PET Phased Echo Theory

Microscopic physical laws are typically reversible, yet actions and events appear irreversible at macroscopic scales. We present Phase–Echo Theory (PET), a framework that shifts the focus from state evolution to the recoverability of action histories by observers embedded in the physical system. Actions are modeled as physical interventions within reversible dynamics, while observers are characterized by coarse–graining maps representing limited access to degrees of freedom. We define the echo of an action as the information about that action recoverable from observer–accessible data and show that apparent irreversibility corresponds to the collapse of distinguishability between action histories under coarse–graining, not to destruction of information. We formalize operational reality as an equivalence class of global states, introduce quantitative measures of recoverability and action significance, and provide explicit quantum and classical models demonstrating generic echo collapse. The theory explains the emergence of time’s arrow and the finality of past actions without invoking fundamental irreversibility or modifying microscopic dynamics.