Derivation of the Navier-Stokes Equation within World Quantum Theory

The Navier-Stokes equation is the fundamental equation describing fluid motion, traditionally treated as a phenomenological model based on the continuum hypothesis and Newton's law of viscosity. Within the framework of World Quantum Theory, starting from the fundamental postulate c2=v2+d2, this paper reduces space and time to macroscopic projections of the momentum component v and the rest mass component d, and reformulates the velocity field, pressure, and density of a fluid in terms of these two components. We further demonstrate that the macroscopic velocity field itself is the phase gradient field of the world quantum: u∝∇ϕ, thereby reducing the Navier-Stokes equation to a convection-diffusion equation for the phase field. Through analyzing phase synchronization and momentum transfer among world quanta on an anchor-point network, the inviscid Euler equation is shown to be a consequence of momentum conservation under perfect phase locking, while the viscous term originates from momentum dissipation due to phase desynchronization between adjacent anchors. Consequently, the complete Navier-Stokes equation is rigorously derived as a necessary corollary of World Quantum Theory. Keywords: World Quantum Theory; Navier-Stokes equation; momentum-rest mass decomposition; phase desynchronization; nature of viscosity; phase gradient field