Questions related to the Deflection of Light by Gravity determined by Soldner, Einstein and Schwarzschild
Klaus Wilhelm, Bhola N. Dwivedi, Karsten Muller
TL;DR
The paper reexamines the gravitational deflection of light and related redshift by revisiting Soldner, Einstein, and Schwarzschild within a framework where the coordinate speed of light $c_r$ depends on the gravitational potential $\Phi$. It argues that photon energy remains fixed while momentum adjusts through an interaction region, yielding the redshift $(\nu'-\nu_0)/\nu_0 \approx (\Phi-\Phi_0)/c_0^2$ and a light bending of approximately $1.7^{\prime\prime}$ for grazing rays, in agreement with solar eclipse measurements; it also discusses historical discrepancies (notably a factor-of-two error in early 1916 results) and debates about the necessity of full General Relativity for these weak-field effects. The author contends that energy- and momentum-conservation arguments suffice to explain both redshift and light deflection, and clarifies the historical record by emphasizing the interaction-region mechanism and the correct use of a varying $c_r$. Overall, the work highlights how foundational principles can reproduce key solar-system tests and reconciles differing historical claims without appealing to the full curvature description in the weak-field regime.
Abstract
Before we discuss the deflection of light in a gravitational field, we give a brief overview of some basic physical formulas on photon properties, generation and propagation. The much debated problems of the redshift and the photon propagation in a gravitational field is then considered and applied to the calculation of the speed of light. Many citations are given in direct quotations to avoid any misunderstandings. If the quotations are in German, an English translation is provided. Based on this speed, calculated and measured results are recalled on the deflection of light, with emphasis on the deflection near the Sun. We conclude that the speed of light and the deflection angle can be determined by energy and momentum conservation principles.