  Analogue physics has successfully tackled the problems of chromodynamics,
event horizons, Big Bang and Universe expansion, and many others. Here, we
suggest a photonic model system for a "time machine" based on the paraxial beam
approximation. We demonstrate how the closed time-like curves and the
well-known grandfather paradox can be studied experimentally in this system. We
show how the Novikov's self-consistency principle is realized in quantum
mechanics thanks to the Heisenberg's uncertainty principle.
