Relational Time and Records: Quantum Clocks, Conditional Dynamics, and Temporal Addressability Without a Global Clock

This paper develops a narrow interpretive account of how already-formed physical records acquire temporal addresses in a history lacking a privileged global clock. It distinguishes causal order, clock-relative temporal location, and the thermodynamic arrow. Causal order determines which causally related event precedes which but supplies neither a time scale nor a duration; the paper addresses only the clock question. A record need not contain an absolute timestamp. When its temporal location is required, that address can be assigned relationally through correlations with physical clock degrees of freedom within the clock’s operational domain or through a calibrated network of clock-bearing records. The idealized, noninteracting Page–Wootters construction serves as the worked model: a state satisfying a Hamiltonian constraint is invariant under the constraint-generated flow while supporting effective Schrödinger dynamics for a subsystem conditioned on an appropriate clock state. This is not a claim that arbitrary correlations generate time. The paper sharply separates a conditional state from a physical record. Conditioning on a clock state is descriptive; a temporal record requires a record-bearing subsystem that retains a physical correlation between a clock indication and an event. It also treats changes of temporal quantum reference frame. Where two descriptions are admissible and a well-defined transformation exists, corresponding states, observables, operations, and conditioning procedures can be mapped across their common domain so as to preserve relational probabilities. This is a domain-restricted conditional covariance claim, not the equivalence of all clock choices. Finite-resolution clocks limit the precision of temporal addresses, and interacting or measurement-extended clocks may modify the effective dynamics. The framework derives no new result in quantum mechanics or quantum gravity, does not claim that the universe is literally timeless, and does not solve the problem of time. Its central thesis is that clocks do not create history; they index correlations within it.