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

TL;DR

This paper demonstrates that in quantum gravity, topology and geometry cannot be fully determined by operator measurements, as superpositions can alter classical spacetime limits, challenging traditional measurement assumptions.

Contribution

It introduces the idea that superpositions of classical states can change spacetime topology, suggesting topology and geometry are not directly measurable operators.

Findings

Superpositions of classical states can lead to new classical spacetime limits.

Topology and geometry are not obtainable through operator measurements.

Reconciliation with semiclassical gravity requires new interpretative frameworks.

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.