  Controlling the group velocity of an optical pulse typically requires
traversing a material or structure whose dispersion is judiciously crafted.
Alternatively, the group velocity can be modified in free space by spatially
structuring the beam profile, but the realizable deviation from the speed of
light in vacuum is small. Here we demonstrate precise and versatile control
over the group velocity of a propagation-invariant optical wave packet in free
space through sculpting its spatio-temporal spectrum. By jointly modulating the
spatial and temporal degrees of freedom, arbitrary group velocities are
unambiguously observed in free space above or below the speed of light in
vacuum, whether in the forward direction propagating away from the source or
even traveling backwards towards it.
