Volume operator
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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 \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.
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 \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. ==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, Quantum Theory of Geometry II: Volume operators
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