Modeling of causality with metamaterials

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.