Editing Openai/6897769e-4ee4-800f-aba5-69cca34f701c (section)

==== A lump of matter at distance rrr “sinks” a fraction of ambient EM rays by absorption/scattering. To first order this produces: ====
* a tiny solid-angle deficit (“shadow cone”) δΩ∼πa2/r2\delta\Omega \sim \pi a^2/r^2δΩ∼πa2/r2 for a lump with effective area a2a^2a2,
* a small dipole anisotropy in the incident intensity at the test shell,
* and a net increase in local event rate if the re-emission is phase-lagged/decohered (more events counted locally per unit lab time).

Linearizing,

δR  ≈  1h∫ ⁣ ⁣∫∂∂I ⁣(σIω) δI(ω,Ω)  dω dΩ  ∝  1r2.\delta R \;\approx\; \frac{1}{h}\int\!\!\int 
\frac{\partial}{\partial I}\!\left(\frac{\sigma I}{\omega}\right)\,
\delta I(\omega,\Omega)\; d\omega\, d\Omega
\;\propto\; \frac{1}{r^{2}}.δR≈h1∫∫∂I∂(ωσI)δI(ω,Ω)dωdΩ∝r21.
Because RRR is a surface integral over the 2-D sphere, the 1/r21/r^{2}1/r2 geometry appears naturally (Gauss-style). No new fields are introduced.