Higher-order validity of the bubble–Fresnel–relativity equivalence

Determine whether the mathematically exact first-order equivalence among bubble acoustics in bubbly liquids, Fresnel drag in moving transparent media, and special relativity’s velocity addition law extends to second-order and higher-order terms in the drift-to-wave-speed ratio, or whether the correspondence is only a first-order formal parallel.

Background

The paper establishes that three systems—acoustic waves in bubbly liquids, optical Fresnel drag in moving media, and special relativity’s velocity addition—share an identical first-order transport law for observed wave speed as a function of drift, angle, and frequency. This equivalence is asserted to be exact at first order.

Because the derivation matches only the first-order term, an unresolved issue is whether the equivalence persists beyond first order. The authors explicitly flag uncertainty about higher-order terms, leaving open whether the mechanical picture provided by bubble acoustics remains quantitatively consistent with relativistic predictions at second order and beyond or is merely a suggestive first-order parallel.