Geometrical Interpretation of Electromagnetism in a 5-Dimensional Manifold

TL;DR

This paper revisits Kaluza-Klein theory, interpreting electromagnetism geometrically in a 5D manifold, and explores its implications, covariance issues, and experimental predictions.

Contribution

It introduces a shearing deformation perspective of electromagnetic potential in 5D and proposes a particle-thread concept for matter consistency.

Findings

Electromagnetic potential as a shearing deformation in 5D

Charge-to-mass ratio linked to motion along the 5th dimension

Experimental implications derived for weak potentials

Abstract

In this paper, Kaluza-Klein theory is revisited and its implications are elaborated. We show that electromagnetic 4-potential can be considered as a shearing-like deformation of a 5-dimensional (5D) manifold along the fifth (5th) axis. The charge-to-mass ratio has a physical meaning of the ratio between the movement along the direction of the 5th axis and the movement in the 4D space-time. In order to have a 5D matter which is consistent with the construction of the 5D manifold, a notion of particle-thread is suggested. Examinations on the compatibility of reference frames reveal a covariance breaking of the 5th dimension. The field equations which extend Einstein's field equations give the total energy-momentum tensor as a sum of that of matter, electromagnetic field, and the interaction between electric current and electromagnetic potential. Finally, the experimental implications are calculated for the weak potential case.