Relativistic Newton and Coulomb Laws

TL;DR

This paper derives relativistic forms of Newton and Coulomb laws, showing their similarities and differences, and demonstrates how gravitational law can be obtained from Coulomb law by specific parameter choices.

Contribution

It presents a unified relativistic framework for electromagnetic and gravitational interactions, deriving Newtonian gravity from Coulomb law through parameter adjustments.

Findings

Relativistic Coulomb law derived using wave equations and Lienard-Wiechert potentials.

Maxwell equations are fully determined by the relativistic Coulomb law.

Newton gravity law can be obtained from Coulomb law by specific constant choices.

Abstract

The relativistic equations for the electromagnetic and gravitation interactions are similar: The only Lagrangian equation is the equation with Lorentz force. The potential satisfies the wave equation with the right - hand side proprtional to the velocity of another particle multiplied by the delta - function concentrated at the position of another particle. If the interaction propagates at the speed of light, then the wave equation has the unique solution: the Lienard - Wiechert potential. The Maxwell equations are completely defined by the obtained relativistic Coulomb law. The Coulomb law and the Newton gravity law differ from each other only in the choice of the constants. If we choose in Coulomb law the electric charges equal to the masses and choose the interaction constant of another sign, then we get Newton gravity law. If we choose in the relativistic Coulomb law the electric charges equal to the masses and choose the interaction constant of another sign, then we get the relativistic Newton gravity law.