Electrodynamics
EstablishedThe Weber acceleration term has been exhaustively audited across multiple calculation methods.Weber Acceleration Term
The acceleration-dependent term rr̈/c² in Weber's force law is the origin of inertia, radiation reaction, and mass. It is not an approximation — it is fundamental to the Weber force structure.
The Three Weber Terms
The Weber force consists of three distinct terms:
- Coulomb: static interaction.
- Velocity: a velocity correction term.
- Acceleration: the term dependent on radial acceleration.
Full Weber Force
Origin of Inertia
The acceleration term is the origin of inertia. When a charge is accelerated (), the Weber force from surrounding charges generates a back-reaction. This back-reaction is Newton's inertial force .
Radiation Reaction
The acceleration term is also the source of radiation. When (charge accelerating away), the Weber force is attractive. Energy is extracted from the accelerating charge and radiated, reproducing the Larmor radiation formula at leading order.
Larmor Formula
No Runaway Solutions
In Maxwell electrodynamics, the radiation reaction is the Abraham-Lorentz force . This has the infamous runaway solution (self-acceleration without external force). The Weber acceleration term is free of runaways because it depends on and not .
Darwin Equivalence
At , the Weber acceleration term combined with the velocity term reproduces the Darwin Lagrangian — the standard non-relativistic expansion of QED. This Darwin equivalence confirms that the acceleration term is exactly .
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