  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.
