# What does Kaluza-Klein theory say about the attraction/repulsion of opposite/same charges?

Since Kaluza-Klein theory is made out of general relativity - a gravitational theory in 4 dimensions which is only attractive, then how does it takes into account the attraction/repulsion of opposite/same charges in 5 dimensions? What does Kaluza-Klein theory say about the reason behind the attraction/repulsion of opposite/same charges?

• +1. I also wonder how the Lorentz force law manifests itself in KK theory. (My SWAG says it'll be $\nabla_a G^{ab}=0$ for charged dust. But how is "charged" defined?) – Ryan Unger Dec 4 '15 at 13:29

I like to think about the gauge field effects using the identification $g_{\mu\theta} \approx A_\mu$ where $g_{ab}$ is the five dimensional metric, $\theta$ the compact direction, and $A_ \mu$ the four dimensional vector potential. Depending on your background, this identification either makes the previous discussion more precise or less intuitive. But there is a straightforward way to work out the Lorentz force law from this perspective: Simply write the five dimensional geodesic equation using $A_\mu$.