MUT v5.8.14: Supplement XI: Refraction as a Function of Background Scalar Field Scaling Factor z

This supplement reinterprets classical optical refraction within the deterministic MUT v5.8 framework. In this model, the velocity of information transport in a medium is proportional to the local scaling factor of the Background Scalar Field (ΦA).When light or other waves traverse regions with different scalar field scaling factors, the phase velocity adjusts to preserve coherence with the substrate. The refractive index emerges as the inverse of the local scaling factor, providing a direct physical explanation for optical density.Furthermore, Snell’s Law is derived from the principle of least action applied to the scalar field flux, showing that the ratio of sine angles at an interface is equivalent to the ratio of local scaling factors. This links classical optics to the scalar field evolution, unifying light propagation with the deterministic properties of ΦA.This work demonstrates that refraction is not merely a phenomenological effect but a geometric and field-theoretic consequence of the underlying Background Scalar Field dynamics.Series Note:Part of the MUT v5.8 Optical & Temporal Series, building upon Supplement X (Universe Age via Scalar Field Evolution) and integrating optical phenomena into the Background Scalar Field framework.