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

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.