Functional differential equations. 3: Radiative damping

C. K. Raju

UOP

What is the solution of the equation of motion of a single classical charged particle with radiative damping? Contrary to the physical expectation, the mathematical solution is anti-damped! Attempts to curb these runaway solutions lead to pre-acceleration. Worse, despite a century of effort, there is still no way to obtain a proper solution in a general context. This failure of classical electrodynamics is intrinsic, irrespective of the hydrogen atom, and hence needs to be remedied. We outline a general method to resolve the infinities of quantum electrodynamics (renormalization problem). The same method was recently applied to resolve the infinities of classical electrodynamics. This involves a modification of Maxwell’s equations at the microphysical level. The resulting equations of motion of even a single charged particle with radiative damping are functional differential equations (FDEs). These FDEs can and have been solved. The implications for quantum mechanics are postponed to the next article