Low-Energy Quantum Gravity Effective Field Theory Framework: Massless Graviton BEC and Tensor Gross-Pitaevskii Equation

The low-energy conflict between general relativity (GR) and quantum mechanics (QM) remains a long-standing puzzle in fundamental physics. In this work, we propose a novel effective field theory (EFT) framework based on massless graviton Bose-Einstein condensation (BEC), deriving a Lorentz-covariant tensor-type Gross-Pitaevskii (GP) equation for the first time. Key results include: (1) Rigorous dimensional consistency of all terms in the tensor GP equation, resolving the polarization contradiction between gravitational wave observations (LIGO) and previous quantum gravity EFTs; (2) Weak-field limit of the framework reproduces the Schwarzschild metric with a relative deviation < 0.01%, fully compatible with classical GR experiments; (3) A verifiable prediction of frequency-dependent gravitational wave amplitude correction (δh(f) ∝ (f/f₀)^0.3), which can be detected by LIGO A+ with ~10 binary black hole events. This work lays the foundation for the subsequent 7-part series on 100 TeV force unification and Planck-scale physics.