{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"7d968ca3653c98fa74c53f3cae17fcabf5a9d2177e580149d1b7a05e872b0773","created":"2026-10-03T07:18:08Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"ebd82da42e3276e65cafc8a35491d9ae9f10a8e392c34f799def2afda2abfccc","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":"1","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 $\\tau_0 = 2 e^2/(3 m c^3) \\sim 6.3e-24\\,\\mathrm{s}$, 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":null,"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 QED","topic_ref":"3337c3246637e5a9ce5f1a9514d7a2963fbb3cc69be03c6f6e2fbd8c411acb69"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"016f3ff66a213638892b7fa1b3014a27b69ee8c94a113c079e7137f4fd56824c","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"a6b7fceb72770fbda30f935a362b8e02332dc36f2fc386dcf12a4fbc6c785f37","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"EuCWsFl9H5ssgWnsErrrejLicU3gFQDcMVLSbmTVoDNm64bOAB7TQQkhbi1vfLiL0aEYpzaES0PRGeWwRYqUDA"},"schema":"pubphys.envelope/1"},"record_hash":"016f3ff66a213638892b7fa1b3014a27b69ee8c94a113c079e7137f4fd56824c","leaf_index":1854}