Intrinsic time in Wheeler–DeWitt conformal superspace

Abstract

Intrinsic time in geometrodynamics is obtained using a scaled Dirac mapping. By addition of a background metric, one can construct a scalar field which is suitable for the role of intrinsic time. The Cauchy problem was successfully solved in conformal variables because they are physical. Intrinsic time as a logarithm of the spatial metric determinant was first applied to a cosmological problem byMisner. Global time exists under the condition of a constant mean curvature slicing of spacetime. A coordinate volume of a hypersurface and the so-called York’s mean time are a canonical conjugated pair. So, the volume is intrinsic global time by its sense. The experimentally observed redshift in cosmology is an evidence of its existence.