tourmaline said:
Hi there, I have a question about something that has been bothering me for quite some time now: Doesn't the notion of gravity being a curvature (or "warp") in the fabric of the universe created by a body of matter presuppose the idea of an already larger gravitational force/curvature acting upon that matter?
This has been discussed a lot in the relativity forum - basically, the "rubber sheet" analogy is OK, but is weak for the reasons you cite.
There are better analogs out there in GR textbooks, but they aren't as widely popularized. MTW's "Gravitation" has some nice fairly simple anologies, mixed together with some formidable tensor calculus. I'm not aware of any source that presents only the simple anologies without the advanced math, unfortunatly. A brave enough reader could pick up the book, read the simple parts, and ignore the parts that are too advanced (which is most of the book! not that that's a real obstacle).
There are probably better, simpler books, but unfortunately I don't know what they are.
The topic really needs pictures, but I'll do what I can in words. Imagine drawing a space-time diagram of a simple system with one spatial dimension and one time dimension on a flat sheet of paper.
If a horizontal line on the paper represents our observer, who is always at x=0 for all t, a slanted line on the paper represents an observer moving with some velocity 'v'. An observer moving at a velocity 'v' moves in a straight line - so does our observer - and both straight lines follow the rules of Euclidean geometry.
Now, we introuduce curvature into the picture. NOte that we are curving space-time, not just space - an important point, lacking from the usual "rubber sheet" anology.
Imagine drawing the same space-time graph on a curved surface, such as the surfacae of a sphere. One of the problems you will face is that the sphere is finite, while your sheet of paper is infinite. If you can't imagine wrapping an infinite sheet of paper around a sphere in both directions (not possible in 3d, I think it's possible with an additional spatial dimension or two), you might imagine wrapping a strip of paper many times around the equator of the sphere (wrapping it around only in one direction, and limiting the height of the paper). This is possible in 3d. Or you can ignore the problem completely, that's the favorite approach of most texts, because it doesn't really affect the results any.
Now you have to imagine what happens when you draw your space-time diagrams on this curved piece of paper. Objects that follow the straightest possible paths will be following "great circles" rather than straight lines. If you plot the path of an observer moving with a velocity 'v' following such a "straight line", you see an interesting effect. As he moves away from the origin, he reaches a maximum distance, and then starts to move back - because two great circles on a sphere through the same point diverge, but eventually re-converge. This is something that doesn't happen in Euclidean geometry, but it happens in spherical geometry.
A detailed analysis of the situation really requires quite a bit of math, but one finds that drawing a space-time diagram on such a curved sheet of paper is functionally equivalent to saying that there is a "force" between the observer and the moving object. Thus the idea of "force" can be and is replaced with the idea of "curvature".
Some keywords for more reading - this idea is known as "Geodesic deviation", and is a very important part of GR.
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. Ah well, I'm extremely curious about, and interested in, physics. It's just frustrating to want to know everything (especially all of those intriguing symbols which are able to communicate complex ideas so thoroughly and compactly: I'm dying to understand what they all mean...but I guess I'll have to wait for Calc class 
). I have a conceptual physics textbook, and it has a section on Geodesic Deviation, so I'm really glad you pointed me in that direction. Thanks alot!
