Irreversible Diagonalization of Mechanical Quantities and the EPR Paradox

TL;DR

This paper challenges the traditional understanding of quantum measurement by proposing that the EPR paradox is a fallacy that can be resolved through irreversible diagonalization of physical quantities, questioning the closure relation of projection operators.

Contribution

It introduces a new perspective on quantum measurement, emphasizing irreversible diagonalization to resolve the EPR paradox and questioning the validity of the closure relation in quantum mechanics.

Findings

Closure relation of projection operators can be falsified under unitary transformations.

Simultaneous diagonalization of angular momentum and coordinates is achieved in Fock states.

EPR paradox is resolved by irreversible diagonalization, not reversible.

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.