Space-time refraction of space-time wave packets

Refraction is usually understood as a boundary rule relating the direction and frequency of a wave across an interface. In space-time photonics, this picture is incomplete because both the medium and the wave can carry space-time structure. A space-time index modulation can form a synthetic moving boundary, whereas a space-time wave packet carries a prescribed group velocity through spatio-temporal spectral correlations. We show that their interaction is governed not by isolated spectral components alone, but by how the moving boundary transforms the geometry of the space-time spectrum as a whole. We develop a theory of space-time refraction for multiple space-time wave-packet families at a translating planar interface between homogeneous, nondispersive media. Even without material dispersion, and for the same two media and interface velocity, different packet families follow different group-velocity maps. This leads to effects with no spatial counterpart, including velocity compression, where many incident group velocities map to a narrow transmitted band, and velocity fission, where a single incident wave packet splits into two propagation-invariant branches with different velocities. The results identify moving interfaces as programmable transformations of structured light, with implications for programmable delay control, signal routing, controlled quantum emission, and analog-gravity platforms.