Violation of \(U_1\) Gauge Symmetry by Yang-Mills Gravity and Deflection of Light Experiment

• Published in: arXiv.org 2019-09
• Main Authors: Hsu, Leonardo, Jong-Ping Hsu, Yun Hao
• Format: Article
• Language: English
• Subjects: Deflection; Eikonal equation; Electrodynamics; Gravitation; Mathematical analysis; Symmetry; Systematic errors; Tensors
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1909.07777

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.