# Predicting lightpaths after gravitational bending

In this image, we can see the bending of light by gravity. Suppose I put a big glass (it almost has zero weight) of considerable thickness near sun (near the split of the two light paths) which will refract light coming from the star and will change the direction of light.

We can predict the path of light in first case using general relativity. But to predict path of light in the second case, we need general relativity and electromagnetism.

I don't want to use geometrical optics, I want answer using Electromagnetism and General relativity.

Now my question is, to predict path of light in second case do we need Electromagnetism (or QFT) in curved spacetime or do we need to unify Electromagnetism (or QFT) with General relativity into one single theory to predict the path of light?

• Let me ask you a leading question. Suppose you have an electron moving at non relativistic speeds under the influence of a given electric field and of gravity. Do you need to unify EM and gravity to predict its movement? – Javier Aug 18 '15 at 23:54
• Isn't classical electromagnetism already unified with general relativity? Just put in the initial electromagnetic fields, the initial metric and the initial derivatives of the metric. Then the time derivatives of the electromagnetic fields are given by the spatial variations and the second time derivatives of the metric are given by the stress-energy tensor. I'm not sure what difference you want for EM in curved spacetime versus the unification are you saying you want to have EM act on a background metric they don't influence? Like EM on a vacuum spacetime? – Timaeus Aug 19 '15 at 1:56
• @Timaeus Basically I want a single equation, that will predict the path of light in the second image.What I meant by EM in curved spacetime is (en.wikipedia.org/wiki/Maxwell%27s_equations_in_curved_spacetime) and by unifying I mean something like this (en.wikipedia.org/wiki/Kaluza%E2%80%93Klein_theory) Which of these two will give me right answer? – Gary Grey Aug 19 '15 at 2:05
• @GaryGrey I wouldn't use Kaluza Klein but even glass in a flat spacetime can be complicated. Is the glass isotropic? Is it a linear media? You need some way to get the displacement and H fields from knowing the electric and and B fields. In general you need constitutive equations, do you have them already? – Timaeus Aug 19 '15 at 2:33
• KK theory, from memory only, was not able to deal with changes in B and H fields with respect to time. I will delete this if incorrect though. – user81619 Aug 19 '15 at 3:03