Modular Entropy Retrieval in Black-Hole Information Recovery: A Proper-Time Saturation Model
Evlondo Cooper · Preprints.org · 2025
The black hole information paradox persists because no existing framework shows how the encoded information becomes operationally accessible to a physical observer. Starting from Tomita–Takesaki modular flow, we derive an observer-dependent retrieval law: dS_retrieved/dτ = γ(τ) [S_max − S_retrieved(τ)] tanh(τ / τ_char) This converts global entropy conservation into a Lorentzian-causal, time-resolved recovery process. The law predicts class-specific trajectories and an acceleration-dependent g^(2)(t1, t2) interference envelope detectable in current Bose–Einstein condensate analog black holes (10–100 ms). Simulations on a 48-qubit MERA lattice (bond dimension 8) confirm numerical robustness, and an observer-modified Ryu–Takayanagi prescription embeds the framework in AdS/CFT without requiring replica-wormhole or island constructions. By replacing ensemble-averaged Page curves with a causal, observer-specific mechanism, the model transforms the paradox from a bookkeeping puzzle into a falsifiable dynamical prediction. Here, S_max is the Bekenstein–Hawking entropy, γ(τ) is the modular-flow retrieval rate, and τ_char is a characteristic proper-time scale (geometric units c = G = 1).