Relational Temporal Self-Measurement: A Conceptual Framework for the Internal Construction of Temporal Order in Closed Systems

This preprint introduces Relational Temporal Self-Measurement (RTSM), a conceptual framework for analysing how a closed or effectively closed physical system may internally construct, quantify, and preserve temporal order without requiring an external physical clock. The framework distinguishes between a minimal relational architecture, in which an internal clock subsystem (C) is correlated with an observed subsystem (S), and a stricter form of temporal self-measurement in which a physical memory subsystem (M) preserves distinguishable records of clock–system correlations. This leads to the operational architecture (C ⊗ S ⊗ M). RTSM is developed in relation to the Page–Wootters mechanism, quantum temporal reference frames, periodic internal clocks, thermal time, entropic internal time, autonomous quantum clocks, and the thermodynamic and informational costs of timekeeping. Particular attention is given to periodic-clock ambiguity, memory persistence, operational factorisation, measurement backreaction, finite recording regimes, and the trade-off between temporal information and physical disturbance. The framework does not claim that time is conscious, universally entropic, or proven to be fundamentally emergent. Its more limited objective is to identify the physical and operational conditions under which a system can contain both the processes that transform and the internal references and records through which those transformations become temporally measurable. The manuscript also proposes a set of falsifiable, model-dependent hypotheses and experimental directions concerning internal-clock switching, memory-assisted chronology, entropic clocks, information–disturbance trade-offs, and networks of local clocks. Version: 1.1Status: PreprintDOI: 10.5281/zenodo.22083883