Just noticed this part of this post.
WRONG
All our physics still work perfectly fine in four dimensional space. A 4-sphere colliding with another 4-sphere or the gravity coming off of them can be represented with the same equations, we just have to use 4D vectors and rotation instead of 3D vectors and rotation.
Xalos, let me explain to you why you can't represent the Klein bottle in 3d, and that will also apply to why our physics would no longer work in 4-d.
The Klein bottle, a real one, has no self-intersection. If you represent it in 3d, no matter how you do it, there will always be a self-intersection.
Why? Because you can't represent an object of dimension n in any lower dimension without forming some sort of contradiction.
For example, take a 2d square. Now, take that and make it 3d. (ie coordinates 1,2 would become 1,2,0)
But, there's a contradiction!
The 3d square is infinitely thin! It has no depth! None! That's not physically possible!
See? Because of this, yes our 3-d physics equations may be right, but they cannot function properly in the next dimension without having some sort of breaking point.