Generalizing the Lorentz transformations

TL;DR

This paper proposes an eight-dimensional extension of spacetime to generalize Lorentz transformations, which preserves Maxwell's equations and offers new insights into electromagnetic theory and magnetic monopoles.

Contribution

It introduces a novel eight-dimensional spacetime framework that generalizes Lorentz transformations while maintaining electromagnetic invariance, providing new perspectives on electromagnetism and monopoles.

Findings

Generalized transformations reduce to conventional Lorentz transformations when magnetic monopoles are absent.

The extended framework preserves Maxwell's equations under the new transformations.

Potential to explain quasi magnetic monopoles in spin-ice systems.

Abstract

In this paper we develop a framework allowing a natural extension of the Lorentz transformations. To begin, we show that by expanding conventional four-dimensional spacetime to eight-dimensions that a natural generalization is indeed obtained. We then find with these generalized coordinate transformations acting on Maxwell's equations that the electromagnetic field transformations are nevertheless unchanged. We find further, that if we assume the absence of magnetic monopoles, in accordance with Maxwell's theory, our generalized transformations are then restricted to be the conventional ones. While the conventional Lorentz transformations are indeed recovered from our framework, we nevertheless provide a new perspective into why the Lorentz transformations are constrained to be the conventional ones. Also, this generalized framework may assist in explaining several unresolved questions in electromagnetism as well as to be able to describe quasi magnetic monopoles found in spin-ice systems.