23 upvotes, 1 direct replies (showing 1)
View submission: Why are spin states in the x, y, and z directions not orthogonal?
Spin states are not vectors in 3D space, they are vectors in C^2 , a two dimensional complex vector space. As another example, a 2pi rotation around the z axis does not leave a spinor untouched, like it would leave an R^3 vector: it introduces a negative sign (phase term). You need a 4 pi rotation instead.
The fact that they are measured in some direction does not mean that the spin states themselves are actual vectors pointing in these directions, basically.
Comment by waffletastrophy at 19/04/2024 at 07:37 UTC
4 upvotes, 2 direct replies
Sure, mathematically I can understand this. What is the intuition behind it? Why is a particle's spin along the x-axis related to its spin along the y-axis, rather than them being independent of each other? Is that "just the way it is" or is there some deeper reason?