Informational Pressure Waves: An Information-Based Analogy to Gravitational Waves

This paper derives a wave equation for informational pressure from an information-based ontology, introducing the concept of informational pressure waves as an information-based analogy to gravitational waves. Building upon a model where distance is defined as an informational state, space as a path-length structure, and informational pressure as a universal dynamical quantity, we demonstrate that perturbations within the informational pressure field propagate as waves. The resulting wave equation possesses both a continuous form and a discrete version on graphs, opening up the possibility of connecting information-based dynamics with field-theoretic and cosmological concepts.