Metrological Theory of Time: Structural Uncalibratability between Irreversible Decay and Reversible Cycles

Time standards are not merely descriptions of nature; they are socio-technical infrastructures and protocols that enable measurement, synchronization, and institutional coordination. This paper reconceives “time” not as a universal dimension or physical entity, but as a metrological interface that operates only by coupling two heterogeneous kinds of physical processes. It distinguishes (a) irreversible thermodynamic processes (entropy increase, aging, deterioration, diffusion) and (b) dynamical processes that, under idealization, are reversible and periodic (rotation, oscillation), and analyzes the structural problem inherent in using the latter to operationalize the former. The central thesis is that what humans call “time” is an instrumental abstraction constituted by projecting irreversibility onto reversibility. Because irreversible decay processes are difficult to handle as direct measures, we adopt periodic motion as a proxy variable and normalize irreversible change by mapping it onto cycles. What this proxy relation lacks, however, is a canonical calibration map from the cycle count to a universal vector quantity expressing degrees of aging, dissipation, and loss in general. Under local conditions, it is possible to construct stable correspondences between cycle-type indicators and irreversible processes on the basis of theoretical models; but such validity is confined to those conditions and cannot be generalized universally across domains. We call this absence of meta-level justification (the non-uniqueness and non-portability of calibration) “structural uncalibratability.” In metrological terms, it is a failure of traceability: there is no single implementation- and condition-invariant calibration that would make cycle counts portable as a standard for heterogeneous irreversible vectors. The metrological claim advanced here does not deny that statistical or causal-historical couplings can hold in particular domains. Rather, it shows that this mismatch simultaneously illuminates (i) a metrological paradox at the core of time measurement, (ii) a distinctive incompatibility in lived experience, and (iii) why clock-based artificial intelligence lacks the human sense of temporality.