{"schema":"pubphys.bundle/1","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"},"content_withheld":"false","files":[],"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"016f3ff66a213638892b7fa1b3014a27b69ee8c94a113c079e7137f4fd56824c","schema":"pubphys.attested/1"},"id_token":null,"id_token_withheld":"false","envelope":{"attested_hash":"a6b7fceb72770fbda30f935a362b8e02332dc36f2fc386dcf12a4fbc6c785f37","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"EuCWsFl9H5ssgWnsErrrejLicU3gFQDcMVLSbmTVoDNm64bOAB7TQQkhbi1vfLiL0aEYpzaES0PRGeWwRYqUDA"},"schema":"pubphys.envelope/1"},"ots":{"attested":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEIprf863J3D72jD5NaNiuOAjMtw28vw4bc8SpPvGx4XzfxIKaz2IeZ00sNRUXkG7ewqzABn9ap-wvw2cLjiehdOmbfCPEgacEOF99mdp6r3yI4FtpHYKWhbAaO3TXzUlQLYDz7XasI8SC0aLiT4gjBB9ZPfOTrqGvPa5uJXETjEK2HgQdVNmN7igjxIGD89lWJPM5HYefmIwXJAFJtx4_5rYw4ZjBvVQr3SHrBCPEg4T5BRqIC-5iB6Z8EUGSIFedoP3GdVlBEHzo6TcDlEGcI8SBAb3KB6Gtdfdwms_3hRA8LRJmKBxkW8oNiIhUg-XUAZAjwIJPsrh2yAs-Q-tN7WiRC5DpdLPxhgPCZUvw9VyDb326QCPEgrA74zq9OS_EO_vifvlqDPPUyYaAxJJae8fQw9_OOt1II8CB0Pk63gwyd_u5K2K1drJW3UxU3mXTBkDKQdutj6_nnEgjxIFf8EhaVa-ubjpYx3wEAcKGxkzfUQq6B-8jimpRd8IqnCPAgy6DmLQtIuWm-zrDRmaSy95vcFWsjvWyppQO7wIWrfC4I8SAQuuTPkAGyvS_wKMy9BtKvnki2puESdY2vXem8hT1uIQjwIBGYo5Vxy-d7U5zKv5vp3Ii7hJPH_BDLCzA13c47p9q7CP_wCHbghVgOFMuNCPAQPZK2lHbTMqcCYUotzOQcmQjwIJ7ruRIs6HnufKxCpmLUgeUl0aUu0ov4_3PqcppS-bddCPEgI530vHzdwz_3o9jYQ3WablSaV64Wfn7Pmby5WLyI-A0I8QRqwKw78AhITF7Tr3a1xP8Ag9_jDS75DI4sK2h0dHBzOi8vYm9iLmJ0Yy5jYWxlbmRhci5vcGVudGltZXN0YW1wcy5vcmcI8CBXWeNiWFWltfHE0nkDXsVKIykUUwuObhsnN-2fvBt98gjwIM5Vf7j68sOFgVysYMc5S09Hho-fqxYW3oQ4oKUX7JpPCPAgaKHHQB3sdd9w1hu4NMh7vmb-p0X2r4uyVKKCj1G7S28I8SAW2Mg6Bzi9ygjrrjIYB7w90fwMcxH24SsqLmzPyAMGfwjwIMQ863zlveYIpNKWVrZaDOa4vowwoOg2CcTW8gXtxK3dCPEgrZxGGAf-t8jhz_eLMUyBN1IhNrdYDRcNHWvQcwNG9woI8CCVOUHG1YXudbaFIgUYvrCIevRWvb2ubhQAo-z0duD0rQjxIDBeKerVGkO3J2eXDwdraSioXbIWsdIPEN1s8pIwJIS2CPAgV2kB3n3JZ5HwBQjpRL1CWKnqvdCjZk3RcALk6N2wHigI8CB-wbljNlfqElD25uZkNg6taS81YDRU2vfMqGVQ420O9AjxWQEAAAABJM43UU6MLMRrPlCUqossvu1q_knons5yylyWTgxZzWUAAAAAAP7___8CLgABAAAAAAAWABQrYt3E7OllKRCEmL3FL589l78_5wAAAAAAAAAAImog8ATiyw4ACAjxILmbcIO7ixv3pCtwUMZ1VQGKus54F9lZ8-w5ECD5ZuiICAjwIG6ynCyFTLPE7Rgk-0ZGCtBDyqNQx8YvaSZNHy8D8p8jCAjwIMX8zoD2Be1YWvcx_bexVPRmBX0hK-do8b8t9SarimQVCAjxIG6XtpqIEclLlhzcK1LVjqoPGrjjmLnyno8tcETMzECECAjwIF6mlfXOFY51JhrK4eze8zQlKV75OYZYqbtyi8BWxmAsCAjwIKKUcJmVoz-u-geiRV_-ZHdF0VEPXaEPFWf_JX_0e7G2CAjxIGMeD0Z5QWNKBcAEpHht007FFIILW6aSJ8f3CMkKNsneCAjwIBFr6Je8rkB7kwhPGbq0yRgFwZsvW9JhY5sXDRtrq0QwCAjwIAHAwXaus-yUgKICJB5mVvx8VZuJgjwnpb0qWPg1pi6DCAjxIAJhb8cefkVHTAMymdsxa-_i-tUua62LcpALQnPG7R9_CAjwIDvsFqBhPfAL6TCtXZd7gBWmMpx6iiZ-Ug0Jf_LlcstgCAjwIDJRBX6Q0Vge-ra-k1_g76yJWTEp6WWF13I3JpTnsZPJCAjwILykZCbkC9VQgl5gytPKKir6T9nTvKR6y05iWSHBTQgzCAgABYiWDXPXGQED45c78Ah-sGbmQAwfZwjwEAYqxtHnZiPZnJEGPx_JvKsI8SDXkqDg17YsZIrEz5acRx7mBXCKW5mKNgRYnw_-U2cpDgjxBGrArDrwCEfK6Mono428_wCD3-MNLvkMji4taHR0cHM6Ly9hbGljZS5idGMuY2FsZW5kYXIub3BlbnRpbWVzdGFtcHMub3JnCPAg10nyJ6Jn4kshQQQCKE0Lvj3hBC6nLRBVIzaPV4eh8VwI8CCQaAqWlxEbac_XOq1MOlf9iOKHEsxXspzbjK0vLpy8BwjwII3iRbRXUcDxrhAdkZmFlI15nySCSEZ7g922tF1Xln5DCPEgYYvZ1L4v4rPu_UqLfcHPtwSb2OH2GhPgVcVhhH6DpkQI8CDZCIoR20sC-uchP40oAmcLm9EJFV7xzwplj54AeVadXQjxILvLBjPFpCoz29m9Yf2qRnV7PI9GqxE8ozVQfk9QwCqrCPEgZXcMudvEoB_MJ8tqOW2PLTKAIeQBnE-1bfzptRc2gR8I8VkBAAAAAfXq-bmxWqOz7B5wKkwjzHGv2R4s7Y0Z76LqXWYNhmz0AAAAAAD-____Av0cAAAAAAAAFgAUl-skmdZDtn7Hnub6mF4HP2uVn7oAAAAAAAAAACJqIPAE4MsOAAgI8CBDmQsbEXc46Hu8DivhCBM1LGExa4TTM-wo7HpoCVjBTQgI8CCty5vkQtPHzzs8xqArOYhVSjgaDoG1ou3cojv5_P7wQQgI8SDQWB0kdXCTwbk-TqTt0QfRMyzDNLOtU1XXFgvGSRlW8wgI8CC2PKa_QCIBZtrXodq1GdEzppISMsMRDOnzr2gFjLKOAAgI8CCwQ_QF67bcFk_uJ2s0VCZmf5PGIjTmTCpt_qnVY5p_8AgI8SAbzyx7z-oxPMju6PvtQhzrJIQyH2ZAc9oyLuYemzbmZQgI8CC5bh7J74uUk91r8LwybHQFCNBC3PWeuwtMCCNFKWj19AgI8SAf4R2TUNPjaX_PWDUImpoITK0JoW89zaMKnD1wlEEi8AgI8SC2vNmdm7eyP5Ytl1yTzT0njliMdALl1ViKG-s3bG2zswgI8CCpbIVNz1GFVXdJk2zd82hBUoNFFemUPBt7IJdWEOciPwgI8CBtYdRQcrtX1FtCm1SxF7sx-5cO04U8KzbJh8fqBkyReAgI8CBHs2LGmX6gI-lV7yp1RrV7_tGfdiBAwnEFF6B6yXHzAQgI8CATotVmbXBMAixhZ-QKy5Q4lR0FusdA_wcIC1TbB7GmxAgIAAWIlg1z1xkBA-KXOw"],"envelope":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEIgCMf2BRKlFhbi3jMMMLPM6vumXLUd1mJl-6ziLEF-d3wIIA-HTSvGdCXDmU4dbxtkTCNlipn8TG7IyY62fpIz0WlCPEg6thbVUg4phQg3TkkJbcjLkJHBhBZR7YGl-b4mhvYBZ0I8CCmGDkET8PYvp2Q3pBPoThcp_iLv7QinYSrGGjrok84EAjwIAnvG-RoMDgLxua2x1lnLRiNzJurxyN5LsI-BNQlH9_CCPAgAzMjJMJCuYZyhXrcnUKsibyUAfJ5hSHXuqgAjjJNT8kI8CDV-VrDeBU4Rd2bdiIF8sD3kaoaI1e591WQPNBrVmYJsAjxILgyucegs6Hj0k-Cn4WCqTsz35fOCSyIA5vaVrSM5ConCPAgIc68cJ-EOb_p9fBzMx1sIuwuI-BGalPIOj3vrhU7YtUI8CBxK_WraVEkFPQAC7yAevXyyf-CupxAva0AtHIOkj6nkwjwIIhzmnVeFxVHRiBmi7SsQd_gIBRvsrzzZf-fzyEkp8wnCPAgy6DmLQtIuWm-zrDRmaSy95vcFWsjvWyppQO7wIWrfC4I8SAQuuTPkAGyvS_wKMy9BtKvnki2puESdY2vXem8hT1uIQjwIBGYo5Vxy-d7U5zKv5vp3Ii7hJPH_BDLCzA13c47p9q7CP_wCHbghVgOFMuNCPAQPZK2lHbTMqcCYUotzOQcmQjwIJ7ruRIs6HnufKxCpmLUgeUl0aUu0ov4_3PqcppS-bddCPEgI530vHzdwz_3o9jYQ3WablSaV64Wfn7P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