Commitment Time, Metric Time, and Physical Temporal Interfaces

This is the 4th paper in the series, which is preceded by the three part Semantic Observers: A Functional Criterion for Observer-Systems in the Quantum Measurement Problem. Zenodo. https://doi.org/10.5281/zenodo.21711777 Commitment Time, Metric Time, and Physical Temporal Interfaces Proper Time, Clocks, Synchronization, Addressability, and Durable Commitment This work develops a unified physical architecture for the many different quantities that physics calls “time.” Modern theories routinely move between coordinate time, proper time, clock readings, detector timestamps, synchronization conventions, thermodynamic arrows, quantum relational clocks, record formation, inference, and historical reconstruction. These quantities are often written with the same symbol t even though they arise from different physical systems and perform different roles. The central claim of this paper is that temporal quantities are strongly typed. A proper-time interval is generated by a metric and a worldline. A clock reading is generated by a material clock, a readout instrument, and a calibration. A detector timestamp is generated by switching, response, record formation, and estimation. A shared operational time is generated by signal exchange and a maintained clock ledger. Semantic time is generated by physically realized interactions that create addressable distinctions. Thermodynamic time is generated by routed physical exchange. Modular time is generated by an algebra–state pair. Lifecycle time is generated by a branch-history coordinate. These temporal objects can be compared, synchronized, or mapped into one another only through explicit physical bridges. Numerical agreement does not make them the same object. The paper collects the principal temporal coordinates into the owner-complete family 𝔗ₑₓₜ(Ξ)= (t, τγ, qC, τ̂C, Tₒₚ, Iᴰ, t̂ₑ, τˢᵉᵐₚᵣₒₚ, Tᵣₑc, Tₐddr, Tcmp, Tinf, Tlock, τedge, smod, u). Here: t is a coordinate parameter; τγ is metric proper time along a worldline γ; qC is the raw output of a physical clock C; τ̂C is a calibrated estimate derived from that output; Tₒₚ is synchronized operational time constructed through signal exchange and a maintained timing ledger; Iᴰ is the detector’s physical operating support; t̂ₑ is an estimated timestamp assigned to an event e; τˢᵉᵐₚᵣₒₚ counts physically realized semantic interaction steps; Tᵣₑc is the first time an extant carrier becomes readable as a record; Tₐddr is the first time the record becomes physically addressable; Tcmp is the first realized comparison time; Tinf is an inference stopping time; Tlock is the time at which a commitment enters a durable shared ledger; τedge is a coordinate generated by routed thermodynamic export; smod is a modular-flow parameter; u is a lifecycle gauge. The complete package Ξ includes the event, worldline or interaction process, clock subsystem, detector, ledger, route data, calibration data, and any thermodynamic, modular, horizon, or lifecycle structure used by the selected branch. A temporal bridge is represented as a partial typed map: ℬA→B : Dom(ℬA→B) ⊆ 𝕋A × ℝA→B → 𝕋B. Every bridge must identify its source type, target type, carrier, causal support, units, domain, calibration, hypotheses, thresholds, uncertainty, exchange law, and failure surface. When the bridge fails, the source temporal quantity remains meaningful; the target comparison simply remains undefined. This framework replaces the assumption of one universal temporal variable with a network of physically realized temporal interfaces. Relativistic addressability Relativistic causal support is necessary for an event to become available at a later anchor: x ∉ J⁺(e) ⇒ qᵛᵃˡₑ,ₓ = 0. An event outside the causal future J⁺(e) cannot be physically delivered to x. Causal accessibility alone is not sufficient. A record becomes addressable only when a surviving carrier reaches the anchor, enters the detector’s operating support, passes the decoder and validation gates, and is written into an actionable register. The paper therefore distinguishes: causal reach,physical delivery,readability,addressability,comparison,inference,and durable commitment. These stages may occur at different times, and some may never occur. Proper time and physical clocks Proper time is generated by metric geometry along a worldline. A material clock is a dynamical system that evolves along that worldline. Its displayed value is a physical measurement outcome, not proper time itself. A clock reading becomes an estimate of proper time only through a calibration map. Periodic clocks also require cycle provenance: the phase shown on a dial does not by itself identify how many complete cycles have elapsed. The paper proves that proper time and clock readout remain type-distinct even when the clock is highly accurate. Their numerical agreement is produced by a calibrated physical bridge. This distinction becomes decisive in accelerated motion, gravitational redshift, horizon-limited observation, finite detector windows, and quantum clocks. Synchronization and clock ledgers Synchronization is not a property that two distant clocks possess automatically. It is produced through signal exchange, a propagation model, calibration, and a maintained ledger of timing relations. Two-way timing protocols contain route-dependent biases whenever the outward and return propagation conditions differ. A synchronization convention can remove some ambiguity only after the propagation model and admissible equivalence class have been declared. Operational time is therefore a constructed relational product. It belongs to the clock network and its synchronization procedure, not to either clock in isolation. The paper separates static order agreement from dynamical entrainment. Two clocks can preserve the same event ordering without matching rates, phases, or physical mechanisms. Semantic time and interaction anchors Semantic time records the order in which physical distinctions become available for downstream action. Its basic increment occurs at a realized interaction anchor: emission, scattering, absorption, detection, amplification, decoding, comparison, or record formation. Free propagation between anchors carries causal support but does not create an intermediate semantic tick. For a free null carrier, ds² = 0, and the carrier accumulates no proper time. The same free segment also produces no intermediate semantic-interaction increment: Δτˢᵉᵐₚᵣₒₚ = 0. The timelike source and receiver can accumulate proper time, operate clocks, and create records. The freely propagating null carrier connects those interactions without generating a chain of local commitment events between them. This gives a precise temporal account of photons, communication channels, interferometers, and delayed-choice experiments. Finite measurement duration Measurement is not instantaneous. Every physical detector has an operating window, switching dynamics, response latency, finite bandwidth, resolution limits, and a nonzero probability of failure. A timestamp is generated only after the detector response has been transformed into a record and processed by an estimator. The achievable precision depends on the measurement duration, signal energy, distinguishability, detector dynamics, and calibration. The paper keeps three limits separate: the quantum speed limit governing how quickly states can become distinguishable; the detector’s finite response and operating support; the statistical precision of the timestamp estimator. Records, inference, and durable commitment A registration can exist before it becomes readable. A readable record can exist before it becomes semantically addressable. An addressable record can exist before comparison. An inference can be reached before the result is locked into a durable shared ledger. The corresponding stopping times satisfy no universal equality: Tᵣₑc ≠ Tₐddr ≠ Tcmp ≠ Tinf ≠ Tlock. Their order depends on the realized physical architecture. A durable commitment requires more than a transient signal. It requires a surviving carrier, decoding, validation, admission, maintenance, and sufficient resistance to noise and decay. The paper distinguishes live semantic activity from durable recorded stock. A system may be processing and transmitting information without having written a stable commitment. Conversely, a durable record may survive after the process that created it has ended. Quantum clocks and relational dynamics In relational quantum-clock models, one subsystem acts as a clock relative to which another subsystem is conditioned. A conditional quantum state can represent correlations between the clock and the system. It does not automatically produce a physical timestamp. A timestamp additionally requires a clock readout, detector, calibration, record, and address route. Relational conditioning and operational clock measurement are therefore connected but type-distinct. This resolves a recurring ambiguity in quantum-clock discussions: a parameter appearing in a conditional state is not automatically the reading of a realized physical clock. Horizons and limited temporal access Black-hole and accelerated-observer settings reveal the difference between a temporal quantity and access to that quantity. A remote event may possess a well-defined local proper time while remaining inaccessible to an exterior detector. A horizon can limit carrier delivery, redshift signals, stretch detector response, or prevent a record from ever becoming addressable at a selected exterior anchor. The paper keeps distinct: local proper time,exterior clock time,horizon temperature,surface gravity,entropy,detector response,and record-access time. These quantities can be related through physical bridges without being identified. Delayed choice and comparison time The delayed-choice analysis separates two branches. In a post-registration comparison branch, a