Abstract
We consider a quantized dust-filled closed Friedmann universe in Ashtekar-type variables. Due to the presence of matter, the ‘timelessness problem’ of quantum gravity can be solved in this case by using the following approach to the Hamiltonian operator.The arising Wheeler–DeWitt equation appears as an eigenvalue equation for discrete values of the total mass.Its gravitational part is considered as the generator of the time evolution of geometry.Superpositions of different eigenfunctions with time behaviour governed by the corresponding eigenvalues of mass are admitted.Following these lines, a time evolution with a correct classical limit is obtained.
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