Quantum Gravity from Operator Entropy: Emergence of Spacetime, Gauge Fields, and Hidden Sectors

We introduce a statistical operator approach to quantum gravity, in which spacetime and gauge dynamics emerge from entropy maximization in a Diagram Hilbert Space of microscopic interaction histories. A complex operator Z = M + iQ encodes both mass-energy and electric charge, with entropy projections yielding Einstein’s equations from the real sector and Maxwell’s equations from the imaginary sector. We provide explicit derivations of these field equations from entropic extremization, and extend the framework to explain galactic rotation curves, the cosmological constant, and black hole thermodynamics. Photons appear as fundamental quanta, while gravitons are emergent collective excitations of the mass operator sector. This entropic operator framework thus connects QCD partition functions at the microscopic level to large-scale spacetime geometry, bridging quantum field theory and gravity.