Anomalous Magnetic Moment

In quantum field theory, the magnetic moment of a spin-$\frac{1}{2}$ particle like the electron is predicted to be:

But observation shows:

This small but persistent discrepancy is traditionally explained by loop corrections in quantum electrodynamics (QED), involving virtual particles and renormalisation. In modal dynamics, no such corrections are needed.

The anomalous magnetic moment arises directly from the internal phase structure of the mode.

Anchored Spin Modes

An electron is a coherence-anchored, spin-$\frac{1}{2}$ mode. Its internal phase structure includes:

• A nontrivial topological winding
• A persistent rotational asymmetry (spin)
• A distortion of the surrounding coherence field due to anchoring asymmetry (charge)

This configuration generates a local field structure—not by emitting a field, but by shaping the anchoring landscape $B(x)$ through its phase surface.

Coherence Circulation

The spin of the mode causes a circulation in the surrounding phase gradient. This circulation creates a bias distortion—a twisting of the coherence field that mimics a magnetic dipole.

The strength of this distortion depends on:

• The rate of internal phase rotation
• The asymmetry of anchoring across the mode’s surface
• The interaction between phase winding (charge) and topological rotation (spin)

This interaction is not perfectly symmetric, and the mismatch between idealised spin and real anchoring curvature produces a small deviation from $g=2$.

Structural Correction

The observed anomalous value arises from a coherence-induced torsion—an interference between:

• The spin-induced phase circulation
• The charge-induced anchoring asymmetry

This generates a small shift in the mode’s effective magnetic dipole. Crucially, this shift:

• Requires no external field theory
• Requires no quantum corrections
• Is a natural outcome of the phase topology and anchoring interaction

The deviation is not noise—it is a fingerprint of modal coherence mechanics.

Why It Is Stable

The value $g\approx 2.002319$ is remarkably stable because:

• The internal structure of the mode is stable under perturbation
• Anchoring stiffness and coherence distortion are robust
• There is no field coupling to disrupt or renormalise the mode

This stability is a powerful confirmation that the mode’s structure—not external interaction—determines its properties.

(See Appendix AF — Anomalous Magnetic Moment.)

The anomalous magnetic moment is not a quantum loop effect.
It is anchoring geometry twisted by spin.