Topology and geometry cannot be measured by an operator measurement in quantum gravity

TL;DR

In the context of Lin-Lunin-Maldacena geometries, it is shown that superpositions of classical coherent states of trivial topology can give rise to new classical limits where the topology of spacetime has changed, and it is argued that this phenomenon implies that neither theTopology nor the geometry of spacetimes can be the result of an operator measurement.

Abstract

In the context of LLM geometries, we show that superpositions of classical coherent states of trivial topology can give rise to new classical limits where the topology of spacetime has changed. We argue that this phenomenon implies that neither the topology nor the geometry of spacetime can be the result of an operator measurement. We address how to reconcile these statements with the usual semiclassical analysis of low energy effective field theory for gravity.

Figures (2)

• Figure 1: A geometric fluctuation of the vacuum, characterized by $h(\theta)$
• Figure 2: A two coloring with non-trivial geometry. The areas $L,M$ have quantized are $L,M$ respectively.