  The infinite superpositions of random plane waves are known to be threaded
with vortex line singularities which form complicated tangles and obey strict
topological rules. We observe that within these structures a timelike axis
appears to emerge with which we can define vortex velocities in a useful way:
with both numerical simulations and optical experiments, we show that the
statistics of these velocities match those of turbulent quantum fluids such as
superfluid helium and atomic Bose-Einstein condensates. These statistics are
shown to be independent of system scale. These results raise deep questions
about the general nature of quantum chaos and the role of nonlinearity in the
structure of turbulence.
