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

Relativistic coupling of internal and center of mass dynamics in classical and simple bound quantum mechanical systems