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A quantum field theory of general relativity provides operators that measure the geometry of spacetime. The volume operator V {\displaystyle V} of a region R {\displaystyle R} is defined as the operator that yields the expectation value of a volume measurement of the region R {\displaystyle R} , given a state ψ {\displaystyle \psi } of quantum General Relativity. I.e. ⟨ ψ , V ψ ⟩ {\displaystyle \langle \psi ,V\psi \rangle } is the expectation value for the volume of R {\displaystyle R}. Loop Quantum Gravity, for example, provides volume operators, area operators and length operators for regions, surfaces and path respectively.