Spacetime as emergent order: a testable framework from string-net condensation to geometric thermodynamics

Abstract

The nature of spacetime in quantum gravity remains a fundamental problem, rooted in the conflict between the background independence of general relativity and the fixed-background structure of quantum field theory. This paper proposes a concrete, emergentist framework in which classical continuous spacetime is not fundamental but arises as a low-energy effective description of an underlying quantum information structure. We construct this emergence explicitly, starting from a unitary fusion category as the “algebraic DNA”, realizing it via a string-net condensate, and employing an equivariant tensor renormalization group flow to reach a geometric fixed point. Within this derived geometry, we introduce two key macroscopic variables: the entropy current vector (ECV) s μ , which describes the flow of entanglement entropy in spacetime, and the cosmological enthalpy (CE) H c , an effective thermodynamic potential that incorporates pressure-volume work. We show that the Einstein field equations emerge as conditions of entanglement equilibrium, with the effective gravitational constant determined by categorical data. Crucially, this framework is not merely a conceptual narrative; it yields concrete, falsifiable predictions. We provide an explicit blueprint for near-term quantum simulation experiments—using ultracold atoms or superconducting qubit arrays—to measure the predicted area-law entanglement, the topological entanglement entropy, and the emergent graviton mode, thereby transforming the hypothesis of spacetime emergence into an empirically testable scientific program.