3 ms·
There's an accidental similarity between the groups SO(3) and SU(2), which works for spin. There are other quantum numbers such as flavor SU(3) for there is no
by tagrun 10y ago
There's an accidental similarity between the groups SO(3) and SU(2), which works for spin. There are other quantum numbers such as flavor SU(3) for there is no mathematical coincidence and such analogies won't work.
The differences between SU(2) and SO(3) go beyond just "rotate 720 rather than 360 and you're back where you started".
While I understand the urge of expressing new things in terms of what you know, sometimes, analogies aren't helpful and distort reality, and you just need to accept that there can be things in the nature that doesn't correspond to anything in your daily life in the real sense of the word.
That being said, the original parent post (which I quoted, so it's actually there) is total nonsense.
- stephengillie 10y agoCould you recommend a good entry point for understanding group theory? It's always been particularly impenetrable, and the wiki page doubly so. Book or video or blog post or even private college course - anything would be appreciated. Is spin the exact same physical phenomena as 'macroscopic' spin, but on a quantum scale? If not, just curious, why use the same word?
- tagrun 10y agoI can recommend Howards Georgi's Lie Algebras in Particle Physics which is a good introduction in the context of particle physics (yes, it covers both Lie algebras and groups). No, it is nothing like the angular momentum of a spinning object. The name is rooted in a historical misconception. It is a form on angular momentum, which caused the misunderstanding. As of today, we still do not have a deeper understanding of spin in quantum mechanics: it's just some intrinsic angular momentum with SU(2) symmetry, and the value of angular momentum is in general different between particles (corresponding to the irreducible representations of SU(2), and the angular momentum is mostly 1/2 or 1 in units of reduced Planck constant except for some exotic/composite particles).