Paper detail

Ambiguity in deriving Larmor's formula from the LAD equation of motion

The power radiated by a moving charge is given by Larmor's formula which can be derived by integrating the Liénard-Wiechert potential over the whole past history of the charge. However, extracting the same result from the Lorent-Abraham-Dirac (LAD) equation of motion is problematic. This is well known for uniform proper acceleration for which case the radiation force vanishes and hence the very origin of the radiated energy is not clear, leading to an energy balance paradox. The purpose of this letter is first to evince that this problem occurs in the general case and not only for uniform acceleration. Second we show that the widely accepted treatment based on the bound field technique cannot fix the energy balance discrepancy. Indeed the related Schott term is not a legitimate four-momentum for being indefinite and not conserved.