What a tiny electron can tell us about the structure of the universe

What is the shape of an electron? If you recall pictures from your high school science books, the answer seems quite clear: an electron is a small ball of negative charge that is smaller than an atom. This, however, is quite far from the truth.

A simple model of an atom with the nucleus of made of protons, which have a positive charge, and neutrons, which are neutral. The electrons, which have a negative charge, orbit the nucleus.Vector FX / Shutterstock.com

The electron is commonly known as one of the main components of atoms making up the world around us. It is the electrons surrounding the nucleus of every atom that determine how chemical reactions proceed. Their uses in industry are abundant: from electronics and welding to imaging and advanced particle accelerators. Recently, however, a physics experiment called Advanced Cold Molecule Electron EDM (ACME) put an electron on the center stage of scientific inquiry. The question that the ACME collaboration tried to address was deceptively simple: What is the shape of an electron?

Classical and quantum shapes?

As far as physicists currently know, electrons have no internal structure – and thus no shape in the classical meaning of this word. In the modern language of particle physics, which tackles the behavior of objects smaller than an atomic nucleus, the fundamental blocks of matter are continuous fluid-like substances known as “quantum fields” that permeate the whole space around us. In this language, an electron is perceived as a quantum, or a particle, of the “electron field.” Knowing this, does it even make sense to talk about an electron’s shape if we cannot see it directly in a microscope – or any other optical device for that matter?

To answer this question we must adapt our definition of shape so it can be used at incredibly small distances, or in other words, in the realm of quantum physics. Seeing different shapes in our macroscopic world really means detecting, with our eyes, the rays of light bouncing off different objects around us.

Simply put, we define shapes by seeing how objects react when we shine light onto them. While this might be a weird way to think about the shapes, it becomes very useful in the subatomic world of quantum particles. It gives us a way to define an electron’s properties such that they mimic how we describe shapes in the classical world.

What replaces the concept of shape in the micro world? Since light is nothing but a combination of oscillating electric and magnetic fields, it would be useful to define quantum properties of an electron that carry information about how it responds to applied electric and magnetic fields. Let’s do that.

This is the apparatus the physicists used to perform the ACME experiment. Harvard Department of Physics, CC BY-NC-SA

Electrons in electric and magnetic fields

As an example, consider the simplest property of an electron: its electric charge. It describes the force – and ultimately, the acceleration the electron would experience – if placed in some external electric field. A similar reaction would be expected from a negatively charged marble – hence the “charged ball” analogy of an electron that is in elementary physics books. This property of an electron – its charge – survives in the quantum world.

Likewise, another “surviving” property of an electron is called the magnetic dipole moment. It tells us how an electron would react to a magnetic field. In this respect, an electron behaves just like a tiny bar magnet, trying to orient itself along the direction of the magnetic field. While it is important to remember not to take those analogies too far, they do help us see why physicists are interested in measuring those quantum properties as accurately as possible.

What quantum property describes the electron’s shape? There are, in fact, several of them. The simplest – and the most useful for physicists – is the one called the electric dipole moment, or EDM.

In classical physics, EDM arises when there is a spatial separation of charges. An electrically charged sphere, which has no separation of charges, has an EDM of zero. But imagine a dumbbell whose weights are oppositely charged, with one side positive and the other negative. In the macroscopic world, this dumbbell would have a non-zero electric dipole moment. If the shape of an object reflects the distribution of its electric charge, it would also imply that the object’s shape would have to be different from spherical. Thus, naively, the EDM would quantify the “dumbbellness” of a macroscopic object.