Geometrical Interpretation of Electromagnetism in a 5-Dimensional Manifold
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.
Keywords
Cite
@article{arxiv.1507.03184,
title = {Geometrical Interpretation of Electromagnetism in a 5-Dimensional Manifold},
author = {TaeHun Kim and Hyunbyuk Kim},
journal= {arXiv preprint arXiv:1507.03184},
year = {2017}
}
Comments
23 pages, Latex, grammatical errors in text and a few index errors in equations were corrected to be consistent with the published version