Non-Markovian Abraham-Lorentz-Dirac equation: Radiation reaction without pathology

Motion of a point charge emitting radiation in an electromagnetic field obeys the Abraham--Lorentz--Dirac equation, with effects reaction or self-force incorporated. This class equations describing backreaction, including also for gravitational Einstein's equation cosmology driven by trace anomaly, contains third-order derivative terms. They are known to have pathologies like possession runaway solutions, causality violation preacceleration, and need extra second-order initial condition. In our current program we reexamine this old problem from different perspective, that non-Markovian dynamics open systems. conceptual technical framework has been applied earlier study backreaction quantum on mass motions early universe cosmology. Here consider moving atom whose internal degrees freedom, modeled harmonic oscillator, coupled scalar same manner as electrodynamics. Due way it is charged particle, acts effectively supra-Ohmic environment, although itself actually Ohmic spectral density. We thus cast Brownian oscillator environment. Our analysis shows (a) there no specifying second condition, (b) preacceleration. These undesirable features conventional treatments arise inconsistent Markovian assumption: these were regarded ab initio, not limit backreaction-imbued motion. If one starts full dynamical takes proper judiciously, harms done. Finally, c) causal relation between higher-derivative term motion existence solutions. The behavior consequence memory time environment shorter than critical value, which case particle classical radius. effective size greater its stable. When reasonable condition met, understood treated correctly non-Ohmic still but does require