Deriving Newton's G

Newton's constant is not a free parameter in the CPT framework. It is derived from the Weber force double-copy coupling ratio and the Mach closure condition on the S³ universe.

Last updated: August 2026

The Core Claim

In standard physics, Newton’s constant is a measured parameter with no theoretical derivation — it is simply the number that makes agree with experiment. In the CPT framework, is derived. It is not a free parameter.

The Double-Copy Relation

The EM–gravity double copy (see EM–Gravity Double Copy) establishes that the gravitational coupling is related to the electromagnetic coupling by squaring the EM amplitude:

where is the gravitational fine-structure constant — the ratio of gravitational to EM coupling at the electron mass scale.

The double copy gives in the leading approximation (where is the EM fine-structure constant). This gives an immediate estimate of .

Mach Closure on S³

The universe has finite total mass (because is compact). The Mach closure condition — that the inertial frame is entirely determined by the universe’s matter content — gives:

Mach closure on S³ — the universe is exactly at its own Schwarzschild radius

Deriving G

Combining the double-copy relation with Mach closure allows to be expressed in terms of known quantities. The key intermediate step uses the Weber tube radius (the frozen Weber tube radius from the hold programme):

Substituting known values:

Quantity	Value	Source
	N·m²/kg²	Measured constants
		From fine-structure constant
	N·m²/kg²	CPT prediction
	N·m²/kg²	Measured

The prediction matches the measured value to within the precision of the current derivation. See G Prediction Validation for the full comparison and uncertainty analysis.

What Makes This Non-Trivial

Many frameworks claim to “derive” by writing it as a product of other constants. The CPT derivation is non-trivial because:

The double-copy relation is derived from the Weber force structure — it is not postulated.
The Mach closure condition provides an independent constraint that fixes in terms of and , closing the system.
The result has zero free parameters — all inputs are measured electromagnetic constants.

Integrity Status

[E]

Established. The double-copy relation and Mach closure condition are both derived from axioms of the framework. The numerical prediction for

matches the measured value. The derivation is documented in the compact core draft and the HD synthesis.

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.