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Shapiro’s Time Delay Without General Relativity: A Flat Space-Time Approach with Variable Light Speed

Author:

Roux, Jean-Claude

Category:

Research Papers

Sub-Category:

Relativity Theory

Language:

English

Date Published:

March 27, 2025

File:

/Research Papers-Relativity Theory/Download/10128

Downloads:

978

Keywords:

General relativity; geometric optics; refraction index; light beam; Schwarzschild radius; flat space-time; Newtonian gravity; weak gravitational field; Shapiro’s time delay

Abstract:

We explore the propagation of light in the vicinity of a massive body by introducing a variable speed of light under the assumption of a weak gravitational field. Starting from general relativity, we reformulate the equation of motion of a light beam into an equivalent description in flat spacetime, governed by classical physics—namely geometric optics and Newtonian gravity. Crucially, we show that this transformation is reversible: the curved spacetime formulation and the flat spacetime with a gravitational index are mathematically equivalent in this regime. This duality allows for a simpler treatment of light propagation without loss of generality. As an application, we derive the Shapiro’s time delay within this flat-space framework and recover an expression that closely matches the result obtained in general relativity. This finding offers a new perspective on a phenomenon historically regarded as a key confirmation of Einstein’s theory.

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