Effective field theories consistent with quantum gravity obey surprising finiteness constraints, appearing in several distinct but interconnected forms. In this work we develop a framework that unifies these observations by proposing that the defining data of such theories, as well as the landscape of effective field theories that are valid at least up to a fixed cutoff, admit descriptions with a uniform bound on complexity. To make this precise, we use tame geometry and work in sharply o-minimal structures, in which tame sets and functions come with two integer parameters that quantify their information content; we call this pair their tame complexity. Our Finite Complexity Conjectures are supported by controlled examples in which an infinite Wilsonian expansion nevertheless admits an equivalent finite-complexity description, typically through hidden rigidity conditions such as differential or recursion relations. We further assemble evidence from string compactifications, highlighting the constraining role of moduli space geometry and the importance of dualities. This perspective also yields mathematically well-defined notions of counting and volume measures on the space of effective theories, formulated in terms of effective field theory domains and coverings, whose finiteness is naturally enforced by the conjectures.
Effective field theories consistent with quantum gravity obey surprising finiteness constraints, appearing in several distinct but interconnected forms. In this work we develop a framework that unifies these observations by proposing that the defining data of such theories, as well as the landscape of effective field theories that are valid at least up to a fixed cutoff, admit descriptions with a uniform bound on complexity. To make this precise, we use tame geometry and work in sharply o-minimal structures, in which tame sets and functions come with two integer parameters that quantify their information content; we call this pair their tame complexity. Our Finite Complexity Conjectures are supported by controlled examples in which an infinite Wilsonian expansion nevertheless admits an equivalent finite-complexity description, typically through hidden rigidity conditions such as differential or recursion relations. We further assemble evidence from string compactifications, highlighting the constraining role of moduli space geometry and the importance of dualities. This perspective also yields mathematically well-defined notions of counting and volume measures on the space of effective theories, formulated in terms of effective field theory domains and coverings, whose finiteness is naturally enforced by the conjectures.
We present a collection of recent results concerning quantum information theory applied to quantum gravity. We first study the entanglement structure of Euclidean path integral states in SU(2) Chern-Simons theory, where we elucidate a connection between topological entanglement and quantum mechanical entanglement. We prove that the topology of certain three-manifolds controls the entanglement structure of the resulting quantum state, and conjecture a more general relationship for arbitrary three-manifolds. We then analyze the quantum circuit complexity of the time evolution operator in the Sachdev-Ye-Kitaev model, a theory of near-extremal black hole microstates. We find that this complexity grows linearly for a time exponential in the entropy, modulo a caveat concerning global obstructions to the growth of the distance function along geodesics, which we do not rule out. This constitutes a partial proof of Susskind’s conjecture about the complexity growth of black holes. Finally, we address the black hole information paradox in three dimensions by considering a toy model of black hole microstates in the form of an end-of-the-world brane. This brane carries a quantum theory which is itself holographic, and we compute entanglement entropies in the glued dual geometry by using a Ryu-Takayanagi formula where the minimal entropy surface can pass through the gluing surface.
We present a structural framework for analyzing dynamics in background-independent theories based on admissible transport on configuration spaces. The approach reformulates canonical evolution not in terms of a fixed Hamiltonian, but via constrained transport maps acting on an admissible subspace of states, preserving constraint closure and covariance by construction. Within this setting, we show that admissible dynamics admit a dual description in terms of state transport and observable transport, related by an adjoint pairing, and we establish conditions under which validation metrics are invariant under this duality. We further prove that admissibility enforces contraction bounds on accumulated deviations under composition, providing a structural explanation for stability without specifying a particular microscopic dynamics. The framework is applied to canonical Loop Quantum Gravity as a consistency analysis rather than as a proposal for new dynamics. We clarify how transport-based formulations relate to existing spin- network and spin-foam constructions, and we identify precise conditions under which such formulations remain anomaly-free. No claim is made to resolve the full dynamics problem or to derive novel physical predictions. Instead, the results provide a controlled language for distinguishing structurally stable evolutions from inadmissible ones in background-independent quantum theories. This work is an information-theoretic framework concerned with admissible transport and stability of information under composition. Physical theories, including Loop Quantum Gravity (LQG), are used solely as structured test cases rather than as the primary object of study. LQG serves as a representative background-independent information system. This manuscript is information theory under constraints, not physics. CIFT is an information-theoretic framework in which conserved quantities are measured in bits and are conditional on explicit admission and boundary exchange.
Across the foundations of modern physics, a recurring pattern of breakdowns appears: global state descriptions fail at horizons, singularities invalidate geometric extrapolation, quantum measurement resists dynamical closure, irreversibility persists despite time-reversal invariant laws, and cosmology relies on finely tuned initial conditions. These failures are typically treated as distinct problems, each motivating new mechanisms or interpretations. This paper advances a single, unifying diagnosis: global physical description fails whenever it demands the simultaneous enforcement of more distinctions than a finite system can support. The breakdowns of geometry, probability, reversibility, and global state assignment are not dynamical anomalies, but structural consequences of finite correlation capacity and the non-closure of jointly enforceable distinctions. This perspective resonates with earlier insights from systems theory and cybernetics. Ashby’s Law of Requisite Variety formalized the impossibility of global control without sufficient internal capacity, while related results across systems theory emphasize that coordination limits, not dynamics, set the boundary of coherent description. This paper argues that physics is subject to the same structural constraint: distinctions are physically meaningful only insofar as they can be jointly enforced under finite resources. The diagnosis also sharpens themes articulated by David Bohm concerning non-separability and the limits of global description. Rather than invoking hidden variables or epistemic restriction, we identify the missing structural element as finite enforceability. Physical meaning attaches not to isolated distinctions, but to sets of distinctions that can coexist without violating global consistency. Paper 52 introduces no new dynamics, fields, or ontologies. Its role is diagnostic and pre-dynamical. It makes explicit a constraint already respected wherever physical description succeeds, and violated precisely where it fails. By locating foundational breakdowns in enforceability rather than dynamics, this paper establishes the starting point for Admissibility Physics, with subsequent work developing the constructive consequences for geometry, entropy, irreversibility, and time. Admissibility Physics Enforceability of distinction Finite correlation capacity Global description failure Non-closure under composition Structural constraints Pre-dynamical foundations Systems theory Cybernetics Requisite variety Non-separability David Bohm Physical meaning Global consistency Limits of coordination
In this thesis, we lay out the goal, and a broad outline, for a program that takes quantum mechanics in its minimal form to be the fundamental ontology of the universe. Everything else, including features like space-time, matter and gravity associated with classical reality, are emergent from these minimal quantum elements. We argue that the Hilbert space of quantum gravity is locally finite-dimensional, in sharp contrast to that of conventional field theory, which could have observable consequences for gravity. We also treat time and space on an equal footing in Hilbert space in a reparametrization invariant setting and show how symmetry transformations, both global and local, can be treated as unitary basis changes. Motivated by the finite-dimensional context, we use Generalized Pauli Operators as finite-dimensional conjugate variables and define a purely Hilbert space notion of locality based on the spread induced by conjugate operators which we call "Operator Collimation." We study deviations in the spectrum of physical theories, particularly the quantum harmonic oscillator, induced by finite-dimensional effects, and show that by including a black hole-based bound in a lattice field theory, the quantum contribution to the vacuum energy can be suppressed by multiple orders of magnitude. We then show how one can recover subsystem structure in Hilbert space which exhibits emergent quasi-classical dynamics. We explicitly connect classical features (such as pointer states of the system being relatively robust to entanglement production under environmental monitoring and the existence of approximately classical trajectories) with features of the Hamiltonian. We develop an in-principle algorithm based on extremization of an entropic quantity that can sift through different factorizations of Hilbert space to pick out the one with manifest classical dynamics. This discussion is then extended to include direct sum decompositions and their compatibility with Hamiltonian evolution. Following this, we study quantum coarse-graining and state-reduction maps in a broad context. In addition to developing a first-principle quantum coarse-graining algorithm based on principle component analysis, we construct more general state-reduction maps specified by a restricted set of observables which do not span the full algebra (as could be the case of limited access in a laboratory or in various situations in quantum gravity). We also present a general, not inherently numeric, algorithm for finding irreducible representations of matrix algebras. Throughout the thesis, we discuss implications of our work in the broader goal of understanding quantum gravity from minimal elements in quantum mechanics.
Abstract Entanglement entropy, or von Neumann entropy, quantifies the amount of uncertainty of a quantum state. For quantum fields in curved space, entanglement entropy of the quantum field theory degrees of freedom is well-defined for a fixed background geometry. In this paper, we propose a generalization of the quantum field theory entanglement entropy by including dynamical gravity. The generalized quantity named effective entropy, and its Renyi entropy generalizations, are defined by analytic continuation of a replica calculation. The replicated theory is defined as a gravitational path integral with multiple copies of the original boundary conditions, with a co-dimension-2 brane at the boundary of region we are studying. We discuss different approaches to define the region in a gauge invariant way, and show that the effective entropy satisfies the quantum extremal surface formula. When the quantum fields carry a significant amount of entanglement, the quantum extremal surface can have a topology transition, after which an entanglement island region appears. Our result generalizes the Hubeny-Rangamani-Takayanagi formula of holographic entropy (with quantum corrections) to general geometries without asymptotic AdS boundary, and provides a more solid framework for addressing problems such as the Page curve of evaporating black holes in asymptotic flat spacetime. We apply the formula to two example systems, a closed two-dimensional universe and a four-dimensional maximally extended Schwarzchild black hole. We discuss the analog of the effective entropy in random tensor network models, which provides more concrete understanding of quantum information properties in general dynamical geometries. We show that, in absence of a large boundary like in AdS space case, it is essential to introduce ancilla that couples to the original system, in order for correctly characterizing quantum states and correlation functions in the random tensor network. Using the superdensity operator formalism, we study the system with ancilla and show how quantum information in the entanglement island can be reconstructed in a state-dependent and observer-dependent map. We study the closed universe (without spatial boundary) case and discuss how it is related to open universe.
We study the dynamics of Krylov state complexity in finite-dimensional quantum systems. Orthogonal polynomials built on a discrete energy spectrum crowd away from regions where the density of states is low at large Krylov index. The physical implication of this result is that, even using a minimalist Krylov state complexity which is defined over the entire spectrum, the Krylov complexity provably stops growing a little past the Heisenberg length in every low-energy state. This has interesting implications for the proposal that Krylov complexity is related to the wormhole length in 2D quantum gravity.