  The usual multipolar Hamiltonian for atom-light interaction features a
non-relativistic moving atom interacting with electromagnetic fields which
inherently follow Lorentzian symmetry. This combination can lead to situations
where atoms appear to experience a friction force, when in fact they only
change their internal mass-energy due to the emission or absorption of a
photon. Unfortunately the simple Galilean description of the atom's motion is
not sufficient to distinguish between a change in momentum due to acceleration
and a change in momentum due to a change in internal mass-energy. In this work
we show how a low-order relativistic correction can be included in the
multipolar atom-light Hamiltonian. We also give examples how this affects the
most basic mechanical interactions between atoms and photons.
