  We apply the reduced phase space quantization to the Kasner universe. We
construct the kinematical phase space, find solutions to the Hamilton equations
of motion, identify Dirac observables and arrive at physical solutions in terms
of Dirac observables and an internal clock. We obtain the physical Hilbert
space, which is the carrier space of the self-adjoint representation of the
Dirac observables. Then we discuss the problem of time. We demonstrate that the
inclusion of evolution in a gravitational system, at classical level as well as
at quantum level, leads respectively to canonically and unitarily inequivalent
theories. The example of Hubble operator in two different clock variables and
with two distinct spectra is given.
