Weber Force Law

The single fundamental interaction of the CPT framework. A velocity- and acceleration-dependent generalisation of Coulomb's law that reproduces Maxwell electrodynamics in the appropriate limit.

Last updated: August 2026

The Weber Force Law

For two charges and separated by a distance with relative radial velocity and radial acceleration , the Weber force on due to is:

Weber (1846) · · action at a distance, no field postulate

Why Weber — and not Coulomb + Lorentz?

Standard electrodynamics uses two separate laws: Coulomb’s law for static fields and the Lorentz force for moving charges. These are augmented by Maxwell’s field equations to handle radiation. Weber’s law combines all of this into a single action-at-a-distance expression — no separate field is postulated.

Static limit (ṙ = 0, r̈ = 0)

F = kqq'/r² — Coulomb's law exactly

Two parallel current-carrying wires

Weber correctly gives Ampère's force law, including the 1/r dependence

Energy radiated by accelerating charge

The rr̈/c² term drives radiation reaction — Larmor formula recovered

Weber Force in the CPT Framework

The ontology freeze (Axiom A1) states: the only fundamental interaction is Weber’s electrodynamic force law. This means:

Gravity is not a separate force — it is the double copy of the Weber force (see EM–Gravity Double Copy).
Nuclear forces emerge from Weber interactions at very short range where the velocity-dependent terms dominate.
No photon field is postulated. The confined photon (see Confined Photon) is a topological trajectory, not a field quantum.

The Weber Potential Energy

Weber’s law is conservative — it derives from the potential:

This is the quantity that enters the Hold stability analysis. The velocity-dependent term is the key ingredient in the proton hold: it provides a stabilising potential well that keeps the confined photon in its torus knot trajectory. See Proton Structure.

Relationship to Maxwell’s Equations

In the limit of many charges and slow motion relative to , the statistical average of Weber interactions over an ensemble of charges reproduces Maxwell’s equations. This is the Maxwell limit. See Maxwell Limit for the full derivation. This establishes that CPT is consistent with all classical electromagnetic predictions — it is a generalisation, not a contradiction.

Integrity Status

[E]

Established.Weber’s force law is a constitutional axiom. Its derivation from the Weber potential is a standard classical mechanics result (Euler–Lagrange). Its equivalence to Coulomb in the static limit and to Ampère for currents are established results in Weber electrodynamics.

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.

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