A modified Kaluza-Klein theory is proposed in which propagation takes place only at the speed of light. The propagation can be confined to a small volume, forming a particle with rest mass. The usual four space-time coordinates locate the confinement volume, and Kaluza's fifth coordinate is replaced by an internal degree of freedom. Electromagnetism corresponds to a gauge field on the phase of the internal motion. Self-gravity might create the confinement, as in a geon, but the particle would have a Planck mass. This large mass could be made closer to the masses of observed particles if gravity were allowed to increase in strength within the confinement volume.