  The Casimir-Polder force is an attractive force between a polarizable atom
and a conducting or dielectric boundary. Its original computation was in terms
of the Lamb shift of the atomic ground state in an electromagnetic field (EMF)
modified by boundary conditions along the wall and assuming a stationary atom.
We calculate the corrections to this force due to a moving atom, demanding
maximal preservation of entanglement generated by the moving atom-conducting
wall system. We do this by using non-perturbative path integral techniques
which allow for coherent back-action and thus can treat non-Markovian
processes. We recompute the atom-wall force for a conducting boundary by
allowing the bare atom-EMF ground state to evolve (or self-dress) into the
interacting ground state. We find a clear distinction between the cases of
stationary and adiabatic motions. Our result for the retardation correction for
adiabatic motion is up to twice as much as that computed for stationary atoms.
We give physical interpretations of both the stationary and adiabatic atom-wall
forces in terms of alteration of the virtual photon cloud surrounding the atom
by the wall and the Doppler effect.
