# 13. Gravity as Refraction Gravity appears here as electromagnetic refraction: the bending of energy transport paths caused by a spatially varying propagation speed induced by concentrated energy density. The propagation speed of electromagnetic energy in vacuum is: $$ c = \frac{1}{\sqrt{\varepsilon_0 \mu_0}}. $$ A dielectric does not work by letting light pass through inert matter. The incident field drives an existing electromagnetic organization in the medium, and that response emits a secondary electromagnetic field. The macroscopic summary of that response is a change in the constitutive coefficients. Linearity does not forbid this. It means only that a probe field propagates linearly through coefficients set by a background. The same idea is used here. Mass is self-confined energy. A massive body is therefore a concentrated background organization of electromagnetic energy flow. A passing field perturbs that background, and the background response contributes a secondary electromagnetic field. In chapter 7, $\mathbf{E}$ and $\mathbf{B}$ were identified as complementary aspects of one organized flow. The constitutive closure adopted here therefore shifts both constitutive channels together: $$ \varepsilon_\text{eff}(r)=\varepsilon_0\bigl(1+2\eta(r)\bigr), \qquad \mu_\text{eff}(r)=\mu_0\bigl(1+2\eta(r)\bigr), $$ with $$ \eta(r)=\frac{GM}{rc^2}. $$ This symmetric change preserves the local vacuum impedance, $$ Z_\text{eff}=\sqrt{\frac{\mu_\text{eff}}{\varepsilon_\text{eff}}}=Z_0, $$ while lowering the local propagation speed: $$ c_\text{local}(r)=\frac{1}{\sqrt{\varepsilon_\text{eff}(r)\mu_\text{eff}(r)}} =\frac{c}{1+2\eta(r)}. $$ The corresponding refractive index is therefore $$ n(r)=\frac{c}{c_\text{local}(r)} =1+\frac{2GM}{rc^2}. $$ If only one constitutive channel were perturbed, this first-order shift would be halved, giving the Newtonian half-value. Within this symmetric electromagnetic constitutive closure, the full factor of two follows. In optics, when a wave propagates through a medium of varying speed, it bends toward the slower region. This is refraction. Gravity, in this framework, is that refraction applied to all energy transport. The trajectory of any moving configuration curves toward regions of high energy density, because those are the regions of lower propagation speed. For a ray passing a body with impact parameter $b$, the weak-field bending is $$ \theta \approx \int_{-\infty}^{\infty}\nabla_\perp n\,dz = \frac{4GM}{bc^2}. $$ At the solar limb this is about $1.75$ arcseconds. On this reading, light bending follows from index-of-refraction arguments within the transport picture. Spacetime curvature, in this reading, is a geometric restatement of the same refraction. The geometry follows from the transport, not the other way around.