Quantum Gravity Derivation from Locally Invariant Energy Field Theory

Locally Invariant Energy Field (LIEF) theory treats every massive particle as a self contained, spinning, spherical wave whose compression–expansion cycle modulates transmission of a universal substrate field. During compression, the particle surface temporarily blocks field flow, drawing in energy and creating a local deficit that surrounding field attempts to erase. This imbalance appears as gravitational attraction and must be released each Compton period as a graviton like wave. By replacing the mass term in the classical potential formula with its Compton expression and adopting half the Compton wavelength for the effective radius, we obtain U=-Gh/\left(\lambda_C^2c\right). Summing these per particle energies for all protons, neutrons, and electrons expected inside Earth reproduces surface gravity to within three percent; introducing a small coupling factor \alpha\ =\ 0.98459335 brings the value to g=9.798ms^{-2}. Re expressing the result in frequency space reveals a new constant, k_gHz=-1.01296\times{10}^{-69}JHz^{-2}, which implies that gravitational potential scales with the square of a particle’s Compton frequency rather than its rest mass. Photon redshift analysis shows that the same constant energy loss per oscillation applies to red and blue photons alike, the derivation conflicts with ΛCDM metric expansion, which predicts an energy decrement proportional to 3D metric expansion. The result offers a quantitative path to address the current H₀ tension and places redshift on a field interaction footing instead of geometric stretching.