Problematic aspect of extra dimensions

TL;DR

The paper demonstrates that multidimensional Kaluza-Klein models predict perihelion shifts inconsistent with observations unless space is three-dimensional, highlighting a fundamental problem with these models.

Contribution

It derives a formula for perihelion shift in multidimensional Kaluza-Klein models and shows its inconsistency with experimental data for dimensions other than three.

Findings

Perihelion shift formula depends on total spatial dimensions D

Agreement with data only when D=3

Extra dimensions do not affect the perihelion shift prediction

Abstract

We show that in multidimensional Kaluza-Klein models the formula of the perihelion shift is $D\pi m'^2c^2r_g^2/[2(D-2)M^2]$ where $D$ is a total number of spatial dimensions. This expression demonstrates good agreement with experimental data only in the case of ordinary three-dimensional $(D=3)$ space. This result does not depend on the size of the extra dimensions. Therefore, considered multidimensional Kaluza-Klein models face a severe problem.