# Gravitation as varying density of a space-propertime manifold?

bcrelling
Originally I asked on another thread whether the GR effects on light can be described as light passing through a medium of varying density- so exerting its effects by refraction.

A.T. kindly posted the following links:

http://www.newscientist.com/article/dn24289#.UlsOR-B3Zmh
http://www.nature.com/nphoton/journal/vaop/ncurrent/full/nphoton.2013.247.html

However his the post was erased(I can only assume for necroposting as Nature Photonics is peer reviewed).

The links seem to confirm my original suspicions that the gravitational effect on light is caused by refraction, and A.T. suggested this medium would be varying densities of "space-proper time".

Does anyone have issues with this explanation as it is much simpler to understand and would be a useful teaching aid if it were correct?

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Does anyone have issues with this explanation as it is much simpler to understand and would be a useful teaching aid if it were correct?
How many issues would you like to see? The first one is a general philosophical objection to "simpler models that are easier to understand." This usually means trying to explain relativity or quantum mechanics in classical terms. So we pretend that gravity causes an index of refraction, and avoid thinking about all that curved space stuff. But the problem with simplistic models is that they get taken too seriously. Every model has limitations. Soon the limitations get overlooked. People start to think it's the index of refraction of some real substance. Causing more puzzlement than if they had learned about the curved space stuff to begin with.

Ok, other objections. This is an ancient idea, but to make the model at all plausible, the index of refraction at a point should be the same in all directions. That is, you need to use isotropic coordinates. First you will have a hard time explaining why the speed of light we measure in the lab is c, even though n here on Earth is greater than 1.

What happens to the value of n when you perform a Lorentz transformation?

Next, a static metric in isotropic coordinates has two independent functions, gtt and grr. You're replacing them with one function n(r), and this represents a loss of information. In other words, you'll be able to choose n(r) to fit the light deflection, but not other effects. In particular, I believe you'll get the wrong answer for the Shapiro delay.

At the surface of a black hole, which is a stationary null surface, you'll need to let n go to infinity.

And for a rotating solution like Kerr, you won't be able to use this idea at all. The light paths in Kerr depend on whether you're going clockwise or counterclockwise, and one index of refraction won't suffice to explain both.

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