Subtime: Reversible Information Exchange and the Emergence of Classical Time

We formalize the concept of subtime - a reversible mode of information interchange within entangled systems - and show how classical time emerges as an asymptotic limit through decoherence. Building on the photon clock model, in which a single photon confined between two ideal mirrors creates an alternating causality regime, we develop a process-theoretic formalization using the Oreshkov--Costa--Brukner framework extended with an explicit time-reversal duality condition. We introduce Perfect Information Feedback (PIF) as the information-theoretic realization of this reversibility, demonstrating that mutual information is conserved in any closed causal loop and that entropy quantifies the degree of unreflected causality. We define the Reversible Causal Principle (RCP): every causal relation possesses a conjugate dual, and entropy, energy dissipation, and the classical arrow of time appear only when these alternating components decohere or fail to reflect perfectly. The framework unifies Wheeler--Feynman absorber theory, Bennett's reversible computation, Shannon's communication theory, and the process matrix formalism under a single symmetry principle, and identifies experimentally accessible signatures in reversible digital links and quantum switch experiments. The arrow of time, in this picture, records the universe's imperfect causal echo.