They don't. A photon absorbed by an atom/molecule can be re-emitted in any direction. Imagine a thick piece of glass being traversed by a light beam: most of the photons will traverse it undisturbed (and thus maintain their original direction), but a few will be scattered all around (and that's the light you can see if you watch "inside" the glass from one of its sides). On the other hand, depending on the light frequency and the crystalline structure of the material, photons can be scattered by the whole lattice itself, rather than by the single atoms/molecules. In this case, the direction follows the "rule of the mirror", which is dictated by quantum mechanics.

On average it's a requirement of the conservation of momentum. But note that sometimes photons come out in a different direction (scattered), including to opposite direction (reflection). In these cases the momentum is absorbed by the medium.

This is actually a very deep question. If you want a better answer than I'm about to give, read Feynman's QED lecture videos [1] or read the book [2].

The short answer is, they don't. They emit the photon in a random direction.

Fine, you say, but what about refraction and reflection, there the photons are emitted in another direction. What makes the atom "decide" what direction to emit a photon after it's absorbed?

They don't decide anything, they still just emit in a random direction. The mind fuck is that on the whole, statistically, almost all photons except for those travelling in the direction of refraction/reflection destructively interfere!

[1] http://vega.org.uk/video/subseries/8 [2] http://www.amazon.com/QED-Strange-Theory-Light-Matter/dp/069...

Very good question. Here's the gist of it, a rough way of thinking about it.

A time varying electromagnetic field is produced by moving charges (except for a minor distinction about steady currents). The direction of motion of the charges determines the polarization of the emitted field. Later on, when the field encounters matter it produces an identical motion of charges i.e; if originally an East-West charge motion produced a North-South field then a N-S field will induce an E-W motion among new charges which in turn re-emit N-S light. The original light and the re-emitted light interfere, the delay is what slows the light down, as noted by others. But you can see why the direction is the same.

Note: I suppose this picture is somehow tied to reciprocity of the Maxwell equations between sources and fields, I need to go look it up again.

They don't. But the re-emitted photons become part of a coherent wavefront through what Richard P. Feynman called a Path Integral:

http://en.wikipedia.org/wiki/Path_integral_formulation

So the reason you have a coherent wavefront moving through a lens, as one example, is not because the photons are emitted in a particular direction, but at a particular time.

They don't -- they are re-emitted in random directions that are statistically related to the original direction: http://en.wikipedia.org/wiki/Scattering .