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

Abstract (English)

The Standard Model of particle physics [23–25] relies heavily on empirical parameterization, offering no fundamental derivation for the invariant mass eigenvalues of elementary particles, the generational hierarchy, or the geometric origins of gravity. Building upon the historically marginalized lineage of continuous topological models (Helmholtz, Kelvin, Skyrme, Faddeev-Niemi), this paper proposes a deterministic, parameter-free derivation of all fundamental forces by modeling the physical vacuum as a zero-entropy barotropic scalar condensate, mathematically mapped to a non-linear O(3) sigma model operating within a non-commutative S3 geometry. It is demonstrated that localized subatomic matter can be modeled strictly as topologically stabilized, continuous knotted vortices (Hopfions). By applying established hydrodynamic constraints, the calculation yields the invariant bare mass of the nucleon (mp ≈ 938 MeV) and the electron (me ≈ 0.511 MeV) purely via intermediate hypersphere volume integrals and the Vakulenko-Kapitanski inequality. Subsequently, introducing the novel concept of topological crossing friction to mathematically account for empirical mass dressing, natively redefining the physical mechanism of the fine structure constant (α) as a geometric fluid drag limit. Quantum Electrodynamics (QED) is recovered via classical fluid mechanics, redefining antimatter as topological chirality and annihilation as geometric dissipation. The strong interaction is modeled as internal fractional strain of multi-crossing knots, while the weak interaction is formalized as classical vortex reconnection. Resolving the incompatibility of General Relativity and quantum mechanics, spatial curvature is redefined as Non-Linear Acoustic Radiation Pressure, deriving Newton’s Gravitational Constant (G) from wave impedance and recovering relativistic anomalies via kinematic acoustic refraction.