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Nonlocal-Unification-Informed Bayes Rule With Implications for Background Independence

Aman Chawla

Published May 4, 2026• 0 citations
Publisher

Abstract

Schack, Brun, and Caves derived a quantum Bayes rule for exchangeable quantum states by showing that, under generalized measurements, the posterior state of unmeasured systems may be represented as a Bayesian update over density operators. The present article proposes a Nonlocal-Unification-informed extension of that rule. In Nonlocal Unification (NU), an observer is not only an abstract user of probabilities, but an embodied sampling function acting on a nonlocal informational substrate. The proposed update therefore acts on a joint model of quantum state and observer function. The ordinary quantum Bayes rule is recovered when the sampling architecture is fixed. The article further examines NU information conservation, Frechet convergence of observer functions to a limiting observer, and a two-observer toy universe in which one observer reconstructs the internal spacetime of another. The resulting framework connects Bayesian inference, observer-relative spacetime reconstruction, and the informational field-equation side of NU.

DOI
10.5281/zenodo.20024035

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This study posits that information is a conserved and fundamental quantity underlying the dynamics of quantum systems, classical measurement, and consciousness. Building on the author’s conservation of information principle and the theory of Local Consciousness Instruments (LCIs), we integrate this view with Hardy’s reconstruction of quantum mechanics and reinterpret Einstein’s field equations as emergent expressions of informational geometry. We propose that a global structure, termed Nonlocal Consciousness (NC), unifies quantum theory and spacetime by serving as an informational limit toward which all observers converge. This framework presents a paradigm in which quantum and gravitational phenomena arise from a universal informational field. The theory is falsifiable through probes investigating quantum gravity corrections to canonical commutation relations.
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Abstract This paper develops a discrete information-theoretic framework in which physical systems are modeled on a graph or lattice of locally interacting space cells. Its principal contribution is an integrated architecture separating exact consequences of locality and unitarity, continuum-limit derivations, model-family results, toy-model mechanisms, and unresolved physical mappings. Matter-like identity is treated as propagated relational information rather than persistence of the same occupied cells, and candidate mechanisms are audited for causal locality, conservation or ledger closure, and false reconstruction. The quantum branch assumes finite-dimensional local Hilbert spaces and local unitary or completely positive trace-preserving (CPTP) updates. Under those assumptions, norm preservation, finite causal cones, and reduced-state no-signaling follow directly; spinor quantum walks admit a Dirac-like long-wavelength limit and a secondary nonrelativistic Schrödinger envelope. A representative reciprocal q–χ lattice action shows how compact local dynamics can support continuity, spectral response, action-derived scattering, and internal symmetry/charge, while later extensions supply a provisional local gauge/Gauss/holonomy structure. Two geometric realizations remain deliberately distinct: distortable cells and scalar extrinsic-χ compression. Toy models provide mechanism and failure-boundary evidence for relational identity, reconstruction, scattering, photon-like bookkeeping, and topology/charge-current response. The framework does not derive the Standard Model, quantum field theory, or general relativity; it defines a falsifiable program for testing whether compact local information-processing laws can recover required low-energy structures without hidden nonlocal repair or post-hoc tuning.