GUP/BEB correspondence

TL;DR

This paper develops an expectation-value framework linking the GUP and Bekenstein--bound, revealing how information and confinement scales emerge and connect to entropy and horizon physics.

Contribution

It introduces a fully expectation-value formulation of the GUP/BEB correspondence, resolving EPR tension and deriving confinement scales from a self-consistent approach.

Findings

Reproduces hydrogen and proton radii from GUP

Predicts a crossover from complex to real regimes with symmetry flow

Connects entropy extremality to GUP at the expectation level

Abstract

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.