{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"260a015e03cdb02ec28f6b68d97a94dc7774c666dcd61e4b1e4599e0f9f62658","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["016f3ff66a213638892b7fa1b3014a27b69ee8c94a113c079e7137f4fd56824c","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"95230c69419d23b77a08397a6a6bf1f8bbdb8b010ed6dac177f27044be4b74e8","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"identification","assisted_by":[],"external_id":"plasma.radiation-reaction.classical-limit-equation","kind":"well-posed","literature_status":"partially-resolved","n":"2","parents":[],"plain":"The classical Abraham-Lorentz-Dirac equation predicts electrons that run away or accelerate before a force arrives, so physicists use a cleaned-up version, the Landau-Lifshitz equation. The question is which equation quantum theory actually reduces to when quantum effects are switched off.","posed_since":"","precise":"The Lorentz-Abraham-Dirac (LAD) equation, third order in time with characteristic time $\\tau_0 = 2 e^2/(3 m c^3) \\sim 6.3 \\times 10^{-24}\\,\\mathrm{s}$, has runaway and preaccelerating solutions; restricting LAD to its non-runaway (critical) manifold gives a second-order equation whose first-order approximation in $\\tau_0$ is the Landau-Lifshitz (LL) equation; the two differ from order $\\tau_0^2$ on. Determine the classical limit ($\\hbar \\to 0$ at fixed classical field parameters) of QED for a point charge in a background field to all orders in $\\tau_0$, and identify whether it coincides with LL, with LAD on the critical manifold, or with another second-order equation (for example Ford-O'Connell), at orders beyond the leading one in $\\alpha$.","problem_ref":"016f3ff66a213638892b7fa1b3014a27b69ee8c94a113c079e7137f4fd56824c","references":"","settled_by":"A derivation from QED in a general (at least plane-wave) background of the classical equation of motion to second and higher order in $\\tau_{0}$, compared term by term with LL and with the critical-manifold reduction of LAD.","status_note":"The LL equation has been recovered from QED at leading order in $\\alpha$ in plane-wave backgrounds; I do not have a verified source for an all-order result as of 2026.","title":"Which classical radiation-reaction equation is the classical limit of 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