Physicist Polykarp Kusch was born #OTD in 1911. His measurements of the magnetic moment of the electron revealed that its value disagrees with naive predictions by a tiny amount — about 0.1%. Quantum Electrodynamics offers a marvelous explanation of this discrepancy.
Image: AIP

So what is a magnetic moment, why does the electron have one, and why is its value different than what we expect? Imagine you have some current circulating in a little loop. In a magnetic field, this loop of current would prefer to orient itself in a particular way.

The rule for how this works is pretty simple. Curl the fingers of your right hand around the direction that the current is moving. If you place the current loop in a magnetic field, it wants to turn or flip so that your thumb points in the same direction as the magnetic field.

One orientation (aligned with the magnetic field) has a lower energy than the other orientation (anti-aligned), the same way a ball at the bottom of a hill has a lower potential energy than it would at the top.

The property of the loop of current that governs the size of this effect is referred to as its “magnetic moment.” There’s a number associated with it (proportional to the amount of current and the area of the loop) as well as a direction (which way your thumb is pointing).

Now, an electron is NOT a little loop of current. But it does have a property called “spin” that causes it to feel the effect of a magnetic field in an analogous way. We say that it has an intrinsic (or built-in) magnetic moment.

We can write down an expression for this magnetic moment that looks an awful lot like the expression we'd write for a loop of current. It follows from the Dirac equation for the electron. And there’s a factor in it, usually denoted “g,” that should be precisely equal to 2.

But many of the quantities that show up in our basic description of fundamental particles like the electron receive quantum corrections — small shifts in their expected values as a result of the virtual processes allowed by quantum mechanics.

Quantum Electrodynamics is the theory that describes electrons, electromagnetic fields, and their interactions. It predicts that an electron’s response to a magnetic field might be altered a bit by the electron emitting and then reabsorbing a photon — the quanta of the EM field.

More complicated versions of this quantum mechanical process can also play out, nested within themselves, leading to additional small shifts in how the electron responds to the presence of a magnetic field.

The result is a small correction to this factor “g,” which wasn’t *quite* equal to 2 when Polykarp Kusch (remember him?) measured it.

Perturbative calculations in Quantum Electrodynamics (QED) predict we should measure a value of g given by:

g = 2 + α/π + 0.656 α²/π² + …

where the “…” are additional, smaller corrections. With α=1/137, this gives g=2.0023 and explains the 0.1% difference measured by Kusch.

(Actually, even though increasingly complex processes individually give diminishing corrections, the number of possible processes piles up so fast that this way of accounting for quantum mechanical corrections in QED eventually breaks down. Read more in the thread below.) https://twitter.com/mcnees/status/1059530403000844290

In the years since Kusch’s work, precision measurements of the electron magnetic moment have pinned down its g-factor out to 12 or 13 decimal places.

That’s like measuring the circumference of the Earth’s equator with a precision comparable to the width of a human hair.

(The circumference of the Earth at the equator is about 40 million meters, and a typical human hair is around 100 micrometers across. That’s about 2 parts per trillion.)

The predictions of QED (which require increasingly complex calculations) have kept pace with these refined measurements, making it one of the most precise and well-tested theories ever devised.

Like many noted American scientists of his generation, Kusch was an immigrant. His parents left Germany when he was one; he became a US citizen at age eleven. He worked at a public library to save money for college, and contributed research during WWII. He won the Nobel in 1955.

That’s a path that has seemed hard to imagine for the last four years, but maybe not so much as of a week ago.