Editing Æther Research & Development (section)

== Equations for Æther Dynamics ==

=== Modified Navier-Stokes Equations for Æther Dynamics ===
The modified Navier-Stokes equations for Æther dynamics introduce additional terms to account for Æther viscosity, density, and flow behavior. While there isn't a single standard form, a modified version could look like:
* Continuity equation: <math> \frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{v}) = 0 </math>
* Momentum equation: <math> \rho \left( \frac{\partial \mathbf{v}}{\partial t} + (\mathbf{v} \cdot \nabla) \mathbf{v} \right) = -\nabla p + \mu \nabla^2 \mathbf{v} + \rho \mathbf{g} </math>
* Energy equation: <math> \frac{\partial e}{\partial t} + \nabla \cdot (\mathbf{v} e) = -p \nabla \cdot \mathbf{v} + \nabla \cdot (\mathbf{q} + \rho \mathbf{v} \cdot \mathbf{v}) + \mu \nabla^2 \mathbf{v}^2 </math>

=== Modified General Relativity Equations ===
Field equations from general relativity are adapted to incorporate Æther as a background medium, introducing additional terms to the metric tensor to account for its effects on spacetime curvature and gravitational interactions.
The modified Einstein field equations incorporating Æther as a background medium introduce additional terms to the metric tensor to account for its effects on spacetime curvature. A simplified form could be:
* <math> G_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu} + \Lambda g_{\mu\nu} + \kappa T^{\text{Æther}}_{\mu\nu} </math>
Where <math> T^{\text{Æther}}_{\mu\nu} </math> represents the stress-energy tensor for the Æther field.