--- { "id": "ASD-DOC-EN-THEORY-TIME-CLOCKS-AND-FREQUENCY", "path": "/en/theory/time/clocks-and-frequency", "title": "Time · Clocks and Frequency", "title_en": "Time · Clocks and Frequency", "category": "Foundations & Dynamics", "summary": "Specify how spatial scales enter clock frequency and phase, separating published observations from proposed discriminatory comparisons.", "template": "theory", "version": "1.0.0", "updated": "2026-10-24", "canonical": true, "source_tier": "canonical", "theory_status": "FOUNDATION", "evidence_status": "UNTESTED", "locale": "en", "module_key": "time", "module_navigation": [ { "path": "/en/theory/time", "label": "Overview", "en": "Overview" }, { "path": "/en/theory/time/measurement-and-process", "label": "Measurement & Process", "en": "Measurement & Process" }, { "path": "/en/theory/time/clocks-and-frequency", "label": "Clocks & Frequency", "en": "Clocks & Frequency" }, { "path": "/en/theory/time/comparison", "label": "Comparison", "en": "Comparison" } ], "canonical_scope": "Preface · Chapters 1–2", "source_chapter": "Chapters 1–2", "source_reference": "Chapter 2 §§I.1–I.2, Eqs. (2.1)–(2.4); Chapter 1 Eq. (1.47)", "source_version": "ASD-BOOK-ddbade997b45", "source_sha256": "dace8ff491b4e4ae8a59b2b98e2a6c9c10e689079021ce0bc117985baba68e86", "source_kind": "manifest", "source_records": [ { "id": "ASD-BOOK-ddbade997b45", "title": "各向异性空间动力学（最终合订稿）", "filename": "各向异性空间动力学.docx", "format": "docx", "size_bytes": 503564, "sha256": "ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e" } ], "last_reviewed": "2026-09-14", "depends_on": [ "/en/theory/time/measurement-and-process", "/en/theory/lve" ], "related": [ "/en/theory/time/comparison", "/theory/gravity" ], "open_problems": [ "/open-problems/clock-response" ], "equations": [ "time-phase-length", "time-scale", "grv-frequency-ratio", "time-weak-redshift" ], "sources": [ { "label": "Final combined manuscript — adopted scope documented on this page", "kind": "final-combined-manuscript", "url": "/downloads/ASD_Final_Manuscript_Source_Manifest.json" }, { "label": "Previous source: PREF-125df9543371 · 序章.pdf", "kind": "historical-source" }, { "label": "Previous source: CH1-46d43c8c39bf · 第一章(2).pdf", "kind": "historical-source" }, { "label": "Previous source: CH2-f9598318d123 · 第二章-ASD理论-修订书稿 (2).pdf", "kind": "historical-source" }, { "label": "Bothwell et al. (2022)", "kind": "external-primary-reference", "url": "https://www.nature.com/articles/s41586-021-04349-7" }, { "label": "BIPM · Practical realization of the second", "kind": "external-definition-reference", "url": "https://www.bipm.org/en/publications/mises-en-pratique" } ], "outline": [ "From oscillation to reading · Clock Model", "Technologies and physical inputs · Clock Technologies", "Scale coupling in gravity · Scale and Frequency", "Published observations and interpretation · Experimental Relations", "A direction for discriminatory work · Proposed Comparison", "Review conditions and sources · Review and Sources" ], "seo_title": "Time · Clocks and Frequency | Anisotropic Space Dynamics", "canonical_url": "https://asd-physics.org/en/theory/time/clocks-and-frequency", "translation_path": "/theory/time/clocks-and-frequency", "equation": "time-phase-length", "translation_of": "/theory/time/clocks-and-frequency", "translation_version": "1.0.0", "mathematical_review": "CONDITIONAL", "review_path": "/en/theory/time/clocks-and-frequency#review-notes", "review_note": "Process identities do not determine a clock’s response. Frequency and phase predictions require a specified oscillator, coupling law and comparison protocol.", "experiments": [ { "id": "time-test-redshift", "name": "Gravitational frequency shift within a millimetre-scale atomic sample", "category": "REINTERPRETED", "observed": "Bothwell et al. (2022) measured a frequency gradient across a millimetre-scale strontium sample consistent with gravitational redshift.", "asd": "Eq. (2.2) adopts scale–frequency coupling; final Eq. (2.2a) gives the exact static frequency ratio, whose first-order expansion connects to near-Earth weak-field shifts. No raw-data refit was performed.", "established": "GR gives Δf/f ≈ ΔΨ/c² at corresponding weak-field order and with a common frequency-comparison convention.", "numerical_difference": "NO · The adopted weak-field relation is the same at this order.", "interpretation_difference": "YES · ASD attributes the response to spatial scale/wavelength and oscillation processes.", "distinguishes": "NO", "current_status": "The observation is published; the ASD relation is consistent in its direction. An independent apparatus-level comparison is not complete.", "evidence_status": "CONSISTENT", "required_precision": "The chapter supplies no ASD–GR prediction difference for this setup; experimental resolution is not a discriminatory precision target.", "source_reference": "Chapter 2, Eqs. (2.2)–(2.2a), reference [3]; Bothwell et al., Nature 602, 420–424 (2022). DOI: 10.1038/s41586-021-04349-7" }, { "id": "time-test-moving", "name": "Transported clocks · Ideal motion and actual flights", "category": "POTENTIALLY DISCRIMINATING", "observed": "Hafele–Keating reported clock differences between transported clocks on different flight directions and ground references. Actual flights include motion and gravity.", "asd": "The ideal uniform equatorial circuit in Chapter 1 gives T′/T = √[(1−β)/(1+β)].", "established": "Standard calculations accumulate kinematic and gravitational contributions along actual trajectories. The constant-speed gravity-free baseline is dτ/dt = √(1−β²).", "numerical_difference": "Formally YES: the manuscript expression has a first-order speed term. Total clock differences for matched trajectories and timing quantities remain to be aligned.", "interpretation_difference": "YES · ASD interprets the result through a change in process length.", "distinguishes": "POTENTIALLY / PROPOSED TEST", "current_status": "The original expression and its low-speed check are retained. Actual clock-transport observations are not described as verification of Eq. (1.47).", "evidence_status": "UNTESTED", "required_precision": "Specify the velocity reference background, complete trajectory, total elapsed time, synchronization and gravity corrections before setting an error budget.", "source_reference": "Chapter 1, Section 3.6, Eq. (1.47); references [19], [20]" }, { "id": "time-test-cross-clock", "name": "Common-background response across clock technologies", "category": "POTENTIALLY DISCRIMINATING", "observed": "The supplied manuscript contains no joint dataset for atomic standards, optical cavities and other oscillators under one comparison protocol.", "asd": "Derive each clock’s scale/transition/path response in frequency and phase, then form ratios in a common background.", "established": "Compute established-theory outputs for the same apparatus, environment and transfer protocol.", "numerical_difference": "Undetermined; complete ASD apparatus response functions are missing.", "interpretation_difference": "YES · The proposed response mechanisms differ.", "distinguishes": "POTENTIALLY / PROPOSED TEST", "current_status": "A research task is defined; no numerical difference, fit or discriminatory conclusion is available.", "evidence_status": "UNTESTED", "required_precision": "Determine the prediction difference first, then budget clock noise, transfer noise and systematic errors.", "source_reference": "Process account of time in the Preface; Chapter 2, §§I.1–I.2; website task OP-TIME-01" } ], "source_manifest": "final-manuscript-source-manifest.json", "source_manifest_url": "/downloads/ASD_Final_Manuscript_Source_Manifest.json", "final_source": { "source_id": "ASD-BOOK-ddbade997b45", "chapter": "Chapters 1–2", "reference": "Chapter 2 §§I.1–I.2, Eqs. (2.1)–(2.4); Chapter 1 Eq. (1.47)", "locators": [ "p0554", "p0558", "p0562", "p0566", "p0570", "p0571", "p0573", "p0500" ], "adopted_scope": "Exact static frequency ratio and first-order weak-field expansion, with clock-technology and transported-clock conditions retained", "conditions": [ "Common reference calibration; static constitutive relation Φ=Ω⁻¹", "Exact ratio requires 1+2Ψ/c²>0; weak-field expansion also requires |Ψ|/c²≪1" ], "unresolved": [ "FINAL-CH1-CLOCK-PROTOCOL" ], "migration_status": "reviewed", "manuscript_sha256": "ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e", "source_manifest": "final-manuscript-source-manifest.json", "body_review": "updated" }, "previous_source": { "source_chapter": "Preface; Chapter 1; Chapter 2, Static Spatial Anisotropy", "source_reference": "Chapter 2, §§I.1–I.2, Eqs. (2.1)–(2.2a), PDF pp. 1–3; Chapter 1, Eq. (1.47), and the LVE v1.1 clock entry", "source_version": "FND-3dde8d8e081d", "source_sha256": "3dde8d8e081d92271ff1305018fd6bbdfee8458c714a6d30c2c646a8c7318dfd", "source_kind": "manifest", "source_records": [ { "id": "PREF-125df9543371", "title": "序章.pdf", "sha256": "125df9543371f89656a2c29d552e1166e5edcc9ff5f6ec1ef1e438c7688d6ec5", "pages": 8 }, { "id": "CH1-46d43c8c39bf", "title": "第一章(2).pdf", "sha256": "46d43c8c39bfd47f06ad699a6780e1142adc14bdd3520e2d5603d37a696cd9e9", "pages": 23 }, { "id": "CH2-f9598318d123", "title": "第二章-ASD理论-修订书稿 (2).pdf", "sha256": "f9598318d123c1f85a7d720af9cecbed8392e0b399910e3f9bfb675d49494709", "pages": 27 } ], "source_manifest": "foundations-source-manifest.json", "source_manifest_url": "/downloads/ASD_Foundations_Source_Manifest.json", "sources": [ { "label": "PREF-125df9543371 · 序章.pdf", "kind": "supplied-final-manuscript" }, { "label": "CH1-46d43c8c39bf · 第一章(2).pdf", "kind": "supplied-final-manuscript" }, { "label": "CH2-f9598318d123 · 第二章-ASD理论-修订书稿 (2).pdf", "kind": "supplied-final-manuscript" }, { "label": "Bothwell et al. (2022)", "kind": "external-primary-reference", "url": "https://www.nature.com/articles/s41586-021-04349-7" }, { "label": "BIPM · Practical realization of the second", "kind": "external-definition-reference", "url": "https://www.bipm.org/en/publications/mises-en-pratique" } ] } } --- ## From oscillation to reading · Clock Model ASD explains clock-frequency changes through the interaction of the timing structure with its spatial state. In gravity, the background first changes the characteristic scale and associated wavelength of a standard process; at the same local vacuum propagation speed and common reference calibration, frequency and period change, and accumulated oscillations determine the display. We proceed from the phase length of one cycle to the static scale–frequency relation, then connect that analytic relation to clock technologies and comparison links. Chapter 2 discusses periods through propagation or phase processes. For an atomic standard, $S_{\mathrm{cyc}}$ is a characteristic phase length defined by the period. It is neither an electron trajectory nor a photon round trip inside the atom. Defining an equivalent length and determining its environmental response are separate steps. ## Technologies and physical inputs · Clock Technologies | Clock or standard | Counted physical process | Inputs needed for an ASD calculation | | --- | --- | --- | | Microwave atomic clock | An atomic transition references the oscillator frequency | Transition–structure coupling, atomic motion and environmental perturbations | | Optical atomic clock | Optical atomic/ionic transition and a comparable frequency signal | Optical-transition response, readout chain and frequency reference; a geometric cavity model cannot simply replace them | | Optical cavity | Resonant phase condition | Effective optical path, boundaries, material and mode response; how length enters frequency | | Frequency standard | An evaluated reference calibrates other oscillators | Local realization, frequency transfer, calibration frequency and compared readings | | Moving clock | Cycles and phase accumulated during motion | Velocity background, direction, full trajectory, internal clock response and comparison events | | Clock in gravity | Frequency ratio or accumulated phase difference between positions | Background scale, comparison reference, signal link and local versus remote quantities | This table organizes the apparatus tasks implied by the manuscript; it does not claim six completed microscopic ASD clock models. BIPM realization guidance describes the local second as a unit of proper time and addresses realization and comparison corrections. Its metrological procedures are cited here without recasting them as ASD ontology. [BIPM: practical realization of the second](https://www.bipm.org/en/publications/mises-en-pratique) ## Scale coupling in gravity · Scale and Frequency In a common reference calibration, the manuscript denotes a spatial length-scale ratio by $\Omega(r)$ and connects a corresponding change of periodic scale to oscillation frequency. This connection is a physical coupling input, not a consequence of the SI numerical definition of $c$. Increasing $\Omega$ means a larger characteristic length or wavelength and a lower frequency. Chapter 2 uses this sequence to interpret gravitational redshift. ASD does not begin by assigning the change to the flow of an independent time entity. Frequencies at both positions must use one comparison reference. Equation (2.2a) of the final manuscript is an exact ratio, not merely the weak-field expression. With $\Phi=\Omega^{-1}=\sqrt{1+2\Psi/c^2}$, the specified static background and common reference calibration give: Here $\Phi$ is a dimensionless line-density coefficient, not a volume density; $\Psi$ has dimensions of speed squared, and both positions require $1+2\Psi/c^2>0$. The isolated spherical exterior solution uses $\Psi=-G_0M/r$. This constitutive model supplies the full analytic ratio. Expanding to first order when $|\Psi|/c^2\ll1$ at both positions gives: Chapter 2’s potential convention has $\Psi<0$ near a positive mass. At weak-field order, moving to higher potential gives a higher relative frequency in the first-order expansion of Eq. (2.2a). Weak-field redshift constrains a low-order relation; it does not uniquely determine a full strong-field scale law. The current [gravitational-redshift topic](/en/theory/gravity/gravitational-redshift) develops the background, scale law and scope. This page explains the interface between standard processes and frequency readings; the full static background still requires that topic’s stated constitutive relation and does not follow from weak-field frequency shifts alone. Here $f(r)$ is the frequency of the same class of standard process expressed against a common reference. The [cycle-count discussion](/en/theory/gravity/gravitational-redshift#redshift-counts) distinguishes it from nominal clock readings and the frequency after transmission to a receiver. A transfer link or directional-clock output still requires its own apparatus model. ## Published observations and interpretation · Experimental Relations The experimental paper supplies the observation; the manuscript supplies ASD’s mechanism interpretation. [Bothwell et al.: original paper](https://www.nature.com/articles/s41586-021-04349-7). This page generates no new data points or recalculated statistical precision. This card continues the [transported-clock entry in LVE v1.1](/en/theory/lve/tests#lve-test-clock). Chapter 1 Eq. (1.47) and Chapter 2’s requirement for a concrete physical-process response must be aligned for one trajectory and one timing observable. The new module does not treat that task as resolved. ## A direction for discriminatory work · Proposed Comparison [OP-TIME-01 (Chinese)](/open-problems/clock-response) calls for clock response functions, predictions from both frameworks with common inputs, and an uncertainty budget. Discriminatory power requires a measurable residual difference in those calculations; different mechanism language alone is not an experimental criterion. ## Review conditions and sources · Review and Sources
1. **Definition and coupling:** $S_{\mathrm{cyc}}=c/f$ defines a phase length. Predicting $f$ requires an independently specified background response of $S_{\mathrm{cyc}}$. 2. **Local and remote quantities:** Specify the references for $f_0,f(r)$, length scales and transfer signals in Eq. (2.2). Commonly calibrated quantities are not automatically raw local display values. 3. **Clock technologies:** Atomic transitions, cavity boundaries and mechanical structures require individual response models. Their universality must follow from those models. 4. **Moving-clock continuity:** How Chapter 1 Eq. (1.47)’s directional path expression enters an accumulated clock difference still requires examination. This page preserves LVE v1.1’s status and question. These are conditions and matching tasks, without changing Chapter 2’s spatial-scale interpretation. Response coefficients, fits and precision targets absent from the manuscript are not supplied here.