Gravity

Modelled[M] modelled package. α stays INPUT. Weber drag is not a live α seat and does not derive G. Not a free public theorem.

Alpha Screening

The fine-structure constant α is screened by gravitational interaction at cosmological scales. This connects the EM and gravitational sectors and may resolve the coincidence problem.

Last updated: August 2026

Reading this entry

Alpha screening places a scale-dependent fine-structure value on the double copy, with the laboratory α kept as the input α₀. The running stays small at terrestrial scales because α_G is tiny, and the page joins the large ratio α/α_G to Mach closure on S³.

What this is used for

Use this page to read α_eff(r) for r much larger than the Compton length, the loop equation μ dα/dμ = −(α²/π) α_G, and the Mach condition 2GM_U/(R_Uc²) = 1 beside α_G ≈ 1.75×10⁻⁴⁵.

Walk through

Gravity enters as the double copy, so each electromagnetic coupling has a gravitational counterpart of order α_G = Gm_e²/(ke²), small at sub-atomic distances and relevant near R_U. The screened value is α_eff(r) = α₀/(1 + α₀ ln(r/λ_C)²/π), for r ≫ λ_C, with α₀ the input. The panel writes μ dα/dμ = −(α²/π)·Gm_e²/(ke²), integrates from μ₀ = mc²/ℏ to μ_U = c/R_U, and gives 1/α_U − 1/α₀ = (1/π) ln(R_U/λ_C)·α_G with α_G ≈ 1.7×10⁻⁴⁵. The displayed coupling is α_G = Gm_e²/(ke²) ≈ 1.75×10⁻⁴⁵, and α/α_G ≈ 10⁴³ sits next to ∼10⁸⁰ and (R_U/λ_C)^{3/2}. Mach closure 2GM_U/(R_Uc²) = 1 relates R_U and M_U to G, and the page points on to the banked α¹ dipole scaling.

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.

The Screening Mechanism

In the CPT framework, gravity is the double copy of electromagnetism. This means every electromagnetic interaction has a corresponding gravitational counterpart at order . At short distances (sub-atomic), this gravitational coupling is negligible. At cosmological scales (order ), it is not.

The effective fine-structure constant at scale is:

Gravitationally screened α · valid for

The Coincidence Problem

The gravitational coupling constant is:

The ratio is a famously mysterious large number. The coincidence problem asks: why does this ratio happen to be close to the number of atoms in the observable universe () divided by the ratio ?

In the CPT framework on , this is not a coincidence. The Mach closure condition relates and to . Combined with the double-copy relation, the large-number ratio is fixed by the geometry of .

Wave-Mechanical Alpha

The wave-mechanical investigation of (documented in a_geom_gap2_wave_mechanical_alpha_results) confirmed power-law scaling via sub-wavelength dipole source coupling. This is tagged [E] and banked (August 2026). See Wave-Mechanical α for the full result.

Integrity Status

[M]

Modelled package. The gravitational running of

follows from the double-copy structure of Weber gravity. The numerical smallness of the correction at laboratory scales is established. The connection to the coincidence problem is a consequence of Mach closure.

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.