Negative refraction by quantum vacuum

The phase velocity of light is co-parallel to the direction of energy flow in classical vacuum. However, in certain uncommon materials, these two vectors can be oppositely directed, in which case the phase velocity is termed `negative'. This negative phase velocity (NPV) gives rise to many exotic phenomenons, such as negative refraction, inverse Doppler shift and inverse Cerenkov radiation, and has technological allure. According to quantum electrodynamics, the presence of a magnetostatic field makes vacuum an anisotropic medium for the passage of light. Under the influence of a sufficiently strong magnetostatic field, vacuum supports NPV. Such ultrastrong magnetic fields are believed to arise due to dynamo action in newborn neutron stars and in binary neutron star mergers, for examples. In view of the possible occurrence of negative refraction, the influence of ultrastrong magnetostatic fields must be carefully taken into account in astronomical observations relating to neutron stars and associated gamma-ray bursts.