[WeniTheElder]

I still dont grasp what a spin of an electron is. The image of a spinning sphere doesnt help - as if you can roll this sphere you will see there is no different spin - it has only one spin direction and you cant differ two spheres apart by its spin. Even worse if I would consider a point - how should it spin as it is the same in every direction of the space. As it is described by mathematical spinors (tensor) I still would like to see an equivalent in my sphere of experience to grasp it completely. (spin plus minus 1/2). Odd enough the spin can combine and couple with the angular momentum it feels like the spin should be something that ought be visualised.

[vrighter]

don't imagine a ball spinning. Imagine a spinning top. It acts as a gyroscope. When a force is applied to it it tries to resist it, but it also causes precession. The equations for that precession can be used for electrons in a particular context. This is how we discovered that particles have angular momentum in the first place. Whatever we measure in that context, is what we call a particle's spin. It's all about the angular momentum and the precession caused by an external force.

tldr: nothing is spinning in a particle. what we refer to as spin refers to how angular momentum is affected by external forces, which happens to behave similarly to a spinning gyroscope. So we called that property "spin"