General Relativity, Gravity, Help!!

I'm a little confused with the whole idea of matter warping the 'fabric of space.' I'm a junior in high school and I'm just in Algebra 2, so a strict mathematical definition isn't exactly what I'm looking for. In fact, the only knowledge I have about this is based on illustration and brief description. There are two main things I'm confused about.The Paper ModelIt seems like a lot of the illustrations I see for distorted space are shown as warped pieces of paper, or malleable surfaces. I was watching that thing on string theory via the NOVA website the other night and it used the image of the sun as a heavy ball on a trampoline. This confused me because it illustrates space as sitting on one invisible surface. Are illustrations such as these used to show only one of the infinite amount of planes affected by the matter depicted? If so, that makes sense. But that brings me to my next question...'In' or 'Out'?Here I have two seemingly contradictory images of how matter affects the space around it. The first is a very common illustration and one I already mentioned, the ball on a trampoline illustration. To me, this is showing matter stretching space out around it (the lines curving under the ball to slide around it).I have a different picture in a book, though. I'm sorry that I can't find anything online resembling it, but it's an image in book called Big Bang: The Story of the Universe by Heather Couper and Niegel Henbest (page 39). It's an illustrated, layman's guide to the Big Bang. Anyway, for those who don't have (access to) it, it shows an illustration of a cube with a massive object in the middle. The object seems to distort the cube by sucking in the space around it (obviously, the space closest to the object is more distorted and the cube shape is gradually reformed as you move away from the object), whereas in the other drawing, the object seemed to distort space in the opposite direction.The cube model makes more sense to me, but considering the fact that both models seem to be valid/used a lot, I'm assuming that they really are compatible and that the problem is just my understanding of them.NOTE: If you'd prefer to just explain the subject in general without directly addressing my specific questions, that's fine (but I'd appreciate it if the questions were answered somewhere in the explanation). Suggested reading for someone at my level would be nice, too.Thanks!

Both of those are analogies. Neither of them are true. They're both equally right.Basically there's no such thing as the "force" of gravity. There's only straight-line motion through warped space. Because we're in space, and light follows the warps, we don't see them, and the paths of objects appear to bend.In what direction does space warp? Not in a direction we can percieve. That's why we can only see it when something travels through the warped space. Basically the space (and time, they're the same) stretches into another dimension that we can't percieve.Does that help? The reason there's math for this is because the math is the only way you can accurately understand it. The analogies help explain but they're ultimately only approximations of what's going on.

I just wanted to complement your writing ability. Clear, well-organized, well-expressed. Next time some youngster writes, "hey, dont be to harsh or criticle, im just in high school," I'm going to point him to your post.--Percy

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This confused me because it illustrates space as sitting on one invisible surface. Are illustrations such as these used to show only one of the infinite amount of planes affected by the matter depicted? If so, that makes sense. But that brings me to my next question...

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You can think of a volume as containing an infinite number of 2D planes. You've obviously noticed that the analogy is strictly 2 dimensional, with the sun and planet only being able to move along an X,Y axis. So long as you keep as a 2D analogy, you should run into problems. Asking what direction space is curving in does not work, much like how the conmcept of up and down would be unimaginable to a 2D stick person. Since humans can only see 2 dimensional planes, we cannot even begin to imagine what a curved volume would look like.

Thanks for the compliment, Percipient!All right. So basically, an accurate illustration of the way space is warped is impossible, because it exceeds the dimensions that we as humans commonly interact with. And the only way to really understand it is to understand the mathematical concepts involved.Is the concept similar to that of infinity? An illustration or tangible example is impossible to accurately provide/comprehend, but it can be comprehended mathematically.

• As to your first part of your question. Yes, that is correct. Because in theory the universe has been estimated to have 12 dimensions total (the most common) but some radical theorists even go to the limit of saying 20.
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• Infinity could be expressed in a way to this concept but a new theory is that the universe is a dodecahedron and layered with steps, therefore eliminating the possibility of infinity. I'm not sure if I agree with this but it would make sense as for universal curvature.

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Basically there's no such thing as the "force" of gravity. There's only straight-line motion through warped space.

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So, what we perceive as gravity is really just the effects of warped space? How do gravitons fit into this picture?[This message has been edited by Tsegamla, 11-04-2003]

Gravitons don't. That's the big problem of Physics.Warped space comes from General Relativity, gravitons come from Quantum Mechanics, the two don't play nice together.

On that NOVA string theory program, they said that string theory was supposed to 'bridge the gap' between Quantum Mechanics and concepts like General Relativity. They made gravitons seem crucial to string theory, so why don't they agree?

I think it's something like this - every particle in the universe is attracted to every other one. That means that every particle is constantly trading gravitons with every other particle in the universe. That's a lot of particles. Of course, the gravitons themselves are particles, so they're also exhcanging gravitons. Eventually you have an infinite number of gravitons, which, if they have mass, collapses the universe into a singularity instantly. If they don't have mass, they're a pretty weird particle, and it wouldn't be clear how they could do their job at all.Or something like that. I'm sure I'm wrong somewhere, there.

Gravitons do work in String Theory, that's why people are excited about String Theory; because it looks like it can unify QM and GR. As I understand it however, String Theory is by no means 'finished', and there is no experimental support for the Theory as yet.

String theory, and its latest exponent M-wave theory, are indeed the "hot" thing, but as I understand it we need a particle accelerator the size of the solar system to confirm the predictions it makes experimentally. There are some indirect things we might observe but even that needs substantially higher energy accelerators.On the issue of gravitons, I think they are indeed supposed to be massless, much like photons. Not sure how that works exactly though.To get back to the original question, I have always found the analogy of the plane flying over a hilly area useful. On the 2-dimensional surface of the hills, the shadow of the plane seems to follow a very curved path. Through the 3-dimensional space it is following a straight line however.

JIM writes:

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Because in theory the universe has been estimated to have 12 dimensions total (the most common)

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Just because I'm being picky:Not twelve. Eleven.The common model from M-theory is that the universe has 11 dimensions...10 spatial and 1 temporal. There are the three dimensions we commonly deal with, six curled up dimensions which strings need if they are going to do what we want them to do, and a larger, cosmic dimension for M-theory to work in.This 11th dimension is what helps to explain why gravity is such a weak force compared to the other three. Previous models of string theory essentially had all strings as being closed loops. M-theory has most strings being non-loops where the ends are connected to the brane in which we exist, but gravity is a closed loop string. Thus, the other three forces are essentially trapped (for lack of a better term on my part) in this brane but gravitons can leave the brane.------------------
Rrhain
WWJD? JWRTFM!

Tsegamla writes:

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The cube model makes more sense to me, but considering the fact that both models seem to be valid/used a lot, I'm assuming that they really are compatible and that the problem is just my understanding of them.

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If I understand your description of the cube picture, these two representations are essentially identical. The trampoline model is sort of a two-dimensional way of looking at it while the cube method is a more three-dimensional model.The trampoline model, too, is more amenable to actual construction. That is, you can actually take a sheet of rubber, stretch it, place a heavy ball in it, and then roll a light ball along it and watch how the motion of the light ball curves around the heavy ball.To make the cube model, you'd have to find some way to fill the cube with a stretchy material and then uniformly pull all of it towards the center...and then find some way to move another object through all this material in order to see it curve around the point of pulling...not exactly an easy thing to do.The problem with the trampoline model is that it requires a third dimension to have work...and it also requires gravity. The trampoline model makes it look like space is curving into some other dimension and that some force is pulling it into that dimension when actual gravity doesn't work like that. It curves in on itself like the cube model.Does that help?------------------
Rrhain
WWJD? JWRTFM!

crashfrog writes:

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Of course, the gravitons themselves are particles

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Incorrect.Gravitons are strings. Strings are not particles. The problem with the standard model of quantum mechanics is that it defined things in terms of particles. At first, things like electrons and protons were particles. Then we discovered quarks and those were considered particles. But that didn't quite solve the problems. String theory does away with particles. At the very least, it claims that things like quarks are made up of strings which aren't particles.

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so they're also exhcanging gravitons.

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Incorrect.Gravitons do not emit gravitons.

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If they don't have mass, they're a pretty weird particle, and it wouldn't be clear how they could do their job at all.

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Since they're not particles at all....------------------
Rrhain
WWJD? JWRTFM!