Bridging the Microcosmos and Macrocosmos: From QCD Partition Functions to the Emergent Einstein–Maxwell Equations

We propose a unifying framework that connects the microscopic domain of quantum chromodynamics (QCD) with the macroscopic dynamics of spacetime described by general relativity and electromagnetism. The central element is a complex operator defined in a diagram Hilbert space, where its eigenvalues encode both particle masses and charges. On the microscopic side, appears naturally in the exponential structure of the QCD partition function, giving rise to the effective mass spectrum of hadrons and leptons. On the macroscopic side, a projective mapping combined with entropy maximization yields the Einstein–Maxwell field equations, where the real and imaginary components of serve as sources for gravitation and electromagnetism, respectively. Crucially, space and time themselves emerge from the entropic structure of the microscopic Hilbert space, providing a unified view in which both geometry and fields are consequences of the underlying quantum–topological operator framework.