Thank you for your answer. I have got another question reading your answer. Why are we relying on established quantum facts (i.e. no 3 definite values for spin simultaneously) than hidden variable model? We are rejecting the idea that hidden variable model could give room to both quantum...
Let's consider Bohm's paradox (explaining as follows). A zero spin particle converts into two half-spin particles which move in the opposite directions. The parent particle had no angular momentum, so total spin of two particles is 0 implying they are in the singlet state.
Suppose we measured Sz...