Brane-World Gravity Leakage

Extra-Dimension Setup

Extra dimensions n 2

Compactification size R 1.20

Source mass M 1.0

Probe distance r 2.00

Measured on the Brane

F(r) / F_Newton(r)

1.00×

Local exponent d(ln F)/d(ln r)

2.00

Regime

r ≫ R

Bulk volume ∝ Rⁿ

1.99

How it works

In the Arkani-Hamed–Dimopoulos–Dvali (ADD) model, ordinary matter, light and every Standard-Model force are trapped on a thin 3-brane, but the graviton is not — it can propagate into n extra spatial dimensions compactified on a size R. Gauss's law then says gravitational field lines spread through the full (3+n)-dimensional bulk near the source, and are squeezed back into just 3 dimensions once they travel farther than R:

V(r) ≈ -(G₄Mm/r)·[1 + n·(R/r)ⁿ]   (leading Kaluza-Klein correction)
r ≫ R:  V → -G₄Mm/r            ordinary 4D Newtonian gravity
r ≪ R:  V → -G_bulk·Mm/r^(n+1)  full (4+n)-dimensional 1/r^(n+1) law

n — how many extra dimensions the graviton can leak into; more dimensions means a steeper short-range law.
R — the size of the compact extra dimensions, rendered as the translucent slab; gravitons that stray farther than R along the bulk axis bounce back, since a compact dimension has nowhere else to go.
Probe distance r — moves the yellow marker along the brane; the readouts show how far the measured force deviates from pure 1/r² Newtonian gravity at that distance.
Emit graviton burst — releases particles from the source in all bulk directions so you can watch flux fill the compact slab near the mass, then thin out to spreading only along the brane once r > R.

This is the real mechanism proposed to explain why gravity is so much weaker than the other three forces (the "hierarchy problem") without any fine-tuning — the true (4+n)-dimensional gravity could be as strong as the other forces, just diluted by leaking into a large bulk. Sub-millimetre torsion-balance experiments (Eöt-Wash) test exactly this deviation from 1/r².

3-brane (our space) Probe / graviton flux Source mass

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.