Environment-Dependent Speed of Light in the Logarithmic Superfluid Vacuum: Consistency, Constraints, and Observational Tests

Abstract

This revision sharpens where the paper sits relative to the rest of the framework, and tightens the static-structure section. The paper's results are unchanged: the speed of light varies with vacuum density as δc/c = −ε exactly at the background exponent; that variation vanishes to first order around gravitating masses, because the Painlevé-Gullstrand configuration carries no first-order density perturbation, which makes solar-system constancy of c a derived fact rather than an assumption and Cassini consistency automatic; gravitational and electromagnetic waves share one medium and one speed, giving an exact null multi-messenger lag as a structural prediction rather than a suppressed one; and lensed repeating fast radio bursts define a reachable window eight orders of magnitude below current bounds. What changed is the treatment of static vacuum density structure. The naive refractive channel through a static density well gives a refractive index equal to minus one half the general-relativistic Shapiro index of the same potential — wrong sign in both faces, early arrivals and divergent deflection. The revised section states this as an independent optical exclusion that parallels the companion paper's gravitational no-go for the static density channel, at the same amplitude and from unrelated data: time-delay cosmography already excludes the naive channel, and any static vacuum structure is bounded to a few percent of the Shapiro index. The section no longer frames this as a requirement on a particular dark-matter mechanism; it bounds the photon coupling to static structure generally, which is what the argument actually establishes. Citations to the companion gravity and cosmology papers are updated to their current titles.