Observers, $α$-parameters, and the Hartle-Hawking state

TL;DR

The paper explores how observers and third-quantized cosmologies can be reconciled in a Hartle-Hawking framework, arguing that Harlow's observer decoherence enables a BUFT-like description to emerge from a fixed holographic theory with a one-dimensional Hilbert space, eliminating the need for $\alpha$-parameters. It draws connections between holography, gravitational path integrals, and ensemble averaging, and uses simple code models to illustrate how BUFT and AH relate to canonical gravity. The work also analyzes the role of patch operators as observer-dressed probes that recover semiclassical physics when the sphere partition function is large, and applies these ideas to landscapes with AdS and dS vacua to illuminate potential Boltzmann-brain biases. Overall, the results clarify when averaging over boundary sources suffices to realize gravitational physics in fixed holographic theories and how observer-based rules modify predictions in cosmological settings. The findings have implications for understanding the quantum mechanics of the universe, holographic coding, and the fate of observers in landscape cosmologies.

Abstract

In this paper we extend recent ideas about observers and closed universes to theories where observers can be fluctuated into existence in the Hartle-Hawking state. This introduces a phenomenon that was not considered in these earlier discussions: the dominant transition from one cosmological state to another can go through a fluctuation that annihilates the universe and creates a new one. We nonetheless argue that the observer decoherence rule allows for the third-quantized description of such a theory to emerge from a factorizing holographic theory with a one-dimensional Hilbert space, without any need for $α$-parameters. We also point out a close analogy between the observer rule in this context and the coarse-graining of the spectral form factor at late times for AdS black holes. Along the way we clarify several aspects of the relationship between holography, the gravitational path integral, and $α$-parameters. We also explain why string theory scattering amplitudes do not lead to a one-dimensional Hilbert space on the worldsheet, despite being computed by a gravitational path integral with a sum over topology. Finally we point out that using the path integral to compute integrated local operators conditioned on an observer in the context of a theory with a landscape can lead to rather surprising conclusions. For example we argue that in a landscape with one AdS minimum and one dS minimum, both of which can support observers, an observer almost surely finds themself in dS and not AdS even if the boundary conditions are dual to a state with an observer in AdS.

Figures (22)

• Figure 1: The closed universe inner product in baby universe field theory. The disconnected contribution is not present in the canonical gravity calculation of this inner product, so when it is big it gives a large deviation from quantum field theory in a fixed background even when $G_N$ is small.
• Figure 2: Computing the closed universe inner product in canonical quantum gravity. On the left the Lorentzian path integral computes the matrix elements of the projection onto diff-invariant states in the field basis as in \ref{['phiip']}, while on the right we use the Euclidean path integral to compute the inner product between states prepared by Euclidean AdS boundaries with sources $J$ an $J'$ as in \ref{['CQGIP']}.
• Figure 3: Computing the overlap of a one-universe state and a two-universe state in BUFT. The disconnected vacuum bubbles factor out and exponentiate. In CQG none of these topologies would contribute and the overlap would be zero.
• Figure 4: Some of the topologies that contribute to $\aleph^{-1}[J_3J_4|J_1J_2]$ but not $\aleph^{-2}[J_3|J_1][J_4|J_3]$.
• Figure 5: Computing the square of a scattering amplitude in string theory using BUFT. We emphasize that there are no worldsheets connecting the S-matrix and its complex conjugate.