Metamaterials, gamma-ray bursts, quantum gravity, and the search for the missing half of the maxwell equations

Although microwave metamaterials may seem unrelated to gamma-ray astrophysics, it is shown that both phenomena may be expressed using left-handed extensions to Maxwell's equations. For metamaterials, such extensions represent the left-handed behavior of materials. For gamma-ray bursts, such extensions represent unknown dispersive processes, such as quantum gravity, where GeV gamma rays commonly arrive significantly later than low-energy photons. Recent quadratic gamma-ray dispersion models then lead to modified Helmholtz equations and concomitant extensions to Maxwell's equations. The resulting differential equations are shown to be identical to certain metamaterial models, with right-handed low-frequency behavior, a forbidden band, and left-handed high-frequency behavior.