Chirality and the Positron’s Mustache

Woke up this morning to the happy news that my post “The Fine Structure Constant is Probably Constant” walked away with the Charm Quark (i.e., tied for third place) in this year’s 3QuarksDaily science blogging prizes. Many thanks to Lisa Randall for judging and Abbas Raza and the 3QD crew for hosting. And of course congrats to the other winners:

  1. Top Quark: SciCurious, Serotonin and Sexual Preference: Is It Really That Simple?
  2. Strange Quark: Anne Jefferson, Levees and the Illusion of Flood Control
  3. Charm Quark: Ethan Siegel, Where Is Everybody?

I already have a great nominee for next year’s contest. One of the most confusing things in particle physics is the notion of “chirality.” The related notion of a particle’s “helicity” is relatively easy to explain — is the particle spinning in a left-handed or right-handed sense when compared to its direction of motion? But a massive particle need not have a direction of motion, it can just be sitting there, so the helicity is not defined. Chirality is the same as helicity — left-handed or right-handed — for massless particles moving at the speed of light, but it’s always defined no matter how the particle is moving. It had better be, since the weak interactions couple to particles with left-handed chirality but not ones with right-handed chirality! (And the opposite for antiparticles.)

It all gets a bit heady, and you can’t give a real explanation without going beyond simple pictures and actually talking about the quantum wave function. But Flip Tanedo at Quantum Diaries has given it an heroic effort, which I insist you go read right now. I don’t want to reproduce the whole thing — Flip was more careful and thorough than I ever would have been, anyway — but I will tease you with this one picture.

Isn’t that the cutest pair of elementary particles you’ve ever seen? I smell a Quark in this lepton’s future.

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16 Responses to Chirality and the Positron’s Mustache

  1. Low Math, Meekly Interacting says:

    Holy crap, that was awesome.

  2. ad says:

    I’m wondering if in the Zitterbewegung interpretation of the Dirac equation since all particles are moving at velocity c that helicty and chirality will always be the same?

  3. Cristi says:

    In the Zitterbewegung interpretation the electron rotates at the speed of light, in a helical motion. In one reference frame it may appear to rotate clockwise, and in another counterclockwise with respect to the relative motion. So I guess the helicity/chirality distinction is maintained.

  4. Sili says:

    I thought it was supposed to be goatees.

  5. David says:

    I was a chemistry major and chirality in chemistry is easy to understand. I read that article and still don’t understand what he means by chirality. Also, how is an electron different from an anti-positron? They travel in the same direction, they spin in the same direction, they have the same charge and mass how are they not the same particle?

  6. James says:

    Hmm, not sure I like describing a right-handed electron as an anti-positron. Seems to be just confusing the matter, so to speak.

  7. Even cuter particles can be found in The Particle Zoo iPhone app. I especially like the three-eyed Strange Quark and the masked Neutrinos. And you can buy plushie versions of any of the particles.

  8. Anchor says:

    @#6 James: That’s what I was thinking too.

  9. Flip says:

    Hi Sean! Congrats on the charm quark win, and thanks for the very kind shout out.

    I’m not used to replying to comments on *other* blogs, but since I’m here I thought I’d join in on the discussion. :-)

    @#5 David: Hi! This is mostly my fault for not writing things more clearly, I apologize. The point is that there are four particles: the electron, the anti-electron, the positron, and the anti-positron. The electron and anti-electron interact with the W-boson. Meanwhile, the positron and anti-positron do not interact with the W boson.

    You’re right that the electron and the anti-positron have the same spin, but they have totally different interactions with the other particles in the theory.

    Ultimately, the thing which I call a “physical electron,” i.e. the thing which most people mean when they say “electron,” is a combination of the electron and anti-positron. This mixing occurs because of a [Dirac] mass. Note that this one “physical electron” is really the combination of *two* chiral particles: the electron and the anti-positron.

    @#6 James: I agree, it’s not optimal. And again, this is a problem with nomenclature. Most physicists call these things eL and eR. But this is the thing which is rather subtle because at first glance one can’t tell if the “left” and “right” refer to helicity or chirality. I wanted to use “electron” and “positron” to refer to the states of different chirality so that I could try to emphasize that these are two different particles (i.e. they have different Standard Model quantum numbers). Of course, this requires that one momentarily lets go of the conventional nomenclature that the electron and positron are mass basis Dirac fermions and are anti-partners of one another.

    I’ll see if I can add some remarks to help clarify this (giving credit to both of you for pointing out the confusion.)


  10. Razib Khan says:


  11. Erwin says:

    Far from being an math-head but from what I understand, could a simple analogy in every-day life for chirality not be left- or right-handed thread? The direction of the thread is fixed, but it gives a different spin depending on the relative direction your particle is moving.

  12. Pingback: Charity Pitches | Cosmic Variance | Discover Magazine

  13. Jimbo says:

    Of course the fine structure constant (alpha) IS constant: It has NO Choice except to follow its partner in crime, the cosmological constant:

    R^2*CC = {lp/R}^4 = 1.08E-81 ,

    where R = alpha* lambda, is the Lorentz radius of the electron, lambda the electron Compton wavelength, & lp the Planck length.

  14. David George says:

    #14 Jimbo — I have an equation too! It illustrates where the fine structure constant appears as a characteristic of the electron-proton system. The equation is: delta A(e) = 4 pi alpha^2. It means that the change in the surface area of the electron per rotation is 1/137 of the radius of the electron — if the radius is set to unity (a “natural” selection). (Otherwise, delta A(e) = 4 pi alpha^2 R^2.) This is the scenario in which the electron is a rotating sphere occupying the orbital midway between the Compton and Bohr radii (separated from each by the factor of alpha & inverse alpha).

    Change in surface area means change in circumference, meaning change in frequency/wavelength. The change in frequency of an electron during one rotation (I think) is the reason why measurements cannot guarantee the value. So the probability approach becomes a measurement of the position of the electron (in its oscillation cycle) at the time of the measurement.

    The change in frequency is interpreted in quantum mechanics as a wave packet, ultimately a statistical ensemble (Einstein’s words, not mine). But really there is just this oscillating rotating sphere of rotating space.

    The equation in #13 is also awesome. I never saw it before. Where does it come from?

  15. Jimbo says:

    David G,
    Have to be careful with mechanical inferences regarding the spinning classical electron. An erroneous result of which is that the `surface’ spins ~ 137 c, obviously a relativistic no-no. Several people have deduced relations analogous to the one posted above, going back to Zeldovich in the late 60’s. The precise form was deduced by Beck in `07. Clearly the electron plays a special role in the cosmos.

  16. David George says:

    #15 Jimbo,

    However if you take Schrodinger’s idea of the “smeared out” charge and stipulate that the electron is a massless superconducting current, then it moves at c. The current must flow in such a way that it resembles a triaxial rotation. Then it is possible to find the electron’s spatially extended (large) dimensions, and using the fundamental constants it actually “plugs in” to the conventional electron-proton scenario (but no quarks please). Additionally it makes plain what is going on with “spin”.