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The Intrinsic Architecture of Physical Law: From Pre-Quantum Distinguishability to the Emergent Dark Sector in Universal Modular Dynamics

Oleg Nesen

Published Sep 25, 2026• 0 citations
Publisher

Abstract

We develop an extended formulation of Universal Modular Dynamics (UMD) in which physical law is organized as a hierarchy of nested, renormalization-stable informational phases emerging from a pre-quantum domain of distinguishability. The construction does not assume spacetime, locality, quantum fields, or graph structure as fundamental. Instead, the primitive level is defined through relations of distinguishability between pre-physical configurations, whose dynamically persistent sectors provide the substrate from which effective operator states and subsequent physical structures emerge. Within this architecture, previously derived pre-string configurations are interpreted as a particular low-dimensional stable sector of the broader UMD pre-quantum state space, rather than as the universal starting point of the theory. Their collective scaling behavior admits an effective graph limit, providing a controlled route from pre-string organization to relational connectivity and, subsequently, to operational subsystem structure. This graph limit is therefore emergent and sector-dependent, rather than ontologically primitive. At the operator level, the density matrix ρ becomes the carrier of distinguishability and generates modular structure through K = −log ρ, Kρ|σ = −log ρ + log σ. Relative modular dynamics, together with completely positive open-system flows, defines a sequence of scale-dependent transformations through which stable subsystem decompositions, operational locality, and finite-speed information propagation emerge. The resulting causal structure is established before continuum spacetime geometry and is governed by Lieb– Robinson-type bounds on the transport of quantum correlations. A central aim of the present work is to sharpen the transition from discrete relational organization to continuum spacetime. We explicitly distinguish the geometry of quantum state space from physical spacetime geometry and formulate the intermediate coarse-graining and scaling conditions required to connect Bogoliubov–Kubo–Mori information geometry, correlation-based relational distances, and an effective continuum metric. Einstein-type dynamics is then interpreted as an entropic consistency condition of the emergent geometric phase, arising from local information balance and variational stability rather than from a fundamental spacetime background. The same hierarchical framework is extended to access-relative vacuum structure and hidden-sector dynamics. Dark-energy-like behavior is associated with stable entropic vacuum drift relative to an observer-accessible algebra, while dark-matter-like effects arise from correlations and backreaction between visible and inaccessible sectors. These mechanisms are embedded within the same renormalization hierarchy rather than introduced as independent cosmological components. We further characterize regimes in which metricity, causal ordering, and stable factorization fail, defining non-geometric phases relevant to the breakdown of the spacetime description in extreme gravitational and early-universe regimes. Throughout the construction, we distinguish theorem-level results, conditional emergence statements, numerical evidence, and phenomenological predictions, and we identify explicit falsifiability conditions for the principal UMD claims. The resulting picture is that physical law is not represented by a single primitive dynamical equation imposed on a pre-existing arena, but by a recursively organized hierarchy of informational structures whose stable renormalization sectors generate quantum states, locality, causality, geometry, gravitation, and effective dark-sector phenomena.

DOI
10.24108/preprints-3116477

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We develop a structural framework in which physical reality is derived from the spectral properties of quantum states. Within the approach of Universal Modular Dynamics (UMD), the density operator ρ is taken as the fundamental object, and its modular generator K =−log ρ provides a representation of informational content. We show that the distribution of modular energies, defined by the spectrum of K, serves as a primary structure from which higher-level physical organization emerges. In particular, we demonstrate how spectral distributions give rise to stable structures, induce locality through optimal partitioning, and generate geometric relations via correlation-based distances. Dynamics is introduced as an intrinsic ordering of states under modular evolution, while renormalization appears as a spectral phenomenon governed by statistical properties of the modular spectrum. This establishes a connection between informational structure and physical scale. The resulting construction defines a sequential chain of emergence, ρ → p(k) → structure → locality → geometry → dynamics → scale, in which each level arises from properties of the previous one without introducing external assumptions. This work provides a unified perspective in which physical structure is understood as an emergent consequence of spectral information encoded in quantum states.
We develop a unified framework in which physical reality emerges from the spectral properties of informational states. Starting from the density operator ρ, we construct the modular generator K = −log ρ and its spectral distribution p(k) as the fundamental objects. We demonstrate that structure, locality, geometry, dynamics, and scale arise sequentially from properties of the modular spectrum. Renormalization is reinterpreted as spectral flow, and physical phases are defined through optimal partitions of informational structure. We further show that stable spectral modes correspond to matter-like structures, while gauge symmetry emerges as an access-relative redundancy. A universal dynamical equation is formulated, governing all physical regimes in a phase-dependent manner. The framework is supported by a reproducible numerical program and extended to flavor physics, where we derive the structure of quark mixing and CP violation from spectral hierarchy. This work establishes a unified perspective in which physical structure is understood as an emergent consequence of distinguishability and spectral organization.
We present a minimal and testable mechanism for the emergence of spacetime from quantum information within the framework of Universal Modular Dynamics (UMD). Starting from the density operator ρ and the modular generator K = −log ρ, we construct a robust operator-level geometry via commutator structures. We demonstrate that all static information-theoretic constructions—including entropy, mutual information, and spectral embeddings—fail to generate a consistent notion of spacetime. We then introduce dynamical diagnostics based on the propagation of distinguishability and show that spacetime emerges if and only if distinguishability propagates with finite speed and maintains locality, forming a light-cone structure. This leads to a phase classification of quantum dynamics into three regimes: no propagation, fast mixing, and localized propagation, the latter uniquely corresponding to emergent spacetime. Our results establish spacetime as a dynamical phase rather than a fundamental structure and provide a concrete, falsifiable criterion for its existence.
We develop a pregeometric reconstruction framework in which quantum mechanics, gauge symmetry, probabilistic structure, matter, Lorentzian spacetime geometry, gravitation, and physical constants emerge from recursively stabilized coherent relational transport organization. The framework begins from a primitive causal-relational substrate consisting only of fluctuating accessibility relations and compositional transport structure. No background spacetime manifold, metric geometry, particle ontology, or external temporal parameter is assumed fundamentally. The theory further proposes that the preconditions underlying Einsteinian physics must already exist at the pre-geometric level as deeper relational consistency principles. Lorentz invariance, causal structure, covariance, conservation laws, and gravitational equivalence are interpreted as emergent macroscopic expressions of more primitive coherent accessibility constraints. A generalized spectral transport operator governs coherent relational evolution and generates stable eigensectors corresponding to persistent physical structure. Quantum mechanics emerges from coherent compositional consistency and norm-preserving recursive transport flow. Gauge symmetry emerges as local redundancy of coherent transport representation. Classical mechanics emerges through stationary coherent transport stabilization. A reconstruction of the Born rule is proposed in which quadratic probability amplitudes arise from multiplicative persistence consistency under independent coherent composition. Lorentzian spacetime geometry emerges statistically from stabilized causal accessibility organization, while gravitation emerges thermodynamically as equilibrium relaxation of coherent accessibility geometry. The framework further proposes that physical constants correspond to frozen stability invariants selected during primordial coherent transport evolution. In particular, the fine-structure constant is interpreted as a stable surviving coherent phase-accessibility ratio associated with recursive phase closure. The theory therefore attempts not merely to reproduce known equations, but to explain why physical reality universally organizes itself through Hilbert structure, gauge redundancy, localization, Lorentzian geometry, and thermodynamic gravitational dynamics. In particular, the framework proposes that Einsteinian spacetime physics emerges from deeper pre-Einsteinian coherent relational conditions governing recursive transport accessibility before spacetime itself exists.
We develop an operator-based framework in which quantum dynamics, interaction structure, and geometric features arise from the modular properties of a density operator constructed from a non-commuting pair of Hermitian operators. A positive state is defined via exponential coarse-graining, and time evolution is derived from the associated modular Hamiltonian rather than postulated. Using a systematic Baker–Campbell–Hausdorff expansion, interaction terms are shown to be organized by nested commutators, yielding a natural algebraic hierarchy analogous to effective field theory. Interpreting the coarse-graining parameter as a renormalization scale, we derive flow equations for operator-valued couplings, establishing a renormalization group structure in operator space. A continuum field-theoretic extension and a lattice regularization suitable for numerical investigation are constructed. Local automorphisms of the operator algebra give rise to gauge connections, while the quantum Fisher information metric defines an emergent notion of geometry. Under additional assumptions of locality and approximate equilibrium, the framework reproduces the structure of entropic approaches to gravitational dynamics. These results provide a unified algebraic perspective in which dynamics, interactions, and geometry are encoded in the modular structure of quantum states.