J. Heisenberg Uncertainty and the 2D spin

The 2D structured spin gives an example which provides a basic understanding of how Heisenberg Uncertainty Principle works. The mathematical basis for this Principle follows because observables in quantum mechanics sometimes do not commute.  Examples are position-momentum; energy-time; difference orthogonal components of the angular momentum vector. For spin, the Pauli spin operators do not commute.

Immediately it should jump out that the two components of the 2D spin are orthogonal and cannot simultaneously be measured. Each carries a magnetic moment and hence each has a spin operator which must be orthogonal. It follows from Heisenberg that only one of the two components can be measured in one experiment. One is always missed.

This point becomes important in analyzing EPR experiments. It also means that one cannot properly characterize spin by measuring it because the √2 spin states cannot be observed.

Here, my plan is to give a visualization of how only one of the two axes can be measured and the other one not.