---
{
  "id": "ASD-DOC-EN-THEORY-DYNAMICS-TESTS",
  "path": "/en/theory/dynamics/tests",
  "title": "Dynamics · Experimental Relations and Tests",
  "title_en": "Dynamics · Experimental Relations and Tests",
  "category": "Foundations & Dynamics",
  "summary": "Separate mathematical checks, observational constraints on universal coupling and dynamical tests that still need apparatus models.",
  "template": "theory",
  "version": "1.0.0",
  "updated": "2026-10-24",
  "canonical": true,
  "source_tier": "canonical",
  "theory_status": "DERIVED",
  "evidence_status": "UNTESTED",
  "locale": "en",
  "module_key": "dynamics",
  "module_navigation": [
    {
      "path": "/en/theory/dynamics",
      "label": "Overview",
      "en": "Overview"
    },
    {
      "path": "/en/theory/dynamics/momentum",
      "label": "Inertia & Momentum",
      "en": "Inertia & Momentum"
    },
    {
      "path": "/en/theory/dynamics/energy",
      "label": "Energy & Action",
      "en": "Energy & Action"
    },
    {
      "path": "/en/theory/dynamics/force-and-work",
      "label": "Force & Work",
      "en": "Force & Work"
    },
    {
      "path": "/en/theory/dynamics/tests",
      "label": "Tests",
      "en": "Tests"
    }
  ],
  "canonical_scope": "Preface · Chapters 1–2",
  "source_chapter": "Chapter 2",
  "source_reference": "§III.5 (2.24c)—(2.24d) and chapter summary",
  "source_version": "ASD-BOOK-ddbade997b45",
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      "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",
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  ],
  "last_reviewed": "2026-09-14",
  "depends_on": [
    "/en/theory/dynamics/momentum",
    "/en/theory/dynamics/energy"
  ],
  "related": [
    "/en/theory/dynamics/force-and-work",
    "/theory/gravity"
  ],
  "open_problems": [
    "/open-problems/inertial-closure"
  ],
  "equations": [
    "dyn-mass-coupling",
    "dyn-external-coupling"
  ],
  "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": "Touboul et al. (2022)",
      "kind": "external-primary-reference",
      "url": "https://arxiv.org/abs/2209.15487"
    }
  ],
  "outline": [
    "Reading experimental relations · Evidence Scope",
    "Recomputable results · Mathematical Checks",
    "Coupling different mass responses · Universal Coupling",
    "An existing observation · Published Observation",
    "A direction for comparison · Proposed Tests",
    "Review and source · Review and Sources"
  ],
  "seo_title": "Dynamics · Experimental Relations and Tests | Anisotropic Space Dynamics",
  "canonical_url": "https://asd-physics.org/en/theory/dynamics/tests",
  "translation_path": "/theory/dynamics/tests",
  "equation": "dyn-mass-coupling",
  "translation_of": "/theory/dynamics/tests",
  "translation_version": "1.0.0",
  "mathematical_review": "CONDITIONAL",
  "review_path": "/en/theory/dynamics/momentum#review-notes",
  "review_note": "Momentum follows after the inertial constitutive closure; total energy additionally uses E₀ = m₀c². These inputs remain explicit and require microscopic matching.",
  "experiments": [
    {
      "id": "dyn-test-microscope",
      "name": "MICROSCOPE: free fall of differently composed test bodies",
      "category": "REINTERPRETED",
      "observed": "MICROSCOPE’s differential-acceleration measurement with titanium and platinum alloys found no significant weak-equivalence-principle violation, with constraints at the 10⁻¹⁵ scale.",
      "asd": "Chapter 2 adopts universal mass coupling. At fixed internal state and weak field, the same m₀ cancels between force and inertia, giving composition-independent free fall.",
      "established": "The equivalence principle expects universal free fall under the same test conditions.",
      "numerical_difference": "NO · The current ASD relation with universal coupling predicts no composition-dependent difference.",
      "interpretation_difference": "YES · ASD interprets the mass types as different responses of one spatial core.",
      "distinguishes": "NO",
      "current_status": "Consistent with the universal-coupling condition; no ASD mission-data refit or microscopic topology verification has been performed.",
      "evidence_status": "CONSISTENT",
      "required_precision": "The reported 10⁻¹⁵ scale characterizes this test. The chapter supplies no nonzero ASD–standard difference and hence no additional discriminatory precision target.",
      "source_reference": "Chapter 2, §III, Eqs. (2.24c)–(2.24d), reference [4]; Touboul et al., PRL 129, 121102 (2022). DOI: 10.1103/PhysRevLett.129.121102"
    },
    {
      "id": "dyn-test-response",
      "name": "Controlled momentum–energy and directional-response comparison",
      "category": "POTENTIALLY DISCRIMINATING",
      "observed": "Chapter 2 §III supplies no beam dataset, apparatus inputs or speed–energy table ready for fitting.",
      "asd": "Use this module’s momentum, work and directional response as a baseline, then model the actual force, detection and nonuniform structural response.",
      "established": "Compare results using identical calibrations, trajectories, internal states and apparatus responses, beyond matching formula names.",
      "numerical_difference": "The free-motion baseline has the same form; a measurable difference from further constitutive effects has not been derived.",
      "interpretation_difference": "YES · Structural interpretations of inertia and energy differ.",
      "distinguishes": "POTENTIALLY / PROPOSED TEST",
      "current_status": "An apparatus-modelling task only; no experimental prediction curve or reproduction record has been generated.",
      "evidence_status": "UNTESTED",
      "required_precision": "First calculate a difference from a completed apparatus model, then evaluate speed, force, energy, direction and detection noise.",
      "source_reference": "Chapter 2, §III, Eqs. (2.11)–(2.24b); website task OP-DYN-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": "Chapter 2",
    "reference": "§III.5 (2.24c)—(2.24d) and chapter summary",
    "locators": [
      "p0669",
      "p0671",
      "p0672",
      "p0674",
      "p0675",
      "p0936"
    ],
    "adopted_scope": "Core–accompanying-field inertial constitution, momentum integration, inverse force response and energy; retain correct existing derivations.",
    "conditions": [
      "Uniform background, fixed internal state, 0≤v<c and no net radiation.",
      "The LVE directional law and inertial angular weight are separate inputs.",
      "m₀=C_m m_def; adopt C_m=1 and universal mass normalization."
    ],
    "unresolved": [
      "The microscopic core profile, inertial weight and four mass responses still require one common structural solution."
    ],
    "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, §III, Eqs. (2.24c)–(2.24d), PDF p. 10; reference [4]; test interface for Eqs. (2.11)–(2.24b)",
    "source_version": "FND-3dde8d8e081d",
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      {
        "id": "CH1-46d43c8c39bf",
        "title": "第一章(2).pdf",
        "sha256": "46d43c8c39bfd47f06ad699a6780e1142adc14bdd3520e2d5603d37a696cd9e9",
        "pages": 23
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      {
        "id": "CH2-f9598318d123",
        "title": "第二章-ASD理论-修订书稿 (2).pdf",
        "sha256": "f9598318d123c1f85a7d720af9cecbed8392e0b399910e3f9bfb675d49494709",
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    ],
    "source_manifest": "foundations-source-manifest.json",
    "source_manifest_url": "/downloads/ASD_Foundations_Source_Manifest.json",
    "sources": [
      {
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        "kind": "supplied-final-manuscript"
      },
      {
        "label": "CH1-46d43c8c39bf · 第一章(2).pdf",
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        "label": "CH2-f9598318d123 · 第二章-ASD理论-修订书稿 (2).pdf",
        "kind": "supplied-final-manuscript"
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      {
        "label": "Touboul et al. (2022)",
        "kind": "external-primary-reference",
        "url": "https://arxiv.org/abs/2209.15487"
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}
---
ASD organizes stored energy, translational inertia, active gravitational sourcing and passive response within one core–accompanying-field system. Final equation (2.24c) adopts universal matching, and (2.24d) implements it in weak-field external potential energy; experiments test that matching together with the apparatus response.

## Reading experimental relations · Evidence Scope

Recomputable dynamical formulas do not establish that experiments have independently selected their microscopic interpretation. This page states the matching results and normalization conditions, then records observations actually cited by Chapter 2. A calculation without apparatus and data is not entered as an experimentally reproduced result.

DERIVED refers to derivation within the framework under explicit premises. The module’s overall evidence status remains UNTESTED. Individual cards use CONSISTENT or UNTESTED according to their own source material.

## Recomputable results · Mathematical Checks

| Check | ASD conditions and result | Mathematical comparison | Experimental verification? |
| --- | --- | --- | --- |
| Low-speed limit | $p\to m_0v$, $E_k\to m_0v^2/2$ | Same form | NO; a limit check |
| Directional force | $F_\parallel=m_0\gamma^3a_\parallel$, $F_\perp=m_0\gamma a_\perp$ | Same form for fixed mass and common variables | NO; a derivative result |
| Energy consistency | With rest-energy normalization, $E^2-c^2p^2=m_0^2c^4$ | Same form | NO; an algebraic check |
| Free action | Integrating momentum and fixing a constant gives Eq. (2.24b) | Same form | NO; constitutive and normalization inputs remain |

Chapter 2 §III provides no independent beam-data reanalysis. This page does not invent observations or fits to fill a REPRODUCED category. A future data comparison should retain instruments, input quantities, residuals and uncertainties.

## Coupling different mass responses · Universal Coupling

Chapter 2 distinguishes energy mass, inertial mass, active gravitational mass and passive gravitational mass. If a common topological parameter $Q_0$ gives

$$
m_i=C_iQ_0,\qquad m_g^{(a)}=C_aQ_0,\qquad m_g^{(p)}=C_pQ_0,
$$

universal free fall requires $C_p/C_i$ to be composition independent. This observational requirement does not by itself establish equality of every coefficient or directly measure active gravitational mass.

<ArgumentStep kind="Normalization" title="The common coupling adopted in the chapter">

<Equation name="dyn-mass-coupling" />

</ArgumentStep>

A complete structural theory must test the common origin of these responses. Binding energy, internal stresses and self-gravity enter composite totals; one cannot simply sum constituent rest masses.

<Equation name="dyn-external-coupling" />

Here $X=1+2\Psi/c^2$ and $\mathbf g_X=-\nabla\Psi$ are Chapter 2’s weak-field external variables. This is the weak-field interface to the current [orbital topic](/en/theory/gravity/orbital-dynamics). This page checks inertial closure and limits without duplicating external-field solutions or orbital equations.

## An existing observation · Published Observation

<ExperimentCard name="dyn-test-microscope">

[The mission team’s original paper and results](https://arxiv.org/abs/2209.15487). This observation constrains the weak equivalence principle. It does not directly measure ASD’s near-core density profile, inertial angular distribution or stable topology.

</ExperimentCard>

## A direction for comparison · Proposed Tests

<ExperimentCard name="dyn-test-response">

Matching free-motion $p,E$ alone supplies no distinguishing signal. If a force is electromagnetic, the field and probe relations must also be declared. A standard Lorentz force must not silently replace an ASD response not yet established for that configuration. [OP-DYN-01 (Chinese)](/open-problems/inertial-closure) first addresses constitutive and normalization origins.

</ExperimentCard>

## Review and source · Review and Sources

The tasks are to compute inertial weight, static energy and mass couplings from one microscopic structure, then map them to the same measured output in an actual apparatus. If baseline predictions still agree, report no discrimination. If a response function is absent, retain an undetermined result.

This module does not expand Chapter 2’s deflection, Shapiro-delay or orbital results or use their observations as independent verification of this inertial closure.

<CanonicalSource />