[Paper Review] Bending of light caused by gravitation: the same result via totally different philosophies

Tolga Yarman, Alexander Kholmetskii+1 more|arXiv (Cornell University)|Jan 14, 2014

Relativity and Gravitational Theory5 references3 citations

TL;DR

This paper derives the gravitational bending of light near a star using energy conservation and the weak equivalence principle, yielding the same result as general relativity (1.75 arcseconds for the Sun) without distinguishing light from matter. The approach is fundamentally classical yet potentially compatible with quantum mechanics, and it also predicts planetary perihelion precession, demonstrating consistency across phenomena with a unified framework.

ABSTRACT

We offer a concise and direct way to derive the bending angle of light (i.e. as generally called, gravitational lensing), while light grazes a star, through the approach suggested earlier by the first author, which is fundamentally based on the energy conservation law and the weak equivalence principle. We come out with the same result as that of the general theory of relativity (GTR), although the philosophies behind are totally different from each other. We emphasize that in our approach, there is no need to draw a distinction between light and ordinary matter, which makes our approach of gravity potentially compatible with quantum mechanics. Furthermore, our equation that furnishes gravitational lensing, also furnishes the result about the precession of the perihelion of a planet. The results obtained are discussed.

Motivation & Objective

• To derive the gravitational bending of light using a novel classical approach based on energy conservation and the weak equivalence principle.
• To show that this method yields the same result as general relativity despite differing foundational philosophies.
• To eliminate the distinction between light and matter in gravitational interactions, enhancing compatibility with quantum mechanics.
• To demonstrate that the same equation also accounts for planetary perihelion precession, indicating theoretical unification.
• To provide a physically intuitive, alternative derivation of gravitational lensing without relying on curved spacetime.

Proposed method

• The derivation starts from the energy conservation law applied to photons in a gravitational field.
• It applies the weak equivalence principle to treat photons as having inertial and gravitational mass, consistent with classical mechanics.
• The trajectory of light is calculated by integrating the gravitational force along the path, assuming a weak field and small deflection.
• The bending angle is derived from the change in momentum due to the gravitational potential, using classical mechanics principles.
• The resulting equation is shown to reproduce the standard GTR result for light deflection near the Sun.
• The same formalism is extended to derive the perihelion precession of Mercury, confirming consistency with planetary motion.

Experimental results

Research questions

• RQ1 Can the bending of light by gravity be derived without invoking general relativity or curved spacetime?
• RQ2 Does a classical approach based on energy conservation and the weak equivalence principle yield the same deflection angle as general relativity?
• RQ3 Can such a framework treat light and matter identically in gravity, enabling compatibility with quantum mechanics?
• RQ4 Is the same equation capable of predicting both light deflection and planetary perihelion precession?
• RQ5 What are the foundational differences between this approach and general relativity, despite yielding identical results?

Key findings

• The derived bending angle of light grazing the Sun is 1.75 arcseconds, matching the prediction of general relativity.
• The result is obtained using only energy conservation and the weak equivalence principle, without assuming spacetime curvature.
• The approach treats photons identically to massive particles in gravity, suggesting potential compatibility with quantum mechanics.
• The same equation that predicts light bending also correctly predicts the anomalous perihelion precession of Mercury.
• The derivation is self-consistent and based on classical principles, yet reproduces relativistic results through a different philosophical foundation.
• The method provides a physically intuitive alternative to general relativity for gravitational lensing phenomena.