The Grand Unification: A Deterministic Continuum Theory of Subatomic and Cosmological Mechanics

The Standard Model of particle physics successfully describes many subatomic phenomena but relies on empirical parameters rather than providing fundamental derivations for particle masses and the origins of gravity. This paper proposes a deterministic, parameter-free unification of all fundamental forces by modeling the physical vacuum as a continuous, fluid-like topological space. In this framework, elementary particles are modeled not as zero-dimensional points, but as stable, knotted vortices. Using classical fluid mechanics and geometry, the invariant rest masses of the proton and electron are derived directly from the physical spatial volume required to fold these subatomic knots. The fine-structure constant emerges naturally as a geometric limit of fluid friction. Furthermore, the strong and weak nuclear forces are respectively explained as internal knot strain and classical vortex reconnection. Finally, the incompatibility between General Relativity and quantum mechanics is resolved by redefining gravitational spatial curvature as acoustic radiation pressure. This continuous mechanical framework derives Newton's Gravitational Constant directly from fundamental wave impedance, offering a comprehensive and classical description of the universe without the need for unobservable point-particles or disjointed force carriers.