Gravity
EstablishedMach Closure
Mach's principle is satisfied by the S³ geometry. The inertial frame is defined by the finite total mass of the S³ universe, which must equal its own Schwarzschild mass.
Mach's principle
Inertia is not an intrinsic property — it arises from the interaction of each body with all other matter in the universe.
Why S³ satisfies Mach
S³ is compact → finite total mass → the Mach sum converges and equals 1 (the Mach closure condition).
The closure condition
— the universe is at its own Schwarzschild radius.
Why flat ℝ³ fails Mach
The Mach sum diverges for a uniform density infinite universe — the integral diverges.
Numerical estimate
kg (observed baryonic + dark matter), m → depending on mass estimate (order-of-magnitude consistent).
Connection to G derivation
Mach closure + double-copy → G determined.
The Brans–Dicke connection
Mach closure in S³ gives (recovering GR-like behaviour) while satisfying Mach.
The Mach closure condition
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.