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arXiv:2602.05939

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

Ying Zhao

hep-thgr-qcquant-phSubmitted Feb 5, 2026• Announced Feb 6, 2026• Revised Sep 21, 2026 (v3)
v1 · Feb 5, 2026v2 · Feb 9, 2026v3 · Sep 21, 2026
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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.

Journal reference
JHEP 09 (2026) 252
DOI
10.1007/JHEP09(2026)252
Comments
45+8 pages; v2: clarifications in Sec. 4.4.2; added Sec. 4.4.5 on the Hartle-Hawking wave function; added Footnote 2; v3: minor clarifications; published version in JHEP

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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 ααα-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.
The definition of entropy in both classical and quantum contexts relies on a coarse-graining of the underlying microscopic description. While this dependence is widely acknowledged, the physical constraints that determine which coarse-grainings are admissible are rarely made explicit. This issue becomes particularly acute when the universe is treated as a closed system, where no external observer or privileged level of description can be assumed. Any characterization of entropy — including claims about the low-entropy initial conditions of the universe — must then be grounded in descriptions that can be physically instantiated from within the system itself. In this work, we introduce a rigorous operational framework that establishes explicit physical selection principles over the space of admissible descriptions. We organize these criteria into necessary conditions (local accessibility and physical implementation via internal interactions) and practical sufficiency conditions (finite resource requirements anchored in Landauer’s principle, dynamical stability, and effective consistency). To demonstrate the validity of our framework, we introduce a concrete one-dimensional spin-chain toy model, illustrating how mathematically valid global partitions fail to be physically realizable due to dynamic propagation limits and informational constraints. We analyze the far-reaching implications of this restriction across three domains. In classical statistical mechanics, it limits the arbitrariness of macrostate definitions. In quantum theory, it identifies environment-induced decoherence (einselection) not merely as a formal tool, but as the objective dynamical mechanism that forces the emergence of admissible internal partitions. In cosmology, it resolves foundational circularities in the quasi-classical histories framework and reframes the thermodynamic arrow of time as a "doubly relational" property—dependent both on cosmic boundary conditions and on the material limits of internal subsystems. Our framework clarifies the operational status of entropy as an emergent property of physically instantiated descriptions within a universe that observes itself.
We revisit whether a semiclassical closed baby universe in AdS/CFT necessarily possess a trivial one-dimensional Hilbert space or may instead carry a large entropy. Recent results on Haar random encoding suggest a breakdown of complementary recovery, in which no logical operators can be reconstructed from individual bipartite subsystems. Motivated by this, we propose an interpretation where a baby universe emerges as logical degrees of freedom that cannot be accessed from either boundary alone, assuming pseudorandom dynamics in holographic CFT correlators. We then analyze two conceptual puzzles: an apparent cloning of baby-universe microstates and its eventual fate at the singularity. Both puzzles are avoided because no single boundary observer can access the baby-universe degrees of freedom, be it classical or quantum, reflecting an emergent form of complementarity due to the structure of random encoding. In this interpretation, observers arise naturally: the same heavy operator that prepares the baby-universe geometry also serves as observer-like degrees of freedom that define an observer-dependent baby-universe microstate.
It is broadly believed that everything in the universe is found to be made from a few basic building blocks called fundamental particles, governed by four fundamental forces. However, physicists such as John Archibald Wheeler suggested that information is fundamental to the physics of the universe. According to this it from bit doctrine, all things physical are information-theoretic in origin. This doctrine is based in the old Copenhagen interpretation of quantum mechanics; an interpretation which is internally inconsistent and no applicable to the cosmos as a whole. Modern consistent interpretations of quantum mechanics eliminate the old myths about measurement processes and observers' consciousness and reintroduce the idea of a wholly physical reality, invalidating the it from bit doctrine. Utilizing a new phase space formulation of quantum mechanics developed recently by the author, the concepts of bit and it are reconsidered. We introduce the new states D as quantum bits and the new Hamiltonians H as quantum its. The new concepts of it and bit introduced in this work have a well-defined and rigorous definition, unlike Wheeler's concepts. Moreover, the new concepts apply on situations where the traditional wavefunction theory does not work. The it H is not derivable from the bit D and, as a consequence, the old it from bit doctrine gets substituted by the new it and bit. After showing why the physical entropy used in the science of thermodynamics is not a measure of the ignorance of human observers, the final part of this Essay is devoted to emphasize the importance that the bit acquires in modern science when confronted to the delicious multiplicity of the far-from-equilibrium regimes, where the certainty of Newtonian and Schrodinger motion begin to fade in favour of a complex non-geometrical, 'living', conception of Nature: an it and bit conception.
We combine the ideas of Dirac's orthonormal representation, Everett's relative state, and 't Hooft's ontological basis to define the notion of a world for quantum mechanics. Mathematically, for a quantum system Q\mathcal{Q}Q with an associated Hilbert space H,\mathbb{H},H, a world of Q\mathcal{Q}Q is defined to be an orthonormal basis of H.\mathbb{H}.H. The evolution of the system is governed by Schrödinger's equation for the worlds of it. An observable in a certain world is a self-adjoint operator diagonal under the corresponding basis. Moreover, a state is defined in an associated world but can be uniquely extended to the whole system as proved recently by Marcus, Spielman, and Srivastava. Although the states described by unit vectors in H\mathbb{H}H may be determined in different worlds, there are the so-called topology-compact states which must be determined by the totality of a world. We can apply the Copenhagen interpretation to a world for regarding a quantum state as an external observation, and obtain the Born rule of random outcomes. Therefore, we present a mathematical formalism of quantum mechanics based on the notion of a world instead of a quantum state.
It has been argued that a finite effective temperature emerges and characterizes the thermal property of double-scaled SYK model in the infinite temperature limit. Meanwhile, in the static patch of de Sitter, the maximally entangled state satisfies a KMS condition at infinite temperature, suggesting the Type II1_11​ nature of the observable algebra gravitationally dressed to the observer. In this work, we analyze the double-scaled algebra generated by chord operators in the double-scaled SYK model and demonstrate that it exhibits features reflecting both perspectives. Specifically, we prove that the algebra is a Type II1_11​ factor, and that the empty state with no chord satisfies the tracial property, in agreement with expectations from earlier work. We further show that this state is cyclic and separating for the double-scaled algebra, based on which we explore its modular structure. We then explore various physical limits of the theory, drawing connections to JT gravity, the Hilbert space of baby universes, and Brownian double-scaled SYK. We also present analytic solutions to the energy spectrum in both the zero- and one-particle sectors of the left/right chord Hamiltonian.
We reformulate the problem of the "interpretation of quantum mechanics" as the problem of DERIVING the quantum mechanical formalism from a set of simple physical postulates. We suggest that the common unease with taking quantum mechanics as a fundamental description of nature could derive from the use of an incorrect notion, as the unease with the Lorentz transformations before Einstein derived from the notion of observer independent time. Following an an analysis of the measurement process as seen by different observers, we propose a reformulation of quantum mechanics in terms of INFORMATION THEORY. We propose three different postulates out of which the formalism of the theory can be reconstructed; these are based on the notion of information about each other that systems contain. All systems are assumed to be equivalent: no observer-observed distinction, and information is interpreted as correlation. We then suggest that the incorrect notion that generates the unease with quantum mechanichs is the notion of OBSERVER INDEPENDENT state of a system.