A Brief History of the Electron’s Shape – Part 1

As I’ve shared in a series of blog posts, I currently work on an experiment measuring the electric dipole moment (or EDM) of the electron. Colloquially, we like to call it the “shape” of the electron. (To be a little bit more accurate, it’s really the shape of the electric field produced by the electron.)

While my experiment has been around for about 10 years, the search for the electron EDM has been going on for quite a long time – since the 195os, at least. The motivation has always been the same, which is that the existence of a permanent EDM in any particle (electrons, proton, neutrons, atoms or molecules) would violate the symmetry of time. (Click here if you want to learn more about the pesky details why.) And physicists are always interested to learn if the symmetries they take for granted in their equations are actually followed by nature or not.

Here is a plot taken from the PhD thesis of Paul Hess (2014), a past graduate in my lab. The horizontal axis is year, and the vertical axis is the upper limit of the electron EDM. The units used are e \cdot cm – a unit of charge times a unit of length. (Note that the vertical axis uses a logarithmic scale.) The various markers (squares, triangles, stars, etc.) denote a published experimental result measuring the electron EDM.

What we can learn from this plot is that except for a dry period in the 1970s, there have always been experiments searching for the electron EDM, and while they have not found anything (which is why this is a plot of upper limits to the value of the EDM), they have gotten more and more precise – an average of 1-2 orders of magnitude every decade.

Let’s get into a little bit of this history as seen in the above plot.

The Pioneers – Purcell, Ramsey, Sandars

The history of searching for EDMs in atoms and elementary particles could be said to have begun with short letter to the editor of the Physical Review by Edward Purcell and Norman Ramsey in 1950 (marked with an exclamation mark). Both men would later go on to win Nobel Prizes (Purcell in 1952, Ramsey in 1989).1 The title was simply “On the Possibility of Electric Dipole Moments for Elementary Particles and Nuclei”. Here, they argued that there were no definitive theoretical arguments against the existence of EDMs in elementary particles, so the question becomes, in their own words, “a purely experimental matter.” Thus began the quest to search for EDMs in protons, neutrons, electrons, and possibly all other kinds of fundamental particles.2

(I note that this would mean “EDM” stood for “electric dipole moment” way before it started to stand for “electronic dance music”!)

The subsequent three black shapes on the plot above (Lamb shift, g factor, He scattering) would all set an upper limit on the electron EDM. However, none of these were dedicated experiments specifically looking for it. The game really changed with the second exclamation mark on the plot, which is a paper by P. G. H. Sandars, an experimental physicist at Oxford (who would also teach Stephen Hawking).

Sandar’s paper is very simply titled, “The Electric Dipole Moment of an Atom.” It contains some very technical arguments, but the main point is that we can look for electric dipole moments of electrons and neutrons by looking for an electric dipole moment of an atom. In other words, if the electron EDM is non-zero, then an electron zooming around a nucleus (as it is the case inside an atom) would have a noticeable effect on the properties of the whole atom. Interestingly, this is the case even if the atom itself has a total charge of zero. Prior to this, people had thought (roughly) that neutral, uncharged atoms could not possibly have an EDM. But Sandars showed that this was not the case if you took into account special relativity.

Why is this important? Because it’s quite hard to measure the electron EDM well by examining isolated electrons directly. They are tiny, charged particles. Most free electrons in nature quickly get absorbed up by something. In contrast, doing experiments with neutral atoms is far more flexible. In fact, you don’t need to trap them – you can just spray a gas of atoms in a beam and look at them as they go past by. In addition, Sandars also showed in this paper that the EDM of an electron in certain atoms is significantly enhanced, meaning that if it was non-zero it would show up as a larger, more easy to measure effect in the atom’s energy structure. This can be expressed with the simple formula

d_a = R d_e,

where d_a is the atom EDM, d_e is our old friend the electron EDM, and R is the enhancement factor. For some atoms, R could be very large – Sandars suggested cesium, which was predicted to have R \approx 100.3 This means that the effect of an electron EDM is magnified a hundred-fold if you look for it using cesium.

What a great insight this was! Sandar’s paper can be said to be responsible for the next seven decades of electron (and other) EDM experiments, up to today, including my own experiment. In the next post, we will start talking in more detail about some of these experiments. Stay tuned!

  1. Both also worked at Harvard.
  2. Because I work specifically on the electron EDM, that’s what I’m going to focus on in this post. However, I would suspect that the history of other EDMs – particularly proton and neutron – would be similar, given that some of the experiments searching for them are very similar to those looking for electron EDMs.
  3. It’s pretty difficult to accurately calculate R for a given atom – you have to do detailed calculations on the atomic structure. Roughly, it’s larger the heavier the nucleus of the atom is, which kind of explains why my experiment uses thorium monoxide – thorium is one of the heaviest elements, having an atomic number of 90.

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