So Just HOW Do You Measure the Shape of the Electron?

A paper recently published in Nature is generating quite a bit of media buzz. [PhysOrg, BBC, Fox, PhysicsWorld]

The paper is entitled ‘Improved measurement of the shape of the electron’ and describes, well, a new method for measuring the electron’s shape.

I love when physics paper titles are easy to understand :)

Anywho, the main thrust of the paper is that the electron appears to be spherical to a very high degree of accuracy. In fact, the press release from the Imperial College of London states that,

the electron differs from being perfectly round by less than 0.000000000000000000000000001 cm. This means that if the electron was magnified to the size of the solar system, it would still appear spherical to within the width of a human hair.

Wow! Now that is pretty darn spherical.

But now you’re thinking “Hey wait, I thought the electron was a wave? Or a string of energy? Or a cloud of virtual particles? How can it actually be spherical?”

These are excellent questions. Indeed, when we first learn about atomic structure in science class the electron, protons and neutrons are all depicted as perfect spheres. As we learn more, we know that this is only an approximation, an easier way of visualizing the complicated subatomic structure.

The truth is, the electron isn’t (well, probably not) spherical. We don’t really know for sure. Current theories point to the most accurate picture being that the electron is a cloud of particles, blinking in and out of existence, which contribute to its mass and size.

So what this paper and these news outlets are actually saying is that this experiment has shown that the electron behaves as though it is a sphere.

Even more accurately, the electric dipole moment of the electron is approximately zero, which is what we would expect from a perfect sphere with uniform charge distribution.

Ok, I know I just said a mouthful. So let’s go through exactly what I mean about the electric dipole moment, and then we’ll go through what this paper actually measured.

Let’s begin with what an electric dipole moment actually is. Imagine you had two particles, one with a negative charge (-q), and one with a positive charge (+q). If you put these two charges close together, you will create special electric field pattern. This type of arrangement creates what is called an electric dipole moment (EDM). The EDM vector (p) is defined as the of the charge on the two particles (q) times the displacement vector between them (d).

The electric dipole moment vector (blue arrow) points, by definition, from the negative charge to the positive charge.

However, you can also create an EDM if you were to have a particle with an uneven charge distribution.

For example, imagine you had a sphere with a total charge +q. In this case, the charge is evenly distributed and you don’t get an EDM.

A perfect sphere with a uniform charge distribution does not have an electric dipole moment.

But now imagine you had an oddly shaped particle that was “squished” at one end.

In this case, there is more charge at one end of the particle than there is at the other. This uneven charge distribution gives the particle its own EDM.

A not-so-perfect sphere has a non-uniform charge distribution. The higher concentration of positive charge at one end creates an electric dipole moment (red arrow).

So if the electron is not perfectly spherical, it should have an EDM. If it has an EDM, we should be able to measure it to infer the electrons shape. Simple, right?

Now, the Standard Model of Physics predicts that the EDM of the electron is too small for us to currently measure; our equipment is just not sensitive enough. But there are variations on the theory that say the electron’s EDM may actually be larger enough to measure using our current technology.

So finding the electron’s EDM will help narrow down our current theories on the subatomic universe.

The existence of an EDM may also help explain why there is so much matter in the Universe and so little antimatter. If the reason for this apparent imbalance in matter and antimatter is the result of an as-of-yet-undiscovered particle interaction, then the current theories of particle physics predict that there should be a measurable EDM for the electron.

So this explains why this experiment is so important. Now lets explain the experiment.

In a simplified picture, the electron EDM in an applied electric field will either point in the same direction as the field, or in the opposite direction. The energy of an EDM in an electric field depends on the direction of the EDM in relation to the electric field.

This means that the EDMs that align with the electric field will have a different energy than those that align against the field. This difference in energy is proportional to the magnitude of the EDM.

So how does one measure this energy difference? One way is to align the spins perpendicular to the field, which will cause them to precess and you can then measure the precession rate, which is proportional to the energy difference.

This effect can also be described in terms of how the two energy states interfere with one another. This interference between the two states can be measured using an interferometer. If there is an EDM present, then a phase shift should be seen in the interferometer signal. If the applied electric field is reversed, then the phase shift should change sign.

So the authors of the paper went looking for this phase shift. They used molecules of Yttrium Fluoride and fired them at a speed of 590 m/s into an apparatus which has a constant electric and magnetic field.

A radiofrequency pulse is applied which excites the molecules into their respective energy states. They are then allowed to interact for a certain amount of time (a few milliseconds) and it is during this time that the molecules in the different energy states develop a phase difference.

A second radiofrequency pulse is applied and the number of molecules which end up in the lower energy state is measured and is proportional to the phase difference they developed during their interaction time in the electric field.

This phase difference is measured via the applied magnetic field and creates an interference curve.

An example of an interference curve from measuring the phase difference via the magnetic field. (Figure 3 from this paper)

If the electric field is reversed, then a small phase shift in the interference curve is seen. Remember that the phase shift is proportional to the electron EDM.

So by varying certain parameters like the magnetic field and the frequency of the radiofrequency pulses, the authors were able to extract the numerical of the electron EDM from the data.

Over 25 million pulses of YbF were used to collect this data. Not only that, but many experiments had to be done to determine systematic sources of error in the experimental setup.

Things like fluctuations in the applied magnetic field, electric field plate potentials not being completely symmetric, magnetic fields generated in the magnetic shielding during switching of the electric field are all sources of error which had to be considered.

So after all this work they finally arrived at their calculated value of the EDM for the electron. The value turned out to be de = (-2.4 ± 5.7_stat ± 1.5_syst) × 10^-28 e · cm, where the first error term is from statistical uncertainty and the second is from systematic uncertainty.

Notice that the error on this measurement makes it consistent with zero and consistent with previous work.

However, this measurement is 54 times more precise than the previous one the author’s previous measurement and puts an upper limit on the EDM of the electron which must be less than 10.5 × 10^-28 e · cm.

The next step in these types of experiments is to reduce the uncertainty of the measurements. The authors believe that they should be able to do this using cold molecule techniques and get their measurement down into the 10^-29 e · cm range.

Be sure to check out another blog post about this paper by Chad Orzel, author of the blog “Uncertain Principles” and the book “How to Teach Physics to Your Dog”.

Hudson, J., Kara, D., Smallman, I., Sauer, B., Tarbutt, M., & Hinds, E. (2011). Improved measurement of the shape of the electron Nature, 473 (7348), 493-496 DOI: 10.1038/nature10104