zeromodz said:
From what I know, in 2 dimensions gravity works as 1 / R, 3 dimensions is 1 / R^2, and in 4 dimensions 1 / R^3
To discuss force laws in general let me first introduce the concept of 'flux'.
The word 'flux' comes from an analogy with the physics of fluids, so will use fluid as an example. Imagine a pool of fluid, and a tube extends into the pool, giving off a steady influx. Now surround the inlet with, say, a sphere that is made of a material that let's the fluid pass through. Clearly, the amount of fluid passing through the overall surface of the sphere is the amount that comes out of the inlet tube.
Surround with a yet bigger sphere: the same amount of fluid passes through the second sphere's surface. The surface area of a sphere is proportional to the
square of the radius. This means that the velocity of individual fluid particles is inversely proportional to the square of the distance to the source.
Definition of 'flux':
In three dimensions of space an inverse square law has the following property: the
flux of the force-field is the same at every distance to the source of the field.
(This 'flux' concept does not mean that gravity actually involves fluid flow, the analogy should not be taken literally.)
Now, one supposition (among other suppositions) is that whatever the number of spatial dimensions you want the force law to come out as a 'same
flux at every distance' force.
Following that supposition you get 1/R for two spatial dimensions, and 1/R^3 for 4 spatial dimensions.
If you have just 1 spatial dimension, then 'same flux at every distance' means the same force at every distance.