 This work develops a field theory for soft matter systems with two different time scales, allowing for a phase field crystal model for active particles with translational and orientational memory. The resulting theory is of third order in temporal derivatives and can be seen as a spatiotemporal jerky dynamics. The phase diagram shows that the linear stability of the liquid state depends on damping coefficients and sound waves in active fluids have two different mechanisms for propagation, with polarization waves experiencing less damping than usual passive sound waves for certain parameter values and frequencies. This article was authored by Michael T. Rutt, Julian Jegel and Raphael Witkowski.