  Understanding possible universal properties for systems far from equilibrium
is much less developed than for their equilibrium counterparts and poses a
major challenge to present day statistical physics. The study of aging
properties, and how the memory of the past is conserved by the time evolution
in presence of noise is a crucial facet of the problem. Recently, very robust
universal properties were shown to arise in one-dimensional growth processes
with local stochastic rules,leading to the Kardar-Parisi-Zhang universality
class. Yet it has remained essentially unknown how fluctuations in these
systems correlate at different times. Here we derive quantitative predictions
for the universal form of the two-time aging dynamics of growing interfaces,
which, moreover, turns out to exhibit a surprising breaking of ergodicity. We
provide corroborating experimental observations on a turbulent liquid crystal
system, which demonstrates universality. This may give insight into memory
effects in a broader class of far-from-equilibrium systems.
