Internal time and gravity theories
The authors analyze a certain treatment of reparametrization invariant theories that are described by singular Hamiltonians. It is shown that such kind of theories might be equivalent to a set of canonical evolution equations with respect to a certain internal time. This turns out to be much like Rovelli's relational time which replaces the parametric time evolution. If the formalism is used to describe gravitation, the authors find the nonlinear approach to gauge theories of gravity to provide a natural candidate to play the role of internal time. Since the Einstein-Hilbert action is known to be difficult to handle with respect to time evolution the authors propose a Jordan-Brans-Dicke action as an alternative. The authors show that such an action provides an internal time evolution if the scalar field is considered as identical with the nonlinear internal time.
scientific article; zbMATH DE number 1765080