--- { "category": "Metrology & Kinematics", "chapter": "Chapter 1", "template": "theory", "version": "1.1.0", "date_published": "2026-09-13", "updated": "2026-10-24", "canonical": true, "source_tier": "canonical", "theory_status": "DERIVED", "module_key": "lve", "module_navigation": [ { "path": "/en/theory/lve", "label": "Overview", "en": "Overview" }, { "path": "/en/theory/lve/derivation", "label": "Derivation", "en": "Derivation" }, { "path": "/en/theory/lve/physical-meaning", "label": "Physical Meaning", "en": "Physical Meaning" }, { "path": "/en/theory/lve/tests", "label": "Tests", "en": "Tests" } ], "source_chapter": "Chapter 1", "source_version": "ASD-BOOK-ddbade997b45", "source_sha256": "dace8ff491b4e4ae8a59b2b98e2a6c9c10e689079021ce0bc117985baba68e86", "last_reviewed": "2026-09-13", "open_problems": [ "/open-problems/master-equation", "/open-problems/lve-muon-decay" ], "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: Anisotropic Space Dynamics, final Chinese Chapter 1 (supplied manuscript, 23 pages)", "kind": "historical-source" } ], "id": "ASD-DOC-THEORY-LVE-EN", "path": "/en/theory/lve", "title": "Length Vector Effect", "title_en": "Length Vector Effect", "summary": "The core relation, geometric picture, theoretical dependencies and experimental boundaries of motion-dependent real spatial length in ASD.", "evidence_status": "UNTESTED", "equation": "lve", "depends_on": [ "/theory/metrology" ], "related": [ "/en/theory/lve/derivation", "/en/theory/lve/physical-meaning", "/en/theory/lve/tests", "/theory/dynamics", "/theory/electromagnetism/magnetic-force" ], "equations": [ "lve", "lve-direction" ], "source_reference": "Chapter 1 §§II–IV, Eqs. (1.1)–(1.47)", "outline": [ "Core Statement", "Why LVE Arises", "Derivation at a Glance", "Geometric Picture", "Experimental Relations", "Physical Consequences", "Scope and Limitations", "Dependencies", "Canonical Source", "Continue Research" ], "seo_title": "Length Vector Effect (LVE) | Anisotropic Space Dynamics", "canonical_url": "https://asd-physics.org/en/theory/lve", "locale": "en", "mathematical_review": "CONDITIONAL", "review_path": "/en/theory/lve/derivation#review-notes", "translation_path": "/theory/lve", "research_details_from": 7, "translation_of": "/theory/lve", "translation_version": "1.1.0", "final_source": { "source_id": "ASD-BOOK-ddbade997b45", "chapter": "Chapter 1", "reference": "Chapter 1 §§II–IV, Eqs. (1.1)–(1.47)", "locators": [ "p0309", "p0317", "p0327", "p0331", "p0335", "p0348", "p0360", "p0364", "p0510" ], "adopted_scope": "Directional-scale claim, full directional relation, transverse case and links to applications", "conditions": [ "0≤v Here $\beta=v/c$, $\gamma=(1-\beta^2)^{-1/2}$, and $\phi$ is the angle between relative velocity and the specified propagation or measurement direction. The quantities $r,r'$ are effective lengths in the paired measurements. Events, paths and standards are specified before using this ratio; it is not a formula for the Euclidean norm of an arbitrary three-dimensional vector. Setting $\phi=\pi/2$ gives the transverse case: $L_\perp$ is the reference transverse length; $L'_\perp$ is the transverse true length associated with motion. Here, “true” refers to a physical length relation assigned by ASD to a spatial process. It is more than an alternative coordinate representation of the same geometric object. The website notation $L_\perp$ identifies the transverse scale in manuscript Eqs. (1.17)–(1.19) without changing its physical meaning. ## Why LVE Arises 1. Modern measurement relations 2. Light propagation 3. Realization of length 4. Directionality of motion 5. Spatial length-vector relations The modern definition of the metre connects the length unit to the vacuum speed of light and the second. ASD asks how propagation path, elapsed process time and direction jointly enter the realization of length when the measured object or observer is in relative motion. Chapter 1 expresses $r=ct$ as a directional relation, introduces a scale factor for the moving configuration, and then derives LVE. A common unit does not independently determine the motion response of rods, wavelengths and optical paths; relating them to standard readings still requires the corresponding measurement models. The metrological definition supplies the starting point. The forward and reverse measurement constructions and their pairing condition are ASD inputs; the SI definition alone does not establish them. See [Metrological Foundations](/en/theory/metrology) for unit realization and historical context, and the [BIPM definition of the metre](https://www.bipm.org/en/si-base-units/metre) for the official definition. ## Derivation at a Glance 1. Measurement relation: $r=ct$ 2. Motion geometry: $\mathbf r'=\gamma(\mathbf r-\mathbf v t)$ 3. $\gamma(v)=(1-\beta^2)^{-1/2}$ 4. LVE result: $L'_\perp=\gamma L_\perp$ The general directional relation is $r'/r=\gamma(1-\beta\cos\phi)$. At $\phi=\pi/2$, the directional projection term vanishes and the transverse factor $\gamma$ remains. The full derivation retains the forward and reverse construction, the intermediate calculation of $\gamma$, the directional projection and the component relations. It also identifies the pairing conditions requiring review. [Read Full Derivation →](/en/theory/lve/derivation) ## Geometric Picture
The dashed frame represents the rest reference scale; the solid frame represents the scale associated with motion. Velocity $v$ points horizontally, with $L_\perp$ and $L'_\perp$ perpendicular to it. The slider varies only $\beta=v/c$ and displays the transverse ratio $\gamma$. The horizontal frame width is a drawing convention, not a calculated longitudinal length. **Conceptual / schematic illustration:** this depicts the core formula. It is not experimental data, a particle structure or a reconstruction of the shape of space. Directions, measuring rods and light signals must be identified within a specific measurement configuration. [True length and the transverse scale →](/en/theory/lve/physical-meaning) ## Experimental Relations Chapter 1 applies LVE to optical Doppler relations, Michelson–Morley, Hoek, Fizeau, Sagnac, muons and transported clocks. These relations have different capacities to distinguish theories. - **REPRODUCED:** the same result is calculated for a stated configuration, such as zero differential delay in an ideal equal-arm model. Agreement alone does not distinguish ASD. - **REINTERPRETED:** the explanation emphasizes changes in real spatial length or wavelength. Interpretive differences must be separated from measurable differences. - **POTENTIALLY DISCRIMINATING:** predictions still require comparison within the same apparatus. Directions without a completed numerical model are marked POTENTIALLY / PROPOSED TEST. [Experimental Relations and Tests →](/en/theory/lve/tests) ## Physical Consequences The following links distinguish relations developed in Chapter 1 from applications assigned to later modules. A research relationship does not imply that a later result has already been proved in this chapter. Supporting modules that have not been translated open in Chinese.
[Motion & Momentum: continue to the Chapter 2 topic and identify its additional dynamical assumptions.](/en/theory/dynamics) [Wavelength / Doppler: Chapter 1 develops these from the length relation and the light-speed relation.](/en/theory/lve/physical-meaning#doppler) [Magnetic Interaction: an application to transverse interaction distance; the full force derivation belongs to the electromagnetic module.](/en/theory/electromagnetism/magnetic-force) [Orbital Dynamics: a related topic; Chapter 1 does not supply complete gravitational or orbital equations.](/en/theory/gravity/orbital-dynamics) [Experimental Tests: inspect each observable, interpretation and current comparison status.](/en/theory/lve/tests)
## Scope and Limitations Theory Status **DERIVED** identifies the result within the assumptions and derivation chain of Chapter 1. Mathematical Review **CONDITIONAL** records the path-pairing conditions still under formal review. Overall Evidence Status **UNTESTED** means a unified test at the apparatus level has not been completed; individual experimental relations carry their own evidence labels. Canonical **YES** identifies the current final manuscript as the source. The **derived content** comprises the directional length relation, its transverse result and the wavelength–frequency relations within the specified moving configuration. The **physical interpretation** assigns these changes to real spatial relations rather than solely to coordinate representation. The full derivation labels these roles separately. Chapter 1 supplies a directional measurement relation as the kinematic entry point; Chapter 5 adds the core–accompanying-field system and coupled-field dynamics. Those later constructions do not replace the geometric check of path pairing, and each apparatus still requires its response model. Propagation in media, actual transported-clock trajectories and decay statistics require additional conditions. Event pairing and normalization in the forward and reverse construction remain explicit mathematical review tasks. These boundaries specify which results can be used directly and which applications require further inputs. They do not alter the ASD transverse-scale claim presented here. ## Dependencies The inputs are the directional measurement relation and the moving measurement construction in Chapter 1. The wavelength–frequency relations depend on LVE and $\lambda f=c$. Downstream magnetic-interaction and momentum modules additionally require their respective interaction laws or dynamical inputs. - [Metrological Foundations](/en/theory/metrology): metrological context; formal assumptions for this module follow Chapter 1. - [Derivation dependency table](/en/theory/lve/derivation#s8): inputs, algebraic results and applications distinguished individually. - [Master equation of space dynamics](/en/open-problems/master-equation): a related microscopic-mechanism task, not an input already used to obtain $\gamma$ in Chapter 1. - [LVE consistency review](/en/theory/lve/derivation#review-notes): forward/reverse construction and directional mapping. ## Canonical Source The core theory uses Section II of Chapter 1; wavelength and experimental relations use Section III; physical comparisons use Section IV. Website equation IDs are stable citation identifiers, with manuscript equation numbers listed separately. The current final manuscript takes precedence over earlier website guides and historical discussions. ## Continue Research Read the [full derivation](/en/theory/lve/derivation), then examine the [physical interpretation](/en/theory/lve/physical-meaning) and [experiment cards](/en/theory/lve/tests) within the same measurement configuration. Cite the page version, website equation ID and Chapter 1 equation number together.