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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2409.15379 |
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| _version_ | 1866913513934422016 |
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| author | Liu, Tao |
| author_facet | Liu, Tao |
| contents | 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 $\{|ϕ_n\rangle\}$ of continuous rotation transformations in Fock states. $\{|ϕ_n\rangle\}$'s time reversal $\{ \mathcal{T} |ϕ_n\rangle \}$ is the zero point of coordinates q and momentum p, and its arbitrary translation transformation $\{ \mathcal{D} \mathcal{T} |ϕ_n\rangle \}$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15379 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Irreversible Diagonalization of Mechanical Quantities and the EPR Paradox Liu, Tao Quantum Physics 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 $\{|ϕ_n\rangle\}$ of continuous rotation transformations in Fock states. $\{|ϕ_n\rangle\}$'s time reversal $\{ \mathcal{T} |ϕ_n\rangle \}$ is the zero point of coordinates q and momentum p, and its arbitrary translation transformation $\{ \mathcal{D} \mathcal{T} |ϕ_n\rangle \}$ 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. |
| title | Irreversible Diagonalization of Mechanical Quantities and the EPR Paradox |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2409.15379 |