The electron is round

Yesterday’s Guardian had a short piece about research showing that the electron is, within experimental error, perfectly round. They also mentioned that this has implications for theories of elementary particles: under certain theories including supersymmetry, there would be particles which would bump into the electron and dent it (I paraphrase crudely). There was a reference to a letter in this week’s Nature.

I was a little bit puzzled. First, I thought that the electron was essentially a point particle (or perhaps a wave, depending on your point of view), so how does shape come into it? Second, it seems odd that symmetry of a particle debunks symmetry of a theory of particles.

So I was interested to see the paper.

The teaser on the front cover said “How round is the electron?” and went on to say, “Precision measurements show no dipole asphericity”. The letter itself is entitled “Improved measurement of the shape of the electron”, by J. J. Hudson et al. (Nature 473 (2011), 493–496; doi: 10.1038/nature10104), but does go on to say very clearly that what they were measuring is the electric dipole moment of the electron. They also point out that the standard model predicts that this is eleven orders of magnitude too small to detect, but that alternative theories such as supersymmetry predict a measurable dipole, as also would the existence of an undiscovered interaction breaking the symmetry between matter and antimatter. So this tabletop experiment provides negative evidence for theories being explored by huge particle accelerators and having implications for cosmology (the excess of matter over antimatter in the Universe).

The connection with elementary particle theories arises because we never have a “naked electron”: according to the Uncertainty Principle, virtual particles flicker in and out of existence even in a vacuum on small time scales, and the ones near the electron will affect its measured properties in a way which depends on exactly which elementary particles are popping up.

To measure this, you put the electron in an electric field and look for precession of its spin axis. If you do this with a uniform field, the electron simply accelerates into the container and emits X-rays: useful, but not the point here. So you use the electric field in a polarised molecule, ytterbium fluoride in this case.

It is a lovely paper. If you have had any exposure to experimental design in traditional fields such as agriculture, you may be interested to know that it is a factorial design: there are nine factors, each with two levels; the observations are divided into blocks of size 4096, each containing each of the 512 combinations of factors eight times; the whole experiment involves about 6000 blocks, with re-tuning of the apparatus between blocks. Possible sources of error, both statistical and systematic, are carefully analysed. The conclusion is that a better upper bound is put on the dipole moment, and the results are consistent with this moment being zero.

But I am left with a question. Why does the shape of the electron depend only on the electric dipole moment? Several things occur to me:

  • There might be quadrupole or higher asymmetries in the electric field; absence of a dipole does not imply that the field is spherically symmetric.
  • We know that the electron is not spherically symmetric; it has a magnetic dipole moment which is known to a very high degree of accuracy.
  • According to Einstein, the electric and magnetic fields do not transform separately under uniform motion, but the electromagnetic field transforms in a Lorenz-like way. Could this possibly create an electric dipole in a moving electron? (If I were not so lazy, I suppose I could do the calculation myself.)

The magnetic dipole results from the spin of the electron. This spin is a quantum parameter living in a different space, not a rotation of the electron in our 3-dimensional space (if I understand these mysteries at all).

The other speculation is how the journalists, both at Nature and at the Guardian, picked up the word “shape” and interpreted it. One could argue about whether we should encourage people to think of electrons as little billiard balls or not; but their view on this debate seems clear.

About Peter Cameron

I count all the things that need to be counted.
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2 Responses to The electron is round

  1. Jony Hudson says:

    A bit late to the party here, but I came across your post while sorting through papers (for REF :-(). I’m one of the authors of the paper you talk about above. Thanks for writing the nice post 🙂

    Interesting questions at the end, which I can partially answer:

    Quadrupole and higher moments: are not possible because of symmetry, specifically rotational symmetry and the fact that the electron has spin 1/2. So the dipole moment does fully characterise the “shape”. The result drops out of considering the impact of the rotational symmetry SO(3) on quantum states – one finds a kind of “triangle rule” that constrains the angular momentum of the states and the operator representing the physical quantity of interest. As the electron has spin 1/2 in its initial and final states, only operators with angular momenta 0 or 1 (i.e. scalar and dipole symmetric properties) have non-zero expectations. Hope that makes some sense! Spin-1/2 particles are indeed strange things.

    Magnetic dipole moment: yes, in that sense, and the sense of it having spin, it’s definitely not spherically symmetric. But in terms of its charge distribution it is. Depends on what you mean by “shape” really (see below).

    Relativistic transformation: interesting question, and not one I’ve thought about. One point that might be relevant is that the electric dipole moment is time-reversal-symmetry asymmetric, whereas the magnetic-dipole moment is T-symmetric. I don’t think a Lorenz boost can change one to the other, so it must work out some way. But I’m also too lazy to work it out!

    Finally, shape: yes, that polarised opinion! A lot of people thought it was just plain wrong, or at least dumbing-down. I don’t agree – perhaps obviously, as it was my idea to describe it that way. Being a resolutely experimental type of chap I would argue for a pragmatic description of shape along the lines of “what an electromagnetic probe feels”. This is essentially the definition people use every day when they pick things up. I prefer not to imagine up some mental construction of how the electron “works” internally, and prefer an operational definition like the above. More importantly though, it does a better job of communicating what we do to non-experts than dipole-moment – and I think those grounds alone justify it 🙂


    • Thanks for your response. As is probably clear, I am not a physicist, but this makes me feel I am on the edge of understanding some of these mysteries. At the time I wrote this, I was meeting with statisticians working in experimental design; received wisdom tends to be that huge designs with nice properties are not of any practial interest, and I was glad to be able to wave the paper in my face and show it is not so.

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