The Heisenberg Andserty Principle Is a Statement About Quantum State Relationships

The heisenburg andserty principle is a statement about what how quantum states relate to observables. In hilbert space, in the space of all possible quantum states, a spin in one direction, let's say spin up, is perpendicular,. as a vector in hilbertspace, to spin in the other direction, which is spin down. So just like position mome or complementary variables in the heisemberg on certainty principle, so are thespin in the z direction and the spin in the ex direction.