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My physics is fairly basic, but I hope someone can answer without being too rude.

A transparent medium such as water or glass refracts light and also reduces its speed, so I was wondering whether since light can be bent by gravity as in gravitational lensing, its speed would also be affected.

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It is true that the speed of light varies in transparent substances, and this variation in the speed of light, combined with some conservation of momentum and wave optics, is what produces effects such as refraction, which is a bending of light.

It is also true that astronomers have observed the bending of light by various astronomical bodies, from the sun to distant galaxies, which often can make the distortions appear quite dramatic.

What is not true, however, is that this effect can be explained by a "slowing" of light in the area around the gravitating body. In particular, you don't see any dispersion effects (in most materials, the speed of light is different for different colors, which blurs multicolored images) when objects gravitationally lens, which is not observed for gravitational lensing.

Now, you might say, what about a qualitatively different "slowing" effect? This might be possible (I at least don't know of any direct measurements of the speed of light varying near massive bodies), but there is a compelling theoretical reason to think that this is NOT what is happening - General relativity is the currently accepted theory of gravity, and general relativity explains gravity by a curving of spacetime. It therefore predicts a bending of light near massive bodies because the light is travelling through a curved spacetime. The space is still empty, it's just been affected by the massive body.

Relativity was invented to explain other anamolies in theory and experiment (an inconsistency between gravity and special relativity, along with a known flaw of Newtonian mechanics in explaining errors in the orbit of Mercury, amongst other things), and this bending is something that it actually PREDICTED -- Eddington's expedition to observe the bending of light by the sun, and his measuremnt agreeing with the predictions of general relativity was the point where the theory started to advance into mainstream acceptance. Similarly, relativity was used to predict the expansion of the universe, in contradiction to most of the existing literature on the topic at the time.

So, if you did away with the explanation of gravitational lensing in terms of general relativity, you'd have to find another way to predict all of the things that relativity gets right.

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Thank you, though I would still be interested to know whether it had been checked. Even the difference between gravity at sea level and the international space station might be sufficient to enable this to be done without needing reference to a really massive body such as the sun. Part of my reasoning for asking was that I was thinking of the variation of atomic clocks with gravity affecting the atomic state transition rates for which quantum theory might be more appropriate, and wondering whether light might be similarly affected. –  Robert Jones Jan 27 at 5:11
    
Additionally, to go off at a tangent, since space is not a vacuum and given the vast distances involved, might the increased (albeit still locally very sparse) amount of matter nearer large bodies itself cause refraction and consequently add to gravitation lensing. –  Robert Jones Jan 29 at 21:36
    
Thinking about it a little more, one would then expect to see some dispersion effects, which you say don't occur. –  Robert Jones Jan 29 at 21:56
    
Still trying to get my head around this, but I think that since gravity affects time, then the speed of light in a vacuum would vary with regard to a single reference point, but would always be travelling at the accepted value of around 300,000 kms/sec, it's just that the seconds would be of different lengths according the gravitational field that it had passed through. –  Robert Jones Jan 31 at 0:01

It's actual speed remains constant as long as it is passing through a vacuum. Light slows down in various media because the photons are bouncing off of the atoms comprising the media. Therefore the denser the medium, the slower the light because these atoms and molecules are closer together. But the same does not apply in a vacuum. Whenever light is in a vacuum, its speed is C. It's direction can change due to gravity but its actual speed remains constant.

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I don't think it's actually due to photons bouncing around. If it were they'd be imparting a bit of momentum each time they did and lose energy. Instead I think it's the interaction between the varying electric field of the photon inducing a variation in the electric field of the material it is passing through and interacting with this oscillation which slows it down. –  Brandon Enright Jan 29 at 6:07

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