How two electric charges know about each other?

Question

Suppose we have two electric charges $q_1$ and $q_2$ a distance $r$ apart in euclidean three-space. Coulomb's force law states that there's a force

$$\mathbf{F}_{12} = \dfrac{1}{4\pi\epsilon_0} \dfrac{q_1q_2}{r^2}\hat{\mathbf{r}}$$

between them. Now, what I'm wondering is how the two charges know about each other? How can one charge know that there's another charge there exerting a force over it? One way I believe could explain this was: "charge $q_i$ generates an electric field $\mathbf{E}_i$ which is felt by charge $q_j$" but this ends up bringing two other questions:

The electric field is introduced more as a mathematical object than a physical object. We introduce the field $\mathbf{E}$ so that the force exerted on a charge $q$ is $q\mathbf{E}$. The field itself can then be considered the force per unit charge with this charge made small enough so that it won't change the original configuration. In that case, what it would really mean to generate a field and percept a field?
Even if we explain with the field, the second question naturally is: how the other charge knows that a field is there and how this field interacts with it really?

I didn't study quantum field theory yet, however, I imagine the more fundamental explanation would have to do with photons intermediating the process by which one charge feels the other. Is it really the case? How can we really understand how two charges know each other and by which mechanism they interact?

possible duplicate of 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? — Sofia, Mar 04 '15 at 01:07
Possible duplicates: http://physics.stackexchange.com/q/197/2451 , http://physics.stackexchange.com/q/2244/2451 and links therein. — Qmechanic, Mar 04 '15 at 06:39

score 1 · Answer 1 · answered Mar 04 '15 at 01:48

The electric field is introduced more as a mathematical object than a physical object.

The electromagnetic field is an entity that both stores and transports energy and momentum. Radio and light depend on the existence of this entity. When quantized, the electromagnetic field (four-potential) quanta are physical entities; photons.

How the other charge knows that a field is there and how this field interacts with it really?

In a very real sense, that which interacts with the electromagnetic field defines electric charge; electric charge is that which 'knows' (interacts with) the electromagnetic field.

I imagine the more fundamental explanation would have to do with photons intermediating the process by which one charge feels the other. Is it really the case?

It is really the case that quantum electrodynamics (QED) models reality this way.

How two electric charges know about each other?

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