From Quantum Interactions to Emergent Spacetime: A Dual Operator Framework

We develop a dual-direction framework that connects the microcosmos of quantum chromodynamics (QCD) with the macrocosmos of Einstein’s general relativity and Maxwell’s electromagnetism. Central to our approach is the complex operator , defined in a diagram Hilbert space, whose eigenvalues encode particle masses and charges. On the microscopic side, the exponential structure of the QCD partition function generates effective hadron and lepton masses through the summation of multi-quark and multi-gluon interactions. On the macroscopic side, a projective mapping and entropic maximization yield the Einstein–Maxwell equations, with the real and imaginary parts of sourcing gravitation and electromagnetism, respectively. Crucially, space and time themselves emerge as entropic constructs, organizing microscopic degrees of freedom into classical geometry. This dual perspective unifies QCD mass generation and spacetime emergence in a single entropic–topological operator framework.