I believe I understand the mathematical derivation of the Dirac equation. I understand how the four 4X4 matrices, and their relation to the 2X2 Pauli Matrices, arise from that derivation. I understand that the 3 spin observables for Fermions are ALSO represented by the 3 Pauli Matrices. But, I do not understand why the 3 Pauli Matrices that arise from the Dirac equation derivation MUST be physical spin. How do we know that it is not just a mathematical coincidence that the 3 Pauli Matrices embedded in the Dirac equation also happen to be the 3 spin observables/operators? Comments? Thanks, in advance.