PET Multi Observer Phase Echo Theory

Multi-Observer Phase–Echo Theory (PET-MO) extends Phase–Echo Theory to systems involving multiple embedded observers with distinct information access. While PET-Core formalizes irreversibility as the operational loss of distinguishability for a single observer, PET-MO provides a rigorous mathematical framework for understanding disagreement, partial agreement, and consensus among multiple observers deriving information from the same global physical state. In PET-MO, each observer is characterized by an access map that determines which degrees of freedom influence their operational reality. Distinct access maps induce distinct equivalence classes of global states, leading to observer-relative operational realities even under identical underlying dynamics. The theory introduces shared operational reality and consensus regions as intersections of observer equivalence classes, formalizing agreement as an overlap of accessible information rather than an absolute or observer-independent property. PET-MO demonstrates that observer disagreement is generic and structurally inevitable under restricted access, while consensus is fragile, context-dependent, and contingent on overlapping informational reach. Communication and coordination are modeled as physical processes that expand shared access but cannot recover distinctions already lost to coarse-graining. This framework provides a non-relativistic, non-subjective account of observer relativity grounded entirely in information accessibility. Multi-Observer Phase–Echo Theory offers a mathematically precise foundation for understanding measurement agreement, social facts, shared records, and collective knowledge in irreversible environments. It unifies individual perception, communication, and consensus formation within a single conservative physical framework and serves as a foundation for future work on multi-agent systems, distributed intelligence, and observer-relative dynamics. This work is a self-contained extension of Phase–Echo Theory and is intended as a foundational contribution to the study of observer plurality and consensus under irreversible information loss.