GUP/BEB correspondence
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912737462845440 |
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| author | Ali, Ahmed Farag |
| author_facet | Ali, Ahmed Farag |
| contents | We develop a fully expectation--value formulation of the GUP/Bekenstein--bound (BEB) correspondence, building on \cite{Ali:2024tbd,Ali:2022ckm,Ali:2022ulp}. Using Dirac's commutator--Poisson equivalence, the BEB supplies an information backreaction on the GUP--deformed bracket; at saturation the residual uncertainty in a sector cancels, enabling \emph{operational} simultaneity of conjugate expectations and resolving the EPR tension without hidden variables. A single self-consistency then fixes intrinsic confinement scales: the full (linear$+$quadratic) GUP reproduces the hydrogen Bohr radius (electron) and the proton charge radius (hydrogen nucleus). The same correspondence predicts an information--controlled crossover from a short--distance complex (evanescent) regime to an emergent real (Lorentzian) regime, with a symmetry flow from complex $SU(4)$ frames to $SO(1,3)$; under scale transmutation the short--distance $SU(4)$ is repurposed as the Pati--Salam $SU(4)_c$. Incorporating exterior--field entropy at horizons defines an effective Planck constant consistent with generalized--entropy extremality, tying entropy--area physics directly to the GUP at the expectation level. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08661 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | GUP/BEB correspondence Ali, Ahmed Farag General Relativity and Quantum Cosmology We develop a fully expectation--value formulation of the GUP/Bekenstein--bound (BEB) correspondence, building on \cite{Ali:2024tbd,Ali:2022ckm,Ali:2022ulp}. Using Dirac's commutator--Poisson equivalence, the BEB supplies an information backreaction on the GUP--deformed bracket; at saturation the residual uncertainty in a sector cancels, enabling \emph{operational} simultaneity of conjugate expectations and resolving the EPR tension without hidden variables. A single self-consistency then fixes intrinsic confinement scales: the full (linear$+$quadratic) GUP reproduces the hydrogen Bohr radius (electron) and the proton charge radius (hydrogen nucleus). The same correspondence predicts an information--controlled crossover from a short--distance complex (evanescent) regime to an emergent real (Lorentzian) regime, with a symmetry flow from complex $SU(4)$ frames to $SO(1,3)$; under scale transmutation the short--distance $SU(4)$ is repurposed as the Pati--Salam $SU(4)_c$. Incorporating exterior--field entropy at horizons defines an effective Planck constant consistent with generalized--entropy extremality, tying entropy--area physics directly to the GUP at the expectation level. |
| title | GUP/BEB correspondence |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2511.08661 |