"It from Bit": The Hartle-Hawking state and quantum mechanics for de Sitter observers

Abstract

The one-state statement for closed universes has sparked considerable discussion. In this paper, we examine its physical meaning in the context of the Hartle-Hawking state and de Sitter space. We argue that the one-state property of closed universes is fully compatible with the finite-dimensional quantum mechanics experienced by observers inside de Sitter space, and that this compatibility requires neither mixing of $α$-sectors nor any modification of the rules of the gravitational path integral. The apparent tension is resolved by sharply distinguishing the baby-universe Hilbert space, namely the space of closed universes viewed from the outside, from the bulk Hilbert space that governs quantum mechanics for an observer inside a single de Sitter universe. The baby-universe Hilbert space, together with its commutative operator algebra, is not a quantum-mechanical Hilbert space: it is merely a mathematical repackaging of classical probability theory and carries no quantum-mechanical structure at all, a direct consequence of the one-state property of closed universes. Accordingly, attempting to formulate quantum mechanics directly on the baby-universe Hilbert space conflates two logically distinct structures and leads to physically incorrect conclusions. By contrast, the quantum mechanics experienced by an observer inside de Sitter space emerges from the classical statistics encoded in the baby-universe Hilbert space, providing a concrete realization of Wheeler's idea of "It from Bit." We demonstrate these features by completely solving a topological toy model of one-dimensional de Sitter spacetime. Along the way, we clarify the physical meaning of de Sitter entropy, showing that it corresponds to the coarse-grained entropy of the underlying state.