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Onto-Physical Entanglement and Quantum Proper-Time Readout: CPT-Coherence Theory, Optical Ion Clocks, and the Experimental Interface Between Identity and Evolution

Joseph Julian

Published Jul 1, 2026• 0 citations
Publisher

Abstract

Optical ion clocks now approach a regime in which relativistic time dilation is no longer exhausted by a classical proper-time parameter read by a quantum sensor. Recent work by Sorci, Foo, Leibfried, Sanner, and Pikovski shows that harmonically trapped optical clock atoms can exhibit vacuum-induced, squeezing-induced, and intrinsically quantum corrections to the second-order Doppler shift, with time-dilation-induced entanglement between motional and internal clock degrees of freedom becoming observable in strongly squeezed trapped-ion motion. This paper develops the significance of that result within CPT-Coherence Theory. The central principle of CPT-Coherence is Onto-Physical Entanglement: what a system is cannot be separated from how it is allowed to remain coherent under admissible transformation. In the clock setting, this principle appears in branch-visible form. The internal clock transition is not merely an isolated label transported through spacetime; its phase identity is dynamically bound to the motional state through the relativistic proper-time operator. Proper-time interferometry therefore supplies a laboratory instance of a more general structural rule: physical identity is stabilized only through the admissible evolution channels by which it can be read out. The paper distinguishes the relativistic proper time of the ion-clock experiment from the coherence-depth coordinate of CPT-Coherence. The former is a branch-visible observable associated with worldline evolution; the latter is a structural coordinate organizing parent-boundary admissibility, trace access, Schur response, and stable observable descent. Their relation is not identity but projection: quantum proper-time readout provides an experimentally precise interface through which branch observers can test how internal identity, motion, coherence, and record formation remain coupled. We formulate a CPT-Coherence clock-readout sector in which a quantum clock is represented by a triple consisting of an internal identity generator, an external motion algebra, and a proper-time readout operator. The Sorci-Foo-Leibfried-Sanner-Pikovski protocol is then interpreted as a high-precision realization of an OPE readout channel: classical time dilation corresponds to scalar proper-time averaging; vacuum and squeezing shifts correspond to state-dependent branch corrections; and visibility loss corresponds to trace-visible entanglement between identity and admissible motion. This establishes optical ion clocks as a natural experimental grammar for CPT-Coherence, while CPT-Coherence supplies a unifying interpretation of why such experiments probe not simply clock rates, but the inseparability of physical being and physical evolution. Scope note: the quantitative predictions below coincide with those of standard relativistic quantum clock theory; CPT-Coherence contributes an interpretation and vocabulary, together with an explicit falsification target for that interpretation.

DOI
10.5281/zenodo.21152289

Related papers

Time as Record: Proper Time, Psychological Time, and Onto-Physical Entanglement: A CPT-Coherence Framework for Distinct Temporal Readout Regimes

Joseph Julian

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.

•Jul 1, 2026•0 citations

Quantum Signatures of Proper Time in Optical Ion Clocks

Gabriel Sorci, Joshua Foo, Dietrich G. Leibfried +2 more

Optical clocks based on atoms and ions probe relativistic effects with unprecedented sensitivity. They resolve time dilation due to atom motion or different positions in the gravitational potential through frequency shifts. However, all measurements of time dilation so far can be explained effectively as the result of dynamics with respect to a classical proper time parameter. Here we show that atomic clocks can probe effects where a classical description of the proper time dynamics is insufficient as superpositions of proper time emerge. We apply a Hamiltonian formalism to derive time dilation effects in harmonically trapped clock atoms and show how second-order Doppler shifts due to the vacuum energy, squeezing, and quantum corrections to the dynamics arise. We also demonstrate that time-dilation-induced entanglement between motion and clock evolution can become observable in state-of-the-art clocks when the motion of the atoms is strongly squeezed, realizing proper time interferometry. Our results show that experiments with trapped ion clocks are within reach of probing relativistic evolution of clocks for which a quantum description of proper time becomes necessary.

arXiv:2509.09573•Physical Review Letters•Feb 27, 2026•3 citations

Quantum Proper-Time Clocks as Temporal Interfaces: A Diagnostic Note on Clockability, Proper Time, and Temporal Exportability

Danilo Tavella

This technical note treats recent work on quantum signatures of proper time in optical ion clocks as an external stress reference for the Clockability cluster. The note does not propose a new theory of time, nor does it interpret quantum optical clocks as confirming Clockability. Instead, it distinguishes proper-time accumulation, physical clock readout, trace comparability, and temporal exportability as separate descriptive levels. Optical ion clocks are analyzed as temporal interfaces: finite physical architectures through which proper-time signatures become accessible under specific conditions of state preparation, motional structure, coherence, and readout. The aim is diagnostic only: to clarify how high-precision quantum-clock regimes make visible the distinction between local proper-time dynamics and the operational availability of temporal order.

•May 19, 2026•0 citations

Commitment Time, Metric Time, and Physical Temporal Interfaces

David Betzer

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

•Aug 1, 2026•0 citations

Necessity Recursion and a Pre-Registered φ-Attractor Prediction for Proper-Time Superposition in Optical Ion Clocks

Abby Davis

On 20 April 2026, Sorci, Foo, Leibfried, Sanner, and Pikovski (Phys. Rev. Lett.) proposed that next-generation optical ion clocks with squeezed-state preparation can probe whether proper time exists in quantum superposition — a single clock ticking faster and slower at once. Their work establishes the protocol; the laboratory measurement is forthcoming. That prospective window permits a genuine pre-registered prediction. Fibonacci Causal Loop Theory (FCLT) holds that any stable system governed by depth-2 necessity recursion, S(n)=S(n−1)+S(n−2), is driven to the golden ratio φ=(1+√5)/2 — the unique algebraically forced attractor of its characteristic equation x²−x−1=0. We advance the hypothesis that proper-time superposition is such a system, the two temporal branches playing the role of the two prior states, so that the ratio of fast- to slow-ticking amplitudes approaches φ upon decoherence. From this we obtain one parameter-free, falsifiable prediction — t₊/t₋ → φ ≈ 1.61803, with δ = |R−φ|/φ and falsification at δ > 0.10 — logged under Protocol V3.1 prior to experimental resolution. We claim no confirmation: the prediction is offered as not-yet-tested, to be adjudicated by the Stevens/NIST program. A second, independent signature (φ-structured fringe spacing in the squeezed regime) provides an internal consistency check.

•May 10, 2026•0 citations

Operational Recoverability Bounds for Proper-Time Interferometry with Open Quantum Clocks

K Z Zhao

Abstract Clock interferometry probes general-relativistic proper-time differences through the entanglement between a particle's center-of-mass path and its internal degrees of freedom. Existing analyses treat the internal clock as either a closed system or study how environmental noise modifies the interferometric visibility. Here we address a distinct question: what fraction of the proper-time-induced visibility loss remains recoverable when the experimentalist is restricted to local unitary control of the internal clock? We model the clock as a two-level system undergoing amplitude damping with branch-dependent proper times in a Mach-Zehnder interferometer and derive the visibility both without and with a spin-echo refocusing pulse. In the closed-system limit ($\gamma\to0$), the echo restores full visibility; for $\gamma>0$, the no-jump survival probability imposes a strict upper bound on echo-recovered visibility that no internal-only unitary can exceed. We establish the conditions under which a proper-time-parametrized Gorini-Kossakowski-Sudarshan-Lindblad equation is valid by appealing to the local comoving frame and the equivalence principle, distinguishing comoving-bath and laboratory-bath parametrizations. Numerical simulations with QuTiP confirm all analytic results. We provide experimental parameter estimates for cold-atom and cavity-QED platforms, showing that the irrecoverable visibility deficit is within reach of near-future clock-interferometry experiments. The echo-recovery deficit constitutes an operational witness that separates irreversible environmental decoherence from the formally reversible path-clock entanglement of the Pikovski mechanism.

International Journal of Theoretical Physics•Aug 28, 2026•0 citations
Optical ion clocks now approach a regime in which relativistic time dilation is no longer exhausted by a classical proper-time parameter read by a quantum sensor. Recent work by Sorci, Foo, Leibfried, Sanner, and Pikovski shows that harmonically trapped optical clock atoms can exhibit vacuum-induced, squeezing-induced, and intrinsically quantum corrections to the second-order Doppler shift, with time-dilation-induced entanglement between motional and internal clock degrees of freedom becoming observable in strongly squeezed trapped-ion motion. This paper develops the significance of that result within CPT-Coherence Theory. The central principle of CPT-Coherence is Onto-Physical Entanglement: what a system is cannot be separated from how it is allowed to remain coherent under admissible transformation. In the clock setting, this principle appears in branch-visible form. The internal clock transition is not merely an isolated label transported through spacetime; its phase identity is dynamically bound to the motional state through the relativistic proper-time operator. Proper-time interferometry therefore supplies a laboratory instance of a more general structural rule: physical identity is stabilized only through the admissible evolution channels by which it can be read out. The paper distinguishes the relativistic proper time of the ion-clock experiment from the coherence-depth coordinate of CPT-Coherence. The former is a branch-visible observable associated with worldline evolution; the latter is a structural coordinate organizing parent-boundary admissibility, trace access, Schur response, and stable observable descent. Their relation is not identity but projection: quantum proper-time readout provides an experimentally precise interface through which branch observers can test how internal identity, motion, coherence, and record formation remain coupled. We formulate a CPT-Coherence clock-readout sector in which a quantum clock is represented by a triple consisting of an internal identity generator, an external motion algebra, and a proper-time readout operator. The Sorci-Foo-Leibfried-Sanner-Pikovski protocol is then interpreted as a high-precision realization of an OPE readout channel: classical time dilation corresponds to scalar proper-time averaging; vacuum and squeezing shifts correspond to state-dependent branch corrections; and visibility loss corresponds to trace-visible entanglement between identity and admissible motion. This establishes optical ion clocks as a natural experimental grammar for CPT-Coherence, while CPT-Coherence supplies a unifying interpretation of why such experiments probe not simply clock rates, but the inseparability of physical being and physical evolution. Scope note: the quantitative predictions below coincide with those of standard relativistic quantum clock theory; CPT-Coherence contributes an interpretation and vocabulary, together with an explicit falsification target for that interpretation.
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.
Optical clocks based on atoms and ions probe relativistic effects with unprecedented sensitivity. They resolve time dilation due to atom motion or different positions in the gravitational potential through frequency shifts. However, all measurements of time dilation so far can be explained effectively as the result of dynamics with respect to a classical proper time parameter. Here we show that atomic clocks can probe effects where a classical description of the proper time dynamics is insufficient as superpositions of proper time emerge. We apply a Hamiltonian formalism to derive time dilation effects in harmonically trapped clock atoms and show how second-order Doppler shifts due to the vacuum energy, squeezing, and quantum corrections to the dynamics arise. We also demonstrate that time-dilation-induced entanglement between motion and clock evolution can become observable in state-of-the-art clocks when the motion of the atoms is strongly squeezed, realizing proper time interferometry. Our results show that experiments with trapped ion clocks are within reach of probing relativistic evolution of clocks for which a quantum description of proper time becomes necessary.
This technical note treats recent work on quantum signatures of proper time in optical ion clocks as an external stress reference for the Clockability cluster. The note does not propose a new theory of time, nor does it interpret quantum optical clocks as confirming Clockability. Instead, it distinguishes proper-time accumulation, physical clock readout, trace comparability, and temporal exportability as separate descriptive levels. Optical ion clocks are analyzed as temporal interfaces: finite physical architectures through which proper-time signatures become accessible under specific conditions of state preparation, motional structure, coherence, and readout. The aim is diagnostic only: to clarify how high-precision quantum-clock regimes make visible the distinction between local proper-time dynamics and the operational availability of temporal order.
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
On 20 April 2026, Sorci, Foo, Leibfried, Sanner, and Pikovski (Phys. Rev. Lett.) proposed that next-generation optical ion clocks with squeezed-state preparation can probe whether proper time exists in quantum superposition — a single clock ticking faster and slower at once. Their work establishes the protocol; the laboratory measurement is forthcoming. That prospective window permits a genuine pre-registered prediction. Fibonacci Causal Loop Theory (FCLT) holds that any stable system governed by depth-2 necessity recursion, S(n)=S(n−1)+S(n−2), is driven to the golden ratio φ=(1+√5)/2 — the unique algebraically forced attractor of its characteristic equation x²−x−1=0. We advance the hypothesis that proper-time superposition is such a system, the two temporal branches playing the role of the two prior states, so that the ratio of fast- to slow-ticking amplitudes approaches φ upon decoherence. From this we obtain one parameter-free, falsifiable prediction — t₊/t₋ → φ ≈ 1.61803, with δ = |R−φ|/φ and falsification at δ > 0.10 — logged under Protocol V3.1 prior to experimental resolution. We claim no confirmation: the prediction is offered as not-yet-tested, to be adjudicated by the Stevens/NIST program. A second, independent signature (φ-structured fringe spacing in the squeezed regime) provides an internal consistency check.
Abstract Clock interferometry probes general-relativistic proper-time differences through the entanglement between a particle's center-of-mass path and its internal degrees of freedom. Existing analyses treat the internal clock as either a closed system or study how environmental noise modifies the interferometric visibility. Here we address a distinct question: what fraction of the proper-time-induced visibility loss remains recoverable when the experimentalist is restricted to local unitary control of the internal clock? We model the clock as a two-level system undergoing amplitude damping with branch-dependent proper times in a Mach-Zehnder interferometer and derive the visibility both without and with a spin-echo refocusing pulse. In the closed-system limit (γ→0\gamma\to0γ→0), the echo restores full visibility; for γ>0\gamma>0γ>0, the no-jump survival probability imposes a strict upper bound on echo-recovered visibility that no internal-only unitary can exceed. We establish the conditions under which a proper-time-parametrized Gorini-Kossakowski-Sudarshan-Lindblad equation is valid by appealing to the local comoving frame and the equivalence principle, distinguishing comoving-bath and laboratory-bath parametrizations. Numerical simulations with QuTiP confirm all analytic results. We provide experimental parameter estimates for cold-atom and cavity-QED platforms, showing that the irrecoverable visibility deficit is within reach of near-future clock-interferometry experiments. The echo-recovery deficit constitutes an operational witness that separates irreversible environmental decoherence from the formally reversible path-clock entanglement of the Pikovski mechanism.