---
id: ASD-GRV-GRAVITY-EN
path: /en/tests/gravity
title: Gravity · Experimental Relations and Tests
title_en: Gravity · Experimental Relations and Tests
category: Gravity
summary: Distinguish reproduced results, physical reinterpretations and proposed discriminating tests.
template: theory
version: 1.0.0
updated: '2026-09-14'
canonical: true
source_tier: canonical
theory_status: EFFECTIVE MODEL
evidence_status: UNTESTED
locale: en
module_key: gravity
module_navigation:
- path: /en/theory/gravity
label: Overview
en: Overview
- path: /en/theory/gravity/gravitational-redshift
label: Redshift
en: Redshift
- path: /en/theory/gravity/light-deflection
label: Deflection
en: Deflection
- path: /en/theory/gravity/shapiro-delay
label: Shapiro delay
en: Shapiro delay
- path: /en/theory/gravity/orbital-dynamics
label: Orbits
en: Orbits
- path: /en/theory/gravity/compact-objects
label: Compact objects
en: Compact objects
- path: /en/tests/gravity
label: Tests
en: Tests
canonical_scope: Chapter 2 · macroscopic constitutive theory
source_chapter: Chapter 2 · Static Spatial Anisotropy
source_reference: Chapter 2 / 第二章 §§I, IV–V, pp. 1–5, 11–25
source_version: FND-3dde8d8e081d
source_sha256: 3dde8d8e081d92271ff1305018fd6bbdfee8458c714a6d30c2c646a8c7318dfd
source_kind: manifest
source_records:
- id: PREF-125df9543371
title: 序章.pdf
sha256: 125df9543371f89656a2c29d552e1166e5edcc9ff5f6ec1ef1e438c7688d6ec5
pages: 8
- id: CH1-46d43c8c39bf
title: 第一章(2).pdf
sha256: 46d43c8c39bfd47f06ad699a6780e1142adc14bdd3520e2d5603d37a696cd9e9
pages: 23
- id: CH2-f9598318d123
title: 第二章-ASD理论-修订书稿 (2).pdf
sha256: f9598318d123c1f85a7d720af9cecbed8392e0b399910e3f9bfb675d49494709
pages: 27
source_manifest: foundations-source-manifest.json
source_manifest_url: /downloads/ASD_Foundations_Source_Manifest.json
last_reviewed: '2026-09-14'
depends_on:
- /en/theory/gravity/gravitational-redshift
- /en/theory/gravity/light-deflection
- /en/theory/gravity/shapiro-delay
- /en/theory/gravity/orbital-dynamics
- /en/theory/gravity/compact-objects
related:
- /en/theory/gravity
- /en/theory/gravity/gravitational-redshift
- /en/theory/gravity/light-deflection
- /en/theory/gravity/shapiro-delay
- /en/theory/gravity/orbital-dynamics
- /en/theory/gravity/compact-objects
open_problems:
- /en/open-problems/gravity/strong-field-closure
- /en/open-problems/gravity/orbital-discriminator
- /en/open-problems/gravity/rotating-background
- /en/open-problems/gravity/source-coupling
equations:
- grv-frequency-ratio
- grv-deflection
- grv-delay-distance
- grv-precession
- grv-photon-sphere
- grv-shadow
sources:
- label: CH2-f9598318d123 · 第二章-ASD理论-修订书稿 (2).pdf
kind: supplied-final-manuscript
- label: Bothwell et al., Nature 602, 420–424 (2022)
url: https://www.nature.com/articles/s41586-021-04349-7
kind: external-reference
- label: Will (2014), The Confrontation between General Relativity and Experiment
url: https://arxiv.org/abs/1403.7377
kind: external-reference
- label: NASA/JPL · Astrodynamic Parameters
url: https://ssd.jpl.nasa.gov/astro_par.html
kind: external-reference
- label: IAU 2015 Resolution B3
url: https://arxiv.org/abs/1510.07674
kind: external-reference
- label: NASA/JPL · Cassini radio-science experiment (2003)
url: https://www.jpl.nasa.gov/news/saturn-bound-spacecraft-tests-einsteins-theory/
kind: external-reference
outline:
- Reading the Matrix
- Gravity Tests Matrix
- REPRODUCED
- REINTERPRETED
- POTENTIALLY DISCRIMINATING
- Data and Sources
seo_title: Gravity · Experimental Relations and Tests | Anisotropic Space Dynamics
canonical_url: https://asd-physics.org/en/tests/gravity
translation_path: /tests/gravity
mathematical_review: CONDITIONAL
review_path: /en/theory/gravity#review-notes
review_note: Results are conditional on the stated scale, path and coupling inputs; mathematical reproduction
and microscopic closure are distinct.
evidence_note: Evidence is assigned per observable in the tests matrix. Canonical is a source designation,
not experimental proof.
translation_of: /tests/gravity
translation_version: 1.0.0
experiments:
- id: GRV-EXP-001
name: Static atomic-clock height shift
category: REINTERPRETED
observed: Bothwell et al. report a gravitational frequency gradient across a millimetre-scale strontium sample.
asd: Ω and the standard-process response give Δf/f = ΔΨ/c².
established: The same static weak-field clock ratio.
numerical_difference: NO — same at this order.
interpretation_difference: YES — spatial/wavelength response versus proper-time construction.
distinguishes: NO — the shared ratio does not select an ontology.
current_status: Macroscopic consistency; no raw-data refit or microscopic atomic closure.
required_precision: No independent difference is specified, so no discriminating precision is assigned.
source_reference: Chapter 2 §I, (2.2a); Bothwell et al. (2022)
evidence_status: CONSISTENT
- id: GRV-EXP-002
name: Weak-field light deflection
category: REPRODUCED
observed: Deflection is an established observable; the chapter calculates about 1.75 arcseconds for solar
grazing.
asd: Integration of the full optical gradient gives 4G₀M/(c²b).
established: The same result for matching distant endpoints and weak-field order.
numerical_difference: NO — same order.
interpretation_difference: YES — spatial stretching and phase-path selection.
distinguishes: NO — weak field.
current_status: Analytic and chapter-number reproduction; no new optical/radio data fit.
required_precision: No nonzero model difference is defined, hence no precision threshold.
source_reference: Chapter 2 §IV.5, (2.43)–(2.50); JPL / IAU; Will (2014)
evidence_status: CONSISTENT
- id: GRV-EXP-003
name: Shapiro / Cassini link
category: REPRODUCED
observed: Near-Sun Cassini radio links recorded frequency and round-trip light-time changes.
asd: The one-way logarithm has coefficient 2G₀M/c³; a static round trip is approximately twice this.
established: The same first-order delay after matching endpoints and order.
numerical_difference: NO — same in this static approximation.
interpretation_difference: YES — spatial accumulation of full reference optical length.
distinguishes: NO — at this order.
current_status: Analytic term reproduced; the illustration does not replace Cassini orbit, plasma and clock
modeling.
required_precision: A real link needs an error budget; no unique-difference precision is defined.
source_reference: Chapter 2 §IV.6, (2.51)–(2.58); NASA/JPL Cassini (2003)
evidence_status: CONSISTENT
- id: GRV-EXP-004
name: Mercury central-field periapsis advance
category: REPRODUCED
observed: Mercury orbital tests include a relativistic central-field advance; full observations include other
perturbations.
asd: Eq. (2.42) gives about 0.1035 arcseconds/orbit or 43.0 arcseconds/Julian century with chapter parameters.
established: The same value for matching central field, parameters and first order.
numerical_difference: NO — same model and order.
interpretation_difference: YES — spatial-length and inertia-action construction.
distinguishes: NO — the current static spherical action is mathematically equivalent.
current_status: Central-field calculation reproduced; no independent ephemeris fit.
required_precision: First establish a difference not absorbed into mass, distance or orbital parameters.
source_reference: Chapter 2 §IV.1–3, (2.25)–(2.42); JPL; Will (2014)
evidence_status: CONSISTENT
- id: GRV-EXP-005
name: Static photon sphere and critical shadow scale
category: REPRODUCED
observed: No fitted shadow image or emission-ring dataset is published in this module.
asd: The adopted exterior gives r_ph = 3ℓ_g and b_c = 3√3ℓ_g; capture additionally requires absorption.
established: Schwarzschild static optics gives identical critical scales.
numerical_difference: NO — for the adopted static exterior optical path.
interpretation_difference: YES — continuum termination is a separately stated ontological hypothesis.
distinguishes: NO — for these scales themselves; other boundary responses remain undetermined.
current_status: Conditional mathematics; emission, transfer and instrument modeling remain unfinished.
required_precision: No image difference or error budget is established.
source_reference: Chapter 2 §V.1–3, (2.59)–(2.71)
evidence_status: UNTESTED
- id: GRV-EXP-006
name: Nondegenerate higher-order, boundary or rotation observables
category: POTENTIALLY DISCRIMINATING
observed: No independent difference or validating dataset has been published in this module.
asd: Determine new responses from master equations or boundary/rotation dynamics, then calculate shared apparatus
readouts.
established: Compute a baseline using identical mass, distance, source structure, endpoints and order.
numerical_difference: TBD — neither second order nor strong field guarantees a difference.
interpretation_difference: Possible; identify the additional constitution and process response.
distinguishes: POTENTIALLY / PROPOSED TEST — existence of a discriminator is not established.
current_status: Open research; higher-order expansion of the present static action and optics can remain
identical.
required_precision: TBD — after a difference model and parameter-degeneracy analysis.
source_reference: Chapter 2 §IV conclusion, §V.4–8; OP-GRV-001–004
evidence_status: UNTESTED
---
## Reading the Matrix
Compare the **same observable, parameter calibration, endpoints and approximation order**. REPRODUCED, REINTERPRETED and POTENTIALLY DISCRIMINATING are relationship categories; evidence status is separate. Identical formulas are not independent experimental verification.
## Gravity Tests Matrix
| Observable | ASD | GR | Same numerically? | Distinguishing? |
| --- | --- | --- | --- | --- |
| Static redshift | $\Phi_2/\Phi_1$, weak field $1+\Delta\Psi/c^2$ | Same static ratio | Yes, matching calibration | NO |
| Weak deflection | $4\ell_g/b$ | Same at this order | Yes | NO at weak field |
| Shapiro | $2G_0M/c^3$ times endpoint logarithm | Same at this order | Yes, fixed endpoints | NO at this order |
| Periapsis advance | $6\pi\ell_g/p_{\rm orb}$ | Same at this order | Yes, first-order central field | NO; higher order need not differ |
| Static photon sphere / shadow | $3\ell_g$ / $3\sqrt3\ell_g$ | Same static scales | Yes, adopted exterior | NO for these scales |
| Boundary, rotation, nondegenerate terms | Dynamical closure pending | Matching observing model needed | TBD | Potential; no difference yet |
## REPRODUCED
Reproduction here includes matching chapter expressions to established results. Each card states whether data were refitted. The static strong-field optics card remains UNTESTED as evidence.
## REINTERPRETED
The [Bothwell paper](https://www.nature.com/articles/s41586-021-04349-7) supplies the observation; Chapter 2 supplies the ASD interpretation. These sources have distinct roles.
## POTENTIALLY DISCRIMINATING
Second order, strong field and rotation are not substitutes for a nonzero difference calculation. Current static spherical actions and optical paths are equivalent; parameter and coordinate degeneracies must be excluded first. See the [open research tasks](/en/open-problems/gravity/strong-field-closure).
## Data and Sources
No new raw-data fit, residuals, confidence interval or underived prediction is published here. S301 stays an [independent case study (Chinese)](/tests/case-studies/s301), awaiting complete data before reproducible fitting.
Parameters use [JPL](https://ssd.jpl.nasa.gov/astro_par.html) and [IAU B3](https://arxiv.org/abs/1510.07674). Link observations are described by the [Cassini project](https://www.jpl.nasa.gov/news/saturn-bound-spacecraft-tests-einsteins-theory/); established-test context is in [Will (2014)](https://arxiv.org/abs/1403.7377). These are external references, not independent ASD validation reports.