A quantum field theory of general relativity provides operators that measure the geometry of spacetime. Loop Quantum Gravity, for example, provides volume operators, area operators and length operators for regions, surfaces and path respectively.

Sources

• Carlo Rovelli and Lee Smolin, "Discreteness of Area and Volume in Quantum Gravity", Nuclear Physics B 442, 593 (1995).

• Abhay Ashtekar and Jerzy Lewandowski,