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Quantum mechanics and observers for gravity in a closed universe

Daniel Harlow, Mykhaylo Usatyuk, Ying Zhao

TL;DR

The paper tackles how quantum gravity in a closed universe can accommodate observers when the fundamental Hilbert space appears one-dimensional. It proposes an observer-inclusive holographic encoding in which an external cloned observer $Ob'$ is entangled with inputs, yielding an effective Hilbert space of size ~$e^{S_{Ob}}$ with errors exponentially small in $S_{Ob}$. The authors develop and test this idea through a simple code model, a 1+1D topological gravity model, and JT gravity, and then provide a fixed-microscopic ETH realization to avoid ensemble averaging. They further extend the framework to black holes, showing how islands and quantum extremal surfaces act as bottlenecks for reconstruction, and that observer entropy controls the emergence of semiclassical interior physics. Collectively, the work links gravitational path integrals, holography, and ETH to present a coherent observer-inclusive picture of quantum gravity in closed universes and black hole interiors.

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.

Quantum mechanics and observers for gravity in a closed universe

TL;DR

The paper tackles how quantum gravity in a closed universe can accommodate observers when the fundamental Hilbert space appears one-dimensional. It proposes an observer-inclusive holographic encoding in which an external cloned observer is entangled with inputs, yielding an effective Hilbert space of size ~ with errors exponentially small in . The authors develop and test this idea through a simple code model, a 1+1D topological gravity model, and JT gravity, and then provide a fixed-microscopic ETH realization to avoid ensemble averaging. They further extend the framework to black holes, showing how islands and quantum extremal surfaces act as bottlenecks for reconstruction, and that observer entropy controls the emergence of semiclassical interior physics. Collectively, the work links gravitational path integrals, holography, and ETH to present a coherent observer-inclusive picture of quantum gravity in closed universes and black hole interiors.

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 in a closed universe can be approximately described by a quantum mechanical theory with a Hilbert space whose dimension is roughly , where is the number of degrees of freedom of . Moreover we argue that the errors in this description are exponentially small in . 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.
Paper Structure (22 sections, 107 equations, 30 figures)

This paper contains 22 sections, 107 equations, 30 figures.

Table of Contents

  1. Introduction
  2. Why is the Hilbert space one-dimensional?
  3. Arguments for a one-dimensional Hilbert space
  4. Consequences of a one-dimensional Hilbert space
  5. Entanglement and observers
  6. An observer in a closed universe
  7. A simple code model
  8. Topological model
  9. JT gravity
  10. A microscopic model
  11. An observer in a black hole
  12. Review of non-isometric codes for the black hole interior
  13. Including the observer in the black hole code
  14. Including the observer in JT gravity
  15. Discussion
  16. ...and 7 more sections

Figures (30)

  • Figure 1: Encoding the effective field theory Hilbert space of a close universe into a one-dimensional fundamental Hilbert space.
  • Figure 2: Modified encoding map $\hat{V}$ including an entangled observer $Ob'$ who is cloned out of the system. The orthogonal map $O$ is the same as in figure \ref{['Ocodefig']}.
  • Figure 3: Competing entanglement wedges, shaded in blue, for a reference system $S'$ entangled with a system $S$ in a closed universe. On the left is the case where the entanglement wedge doesn't include the closed universe, while on the right is the case where it does. The wedge on the right always wins, so it is impossible to be nontrivially entangled with a closed universe.
  • Figure 4: Using the gravitational path integral to compute the average of the closed universe inner product.
  • Figure 5: Computing the averages of the two sides of \ref{['Mreq']} using the gravitational path integral; they are equal by the permutation invariance of the set of things we sum over Penington:2019kki.
  • ...and 25 more figures