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Controlling the group velocity of an optical pulse typically requirestraversing a material or structure whose dispersion is judiciously crafted.Alternatively, the group velocity can be modified in free space by spatiallystructuring the beam profile, but the realizable deviation from the speed oflight in vacuum is small. Here we demonstrate precise and versatile controlover the group velocity of a propagation-invariant optical wave packet in freespace through sculpting its spatio-temporal spectrum. By jointly modulating thespatial and temporal degrees of freedom, arbitrary group velocities areunambiguously observed in free space above or below the speed of light invacuum, whether in the forward direction propagating away from the source oreven traveling backwards towards it.

Optical space-time wave packets having arbitrary group velocities in free space