Relational Time and Records

This paper is the eighth in a sequence developing an interpretive framework that redescribes physicalreality as a causally consistent history of information updates rather than as a collection of objectsindependently existing within spacetime. Its question is set by the second paper (Uchida, 2026b),which refused privileged global structure in the physical core—no global clock, no preferred foliation,no cosmic coordinator—and established that a causal partial order can hold among events withoutany external clock. That left a successor question untouched, and it is a narrow one: how arecord that lies within the operational domain of a physical clock—or within a calibrated networkof clock-bearing records—can be assigned a relational temporal label, an instant or a duration,compatible with that order. A clock does not metrize the entire causal order; it addresses onlywhat is operationally related to it. The framework separates three questions about time. Theorder question—which event precedes which—was the second paper’s. The arrow question—whyrecords accumulate in one direction—is deferred to a later paper and is, in the framework’s view,a thermodynamic matter that requires low-entropy boundary conditions the present paper doesnot supply. This paper takes only the middle question, the clock question: how an already-formedrecord, lying in the operational domain of a clock or a calibrated clock network, can be assigned atemporal address compatible with the causal order.The central claim is conditional and structural, and it is deliberately weak in three places wherea stronger claim would overreach. First, records need not carry absolute timestamps. A physicaltrace may qualify as a record without any explicit clock reading, provided the relevant imprinting,retention, and stability conditions are met; it is not the case that every trace is thereby a record.When a temporal address is required, that address can be assigned relationally, through correlationswith physical clock degrees of freedom. The idealized, noninteracting Page–Woottersconstruction is the worked model: a physical state annihilated by a Hamiltonian constraint, henceinvariant under the one-parameter flow that the constraint generates (a flow treated as gauge in theDirac-constrained reading adopted here), nonetheless supports an effective Schrödinger dynamicsfor a system conditioned on a clock indication. The reading is not that time emerges from correlation;it is that effective subsystem dynamics can be relationally indexed by clock–system correlationsunder a suitable constraint structure. Beyond the idealized case, covariant clock POVMs describenonideal clocks without by themselves implying approximation, finite-resolution clocks bound theprecision of a temporal address, and interacting or measurement-extended clocks can modify theeffective dynamics.Second, conditioning on a clock state is a descriptive operation, not by itself a physicalrecord-forming process. A conditional system state is not yet a record; a temporal recordadditionally requires a record-bearing subsystem that retains a physical correlation between aclock indication and an event. In the clean direct case this is a memory holding the joint correlation𝑀 records (𝑡, 𝑒); more generally an already-formed event record acquires a temporal addressthrough a calibrated network of relations to clock-bearing records. This is the temporal counterpartof the sixth paper’s separation of decoherence, imprinting, and retention. Third, the agreementof different clock descriptions is conditional: where two temporal quantum-reference-framedescriptions are both admissible and a well-defined transformation exists between them, correspondingstates, observables, operations, and conditioning procedures can be mapped across the overlapof their domains so as to preserve the associated relational probabilities. This is a conditionalcovariance claim, not the assertion of a globally valid clock perspective, and it stands in structuralanalogy with—but is not identical to—the representational redundancy of the seventh paper. Theframework derives no result in quantum mechanics or quantum gravity, does not claim that theuniverse is literally timeless, does not claim that all clock choices are equivalent, and does not solvethe problem of time. Its disciplined thesis is that clocks do not create history; they indexcorrelations within it.