Paradox of radiation of charged particles in a gravitational field fields. One of the first to study this problem was Max Born in his 1909 paper about the consequences of a charge in uniformly accelerated frame. Earlier concerns and possible solutions were raised by Wolfgang Pauli (1918), Max von Laue (1919), and others, but the most recognized work on the subject is the resolution of Thomas Fulton and Fritz Rohrlich in 1960. It is a standard result from Maxwell's equations of classical electrodynamics that an accelerated charge radiates. That is, it produces an electric field that falls off as formula_1 in addition to its rest-frame formula_2 Coulomb field. This radiation
Refraction wave vector depend on the wave speed this requires a change in direction of the wave vector. The relevant wave speed in the discussion above is the phase velocity of the wave. This is typically close to the group velocity which can be seen as the truer speed of a wave, but when they differ it is important to use the phase velocity in all calculations relating to refraction. A wave traveling perpendicular to a boundary, i.e. having its wavefronts parallel to the boundary, will not change direction even if the speed of the wave changes. Refraction of light can