Does The Force From an Extra Dimension Contradict Physics in 4D?

Abstract

We examine the question of whether violation of 4D physics is an inevitable consequence of existence of an extra non-compactified dimension. Recent investigations in membrane and Kaluza-Klein theory indicate that when the metric of the spacetime is allowed to depend on the extra coordinate, i.e., the cilindricity condition is dropped, the equation describing the trajectory of a particle in one lower dimension has an extra force with some abnormal properties. Among them, a force term parallel to the four-velocity of the particle and, what is perhaps more surprising, $u_μf^μ \neq u^μf_μ$. These properties violate basic concepts in 4D physics. In this paper we argue that these abnormal properties are {\em not} consequence of the extra dimension, but result from the formalism used. We propose a new definition for the force, from the extra dimension, which is free of any contradictions and consistent with usual 4D physics. We show, using warp-products metrics, that this new definition is also more consistent with our physical intuition. The effects of this force could be detected observing objects moving with high speed, near black holes and/or in cosmological situations.