How can a particle with no size have angular momentum? I was recently reading about Higgs boson and particle spin and I stumbled upon a question that explains what is spin.
It explains that electrons have no size yet they have angular momentum. I don't understand what exactly is meant by that. Does it refer to the angular momentum of the magnetic field? I just don't see how something with no size can have any sort of angular momentum. 
 A: It means exactly what it says--- the point particle has an angular momentum. In quantum mechanics, angular momentum is dimensionless (since hbar has units of angular momentum), and saying the spinning electron has angular momentum means that if you have a large number of electrons with spin up sitting on a disk (like a disk magnetized with a B field going in one direction perpendicular to the disk), and you suddenly reverse the B, so that all the electrons flip their spin to the other direction, then the disk starts spinning to conserve the angular momentum of the flip. This is the famous Einstein deHaas experiment that established that magnetization is carried by electron spin.
A: As a answer, first I'd like to ask why you're asking a quantum mechanics problem with classical mechanics mental model.
There are two types of angular momentum in quantum mechanics:


*

*Orbital angular momentum, which is a generalization of angular momentum in classical mechanics (L=r×p). I think, you shouldn't have problem with this because Orbital has size.

*Spin, which has no analogue in classical mechanics. You can understand it as a number appeared in quantum equation. It can be understood like charge(with physical dimension), which is a number  to denote one of basic attributes of particles. Yes, Spin does have physical dimension of angular momentum. But, its because it is a type of angular momentum, mathematically.
