No Universal Plant Clock: Temporal Failure Geometry in Distributed Control Systems

Version 1.1: adds §6.4 formalization paragraph; corrects references [1] and [3] Modern distributed systems routinely behave as though they possess a shared present, interchangeable clocks, fresh state observations, and timely control channels. In practice, none of these assumptions is guaranteed. This paper introduces a four-layer model of temporal failure in distributed control systems: (1) gauge mismatch in the construction of shared temporal reference frames, (2) clock divergence in the accumulation of local elapsed time, (3) retarded-state estimation under delayed observation, and (4) delayed actuation in closed-loop control. The framework treats temporal coherence not as a metaphysical property but as an operational constraint and, in many systems, a scarce control resource. Relativistic systems make these constraints explicit, but the same failure geometry appears at ordinary engineering scales in asynchronous networks, multi-agent control, remote operation, and institutional decision systems. We argue that many coordination failures are best understood as temporal failures wearing other labels. We introduce characteristic timescale ratios -- observation lag to plant dynamics, actuation lag to plant dynamics, synchronization uncertainty to plant dynamics, and contract duration to clock divergence horizon -- and show that the dominant failure mode in a given system is determined by which ratio exceeds its critical threshold first. The result is a diagnostic vocabulary for identifying which temporal layer dominates, what assumptions are being smuggled in by design, and how coherence budgets can be measured, allocated, and governed.