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okaythanksbud

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1: clearly there's no objective "up" or "down"--the directions are measured relative to the magnetic field, correct? And well always find just 2 spots of equal and opposite distance on the detector, implying the magnetic moment of the electron always has z component (well take z as the direction the B field is pointing) of either +/-K for some value K?

2: if our B field only varies in the direction it points (i.e if it points in the z direction it'll change only over the z direction), our results will only tell us about the spin in the z direction. is there anything we can infer about the spin in the other 2 dimensions? I'm assuming it is still in superposition since we dont actually measure these components, but in general can the spin in either of the two dimensions be nonzero? My question is essentially whether or not upon measurement the particle aligns its spin entirely with the B field. This would make some shred of sense since its potential energy would be extremized but it seems too idealized

3: is the presence of only two dots true in general? or can the spin take on different values like the energy of a particle in a box? Im assuming we'll get a discrete spectrum but am wondering how many values it can take.

4: if (2) is not true (dipole moment can have nonzero components orthogonal to the B field), wouldn't induced torque complicate the experiment? Im also assuming this would cause a range of values on the detector since the torque would change the z component of the magnetic moment over time, so discreteness doesn't seem like it would hold (there would have to be a cluster around.

5: again, if (2) is not true, can't we determine the total spin using a magnetic field like B=<c1x,c2y,c3z>? This should measure the spin in all 3 dimensions. would the total angular momentum be quantized like <Lx,Ly,Lz> with each L only being able to take on a discrete set of quantities?

So overall I'm wondering if angular momentum in a particle is just quantized in each dimension (so that if measured the spin can take on a wide range of values, but discrete), and if the SG experiment just uncovers the spin in one dimension to make the interpretation simpler.