  We show that there exist non-relativistic scattering experiments which, if
successful, freeze out, speed up or even reverse the free dynamics of any
ensemble of quantum systems present in the scattering region. This time
translation effect is universal, i.e., it is independent of the particular
interaction between the scattering particles and the target systems, or the
(possibly non-Hermitian) Hamiltonian governing the evolution of the latter. The
protocols require careful preparation of the probes which are scattered, and
success is heralded by projective measurements of these probes at the
conclusion of the experiment. We fully characterize the possible time
translations which we can effect on multiple target systems through a
scattering protocol of fixed duration. The core results are: a) when the target
is a single system, we can translate it backwards in time for an amount
proportional to the experimental runtime; b) when n targets are present in the
scattering region, we can make a single system evolve n times faster (backwards
or forwards), at the cost of keeping the remaining systems stationary in time.
For high n our protocols therefore allow one to map, in short experimental
time, a system to the state it would have reached with a very long unperturbed
evolution in either positive or negative time.
