Newton's laws for a biquaternionic model of the electro-gravimagnetic field, charges, currents and their interactions

TL;DR

This paper introduces a biquaternionic model of the electro-gravimagnetic field based on Hamiltonian Maxwell's equations, deriving new interaction laws, invariance properties, and relativistic transformations, with solutions to related equations.

Contribution

It presents a novel biquaternionic framework for EGM fields, including modified Maxwell's equations and Newton-like laws for charges and currents, extending classical electromagnetism.

Findings

Derived new interaction equations for EGM fields.

Proved invariance of equations under Lorentz transformations.

Provided solutions to charge-current transformation equations.

Abstract

With use the Hamiltonian form of the Maxwell's equations one biquaternionic model for electro-gravimagnetic (EGM) field is offered. The equations of the interaction of EGM-fields, which are generated by different charge and current, are built. The field analogs of three Newton's laws are offered for free and interacting charge-currents, as well as total field of interaction. The invariance of these equations at Lorentz transformation is investigated, and, in particular, of the charge-current conservation law. It is shown that, by fields interaction, this law differs from the well-known one. The new modification of the Maxwell's equations is offered with entering the scalar resistance field in biquaternion of EGM-field tension. Relativistic formulae of the transformation of density of the masses and charge, current, forces and their powers are built. The solution of the Cauchy problem is given for equation of charge-current transformations.