The Hartle-Hawking state and quantum mechanics for de Sitter observers

The one-state statement for closed universes has sparked considerable discussion. In this talk, 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. 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. 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.