--- { "category": "Metrology & Kinematics", "chapter": "Chapter 1", "template": "theory", "version": "1.1.0", "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-TESTS-EN", "path": "/en/theory/lve/tests", "title": "Experimental Relations and Tests", "title_en": "Experimental Relations and Tests", "summary": "Seven experimental relations from Chapter 1: numerical agreement, interpretive differences, discrimination and the conditions still required for quantitative tests.", "evidence_status": "UNTESTED", "equation": "lve", "depends_on": [ "/en/theory/lve" ], "related": [ "/en/theory/lve", "/en/theory/lve/derivation", "/en/theory/lve/physical-meaning", "/tests/experimental-proposals" ], "equations": [ "lve-mm-parallel", "lve-mm-transverse", "lve-loop", "lve-sagnac", "lve-frequency", "lve-hoek", "lve-process", "lve-muon", "lve-clock" ], "source_reference": "Chapter 1 §§3.1–3.6, Eqs. (1.21)–(1.47)", "experiments": [ { "id": "lve-test-mm", "name": "Michelson–Morley · Equal-arm interference", "category": "REPRODUCED", "observed": "No systematic fringe shift of the magnitude expected from the classical stationary-ether model at Earth’s orbital speed was observed. The null result refers to experimental limits on that differential signal.", "asd": "Chapter 1 calculates the longitudinal and transverse round trips as 2γL/c each, giving zero differential delay in the ideal equal-arm model.", "established": "Standard relativity also predicts zero directional differential delay for the ideal apparatus.", "numerical_difference": "NO · For the zero arm-to-arm difference compared here.", "interpretation_difference": "YES · ASD uses directional lengths and optical paths.", "distinguishes": "NO", "current_status": "The ideal manuscript model can be recalculated; the original apparatus data have not been refitted.", "evidence_status": "REPRODUCED", "required_precision": "No nonzero difference is predicted here. A discriminatory precision cannot be set from the shared factor alone.", "source_reference": "Chapter 1, Section 3.2, Eqs. (1.26)–(1.30); reference [10]" }, { "id": "lve-test-sagnac", "name": "Sagnac · Rotating closed optical path", "category": "REPRODUCED", "observed": "Co- and counter-propagation in a rotating closed optical path produce a phase or arrival-time difference. The chapter cites Sagnac’s interference observations.", "asd": "The directional elapsed-time difference and R′ = γR give Δt = 4ωS′/c².", "established": "The usual low-speed loop relation for a specified area is Δt ≈ 4ωA/c². Exact results require explicit time and area definitions.", "numerical_difference": "NO · For the usual form after matching area, timing and low-speed approximation. The all-orders correspondence is incomplete.", "interpretation_difference": "YES · ASD uses directional optical paths and an area associated with motion.", "distinguishes": "NO · For the shared area form considered here.", "current_status": "The area form has been recalculated; correspondence between R, R′ and the timing definitions remains a condition.", "evidence_status": "CONSISTENT", "required_precision": "To investigate higher-order differences, fix area and timing conventions, derive a prediction difference and then construct an error budget.", "source_reference": "Chapter 1, Section 3.5, Eqs. (1.36)–(1.43); reference [16]" }, { "id": "lve-test-doppler", "name": "Optical Doppler / Ives–Stilwell", "category": "REINTERPRETED", "observed": "Ives–Stilwell measured combinations of forward and backward spectral lines from moving atoms to test their second-order shift relation.", "asd": "Frequency follows from λ′ = λγ(1−βcosφ) and λ′f′ = c. The manuscript’s transverse case gives f′ = f/γ.", "established": "SR gives the corresponding second-order Doppler relation. Emission-frame angles, reception-frame angles and aberration must be distinguished.", "numerical_difference": "The shared transverse redshift or second-order relation can agree. Arbitrary-angle equivalence still requires source–receiver and angle mapping and has not been asserted.", "interpretation_difference": "YES · ASD interprets the shift through a change in wavelength as a length quantity.", "distinguishes": "NO · The shared frequency-shift relation alone does not distinguish ASD.", "current_status": "The manuscript’s algebraic chain is retained; full angle mapping and spectral-line fitting for the original experiment remain to be organized.", "evidence_status": "CONSISTENT", "required_precision": "Chapter 1 supplies no nonzero difference in an aligned observable and no target precision.", "source_reference": "Chapter 1, Section 3.1, Eqs. (1.21)–(1.25); reference [9]" }, { "id": "lve-test-hoek", "name": "Hoek · Vacuum and medium optical paths", "category": "REINTERPRETED", "observed": "Chapter 1 reports that Hoek found no expected first-order directional fringe shift.", "asd": "Using nL as effective optical path, a simplified balance Lvac = nLmed gives equal round-trip times in the two-segment model.", "established": "Standard treatment of propagation in media, boundaries and phases also accounts for the corresponding null result.", "numerical_difference": "NO · For the stated null result. A segment-by-segment numerical comparison with the original apparatus is incomplete.", "interpretation_difference": "YES · ASD organizes the explanation through the length-vector response of effective optical path.", "distinguishes": "NO", "current_status": "The simplified model is displayed. Its mapping to Hoek’s apparatus topology and phases requires formal review.", "evidence_status": "CONSISTENT", "required_precision": "Chapter 1 supplies no nonzero difference confirmed by a complete apparatus model and no target precision.", "source_reference": "Chapter 1, Section 3.3, Eqs. (1.31)–(1.35); reference [14]" }, { "id": "lve-test-fizeau", "name": "Fizeau · Phase difference in a moving medium", "category": "POTENTIALLY DISCRIMINATING", "observed": "The chapter cites the interference-fringe change caused by flowing water, involving medium speed and refractive-index dependence.", "asd": "The manuscript incorporates medium optical path into LVE and suggests t = nL/c in Eq. (1.38), without a complete phase model.", "established": "To first order without dispersion, velocity composition gives c/n + w(1−1/n²). Actual fringes also depend on apparatus segments and dispersion.", "numerical_difference": "The refractive-index dependence of the direct substitution has not been aligned with the standard medium model. Numerical agreement cannot be claimed.", "interpretation_difference": "YES · The physical inputs to the explanations differ.", "distinguishes": "POTENTIALLY / PROPOSED TEST · Complete a calculation for the same apparatus first.", "current_status": "An unresolved tension remains between the chapter’s substitution and the medium-propagation coefficient. Complete experimental reproduction is absent.", "evidence_status": "TENSION", "required_precision": "Specify traversal counts, L, w, n and dispersion, then derive the prediction difference before setting precision.", "source_reference": "Chapter 1, Sections 3.4–3.5, medium application of Eq. (1.38); reference [15]" }, { "id": "lve-test-muon", "name": "Muon survival · Moving particles", "category": "POTENTIALLY DISCRIMINATING", "observed": "Muons exhibit measurable decay or survival differences with motion, and muons produced at altitude can be detected at ground level.", "asd": "Eqs. (1.45)–(1.46), with L′=643 m and β=0.998, give 643√999 m≈20323.276089 m, or 20323.3 m to one decimal place. These illustrative inputs do not carry that experimental precision.", "established": "Standard relativity calculates laboratory survival using proper lifetime, speed and momentum distributions. An ideal constant-speed mean path includes γ.", "numerical_difference": "Formally YES: the inverse factor is γ(1+β), not γ. Whether the expressions refer to the same statistic must be established first.", "interpretation_difference": "YES · ASD attributes the effect to process-path change; SR uses proper-time relations.", "distinguishes": "POTENTIALLY / PROPOSED TEST · Compare survival distributions of the same particle population.", "current_status": "The manuscript number has been recalculated. No ASD flux or lifetime-distribution fit can be claimed as successful.", "evidence_status": "TENSION", "required_precision": "Energy spectrum, paths, losses, efficiency and statistical errors are required. Chapter 1 gives no target precision.", "source_reference": "Chapter 1, Section 3.6, Eqs. (1.44)–(1.46); references [17], [18]" }, { "id": "lve-test-clock", "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]" } ], "outline": [ "Reading the Tests", "REPRODUCED", "REINTERPRETED", "POTENTIALLY DISCRIMINATING", "Sources and Next Steps" ], "seo_title": "Length Vector Effect (LVE) — Experimental Relations and Tests | Anisotropic Space Dynamics", "canonical_url": "https://asd-physics.org/en/theory/lve/tests", "locale": "en", "mathematical_review": "CONDITIONAL", "review_path": "/en/theory/lve/derivation#review-notes", "translation_path": "/theory/lve/tests", "translation_of": "/theory/lve/tests", "translation_version": "1.1.0", "final_source": { "source_id": "ASD-BOOK-ddbade997b45", "chapter": "Chapter 1", "reference": "Chapter 1 §§3.1–3.6, Eqs. (1.21)–(1.47)", "locators": [ "p0401", "p0412", "p0420", "p0444", "p0451", "p0462", "p0473", "p0484", "p0494", "p0496", "p0500" ], "adopted_scope": "Existing apparatus models and full muon arithmetic/rounding; unresolved apparatus calculations retained", "conditions": [ "Apparatus, direction and counting conditions remain with each entry", "Muon inputs are illustrative approximations, not a complete survival fit" ], "unresolved": [ "FINAL-CH1-FIZEAU-DIMENSION", "FINAL-CH1-MUON-OBSERVABLE", "FINAL-CH1-CLOCK-PROTOCOL" ], "migration_status": "reviewed", "manuscript_sha256": "ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e", "source_manifest": "final-manuscript-source-manifest.json", "body_review": "updated" }, "previous_source": { "source_chapter": "Chapter 1 · The Vector Effect of Length — From Constant Light Speed to Anisotropy of Moving Space", "source_reference": "Chapter 1, Sections 3.1–3.6, Eqs. (1.21)–(1.47), PDF pp. 10–20; references [9]–[20]", "source_version": "CH1-caf38018fc5a", "source_sha256": "caf38018fc5aed65b6565668de0325599f46341fd7e893ea923571ac7c2e3961", "sources": [ { "label": "Anisotropic Space Dynamics, final Chinese Chapter 1 (supplied manuscript, 23 pages)", "kind": "supplied-final-manuscript" } ] }, "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" } ], "source_manifest": "final-manuscript-source-manifest.json", "source_manifest_url": "/downloads/ASD_Final_Manuscript_Source_Manifest.json" } --- ## Reading the Tests Chapter 1 uses one directional length relation to organize Doppler shifts, equal-arm interference, moving media, rotating loops and moving processes. Recalculable results include equal round-trip times in the ideal two-arm model, the area form for a circular loop, and inversion of the muon path relation for specified inputs. This page presents those calculations and connects each to the frequency, phase, survival distribution or accumulated clock difference actually measured. REPRODUCED means only that the relation or ideal model specified on the card can be recalculated; it does not mean ASD has been independently proved. POTENTIALLY / PROPOSED TEST identifies a direction requiring further work, not a VERIFIED result. Required precision remains undetermined where a numerical prediction or error budget is missing. Overall Evidence Status is UNTESTED: the chapter has not yet supplied a unified test at the apparatus level. Existing numerical relations and specific tensions are labeled separately on the cards. [Recalculated relations](#s1) · [Different interpretations](#s2) · [Potential discrimination](#s3) · [Sources](#s4) ## REPRODUCED Apply the general directional factors to the two longitudinal legs separately, then add: For each transverse leg, set $\phi=\pi/2$: The ideal equal-arm model therefore gives $T'_\parallel-T'_\perp=0$. The common factor $\gamma$ cancels from this difference. A null differential result alone does not measure the transverse true scale. Original observation: [Michelson & Morley (1887)](https://ajsonline.org/article/62505-on-the-relative-motion-of-the-earth-and-the-luminiferous-ether), Chapter 1 reference [10]. Using this section's convention for the direction of object motion, first write the counter- and co-directional elapsed times: Then use the rest radius, the radius associated with motion and the area in sequence: The substitution is $\Delta t=(2\pi R/c)(2R'\omega/c)\gamma$. With $\gamma R=R'$, it yields the area expression. The manuscript retains $\gamma$ here and absorbs it into $R'$. Agreement in form with the standard low-speed area relation does not establish an all-orders comparison between the two timing definitions. The observation reference follows Chapter 1 [16]: Sagnac (1913), Comptes Rendus 157, 708–710. This website has not refitted the original fringe data. ## REINTERPRETED In the chapter's transverse case, $\phi=\pi/2$ gives $f'/f=1/\gamma$ and a wavelength ratio of $\gamma$. The forward/backward spectral-line combination in Ives–Stilwell is not the same apparatus as a directly drawn ninety-degree light path. Its actual spectral combination must be mapped to the manuscript's angle convention. Original paper: [Ives & Stilwell (1938)](https://opg.optica.org/josa/abstract.cfm?uri=josa-28-7-215), Chapter 1 reference [9]. The general wavelength–frequency derivation is on the [physical-meaning page](/en/theory/lve/physical-meaning#doppler). Under the manuscript's simplified balancing condition $L_{\mathrm{vac}}=nL_{\mathrm{med}}$, the vacuum-segment expression $2\gamma L_{\mathrm{vac}}/c$ equals the medium-segment expression $2n\gamma L_{\mathrm{med}}/c$. This calculation is conditional. Its correspondence to the closed optical path, segment directions and phases in Hoek's original apparatus requires a segment-by-segment check against the apparatus diagram. The observation reference follows Chapter 1 [14]: Hoek (1868), Archives Néerlandaises 3, 180–185. The chapter does not provide a complete apparatus data table for direct recalculation. ## POTENTIALLY DISCRIMINATING The following three directions retain the formal Chapter 1 expressions and identify the work still needed to connect them to experimental readings. This category does not claim the existence of results uniquely verifying ASD. Chapter 1, Section 3.4, interprets the experiment using effective optical path in a medium. Section 3.5 applies Eq. (1.38) to a linearly moving medium and proposes $t=nL/c$. Direct substitution into the manuscript's $\Delta t=2t\beta\gamma$ gives: $$ \Delta t_{\mathrm{substitution}}=\frac{2nLw}{c^2}\gamma(w). $$ This is the website's explicit expansion of the substitution described in the chapter. It has no separate manuscript equation number. It does not yet account for all propagation segments, boundaries and phases of the same apparatus. Define $L$, medium speed $w$ and the number of traversals first, then check refractive-index and dispersion dependence. A complete reproduction of Fizeau fringes cannot yet be claimed from this substitution. The original observation follows Chapter 1 reference [15]: Fizeau (1851), Comptes Rendus 33, 349–355. The standard velocity-composition comparison uses [Einstein 1905, Section 5](https://www.fourmilab.ch/etexts/einstein/specrel/www/). It is an independent comparison and does not enter the ASD derivation. The final manuscript’s standard-theory comparison in §3.4 prints a velocity-addition denominator that is not dimensionless when $w$ is a speed. This source issue is recorded explicitly; the page does not use that typography as a valid comparison formula or change ASD Eq. (1.38) on its basis. The Fizeau apparatus model and refractive-index dependence remain the specific tasks stated above. The manuscript inverts the relation using $L'=643\,\mathrm m$ and $\beta=0.998$: Here $L$ is the path from production to reception in the ground reference, $L'$ is the effective path assigned to the moving process in Chapter 1, and $\beta=v/c$. The website expands manuscript Eqs. (1.45)–(1.46) for the stated example inputs as $$ \begin{aligned} L&=L'\sqrt{\frac{1+\beta}{1-\beta}}\\ &=643\sqrt{\frac{1.998}{0.002}}\,\mathrm m =643\sqrt{999}\,\mathrm m\\ &=1929\sqrt{111}\,\mathrm m \approx20323.276089\,\mathrm m. \end{aligned} $$ Rounding to one decimal place gives $20323.3\,\mathrm m$, consistent with the manuscript’s approximate $20323\,\mathrm m$. The intermediate radicals and extra digits are a website arithmetic check. The inputs $643\,\mathrm m$ and $0.998$ remain approximate illustrative values, not measurements with this many significant digits. ASD links process duration here to a directional effective path rather than introducing a separate change in a flow of time. This algebraic calculation must be distinguished from an experimental measurement. Eq. (1.46) provides no particle populations at different energies, initial flux, energy losses, detector efficiency or survival fit. The fact that some particles reach the ground is insufficient to test a particular factor for a mean distance. As a website consistency check, inversion of Eq. (1.45) gives $L/L'=\gamma(1+\beta)$. This differs from the SR factor $\gamma$ when the same $L'$ is interpreted as a constant-speed path associated with proper lifetime. The author must specify the statistic and endpoints represented by $L'$. The two factors cannot yet be treated as completed predictions for the same experiment. [Continue with OP-LVE-01: muon survival under the LVE path interpretation →](/open-problems/lve-muon-decay) Original observations: [Rossi & Hall (1941)](https://journals.aps.org/pr/abstract/10.1103/PhysRev.59.223), Chapter 1 [17]; Frisch & Smith (1963), American Journal of Physics 31, 342–355, reference [18]. These studies measured relations between decay or survival and motion, not the illustrative number in Eq. (1.46) directly. To identify a possible difference, the website expands the manuscript expression at low speed: $$ \sqrt{\frac{1-\beta}{1+\beta}} =1-\beta+\frac{\beta^2}{2}+O(\beta^3). $$ For constant speed in the same inertial background with gravity omitted, the standard proper-time relation is $d\tau/dt=\sqrt{1-\beta^2}$, whose first correction is second order. **This is a formal comparison of two expressions.** The speed and process path of the manuscript's equatorial circuit have not yet been fully aligned with standard coordinate time. Actual clock transport requires flight trajectories, Earth rotation, gravitational potential, stop durations and the clock-comparison procedure. Chapter 1 supplies neither these inputs nor a total clock difference. Hafele–Keating observations are therefore not labeled as verification of Eq. (1.47). Precision requirements should follow matched-trajectory predictions and an error budget. Original report: [Hafele & Keating, Observed Relativistic Time Gains (1972)](https://pubmed.ncbi.nlm.nih.gov/17779918/), Chapter 1 reference [20]; the accompanying prediction is reference [19]. For the standard constant-speed timing relation, see [Einstein 1905, Section 4](https://www.fourmilab.ch/etexts/einstein/specrel/www/). ## Sources and Next Steps This page is a structured entry to the experimental relations in Chapter 1, Section III, not a database of original experiments. Measurement errors, apparatus details and predictions absent from the manuscript have not been invented. Quantitative derivations in other chapters not yet loaded into the website have not been attributed to this chapter. The next deliverables are specific: source–receiver angle mapping for Doppler; complete phase calculations for Hoek and Fizeau; area and time definitions for Sagnac; a muon survival distribution; and transported-clock differences along matched trajectories. These tasks can be organized through the [experimental-proposal framework](/en/tests/experimental-proposals). The core mathematical pairing question is in the [derivation review](/en/theory/lve/derivation#review-notes). [Return to the LVE overview →](/en/theory/lve)