PET-V: Conditions for Temporal Inference Under Operational Irreversibility

PET-V (Temporal Inference) is a formal extension of Phase–Echo Theory (PET) that analyzes the conditions under which information about past events may be inferred from present observations. Rather than assuming or denying the possibility of “time viewing,” PET-V rigorously defines what such a capability would mean in information-theoretic and operational terms. Within the PET framework, global physical evolution is reversible while irreversibility arises from observer-relative coarse-graining. PET-V builds on this foundation by introducing event variables and temporal inference as mutual-information problems. A “time viewer” is defined precisely as an observer whose accessible measurements retain nonzero mutual information with a past event variable. PET-V proves that temporal inference is possible if and only if such information remains accessible, and impossible once all relevant correlations have collapsed under every realizable access map. The theory establishes strict limits on temporal inference under standard physics and demonstrates why universal or arbitrary “time viewers” are forbidden without additional physical assumptions. PET-V is fully compatible with PET-X (Exogenous Echo Access), which hypothesizes the existence of additional observation channels, but does not assume such channels exist. Instead, PET-V specifies the exact conditions any proposed extension would have to satisfy in order to enable genuine temporal viewing. By reframing time viewing as an information accessibility problem rather than a metaphysical paradox, PET-V provides a mathematically precise framework for evaluating claims about past-state recovery, historical reconstruction, and observer-dependent memory persistence. This work serves as a foundational reference for future experimental, theoretical, or speculative research into temporal inference, observer access, and the limits of irreversibility.