Quantum mechanics and observers for gravity in a closed universe

TL;DR

This paper proposes that observers in a closed universe can be approximately described by quantum theories with Hilbert spaces of size e^{S_{Ob}}, reconciling the one-dimensional global Hilbert space with complex individual experiences.

Contribution

It introduces a framework where local observer experiences are modeled by quantum theories with large Hilbert spaces, consistent with gravitational path integral evidence.

Findings

Observer experiences are well-approximated by quantum theories with exponential Hilbert space dimension.

Errors in this approximation are exponentially small in the number of degrees of freedom.

Similar effects are identified in black hole physics under certain conditions.

Abstract

Recent arguments based on the quantum extremal surface formula or the gravitational path integral have given fairly compelling evidence that the Hilbert space of quantum gravity in a closed universe is one-dimensional and real. How can this be consistent with the complexity of our own experiences? In this paper we propose that the experiences of any observer $Ob$ in a closed universe can be approximately described by a quantum mechanical theory with a Hilbert space whose dimension is roughly $e^{S_{Ob}}$, where $S_{Ob}$ is the number of degrees of freedom of $Ob$. Moreover we argue that the errors in this description are exponentially small in $S_{Ob}$. We give evidence for this proposal using the gravitational path integral and the coding interpretation of holography, and we explain how similar effects arise in black hole physics in appropriate circumstances.