Ah, but that is the point isn't it ? If physical reality was actually more than 3 dimensions, the math for 3 spatial dimensions would still exist and be exact in itself ? Because your physical reality was different you just wouldn't apply it !Bade wrote:In the context of 1/r potential discussion above, if there are extra dimensions indeed, one can see already that simply assuming 3 spatial dimensions and doing Gauss's theorem in this space will only give an incomplete solution to the true nature of the potential.
For instance, using circulation theory, the flow around a cylinder /Lifting line is Exactly described mathematically . Now if you apply a Joukowski transform with a Kutta condition, you describe an airfoil! Now instead of air/water/ fluids described using potential flow , there was something else in say some alternate universe, this particular math and the phenomeno that can be described using this wont work, but that doesn't mean it is "wrong" or inexact in itself. It is just that it doesn't apply.
IMHO, it is something like this. If you solve a quadratic equation in highschool, you are told to ignore "results" that seem "nonsensical" /which are not what we are looking for , given the "problem". Not that the result was wrong, but just that we really dont want it in our physical experience. How about "imaginary" numbers, you cant have anything "imaginary" in the physical world. But you use that in a lot of physics /engg/whatever, because the math describes a lot of it in the physical world pretty well.