or \bar{e}_R in LaTeX code), as I’m now referencing the left-handed fields.

Now, it turns out that each Weyl spinor, by themselves, is massless. Why? Well, it’s because of my instance on calling them “left-“ or “right-spinning.” I defined that relative to some direction of motion. But, imagine that they were massive particles. Then by *definition* they are moving slower than light. Then I can imagine running faster than the Weyl spinor. Do the following experiment: spin your hand in one direction, say clockwise. Now, while continuing to spin it in the same way, move your head to the other side, so your perspective is reversed. What happened? The spin “direction” flipped: right-handed became left-handed.

The same thing would happen if I ran past a Weyl spinor: LH becomes RH, but I wouldn’t see the charge flip. But the Weyl spinor e_L lacks the ability to mathematically describe a right-spinning electron (only a right-spinning positron). I need \bar{e}_R for that. But that’s a different Weyl spinor.

So, for a massive particle, I need two Weyl spinors, and then I need to tie them together, so that when I run past a e_L, it transforms into a \bar{e}_R. This wouldn’t be a problem for a massless particle, since massless particles move at the speed of light, and I can never run faster than that, so no spin-flip is needed. In case you are bothered that one particle is “turning into” another, formally what happens is you are “boosting” from one reference frame to another, and during this boost the “tying together” of the two Weyl spinors allows the quantum fields to mix together. (Something similar occurs when you boost from infinitely far away from a black hole to near the horizon; the field configuration that makes up the vacuum near the horizon isn’t the vacuum far away. This results in Hawking radiation).)

So a massive fermion is two Weyl spinors. In the Standard Model, we don’t have any massless spinors; we thought we might in the case of neutrinos, but we discovered in the 90’s that they have small nonzero masses. I’ll come back to the neutrinos in a bit. Returning to electrons, they have mass, so to full describe them, we need two particles: e_L and \bar{e}_R. Then we tie them together with a “mass” term, forcing both particles to have the same mass, which is why we end up seeing both particles as “the same particle.”

In the Standard Model, this gets even more complicated, since the e_L and \bar{e}_R don’t have the same fundamental quantum numbers, so you can’t tie them together with a mass term. You need the Higgs field for that, which is why we say “the Higgs gives particles mass.” I wrote about it previously here. I *could* write down QFTs with electron-like objects that don’t need a Higgs to have mass, these models are called “vector-like.” The Universe decided not to do that, for some reason. It distinguishes left and right-spinors. So we call the theories that are realized “chiral.” Again, just because I can write down a mathematically valid QFT doesn’t mean its useful in particle physics. However, it might be useful in a condensed matter system, since we can build many more “toy” theories there. Either way, creating a massive fermion out of two Weyl spinors results in a “Dirac fermion,” with four components: LH and RH particle and LH and RH antiparticle. Electrons, muons, taus, and all the quarks are Dirac fermions.

Now, if you look carefully back at what I said, you might see a way out of needing two Weyl spinors to get a massive particle. A massive particle needs a particle-LH and a particle-RH, so that my running past it doesn’t break the consistency of my theory. But, why not just identify the antiparticle-RH that appears in a single ( particle LH, antiparticle RH ) Weyl spinor as the particle-RH. Ta-da, I can get away with a massive particle.

Now, for an electron, I can’t do this. Because an electron has charge. So I can tell the difference between particle and antiparticle. But what if I didn’t have any quantum number like charge to distinguish the particle from the antiparticle? Then I certainly can play this trick. Instead of needing two Weyl spinors, I only need one, and I have a “Majorana fermion.” This is a relatively straightforward realization in QFT mathematics: neutral fermions can be their own antiparticles.

Neutrinos *might* be Majorana. We don’t know. All other fermions are Dirac, but all other fermions have charges and can’t be anything but Dirac assuming they have mass. The neutrinos could have Majorana masses, or Dirac masses. Or both (in which case you end up with two sets of Majorana fields with different masses, and what we know of as “the neutrinos” are the lighter sets. It gets a bit complicated). We are looking actively right now to see if neutrinos are Majorana or not, by looking for rare processes called “neutrinoless double beta decays” that would appear to violate a quantum number (called lepton number) that would otherwise be conserved in the absence of Majorana neutrinos. Right now we’re just pushing down limits, but we have a real shot in the next few years.

However, since we never have seen a Majorana neutrino, it is a valid argument that maybe they can’t actually be realized in real QFTs. Maybe they’re just a mathematical curiosity that can’t happen in the real Universe, just in abstraction. So this demonstration that yes, you can build excitations of spinor fields without Dirac masses is important and interesting in its own right: these things can exist. We just haven’t created a “new particle” in the same way that the Higgs was a new particle.

So that’s the deal: all fermions are built of Weyl spinors. Weyl spinors by themselves must be massless and therefore move at the speed of light. All known fundamental fermions except for neutrinos are “Dirac” (indeed, a very odd type of Dirac fermion called “chiral” which makes the Standard Model more complicated than it needed to be, and thus the Higgs is needed). Neutrinos might be Dirac, or they might be Majorana, and thus their own antiparticle. We have never seen the individual component of the Dirac fermion, the Weyl spinor, outside of our equations, and so purely as a fundamental physics result, this quasiparticle is interesting. I have no idea about the actual applications.

Finally, I say “Weyl” like “vile.” Also, Ettore Majorana died in mysterious circumstances, but is regarded as a pioneer of quantum mechanics and a true genius (a word that does not get thrown around in science as much as it gets thrown around about scientists by non-scientists).
posted by physicsmatt at 12:48 PM on July 24, 2015 [19 favorites]

I am right now, by total coincidence, staying in a hotel in Elmshorn, Germany, which Wikipedia says is the birthplace of Hermann Weyl. This pleases me, because I've been reading some very basic stuff on Lie algebras and classical groups recently, which are areas that Weyl did a lot in.
posted by A dead Quaker at 2:54 PM on July 24, 2015 [1 favorite]

Thanks, physicsmatt, I'm fairly sure I grasped some of that!

Incidentally, if anyone's wondering, "Majorana" (named after Ettore Majorana, who disappeared suddenly under mysterious circumstances while going by ship from Palermo to Naples in 1938 and may have lived another twenty years!) is pronounced /maɪəˈrɒnə/ "my-uh-RAH-nuh" (with "my" as in "not yours").
posted by languagehat at 3:20 PM on July 24, 2015 [1 favorite]

[Thunderous Applause]
posted by midmarch snowman at 7:43 PM on July 24, 2015 [1 favorite]


i) That was an awesome display of how-to-explain science skillz. it needs to be side-barred!

ii) TIL I can now legitimately compare myself to Wolfgang Pauli. I don't even have the disadvantage of being a theorist!
posted by lalochezia at 7:15 AM on July 25, 2015 [1 favorite]

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