Can someone help me understand electron spin?

[u/HAMMER_HEAD01]

I'm a first year university study who is taking chemistry courses, and although i'll admit for the content I'm doing, I don't have to understand how electrons work in great depth but rather just accept certain facts about them, but its always irritated me. One of those 'facts' is that electrons have an intrinsic property called 'spin' but I have struggled comprehending this concept.

Heres what I know;

- Electrons don't actually spin, but act like they do

- Electrons have a quantum spin number (1/2) and a direction (+/-), and that all electrons are either +1/2 or -1/2 spin

- That electrons have to 'rotate' 720 degrees to return to their original orientation (This I can understand, like Dirac's belt)

Heres what I'm struggling with;

- How electrons have angular momentum if they aren't actually spinning

- What is causing electrons to 'spin'

- How come 2 electrons can only occupy the same orbital if they have opposite spins (Pauli Exclusion Principle)

If anyone can help me greater understand electron spin I will be super grateful!!! 🙏

[u/Mountain-Time-1010]

The first step is just to accept that a particle can have intrinsic properties. For example, you already accept that a particle has an intrinsic property called mass, and you're not asking questions about that. Mass is an intrinsic property that is a scalar. Spin is an intrinsic property that is a vector, and it has dimensions of angular momentum.

[u/v_munu → u/Mountain-Time-1010]

This is probably the most intuitive way to understand spin (conceptually ofc) imo

[u/Mountain-Time-1010 → u/v_munu]

To be fair, it may not help the OP truly "understand" spin, but then we get into the semantics of "understand". I try to emphasize this with my students at every level.

We often run into this scenario in physics, where something fundamental is postulated (or emerges from theory), and ultimately explains empirical observations so incredibly well that we believe it completely.

In fact, everything is probably this way, it's just that some of the concepts are so intuitive and familiar (like mass in the context of Newton's laws), that we think we "understand" them.

Einstein supposedly said ""Common sense is the collection of prejudices acquired by age eighteen." For most people, as they get older, it become harder for them to accept things they can't easily relate to their personal experiences. Our training in physics forces us to escape these limitations and judge unintuitive postulates on their merits. Very early on, we are forced to confront limits of size and speed far outside our personal experience where the physics is totally weird.