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From States to Seconds: An Operational Information Chain for Physical Timekeeping

Antoine Druilhe

Published Jul 27, 2026• 0 citations
Publisher

Abstract

Physical clocks do not ordinarily produce duration as a context-free observable of their internal dynamics. They generate states, transitions, phases, or trajectories from which a measurement arrangement constructs a calibrated reading. We propose an operational decomposition of physical timekeeping into five components: clockwork, readout, record space, estimator, and calibration specification. This separates information encoded in a time-sensitive physical process from information made accessible by a selected readout and from the numerical duration inferred from the resulting record. Standard data-processing and Fisher-information relations organize this chain. A phase-encoding qubit provides an exact illustration: a measurement in the σₓ basis retains the full local Fisher information, Jₓ = ω², whereas a σ₂ measurement is temporally blind, J₂ = 0. Even the informative readout identifies only the phase ωτ unless the frequency scale is independently calibrated. Thermodynamic costs likewise cannot be assigned to ‘the clock’ without declaring the boundary separating clockwork, readout, memory, and reset. The framework introduces no new ontology of time, clock dynamics, or metrological bound; it clarifies how time-sensitive physical states become accessible records and, through inference and calibration, measured durations.

DOI
10.5281/zenodo.21612207

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Physical clocks do not ordinarily produce duration as a context-free observable of their internal dynamics. They generate states, transitions, phases, or trajectories from which a measurement arrangement constructs a calibrated reading. We propose an operational decomposition of physical timekeeping into five components: clockwork, readout, record space, estimator, and calibration specification. This separates information encoded in a time-sensitive physical process from information made accessible by a selected readout and from the numerical duration inferred from the resulting record. Standard data-processing and Fisher-information relations organize this chain. A phase-encoding qubit provides an exact illustration: a measurement in the σₓ basis retains the full local Fisher information, Jₓ = ω², whereas a σ₂ measurement is temporally blind, J₂ = 0. Even the informative readout identifies only the phase ωτ unless the frequency scale is independently calibrated. Thermodynamic costs likewise cannot be assigned to ‘the clock’ without declaring the boundary separating clockwork, readout, memory, and reset. The framework introduces no new ontology of time, clock dynamics, or metrological bound; it clarifies how time-sensitive physical states become accessible records and, through inference and calibration, measured durations.
SCQG Paper 4 of 28 This paper explains how different physical ways of measuring and ordering time relate to one another. Proper time is defined by the spacetime metric along a path. A material clock produces a reading through its own dynamics and calibration. A detector writes a timestamp, and exchanged signals allow separate clocks to be synchronized. A temporal bridge is a map connecting such coordinates under stated physical conditions. Semantic time counts or orders the interactions through which a physical distinction becomes usable, compared, or maintained. Forward actionability is the resolution of uncertainty into a distinction that a later operation can use. Local grounding depends on forward action making that resolution available to a local interaction; measurement realizes the grounding by writing a registration. Access to a readable record, inference meeting a specified accuracy test, and completed durable maintenance have separate first-success times. The paper derives causal access conditions, timing bounds for finite detector windows, synchronization errors, and relations between physical clock time and interaction counts. It defines agreement between event orders and entrainment: agreement maintained through physical coupling over a stated interval. It also distinguishes the accumulated interaction count from the records that remain readable. Applications include quantum clocks, accelerated observers, black-hole observations, cosmological modes, delayed-choice experiments, and reciprocal cosmological coordinates. Each connection states the physical systems, operations, units, calibration, and conditions under which it holds. 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
This preprint introduces Relational Temporal Self-Measurement (RTSM), a conceptual framework for analysing how a closed or effectively closed physical system may internally construct, quantify, and preserve temporal order without requiring an external physical clock. The framework distinguishes between a minimal relational architecture, in which an internal clock subsystem (C) is correlated with an observed subsystem (S), and a stricter form of temporal self-measurement in which a physical memory subsystem (M) preserves distinguishable records of clock–system correlations. This leads to the operational architecture (C \otimes S \otimes M). RTSM is developed in relation to the Page–Wootters mechanism, quantum temporal reference frames, periodic internal clocks, thermal time, entropic internal time, autonomous quantum clocks, and the thermodynamic and informational costs of timekeeping. Particular attention is given to periodic-clock ambiguity, memory persistence, operational factorisation, measurement backreaction, finite recording regimes, and the trade-off between temporal information and physical disturbance. The framework does not claim that time is conscious, universally entropic, or proven to be fundamentally emergent. Its more limited objective is to identify the physical and operational conditions under which a system can contain both the processes that transform and the internal references and records through which those transformations become temporally measurable. The manuscript also proposes a set of falsifiable, model-dependent hypotheses and experimental directions concerning internal-clock switching, memory-assisted chronology, entropic clocks, information–disturbance trade-offs, and networks of local clocks. Version: 1.1Status: PreprintDOI: 10.5281/zenodo.22083883
We develop a Fisher-informational reformulation of physical time in which clock time is not regarded as a fundamental ontological substance, but as an emergent calibration of causally ordered distinguishability among physical states. The operational starting point is that clocks do not measure time itself; rather, they instantiate reproducible physical processes whose distinguishable states are correlated with other events. We introduce a causal-informational parameter, denoted by Lambda_F, defined as an accumulated Fisher-geometric distance along a causally admissible trajectory in state space. In classical statistical systems, this parameter is generated by the Fisher information metric; in quantum systems, the corresponding construction is associated with quantum Fisher information, the Bures metric, and the Fubini-Study geometry of projective Hilbert space. The manuscript distinguishes model-dependent Fisher information from quantum Fisher information, clarifies the reparameterization of Schrodinger dynamics, and gives explicit examples involving a qubit clock, an exponential decay process, and a Fisher characterization of clock quality. The proposal is positioned relative to relational time, the Page-Wootters mechanism, thermal time, quantum speed-limit relations, information geometry, and the problem of time in quantum gravity. We do not claim that relational or emergent time is new. The specific contribution is the use of Fisher distinguishability as an operational precursor from which ordinary clock time can be reconstructed. In this sense, the central statement of the paper is: time is not measured by clocks; clock time is reconstructed from the Fisher distinguishability accumulated along causally ordered physical changes.
Time is not a single operational object. Laboratory time, relativistic proper time, biological timing, psychological duration, and coherence-depth structure play different roles and are accessed by different readout systems. This paper develops a theoretical framework for distinguishing these temporal regimes while identifying a common structural feature: each becomes physically or experientially meaningful only through a system capable of generating stable records of change. The starting point is quantum proper-time readout in optical ion clocks. In relativistic quantum clock experiments, proper time is not merely an external scalar parameter; it is inferred from an internal phase record whose visibility can be degraded when clock identity becomes entangled with motional history. Such systems provide a controlled physical example of time-as-record: the clock records elapsed proper time only insofar as its internal identity remains coherent under admissible evolution. We use this clock setting to introduce a broader distinction among four temporal objects: tlab, tprop, tpsych, TC. Here tlab is laboratory coordinate time, tprop is relativistic proper time recorded by physical clocks, tpsych is psychological time generated by cognitive and embodied record processes, and TC is the CPT-Coherence structural coordinate organizing admissibility, trace access, and stable observable descent. These quantities are not identical. The central thesis is not that psychological time is quantum proper time, nor that optical clocks measure consciousness or coherence depth. The thesis is narrower: proper time and psychological time are categorically distinct but structurally comparable as readout regimes. Within CPT-Coherence Theory, this comparison is organized by Onto-Physical Entanglement: what a system is cannot be separated from how it remains coherent under admissible transformation. In the clock case, identity persistence is measured by phase coherence and Ramsey visibility. In the cognitive case, psychological duration is modeled as a higher-level record produced by attention, interoception, memory, arousal, prediction, and event segmentation. The proposed object is not a single inner clock, but a cognitive readout functional: Reccog : embodied cognitive state history → (duration, ordering, temporal confidence, felt passage). This permits a disciplined analogy: proper time is physical clock-readout; psychological time is cognitive record-readout; coherence depth is the structural admissibility coordinate of the theory. The paper formulates a temporal-readout taxonomy, introduces record-stability witnesses for both physical and psychological timing, and specifies failure conditions that prevent the framework from collapsing into metaphor. The result is a falsifiable perspective: if psychological duration is a record-stability phenomenon, then distortions of subjective time should correlate not only with estimated duration, but also with measurable changes in attention, bodily-state integration, memory ordering, confidence, and event-boundary structure. Thus, the physics of proper-time readout does not explain psychological time directly; it supplies a rigorous model of how time becomes a record for an embedded system.
We establish two foundational results concerning time and irreversibility within an operational framework where physical measurements correspond to distinguishable, persistent record states. First, we prove that no physical clock can ground time as a fundamental parameter: any clock-induced ordering necessarily reduces to a preorder defined by reachability among record states via admissible transformations. Second, we prove that bounded recording capacity forces accessible irreversibility: any system capable of recording more distinct events than its accessible register capacity must exhibit non-invertible operations at the accessible level. These results are derived without assuming time, entropy, or thermodynamic principles as primitives. Together, they establish that temporal structure and irreversibility are not independent physical laws but emerge from operational constraints on physical memory and distinguishability. The framework is compatible with globally unitary microscopic dynamics while explaining effective irreversibility for bounded observers. We conclude that time is a representational index for record structure rather than an ontological primitive , establishing the necessary foundation for the failure of deterministic prediction addressed in companion work [3]
Time is not a fundamental coordinate but a relation: all physical dynamics are defined on a timeless, global state space, and what we call “time” is the ordered relation between a chosen reference clock and the rest of the system. Formulate the above relational time postulate in an operationally minimal framework aligned with Wheeler–DeWitt constraint dynamics and the Page–Wootters construction, derive a concrete, testable prediction, when the same physical process is parametrized by two physically different “clocks” (e.g. an optical atomic clock and a mechanical phase clock), a small but measurable phase discrepancy can appear after all known effects are calibrated, if time is purely relational, propose a dual-clock interferometric experiment, and present an analytic sensitivity study. Our framework reproduces GR+QM in the ideal clock limit, yet allows for an operational deviation encoded by two dimensionless parameters. A null result yields new upper bounds across disparate frequency bands. A positive, replicated signal would provide the first operational evidence for “time without time”. This document is licensed under CC BY-NC-ND 4.0. The specific measurement protocol described herein, the unique ϵ and χ parametrization, and the associated data analysis algorithms constitute intellectual property. Any experimental realization or software implementation of the mathematical model is subject to the prior written consent of the author.