Gravity and Electromagnetism obey the inverse-square law because the surface area of a 3-dimensional sphere is proportional to 1/r-squared, correct? (The energy is propagating away from its source along the surface of an imaginary sphere.)
If there were any forces that weaken according to an inverse-cube or inverse-4th-power law, then they would propagate away from their source on the “surface” of an imaginary higher-dimensional hypersphere, right?
My question is: Don’t the strong and weak nuclear forces weaken with distance along an inverse-cube or inverse-4th law, or something like that? If so, does that mean that those forces are expanding into other dimensions along the “surface” of imaginary higher-dimensional hyperspheres?*
*I got this idea from the fact that the two nuclear forces only have significant effect at very close distances. Thus, I assumed they dropped off very fast. So, I assumed that they must be obeying something stronger than an inverse-square law. Yes, my question is born from a lot of assuming.
Apparently some people in the past have thought yes, others have thought no, and all in all nobody is really working about it because it would take a long time.
There was some evidence awhile back that stated that some of the constants in the universe have changed a tad wee little bit since the big bang, but once again, nobody gave much of a care cuz hey, looong time before anybody notices any real effects.
Bottom-line: nope. The weak force falls off as an exponential, while the strong force increases roughly linearly with distance. The complication with the latter is that we primarily observe it’s residual effects - but they’re exponential as well.
Absolutely off the cuff, a textbook cite for the strong force being primarily linear would be equation (1.20) from Collins, Martin and Squires Particle Physics and Cosmology (Wiley, 1989). As for the residual effect being exponential, I suppose that’s orignally Yukawa’s Proc.Phys.Math.Soc.Japan.** 17**, 48, 1935. For the weak interaction, you want Weinberg or Salam. Or the experimental paper on W and Z of Banner et al, either of the G. Arnison et al papers or P. Bagnaiaet al, all from 1983.
There have already been some good responses, but I want to add that the inverse-square law only holds if the force carriers have infinite range (true, as far as we know, for the photon and graviton). The weak force decays exponentially because the W and Z bosons (the carriers of the weak force) have short lifetimes. The behavior of the strong force is a little more difficult to explain because the force carriers (the gluons) interact strongly with each other as well as with the quarks.
This idea has been considered recently by some theorists in The Field Formerly Known As String Theory. In some theories, the three forces other than gravity are confined to a three-dimensional surface, while gravity is not. If there are extra dimensions, then gravity would not be inverse-square at short ranges. This is ruled out by experiments down to about the millimeter scale, but it’s pretty tough to do precision tests of gravity at short ranges, so it isn’t ruled out below this level. So there’s currently no evidence to support this idea, either.
