Universal Density Screening Across Fundamental Interactions:From Electrostatics to Gravitation

Weidentify a universal scaling relation governing screening lengths across vastly different physical systems: theinteraction range scales inversely with the square rootof the medium density, λ ∝ ρ−1/2. We demonstratethis universality in five distinct contexts: (i) Debyescreening in classical and quantum plasmas, (ii) Londonpenetration in superconductors, (iii) color screening inquark-gluon plasma, (iv) ionic screening in electrolytes,and (v) gravitational screening in Kaluza-Klein theories.We derive a unified theoretical framework showing thatthis scaling emerges generically from field theories withdensity-dependent effective masses. Compilation of experimental data across 30 orders of magnitude in densityconfirms the universal ρ−1/2 scaling. This unificationsuggests deep structural similarities between electromagnetic, strong, and gravitational screening mechanisms,with implications for both fundamental physics and condensed matter systems.