Absolute entropy and the observer's no-boundary state

TL;DR

This paper explores the no-boundary proposal in quantum cosmology, showing that the observer's no-boundary state is a maximum entropy state represented by the identity operator, with implications for entropy calculations in quantum gravity.

Contribution

It explicitly demonstrates that the observer's no-boundary state is the identity operator in the physical Hilbert space within Jackiw-Teitelboim gravity, linking geometric and quantum informational concepts.

Findings

The no-boundary state is a bra-ket wormhole.

Expectation values define a trace for the observer's algebra.

Von Neumann entropy can be defined as relative entropy with respect to the no-boundary state.

Abstract

We investigate the no-boundary proposal for closed universes with an observer. We argue that the observer's no-boundary state is the identity operator on the physical Hilbert space, i.e., the maximum entropy state and show this explicitly in Jackiw-Teitelboim gravity. Geometrically, the no-boundary state is a bra-ket wormhole. Expectation values in the no-boundary state provide a trace for the observer's algebra, which allows one to define von Neumann entropy for observers in different universes as the relative entropy with respect to the no-boundary state. This result is consistent with all previously discussed cases of traces for invariantly defined regions.