  The interaction of light with superluminally moving matter entails
unconventional phenomena, from Fresnel drag to Hawking radiation and to light
amplification. While relativity makes these effects inaccessible using objects
in motion, synthetic motion - enabled via space-time modulated internal degrees
of freedom - is free from these constraints. Here we observe synthetic velocity
of a reflectivity modulation travelling on an Indium-Tin-Oxide (ITO) interface,
generated by ultrafast laser illumination at multiple positions and times. The
interaction of the moving reflectivity modulation with a probe light beam acts
as a non-separable spatio-temporal transformation that diffracts the light,
changing its frequency and momentum content. The recorded frequency-momentum
diffraction pattern is defined by the velocity of the diffracted probe wave
relative to the modulation. Our experiments open a path towards mimicking
relativistic mechanics and developing programmable spatio-temporal
transformations of light.
