# Curved space (gravity)

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I find this hard to understand, what is the space curving into?

How can space be curved and yet appear flat?

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I find this hard to understand, what is the space curving into?

It's spacetime which is curved - the curvature of time is just as important. It doesn't actually curve "into" anything. The curvature of General Relativity is what is known as "intrinsic curvature," which means that it doesn't rely on being embedded in a higher dimensional space.

How can space be curved and yet appear flat?

Why do you think it appears flat? What would you expect spacetime curvature to "look" like?

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How can space be curved and yet appear flat?

It's because everything you see, ie. light, will follow the curvature of spacetime. So given a curved path of light (a geodesic) between you and some distant source, any signal sent to you from anywhere along that curved path will follow the same path and appear to come from the same direction (thus appearing as a straight line).

Edited by md65536
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I find this hard to understand, what is the space curving into?

How can space be curved and yet appear flat?

Those are just primitive computer models of it's mathematics. In reality its more complex and more about how it get's stretched or bunched, and not how it penetrates itself into a tube shape.

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Is rarefaction and compression of space-time in fact a proper way of looking at this? I seem to be off on a few of my assumptions about relativity, and the fact that these terms are never used makes me ask the question.

Heads up to any that care, it seems that 2nd year physics: relativity and quantum is covered at an introductory level in "Physics for Scientists and Engineers." Giancoli 4th Edition Vol 3. I know I have had a hell of a time finding the appropriate starting point and I am pretty sure this is it . . . after fifteen years of looking--I'm slow! I have volume 1 and will be getting the other two for subsequent courses. The first is just fine for what it does, teaching physics and all.

Edited by Xittenn
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Is rarefaction and compression of space-time in fact a proper way of looking at this? I seem to be off on a few of my assumptions about relativity, and the fact that these terms are never used makes me ask the question.

Heads up to any that care, it seems that 2nd year physics: relativity and quantum is covered at an introductory level in "Physics for Scientists and Engineers." Giancoli 4th Edition Vol 3. I know I have had a hell of a time finding the appropriate starting point and I am pretty sure this is it . . . after fifteen years of looking--I'm slow! I have volume 1 and will be getting the other two for subsequent courses. The first is just fine for what it does, teaching physics and all.

We don't completely know what the fabric of spacetime is exactly, but there's mathematical predictions of things like string theory and calabi yao manifolds on what comprises it.

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We don't completely know what the fabric of spacetime is exactly, but there's mathematical predictions of things like string theory and calabi yao manifolds on what comprises it.

I really don't understand how this works, watch the ball . . .

proposition: Space time is curved.

Response: What does it mean to be curved? Can we use the terms rarefied and condensed instead?

Counter-response: We don't know enough to answer that question . . . . .

My response: Then why are we calling it curved in the first place?

I mean to me this is a graphing statement, space-time sits on a gradient or on a curve with respect to distance and in proportion to a gravitational force.

Honestly for me these are too many words and not enough numbers anyway. Most everything I've read on the subject has put it in words and honestly even if I get the picture the value of the content is almost nil. I hope the text I mentioned solves this!

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We don't completely know what the fabric of spacetime is exactly, but there's mathematical predictions of things like string theory and calabi yao manifolds on what comprises it.

This is unrelated nonsense.

I really don't understand how this works, watch the ball . . .

proposition: Space time is curved.

Response: What does it mean to be curved? Can we use the terms rarefied and condensed instead?

Counter-response: We don't know enough to answer that question . . . . .

My response: Then why are we calling it curved in the first place?

I mean to me this is a graphing statement, space-time sits on a gradient or on a curve with respect to distance and in proportion to a gravitational force.

Honestly for me these are too many words and not enough numbers anyway. Most everything I've read on the subject has put it in words and honestly even if I get the picture the value of the content is almost nil. I hope the text I mentioned solves this!

I don't know whether or not you could model gravity as rarefaction & compression of spacetime. I also don't know whether or not it would be very useful to think about it in this way. For example, would you consider the surface of a sphere to be a rarefied/contracted flat 2-d space?

Curvature in differential geometry is just a measure of how much a vector changes when you parallel transport it. Parallel transporting a vector v means moving it an infinitesimal distance ds so that the vector locally does not change, or dv/ds=0. When you do this over a global region of space the vector may change. This means that parallel lines, when continued in a curved space, do not remain parallel.

Below is a picture of a vector being parallel transported around a closed loop on the surface of a sphere. Notice how the vector has changed from when it returns to its initial location. This means that the surface of a sphere is a curved space.

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I will take some time to try and understand this, thank you for your feedback!

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I take it back Gioncoli's book will not cover curvature, sorry if I inconvenienced anybody!

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Here's how I think it goes. I know this explanation is not rigorous, but I think it gives the gist of what is going on.

Per general relativity, spacetime curvature is the warping or change in spacetime due to the presence of mass/energy. The mass and energy of the Sun, for example, warps both time and space in its vicinity. This warping is what makes planets orbit the Sun. So so-called spacetime curvature is gravity itself.

The word "curvature" is a mathematical term. I don't think it should be taken literally as something curving. In gr, it refers to the generalized spacetime interval (the metric) changing globally in a gravitational field.

Space warp (distance change): Imagine two points in empty space with a certain distance between them. Now place the Sun between the two points. Now, as seen from far away, the distance between the same two points is greater! One can think of this as space having been stretched by the mass/energy of the Sun.

Time warp (time interval change): Imagine a clock in empty space. It runs at a certain rate. Now place the same clock near the Sun. It now runs slower. Time is slowed by the mass/energy of the Sun.

Taken together and represented mathematically by the generalized spacetime interval, this slowing of time and stretching of space in the Sun's presence, this warping of spacetime is spacetime curvature is gravity.

I hope this helps.I welcome comments and corrections.

Edited by IM Egdall
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• 3 weeks later...

Any body travelling through a force field on a non-radial course will be subject to different strengths of that force accross the diameter of the body, on an axis that lies on the field radial. This difference in force causes a difference in drag on opposite sides of the body causing the body to take a curved path. It will also cause the body to spin; the degree of both curvature and spin is determined by the relativity of mass, force and speed.

All points in space are within a G field.

Edited by elas
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I find this hard to understand, what is the space curving into?

How can space be curved and yet appear flat?

Read http://www.eftaylor.com/pub/chapter2.pdf and you'll know what spacetime curvature is.

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The mass and energy of the Sun, for example, warps both time and space in its vicinity.

The phrase "time is warped" or anything similar to it is incorect. A manifold must have more than one dimension for it to be warped.

The physics literature has a lot of idosynchraties in it on points like that so many years ago I got tired of repeating myself so I wrote a paper on it. It is at http://xxx.lanl.gov/abs/physics/0204044 for those who are so inclined to learn about the subject of spacetime curvature in general relativity and its relationship to gravity.

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The phrase "time is warped" or anything similar to it is incorect. A manifold must have more than one dimension for it to be warped.

This seems like more of a problem of language than physics. "Curved time" usually refers to when |g00|≠1 in a diagonal metric (though this doesn't necessarily imply Rabcd=0).

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This seems like more of a problem of language than physics.

I disagree. The purpose of my post was to try to curb the usage of that phrase since it's patently incorrect.

"Curved time" usually refers to when |g00|≠1 in a diagonal metric (though this doesn't necessarily imply Rabcd=0).

Thank you but I understand quite well what people mean when they use the phrase "curved spacetime". Otherwise I wouldn't comment on it.

This seems like more of a problem of language than physics. "Curved time" usually refers to when |g00|≠1 in a diagonal metric (though this doesn't necessarily imply Rabcd=0).

Do you know of any GR text which uses the term "curved time" or "time is curved when" or any variant thereof?

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Do you know of any GR text which uses the term "curved time" or "time is curved when" or any variant thereof?

I've seen it used before, yes. Off the top of my head, Schutz's Gravity from the Ground Up comes to mind (if you consider it a GR text - it's not exactly rigorous).

http://www.gravityfromthegroundup.org/pdf/timecurves.pdf

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I've seen it used before, yes. Off the top of my head, Schutz's Gravity from the Ground Up comes to mind (if you consider it a GR text - it's not exactly rigorous).

http://www.gravityfr.../timecurves.pdf

Hmmm! Interesting. This is one of my favorite texts for gravity. I didn't realize he used this terminology. I guess I should learn the symantics of this terminology regardless of whether I think it's logical or not.

Thanks for the reference.

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