Magnetic Interaction from the Transverse Length Vector Effect in Anisotropic Spatial Dynamics

We derive a geometric mechanism for magnetic interaction within anisotropic spatial dynamics (ASD). The transverse length vector effect identifies the physical interaction distance of two charges moving with a common transverse velocity as rT=γr, where r is the reference separation and γ is the Lorentz factor. Applying Coulomb’s inverse-square law to this distance gives FT=(1-β2 ) F0 and the magnetic interaction difference ΔFm=-β2 F0, with β=v/c. These relations are exact throughout the subluminal interval for this configuration. Magnetism is thus represented as the motion-induced geometric reduction of a single Coulomb interaction. A virtual-work analysis distinguishes the physical force conjugate to rT from the generalized force Qr=F0/γ conjugate to r. This supplies an ASD interpretation of the inverse-Lorentz-factor scaling while preserving the different physical roles of the two force variables. We further prove that rotational and reflection covariance, separate linearity in the source and test velocities, and zero magnetic power determine a unique bilinear quasistatic kernel once its normalization is fixed by the transverse result. Superposition recovers the Biot–Savart representation and the Ampère force between parallel steady currents. Comparison with conventional electrodynamics identifies differences in spatial interpretation, force decomposition, and exact velocity dependence.