A Relativistic-Computational Bound on Information Recoverability: From Quantum Coherence to Black Hole Page Time

We propose a unified operational framework for the emergence of irreversibility in physical systems. Building on the Relativistic Halting perspective, we introduce the dimensionless Relativistic Information Ratio, Ω, defined as the ratio of the causal time window available to an observer to the computational time required to reverse the system's instantaneous dynamics. Crucially, we argue that the quantum-to-classical transition is not a consequence of accumulated historical complexity, but a property of the current action: quantum behavior corresponds to actions where the complexity generation is reversible (Ω >> 1), while classical behavior corresponds to actions where the generated complexity renders the state effectively undecidable (Ω