Robert McNees
Physicist Polykarp Kusch was born #OTD in 1911.
Kusch measured the magnetic moment of the electron and found that its value disagrees with naive predictions by a tiny amount — about 1 part in a thousand, or 0.1%.
Quantum Electrodynamics offers a marvelous explanation of this discrepancy.
Image: AIP
Robert McNees
What is a magnetic moment, why does the electron have one, and why is its value different than what one might expect?
Imagine some current circulating in a little loop. In a magnetic field, this current loop 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 of the current. In a magnetic field, the loop wants to turn or flip so that your right thumb points in the same direction as the field.
Robert McNees
One orientation (aligned with the 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 the magnetic moment (proportional to the amount of current and the area of the loop) as well as a direction (which way your thumb is pointing).
Chèvre Mousse
@mcnees Was Polykarp his given name or is it like polymath but for physicists (or fish-enthusiasts?)
Robert McNees
@legendarybassoon I think that every time, but yet, given name.
Robert McNees
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 an electron has an intrinsic (built-in) magnetic moment.
We can write 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. There’s a factor in it, usually denoted by “g,” that should be precisely equal to 2.
Robert McNees
But quantities that show up in our description of fundamental particles like the electron receive quantum corrections — small shifts in their classical value 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 is altered a bit by the electron emitting and then reabsorbing a photon — the quantum of the EM field.
Robert McNees
More complicated versions of this quantum mechanical process can also play out (basically that same simple process nested within itself over and over) leading to additional small shifts in how the electron responds to the presence of a magnetic field. The more complicated the process, the smaller the shift.
The overall result is a tiny correction to this factor “g,” which wasn’t *quite* equal to 2 when Polykarp Kusch (remember him?) measured it.
Robert McNees
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.
Here α is a combination of the electron charge and vacuum permittivity (this is electromagnetism), Planck's constant (and quantum mechanics), and speed of light (and it's relativistic). Its value comes out to about 1/137.
With α=1/137 we find g=2.0023, which explains the 0.1% difference measured by Kusch!
Robert McNees
ASIDE: Even though increasingly complex processes individually give diminishing corrections in perturbative QED, the sheer number of possible processes piles up so fast that this way of accounting for quantum mechanical corrections eventually breaks down.
You can read more in this thread :
https://mastodon.social/@mcnees/109518685793755929
Robert McNees
Resume thread!
In the years since Kusch’s work, precision measurements of the electron magnetic moment have pinned down its g-factor to an incredible 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.)
Robert McNees
The predictions of QED, which require increasingly complex calculations, have kept pace with these refined measurements. It is one of the most precise and well-tested theories ever devised.
Robert McNees
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 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 harder to imagine in recent years. The idea of an immigrant who works at a library and does federally funded curiosity-driven research reads like a script for a GOP attack ad.
Robert McNees
You can see Polykarp Kusch’s 1948 paper with H. M. Foley here:
https://journals.aps.org/pr/abstract/10.1103/PhysRev.74.250
Ref: Kusch, P. and Foley, H. M. "The Magnetic Moment of the Electron". Physical Review. 74 (3): 250–263, (1948)
David Hovis
@mcnees Good ol’ Polykarp. I actually lived in Kusch Hall for all four years of undergraduate.
Robert McNees
☝️Come for the uncommon name, stay for the explanation of the electron magnetic moment and quantum electrodynamics.
Robert McNees
@artologica I do now!!
Michele Banks
@mcnees hi Robert, did you know that St. Polycarp was the patron saint of earache sufferers?
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