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The tempo of becoming: The physics of ν — law, two cadences, covariance, and the absence of a signature

Patrick Jaubert

Published Sep 12, 2026• 0 citations
Publisher

Abstract

The ontological triplet of Time–Actualization (TA) comprises three primitives, one per temporal mode: ρ (the potential future, the object of quantum mechanics), ⟨P,≺⟩ (the causal past, the object of relativity), and ν (the tempo of the present). The two external primitives are imported. ν is TA's own, and hence the only locus of a physics that might belong to it — within one limit: ν is the cadence of a system, not of the substrate, whose own cadence comes with the causal set. This article details that physics in a single sweep, one section per heading. (A) Law: TA posits a correspondence between ν and an energy scale motivated by quantum speed limits, together with saturation where attainable; a bound on state motion alone does not bound an ontic event count. (B) Two cadences: the tick assigned to a system event is distinct from the substrate's far finer scale, and agreement with substrate proper time remains a correspondence requirement. (C) Covariance: the proposed energy scale is a Lorentz scalar in the effective clock regime considered here; this does not construct a covariant actualization dynamics. (D) No signature: empirical equivalence with quantum mechanics on the causal-set substrate is an admissibility requirement whose full verification remains open. The contribution is a conditional ontological reading of imported physics.

DOI
10.5281/zenodo.22722657

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•Aug 1, 2026•0 citations
The ontological triplet of Time–Actualization (TA) comprises three primitives, one per temporal mode: ρ (the potential future, the object of quantum mechanics), ⟨P,≺⟩ (the causal past, the object of relativity), and ν (the tempo of the present). The two external primitives are imported. ν is TA's own, and hence the only locus of a physics that might belong to it — within one limit: ν is the cadence of a system, not of the substrate, whose own cadence comes with the causal set. This article details that physics in a single sweep, one section per heading. (A) Law: TA posits a correspondence between ν and an energy scale motivated by quantum speed limits, together with saturation where attainable; a bound on state motion alone does not bound an ontic event count. (B) Two cadences: the tick assigned to a system event is distinct from the substrate's far finer scale, and agreement with substrate proper time remains a correspondence requirement. (C) Covariance: the proposed energy scale is a Lorentz scalar in the effective clock regime considered here; this does not construct a covariant actualization dynamics. (D) No signature: empirical equivalence with quantum mechanics on the causal-set substrate is an admissibility requirement whose full verification remains open. The contribution is a conditional ontological reading of imported physics.
Quantum mechanics describes the potential future; general relativity describes the actualized past; the present is the process of actualization that turns the one into the other. That single move is Time–Actualization (TA), the foundational ontology set out here. TA assumes the quantum formalism and the relativistic causal structure, and derives neither: it adds no new physics, makes no new prediction, and asks to be judged on coherence and unifying power rather than on a measurement. It proposes a common ontological reading of measurement, EPR and the structural arrow of time. D5 locates the einselecting environment in the event's causal past; the couplings within that past remain imported, and the system/environment split is relocated rather than removed. In detail. The ontology is a minimal triplet (ρ, ν, ⟨P,≺⟩): a positive normalized state ρ on a local net of algebras (the conditional future potential), a primitive tempo ν (the rate of becoming), and a growing causal set ⟨P,≺⟩ (the past). What is not derived, and is named as such throughout, is the Born rule, Einstein's equations, and the constants. Eight core hypotheses yield seven consequences. A structural arrow of time, prior to thermodynamics (D1). A partial dissolution of the measurement problem (D2), with definiteness posited and the trigger open. Conditional dissolutions of EPR and the signalling worry (D3–D4), requiring a propagation law. A preferred basis anchored in the couplings carried by the causal past (D5). A conditional thermodynamic reading of the structural arrow (D6), requiring a posited bridge to physical reset, and further thermal assumptions for its value. And a conditional coherence lemma (D7): the actualization dynamics is generally covariant and no-signalling once the substrate carries the standard locality of physics. D7 claims less than the Rideout–Sorkin Bell causality condition, which is a screening-off analogue of Bell's local causality and is not inherited. We then develop the proposed physics of the tempo ν: a correspondence with a local quantum speed scale and a saturation choice, both posited. Quantum speed limits alone do not bound an ontic event count. The missing bridge must specify event resolution, additive counting and an applicable composable speed bound. The substrate cadence that reconstructs proper time is kept distinct from a system's tempo; their operational connection remains to be supplied. TA aims at empirical equivalence to quantum mechanics on a causal-set substrate. We label the admissibility requirement P5; its verification, including instrumented multi-time statistics, remains open. No distinctive prediction is claimed. The causal-set "swerve" is inherited from discreteness, generic and not specific to actualization. We close with the open dynamics, its system/substrate interface, the conditional constitution of systems, and the inherited limits of the programme.
Time-Actualization (TA) is a foundational interpretation empirically equivalent to quantum mechanics on a causal-set substrate: it makes no new prediction (a consequence, forced by assuming QM, we label P5). It therefore has, by construction, no value in hard physics -- no algorithm, no measurement, no experimental gap. This essay raises a distinct question: if one adopts TA as the correct reading of the world, what does this commit one to outside physics? We argue that TA delivers a coherent package of foundational stances -- a real objective present, an ontologically open future, an objective chance, a non-classical logic of the contingent, a primary becoming -- whose radiance is limited exactly to those domains that are themselves theories of the foundation: philosophy of time, of logic, of probability, of mind, and process metaphysics. We delimit this radiance without evasion: it is conditional (the premise "the universe is TA" is not establishable against its empirical twins), interpretative (ontological clarity, never a measurable fact), and bounded (nothing in the empirical sciences). This is the profile of a foundational contribution assumed as such.
Presentism and the growing block universe make the present an objective frontier, but presuppose a global "now" that the relativity of simultaneity forbids — the Rietdijk–Putnam argument, which pushes the metaphysics of time toward eternalism (past, present and future equally real). We defend a metaphysical thesis that aims at empirical equivalence with quantum mechanics on a causal-set substrate; full verification of that requirement remains open. In the Time–Actualization (TA) ontology, the present is not a slice of simultaneity but the act of actualization of quantum potentialities into events. Covariance is required: the order of birth of events is gauge, while causal order and regional event count are physical. This reading instantiates a growing block universe without a global present, so the relativistic objection loses its purchase (it targets a global "now" that TA does not have). This dissolution is, originally, Stein's point-relative becoming; TA inherits it and lodges a process within it, uniting Stein's becoming and the covariant growth of Rideout–Sorkin causal sets under a single realist reading. The identification this proposes — becoming is actualization, and the act of actualization is, ontologically, the measurement event (whose basis and readiness TA anchors, with outcome weights imported from Born) — is advanced as programmatic: a conjecture to be earned, not a result already in hand (Sec. 7). The contribution is an ontological synthesis, not a new formalism or a new prediction.
The causal-set programme proposes that spacetime is, at bottom, a discrete poset whose Lorentzian geometry emerges, endowed with a covariant sequential growth dynamics. It leaves open, however, two points that an ontology must settle: the status of the "becoming" of growth (a computational procedure or a real process?), and the basis of its quantum version (quantum sequential growth, QSG, does not specify the basis of the histories). We show that the theory Time–Actualization (TA) proposes an ontological answer: becoming is posited as real actualization, while the basis is selected by the couplings carried by the causal past, where that monitoring supplies a sharp basis. This identifies an environment within the ontology; it does not derive its coupling content or construct the full quantum dynamics. We present the interface as a consistency bridge, not a refoundation. The emergent geometry and its Hauptvermutung remain inherited, and the dynamical law of actualization remains open. The proposed unification concerns a common process reading of flashes, system actualizations and causal-set growth; their different rates still require an explicit interface.
The "preferred-basis problem" — why does measurement produce definite outcomes in this basis rather than another — is treated in opposite ways by the interpretations of quantum mechanics: posited ab initio (spontaneous collapse), drawn from a contingent environment (decoherence), left to the choice of a framework (decoherent histories), avoided (many-worlds, pilot wave). We show that in the Time–Actualization ontology — where measurement is an instance of the universal process of actualizing quantum potentialities into events — the preferred basis is anchored in the causal past of the event, together with a readiness condition: which events that past has made ready to actualize. TA does not introduce a new selection mechanism: it identifies the environment of einselection with the already-actualized causal past — an environment that is not posited outside the formalism (unlike an external classical apparatus), but is part of the same substrate. The causal location of this environment is foliation-independent; its monitoring content depends on the couplings, not on the bare order alone. Covariance of the associated operations requires the locality hypotheses stated below. The uniqueness of outcomes is posited, not explained. Born's rule remains imported, and empirical equivalence with quantum mechanics on the causal-set substrate is a requirement still to be verified for a complete dynamics. The contribution is ontological and local to the preferred-basis question. A symmetric downstream mechanism — the redundant proliferation of the outcome into the causal future (quantum Darwinism) — in addition accounts for the inter-observer objectivity of the actualized fact, without deriving it.
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