Coherence-Limited Localization in Systems with Finite Propagation Speed

This paper presents a structural constraint on the formation of localized wave modes based on the compatibility of phase closure, finite propagation speed, and interaction-limited coherence.

A dimensionless coherence parameter is introduced to quantify the relationship between intrinsic oscillation timescales and coherence lifetime. It is shown that coupling to external degrees of freedom leads to energy uncertainty that scales linearly with the interaction strength at leading order. This induces a finite coherence lifetime that must exceed the time required for a propagation cycle in order for a stable localized structure to exist.

The resulting compatibility condition breaks the scale invariance of simple phase closure arguments and introduces a characteristic localization scale under fixed-energy conditions. This scale is consistent with known relations associated with particle localization, but arises here as a structural consequence rather than through calibration or particle-specific assumptions.

The framework is derived from minimal and explicit assumptions and does not introduce new dynamical laws. Electromagnetic radiation is used as a concrete example to illustrate the mechanism of coherence loss, but the underlying argument applies more generally to any coupled system where propagation, confinement, and interaction coexist.

This work should be interpreted as a constraint on admissible localized solutions rather than a model of specific particles. It provides a consistency condition that any viable description of wave localization must satisfy.