Dynamics of the Topological Spacetime Medium under Sang-Jun Park's Mechanical Laws: Deriving Gravitation and Quantum Mechanics from Navier-Stokes and Euler Formulations

Modern physics remains conceptualized upon a fractured foundation, partitioned by General Relativity governing macro-cosmic geometries and Quantum Mechanics dictating micro-cosmic probabilities. Breaking away from the conventional paradigm that treats mass and charge as independent, intrinsic physical entities, this paper provides a rigorous unification based on Park’s Mechanical Laws. We redefine the universe not as an empty vacuum, but as a continuous ‘Topological Spacetime Medium’ whose intrinsic dynamics are fundamentally governed by the fluid-mechanical principles of the Navier-Stokes and Euler equations.Through deterministic mathematical derivations, we demonstrate that macro-gravitation (the Einstein field equations) naturally emerges as a macroscopic manifestation of the localized viscous stress resistance and geometric shear strain within this spacetime medium. Concurrently, using the Madelung hydrodynamical transformation, we prove that micro-probabilistic wavefunctions (the Schrödinger equation) are actual physical wave phenomena driven by the velocity potential and structural restoration forces (the quantum potential) of the compressible spacetime fluid. Furthermore, quantum entanglement is explicitly formalized as a non-local interaction bridged by a robust topological vortex tube, satisfying Helmholtz’s vorticity theorems across arbitrary spatial distances, while electromagnetism is recovered as pure elastic shear waves propagating through the medium. By reconciling the deterministic continuum of mechanics with quantum behaviors, this unified framework establishes that gravity, quantum mechanics, and electromagnetism are not separate forces, but scale-dependent topological expressions of a singular, underlying spacetime fluid.