On vacuum negative refraction, the effective medium and Sylvester's Inertia Theorem: the resolution of a paradox

Abstract

We previously showed that gravitationally induced negative refraction based on an effective medium analysis is actually a geometric artifact in flat Minkowski spacetime. However, this conclusion apparently conflicts with Sylvester's Inertia Theorem, wherein the effective medium tensors defined by the spacetime metric cannot change signature under linear transformation. Here we resolve the paradox by analysing how the effective medium tensors in 3-space transform in the four dimensions of spacetime.