Empirical Nonlinear Quantum Gravity from the General Theory of Relativity

This article presents an empirical foundation for quantum gravity that accounts for nonlinear gravitational effects, without altering general relativity. We build on a relation from [14] where κ—the constant coupling the energy tensor with spacetime geometry—depends on: the average rest energy of left-chiral neutrinos; the Fermi vacuum expectation value; and ΔE, a neutrino seesaw fulcrum energy. This relation links gravity’s weakness to tiny neutrino masses, revealing nonlinear quantum field interactions within Einstein’s unmodified framework. We uncover multi-graviton scattering by analyzing the Einstein-Hilbert Lagrangian in momentum space for the vacuum solution to the Einstein equation. This analysis relies solely on general relativity’s inherent nonlinearities, without yet incorporating the novel neutrino mass connection. Then, by employing this connection to show gravitation mediated by gravitinos, neutrino loops, and gravitons, which also identifies neutrino loops as dark matter quanta and gravitons as dark energy quanta, we integrate the dark sector, modeling both linear and nonlinear gravitational interactions between matter and the dark energy background. Unlike theories that alter general relativity with new tensors or speculative terms, we rely only upon the unmodified Einstein equation, particle physics data, and cosmological observations. This conservative, empirically grounded approach preserves general relativity, a theory uncontradicted for over a century, while establishing an empirical foundation for quantum gravity.