Paper abstract
Abstract
ChronaQ asks how an internally ordered observable history can arise when the complete quantum description has no preferred external time and admissibility is fixed by two boundaries. This paper gives a finite answer for systems with stable accumulated records. A fixed two-boundary-admissible history carrier is mapped to successively resolved record prefixes. Genuine refinement supplies a later-to-earlier truncation map, and continuation makes that map surjective. The number of surviving record lineages, and therefore its Hartley entropy, cannot decrease. When the rendered record alternatives also carry a positive refinement-consistent probability law, Shannon's chain rule gives a second monotone: the entropy of the accumulated record increases by the nonnegative conditional entropy of the newly resolved record. These results are assembled as CQ1. Survivor-lineage volume provides its structural ontology anchor, while normalized Shannon entropy is selected as the standard dimensionless coordinate for downstream calculations because it is continuous, has an expected-surprisal interpretation, and composes by the chain rule. A six-record two-boundary model exhibits strict growth, unequal information increments, a future-boundary plateau, and an exact clock-labelled history-state embedding. A second exact model asks which positive-looking refinements may enter CQ1: five candidate rereadings pass support and diagonal-Shannon tests, but A3 decoherence and record repeatability uniquely retain the stable pointer family relative to a declared earlier record. Without refitting, that family then gives phase-invariant probabilities and an exact ln(2) information increment on four frozen future-boundary conditions, while the complementary eraser context remains phase-sensitive. The construction therefore identifies both a relational order and a quantum admissibility gate without assigning a background time coordinate. It also separates survivor volume and record information from probability mass, geometric volume, and thermodynamic entropy, thereby providing a precise first interface for the later ChronaQ Foundations papers.
Keywords
- two-boundary quantum mechanics
- decoherent histories
- relational time
- records
- Hartley entropy
- Shannon entropy
- Page-Wootters mechanism
- ChronaQ
Scholarly record
Preferred citation
McIntyre, Stephen J. (2026). ChronaQ Foundations I: Finite Survivor-Lineage Entropy and Relational Order in Two-Boundary Quantum Histories. Working paper, version 0.5. McIntyre Lab. https://mcintyrelab.org/publications/foundations-i/
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Licence
© 2026 Stephen J. McIntyre. Licensed under CC BY 4.0.
Working paper, version 0.5, 3 August 2026. Not peer reviewed.
This licence applies to the text and original figures unless otherwise identified. Software, datasets and third-party material are not included unless explicitly stated. Patent and trademark rights are not granted by this licence.
Open research
Comments and technical feedback
Critical reading, corrections and specific technical questions are welcome while this working paper is being revised. Substantive contributions will be recognised clearly and proportionately.