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ZENODO
Preprint . 2026
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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Scale-Relative Distinguishability Theory: Foundations A Formal Framework for Cross-Scale Information Flow January

Authors: McKinley, Jon;

Scale-Relative Distinguishability Theory: Foundations A Formal Framework for Cross-Scale Information Flow January

Abstract

Scale-Relative Distinguishability Theory (SRDT) is a formal meta-theoretical framework for analyzing what embedded observers can know about fundamental reality. The framework is grounded in a single primitive relation: distinguishability relative to an observer. From this foundation, we develop a rigorous mathematical structure encompassing dynamics (systems that can be observed), observers (specifications of measurement capabilities), the observation operation (constructing models from dynamics via quotient), and a diagnostic methodology for classifying phenomena. The central result: what embedded observers can know is the structure of observation itself—the systematic relationship between observer characteristics and what those observers perceive. This is not a limitation but the most complete answer embedded observers can give. The framework is deliberately agnostic about the nature of finest-grained dynamics 𝓕. Spatial and temporal dimensions are not presupposed—they emerge as observer-constructed interfaces. We establish conditions for deterministic versus probabilistic behavior, prove information-theoretic bounds including a coarsening dominance theorem, and develop a five-category diagnostic methodology for classifying phenomena as intrinsic to 𝓕 versus observer-created. The quotient network—connecting quantum field theory, quantum mechanics, classical mechanics, thermodynamics, and other physical frameworks—is interpreted not as a map of fundamental reality but as a map of human observation: nodes represent characteristic bundles (regions of observer space), and arrows represent transformations from changing observer characteristics. This reframing has profound implications for the Theory of Everything program, requiring that any complete theory specify not only fundamental dynamics but also observer characteristics.

Keywords

course-graining, cross-scale physics, epistemology, measurement problem, observer problem, scale-relative distinguishability, philosophy of physics, observer-dependence, emergence, meta-theory, foundations of physics, Theory of Everything, quotient structure, information theory

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green