Signature change events: A challenge for quantum gravity?

TL;DR

This paper explores the challenges and implications of signature change events in quantum gravity, highlighting issues with quantum fields on such backgrounds and discussing potential phenomenological consequences.

Contribution

It revisits the topic of signature change in general relativity, analyzing quantum field behavior and phenomenological implications within quantum gravity frameworks.

Findings

Quantum fields on signature-changing backgrounds produce infinite particles and energy.

Signature change events resemble quantum barrier penetration and cosmological horizon modes.

Signature transitions may require full quantum gravity theories for proper understanding.

Abstract

Within the framework of either Euclidian (functional-integral) quantum gravity or canonical general relativity the signature of the manifold is a priori unconstrained. Furthermore, recent developments in the emergent spacetime programme have led to a physically feasible implementation of signature change events. This suggests that it is time to revisit the sometimes controversial topic of signature change in general relativity. Specifically, we shall focus on the behaviour of a quantum field subjected to a manifold containing regions of different signature. We emphasise that, regardless of the underlying classical theory, there are severe problems associated with any quantum field theory residing on a signature-changing background. (Such as the production of what is naively an infinite number of particles, with an infinite energy density.) From the viewpoint of quantum gravity phenomenology, we discuss possible consequences of an effective Lorentz symmetry breaking scale. To more fully understand the physics of quantum fields exposed to finite regions of Euclidean-signature (Riemannian) geometry, we show its similarities with the quantum barrier penetration problem, and the super-Hubble horizon modes encountered in cosmology. Finally we raise the question as to whether signature change transitions could be fully understood and dynamically generated within (modified) classical general relativity, or whether they require the knowledge of a full theory of quantum gravity.