The Problem of Time and Quantum Black Holes

TL;DR

This paper examines the challenges in deriving semi-classical equations in quantum gravity, highlighting issues with the interpretation of the Wheeler-deWitt equation and proposing the de Broglie-Bohm interpretation as a potential solution.

Contribution

It explores the problem of time in quantum gravity and introduces the de Broglie-Bohm interpretation as a way to address the issues in black hole evaporation analysis.

Findings

No systematic derivation of semi-classical theory in quantum gravity.

De Broglie-Bohm interpretation can break general covariance.

Implications for the black hole information loss problem.

Abstract

We discuss the derivation of the so-called semi-classical equations for both mini-superspace and dilaton gravity. We find that there is no systematic derivation of a semi-classical theory in which quantum mechanics is formulated in a space-time that is a solution of Einstein's equation, with the expectation value of the matter stress tensor on the right-hand side. The issues involved are related to the well-known problems associated with the interpretation of the Wheeler-deWitt equation in quantum gravity, including the problem of time. We explore the de Broglie-Bohm interpretation of quantum mechanics (and field theory) as a way of spontaneously breaking general covariance, and thereby giving meaning to the equations that many authors have been using to analyze black hole evaporation. We comment on the implications for the ``information loss" problem.