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Larmor \(Q\sim 1/\alpha\) is the right class, not the Gamow \(P\)

\(Q=(3/(2\alpha_{\mathrm{eff}}))(mc^2/\hbar\omega)\) · named \(Q\gg 59\) · damps energy not topology · chips OPEN

CPT Framework — C3-MODES / LEAD-5 / WOBBLE-P / DW-ALD / AL freeze Date: 2026-09-17 Status: CONSIDERATION + PROBE · PASS_LARMOR_Q_HAS_1_OVER_ALPHA_FAIL_AS_P · \(1/\alpha\) in \(Q\) PASS · \(Q=E_0\) FAIL_NUM · Larmor \(=\) \(n\to p\) FAIL_IDENTIFY · no promote Stimulus: User — process that sets \(P\) should scale as \(1/\alpha\); Larmor damping of internal modes, quality factor \(\sim 1/\alpha\) times geometry. Parents: a_geom_p1_c3_lobe_normal_modes.md · a_geom_p1_kramers_c3_lobe_escape.md · a_geom_p1_wobble_period_times_probability.md · weber_larmor_radiation_reaction_results.md · a_geom_dw_sg_schott_goedecke_ontology_freeze.md Probe: scripts/investigations/s3_geometry/p1_larmor_q_c3_modes_probe.py Data: scripts/investigations/s3_geometry/data/p1_larmor_q_c3_modes.json

Tags: [E honesty] · [E algebra] · [E process] · [Programme]

0. One-line

The \(1/\alpha\) is real and it is the same numeral as LEAD-5; it does not pay \(P\). Classical Abraham–Lorentz gives \(Q=(3/(2\alpha_{\mathrm{eff}}))(mc^2/\hbar\omega)\). For \(C_3\) \(E\)-modes that is \(Q\sim 10^3\)–\(10^5\), not \(E_0\approx 59\). Energy lost per cycle \(2\pi/Q\) is \(O(\alpha)\), so \(\tau=T/P\) stays \(10^{-20}\,\mathrm{s}\). \(e^{-Q}\) is the wrong size the other way. Larmor damps oscillation energy, not baryon topology, and AL is not the CPT radiation law. No promote.

1. Why this was the right thing to try

Kramers \(B/T\) is \(\alpha\)-free once \(B\) is MeV Coulomb. A dimensionless action \(\propto 1/\alpha\) is exactly what minutes need (\(E_0=(3/(2\alpha))\varepsilon\)).

Radiation reaction of a dipole oscillator:

\[ \tau_{\mathrm{AL}}=\frac{2\alpha_{\mathrm{eff}}}{3}\frac{\hbar}{mc^2},\qquad Q=\frac{1}{\tau_{\mathrm{AL}}\omega}=\frac{3}{2\alpha_{\mathrm{eff}}}\frac{mc^2}{\hbar\omega}. \]

\(\alpha_{\mathrm{eff}}=\alpha(q/e)^2\). For \(q=e/3\), \(Q\) is nine times the charge-\(e\) value. The prefactor is \(3/(2\alpha)\).

The \(C_3\) \(E\)-mode does carry a linear dipole (probe: \(\partial\mathbf{d}/\partial\mathrm{amp}\neq 0\)). Dipole Larmor applies as classical radiation of that mode.

2. Named numbers

Lobe mass \(m_0/3\). \(\hbar\omega\) from C3-MODES.

| \(R\) | \(q\) | \(Q\) | \(Q/E_0\) | \(\tau=T_{\mathrm{circuit}}/(2\pi/Q)\) | |-------|------|------:|----------:|--------------------------------------:| | Compton \(m_0\) | \(e\) | \(1.64\times 10^3\) | 28 | \(3.5\times 10^{-21}\,\mathrm{s}\) | | Compton \(m_0\) | \(e/3\) | \(1.47\times 10^4\) | 248 | \(3.2\times 10^{-20}\,\mathrm{s}\) | | \(R_p\) | \(e\) | \(1.31\times 10^4\) | 220 | \(2.8\times 10^{-20}\,\mathrm{s}\) | | \(R_p\) | \(e/3\) | \(1.18\times 10^5\) | 1980 | \(2.5\times 10^{-19}\,\mathrm{s}\) |

To force \(Q(e/3)=E_0\) would need \(\hbar\omega\simeq 9.8\,\mathrm{GeV}\), not \(5\)–\(39\,\mathrm{MeV}\).

Finding L0 [E algebra]. \(3/(2\alpha)\) in \(Q\) is the same writing as LEAD-5’s prefactor. That is a clue, not a mill of \(E_0\) (same family as the Hopf/Willmore waiter: the numeral appears, the map to the exponent is not exhibited). Finding L1 [E honesty]. Per-cycle radiated fraction \(2\pi/Q\) is a prefactor \(O(\alpha)\), the same lesson as Kramers \(\omega_0\): \(1/\alpha\) here does not sit in \(e^{-S}\). Putting \(P=e^{-Q}\) uses the named \(Q\sim 10^4\), not \(59\). Finding L2. Radiation reaction cools the mode. It does not change \(T(3,2)\to T(2,3)\). Category error, plus DW-ALD: do not insert point Abraham–Lorentz as the radiation law.

3. Integrity

| Gate | Verdict | |------|---------| | \(Q\sim(3/(2\alpha))(mc^2/\hbar\omega)\) | PASS | | Named \(Q=E_0\) / \(P=2\pi/Q\) or \(e^{-Q}\) \(\to\) minutes | NO | | Larmor \(=\) \(n\to p\) | NO | | Mill \(\alpha\) / shop \(\omega\) | NO | | Promote | NOT APPROVED |

Exit: PASS_LARMOR_Q_HAS_1_OVER_ALPHA_FAIL_AS_P

4. Licensed next

Do not mill AL as \(\Gamma_n\). Do not shop \(\hbar\omega\) to \(9.8\,\mathrm{GeV}\). A later \(1/\alpha\) action still has to be an exponent (Gamow/EM path), not a quality factor. Pair EOM parked. \(T(2,3)\) not proton mass. \(\alpha\) INPUT. \(a\) INPUT. Do not name \(R\). No hub dump.

Looked into (17 Sep, E0-READ): accept LEAD-5 as the exponent law; mill the Coulomb-to-mass reading, not a primitive derivation (a_geom_p1_e0_is_the_law_reading.md).

5. One-line for agents

§LARMOR-Q: classical \(Q\) carries \(3/(2\alpha)\); named \(C_3\) \(Q\gg E_0\); not \(P\); damps energy not topology; chips OPEN; no promote.
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