Volume operator

{{Short description|Operator whose expectation value gives the volume}}

A quantum field theory of general relativity provides operators that measure the geometry of spacetime. The volume operator $V(R)$ of a region $R$ is defined as the operator that yields the expectation value of a volume measurement of the region $R$, given a state $\backslash psi$ of quantum General Relativity. I.e.$\backslash lang\; \backslash psi,\; V(R)\; \backslash psi\; \backslash rang$ is the expectation value for the volume of $R$. Loop Quantum Gravity, for example, provides volume operators, area operators and length operators for regions, surfaces and path respectively.