Irreversible Diagonalization of Mechanical Quantities and the EPR Paradox

• URL: http://arxiv.org/abs/2409.15379v1
• Date: Fri, 20 Sep 2024 14:26:12 GMT
• Title: Irreversible Diagonalization of Mechanical Quantities and the EPR Paradox
• Abstract summary: 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 $|phi_nrangle$ of continuous rotation transformations in Fock states.
• Score: 2.742138546345534
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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