What is the moment of inertia of a free electron?

Well, elementary particles have no moment of inertia $$I$$. But what is the nearest possible answer to the question for a free, spinning electron?

In general, one has a relation with spin $$J$$ given by
$$J = I \omega.$$ For an electron, the magnitude of spin is $$J=\sqrt{3/4} \hbar$$. But since $$\omega$$ is not defined, there is no way to speak about a moment of inertia.

Or can one say more?

• The classical picture of angular momentum doesn’t work for spin angular momentum. Electrons are not actually spinning like a ball. – G. Smith Jul 24 at 23:28
• True! Indeed, I did not say that they were spinning like a ball - just that they are spinning. There are may other ways to spin... – Christian Jul 26 at 5:17
• I’m not clear on whether you got my point or not. They’re not spinning like anything spins in classical mechanics. “Spin” in QM is essentially just a confusing and unfortunate historical misnomer. – G. Smith Jul 26 at 5:26
• See motls.blogspot.com/2012/12/… for a different point of view. – Christian Jul 26 at 15:31
• Lubos is a member of PSE, so perhaps he will answer and tell you what the electron’s moment of inertia is. – G. Smith Jul 26 at 16:29