Question that I was pondering earlier today...

From everything i know (which is very little and could be wrong) gravity whether thought of from a Newtonian perspective or an Einsteinian perspective has no limit to its influence, it simply decreases relative to the square of the distance. Now, if we use the model of space time that everyone loves to use (me too...though im sure its far to simple to be correct) the rubber sheet, this makes sense since we can see the curvature of the sheet would make an 1/r^2 relationship (right?) However, what if the sheet were no longer flat, but a sphere (or even a torus). This would no longer work. The influence of a mass would only extend so far before the curvature of the universe prevented it from extending further. For instance, no matter what the mass of some object in the top hemisphere was, an object on the bottom hemisphere would feel no effect from it.

Does this make sense at all? Just a thought. I could throw together a 3d model if it doesn't make sense as I've writen it. My guess as to the reason this doesn't work is because the rubber sheet model is too simple a way to look at spacetime curvature and is only a good way to introduce someone to it.

-AntonK

" The influence of a mass would only extend so far before the curvature of the universe prevented it from extending further. "

What makes you think that? there is no reason why the change in curvature caused by the mass does not extend "all the way around".

Of course, if you mean precisely a sphere, then, yes, the exact opposite point would feel no "gravitational" force because of the symmetry (it is equally distant from the mass in all directions) but that is not saying that the "curvature prevents it from extending farther".

You may be thinking that the curvature of the earth prevents "line of sight" communication. That's true but that's not relevant here. The influence of the mass is IN the universe, just as a road is "in" the earth (unlike a light beam). The curvature of the earth wouldn't prevent a road from extending to the opposite side.

HallsofIvy,
good reply. I agree. Also, though space might not be completely "flat" (in 3D), it has been shown to be nearly flat. Therefore, gravity acts as though it at least is on a nearly flat sheet as best we can determine.