I admit to not getting this point, so would be grateful for help.hackenslash said:If you take photons as an analogy (they also obey an inverse-square law, as any photographer will tell you), you can see how this works. Photons travel in straight lines, and radiate out from a centre. In a one-dimensional universe, you would receive the same number of photons from a source, regardless of how much you were separated from that course, because there is only line they can travel. In a two-dimensional universe, the light falls off in direct proportion to separation, because the lines they travel are uniformly spread on a circle, and the circumference of the circle is proportional to its radius. In a three-dimensional universe, the fall-off follows an inverse-square law because again, the lines travelled are uniformly spread over the surface of a sphere whose area is proportional to the radius. In a universe with four spatial dimensions, the fall-off would be inversely proportional to the cube of the distance, for exactly the same reasons.
The number of photons emitted from a single source will be different to the number received in any space greater than one dimension - I get that bit (or, possibly, I am mistaken?)
But how will the number of photons measured at any single point on a sphere be different from the number emitted from that singe source if light travels in a straight line? As I understand it, at any equidistant point on a sphere the measured number of photons received for any similar period of time would be roughly equal. What I do not understand is what you mean when you say " the light falls off in direct proportion to separation".