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A time interface (a rapid change of the constitutive parameters of a materialin time), applied within an unbounded medium where a wave travels, can enablefrequency conversion, and is considered the temporal analogue of a spatialinterface between two materials. Here, we study light-matter interactions infour dimensions, 4D (space, x,y,z, and time, t), by exploring the implicationsof applying time interfaces not to the entire space where a wave travels, butto certain regions of space in order to create spatial interfaces in time.Different configurations such as induced perpendicular, parallel, and obliquespatial interfaces via a temporal interface are discussed. It is shown how suchfour-dimensional combinations of temporal and spatial interfaces can enableinteresting features such as the 4D generalized Snell law and the temporalchirp, temporal lensing, and temporal routing of electromagnetic waves. Suchexotic possibilities may provide new ways to manipulate light-matterinteractions via a combination of temporal and spatial interfaces.

Temporal chirp, temporal lensing and temporal routing via space-time interfaces