Length Vector Effect

01Core Statement

The Length Vector Effect (LVE) describes a directional change, associated with motion, in what ASD defines as real spatial length relations. Length is realized through a metrological relation between light propagation and elapsed time. Once motion enters the measurement geometry, the spatial scale depends on relative speed and measurement direction.

In the specified forward and reverse moving measurement configurations, Chapter 1 establishes the full directional relation using a common scale factor, path pairing and normalization:

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.

02Why LVE Arises

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 for unit realization and historical context, and the BIPM definition of the metre for the official definition.

03Derivation at a Glance

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 →

04Geometric 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 →

05Experimental 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 →

06Physical 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.

07Scope 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.