NonMarkovian Abraham--Lorentz--Dirac Equation: Radiation Reaction without Pathology

Abstract

Motion of a point charge emitting radiation in an electromagnetic field obeys the Abraham-Lorenz-Dirac (ALD) equation, with the effects of radiation reaction or self-force incorporated. This class of equations describing backreaction, including also the equations for gravitational self-force or Einstein's equation for cosmology driven by trace anomaly, contain third-order derivative terms. They are known to have pathologies like the possession of runaway solutions, causality violation in pre-acceleration and the need for an extra second-order derivative initial condition. In our current program we reexamine this old problem from the perspective of non-Markovian dynamics in open systems, applied earlier to backreaction problems in the early universe. Here we consider a harmonic atom coupled to a scalar field, which acts effectively like a supra-Ohmic environment, as in scalar electrodynamics. Our analysis shows that a) there is no need for specifying a second derivative for the initial condition; b) there is no pre-acceleration. These undesirable features in conventional treatments arise from an inconsistent Markovian assumption: these equations were regarded as Markovian ab initio, not as a limit of the backreaction-imbued non-Markovian equation of motion. If one starts with the full non-Markovian dynamical equation and takes the proper Markovian limit judiciously, no harms are done. Finally, c) There is no causal relation between the higher-derivative term in the equation of motion and the existence of runaway solutions. If the charge has an effective size greater than this critical value, its dynamics is stable. When this reasonable condition is met, radiation reaction understood and treated correctly in the non-Ohmic non-Markovian dynamics still obeys a third-order derivative equation, but it does not require a second derivative initial condition, and there is no pre-acceleration.

37 pages, 8 figures

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