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So, hi. I am taking a course (astrophysics) for which we are required to write a paper (very freely, about 5 pages, no real limitations) about a subject related to, well, astrophysics. I chose gravitation because I guess I have always been fascinated by it.

I realized rather quickly that this would take me into general relativity, but it took me a while to realize just how big of a problem this would be to someone with my limited mathematical background. I know calc, trig, geometry etc and some very limited linear algebra, but it's not viable for me to learn tensor calculus or more advanced lin. alg. right now. Instead, I would like a more conceptual understanding of the subject. I have had troubles, however, finding anything that isn't either so dumbed down so as to be simply trivia, or so full of mathematical jargon that I can't understand what is going on.

My current understanding of the subject is this: I understand the gravitation/acceleration equivalence, and additionally I understand that in GR gravitation is not a force but instead accredited to the curvature of spacetime, meaning that particles are actually moving in straight lines even though they appear curved in 3D space. "Curvature of spacetime tells matter how to move, matter tells spacetime how to curve". I understand that in dealing with GR one uses very small scales, and everything is local, since only locally is flat timespace a good approximation for curved timespace, and that the math for vectors and coordinates and everything becomes very complicated.

As you can see, my current understanding is sketchy and shaky (I'm hoping I didn't get anything wrong; if I did, please correct me) and easily summarized. I have a few specific questions and a request for a general explanation of the subject suited to my level; I'm not an idiot interested in trivia or in repeating big words like a parrot, but my mathematical background is not enough to, at this point, tackle the tensor calculus and stuff.

My questions are these:

1) Timespace is supposedly "curved". A 2D surface can only be curved in 3 dimensions; spacetime is 4 dimensions and should, then, only be "curved" in 5D. Yet, in the paper by Baez/Bunn (http://arxiv.org/PS_cache/gr-qc/pdf/0103/0103044v5.pdf" [Broken]), they said that we need not involve higher dimensions; indeed, that the tensor calculus took care of it without going to higher dimensions. So how is it curved then? What am I not getting?

2) Is gravitation a force or not? How could it be, if the particles are just going in the straightest possible line and are not "attracted" to each other? But if it is not, then why are we trying to unify gravitation with the other forces and trying to find force carriers for it and stuff?

3) How does this "straight line" constitute acceleration? The particle should move with constant velocity anyway, should it not, and only the direction change?

4) If one walks in a perceived straight line on the 2D surface of a ball, the line is straight in 2D but actually curved in 3D. Yet, in GR, the line which is straight in the higher dimension (4D) seems curved in the lower (3D). While I intuitively feel that if straight in lower dimension can mean curved in higher, then the opposite should also be possible, I can't think of a good example offhand. Am I misunderstanding this and should be looking at it in a "locally straight" kind of way instead?

5) Does anyone know the string theory take on gravitation? (this doesn't belong here, I know, but even so).

Thank you very much for your time and patience. ^^

/Anna

I realized rather quickly that this would take me into general relativity, but it took me a while to realize just how big of a problem this would be to someone with my limited mathematical background. I know calc, trig, geometry etc and some very limited linear algebra, but it's not viable for me to learn tensor calculus or more advanced lin. alg. right now. Instead, I would like a more conceptual understanding of the subject. I have had troubles, however, finding anything that isn't either so dumbed down so as to be simply trivia, or so full of mathematical jargon that I can't understand what is going on.

My current understanding of the subject is this: I understand the gravitation/acceleration equivalence, and additionally I understand that in GR gravitation is not a force but instead accredited to the curvature of spacetime, meaning that particles are actually moving in straight lines even though they appear curved in 3D space. "Curvature of spacetime tells matter how to move, matter tells spacetime how to curve". I understand that in dealing with GR one uses very small scales, and everything is local, since only locally is flat timespace a good approximation for curved timespace, and that the math for vectors and coordinates and everything becomes very complicated.

As you can see, my current understanding is sketchy and shaky (I'm hoping I didn't get anything wrong; if I did, please correct me) and easily summarized. I have a few specific questions and a request for a general explanation of the subject suited to my level; I'm not an idiot interested in trivia or in repeating big words like a parrot, but my mathematical background is not enough to, at this point, tackle the tensor calculus and stuff.

My questions are these:

1) Timespace is supposedly "curved". A 2D surface can only be curved in 3 dimensions; spacetime is 4 dimensions and should, then, only be "curved" in 5D. Yet, in the paper by Baez/Bunn (http://arxiv.org/PS_cache/gr-qc/pdf/0103/0103044v5.pdf" [Broken]), they said that we need not involve higher dimensions; indeed, that the tensor calculus took care of it without going to higher dimensions. So how is it curved then? What am I not getting?

2) Is gravitation a force or not? How could it be, if the particles are just going in the straightest possible line and are not "attracted" to each other? But if it is not, then why are we trying to unify gravitation with the other forces and trying to find force carriers for it and stuff?

3) How does this "straight line" constitute acceleration? The particle should move with constant velocity anyway, should it not, and only the direction change?

4) If one walks in a perceived straight line on the 2D surface of a ball, the line is straight in 2D but actually curved in 3D. Yet, in GR, the line which is straight in the higher dimension (4D) seems curved in the lower (3D). While I intuitively feel that if straight in lower dimension can mean curved in higher, then the opposite should also be possible, I can't think of a good example offhand. Am I misunderstanding this and should be looking at it in a "locally straight" kind of way instead?

5) Does anyone know the string theory take on gravitation? (this doesn't belong here, I know, but even so).

Thank you very much for your time and patience. ^^

/Anna

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