Physical Predictions in Closed Quantum Gravity

TL;DR

This paper develops a framework for extracting stable semiclassical predictions from the seemingly trivial, one-dimensional physical Hilbert space in closed quantum gravity, by conditioning on observational data and limited access.

Contribution

It introduces a method to obtain meaningful predictions in closed quantum gravity through an enlarged Hilbert space and conditioning, addressing the puzzle of classical physics emergence.

Findings

Suppression of ensemble fluctuations restores semiclassical predictability.

Explicit construction including Hartle–Hawking state and gauge-invariant observations.

Generalization to conditioning on histories clarifies classical probabilities and time arrow.

Abstract

Recent developments in gravitational path integrals indicate that the nonperturbative physical Hilbert space of a closed universe is one-dimensional within each superselection sector. This raises a basic puzzle: how can a unique quantum-gravity state give rise to semiclassical physics, measurement outcomes, and classical probabilities? In this paper, we develop a framework in which nontrivial and statistically stable predictions emerge despite the one-dimensionality of the fully constrained Hilbert space. The key idea is to extract physical predictions in an enlarged, unconstrained Hilbert space by conditioning on observational data. We show that partial observability -- reflecting the limited access of observers to the degrees of freedom of the universe -- suppresses ensemble fluctuations associated with microscopic structure in the gravitational path integral, thereby restoring semiclassical predictability with exponential accuracy. We formulate the construction explicitly including contributions from the Hartle--Hawking no-boundary state, define a gauge-invariant Hilbert space for observations via a density operator, and generalize the formalism to conditioning on histories, clarifying the emergence of classical probabilities and an effective arrow of time. Finally, we explore whether this framework can support a realistic cosmology and identify assumptions that the underlying theory of quantum gravity must satisfy.