# Cartesian nature of equal active and passive energies

## TL;DR

This paper explores a Cartesian framework for Maxwell's equations and elementary charges, revealing new insights into energy, mass, and space physics with implications for classical and relativistic theories.

## Contribution

It introduces a Cartesian material space approach to Maxwell's equations, linking complex energies, the Principle of Equivalence, and nondual Einstein analogs, with novel predictions for space physics.

## Key findings

- Radial charges carry equal active and passive imaginary energies.
- Maxwell's equations become 4-vector identities for complex charges.
- Modified Navier-Stokes equations predict pressure and temperature gradients.

## Abstract

The Cartesian material space approach to Maxwell's equations reveals the analytical solution of the continuous radial density for the extended elementary charge. Radial charges and their Coulomb fields carry equal passive and active imaginary energies. The Einstein mass-energy formula can be updated for electricity in complex numbers. The Principle of Equivalence works universally for active/passive masses and for active/passive electric charges. Maxwell's equations for complex continuous charges become 4-vector identities for locally paired flows of energies that correspond to the Chinese yin-yang approach to the nature. Cartesian relativistic physics has its own nondual analog of the Einstein Equation, which leads to geodesic equations for the motion of Ricci material densities and to vortex states of the elementary mass-extension. Non-empty space physics modifies the Navier-Stokes equation by kinematic "living forces". This inertial feedback enables a conceptual choice between Newtonian and Cartesian universes (with localized or extended elementary masses, respectively) because of new predictions of pressure and temperature gradients across laboratory flows of liquids and gases.