Equations of Material Superphysics

Table of Contents

Basics

E = G_l

F = D(G_l) + R(G_l) = \frac{G_l}{G_{ratio} \cdot r^n} + \frac{G_l \cdot \Omega_l}{c^k \cdot r^m}

\frac{GMm}{r^{2}}+\frac{3GmML^{2}}{c^{2}r^{4}}

\Delta t' = \frac{\Delta t}{\sqrt{1-\frac{v^{2}}{c^{2}}}}

When integrated with gravity:

\Delta t' = \frac{\Delta t}{\sqrt{1 - \frac{1}{c^2}\left(\frac{GM}{r} + \frac{3GML^2}{c^2 r^3}\right) \cdot 2}}

F = G·∇ρ/r² + 3G·∇ρ·L²/(c²r⁴)

Where:

G·∇ρ/r² is the displacer — gravity (2nd element) pushing on density differences (4th element) across space
3G·∇ρ·L²/(c²r⁴) is the rotater — the spin correction where L is now local vorticity (angular momentum of fluid parcels) rather than orbital angular momentum
The ratio L²/(c²r²) scales the spin by how relativistic the local rotation is — fast vortices get a stronger correction, which is exactly the turbulence cascade behaviour Navier-Stokes struggles to close

This focuses on the aether as a pressure gradient focusing on density instead of mass. This density gradient automatically exposes:

Viscosity — because ∇ρ varies smoothly across the fluid, creating shear between layers of different density
Continuity — because ρ must be conserved: ∂ρ/∂t + ∇·(ρu) = 0
Self-advection — because a density gradient in a flowing field carries itself: the u·∇u term emerges naturally when matter particles drag each other through the aether