Modeling of causality with metamaterials

Abstract

Hyperbolic metamaterials may be used to model a 2 + 1-dimensional Minkowski space–time 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 space–time. While this model may be used to build interesting space–time analogs, such as metamaterial ‘black holes’ and a metamaterial ‘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. The resulting 2 + 1-dimensional Minkowski space–time appears to be causal. This scenario may be considered as a metamaterial model of the Wheeler–Feynman absorber theory of causality.