Broken Closed Surfaces, Huygens' Principle, and the Emergence of Volume Abstract

This paper develops a unified closed-surface framework that reinterprets Huygens’ construction, Lorentz contraction, and Gauss’ law as complementary manifestations of surface geometry. In this view, a perfectly uniform closed surface—maintaining tangential velocity at the speed of light—remains intact and constitutes matter with mass. When uniformity is broken, however, the closed surface disperses, producing space-generation phenomena rather than true oscillatory waves. Electromagnetic and gravitational waves in vacuum are thus recast as broken closed-surface dispersals, which only manifest as actual wave motion when they resonate with matter. Distortions of concentric spherical wavefronts, originally idealized in Huygens’ diagrams, reduce propagation speed below ccc and can be expressed with angular factors such as sin⁡θ, cos⁡θ, 1−cos⁡θ, or 1−sin⁡θ. These same forms appear in Lorentz contraction and in elastic indentation mechanics, highlighting a universal geometric law across scales. Furthermore, interference of multiple broken closed surfaces at the same time and phase generates apparent volume, linking dispersal phenomena to the emergence of space itself. This unified description provides a geometric interpretation of mass, space, and resonance as outcomes of uniformity versus non-uniformity. It suggests that all phenomena—from light propagation and gravitational radiation to mechanical deformation—are governed by the same closed-surface dynamics.