Dynamics of Matter in a Compactified Kaluza-Klein Model

TL;DR

This paper critiques the traditional 5D geodesic approach in Kaluza-Klein models and proposes a new method based on matter tensor conservation, resolving issues with charge-mass bounds and massive mode generation.

Contribution

It introduces a novel dynamical equation derived from matter tensor conservation, improving matter description in Kaluza-Klein models.

Findings

The new equation avoids charge-mass ratio bounds.

It removes the problematic tower of massive modes.

The approach offers a more accurate matter dynamics framework.

Abstract

A longstanding problem in Kaluza-Klein models is the description of matter dynamics. Within the 5D model, the dimensional reduction of the geodesic motion for a 5D free test particle formally restores electrodynamics, but the reduced 4D particle shows a charge-mass ratio that is upper bounded, such that it cannot fit to any kind of elementary particle. At the same time, from the quantum dynamics viewpoint, there is the problem of the huge massive modes generation. We present a criticism against the 5D geodesic approach and face the hypothesis that in Kaluza-Klein space the geodesic motion does not deal with the real dynamics of test particle. We propose a new approach: starting from the conservation equation for the 5D matter tensor, within the Papapetrou multipole expansion, we prove that the 5D dynamical equation differs from the 5D geodesic one. Our new equation provides right coupling terms without bounding and in such a scheme the tower of massive modes is removed.