I'm a little confused about the idea of spin. It's been non-technically described to me as "like magnetic dipole moment", except only two possible "directions". But I feel like that's a bad analogy, because direction is relative and 3 dimensional.
I understand that under the Ising model, spin has +1 or -1 values, and in the case of a pi meson, 0 (is that because of an alignment of quark-antiquark spins?)
So, then, spin of a particle would be the sum of spin of its quarks, which explains half-spin?
And in light of a recent observation of photons behaving as both a wave and a particle in a single experiment, could one say that spin direction is the direction of the valley and the peak of a wave, and the angular momentum is simply the two dimensional gradient of the wave itself? In other words, is the angular momentum of spin measured as the "up" and "down" "motion" of the compression of energy fields where the spin direction is the alignment of the "up" and "down" peaks/valleys, relative to whatever dimension on which the wave propagates?
I guess what I'm getting at is I'm trying to understand whether particles are just wave interference patterns (actual, not probability) of compressed and decompressed energy across the extra dimensions which we do not call home.