Quantum Geometric Algebra: A Theory of Emergent Spacetime and Matter based on Quantum Relational Networks

This paper proposes a novel theoretical framework termed "Quantum Geometric Algebra," which models the fundamental reality of the universe as a dynamic "quantum relational network," wherein both spacetime geometry and matter fields emerge as low-energy phenomena. This "relational ontology" paradigm aims to fundamentally resolve the deep incompatibility between general relativity and quantum mechanics, as well as the cosmological constant problem. By employing non-commutative geometry and category theory, we construct a rigorous mathematical model of this network—the Dynamic Quantum Spectral Triple—and elucidate how classical continuous spacetime and its physical laws derive from discrete quantum correlations. Under this framework, phenomena such as gravity, quantum measurement, and black hole thermodynamics receive unified and natural reinterpretations. The theory not only intrinsically resolves the cosmological constant problem but also predicts observable quantum geometric imprints in the early universe and the potential evolution of the dark energy equation of state, thereby paving the way for a background-independent, inherently unified theory of quantum gravity.