Central premise (fundamentally different from GR)
Local AM derives from a pre-quantum discrete substrate (time, space, and energy–mass are discrete). Gravity acts as a rescaling of local units, determined by the potential, with invariant c and a single global calibration ψ. We use:
Π(x) = − G₀ M / r (with r = |x|)
α(x) = √(1 + ψ · Π(x))
ψ = 2 / c² (> 0)
There is no curvature postulate and no metric field equation; gravitational effects result from transporting clocks and rulers via the α(x) model. The underlying discrete model has no singularities and is naturally compatible with a prospective operational quantum theory, consistent with the additional action (AM).
Working relations (first order; coincide with the standard formulas)
Clock transport / gravitational redshift (with source and observer moving along the line of sight):
f_e / f_0 = [ α(x_s) / α(x_0) ] × √((1 − β_s)/(1 + β_s)) × √((1 − β_o)/(1 + β_o))
(β_s, β_o are line-of-sight velocities relative to c; set β_o = 0 for a stationary observer.)
LOS velocity inversion (from the total redshift):
β = ((1 + z_total)² − γ_g²) / ((1 + z_total)² + γ_g²), with γ_g ≡ α(x_0)/α(x_s)
Light deflection (point mass): α̂(b) = 4 G₀ M / (c² b)
Perihelion precession (weak field): Δϖ ≃ 6π G₀ M / [ a (1 − e²) c² ] per orbit
Thin-lens equation: β = θ − α(θ), with α(θ) = (D_ls/D_s) · α̂(D_l θ)
Lens potential and convergence:
∇_θ Ψ(θ) = α(θ), κ(θ) = Σ(D_l θ) / Σ_cr, Σ_cr = (c² / 4π G₀) · D_s / (D_l D_ls), ∇_θ² Ψ = 2 κ
Fermat potential and time delays:
Φ_F(θ, β) = ½ |θ − β|² − Ψ(θ),
Δt_{ij} = (1 + z_l) · (D_Δt / c) · [Φ_F(θ_i, β) − Φ_F(θ_j, β)], with D_Δt = D_l D_s / D_ls.
Problems addressed (comparative assessments)
· Gravitational redshift and time dilation: laboratory clock comparisons vs. height; Pound–Rebka; GP‑A.
· S2 at pericenter: total redshift (AM × SR) and LOS velocity via β‑inversion.
· Light deflection by the Sun and Jupiter; Shapiro delay.
· First‑order perihelion precession (Mercury).
· Gravitational lensing: Einstein radius, κ/γ maps, strong‑lens time delays; e.g., RX J1131–1231.
Where AM starts and how to test it
At first order in static weak fields, AM reproduces the standard coefficients. Differences can appear beyond first order or through the background cosmology (AM cosmology yields slightly smaller angular‑diameter distances D_l, D_s, D_ls at the same redshifts and therefore smaller enclosed masses M_E and time‑delay distances D_Δt at fixed θ_E). Clean cumulative tests include:
· Long‑baseline optical clock networks across height/baseline gradients.
· Precision VLBI near solar/planetary limbs.
· Strong‑lens time‑delay cosmography with shared pipelines.
· Continuous pericenter monitoring of S2.
Connection to AM cosmology
The same discrete substrate supports the Alternative Cosmological Model (AM cosmology). Local lensing expressions remain identical at first order, but distances differ because H_AM(z) and curvature differ from ΛCDM; this coherently links local and cosmological predictions without invoking GR curvature.
Open PREreview invited. Please log in with ORCID and click “Start a PREreview”:https://prereview.org/preprints/doi-10.5281-zenodo.17003936
Focused checks:(i) β inversion from (1+z_total, γ_g),(ii) thin-lens kernel equality at O(u),(iii) RX J1131 rescalings under AM cosmology.
Preprint (Zenodo DOI): https://doi.org/10.5281/zenodo.17003936