  We show that all laser beams gradually lose their initial phase information
in nonlinear propagation. Therefore, if two beams travel a sufficiently long
distance before interacting, it is not possible to predict whether they would
intersect in- or out-of-phase. Hence, if the underlying propagation model is
non-integrable, deterministic predictions and control of the interaction
outcome become impossible. Because the relative phase between the two beams
becomes uniformly distributed in $[0,2\pi]$, however, the statistics of the
interaction outcome are universal, and can be efficiently computed using a
polynomial-chaos approach, even when the distributions of the noise sources are
unknown.
