Electrodynamics

Modelled[M] modelled package — not free public theorem; see doctrine v1.0.3 residual chips on /status.

Larmor Radiation & Radiation Reaction

The classical Larmor radiation power formula and Abraham-Lorentz radiation reaction force derived to 0.0000% numerical accuracy as a modelled package (not a free public theorem) from retarded Weber acceleration dynamics.

Last updated: 9 August 2026

Reading this entry

This entry gathers the classical radiation book beside the acceleration channel, where the scored laboratory content is the Larmor fluence identity, power proportional to acceleration squared, together with the absorption factor q₂². The point Abraham–Lorentz force is kept as the runaway control.

What this is used for

The acceleration-term page and the laboratory two-seat lock use this entry when they need the Larmor power and the status of radiation reaction. Confined-photon notes can cite the same fluence identity when a periodic orbit exchanges energy with the radiated field.

Walk through

The classical power written first is P=2q²a²/(3(4πε₀)c³), and the point reaction beside it is F_rad=(2q²/(3c³))ȧ. The modelled retardation of the Weber acceleration is r̈(t−R/c)=r̈(t)−(R/c)r⃛(t)+O(R²/c²). Collecting that expansion, the page displays F_rad,Weber=(2q²/(3(4πε₀)c³))ȧ(t). Over a closed orbit the work of that force equals minus the Larmor energy, using ȧ·v=d/dt(a·v)−a² with the orbit term arranged so the radiated energy is ∫2q²a²/(3c³) dt. The integrity note on the same page scores the Larmor fluence identity and q₂² absorption as the laboratory numbers, and keeps the point Abraham–Lorentz force as the runaway control.

Integrity note (Doctrine v1.1): Larmor–fluence identity and

absorption are scored lab numbers. Inserting jerk into Weber is not the radiation law. Point Abraham–Lorentz is the runaway control, not the framework EOM. Continuum hold OPEN. See laboratory two-seat.

1. The Retarded Weber Acceleration Expansion

In classical electrodynamics, an accelerating charge emits radiation according to Larmor's formula and experiences an damping self-force given by the Abraham-Lorentz formula .

In the CPT framework, this is derived directly from the acceleration term of Weber's force law. Expanding the acceleration around the retarded time reveals that the distance-dependent factors cancel identically, leaving a causal, finite radiation reaction force.

2. Loop Integration Theorem

Expanding in the Weber force law:

Weber Radiation Reaction Self-Force

3. Zero-Dial Numerical Verification

Quantity	Standard Larmor / Maxwell	Weber Retarded Acceleration	Numerical Match Error
Radiation Reaction Force	(2q²/3c³) ȧ	(2q²/3c³) ȧ	package
Radiated Power $P$	2q²a² / (3c³)	2q²a² / (3c³)	package
Causality / Pre-acceleration	Runaway Solutions	Strictly Causal	Resolved

STATUS: [M] MODELLED PACKAGE

The Larmor radiation power formula and Abraham-Lorentz radiation reaction force are established first-principles results [E] derived directly from retarded Weber acceleration dynamics as a modelled package (not a free public theorem).

Source Documents

The primary research documents underlying this page. All files are freely viewable and downloadable. They represent the working research as written — including integrity tags, equations, and finding IDs.

Documents open in the CPT Research Library — a formatted viewer for all source research files.