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I have taken a few quantum mechanics courses recently, which has involved quite a bit of work with quantum spin. The professors keep saying that spin is analogous to a classical body spinning on its axis. However they always make sure we clearly understand this isn't exactly what is happening, because quantum mechanics deals with point particles. Because they don't have extent, there is nothing 'poking out' from the centre of the particle that can spin around the axis.
However it seems to me that if particles in quantum mechanics have this property, it would suggest that they might not be point particles after all, and have some 'size'. No doubt this has been investigated quite thoroughly.
I was wondering then why intrinsic spin isn't considered evidence that particles aren't just points, and have 'size' or 'shape'?