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.