The inverse square law of force tells us that a mass (A) at a distance of radius(r) from mass (D) will experience gravitational (G) and electrical (E) forces that are proportional to 1/r2 (Ref 3, pp.394-398). So for a universe many dimensions larger, this proportionality would simply increase such that in four dimensions G and E would be proportional to 1/r3, in 5 dimensions, to 1/r4 and so on (Ref 3, pp.394-398). Today the race is on to probe distances smaller than a 10th of a millimeter with the aim of detecting any deviation from the inverse square law that might indicate the presence of the additional space dimensions predicted by String theory. As astrophysicists Bernard Carr and Steven Giddings have noted, the spilling over of gravity into adjacent dimensions may provide the avenue through which String theory can truly be tested (Ref 10)
For now, no measurements on gravity have revealed any deviation from the inverse square law. But the Large Hadron Particle Collider, scheduled for completion in 2009, may change this (Ref 10). If the gravitational force really is much stronger than we observe in our three dimensional space and it is leaking out into adjacent dimensions of space as predicted, the production of tiny black holes- objects whose immense gravitational hold trap anything including light- would require much smaller amounts of energy and matter. Such a scenario would be achievable through the high-energy particle collisions that the Large Hadron Collider will be capable of (Ref 10). While Hadron has recently suffered some major technical difficulties (Ref 11) it promises much when it is finally up and running. If the planned experiments do provide evidence for gravitational spilling, we may be one step closer to achieving the String Theorists' dream of unification.
Big physics could end up putting physicists out of a job?
Here is a video about the Collider: