  This paper is an exposition of the author's recent work (arXiv:1001.3382
[hep-th], arXiv:1005.5430 [cond-mat.dis-nn], arXiv:1212.4956 [quant-ph]) on
modeling M-theory vacua and quantum mechanical observers in the framework of a
temporally statistical description of quantum geometrodynamics, including
measurement processes based on the canonical theory of quantum gravity. In this
paper we deal with several fundamental issues of time: the time-less problem in
canonical quantum gravity; the physical origin of state reductions; and
time-reversal symmetry breaking. We first model the observers and consider the
time-less problem by invoking the time reparametrization symmetry breaking in
the quantum mechanical world as seen by the observers. We next construct the
hidden time variable theory, using a model of the gauged and affinized
S-duality symmetry in type IIB string theory, as the statistical theory of time
and explain the physical origin of state reductions using it. Finally, by the
extension of the time reparametrization symmetry to all of the temporal hidden
variables, we treat the issue of time reversal symmetry breaking as the
spontaneous breaking of this extended time reparametrization symmetry. The
classification of unitary time-dependent processes and the geometrizations of
unitary and non-unitary time evolutions using the language of the derived
category are also investigated.
