Emergence of Gravity from Statistical Phase Transition of Electromagnetic Fields: A Unified Framework for Superconductivity and Gravity via Fermion–Boson Duality and Extended Dirac Equation

We propose that gravity is not an independent fundamental force but rather an attractive interaction that emerges from a statistical phase transition of the electromagnetic field—from Bose statistics to Fermi statistics—in the high-density environment inside atoms. This statistical phase transition generates a new attractive contribution to the energy–momentum tensor, producing a gravitational field through the standard Einstein equation without modifying its geometric (left-hand) side. The mechanism is structurally identical to Cooper pair formation in superconductors. The formulation integrates two theoretical tools developed in prior work: (i) fermion–boson duality (FBD) theory Front. Phys. 13, 1618853 (2025), https://doi.org/10.3389/fphy.2025.1618853, which decomposes electron and photon states into four internal components with energy-dependent transition functions; and (ii) the extended Dirac equation based on a 256×256 matrix representation Atoms 14, 14 (2026), https://doi.org/10.3390/atoms14020014, which embeds the spacetime metric directly into the Dirac operator without vierbeins or spin connections. The bosonic gamma matrices Ω automatically select only the physical transverse degrees of freedom of gauge fields, eliminating the need for gauge fixing and Faddeev–Popov ghosts. The framework exactly recovers standard QED and general relativity in the low-energy limit and is structurally analogous to the established phenomenon in which phase transitions inside neutron stars alter the equation of state and spacetime structure. This is a preprint prepared for submission to Foundations of Physics.