Translator This paper reformulates quantum entanglement within the framework of Finite-Resolution Physics (FRP), a finite-coherence version of quantum theory derived from the Reflexive Monoid Algebra (RMA) hierarchy.All experimental predictions of entanglement—joint probabilities, Bell-inequality violations, and Born frequencies—remain identical to those of standard quantum mechanics.The difference lies in structure: entanglement is no longer a separate postulate about tensor-product Hilbert spaces but an algebraic phase-consistency relation (FR3) and typicality constraint (FR4) linking additive subsystems under finite resolution.This reinterpretation explains nonlocal correlations as boundary-level coherence, not superluminal influence, and describes decoherence as the loss of FR3 coherence, marking the transition from quantum (Qμ) to statistical (Sμ) regimes.The work provides a unified algebraic account of entanglement, nonlocality, and decoherence within a finite-resolution operational framework.
Translator This paper reformulates quantum entanglement within the framework of Finite-Resolution Physics (FRP), a finite-coherence version of quantum theory derived from the Reflexive Monoid Algebra (RMA) hierarchy.All experimental predictions of entanglement—joint probabilities, Bell-inequality violations, and Born frequencies—remain identical to those of standard quantum mechanics.The difference lies in structure: entanglement is no longer a separate postulate about tensor-product Hilbert spaces but an algebraic phase-consistency relation (FR3) and typicality constraint (FR4) linking additive subsystems under finite resolution.This reinterpretation explains nonlocal correlations as boundary-level coherence, not superluminal influence, and describes decoherence as the loss of FR3 coherence, marking the transition from quantum (Qμ) to statistical (Sμ) regimes.The work provides a unified algebraic account of entanglement, nonlocality, and decoherence within a finite-resolution operational framework.
Quantum field theory unifies special relativity and quantum mechanics yet relies on externally imposed prescriptions—quantization, renormalization, and probabilistic interpretation—that lack a common algebraic foundation. This work derives these features from a single structural principle: the finite-resolution realization of the additive group [Formula: see text] under four internal consistency constraints. These constraints—finite operational resolution (FR1), multiplicative linearity (FR2), phase coherence (FR3), and statistical typicality (FR4)—generate, without additional postulates, the Hilbert-space formalism of quantum theory, the Born probability rule, and the Kolmogorov structure of statistical mechanics as limiting projections of one additive algebra. When extended to spacetime translations and their automorphisms, the same framework reproduces the kinematic and dynamical structure of quantum field theory while resolving ultraviolet divergences through intrinsic finiteness rather than external renormalization. Quantization and unitarity appear as consequences of additive symmetry, while the gravitational field emerges as the algebraic kernel that transports boundary information into bulk observables without requiring a separate quantization of the metric. The result is a unified, finite, and strictly algebraic foundation for physical law.
This paper presents a finite, regulator-based resolution of quantum entanglement, extending the Dual Regulator Framework to nonlocal correlations while preserving causality, locality of dynamics, and relativistic consistency. Entanglement is shown to arise entirely within the virtual domain, which lacks spatial topology and is regulated by the finite invariant Λφ=ln(φ2),\Lambda_\varphi = \ln(\varphi^2),Λφ=ln(φ2), while decoherence and measurement occur exclusively in the real domain, regulated by the Resolution Gap (RG). Because entangled correlations never propagate through real spacetime, their strength is shown to be exactly independent of spatial separation, without invoking superluminal influence or observer-dependent collapse. Bell inequality violations are derived from domain structure alone. The framework predicts a finite correction to the standard Tsirelson bound arising from virtual-domain regulation, yielding a testable enhancement at high precision. No hidden variables, signaling mechanisms, or modifications to relativistic causality are introduced. Decoherence of entangled systems is shown to be additive across subsystems and governed by regulator ratios rather than ad hoc environmental postulates. The Born rule emerges from symmetric coupling across the virtual–real interface, consistent with prior papers in the series. A companion computational validation script numerically reproduces all constants and predicted correlation bounds using standard numerical libraries. All results are reproducible and contain zero adjustable parameters. This work constitutes Paper III in a planned sequence addressing foundational inconsistencies in quantum field theory, following finite resolutions of measurement and wave–particle duality. Licenses Creative Commons Attribution Non Commercial No Derivatives 4.0 International
Quantum entanglement produces correlations that violate classical locality constraints while remaining fully consistent with relativistic no-signaling. Although standard quantum mechanics predicts these correlations with extraordinary empirical success, the ontological meaning of entangled states and the physical status of wave-function collapse remain deeply debated. This paper develops a speculative but structured informational interpretation in which entangled subsystems are modeled as multiple local realizations of a single shared informational identity within an underlying finite-capacity substrate. The framework is articulated through explicit postulates, density-matrix analysis, entanglement entropy, a toy realization scheme, and an informational identity operator acting on composite states. Within this view, nonlocal correlations arise not from superluminal causal influence but from ontological non-separability at the informational level. Measurement is interpreted as informational resolution: a reduction of degeneracy in the local realization of a shared informational structure. The irreversible stabilization of outcomes is then linked to thermodynamic cost through Landauer-type reasoning. The proposal is not advanced as a replacement for quantum mechanics, nor as a fully worked-out hidden-variable theory, but as an ontological scaffold intended to unify entanglement, collapse, and thermodynamic irreversibility within an informational perspective. Compatibility with Bell inequalities, decoherence, basis selection, and no-signaling is discussed in detail, together with limitations and possible routes toward future formalization and empirical relevance.
This is Paper 142 in the Anaxiomatic Mechanics / pq-Spacetime stack. It develops a finite mechanical account of quantum entanglement within pq-spacetime. Entanglement is identified with the persistence of a non-factorable family of admissible future histories. Two measurement regions can therefore appear as separate local systems in emergent spacetime while still remaining projections of one joint finite closure problem. Bell inequality violation follows because the joint outcomes are not generated by two independent local completion families. No-signalling is nevertheless preserved because complete changes to a distant measurement boundary do not alter the local marginal outcome weights. The paper establishes the Entanglement Closure Theorem and distinguishes microscopic non-factorability from observable entanglement after coarse-graining into stable measurement records. It also gives an explicit minimal singlet construction using two opposed history fibers carrying the relevant four-phase weights. The resulting finite ledger is antisymmetric, nonseparable, and exactly balanced at each local wing. Complete changes of basis on the distant side preserve those local marginals. Using the previously derived Hilbert-space and beta-Dirac bridges of pq-spacetime, the paper recovers the familiar spinor overlap law, the quantum singlet correlation, the maximal Bell-CHSH value, monogamy of maximal entanglement, and decoherence through environmental boundary enlargement. The analysis also explains why no preferred measurement ordering is required and why entanglement remains compatible with relativistic causality. The resulting picture is direct. Entangled systems do not exchange superluminal messages, carry classical answer sheets, or require a force acting across space. Their local outcomes arise from one shared finite admissibility structure whose joint correlations are nonlocal while its controllable local statistics remain causal. Entanglement is therefore physically real, nonclassical, and nonlocal in correlation, but not a signalling mechanism.
Version 2: Replaced Word file with properly formatted PDF. No changes to scientific content. --- We argue that quantum entanglement is best understood as the structural non-factorizability of joint continuation measures in a pregeometric framework — one that presupposes neither a background Hilbert space nor a background spacetime. This thesis has direct implications for the interpretation of Bell non-locality, the debate between ontic and epistemic structural realism, and the question of whether entanglement is a fundamental feature of reality or an artifact of quantum-mechanical representation. Within Temporal Rate Ontology (TRO), physical systems are modelled as directed acyclic graphs (DAGs) of continuation events, and entanglement is defined as the non-existence of a product decomposition of the joint continuation measure — a purely combinatorial condition that requires no wavefunction and no shared configuration space. We prove that this structural condition entails the standard correlated measurement outcomes of quantum mechanics, under a mild non-degeneracy condition on the joint DAG that is generically satisfied. The quadratic probability rule is derived from an aggregation-stability argument within the CLT regime rather than postulated. Bell non-locality is reinterpreted as global DAG coherence rather than superluminal influence. Decoherence is modelled as constraint-induced suppression of continuation multiplicity. The framework is situated against relational quantum mechanics, causal set theory, and ontic structural realism, and philosophical objections concerning subsystem identity, underdetermination, and the emergence of the Hilbert space are addressed directly.
This work introduces a resolution-dependent geometric framework—Quantum Fractal Geometry (QFG)—in which the effective physical description of systems depends explicitly on observational scale. Within this framework, entangled quantum systems are modelled as unified geometric structures at deep resolution, characterised by a scale-dependent metric g_{μν}(ℓ) and a geometric phase field φ(x,ℓ) valued on S¹. Measurement is interpreted as a resolution-dependent projection of this unified structure onto detector-scale observables. A symmetry-constrained coarse-graining map is introduced as the minimal fixed point of resolution flow, identifying antipodal phase configurations (S¹ → S¹/ℤ₂). Under isotropy, continuity, and convex-linearity, the quantum correlation function E(a,b) = −cos(θ_a − θ_b) is recovered as the unique rotationally invariant statistic compatible with the projection structure, saturating the Tsirelson bound. Within QFG, Bell inequality violation arises not from nonlocal signalling or measurement dependence, but from the failure of scale-independent separability. Locality (in the operational no-signalling sense) and measurement independence are preserved. The framework further outlines a programme for deriving the Born rule from resolution-induced measure structure and identifies falsifiable predictions, including resolution-dependent deviations from ideal cosine correlations. This work should be understood as establishing the minimal geometric structure required for the QFG interpretation of Bell correlations, with full dynamical derivations deferred to future work.