Electrodynamics

Established

Maxwell Limit

Weber's force law reduces to Maxwell's equations in the limit of many slowly-moving charges. CPT is consistent with all classical electromagnetic predictions.

If the Weber force is the fundamental law of electrodynamics, why do Maxwell's equations work so exceptionally well? The answer is that Maxwell's equations are the field-theory description of the statistical average of Weber interactions over an ensemble of many charges moving at slow speeds relative to .

The derivation can be sketched as follows:

  1. Consider charges, taking the continuum limit to define a charge density and current density .
  2. The Weber force in this limit yields Poisson's equation for .
  3. The time-derivative of the Weber force directly yields Faraday's law.
  4. The curl structure produces the Ampere-Maxwell law.

The macroscopic limit

What Weber provides beyond Maxwell is explicit inclusion of the radiation reaction term . In Maxwell theory, this appears only through the Abraham-Lorentz force, which notoriously permits non-physical runaway solutions. The Weber formulation is naturally free of runaways.

Maxwell's Equations

CPT therefore makes all the same predictions as classical electrodynamics in the macroscopic regime; it is a generalization, not a contradiction. The single regime where Maxwell and Weber disagree is in the near-field, far from the slow-motion limit. This is precisely where CPT predictions differ from standard QED predictions.

[E]
The reduction to Maxwell is fully mathematically established.

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