Mechanical momentum of the EM field in a continuum? Given an uncharged continuum the EM field produces no force on it. Yet in a discrete system we know that atoms are not uncharged locally and momentum can be exchanged due to the electric field(Which Maxwell's equations are suppose to govern).
viz., The transfer of momentum between atoms is due to the electric field(although it's not as simple as the 1/r^2 version). Maxwell's equations should describe the motion of the atoms exactly when one includes the Lorentz force and Newton's second law.
Yet when one moves up to the continuum these microscopic effects no longer exist and the electric field cannot influence the mechanical motion of density if it is not charged.
How can we include this in Maxwell's equations(or probably instead in the Lorentz force)?
I'm thinking that we simply use and it's conservation law(on the same page)
http://en.wikipedia.org/wiki/Electromagnetic_stress-energy_tensor
but there doesn't seem to be a way of controlling how well the EM energy is coupled to the material(Some materials will experience a larger motion due to the EM field it experiences).
or even
http://en.wikipedia.org/wiki/Maxwell_stress_tensor
in both cases though q = 0 for the continuum. 
I think was thinking that possibly one could temporarily treat the continuum as being charged even though it isn't which will allow the momentum due to the field to propagate and one could compute forces and such. With proper scaling one might get the same effect as if modeling a discrete material. Effectively one is breaking up the material into positive and negative charge, computing the momentum then subtracting... in a continuum this is 0 but for the discrete case it cannot be zero unless there are no particles.
What is a better way? How can one model the microscopic collision transfer of momentum that can be applied to the continuous case?
 A: 
Given an uncharged continuum the EM
  field produces no force on it.

This seems to be a root assumption of your question, so let's examine it a little bit. What do you mean by an 'uncharged continuum'? Would you consider a small glass bead to be an uncharged continuum? If so, this statement is disproved by optical tweezers.
If you mean something else, perhaps you could clarify your question.
EDIT:
Chapter 6.6 of Jackson's Electrodynamics has a pretty nice derivation of how you go from microscopic to macroscopic. Pay particular attention to polarizability.
A: A continuum distribution of matter, even if it is, in the bulk, electrically neutral, does not need to be electrically inert.  In particularly, it is still able to obtain a Polarization density that is dependent on an external electric and magnetic field.  This enables such materials to interact with electromagnetic waves.  
And of course, in principle, there's nothing that is inherently banned by the laws of physics in having light just pass directly through matter without interacting with it.  
A: This is related to the old Abraham-Minkowski controversy: What is the momentum of a  photon in a dielectric?  A long and troubled story!
A  recent  review is  "Momentum of an electromagnetic wave in dielectric media" by 
R. Pfeifer, T. A. Nieminen et al: arxiv 0710.0461.
