Pursuant to the preivous post on the pythagoras theorem, we continue asking ‘why’, in this series of posts. I attempt to share my feeble understanding of why electric forces and gravitational forces closely obey the inverse square law in classical physics.
I like the graivational wave interpretation. Simply put, this pins the cause on the world being three dimensional (disregarding sting theory). The power of any constant flux or flow outward from a central source (even a point source), will dissipate proportional to the area that it is spreading out over. For instance, a sound wave from a speaker suspended high up in the air would travel in all directions uniformly. At any given time, the wavefront would be a set distance away from the source. The distance itself would depend on the speed of sound. But the key point is that it would spread out in a sphere of radius equal to that distance. So the intensity of the sound energy drops proportional to the area of a sphere, whose radius is the distance from the source. Since the area of the sphere depends on the square of the radius, the wave is divided or distributed by a factor proportional to the square of that distance, leading to the inverse square law.
Cars and Physics 