  Einstein's famous equation $E_{\rm rest}=mc^2$ for the rest energy of a
system with mass $m$ requires that the internal energy of the system be
included in $m$. Pursuing this idea using Lagrangian and Hamiltonian dynamics
yields a relativistic coupling between the center of mass motion and the
internal dynamics of the system. Here we explore the consequences of this
coupling, first classically, where we find that the dynamics of the system is
time dilated when moving relative to another inertial frame. We then apply the
dynamics to a quantum 2-level atom bound in a 1-dimensional infinite potential
well, and show that the coupling produces collapses and revivals in quantum
interference.
