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!
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. 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.
When you shine light through glass the maximum propagation speed, the speed at which you start getting photons out the other side, is about 2/3 the speed of light. This implies that the overwhelming majority of photons are adsorbed and re-emitted. So this explanation cannot be correct, as I can look through a pane of glass, but you're saying any photon adsorbed is re-emitted in any direction, and the overwhelming majority of photons must be adsorbed and re-emitted.
Sorry, my fault! We were talking about "absortion"/"stop over" as a way to describe in layman's term the interaction of photons with the glass atomic structure. In this sense, as others pointed out, we are talking about scattering and the final direction is indeed related to the original one. Anyway, light scattering is a quantum process and there is no way of observing the "moment" between "absorption" and "re-emission".
In my comment, I talked about actual absorption, which means that there is a finite time interval when the photon does not exist and the atom/molecule who absorbed it can be observed in a different state than usual (electron in a higher orbital for an atom, different vibrational modes for a molecule). Later, the atom/molecule will go back to its normal state emitting a photon with the same energy as the first one, or several lower energy photons. This actual re-emission will not have a favourite direction. Depending on the typical time scale of the re-emission, you may call this process fluorescence or phosphorescence (http://en.wikipedia.org/wiki/Phosphorescence).
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.
You're either very confused, or you have a much deeper understanding of physics than me. I love that it could be either.
Does the conservation of momentum apply to things with no intrinsic mass?
Yes. You can define a special-relativistic momentum and it's a conserved quantity, and it does have a nonzero value even for things with zero rest mass (which necessarily move at the speed of light).
(It may help to observe that an object with nonzero mass moving at the speed of light would have infinite momentum, and then it maybe makes sense that "zero times infinity" becomes a finite number)
Indeed. That's the idea behind things like solar sails, for instance. Check out the article here- http://en.wikipedia.org/wiki/Radiation_pressure
and scroll down to "Radiation pressure by particle model: photons" if the top is confusing.
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.
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...