Five-dimensional PPN formalism and experimental test of Kaluza-Klein theory

TL;DR

This paper develops a five-dimensional parametrized post-Newtonian formalism to test Kaluza-Klein theory against Solar system experiments, revealing significant deviations from general relativity due to the extra dimension.

Contribution

It introduces a 5D PPN formalism and compares it with 4D results, highlighting the experimental challenges faced by classical Kaluza-Klein theory.

Findings

The PPN parameter γ in 5D Kaluza-Klein theory is half of that in 4D GR.

Extra dimension causes a significant deviation in gravitational predictions.

Experimental tests challenge the viability of classical Kaluza-Klein theory.

Abstract

The parametrized post Newtonian formalism for 5-dimensional metric theories with a compact extra dimension is developed. The relation of the 5-dimensional and 4-dimensional formulations is then analyzed, in order to compare the higher dimensional theories of gravity with experiments. It turns out that the value of post Newtonian parameter $\gamma$ in the reduced 5-dimensional Kaluza-Klein theory is two times smaller than that in 4-dimensional general relativity. The departure is due to the existence of an extra dimension in the Kaluza-Klein theory. Thus the confrontation between the reduced 4-dimensional formalism and Solar system experiments raises a severe challenge to the classical Kaluza-Klein theory.