The reliability horizon for semi-classical quantum gravity: Metric fluctuations are often more important than back-reaction

TL;DR

This paper introduces the 'reliability horizon' in semi-classical quantum gravity, emphasizing that metric fluctuations often limit the theory's applicability more than back-reaction, impacting the understanding of Planck-scale physics and chronology protection.

Contribution

It defines the reliability horizon and demonstrates that metric fluctuations, not back-reaction, primarily constrain semi-classical quantum gravity's validity.

Findings

Large metric fluctuations occur before significant back-reaction.

The reliability horizon bounds the applicability of semi-classical gravity.

Chronology violation is hidden behind the reliability horizon.

Abstract

In this note I introduce the notion of the ``reliability horizon'' for semi-classical quantum gravity. This reliability horizon is an attempt to quantify the extent to which we should trust semi-classical quantum gravity, and to get a better handle on just where the Planck regime resides. I point out that the key obstruction to pushing semi-classical quantum gravity into the Planck regime is often the existence of large metric fluctuations, rather than a large back-reaction. There are many situations where the metric fluctuations become large long before the back-reaction is significant. Issues of this type are fundamental to any attempt at proving Hawking's chronology protection conjecture from first principles, since I shall prove that the onset of chronology violation is always hidden behind the reliability horizon.