Novel and Unique Expression for the Radiation Reaction Force, Relevance of Newton's Third Law and Tunneling

TL;DR

This paper introduces a new expression for the radiation reaction force that is Galilei invariant, avoids problematic derivatives, and incorporates quantum tunneling effects, offering a more consistent classical and relativistic framework.

Contribution

It presents a novel derivation of the radiation reaction force considering source interactions, leading to a Galilei invariant non-relativistic form and a unique relativistic generalization.

Findings

Force is a four-vector when source is included

No third derivatives or runaway solutions in the new formulation

Quantum tunneling regions affect energy requirements

Abstract

We derive the radiation reaction by taking into account that the acceleration of the charge is caused by the interaction with some heavy source particle. In the non relativistic case this leads, in contrast to the usual approach, immediately to a result which is Galilei invariant. Simple examples show that there can be small regions of extremely low velocity where the energy requirements cannot be fulfilled, and which the charged particle can only cross by quantum mechanical tunneling. We also give the relativistic generalization which appears unique. The force is a four-vector, but only if the presence of the source is taken into account as well. It contains no third derivatives of the position as the Lorentz-Abraham-Dirac equation, and consequently no run away solutions. All examples considered so far give reasonable results.