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I read this article. In the General Relativity section, it says this

Even so, in small regions of space, we can say that light in the presence of gravity does have a position-dependent speed; and in that sense, we can say that the "ceiling" speed of light in the presence of gravity is higher than the "floor" speed of light.

The question: Is the article claiming the local speed of light changes as a function of the strength of the gravitational field? Or is the article talking about the prediction from Einstein’s paper?

The prediction is that the speed of light would be changed by a gravitational potential:

$c = c_0 (1 + Φ / c²)$

$c_0 ≔$ speed of light at the origin

$Φ ≔$ the gravitational potential

This Stack Exchange answer explains the above prediction. The conclusion is that the local speed of light is still constant, even if the coordinate speed is different.

Qmechanic
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Aphrontos
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2 Answers2

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Is the article claiming the local speed of light changes as a function of the strength of the gravitational field?

No, it isn't.

When we consider experimentally measuring the speed of light we can consider three length scales that we can conveniently label as local, regional and global. Local means the region very close to us, regional means distances up to around the scale of solar systems, and global means distances large than this.

  • The local speed of light is always $c$, as described in gratuitous detail in the answer (of mine) that you have linked.

  • Globally the speed of light is ... well ... even defining what we mean by the speed of light globally can be problematic. For example the region behind an event horizon is inaccessible to us, so what physical meaning does "the speed of light" have in such circumstances?

  • But in between we have a region that is large enough for the effects of GR to be observable but small enough to be experimentally accessible. An example would be something like the measurements of the Shapiro delay in the Solar System.

And it's this last size range, the range I've called regional, that Steve Carlip, Philip Gibbs and Don Koks describe as small regions of space. The wording is slightly unfortunate since to most of us this will imply sizes on the millimetre scale, but the authors actually means size small in comparison to cosmological scales.

So the bottom line is that we all agree the local speed of light is invariant. It's only on larger scales that we can interpret our observations as meaning that the speed of light changes.

John Rennie
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"To see why a deflection of light would be expected, consider Figure 2-17, which shows a beam of light entering an accelerating compartment. Successive positions of the compartment are shown at equal time intervals. Because the compartment is accelerating, the distance it moves in each time interval increases with time. The path of the beam of light, as observed from inside the compartment, is therefore a parabola. But according to the equivalence principle, there is no way to distinguish between an accelerating compartment and one with uniform velocity in a uniform gravitational field. We conclude, therefore, that A BEAM OF LIGHT WILL ACCELERATE IN A GRAVITATIONAL FIELD AS DO OBJECTS WITH REST MASS. For example, near the surface of Earth light will fall with acceleration 9.8 m/s^2." http://web.pdx.edu/~pmoeck/books/Tipler_Llewellyn.pdf

University of Illinois at Urbana-Champaign: "Consider a falling object. ITS SPEED INCREASES AS IT IS FALLING. Hence, if we were to associate a frequency with that object the frequency should increase accordingly as it falls to earth. Because of the equivalence between gravitational and inertial mass, WE SHOULD OBSERVE THE SAME EFFECT FOR LIGHT. SO lets shine a light beam from the top of a very tall building. If we can measure the frequency shift as the light beam descends the building, we should be able to discern how gravity affects a falling light beam. This was done by Pound and Rebka in 1960. They shone a light from the top of the Jefferson tower at Harvard and measured the frequency shift. The frequency shift was tiny but in agreement with the theoretical prediction. Consider a light beam that is travelling away from a gravitational field. Its frequency should shift to lower values. This is known as the gravitational red shift of light." https://courses.physics.illinois.edu/phys419/sp2011/lectures/Lecture13/L13r.html

That is, as light falls in gravity, its speed and frequency increase proportionally, as predicted by Newton's theory. The wavelength remains constant.

This implies that there is no gravitational time dilation - Einstein's general relativity is nonsense.