  Wave control is usually performed by spatially engineering the properties of
a medium. Because time and space play similar roles in wave propagation,
manipulating time boundaries provides a complementary approach. Here, we
experimentally demonstrate the relevance of this concept by introducing
instantaneous time mirrors. We show with water waves that a sudden change of
the effective gravity generates time-reversed waves that refocus at the source.
We generalize this concept for all kinds of waves introducing a universal
framework which explains the effect of any time disruption on wave propagation.
We show that sudden changes of the medium properties generate instant wave
sources that emerge instantaneously from the entire space at the time
disruption. The time-reversed waves originate from these "Cauchy sources" which
are the counterpart of Huygens virtual sources on a time boundary. It allows us
to revisit the holographic method and introduce a new approach for wave
control.
