Maxwell's equations in 4-dimensional Euclidean space

TL;DR

This paper reformulates Maxwell's equations within a 4-dimensional Euclidean framework, deriving relativistic electrodynamics from space curvature and providing solutions that align with traditional spacetime approaches, linked to a hypersphere universe model.

Contribution

It introduces a novel Euclidean geometric formulation of Maxwell's equations and relativistic electrodynamics, connecting them to a hypersphere universe concept.

Findings

Derived relativistic electrodynamics from Euclidean space curvature

Provided solutions to Maxwell's equations in free space

Linked electromagnetic solutions to a hypersphere universe model

Abstract

The paper formulates Maxwell's equations in 4-dimensional Euclidean space by embedding the electromagnetic vector potential in the frame vector $g_0$. Relativistic electrodynamics is the first problem tackled; in spite of using a geometry radically different from that of special relativity, the paper derives relativistic electrodynamics from space curvature. Maxwell's equations are then formulated and solved for free space providing solutions which rotate the vector potential on a plane; these solutions are shown equivalent to the usual spacetime formulation and are then discussed in terms of the hypersphere model of the Universe recently proposed by the author.