Bidirectional Gravity

Mauricio Maniga

Section 02 · Force dynamics

The theory proposes two competing vectors — attractive Fₘ and compressive F_B — that stabilize each hypersphere without invoking dark energy.

The vector equilibrium equation

Theory

The total gravitational force acting on any mass element inside the hypersphere is the sum of two opposite vectors:

F_{G} = F_{m} + F_{B}

Eq. (3) — bidirectional gravity

$v ec F_{m} = - df r a c GM m r^{2}, ha t r$ is classical General Relativity gravity, attracting toward the local center of mass. $v ec F_{B} a pp r o x P_{t e x t B u l k} c d o t 4 p i R^{2}$ is the confinement pressure exerted by the Bulk's quantum vacuum against the outer surface of the hypersphere.

Vector equilibrium Fₘ + F_B

Simulação

Interior/surface regime of a spherical distribution: Fₘ ∝ R (Newton, shell theorem — gravity inside mass with M ∝ R³); F_B ∝ R² (Bulk pressure on a boundary of area 4πR²). This is not the 1/r² regime of an external point mass. The crossing marks the postulated equilibrium radius.

Section conclusion: there exists a stable equilibrium radius where the two forces cancel, conferring natural stability on the hypersphere. At inner scale, neighboring hyperspheres repel via gradients of $F_{B}$ , making dimensional overlap impossible.

Scientific lens

Speculative

No mathematical contradiction. The 1/r² law describes the field outside a point mass; the chart shows a different regime: gravity in the interior/surface of a spherical distribution with total mass $M (R) p r o pt o R^{3}$ . In that regime, by Newton's shell theorem, $g (R) = (4/3) p i G r h o, R$ , i.e. Fₘ ∝ R — a classical result of gravitation. Simultaneously $F_{B} a pp r o x P_{t e x t B u l k} c d o t 4 p i R^{2} p r o pt o R^{2}$ . The two scalings are internally coherent.

What remains open is empirical, not algebraic: $P_{t e x t B u l k}$ is postulated with no experimental method that isolates it, and the theory does not produce a falsifiable quantitative prediction reproducing the accelerated expansion observed in SN Ia, BAO and CMB — a phenomenon currently well fit by the cosmological constant Λ. That is the empirical bar F_B must clear (deriving H(z), σ₈ and the BAO peak numerically with comparable degrees of freedom) to stop being speculative — there is no direct refutation here, only underdevelopment of the proposal.

Epistemic note: the structure "attraction + boundary pressure" is analogous in spirit to serious proposals in the contemporary program — Verlinde's entropic gravity (2011) and Randall–Sundrum braneworlds (1999). The model is not alone on the map of alternatives to Λ; it only needs a quantitative derivation to enter the game.

Repulsion between hyperspheres via F_B gradients is speculative: no observational evidence, no mechanism derived from first principles.