---
{
  "id": "OP-SD-002-EN",
  "path": "/en/open-problems/space-dynamics/equal-speed",
  "title": "OP-SD-002 · Equal Propagation Speed Condition",
  "title_en": "OP-SD-002 · Equal Propagation Speed Condition",
  "category": "Space Dynamics",
  "summary": "The common vacuum speed is currently effective constitutive matching. Ordered-amplitude feedback in the dual-field candidate can shift the longitudinal low-k speed while leaving the transverse branch at the bare speed.",
  "template": "problem",
  "version": "1.0.0",
  "updated": "2026-09-15",
  "canonical": false,
  "source_tier": "research-notes",
  "theory_status": "OPEN",
  "evidence_status": "UNTESTED",
  "locale": "en",
  "module_key": "space-dynamics-research",
  "module_navigation": [
    {
      "path": "/en/theory/space-dynamics",
      "label": "Overview",
      "en": "Overview"
    },
    {
      "path": "/en/theory/space-dynamics/degrees-of-freedom",
      "label": "Degrees of freedom",
      "en": "Degrees of freedom"
    },
    {
      "path": "/en/theory/space-dynamics/longitudinal-field",
      "label": "Longitudinal field",
      "en": "Longitudinal field"
    },
    {
      "path": "/en/theory/space-dynamics/transverse-field",
      "label": "Transverse field",
      "en": "Transverse field"
    },
    {
      "path": "/en/theory/space-dynamics/wave-propagation",
      "label": "Wave propagation",
      "en": "Wave propagation"
    },
    {
      "path": "/en/theory/space-dynamics/longitudinal-waves",
      "label": "Longitudinal waves",
      "en": "Longitudinal waves"
    },
    {
      "path": "/en/theory/space-dynamics/longitudinal-transverse-coupling",
      "label": "L–T coupling",
      "en": "L–T coupling"
    },
    {
      "path": "/en/theory/space-dynamics/continuum-dynamics",
      "label": "Continuum dynamics",
      "en": "Continuum dynamics"
    },
    {
      "path": "/en/theory/space-dynamics/fcc-model",
      "label": "FCC-like model",
      "en": "FCC-like model"
    },
    {
      "path": "/en/theory/space-dynamics/master-equation",
      "label": "Master equation",
      "en": "Master equation"
    },
    {
      "path": "/en/tests/space-dynamics",
      "label": "Tests",
      "en": "Tests"
    }
  ],
  "canonical_scope": "Continuum foundation; status specified per claim",
  "source_chapter": "Chapter 4 / 第四章 · Chapter 5 / 第五章",
  "source_reference": "Ch. 4 §4.1; Ch. 5 §§4, 6",
  "source_version": "SD-51779505a476",
  "source_sha256": "51779505a4766d2211550c6598875bbbab0c3dac14d68dd3f2107778b05deb0b",
  "source_kind": "manifest",
  "source_records": [
    {
      "id": "CH4-9587f3c44d39",
      "title": "第四章-ASD空间本体论-出版整理稿.docx",
      "sha256": "9587f3c44d3974f44e387ed03d92691fa5473a90d7b1c9c989155adf0622849a",
      "format": "docx"
    },
    {
      "id": "CH5-ca737ec4e327",
      "title": "第五章-出版整理稿.docx",
      "sha256": "ca737ec4e327d72c5507bbc8e00295b6e56029c7583ebad8e505cdb9c68c6262",
      "format": "docx"
    }
  ],
  "source_manifest": "space-dynamics-source-manifest.json",
  "source_manifest_url": "/downloads/ASD_Space_Dynamics_Source_Manifest.json",
  "last_reviewed": "2026-09-15",
  "depends_on": [
    "/en/theory/space-dynamics/wave-propagation"
  ],
  "related": [
    "/en/theory/space-dynamics"
  ],
  "open_problems": [
    "/en/open-problems/space-dynamics/unified-dynamics",
    "/en/open-problems/space-dynamics/stable-topology",
    "/en/open-problems/space-dynamics/continuum-microscopic",
    "/en/open-problems/space-dynamics/longitudinal-wave-detection",
    "/en/open-problems/space-dynamics/source-coupling"
  ],
  "equations": [
    "sd-equal-speed",
    "sd-effective-speeds"
  ],
  "sources": [
    {
      "label": "CH4-9587f3c44d39 · 第四章-ASD空间本体论-出版整理稿.docx",
      "kind": "supplied-manuscript"
    },
    {
      "label": "CH5-ca737ec4e327 · 第五章-出版整理稿.docx",
      "kind": "supplied-manuscript"
    }
  ],
  "outline": [
    "Current baseline",
    "Work required",
    "Reviewable deliverable",
    "Limits and dependencies"
  ],
  "seo_title": "OP-SD-002 · Equal Propagation Speed Condition | Anisotropic Space Dynamics",
  "canonical_url": "https://asd-physics.org/en/open-problems/space-dynamics/equal-speed",
  "translation_path": "/open-problems/space-dynamics/equal-speed",
  "mathematical_review": "INCOMPLETE",
  "evidence_note": "Constraints and proposals are recorded separately; no new experimental fit.",
  "equation": "sd-equal-speed",
  "translation_of": "/open-problems/space-dynamics/equal-speed",
  "translation_version": "1.0.0",
  "problem": {
    "expertise": [
      "Spectral analysis",
      "Constitutive theory"
    ],
    "difficulty": "Open research",
    "missing_result": "Necessary/sufficient conditions for $c_L=c_T=c$, a stable parameter domain and protection mechanism; otherwise a calculable deviation and its validity scale.",
    "deliverable": "Necessary/sufficient conditions for $c_L=c_T=c$, a stable parameter domain and protection mechanism; otherwise a calculable deviation and its validity scale.",
    "current_state": "The common vacuum speed is currently effective constitutive matching. Ordered-amplitude feedback in the dual-field candidate can shift the longitudinal low-k speed while leaving the transverse branch at the bare speed."
  }
}
---
## Current baseline

The common vacuum speed is currently effective constitutive matching. Ordered-amplitude feedback in the dual-field candidate can shift the longitudinal low-k speed while leaving the transverse branch at the bare speed.

<Equation name="sd-equal-speed" />

<Equation name="sd-effective-speeds" />

## Work required

Compute all linearized branches and the mixing matrix of the actual vacuum. Separate bare coefficients from those obtained after eliminating internal modes. Seek constitutive, symmetry or microscopic protection of equality and test its survival under perturbations and effective corrections. Define phase, group and front speeds separately from measured arrival times.

## Reviewable deliverable

Necessary/sufficient conditions for $c_L=c_T=c$, a stable parameter domain and protection mechanism; otherwise a calculable deviation and its validity scale.

## Limits and dependencies

Nearby light and gravitational-wave arrival speeds do not derive ASD coefficient relations or identify tensor gravitational waves with free scalar longitudinal waves.

[Wave propagation](/en/theory/space-dynamics/wave-propagation)

<CanonicalSource />