On observers in holographic maps
Chris Akers (Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, CO, 80309, USA)
; Gracemarie Bueller (Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, CO, 80309, USA)
; Oliver DeWolfe (Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, CO, 80309, USA)
; Kenneth Higginbotham (Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, CO, 80309, USA)
; Johannes Reinking (Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, CO, 80309, USA)
; et al - Show all 6 authors
A straightforward gravitational path integral calculation implies that closed universes are trivial, described by a one dimensional Hilbert space. Two recent papers by Harlow-Usatyuk-Zhao and Abdalla-Antonini-Iliesiu-Levine have sought to ameliorate this issue by defining special rules to incorporate observers into the path integral. However, the proposed rules are different, leading to differing results for the Hilbert space dimension. Moreover, the former work offers a holographic map realized using a non-isometric code construction to complement their path integral result and clarify its physics. In this work, we propose a non-isometric code that implements the second construction, allowing thorough comparison. Our prescription may be thought of as simply removing the portion of the map that acts on the observer, while preserving the rest, creating an effective holographic boundary at the observer-environment interface. This proposal can be directly applied to general holographic maps for both open and closed universes of any dimension.