Quantum reference systems

The author argues that only by taking into account the quantum properties of the bodies that form the reference frames, physical quantum operators can be defined in quantum gravity. The theory of general relativity coupled to matter introduced in a companion paper is considered. Its formal canonical quantization yields two surprising results: the diffeomorphism constraint can be exactly solved; and the Hamiltonian constraint reduces, in the context of a well defined approximation, to a Schrodinger evolution equation. By using the solutions of the quantum constraints of vacuum general relativity recently obtained in the loop representation, and in the context of a 'realistic' local material reference system, he defines a quantum gravitational theory in which the constraints can be solved, the only remaining equation is a regularized Schrodinger equation which expresses the dynamics in the internal clocks, and a class of gauge-invariant physical observables is explicitly displayed.