What question did this study set out to answer?

The aim is to derive a flat-spacetime model where gravity arises from density-dependent length contraction.

March 2, 2026Open Access

Density-Dependent Length Contraction: A Flat-Spacetime Model with Explicit Derivations V2

Key Points

The aim is to derive a flat-spacetime model where gravity arises from density-dependent length contraction.
Developed a scalar model expressing gravity as radial ruler contraction.
Calibrated κ_eff using Gaia DR3 data.
Proposed empirical tests involving muonium and astrophysical observations.
Reproduced Milky Way rotation profiles without invoking dark matter.
Predicted observable effects such as additional stretch in high-redshift supernovae.
Identified falsifiable predictions related to cosmic-ray spikes and gravitational wave strain.

Abstract

A flat-spacetime scalar model where gravity emerges as radial ruler contraction along the line-of-sight: s = max (1 - κₑff ∫ ρ ds, 0. 01), with κₑff = 7. 39 × 10⁵ m² kg^-1 (Gaia DR3 calibrated) scaling as κₑff ∝ 1/ (1 + ρ/ρcrit) ², ρcrit = 10^-24 kg m^-3. Reproduces Milky Way rotation (220 km/s at 8 kpc → 195 km/s at 30 kpc) without dark matter, LIGO strain via density shear, redshift as λₒbs = λ₀ / s. Includes GPS clock match, proposed muonium lab test (Δf ≈ 10^-10 Hz at 1 atm), and falsifiable predictions: JWST z>5 SN extra stretch, Swarm SAA cosmic-ray spike, NANOGrav nHz background from density variance. All open—no funding.

Density-Dependent Length Contraction: A Flat-Spacetime Model with Explicit Derivations V2

Key Points

Abstract

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