The travelling wave group is a stable wave packet. Many surprising results are derived from it. The group is easily quantized for photons and applied, as a solution to the relativistic Klein-Gordon equation, to free particles. Further solutions to the resulting algebraic equation provide a stable wave function for free antiparticles. Consistency with the superstructure of quantum electrodynamics is obtained by an assignment to the electron antiparticle of negative mass and negative charge. Then in 5-dimensional space-time-mass, CPT invariance transforms to M’PT conservation in either charged or neutral particles, while many other consequences are also evident.