  Hyperbolic metamaterials may be used to model a 2+1 dimensional Minkowski
spacetime in which the role of time is played by one of the spatial
coordinates. When a metamaterial is built and illuminated with a coherent
extraordinary laser beam, the stationary pattern of light propagation inside
the metamaterial may be treated as a collection of particle world lines, which
represents a complete history of this 2+1 dimensional spacetime. While this
model may be used to build interesting spacetime analogs, such as metamaterial
black holes and big bang, it lacks causality: since light inside the
metamaterial may propagate back and forth along the timelike spatial
coordinate, events in the future may affect events in the past. Here we
demonstrate that a more sophisticated metamaterial model may fix this
deficiency via breaking the mirror and temporal (PT) symmetries of the original
model and producing one-way propagation along the timelike spatial coordinate.
Resulting 2+1 Minkowski spacetime appears to be causal. This scenario may be
considered as a metamaterial model of the Wheeler-Feynman absorber theory of
causality.
