# Basic electric field - extremely granular question

In an effort to understand a basic electric field at its most granular (as per scientific community collective understanding in 2016) I thought I'd finally ask a question that's been on my mind for too long.

By way of example... There's a proton in space with nothing else around it for miles. Is there actually a field emitted on the space around it by this proton or is the field/field lines construct we use in theory just a statistical way to represent what will happen in a universe of trillions of subatomic particles bumping into each other billions of times a second to settle into a low energy state?

Now if in fact there is a field emitted, do we know what this field actually is...? waves? other particles?

& again, iff a field, then surely an orbiting electron which can't be superimposed on the proton creates a moving imbalance of field as it orbits at a distance? something we don't hear about in the classroom.

We can identify any point in spacetime by its coordinates $(t, x, y, z)$ and at any point in spacetime the electric vector can have some value $\mathbf E$. We use the notation $\mathbf E(t, x, y, z)$ to mean the value of the electric vector at every position in space and every time, and this object is what we call the electric field.
So the electric field is just the value of a vector at every place and time. These values $\mathbf E$ can't be just some random value. The values $\mathbf E(t, x, y, z)$, and the magnetic field $\mathbf B(t, x, y, z)$, are related to each other and to the electric charges present by Maxwell's equations. But the electric field exists everywhere in the universe though at some points $(t, x, y, z)$ its value may be zero.
So if we have a universe then the electric field exists, and has a value, everywhere in that universe. Having a single isolated proton places constraints of the values of the electric field i.e. the field varies according to Gauss' law. If you introduce trillions of subatomic particles bumping into each other billions of times a second then the values $\mathbf E(t, x, y, z)$ will vary with position and time in a very complicated way, but it's still the same electric field and still described in the same way by Maxwell's equations.