A Unified Quantum Gravity Operator Framework: From Hidden Eigenstates to Cosmic Phenomena

We propose a novel operator-based approach to quantum gravity in which a single complex operator 𝑍̂=𝑀̂+𝑖𝑄̂, defined on a diagrammatic Hilbert space ℋ𝐷, encodes both microscopic mass spectra and charge spectra. The real part 𝑀̂ corresponds to gravitational mass, while the imaginary part 𝑄̂ encodes electromagnetic charge. Macroscopic spacetime and gauge fields emerge through an entropy-maximizing projection of 𝑍̂, yielding Einstein’s and Maxwell’s equations as collective laws. This unified formalism naturally addresses several outstanding puzzles in theoretical physics: hidden eigenstates of 𝑀̂ provide a mechanism for dark matter, residual entropic contributions explain dark energy, and black holes emerge as projection end points with entropy saturation. Furthermore, we demonstrate that galactic rotation curves follow from isothermal equilibria of hidden eigenmodes, the weakness of gravity arises from entropic dilution of microscopic degrees of freedom, and gravitons appear as collective excitations valid only in the low-energy regime. Cross-interactions between 𝑀̂ and 𝑄̂ predict small but testable deviations from standard Einstein–Maxwell theory. The framework thus provides a coherent route toward quantum gravity, unification, and explanation of major cosmic anomalies.