Universal Decision Principle from Local Relative Entropy Flux: A Detector Consistent, Falsifiable Criterion for Quantum Record Formation across QM, Mott Tracks, AQFT, and QED
We propose an operational, detector-consistent criterion for identifying when and where a quantum interaction produces a stable classical record. The criterion—termed the Universal Decision Principle (UDP)—is defined from instrument-fixed maps rather than ad hoc collapse parameters and is formulated to remain meaningful from finite-dimensional quantum mechanics to local algebraic quantum field theory (AQFT) and gauge-invariant inclusive quantum electrodynamics (QED). Given an underlying state , an admissible operational reduction to a detector region/channel , and an instrument-defined pointer channel onto a commuting record algebra, we define the pointer-relative entropy where is the Umegaki relative entropy in finite settings and the Araki–Uhlmann relative entropy on local von Neumann algebras in AQFT. In record-formation regimes decreases towards zero; we therefore localise the event by the relative-entropy flux and declare record formation at the statistically significant interior maximum of within an a priori specified analysis window. The protocol is explicitly falsifiable through nonparametric bootstrap confidence intervals, structure-preserving surrogate tests, sensitivity stability gates, and detector timing/jitter budgets; irreversibility is graded independently using data-processing inequality remainders and Petz/universal recovery performance near . We provide domain-specific constructions of and for (i) interferometric and spin measurements, (ii) Mott-type track formation as sequential cellwise events, (iii) local AQFT causal regions, and (iv) gauge-consistent inclusive QED channels. Supplementary materials include literature-derived datasets, analysis spreadsheets and figures, and machine-checkable formal verification artefacts (mathlib) supporting key logical steps.
We propose an operational, detector-consistent criterion for identifying when and where a quantum interaction produces a stable classical record. The criterion—termed the Universal Decision Principle (UDP)—is defined from instrument-fixed maps rather than ad hoc collapse parameters and is formulated to remain meaningful from finite-dimensional quantum mechanics to local algebraic quantum field theory (AQFT) and gauge-invariant inclusive quantum electrodynamics (QED). Given an underlying state , an admissible operational reduction to a detector region/channel , and an instrument-defined pointer channel onto a commuting record algebra, we define the pointer-relative entropy where is the Umegaki relative entropy in finite settings and the Araki–Uhlmann relative entropy on local von Neumann algebras in AQFT. In record-formation regimes decreases towards zero; we therefore localise the event by the relative-entropy flux and declare record formation at the statistically significant interior maximum of within an a priori specified analysis window. The protocol is explicitly falsifiable through nonparametric bootstrap confidence intervals, structure-preserving surrogate tests, sensitivity stability gates, and detector timing/jitter budgets; irreversibility is graded independently using data-processing inequality remainders and Petz/universal recovery performance near . We provide domain-specific constructions of and for (i) interferometric and spin measurements, (ii) Mott-type track formation as sequential cellwise events, (iii) local AQFT causal regions, and (iv) gauge-consistent inclusive QED channels. Supplementary materials include literature-derived datasets, analysis spreadsheets and figures, and machine-checkable formal verification artefacts (mathlib) supporting key logical steps.
Preprint and reproducibility bundle for: “Universal Decision Principle from Local Relative Entropy Flux: A Detector-Consistent, Falsifiable Criterion for Quantum Record Formation across QM, Mott Tracks, AQFT, and QED”. Contents: (1) Manuscript PDF (preprint). (2) Reproducibility bundle (ZIP): literature-derived spreadsheets and figure artefacts, analysis scripts/parameter manifests, and Lean 4/mathlib verification artefacts. Submitted to Physical Review A (TempID: es2026jan01_605). arXiv identifier will be added after arXiv posting.
The quantum measurement problem separates into operational questions: which observables are stable records, how outcome probabilities are represented, how conditional post-event states are updated, and how a detector event time is assigned. We give a compact architecture-conditional framework. In a finite-dimensional detector model, the detector-side relative-entropy flux is differentiated with the exact Fréchet derivative of the matrix logarithm. A noise-regularised timing distribution is defined and, under an explicitly assumed isolated non-degenerate maximum of the calibrated flux, Laplace asymptotics proves concentration at that maximum. Under stated fixed-point and detailed-balance hypotheses, the centre of the fixed-point algebra gives a canonical commutative record algebra. Outcome probabilities admit a POVM representation, and conditional updates use a completely positive (CP) instrument in its standard sense: CP maps whose traces give probabilities and whose normalised outputs give post-event states, summing to a trace-preserving map. Separately, an assumed modular-invariant inclusion of von Neumann algebras admits a state-preserving conditional expectation and CP retraction. A conditional quantum-error-correction lemma bounds accumulated record failure. These results do not derive unique outcomes from unitarity, construct a black-hole algebra inclusion, or resolve the black-hole information problem; they give a conditional framework, a worked illustration, and testable timing and record-stability criteria.
Irreversible records, ultraviolet control, event-like outcomes, and consistent matter sectors are genuine demands on physical theories. They do not, by themselves, force all viable theories into one mathematical universality class. The missing information is the mechanism: which states and operations are admitted, what is projected, what counts as recovery, which dynamics stabilizes records, how ultraviolet errors are controlled, how events are generated, and which global gauge and bundle data define the matter sector. This paper replaces an earlier inevitability claim by a conditional classification framework. A theory is represented by a seven-axis witness record covering operational measurement, descent and recovery, stability, ultraviolet control, event structure, gauge and matter data, and empirical validation. We prove five bounded results: noninjective descent has no left inverse; compact cores of open record regions have positive margins; transverse crossings are locally finite; representations of a specified compact U(1) have integer weights; and multi-axis equivalence classes refine monotonically as comparison requirements are added. Explicit counterexamples show why operational irreversibility need not mean algebraic noninvertibility, low-energy predictivity does not select smooth spectral damping, countable outcomes do not create a causal set, and local anomaly cancellation or charge quantization does not determine the observed Standard Model. Collapse models, monitored circuits, effective field theory, asymptotic safety, loop quantum gravity, causal sets, noncommutative geometry, and Modal Triplet Theory are therefore compared only through completed witness rows. The result is a falsifiable taxonomy and release-ready comparison protocol, not a proof that the apparent plurality of physical theories is illusory.
This preprint investigates structural relations between relative entropy, modular theory, and information geometry in algebraic quantum field theory (AQFT). In finite‑dimensional quantum systems, the Hessian of Umegaki relative entropy coincides with the Bogoliubov–Kubo–Mori (BKM) metric, and modular automorphisms act by isometries of this geometry; these standard results are reviewed as a mathematically controlled reference model. Motivated by this setting, the work formulates minimal structural conditions under which a perturbative modular information‑geometric programme for Type III1_11 von Neumann algebras could become mathematically meaningful. The analysis focuses on admissible perturbation sectors, Araki relative entropy, modular covariance, and the functional‑analytic obstructions caused by unbounded modular operators. A general consequence of positive semidefiniteness of the perturbative entropy Hessian is recorded: whenever the Hessian defines a well‑defined positive semidefinite bilinear form, its null directions annihilate the full form. In the Rindler wedge model, the corresponding regularity problem for candidate perturbations is formulated in terms of spectral properties and domain issues of the Lorentz boost generator. Throughout, explicit separation is maintained between rigorous results, conditional statements, heuristic motivations, and unresolved analytic problems. A conjecture concerning degenerate modular directions is stated together with a necessary falsifiable condition. This document is exploratory in nature and has not been peer reviewed.
A Kernel-Role Determinacy Theorem for Record Fixation, Fixed-Domain Quotients, and Boundary-Trace Normal Form This paper specializes the AASC kernel to the construction and use of quantum measurement records. Its central question is not initially how outcomes are produced, whether a wavefunction collapses, or which interpretation of quantum theory is correct. It asks what must be fixed for a measurement record to function as the same determinate physical and evidential object across retention, prospective use, deliberation, comparison, and report. For any non-degenerate determinate physical object, state, carrier, transformation, record, comparison, or endpoint, the paper takes the governing kernel to be: NDObj(x) ⇒ K(x) = (Adm, Stand, Ref, Irr). Admissibility, standing, reference, and irreversibility are therefore treated as necessary role conditions of determinate record use, not as an optional interpretive overlay added to an otherwise complete physical description. Measurement-record determinacy The manuscript constructs a fixed-domain measurement-record target in which a record must preserve: reference to the same construction token; standing-bearing evidential eligibility; admissible reuse; original act-time qualification; lawful redescription; retained and prospective record use; deliberative and comparative use; reportability and downstream inheritance. The resulting assignment space is quotiented by equivalence of standing-bearing measurement-record content. A rival quotient claiming exactly the same content collapses to the canonical measurement-record quotient. Representational differences that preserve the complete role content are treated as skin; differences affecting record identity, evidential ordering, admissibility, continuation, or downstream use remain physically relevant. Physically non-selective quantum regimes The paper then studies a physically non-selective quantum regime containing unitary branching, entanglement, decoherence, branch-local records, and stable local reports. The central result is conditional and target-specific: The bare unitary-entangling-decohering package can support multiple stable branch-local records without supplying a unique standing evidential record for the fixed construction-relative target. This is not a claim that branch-local records are unreal, unstable, or physically useless. It is a distinction between: physical occurrence of branch-local record structures; local branch-relative reportability; evidential role fixation for a record reused as the same standing object across the measurement practice. The paper shows that non-selective structures may agree on branch weights, density content, decoherence, correlations, instrument sums, channel closure, effect weights, projector orthogonality, and repeatability without selecting one fine record as the standing evidential record. Fixed-domain quotient and fixation commutation The theorem ladder establishes: fixed-domain assignment-space forcing; exact quotient construction for standing-bearing record content; same-scope equivalence collapse; fixation commutation under admissible transformation; inheritance of the original qualification requirement; persistence-bearing reuse; asymmetry exhaustion; anti-weakening; selector exhaustion. If evidential ordering varies across admissible assignments while the target requires one fixed-domain ordering, the ordering is not defined on that scope merely because numerical values or branch-local reports happen to coincide. The paper therefore treats measurement-record fixation as prior to the theory-level evidential reuse that depends on it. Boundary-trace normal form After internal and provenance/indexical routes have been exhausted, the residual same-domain route is a singleton stable boundary trace. Such a trace is not collapse dynamics, hidden-variable selection, or a new physical mechanism. It is an admissibility-preserving role anchor that can fix a record-bearing assignment only when its channel, incidence, transport law, original authority, and singleton-positive condition are independently warranted. The result distinguishes: sound partial selection from complete role fixation; unique trace value from unique original occupant; class-valued record fixation from raw-token fixation; later discovery of an original qualification from retroactive repair; physical record occurrence from standing evidential identity. Finite quantum specialization The paper occupies the abstract structure with an explicit finite two-branch quantum measurement domain containing: two outcomes; two fine records and one merged record; denominator-two branch weights; a balanced integer-amplitude state; density-table realization; selective and non-selective instrument maps; environment-record maps; projective branch maps; complementary effects; zero-product projectors; repeatability operations. On the declared balanced witness, amplitude weights, density weights, branch-map traces, effect weights, pointer records, instrument records, environment records, and channel records agree on the same branch architecture. Selective surfaces preserve the fine-record distinction. Non-selective surfaces agree only on the merged record. The fine records therefore remain separated, while the declared non-selective surfaces supply no singleton fine-record selector. The finite selector-boundary theorem eliminates the disjunction of candidate hidden selectors across the state, instrument, environment, channel, effect, and repeatability surfaces. The resulting diagnosis is precise: the missing structure is admissible fine-record role fixation, not further branch production, weighting, decoherence, stabilization, or repeatability. Scope and non-claims The manuscript establishes a finite, conditional, manuscript-facing theorem. It does not claim: to derive Hilbert-space quantum mechanics; to derive general POVM theory; to derive full projection-valued-measure theory; to reconstruct the full operator algebra; to provide a general Kraus representation theorem; to reconstruct complete positivity; to derive the continuum Born rule; to derive universal physical decoherence theory; to introduce a new collapse dynamics; to prove that no physical collapse process occurs in nature; to prove physical branch selection; to establish interpretive truth; to classify every possible physical measurement mechanism. The absence of a hidden selector on the declared finite non-selective surfaces is therefore not a theorem that no physical collapse or selection process can occur elsewhere. It is the finite theorem that those declared surfaces do not themselves supply the required fine-record selector. Relation to quantum interpretations The result does not deny the practical success of quantum theory, decoherence, branch-relative reporting, instrumental updates, or decision-theoretic methods. A practice aimed only at prediction, branch-local reporting, or instrumental updating may be a different target from the construction-relative record use studied here. If a theory claims to underwrite retained, prospective, deliberative, and evidential reuse of the same record-bearing construction token, it must preserve the relevant kernel roles and admit a standing-bearing fixation regime. Bare Everettian dynamics, without additional dynamics, ontological privileging, or admissible restriction to one constructional class, supplies no fine-record selector on the declared target. A strategy that preserves non-selective physics while restricting admissible record-fixation assignments belongs to a restriction-to-one-constructional-class route. Instrumentalist and QBist strategies instead reduce or redirect the target explanatory burden. Role in the AASC programme This paper provides the record-fixation layer of the AASC Quantum Determinacy Pair. Its companion Bell-scope work addresses the compatibility and no-signaling side of quantum witness determinacy. Together, the pair treats quantum records and witnesses as kernel-governed standing structures rather than as automatically determinate physical occurrences. The paper’s principal contribution is to identify the first failure point in a physically non-selective measurement regime: The initial problem is not necessarily the production of branch-local outcomes. It is the admissible fixation of the record role through which outcomes are retained, reported, remembered, compared, and used as evidence. The public Lean 4 formalization is synchronized with the finite measurement-boundary release v0.9.1 and provides the finite artifact for the declared effect, projector, compatibility, closed-stack, boundary-certificate, and audit layers. Keywords AASC; measurement problem; quantum measurement; measurement-record fixation; physically non-selective regimes; Everettian non-selection; record-role determinacy; fixed-domain quotient; standing equivalence; boundary-trace fixation; selector exhaustion; decoherence; branch-local records; admissibility and irreversibility; Lean 4 formalization
We develop a staged research framework in which physical time is treated not as a primitive external parameter, but as an emergent quantity generated by the quantum dynamical structure of matter-energy configurations. The central working hypothesis is that a physically meaningful temporal increment exists only when state-change distinguishability is both relationally accessible and supported by stable physical records. On this basis, we formulate a Relational Chronometric Principle (RCP) and construct a local chronometric field χℓ(x) from two standard quantum-information-theoretic ingredients: quantum Fisher information and a record-stability factor derived from relative-entropy loss under a calibrated noisy channel (Braunstein & Caves, 1994; Page & Wootters, 1983). The present paper has four limited but explicit goals. First, we formulate the RCP as a minimal axiom set and derive an existence result for a bounded chronometric order parameter, together with a restricted uniqueness result. Second, we introduce a micro-operational definition of χℓ(x), specify the admissible class of coarse-graining maps Cℓ from which it is constructed, and establish a set of core properties for the field including non-negativity, boundedness, and convergence of the operational estimator in the Markovian-Gaussian limit. Third, we analyse the minimal low-energy covariant completion compatible with chronometric universality and show that a scalar-tensor effective field theory provides a controlled representation of emergent proper-time dressing and weak-field gravitational corrections. Fourth, we identify an operational metrology package with full uncertainty propagation and explicit sensitivity targets, a systematic budget for the primary experimental channel, and a three-channel experimental hierarchy based on co-located optical clocks, vertical clock comparisons, and atom interferometry. The framework is deliberately not presented as a final unification theory. It does not provide a UV completion, it does not derive the chronometric coarse-graining map from a fundamental quantum-gravity architecture, and it does not derive the Standard Model gauge sector. Instead, it is advanced as a disciplined low-energy programme that connects three normally separate domains: relational quantum dynamics, weak-field gravity, and precision chronometric observables. Within that restricted scope, the theory yields a falsifiable screened scalar sector, controlled weak-field limits, concrete sensitivity targets, and a cross-channel falsifiability architecture. Keywords: emergent time; relational dynamics; chronometric scalar; quantum Fisher information; scalar-tensor EFT; optical clocks; atom interferometry; screened gravity; coarse-graining maps; record stability