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

TL;DR

This paper investigates whether extra dimensions inherently violate 4D physics and proposes a new, consistent definition of the force from extra dimensions that aligns with established physics principles.

Contribution

The authors introduce a new definition of force from extra dimensions that avoids contradictions and aligns with 4D physics, improving upon previous formalisms.

Findings

The new force definition is free of contradictions.

It is more consistent with physical intuition.

Effects could be observed near black holes or in cosmology.

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, $u_{\mu}f^{\mu} \neq u^{\mu}f_{\mu}$. 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.