# Volume operator

Jump to: navigation, search

A quantum field theory of General Relativity provides operators that measure the geometry of space time. 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 $\psi$ of quantum General Relativity. I.e.$\lang \psi, V(R) \psi \rang$ 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.