An Effective-Geometric Model of Information Transmission Delay: Formal Isomorphism between Medium Refraction and Gravitational Lensing

This paper proposes an effective-geometric model of information transmission delay by formally comparing optical refraction in material media and gravitational lensing in weak gravitational fields. The study does not attempt to unify electromagnetism and gravity, nor does it assign subjective time to light itself. Instead, it defines information arrival time as an operational observable measured by an external observer. In the proposed model, an information carrier is treated as a narrow-band electromagnetic wave packet, and the information arrival delay relative to vacuum propagation is expressed as an effective refractive-index integral. In material media, the delay is described by the group refractive index arising from electromagnetic polarization and dispersion. In weak gravitational fields, the modification of the spacetime metric is represented by an effective refractive index related to Shapiro delay and gravitational lensing. The main claim of the paper is that medium refraction and gravitational lensing are not physically identical phenomena, but they exhibit a formal isomorphism with respect to the restricted observable of externally measured information arrival time.