The local deflection of light

TL;DR

This paper derives the local relationship between radial distance and angle for light near Earth's surface, revealing that general relativity predicts twice the deflection compared to the principle of equivalence, challenging conventional understanding.

Contribution

It demonstrates that, in the weak field limit, the local light deflection predicted by general relativity is twice what the principle of equivalence suggests.

Findings

General relativity predicts twice the local light deflection compared to the principle of equivalence.

The derived relationship shows a factor of two difference in local light trajectory predictions.

Contradicts the common assumption that the principle of equivalence accounts for full light deflection.

Abstract

We have derived the relationship between the radial proper distance, h, and the polar angle, phi, for a light ray that is emitted and travels in the neighborhood of the Earth's surface. General relativity predicts that, even locally, the equation which relates these two physical magnitudes differs from the one stated by the principle of equivalence. More precisely, we have proved that, in the weak field limit, the local physical trajectory, h=h(phi), is the one that would correspond to a massive Newtonian particle in a field two times greater. Therefore, and contrary to the generally accepted fact, the principle of equivalence gives only 1/2 part of the general relativity local deflection of light.