“…a charge-current distribution J , satisfying r J = 0, is speci…ed, and one seeks to …nd the corresponding solution to the Maxwell equations. One could add a second well-de…ned problem: an external electromagnetic …eld ext F and a nonelectromagnetic force nem F are speci…ed, and one seeks to find the worldline z ( ) of a point mass carrying charge q by using the Lorentz force law and solving the resultant equation of motionma = q( ext F u ) + nem F(23)And combining the two also leads to a harmonious situation in that (i) the coupled Maxwell-Lorentz equations have a well-posed initial value problem and (ii) the total stress-energy tensor, consisting of the sum of the stressenergy tensor of the electromagnetic …eld and the mechanical stress-energy tensor of the particle,32 is conserved.Unfortunately, equation(23)is empirically inadequate, for accelerated charges radiate and, as a result, they experience a damping force that is not re ‡ected in (23). 33 The generally accepted equation of motion describing this phenomenon for a point charge in Minkowski spacetime is called the Lorentz-Dirac equation:ma = q( ext F u ) + nem F ext F u ) + nem F + 2 3 q 2 ( + u u ) _ awhere a := a a is the magnitude of the four-vector acceleration and is the Minkowski metric.…”