Phase-Echo-Theory

Phase–Echo Theory (PET) is a foundational theoretical framework that examines irreversibility, memory, and the apparent disappearance of the past in systems governed by reversible microscopic dynamics. Rather than modifying fundamental physical laws, PET reframes irreversibility as an operational phenomenon arising from limited observer access to information.

In this work, actions are modeled as physical interventions within globally reversible dynamics, while observers are treated as embedded subsystems characterized by coarse-graining maps that restrict accessible degrees of freedom. The theory introduces the concept of an action echo, defined as the amount of information about past actions that remains recoverable from observer-accessible data. Apparent irreversibility is shown to correspond to the collapse of distinguishability between action histories under coarse-graining, not to the destruction of information.

The paper formalizes:

• operational reality as an equivalence class of global states,

• quantitative measures of action recoverability and significance,

• and conditions under which past actions become operationally inaccessible.

Explicit quantum and classical models are provided to demonstrate generic echo collapse under entangling or chaotic dynamics. Phase–Echo Theory offers a mathematically precise account of time’s arrow and the finality of past actions without invoking fundamental information loss, retrocausality, or speculative physical mechanisms.

This work is intended as a self-contained foundational contribution and a base framework for future theoretical and applied research on information accessibility, observer-relative dynamics, and irreversibility.