The background as a quantum observable: Einstein's hole argument in a quasiclassical context

TL;DR

This paper demonstrates that in a quasiclassical context, a background-free covariant theory cannot define outcomes of gravitational decoherence experiments, implying the necessity of a shared background for consistent results.

Contribution

It introduces a thought experiment linking gravitational decoherence to the background dependence of covariant theories, highlighting the need for a shared background in such frameworks.

Findings

Covariant theories cannot specify outcomes of gravitational decoherence experiments.

Experiments can reconstruct a common background shared by superposed gravitational fields.

Background dependence is essential for defining measurement outcomes in gravitational contexts.

Abstract

I consider a thought experiment measuring the decoherence for quasiclassical superpositions of gravitational field. A version of the hole argument allows to prove that a covariant (background-free) theory is completely unable to define the outcome of this experiment and is therefore not viable. Instead, the results of experiments of this type allow to reconstruct a common background shared by all superposed gravitational fields.