GUP/BEB correspondence

TL;DR

This work develops an expectation-value formulation of the GUP/BEB correspondence, showing that information backreaction at saturation cancels residual uncertainty in chosen sectors and enables operational simultaneity of conjugate observables, resolving the EPR tension without hidden variables. By equating the GUP deformation to the BEB information budget, a self-consistent framework fixes confinement scales that reproduce the hydrogen Bohr radius and the proton radius, and reveals an information-controlled transition from a short-distance complex regime to a real Lorentzian regime with a symmetry flow from SU(4) frames to SO(1,3) and a scale-transmutation to SU(4)_c. The paper further connects generalized entropy at horizons to an effective Planck constant, tying horizon entropy directly to GUP at the expectation level. Together, these results imply a deep link between quantum information bounds, spacetime symmetry, and confinement physics, with open directions for covariant generalizations and experimental tests.

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.