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. The top panel is a 2D slice through one such extra dimension (vertical axis) and distance along the brane (horizontal axis): drag to pan it, scroll to zoom. Gauss's law says field lines spread through the full (3+n)-dimensional bulk near the source, then get 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 to the potential)
F(r) = -dV/dr = (G₄Mm/r²)·[1 + n(n+1)·(R/r)ⁿ] (force ratio — see note below)
r ≫ R: F → G₄Mm/r² ordinary 4D Newtonian gravity
r ≪ R: F → G_bulk·Mm/r^(n+2) full (4+n)-dimensional 1/r^(n+2) force law
Note: differentiating the potential's own (R/r)ⁿ term picks up an extra factor of (n+1) from the power rule (d/dr[r⁻⁽ⁿ⁺¹⁾] ∝ (n+1)r⁻⁽ⁿ⁺²⁾), so the force-ratio and the local-exponent readouts both carry an n(n+1) coefficient rather than a bare n — otherwise the two readouts would silently disagree with each other and with the stated potential.
- 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 band; 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, and the lower panel plots the same ratio on log-log axes with your probe marked on the curve.
- Emit graviton burst — releases particles from the source in all bulk directions so you can watch flux fill the compact band 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.