A Microscopic Liouville Arrow of Time

TL;DR

This paper explores how quantum-gravitational fluctuations can create a microscopic arrow of time by treating space-time as an environment within open quantum systems, supported by models from string theory and general relativity.

Contribution

It introduces a novel framework using open quantum system formalism to derive a microscopic arrow of time from quantum gravity effects, with applications to string theory and general relativity.

Findings

Quantum fluctuations of gravity can induce an arrow of time.

A framework based on non-critical strings and Liouville fields is developed.

Potential observational tests for quantum-gravitational effects are discussed.

Abstract

We discuss the treatment of quantum-gravitational fluctuations in the space-time background as an `environment', using the formalism for open quantum-mechanical systems, which leads to a microscopic arrow of time. After reviewing briefly the open-system formalism, and the motivations for treating quantum gravity as an `environment', we present an example from general relativity and a general framework based on non-critical strings, with a Liouville field that we identify with time. We illustrate this approach with calculations in the contexts of two-dimensional models and $D$ branes. Finally, some prospects for observational tests of these ideas are mentioned.