Gravity

Modelled[M] modelled package — not free public theorem; see doctrine v1.0.3 residual chips on /status.

Gravitational Lensing

Solar gravitational light deflection θ_lens = 1.75124'' modelled as a Weber double-copy optical refractive index theorem on S³, matching GR and VLBI observations to reported package match. (package — not free theorem)

Last updated: 9 August 2026

Reading this entry

Gravitational lensing on this page is a Weber optical package: a photon at speed c sees the refractive index n(r) = 1 + 2GM/(c²r) on S³. Fermat's principle then returns the solar limb deflection 1.75124 arcseconds, the figure the page quotes for the standard light-bending formula.

What this is used for

Use this page for n(r) = 1 + 2GM/(c²r), for the transverse gradient integral equal to 4GM/(c²b), and for the solar-limb evaluation quoted here, θ = 4GM_⊙/(c²R_⊙) = 1.75124 arcseconds.

Walk through

The page quotes the solar-limb deflection θ = 4GM_⊙/(c²R_⊙) = 1.75124 arcseconds. A photon at v = c grazing mass M sees n(r) = 1 + 2GM/(c²r). Fermat's principle gives θ_sun = ∫|∇_⊥n| dz from −∞ to ∞, equal to 4GM_⊙/(c²R_⊙) = 8.4854×10⁻⁶ rad = 1.75124 arcseconds. The derivation steps restate n(r) = 1 + 2GM/(c²r) and ∫|∇_⊥n| dz = 4GM/(c²b), with solar-surface value 1.751244 arcseconds. The comparison table places that same 1.751244 arcseconds next to the general-relativistic figure, and the status line keeps θ_lens = 1.75124 arcseconds as this refractive-index package on S³.

Integrity note (Doctrine v1.0.3): Quantitative matches on this page are modelled packages unless they appear on the public status board as established free theorems. Public residual chips: continuum hold OPEN; α is INPUT; Foot δ [E INPUT]; Foot K/L [E]; proton mass theorem FORBIDDEN; FL-HEAVY parked. Soft packages are not finished UFT certificates.

1. The Light Deflection Problem

General Relativity predicts that starlight passing close to the Solar limb is deflected by an angle (arcseconds).

In standard GR, this deflection is explained by spacetime curvature tensor . In the CPT framework, gravity is the double-copy of electromagnetism operating via the Weber force, creating an effective optical refractive index in the surrounding space.

2. The Weber Refractive Index Theorem

For a photon traveling at speed grazing a mass , the velocity-dependent Weber potential creates an effective refractive index . Applying Fermat's principle of least time:

Gravitational Lensing Theorem

3. Comparison to Experimental GR & VLBI Target

Parameter	General Relativity	CPT Derived Theorem	Status
Solar Light Deflection $\theta$	1.751244'' (Metric curvature)	1.751244''	Modelled [M] (package match)

STATUS: [M] MODELLED PACKAGE

The solar gravitational light deflection is a modelled programme package [E] derived from velocity-dependent Weber gravitational potential refractive index on as a modelled package (not a free public theorem).

Source Documents

The primary research documents underlying this page. All files are freely viewable and downloadable. They represent the working research as written — including integrity tags, equations, and finding IDs.

Documents open in the CPT Research Library — a formatted viewer for all source research files.