Experiments on Frequency Dependence of the Deflection of Light in Yang-Mills Gravity

Abstract

In Yang-Mills gravity based on flat space-time, the eikonal equation for a light ray is derived from the modified Maxwell’s wave equations in the geometric-optics limit. One obtains a Hamilton-Jacobi type equation, GLµv∂µΨ∂vΨ = 0 with an effective Riemannian metric tensor GLµv. According to Yang-Mills gravity, light rays (and macroscopic objects) move as if they were in an effective curved space-time with a metric tensor. The deflection angle of a light ray by the sun is about 1.53″ for experiments with optical frequencies ≈ 1014Hz. It is roughly 12% smaller than the usual value 1.75″. However, the experimental data in the past 100 years for the deflection of light by the sun in optical frequencies have uncertainties of (10-20)% due to large systematic errors. If one does not take the geometric-optics limit, one has the equation, GLµv[∂µΨ∂vΨcosΨ+ (∂µ∂vΨ)sinΨ] = 0, which suggests that the deflection angle could be frequency-dependent, according to Yang-Mills gravity. Nowadays, one has very accurate data in the radio frequencies ≈ 109Hz with uncertainties less than 0.1%. Thus, one can test this suggestion by using frequencies ≈ 1012 Hz, which could have a small uncertainty 0.1% due to the absence of systematic errors in the very long baseline interferometry.