Bubble Theory: A Relational Framework for Localized Dynamics

Abstract Bubble Theory is introduced as a boundary-centric relational framework in which physical systems are modeled as localized, self-maintaining regions (“bubbles”) whose boundaries encode interaction, information flow, and dynamical constraints. A boundary operator B is defined to capture deformation, coupling, and stability, leading to a general dynamical law for bubble evolution and exchange flux between interacting systems. Worked examples—including spherical and toroidal geometries and a two-bubble interaction model—demonstrate how the formalism generates synchronization, equilibrium-seeking behavior, and emergent coherence in composite systems. The framework yields testable predictions regarding boundary deformation, coupling driven synchronization, and minimal-energy equilibrium shapes. The manuscript concludes with discussion of mathematical extensions, simulation pathways, and potential applications across physical and biological boundary-mediated systems.