  We study the propagation of non-interacting polariton wavepackets. We show
how two qualitatively different concepts of mass that arise from the peculiar
polariton dispersion lead to a new type of particle-like object from
non-interacting fields---much like self-accelerating beams---shaped by the Rabi
coupling out of Gaussian initial states. A divergence and change of sign of the
diffusive mass results in a "mass wall" on which polariton wavepackets bounce
back. Together with the Rabi dynamics, this yield propagation of ultrafast
subpackets and ordering of a spacetime crystal.
