Irreversible Diagonalization of Mechanical Quantities and the EPR Paradox

The closure relation of quantum mechanical projection operators is not entirely true; it can be strictly falsified under unitary transformations in Fock states. The angular momentum $J_x$, $J_y$ and $J_z$ are simultaneously diagonalized under the orthonormal set $\{\mathrm{\mid }{\phi }_n⟩\}$ of continuous rotation transformations in Fock states. $\{\mathrm{\mid }{\phi }_n⟩\}$'s time reversal $\{\mathcal{T}\mathrm{\mid }{\phi }_n⟩\}$ is the zero point of coordinates q and momentum p, and its arbitrary translation transformation $\{\mathcal{D}\mathcal{T}\mathrm{\mid }{\phi }_n⟩\}$ diagonalizes both coordinates and momentum simultaneously. The abstract representation of the Dirac state vector implies the symmetry breaking of the non-Abelian group unit matrix $\{{\mathcal{U}}^{\mathcal{H}}\mathcal{U}\mathrm{\ne }\mathcal{U}{\mathcal{U}}^{\mathcal{H}}\}$. The EPR paradox is merely a fallacy under the reversible diagonalization of physical reality, it is resolved under irreversible diagonalization.