Suppose I have a positively charged conductor with a cavity. There's a positive charge inside the cavity and the system has reached electrostatic equilibrium. Then there's negative charge surrounding the cavity and positive charge on the surface of my conductor. If I apply gauss law to the interior of the conductor I conclude that the electric field is zero at every point of my gaussian surface, and if it weren't so, then charged particles would be accelerating or whatever.
But my question is: why don't the atoms in the interior affect the electric field? I mean, even if the atoms are neutral (consider now a non-conducting material) they have charges inside that should somehow alter the electric field in the neighborhood.
What's going on?