Extension of Discrete Mechanics towards Electromagnetism

TL;DR

This paper extends discrete mechanics to electromagnetism, unifying physical laws through a space-time discretized approach that captures persistent phenomena without continuous media assumptions.

Contribution

It introduces a discrete formulation of electromagnetism using scalar and vector potentials within a unified discrete mechanics framework.

Findings

Accounts for persistent phenomena without excitation

Models magnetic induction and wave propagation

Unifies mechanics and electromagnetism in discrete space-time

Abstract

The attempt to unify the laws of physics is approached from a discrete vision of space and time, abandoning the continuous medium paradigm that presided over the derivation of certain equations of physics-Navier-Stokes., Navier-Lam{\'e}, Maxwell, etc. Acceleration considered as an absolute quantity is expressed as a Hodge-Helmholtz decomposition, the sum of a solenoidal component and an irrotational component. Discrete mechanics, which has already unified mechanics in a relativistic formulation, is extended to electromagnetism with the same equation of motion expressed in terms of scalar and vector potentials. All the variables and parameters of this equation are described with only two fundamental units, those of length and time. The discrete equation makes it possible to account for persistent phenomena in the absence of any excitation, permanent magnetization, pressure, shear stress and purely unsteady effects such as magnetic induction, longitudinal and transversal wave propagation, differential rotation.