Irreversible Diagonalization of Mechanical Quantities and the EPR Paradox

Abstract

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 $\{|\phi_n\rangle\}$ of continuous rotation transformations in Fock states. $\{|\phi_n\rangle\}$'s time reversal $\{ \mathcal{T} |\phi_n\rangle \}$ is the zero point of coordinates q and momentum p, and its arbitrary translation transformation $\{ \mathcal{D} \mathcal{T} |\phi_n\rangle \}$ 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 $\{ \mathcal{U}^ \mathcal{H} \mathcal{U} \neq \mathcal{U} \mathcal{U} ^\mathcal{H} \}$. The EPR paradox is merely a fallacy under the reversible diagonalization of physical reality, it is resolved under irreversible diagonalization.