New Method of Obtaining the Kochen-Specker Theorem

We derive a new type of no-hidden-variable theorem based on the assumptions proposed by Kochen and Specker. We consider N spin-1/2 systems. The hidden results of measurement are either $$+1$$ or $$-1$$ (in $$\hbar /2$$ unit). We derive some proposition concerning a quantum expected value under an assumption about the existence of the Bloch sphere in N spin-1/2 systems. However, the hidden variables theory violates the proposition with a magnitude that grows exponentially with the number of particles. Therefore, we have to give up either the existence of the Bloch sphere or the hidden variables theory. Also we discuss a two-dimensional no-hidden-variables theorem of the KS type. Especially, we systematically describe our assertion based on more mathematical analysis using raw data in a thoughtful experiment.