Derivation of the Generalized Navier-Stokes Equation from the World Quantum Theory Energy Formula
Abstract
This paper derives the complete Navier-Stokes equation — both the left side (inertial terms) and the right side (force terms) — from a single starting point: the World Quantum Theory (WQT) energy formula E = x ħ f_w (c/v)^2. The derivation uses three algebraic identities: (1) x ħ = p λ eliminates ħ; (2) λ f_w = v eliminates wavelength and frequency; (3) v·v = v_x² + v_y² + v_z² decomposes the velocity into three orthogonal components. Since p = (c/d) m v, the dot product p·v = (c/d) m (v_x² + v_y² + v_z²) automatically generates three energy terms, each proportional to v_i²/v². No empirical fluid properties are assumed. No free parameters are introduced. The NS equation is an algebraic identity of the Envelope Interface energy structure. Keywords: Navier-Stokes equation, World Quantum Theory, Envelope Interface, energy formula, force density, orthogonal decomposition
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