As well known, spin could not be thought of as a rotational motion in classical mechanics, i.e. it's an intrinsic property.
But how to prove it? i.e. how to mathematically/experimentally show that the statement, spin could not have any classical (rotational) correspondence, was true?
Edit: "It" here meant:
Is necessarily for spin to be some intrinsic quantity? or rather could be explained, even if it's non classical like Andrei has mentioned.
In experimental setup, could we do a experiment and then claim that it's true for all spin? Because, as Cinaed Simson has mentioned, Stern Gerlach experiment was one experiment to prove this for single electron, i.e. a particular spin $1/2$ system. However, it did not experimentally exclude other spin system jut by itself.
Also, just because the system collapse(in Stern Gerlach), doesn't mean there could not be a orbital motion, right? Quote: Ben Crowell:"...even-even nuclei usually have a first excited state that is spin 2, and this spin is explained correctly in most cases (for open-shell nuclei) as arising completely from the orbital motion of the nucleons (not their spin-1/2's)..." But I didn't quite understand what he meant by even(boson) and odd(fermion). What does even/odd has to do with orbital motion?