  We demonstrate the controlled spatiotemporal transfer of transverse orbital
angular momentum (OAM) to electromagnetic waves: the spatiotemporal torquing of
light. This is a radically different situation than OAM transfer to
longitudinal, spatially-defined OAM light by stationary or slowly varying
refractive index structures such as phase plates or air turbulence. We show
that transverse OAM can be imparted to a short light pulse only for (1)
sufficiently fast transient phase perturbations overlapped with the pulse in
spacetime, or (2) energy removal from a pulse that already has transverse OAM.
Our OAM theory for spatiotemporal optical vortex (STOV) pulses [Phys. Rev.
Lett. 127, 193901 (2021)] correctly quantifies the light-matter interaction of
this experiment, and provides a torque-based explanation for the first
measurement of STOVs [Phys. Rev. X 6, 031037 (2016)].
