
Description Structural Time τ Outperforms Clock-Time Derivatives for Early Degradation Detection: Evidence from 510 Systems Across Four Degradation Domains This work presents one of the most direct empirical tests ever conducted on the concept of internal time as a measurable scientific quantity. For centuries, science has implicitly assumed that system evolution is best measured by external clock time. Engineering, reliability analysis, biological monitoring, and predictive modeling are all built upon this assumption. This paper challenges that foundation through a fully reproducible investigation involving 510 systems across multiple degradation domains, including NASA CMAPSS turbofan benchmarks and electrochemical battery degradation models. The central proposition is simple: Systems do not age according to the observer’s clock.Systems age according to their accumulated structural history. To test this proposition, the paper introduces Internal Structural Time (τ), a measurable quantity derived from burden accumulation, repair capacity, structural continuity, and trajectory curvature. Unlike conventional clock-time derivatives, τ measures how much structural aging a system has actually experienced. The results are substantial. Across all major datasets, τ consistently provides earlier degradation detection than conventional clock-time methods. Most importantly, its advantage increases with operational complexity. On NASA CMAPSS FD002—the most challenging benchmark in the CMAPSS family—τ achieves a 230.7% improvement over clock-time derivatives with highly significant statistical support. This is more than a performance improvement. It provides evidence that the temporal coordinate used to describe system evolution may itself be incomplete. As operating conditions become more complex, external clock time becomes increasingly detached from the true aging process, while internal structural time remains coupled to the underlying structural reality. The implications extend far beyond predictive maintenance. Any system that changes possesses a history of structural transformation. Any system with structural transformation possesses a candidate internal time. Consequently, the framework developed here is potentially relevant to engineering systems, biological organisms, ecological networks, economic systems, financial markets, social institutions, technological infrastructures, artificial intelligence, and complex adaptive systems in general. The significance of this work therefore extends beyond introducing a new indicator. It proposes a fundamental shift in perspective: From asking:“How much clock time has passed?” To asking:“How much structural time has elapsed within the system itself?” The paper is grounded in the Internal Time framework of Union Dipole Theory (UDT) and provides large-scale, reproducible, multi-domain evidence that an operationalized internal-time variable can outperform conventional clock-based measures on real prognostic tasks. All equations, datasets, statistical tests, sensitivity analyses, adversarial tests, and source code are openly provided. Every reported result is independently reproducible. If these findings continue to hold under broad independent validation, the implications are profound. The true temporal coordinate governing the evolution of many real-world systems may not be external clock time, but internally generated structural time. Such a result would extend beyond prognostics and health management and support a genuine paradigm shift in how change itself is measured throughout science. Rather than treating time as an external background against which systems evolve, time becomes a property of the system’s own structural history. Aging, degradation, adaptation, growth, resilience, evolution, and collapse can then be viewed as different manifestations of a common process governed by internal structural dynamics. This work is therefore presented as an open scientific challenge: a fully transparent, fully falsifiable, and fully reproducible hypothesis whose validity can be tested by any researcher. If confirmed across domains, Internal Structural Time may prove to be not merely a useful analytical tool, but a fundamental scientific quantity for understanding change across nature.
