Proposed evolution in Marolf-Maxfield toy model obtained through correspondence to spontaneous collapse theory

TL;DR

This paper proposes a novel correspondence between the Marolf-Maxfield 2D gravity toy model and spontaneous collapse theories, enabling the modeling of evolution from Hartle-Hawking states to superselection sectors.

Contribution

It introduces a new link between topological gravity models and collapse theories, allowing evolution to be incorporated into the Marolf-Maxfield model.

Findings

Derived the evolution of matrix elements using the correspondence.

Established a connection between black hole models and collapse wave functions.

Demonstrated how to obtain expected state evolution in the toy model.

Abstract

The Marolf-Maxfield topological toy model for 2D gravity gives the full spectrum of boundary theories, but can not describe any evolution. In order to obtain the expected evolution from Hartle-Hawking state to one of the superselection sectors, we suggest to consider a correspondence between models of evaporating black holes and models of collapsing wave functions. This note explores this correspondence by equating the Marolf-Maxfield topological toy model and to the Bonifacio model of spontaneous collapse theory. The expected evolution of a matrix element due to a generator of a parameter in Marolf-Maxfield model is obtained.