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Microscopic State Sums and Above-Cutoff Substrate Dynamics

David Betzer

Published Oct 23, 2026• 0 citations
Publisher

Abstract

SCQG paper 19 of 28. Paper 19 develops the microscopic quantum dynamics of the Semantic Commitment / Quantum Gravity framework. It starts with finite physical carriers at the Planck regulator scale. A cell carries registrations, records or comparison data only where the corresponding systems and operations are present. A distinction becomes locally available through the forward physical action that makes it usable. Allowed local changes and their reverse partners define a self-adjoint Hamiltonian. This generator determines quantum evolution, exact sums of transition amplitudes and causal response. The microscopic clock λ is compared with metric time through an explicitly defined positive clock map. Semantic time orders the interactions through which distinctions become usable, compared or maintained. A six-state loop provides an explicit calculation of screen occupation, payload delivery and reciprocal response. Interacting finite chains show how those results change when cells exchange quantum states. The charged construction retains all 8,160 fermionic modes of its stated regulator, together with the links and boundary systems needed to enforce local Gauss constraints. Complete packet exchanges retain the transferred states, correlations and compensating flux. The paper derives exact reduced dynamics with memory and states the additional conditions for quantum channels, memoryless evolution and classical jumps. It constructs positive Euclidean reflection forms from which Hamiltonian dynamics can be recovered, and proves that local observables have well-defined limits as the support grows under the stated locality bounds. Explicit error bounds quantify the comparison between different resolutions. The final sections specify the further action, symmetry, positivity and convergence conditions needed for a relativistic continuum realization and its use by the companion papers.

DOI
10.5281/zenodo.23598432

Related papers

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

Detector-Facing Empirical Protocols for Semantic Commitment Quantum Gravity

David Betzer

SCQG Paper 12 of 28 This paper sets out experiments for testing Semantic Commitment Quantum Gravity. It connects the theory’s physical equations to detector records, matched control interventions and decision rules fixed before data collection. The main laboratory proposal uses light coupled to a mechanical oscillator. It compares three conditions. Arm D adds measured noise independently of the record. Arm C measures the system and uses the result for feedback control. Arm S keeps that physical control matched and changes a stored instruction that selects a later action. The contrast C − D tests active record stabilization. The contrast S − C tests whether instruction content changes later choices on new task cases excluded from training and tuning. The paper gives equations for the cavity and oscillator, continuous measurement, feedback, noise, covariance reconstruction, work and heat. The calculations include the physical bath response, detector bandwidth, control latency and approximation error. Calibration and statistical procedures connect predicted changes in physical variability to quantities estimated from repeated runs. A source–receiver protocol distinguishes when a record becomes physically available from when the receiver can reliably identify its source. A separate clock protocol tests whether retained physical records can distinguish different cycles of a repeating clock. Gravity protocols combine causal order, discrete curvature, screen response, energy flux and tensor reconstruction to test the Einstein equation at specified scales. Each protocol specifies the controls, calibration, uncertainty, held-out evaluation, stopping rules and retained data needed to reproduce the analysis. These conditions determine when a result supports the tested prediction, reveals a physical discrepancy or remains inconclusive. This is Paper 12 of the Semantic Commitment / Quantum Gravity series.

•Oct 21, 2026•0 citations

Relational Quantum Causal Processes: Exact Models, Continuum Limits, and the Boundary of Emergent Gravity

Yipeng Xu

Relational quantum causal processes formulate finite operational contexts as normal positive functionals on local completely positive maps. Response differences generate an influence algebra, and its central projections define jointly readable Boolean events. We develop this starting point through a sequence of exact and controlled models. Fresh-environment unitary collision circuits produce dephasing-exchange kinetics with an exact charge-center fixed algebra, a uniform finite-step limit at fixed response order, and graph-controlled metastable Markov dynamics. An absorbing-state model exhibits a sharp transition between non-Abelian quantum memory and Boolean records. A reversal-covariant defect dynamics generates a locally finite partial order on a restricted graph family without assuming a Lyapunov time. Conditional on a certified order, a positive additive record measure, compactness, and identifiability, we prove subsequential convergence to a Lorentzian metric-measure space, finite reconstruction bounds, and uniqueness of admissible smooth limits. Complementary finite regulators provide controlled tests of modular-to-boost response, null tomography, same-update variational identities, induced quadratic gravity, and compatible common-refinement limits. These results are exact or controlled within their stated models, but they do not yet constitute a single background-independent microscopic law that jointly generates adjacency, time, volume normalization, dimension, signature, nonlinear Einstein constraints, and quantum matter. We therefore present RQCP-QG as a theorem-indexed framework that separates established mechanisms, conditional compositions, and open assumptions.

quant-pharXiv:2607.26672•Jul 30, 2026•0 citations

Quantum Commitment Thermodynamics and Physical Selection

David Betzer

SCQG paper 15 of 28 This paper follows the energy and entropy changes involved in creating, retaining, reading, using and resetting quantum records. It treats the pointers, memories, controllers, work stores and reservoirs as physical systems and counts each energy transfer once. Forward actionability means resolving uncertainty into a distinction that a later operation can use. Local grounding depends on that action making the resolved distinction available. The paper derives exact balances for finite quantum interactions, reset with and without retained side information, and autonomous control. It connects record lifetime and decoding accuracy to the information available for later use, and identifies the instrument-dependent information that enters feedback-work bounds. It also develops capacity-proportional selection, in which an outcome’s probability is proportional to the physical capacity available for that outcome. For nonconstant outcome probabilities, respecting ordinary mixtures of preparations forces this selection law to have positive-operator-valued measure (POVM) form. Agreement with the Born rule then requires the normalized capacity operators to equal the measurement’s outcome effects. The paper gives first-arrival, stationary and quantum-jump realizations and states their no-signalling conditions. The Stoney action equals αℏ, giving the uncertainty bound ΔX ΔP ≥ 1/(2α). Further results relate screen fluctuations, measurement precision, trajectory probabilities and entropy export. The complete physical construction keeps its reservoirs and work sources within their own reciprocal branch and supplies the defined stress interface used by the gravitational papers.

•Oct 22, 2026•0 citations

Emergent Schrödinger dynamics from the relational phase-fiber clock a consistency note for Spectral Quantum Gravity

Karol Frank

This note records a consistency result for the Spectral Quantum Gravity (SQG) framework: that the relational, timeless construction underlying SQG’s emergent time reproduces ordinary Schrödinger quantum dynamics, with departures bound to the framework’s own condensate scale rather than free. In SQG the phase fiber of the substrate carries a conserved U(1) charge Q (bounded below; the conjugate angle compact), and the Osterwalder–Schrader reconstruction supplies a self-adjoint matter Hamiltonian. Conditioning the timeless ground state on the phase-fiber clock, in the Page–Wootters sense, is shown analytically to yield the Schrödinger equation i ∂_θ ψ = (H − E) ψ exactly. This is confirmed numerically to machine precision in a finite model carrying SQG’s two defining features — a generator bounded below and a compact, integer-spectrum clock. The compact, bounded-below clock leaves the equation itself intact and imprints only clock-level fingerprints: a spectral window (modes above the constraint energy cannot be clocked), a finite time resolution of order 1/⟨Q⟩ (the phase states form a covariant POVM; Pauli’s theorem forbids a sharp conjugate time), and a KMS/thermal correction of order T ∝ 1/v from the compact Euclidean direction. All three are governed by the same condensate scale and vanish in the macroscopic-condensate limit, where textbook Schrödinger evolution is recovered. Scope and grade. This is a supplementary, lowest-grade consistency/closure note, conditional on the open decompactification of the phase fiber discussed in the main SQG work. It is explicitly not a derivation of quantum mechanics: the reflection-positive quantum substrate and the self-adjoint generator are inputs, as throughout SQG. The formalism is standard and borrowed — Page–Wootters relational dynamics, covariant (POVM) clocks for generators bounded below, and the KMS structure of a compact Euclidean direction — here applied to SQG’s specific clock. What is computed is the mechanism in a finite model, not the full field-theoretic dynamics of the substrate. The single SQG-specific statement is that any departure from ordinary quantum mechanics is tied to SQG’s own, unobservably small scale. A Python script reproducing all numerical values is included.

•Jun 22, 2026•0 citations

Finite Local Information Capacity in Continuum Dynamics

Florian Neukart, E. J. Marx

Abstract Finite-dimensional local Hilbert spaces are widely used as microscopic regulators and have also been proposed as a fundamental information-capacity property of space-time. A finite local dimension, however, is not equivalent to a spatial lattice spacing, and neither is equivalent to a coarse-graining scale. We formulate a regulator-resolved framework that keeps these three notions separate and defines finite-information deviations operationally as the failure of microscopic and effective time evolution to commute with a specified coarse-graining channel. The resulting deviation is a state- and observable-dependent quantity in a common effective state space, rather than a formal subtraction of generators acting on different domains. We derive a decomposition into capacity, spatial-discretization, and coarse-graining contributions; a finite-time capacity bound controlled by discarded state weight and leakage through the cutoff boundary; observable error bounds; and a sharp continuity bound for subsystem entropies. We further show that block entropy and averaged one-cell entropy differ by a relative-entropy measure of total correlation and therefore cannot be interchanged. An information-geometric expansion of neighboring reduced states yields a nonlinear sigma-model effective action on the manifold of coarse-grained states. A single entropy field follows only under an additional one-dimensional closure condition. Finally, we test the framework in an exactly evolved periodic Klein--Gordon chain with independently variable lattice spacing and local number-state cutoff. Spectral peaks are extracted from dynamical matrix elements rather than imposed. Ground-state, dispersion, reduced-state, and entropy errors converge rapidly with local capacity, while the remaining lattice--continuum discrepancy persists at fixed spacing. The results provide a controlled mathematical and numerical foundation for finite-information models without claiming a unique microscopic theory of quantum gravity.

•Oct 26, 2026•0 citations
SCQG paper 19 of 28. Paper 19 develops the microscopic quantum dynamics of the Semantic Commitment / Quantum Gravity framework. It starts with finite physical carriers at the Planck regulator scale. A cell carries registrations, records or comparison data only where the corresponding systems and operations are present. A distinction becomes locally available through the forward physical action that makes it usable. Allowed local changes and their reverse partners define a self-adjoint Hamiltonian. This generator determines quantum evolution, exact sums of transition amplitudes and causal response. The microscopic clock λ is compared with metric time through an explicitly defined positive clock map. Semantic time orders the interactions through which distinctions become usable, compared or maintained. A six-state loop provides an explicit calculation of screen occupation, payload delivery and reciprocal response. Interacting finite chains show how those results change when cells exchange quantum states. The charged construction retains all 8,160 fermionic modes of its stated regulator, together with the links and boundary systems needed to enforce local Gauss constraints. Complete packet exchanges retain the transferred states, correlations and compensating flux. The paper derives exact reduced dynamics with memory and states the additional conditions for quantum channels, memoryless evolution and classical jumps. It constructs positive Euclidean reflection forms from which Hamiltonian dynamics can be recovered, and proves that local observables have well-defined limits as the support grows under the stated locality bounds. Explicit error bounds quantify the comparison between different resolutions. The final sections specify the further action, symmetry, positivity and convergence conditions needed for a relativistic continuum realization and its use by the companion papers.
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
SCQG Paper 12 of 28 This paper sets out experiments for testing Semantic Commitment Quantum Gravity. It connects the theory’s physical equations to detector records, matched control interventions and decision rules fixed before data collection. The main laboratory proposal uses light coupled to a mechanical oscillator. It compares three conditions. Arm D adds measured noise independently of the record. Arm C measures the system and uses the result for feedback control. Arm S keeps that physical control matched and changes a stored instruction that selects a later action. The contrast C − D tests active record stabilization. The contrast S − C tests whether instruction content changes later choices on new task cases excluded from training and tuning. The paper gives equations for the cavity and oscillator, continuous measurement, feedback, noise, covariance reconstruction, work and heat. The calculations include the physical bath response, detector bandwidth, control latency and approximation error. Calibration and statistical procedures connect predicted changes in physical variability to quantities estimated from repeated runs. A source–receiver protocol distinguishes when a record becomes physically available from when the receiver can reliably identify its source. A separate clock protocol tests whether retained physical records can distinguish different cycles of a repeating clock. Gravity protocols combine causal order, discrete curvature, screen response, energy flux and tensor reconstruction to test the Einstein equation at specified scales. Each protocol specifies the controls, calibration, uncertainty, held-out evaluation, stopping rules and retained data needed to reproduce the analysis. These conditions determine when a result supports the tested prediction, reveals a physical discrepancy or remains inconclusive. This is Paper 12 of the Semantic Commitment / Quantum Gravity series.
Relational quantum causal processes formulate finite operational contexts as normal positive functionals on local completely positive maps. Response differences generate an influence algebra, and its central projections define jointly readable Boolean events. We develop this starting point through a sequence of exact and controlled models. Fresh-environment unitary collision circuits produce dephasing-exchange kinetics with an exact charge-center fixed algebra, a uniform finite-step limit at fixed response order, and graph-controlled metastable Markov dynamics. An absorbing-state model exhibits a sharp transition between non-Abelian quantum memory and Boolean records. A reversal-covariant defect dynamics generates a locally finite partial order on a restricted graph family without assuming a Lyapunov time. Conditional on a certified order, a positive additive record measure, compactness, and identifiability, we prove subsequential convergence to a Lorentzian metric-measure space, finite reconstruction bounds, and uniqueness of admissible smooth limits. Complementary finite regulators provide controlled tests of modular-to-boost response, null tomography, same-update variational identities, induced quadratic gravity, and compatible common-refinement limits. These results are exact or controlled within their stated models, but they do not yet constitute a single background-independent microscopic law that jointly generates adjacency, time, volume normalization, dimension, signature, nonlinear Einstein constraints, and quantum matter. We therefore present RQCP-QG as a theorem-indexed framework that separates established mechanisms, conditional compositions, and open assumptions.
SCQG paper 15 of 28 This paper follows the energy and entropy changes involved in creating, retaining, reading, using and resetting quantum records. It treats the pointers, memories, controllers, work stores and reservoirs as physical systems and counts each energy transfer once. Forward actionability means resolving uncertainty into a distinction that a later operation can use. Local grounding depends on that action making the resolved distinction available. The paper derives exact balances for finite quantum interactions, reset with and without retained side information, and autonomous control. It connects record lifetime and decoding accuracy to the information available for later use, and identifies the instrument-dependent information that enters feedback-work bounds. It also develops capacity-proportional selection, in which an outcome’s probability is proportional to the physical capacity available for that outcome. For nonconstant outcome probabilities, respecting ordinary mixtures of preparations forces this selection law to have positive-operator-valued measure (POVM) form. Agreement with the Born rule then requires the normalized capacity operators to equal the measurement’s outcome effects. The paper gives first-arrival, stationary and quantum-jump realizations and states their no-signalling conditions. The Stoney action equals αℏ, giving the uncertainty bound ΔX ΔP ≥ 1/(2α). Further results relate screen fluctuations, measurement precision, trajectory probabilities and entropy export. The complete physical construction keeps its reservoirs and work sources within their own reciprocal branch and supplies the defined stress interface used by the gravitational papers.
This note records a consistency result for the Spectral Quantum Gravity (SQG) framework: that the relational, timeless construction underlying SQG’s emergent time reproduces ordinary Schrödinger quantum dynamics, with departures bound to the framework’s own condensate scale rather than free. In SQG the phase fiber of the substrate carries a conserved U(1) charge Q (bounded below; the conjugate angle compact), and the Osterwalder–Schrader reconstruction supplies a self-adjoint matter Hamiltonian. Conditioning the timeless ground state on the phase-fiber clock, in the Page–Wootters sense, is shown analytically to yield the Schrödinger equation i ∂_θ ψ = (H − E) ψ exactly. This is confirmed numerically to machine precision in a finite model carrying SQG’s two defining features — a generator bounded below and a compact, integer-spectrum clock. The compact, bounded-below clock leaves the equation itself intact and imprints only clock-level fingerprints: a spectral window (modes above the constraint energy cannot be clocked), a finite time resolution of order 1/⟨Q⟩ (the phase states form a covariant POVM; Pauli’s theorem forbids a sharp conjugate time), and a KMS/thermal correction of order T ∝ 1/v from the compact Euclidean direction. All three are governed by the same condensate scale and vanish in the macroscopic-condensate limit, where textbook Schrödinger evolution is recovered. Scope and grade. This is a supplementary, lowest-grade consistency/closure note, conditional on the open decompactification of the phase fiber discussed in the main SQG work. It is explicitly not a derivation of quantum mechanics: the reflection-positive quantum substrate and the self-adjoint generator are inputs, as throughout SQG. The formalism is standard and borrowed — Page–Wootters relational dynamics, covariant (POVM) clocks for generators bounded below, and the KMS structure of a compact Euclidean direction — here applied to SQG’s specific clock. What is computed is the mechanism in a finite model, not the full field-theoretic dynamics of the substrate. The single SQG-specific statement is that any departure from ordinary quantum mechanics is tied to SQG’s own, unobservably small scale. A Python script reproducing all numerical values is included.
Abstract Finite-dimensional local Hilbert spaces are widely used as microscopic regulators and have also been proposed as a fundamental information-capacity property of space-time. A finite local dimension, however, is not equivalent to a spatial lattice spacing, and neither is equivalent to a coarse-graining scale. We formulate a regulator-resolved framework that keeps these three notions separate and defines finite-information deviations operationally as the failure of microscopic and effective time evolution to commute with a specified coarse-graining channel. The resulting deviation is a state- and observable-dependent quantity in a common effective state space, rather than a formal subtraction of generators acting on different domains. We derive a decomposition into capacity, spatial-discretization, and coarse-graining contributions; a finite-time capacity bound controlled by discarded state weight and leakage through the cutoff boundary; observable error bounds; and a sharp continuity bound for subsystem entropies. We further show that block entropy and averaged one-cell entropy differ by a relative-entropy measure of total correlation and therefore cannot be interchanged. An information-geometric expansion of neighboring reduced states yields a nonlinear sigma-model effective action on the manifold of coarse-grained states. A single entropy field follows only under an additional one-dimensional closure condition. Finally, we test the framework in an exactly evolved periodic Klein--Gordon chain with independently variable lattice spacing and local number-state cutoff. Spectral peaks are extracted from dynamical matrix elements rather than imposed. Ground-state, dispersion, reduced-state, and entropy errors converge rapidly with local capacity, while the remaining lattice--continuum discrepancy persists at fixed spacing. The results provide a controlled mathematical and numerical foundation for finite-information models without claiming a unique microscopic theory of quantum gravity.