Deflection of Light by the Sun in the Unified Theory of Gravity and Electromagnetism and the Theory of the Speed of Time

This work develops a unified macro–micro framework for describing the classical deflection of light near the Sun. The macroscopic level is based on the Unified Theory of Gravity and Electromagnetism (Max G. Yan): the vacuum is modeled as an elastic continuum with a dimensionless deformation potential ϕ = GM/(c²r). The microscopic level is the Theory of the Speed of Time (Sasha Laslov): vacuum oscillators respond to deformation through changes in their effective stiffness and natural frequency. From the weak-field frequency-shift relation Δω/ω₀ = −ϕ and the unified scaling of the electric and magnetic sectors, it follows that α = η = 2, and therefore α + η = 4. This determines the refractive-index profile n(r) = 1 + 2GM/(c²r). The geometric-optics integral yields the deflection angle θ = 4GM/(c²b), which numerically agrees with the weak-field result of General Relativity and observations (~1.75″ at the solar limb). The calculation does not use the Schwarzschild geodesic equations. It demonstrates how the macroscopic description of an elastic gravitational medium (Yan) and the microscopic model of the vacuum response (Laslov) together reproduce the classical solar light deflection. Related works:- Laslov, S. Unification of the Electromagnetic Gravity Theory and the Theory of the Speed of Time. Zenodo. https://doi.org/10.5281/zenodo.22644651- Yan, M. G. Unified Field Theory for Gravity and Electromagnetism. Zenodo. https://doi.org/10.5281/zenodo.4057270