Standard Model 5: Spin-1/2 Particles

One of the simplest quantum systems is a spin-1/2 particle, also known as a spinor. If we measure the angular momentum of a spin-1/2 particle along any axis, there are two possible outcomes: either the angular momentum along that axis is +1/2, or it’s -1/2.

How is it possible for this to be true along every axis? Here I explain this, using the basic rules of quantum physics described last time. In particular, I say how any point on a sphere of radius 1/2 gives a quantum state of the spin 1/2 particle—and vice versa!

Using this, we can understand things like the famous Stern–Gerlach experiment, where we measure the angular momentum of a spin-1/2 particle first along one axis, and then along another.