The Footballhedron: Quantum Gravity from Rotating Quantum Correlations

We propose a unified framework in which spacetime and gravity emerge from the structure of quantum correlations in a single universal wavefunction. In this approach, the full set of allowed correlation patterns of the quantum state is represented geometrically as a high-dimensional convex object, called the correlationhedron. By imposing additional structure on the correlationhedron (namely spherical topology, finite tessellation, and universal constant rotation), we obtain a specialized case dubbed the footballhedron, for its resemblance to a football (soccer ball in American English). Crucially, we show how the footballhedron's radius and angular frequency are linked directly to fundamental quantum information principles, and how this geometric structure is essential for deriving physical laws from the model. Under the footballhedron assumption, key features of relativistic spacetime physics naturally emerge. In particular, the universal correlation rotation speed (analogous to the speed of light) ensures Lorentz symmetry for all observers, while a suitable definition of an emergent metric from the correlation density leads directly to Einstein's field equations of gravity in the emergent spacetime. The finite tessellation assumption (an optional but natural extension) introduces intrinsic informational granularity, providing the theory with a fundamental ultraviolet cutoff at the Planck scale.