Phenomenological unification of gravity, quantum mechanics, and electrodynamics based on super-invariants of general relativity and quantum mechanics

We propose a phenomenological model that unifies general relativity, quantum mechanics, and electrodynamics without introducing dark matter, dark energy, or new particles. The approach is based on two super-invariants: the geometric invariant of general relativity r1 = RµνRµν/R2 and the quantum coherence invariant χ1 = |⟨[ˆx, pˆ]⟩|/ℏ. From Planck 2018 data we find r1 = 1/3 to within 4σ, while for coherent states of quantum mechanics χ1 = 1. We postulate a universal relation χ1 · r1 = 1/3 that holds across all scales to within ∼ 10−3. We show that Maxwell’s equations emerge as the limit χ1 → 1, δr1 → 0. The model quantitatively accounts for four key anomalies in modern physics: the H0 tension, the muon anomalous magnetic moment, the W -boson mass from CDF-II, and the lithium problem, using a single coherence parameter. The model predictions are testable in nonlinear optics, high-multipole analysis of the cosmic microwave background, and experiments with Bose–Einstein condensates.