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Introduction

Gravitational redshift is one of the effects predicted by General Relativity (GR). It is observed when a photon leaves a region with a high gravitational potential and loses part of its energy, leading to an increase in its wavelength (a decrease in frequency). In classical GR, this is explained through the curvature of spacetime. However, what if this effect can be explained differently—through changes in the speed of light in a gravitational field?

In this article, we explore an alternative approach in which the speed of light depends on the gravitational potential, and we demonstrate that it leads to the same result as the standard GR explanation.

1. Standard Explanation of Gravitational Redshift in GR

Within GR, the frequency of a photon moving in a gravitational field changes according to the following formula:

where:

• v_e ​ — the initial photon frequency (at radius r_e ​),
• v_r ​ — the observed photon frequency (at radius r_r ​),
• G — the gravitational constant,
• M — the mass of the gravitating body,
• c — the speed of light (which in GR is considered constant).

This means that a photon loses energy as it moves away from the gravitational center, leading to its «reddening.»

But let’s take a different approach and assume that the speed of light changes in a gravitational field.

2. Hypothesis: The Speed of Light Depends on the Gravitational Potential

Let us assume that the speed of light c′ changes as a function of the gravitational potential Φ:

where c₀​ is the speed of light in a region where gravity is negligibly small, and f(Φ) is some function of the potential. The gravitational potential for a mass M at a distance r is given by:

Assuming the speed of light depends on the gravitational potential as:

where α is a coefficient that determines how strongly gravity influences the speed of light.

3. How Photon Frequency Changes with Variable Speed of Light

From the relation for photon energy:

E=hv

and the fact that the photon’s energy in a moving medium is also expressed via its momentum:

E=pc’

we can write the conservation law:

which leads to:

Substituting the dependence of c′ on gravitational potential:

For small values of

a Taylor series expansion gives:

This is very similar to the Taylor expansion of the GR formula:

If we choose α=−1, then our derived formula matches the GR prediction exactly!

4. Implications: A New Perspective on Gravity and Light

We obtained the same result as GR, but through the change in the speed of light rather than spacetime curvature. This opens new possibilities for interpreting gravitational effects:

1. Gravitational redshift can be explained without spacetime curvature if the speed of light changes in a gravitational field.
2. Gravitational lensing might not result from spacetime geometry but from refraction due to variations in light speed.
3. This provides an alternative explanation for dark matter and the expansion of the universe. If the speed of light depends on the energy density of space, then anomalies in galaxy rotation and cosmic expansion could be linked not to unseen mass, but to a variable refractive index.

5. Conclusion

We explored an alternative approach to gravitational redshift, where the speed of light varies within a gravitational field. This approach leads to the same formulas as GR but offers a new explanation for gravity and optical effects near massive bodies.

If further calculations and experiments confirm this hypothesis, it could revolutionize our understanding of gravity, light, and the nature of space.

This approach offers a new perspective on the nature of mass and its relationship to electromagnetic processes. A more detailed discussion of this hypothesis and its philosophical implications can be found in the following works:

— (dzen)

— (Zenodo)