QUANTUM ENTANGLEMENT TIME: A NONLOCAL RESOLUTION OF BLACK HOLE SINGULARITIES AND MODIFIED HAWKING RADIATION: The Franquero Entropy Framework (FEF)

I propose a novel quantum gravitational framework where time emerges from relative entropy rather than being an external parameter. The central equation of this theory replaces the Wheeler-DeWitt equation and resolves the problem of time. I derive a modified area law S = A/4G1/1-α, a corrected Hawking temperature T_H = T_Hˢᵗᵈ(1-α), and a singularity-free black hole core with radius rcore = η1/(1+α). The effective field theory predicts modified quasinormal modes and gravitational wave dispersion. Numerical simulations using the fractional Laplacian operator (-∇^2)-α/2 confirm exact convergence with analytical predictions. The modular backreaction operator [K̂, ρ] dynamically stabilizes the system at saturation bounds max|φ| = 10.0000 and max Sᵣₑₗ = 0.1000, preventing ultraviolet/infrared divergences. Current LIGO constraints place α < 0.05 for f > 100 Hz, with next-generation detectors probing the full parameter space. This framework offers a new pathway toward a fully quantum description of spacetime.