Quantum State of Wormholes and Topological Arrow of Time

TL;DR

This paper explores how quantum wormholes can exhibit a topological arrow of time due to their mixed quantum states, contrasting with time-symmetric pure states, and discusses implications for quantum gravity.

Contribution

It introduces a mixed state description of quantum wormholes that avoids divergences and demonstrates a topological arrow of time in quantum gravity.

Findings

Pure states of quantum wormholes are time symmetric.

Mixed states involve quantum uncertainty and are time asymmetric.

A topological arrow of time emerges in the quantum state of wormholes.

Abstract

This paper studies the time-symmetry problem in quantum gravity. The issue depends critically on the choice of the quantum state and has been considered in this paper by restricting to the case of quantum wormholes. It is seen that pure states represented by a wave functional are time symmetric. However, a maximal analytic extension of the wormhole manifold is found that corresponds to a mixed state describable by a nondegenerate density-matrix functional that involves an extra quantum uncertainty for the three-metric, and is free from the divergences encountered so far in statistical states formulated in quantum gravity. It is then argued that, relative to one asymptotic region, the statistical quantum state of single Euclidean wormholes in semiclassical approximation is time-asymmetric and gives rise to a {\it topological} arrow of time which will reflect in the set of all quantum fields at low energies of the asymptotic flat region (To appear in Int. J. Mod. Phys. D)