How is light trajectory affected by the trajectory of environment it passes through? There's a sci-fi concept of slow light that I find very amazing:
Imagine a glass material that has index of refraction $n$ say, $3,000,000,000$ which means:
$$v_{glass} = \frac{c_{vacuum}}{n} = 0.0001 ms^{-1} = 0.1 mm\ s^{-1}$$
Simply a glass material that reduces the light propagation speed to $0.1\ mm/s$. A glass that shows what happened 10 seconds ago if it's 1 centimetre thick.
I was thinking about this and I happened to imagine a cube made of the same material, $1\times 1$ meter. Now imagine pointing a laser pointer in the cube. It's going to take $00:16:40$ for the beam to pass.
Now the question: If you move the cube around or rotate it, will you alter the beam rotation?
My guess is yes, but quantum physics doesn't always follow the rules of common sense.
I want to point out that no matter what the answer is, it's not only matter of fictional cubes but the real world too - flowing water in the river, blowing air...
 A: Yes, you will alter the beam direction, but not by the same amount as you rotated the cube.
The reason I think this is what happens is as follows. Light can interact with phonons ('quanta of movement in the material'). For example, acousto-optic modulators make explicit use of this coupling to change the direction of an incoming laser beam. They are often used in the lab. 
So, movement of the material is coupled to the movement of the photon. (This coupling might be strong or weak depending on the material).
Since there is limited time for the movement of the material to be transfered to the change in direction of the photon, it will not rotate the beam by the same angle as you rotated the cube. There will be a certain rate at which rotation of the cube will be transfered to rotation of the photons (depending on the strength of the coupling). When you have very strong coupling and enough time for the rotation of the material to be transfered to the rotation of the photons, the rotation of the photons might approach the rotation of the cube.
