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The original Weber action at a distance theory is valid for slowly varying effects, and it in addition to predicting all of the usual electrodynamical results, leads to crucial effects where the Maxwell theory fails. The Weber’s approach is an alternative to Maxwell electrodynamics, where the Coulomb's law becomes velocity dependent 1-6. Here we prove that the Weber’s theory gives the fine structure energy level splitting for the hydrogen atom without the assumption of mass change with velocity.
Torres‐Silva et al. (Wed,) studied this question.