PatrickPowers wrote:I don't know. I've long wondered whether having an inverse-square law would allow you to have a perpetual motion machine or some other non-obvious problem.
Here in 3D an inverse square law means any complete surface around the source of gravity has the same potential energy. In 4D that's no longer true. The potential energy around the surface increases dramatically the further away you go. That seems like you are getting something for nothing, but any specific problem is beyond me. It makes gravitons impossible but no one has proved they exist.
steelpillow wrote:Assuming a basic Newtonian model, a 4D universe would have an inverse-cube law.
Not even an inverse square law could keep it stable; the 4th dimension means that orbital energy can shuffle between pairs of dimensions (planes), so that no stable orbital plane can exist. So you'd need to postulate some other, unknown law of 4D physics to keep things stable.
quickfur wrote:Yeah my understanding was that an inverse square law would work in any dimension as far as stable orbits are concerned, because as far as a 2-body problem is concerned, the results would be independent of the dimension of the ambient space; the two orbiting bodies only "know" the plane that they are orbiting each other in. However, there may be other unintended consequences.
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