What are the implications of gravity and other dimensions in our universe?

[Alkatran]

Alright, we all know that in our universe, we divide by distance squared to get gravity. I always figured this was because gravity spreads itself out on a sphere, and that if out universe had 2 spatial dimensions, it would only be divided by the distance (not squared).

But I had a thought yesterday. If we had only 1 spatial dimension, gravity would be the same everywhere. It's easy to imagine as particles being launched in either direction left or direction right. They never need to spread out to cover more area so the force is always the same.

But here's where the problem comes in. If we view gravity as curvature in space time, a particle being placed in a one dimensional universe would have the effect of curving the ENTIRE THING (at the speed of gravity). In fact, lowering the enter thing (see bowling ball on rubber sheet) would put everything back to the same level.


In fact, the only way an increase in gravity could continue is if the point with matter on it continued to drop forever. You would end up with a univer made up if two hills (assuming there's only 1 particle). like so: \./

The other possibility is that you divide by distance squared in a one dimensional universe as well (visualize a bowling ball sitting on a string). This would mean that the exponent on distance is not always equal to the number of dimensions -1.

The last possibility, of course, is that gravity can't exist in a one dimensional universe. The curvature created by matter would just cancel itself out everywhere and they'd be a bit "lower" (in hyperspace) than the norm.


So, this means that, if we view gravity as a curvature, either the curvature of gravity is constantly increasing (everywhere uniformely), that the d^2 in the gravity equation could actually be d^2.001, or that gravity has no effect on a one dimensional universe.

I'd like to hear people's thoughts on this.

 

[Antonio Lao]

A fundamental force is always a constant in 1D. In 2D, inverse distance. In 3D, inverse square distance. The 1D and 2D forces still not completely understood by experiments. But they might be the electromagnetic force and weak nuclear force, respectively. The 3D force could also be the strong nuclear force. The 3D force of Newton's universal law of gravitation has been proven down to about a tenth of a millimeter. Any distance less than this, the inverse square law is anybody's guess. The force between zero dimension and 4D is the fifth force with mediator as the Higgs boson. As long as there is a force there is always be a curvature whether in 0D, 1D, 2D, 3D, or 4D. But in 1D, if there are orthogonal forces, the curvatures can be quantized. And when they are quantized, two distinct topologies are formed.