How is the electostatic field propagated by the vacuum? How does a charge feel the presence of another charge when there is NOTHING between them? Is the word "vacuum" equal to "nothing"?
Imagine two charges of opposite sign, far from one another in vacuum, and moving with constant velocity - s.t. none radiates energy, none emits photons.
At some time though, the course of their movement brings them closer. They begin to accelerate toward one another.
How do they feel the presence of one another? During their constant movement no photons are emitted, no "information" spreads in the universe about their presence.
 A: "Vacuum" actually means the ground state of space. When there are real particles in space, "it" is in an excited state, and no longer the vacuum. But we usually think of a small region of empty space as approximating a vacuum, for reasons of locality, etc. If you have two real particles in space, and talk about their mutual interaction, then you necessarily have photons. This is because the force between the two particles is mediated by the electromagnetic field, which, when quantized, leads to photons.  This is because the $\vec{E}$ and $\vec{B}$ fields, like any physical thing, needs a quantum mechanical treatment. For example, if you wanted to "derive" the Coulomb force between two electrons from quantum electrodynamics (this is done as an exercise in Peskin and Schroeder), then you need to consider scattering events like the following:

So it's not that the space between the two charged particles is "empty", but that there is an exchange of virtual photons between them (the $\gamma$ in the diagram).
However, while electron number is fairly good label for a state, photon number isn't (being massless). The state of the EM field with a single (macroscopic) point charge in it is already a horribly complicated wavefunction. But we can say that this state has maximum amplitude around a field configuration for which $\vec{E} = \frac{1}{4\pi\varepsilon_0 r^2} \hat r$. On the other hand, $\vec{E}$ and $\vec{B}$ can roughly be thought of as conjugate pairs, like $x$ and $p$, so there is also an uncertainty relation at play, so our field configuration is not exact. The best we can do is a coherent state. This is all perturbation theory, so it doesn't give the complete picture, but it's a good undergraduate level of understanding.
Maybe someone has a good link for coherent states in quantum optics. This one might be a start.
