General Theory of Collision and Surface Response

This paper proposes a unified theory of collisions based on surface geometry and phase response. Rather than treating collisions as purely mechanical impacts or probabilistic quantum events, the theory reframes them as surface interactions involving tangential momentum alignment and orthogonal deformation or interference. Collisions are classified into three modes: Elastic collisions preserve momentum and energy, with immediate geometric restitution. Semi-elastic collisions involve temporary orthogonal deformation, where part of the energy is converted into sound or internal oscillation. Inelastic collisions result in resonance and structural absorption, leading to irreversible integration or transformation. The framework extends naturally to electromagnetic wave–surface interactions, where reflection, scattering, and absorption are shown to be manifestations of geometric phase matching or resonance with φ-surfaces. A general collision equation is introduced: This expresses the process as temporary phase storage and redistribution across interacting surfaces. The theory also introduces degeneration as a condition: