Operational Limits of Global Time: Clockability, Comparability, and the Role of Closed Loops in Distributed Systems

The concept of a global time is routinely employed across physics, from relativistic systems to quantum networks and distributed measurements. However, the operational conditions under which a global temporal ordering is physically meaningful are often left implicit. In this technical note, an operational criterion for the existence of a global time is provided, based on the comparability of internal temporal registers. While local time may be well defined in multiple subsystems, a global operational time exists if and only if their registers can be related through closed physical loops that allow verification of transitivity and stability. Classes of physically relevant systems are identified—such as…