Violation of electromagnetic U1 symmetry by Yang–Mills gravity and deflection of light experiment

Abstract

Within the gauge symmetry framework, the [Formula: see text] symmetry of electrodynamics is violated in the presence of gravity with spacetime translational gauge symmetry in inertial frames. For a light ray, an eikonal equation with effective metric tensors is derived in the geometric-optics limit. Under these conditions, the angle of the deflection of light by the sun is calculated to be [Formula: see text] in inertial frames without requiring a gauge condition such as [Formula: see text]. In contrast, if the theory is [Formula: see text] gauge invariant, one can impose the gauge condition [Formula: see text] in the derivation of the eikonal equation. In this case, one obtains a slightly different effective metric tensor and a different angle of deflection [Formula: see text]. However, because the precision of experiments in the last century using optical frequencies has been no better than (10–20)% due to large systematic errors, one cannot unambiguously rule out the result [Formula: see text]. We hope that the precision of these data can be improved in order to test Yang–Mills gravity.