That's an interesting idea. In this case, though, I don't think it does. In fact, many radial forces don't scale with the square law--the weak and strong nuclea

That's an interesting idea. In this case, though, I don't think it does. In fact, many radial forces don't scale with the square law--the weak and strong nuclear forces, for example. The fourth-power scaling in the parallel plates example is strictly geometry-dependent, and doesn't apply in other circumstances. I do wonder, however, if power-law forces in general reflect some measure of the "dimension" in which the system's phase space is embedded. I vaguely remember that the zeta regularization scheme is in fact tied to the dimensionality of the quantum algebra for the system... but that's higher math than I can handle. :)