You may think this is a rather poor joke: the spin of spin-1/2 particles must be 1/2, right?
Right. Yes. Let me ask you this: one half of what? What’s the unit here? And why would we take half of it?
If you are a somewhat informed reader, you’ll will be able to answer this: it’s a half-unit of Planck’s (reduced) quantum of action. It must be, right? Spin is expressed in units of ħ/2, isn’t it?
Right. Or not so bad as an answer, at least. Next question: if the Planck-Einstein relation tells us that physical action must come in full (not in half) units of h (we have no need for an E = hf/2 or E = hω/2 relation, do we?), then why would angular momentum (because that’s spin – orbital or spin angular momentum – if you express it in units of ħ or ħ/2, isn’t it?) come in half-units of ħ?
It is just one of those quantum-mechanical rules one cannot really understand, isn’t it? And so we should just accept it and go along with the rest of the story, isn’t it?
Well… No! We don’t agree. It’s not just one of those rules: we should understand what this is about. And the good news is this: we can. Moreover, it is actually not all that difficult. We’ve got the answers: check out the Matter page of this site.
Cheers – JL