John Carlos Baez on Nostr: - now taking a limit where the particle "disappears" doesn't sound so good, but they ...

- now taking a limit where the particle "disappears" doesn't sound so good, but they get interesting results:

"We will show in section III that the worldline, γ, to which the body shrinks down must be a solution to the Lorentz force equations of motion. (As we shall also see in section III, the electromagnetic self-energy of the body makes a finite, non-zero contribution to the mass, m, that appears in the Lorentz force equation.) Self-force effects (as well as dipole force and spin force effects) then arise as a first order perturbative correction to the center of mass motion of the body. We emphasize that our approach removes from any fundamental status both the point charge source (4) and the Lorentz force law (5). Rather, the notion of a “point charge” and the Lorentz force equation that it satisfies will be derived as a lowest order description of the electromagnetic field and bulk motion of a small (but extended) body whose exact evolution is governed by the Maxwell and matter equations (1-3), and (7). Our derivation will enable us greatly clarify what is perhaps the most famous difficulty of the electromagnetic self-force problem: “runaway solutions”."

Equations (1-3) and (7) are all *field equations*: Maxwell's equations, conservation of charge and conservation of energy-momentum.

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