Time and a Temporally Statistical Quantum Geometrodynamics

TL;DR

This paper explores a temporally statistical approach to quantum geometrodynamics, addressing fundamental issues of time in quantum gravity, including symmetry breaking, state reduction, and the modeling of observers within M-theory frameworks.

Contribution

It introduces a hidden time variable theory based on S-duality symmetry in string theory and extends the concept of time reparametrization symmetry to explain time-reversal symmetry breaking.

Findings

Model of observers addressing the problem of time

Physical origin of state reductions explained via S-duality

Classification of time-dependent processes using derived categories

Abstract

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.