Consequences of Gödel’s Theorems on Quantum Gravity

Abstract

This study aims to provide general axioms that should hold for any theory of quantum gravity. These axioms imply that spacetime is an emergent structure, which emerges from information. This information cannot occur in spacetime, as spacetime emerges from it, and hence exists in an abstract mathematical Platonic realm. Thus, quantum gravity exists as a formal system in this Platonic realm. Gödel’s theorems apply to such formal systems, and hence they apply to quantum gravity. This limits the existence of a complete consistent theory of quantum gravity. However, we generalize the Lucas-Penrose argument and argue that a non-algorithmic understanding exists in this Platonic realm. It makes it possible to have a complete and consistent theory of quantum gravity.