  Temporally modulated optical media are important in both abstract and applied
applications, such as spacetime transformation optics, relativistic
laser-plasma interactions, and dynamic metamaterials. Here we investigate the
behaviour of temporal boundaries, and show that traditional approaches that
assume constant dielectric properties, with loss incorporated as an imaginary
part, necessarily lead to unphysical solutions. Further, although physically
reasonable predictions can be recovered with a narrowband approximation, we
show that appropriate models should use materials with a temporal response and
dispersive behaviour.
