Violation of $U_1$ Gauge Symmetry by Yang-Mills Gravity and Deflection of Light Experiment

TL;DR

This paper investigates how $U_1$ gauge symmetry violation in Yang-Mills gravity affects light deflection, predicting a slightly different angle than standard general relativity, and discusses experimental implications.

Contribution

It introduces a gauge symmetry framework where $U_1$ symmetry is violated in gravity, deriving new predictions for light deflection angles without gauge conditions.

Findings

Predicted light deflection angle of approximately 1.75 arcseconds without gauge condition.

Alternative prediction of approximately 1.52 arcseconds if $U_1$ gauge invariance is assumed.

Current experimental precision cannot conclusively distinguish between the two predictions.

Abstract

Based on the gauge symmetry framework, the $U_1$ symmetry of electrodynamics is violated in the presence of gravity with space-time 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 $\d \phi \approx 1.75''$ in inertial frames without requiring a gauge condition such as $\p_\mu A^\mu=0$. In contrast, if the theory is $U_1$ gauge invariant, one can impose the gauge condition $\p_\mu A^\mu=0$ in the derivation of the eikonal equation. In this case, one obtains a slightly different effective metric tensor and a different angle of deflection $\d \phi \approx 1.52''$. 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 $\d \phi \approx 1.52'$. It is hoped that the precision of these data can be improved in order to test Yang-Mills gravity.