# How gravity arises from spacetime curvature?

1. Jun 17, 2004

### weio

Hi there

I've been trying to find out how spacetime curvature actually produce gravity, but all i can find is articles using math, which is far too advanced for me to understand. Can anyone give me a theoretical explanation to how the gravity arise from the spacetime curvature according to the theory of general relativity?

Much appreciated.

weio

2. Jun 17, 2004

### LURCH

Actually, general relativity does not so much propose that gravity is "caused buy" a curvature of space-time. This would be somewhat like stating that waves are caused by Little Hills moving across the surface of water. Rather, it would be more accurate to say that GR and describes gravity as being a curvature of space-time. The actual cause is not known.

Last edited: Jun 17, 2004
3. Jun 18, 2004

### Gza

Maybe i'm off base here, but I do think that GR gives an interpretable cause of gravity. That would be in the form of matter or energy causing the warping of space, thereby giving rise to the phenomenon we call gravity.

4. Jun 18, 2004

### zoobyshoe

I can't make heads or tails of the "warped space-time" explanations either. Space is nothing. How can you warp nothing? Mathematically, I guess.

If I think of space as actually being occupuied by some sort of aether, then I can start to visualize this being "warped" but I have trouble still, since the earth is a sphere and I can't visualize a spherical "warp".

The notion of trying to go straight but ending up going in a curved path, more or less makes sence by analogy to many things, but that's is the only aspect of these descriptions that I can get a handle on.

5. Jun 18, 2004

### Gza

You're not alone. I'd be mighty suspicious of anyone who told me they had a solid physical grasp on these concepts. Einstein couldn't even make the leap and he came up with this stuff!

6. Jun 18, 2004

### zeta101

zoobyshoe, in my opinion (its my opinion since i havent actually ever read this anywhere) space is not nothing, or rather space-time is not nothing. There is something to space-time, something that allows it to be warped. I'm sure you've seen the popular digram of a bowling ball (which represents, say a planet, or a star like our sun) placed on a flat stretched rubber sheet, the bowling ball causes the sheet to warp under its weight.

Obviously this is a 'messy' analogy, but try not to dwell on that. Picture how a rubber sheet would warp in the presence of this bowling ball...this is in TWO dimensions, now try and picture this in 3D, its hard, like picturing many things in 3D. But normalling if you see the 2D case you can accept the 3D case, and just accept its hard for you to visualise.

Also, for weio, I'm sure there is an answer to your question, but it might not be fundemental enough to satisfy you. Having not studied GR yet I can't help you, but you might want to think about the analogy I gave for zoobyshoe about the bowling ball on the rubber sheet, since anything placed on the sheet, like another ball will roll towards the bowling ball due to the curvature, but again, this is a very messy analogy, its not a DIRECT analogy, but its some kind of starting point i suppose.

Last edited: Jun 18, 2004
7. Jun 18, 2004

### NateTG

What happens is that in non-euclidean geometries, the notion of 'straight line' gets a bit wierd.

Imagine an ant walking along the surface of a cylinder. Even though the ant is walking along a 'locally straight line' (a geodesic), it's walking along something that we (as outsiders) might percieve as a curved line. Similarly, if the ant is walking in a locally straight line on a moving turtable, although the ant is moving in a locally straight line, the path it describes is not straight.

Classically, it's assumed that space-time is euclidean (or flat), so a 'locally straight' line is also a straight line. And that gravity is a force that perturbs motion that would otherwise go along this straight line. Einstein postulated that the path that an object takes under the influence of gravity is the 'locally straight' path. This is intemately related to the notion that gravitational and inertial massess are the same. Since we can describe the paths that objects take under the influence of gravity, we can plot them, and describe the 'shape' of space-time.

It's also worth noting that for GR to work, you have to imagine a 4D warped space (which would be embedded in 5-space) and not a 3D space, since GR includes time as one of the dimensions.

8. Jun 18, 2004

### LURCH

I agree with Zeta that the famous "rubber sheet" analogy is the best place to start. The tough part is, as has been stated, excepting the extra dimension. The rubber sheet has two dimensions until a mass is introduced, warping it in a third direction the "up and down" that direction. The marble trying to roll past [in front or behind] the bowling ball or [to the left or the right] of it, will be drawn toward it. This is because the sheet has been warped in the "up and down" that direction.

In moving this phenomenon to 3-D, we see the same behavior exhibited by massive objects in space. It is simply that extra dimension is added, because an object trying to fly past a planet (for example) would have its course altered whether it tried to go [in front of or behind], [to the left or the right], or [above or below] the planet. This is because those three dimensions are curved in a fourth direction, which we cannot see nor even visualize. We can only observe the behavior of objects and logically deduce that this fourth direction exists.

Last edited: Jun 19, 2004
9. Jun 18, 2004

### jcsd

Actually how the curvature of spacetime causes gravity is not the most difficult to conceive part of GR as it's based on suprisingly simple logic.

In SR the worldline of an object in an inertial refernce frame is straight, the worldline of an object that is undergong accelartion is not straight. Gravity cause all objects whether they be photons, protons spaceships or space llamas to accelarate, not only that a gravitional field will cause all objects to accelerate by the same amount. So if we imagine a spacetime continuum containing a gravitional field there will be areas (infact due to the infinite reach of gravity all areas will be affected) where all worldlines curve and not only that they will curve in a simlair manner, depednt only the path that they take. In order for it's worldline not be curved an object has to accelerate, consequently we find the 'shortest' path through spacetime is no longer the straight path but the curved path. This is exactly like manifolds with intrinsic curvature in differential geometry! For example imagine the surface of a sphere, this is a manifold with intrinsic curvature, the shortest paths along it's surfaces are curves traced by great circles (a fact that has long been known by sailors when travelling across the globe). Therefore we can mdoel our gravity in our spacetime as curvature.

Last edited: Jun 18, 2004
10. Jun 18, 2004

### zoobyshoe

Someone quoted Einstein in the Relativity forum, in the past month or two, as having said something to the effect that GR doesn't stand unless there is something along the lines of an aether. (He wasn't talking about the classical notion of the aether, of course, whose properties were proven to be impossible.) Someone else found quotes by Einstein that said things along the same lines last summer, that there must be something we might call an aether. That is vague information, but I think if you keep your eyes open you may run in to these remarks by Einstein.

To the extent that I think of space as the presence of something that might be called an aether it provides something that could be warped but that really only produces more questions about how to visualized this warpage or curvature.

11. Jun 18, 2004

### jcsd

You don't need an aether to explain curvature. Ask yourself this question: should we really assume that spacetime is Minowskian or space is Euclidian?

12. Jun 18, 2004

### zoobyshoe

The problem that Weio and I are having is not with the explanation per se but with all the suggested explanation/visualizations. Once you put a bowling ball on a rubber sheet or an ant on a cylinder you suggest that there is a very physical, Newtonian, way to visualize gravity despite not intending to.

As I said the temptation to visualize an aether that is being warped or curved is strong, but ends up just raising more questions. What I said about Einstein apparently suspecting something like an aether was a vaguely supporting remark to zeta101s opinion that "space is not nothing", and didn't directly apply to the gravity visualization issue.

To the extent that all explanation/visualizations rule out alot of other possible speculations about the nature of gravity, they are extremely useful. It is clear that gravity isn't some form of magnetism, for instance, or electric attraction.

13. Jun 18, 2004

### jcsd

The basic thing to realize is that the way that gravity changes the worldlines in spacetime is analgous to a curved (pseudo-Riemannian) manifold, so we don't need to actually have some sort of physical background.

14. Jun 19, 2004

### Imparcticle

I asked this same question a while ago and I was told that bodies of mass in space (say a planet) had a stream of energy comming from it that warped space-time, thus causing the phenomenon of gravity.

15. Jun 19, 2004

Staff Emeritus
Well that's not a good description. The best mantra is "Space tells matter and energy how to move, and matter and energy tell space how to curve." Both energy in the form of mass (by $$e=mc^2$$) and other kinds of energy determine the curvature of spacetime, according to Einstein's field equations. And the curvature defines what is natural motion (geodesics).

There is no "streaming" of energy; a rock out in space has energy just because it has mass, and that energy causes spacetime to curve a little bit in its neighbothood.

16. Jun 19, 2004

### zoobyshoe

"Manifold: d: a topological space in which every point has a neighborhood that is homeomorphic to the interior of a sphere in Euclidian space of the same number of dimensions."

-Merriam Websters Collegiate Dictionary 10th edition

Is this what you mean by "manifold"?

17. Jun 19, 2004

### jcsd

Yep. Just think of a manifold as something which is locally Euclidian.

18. Jun 19, 2004

### zoobyshoe

Speak to me of these neighborhoods. Each point has a neighborhood homeomorphic to the interior of a sphere.

Why is it "to the interior of a sphere" rather than "to a sphere". If we remove the shell of a sphere, the shape that remains is just another sphere. Or, does this mean empty space with a spherical boundary?

In any event, since all the points have these neighborhoods, all the neighborhoods must overlap into kind of solid, no?

19. Jun 19, 2004

### jcsd

For most curves that we use an individual point on that curve is simlair to a straight line, i.e. it has a gradient whose value is a real number. this becomes obvious when you 'zoom in' on any part of such a curve it becomes more and more like a starightline. A manifold is simalir is this respect to the curve as every point on an n-dimensional manifold is simlair to an n-dimensional Euclidan space, a fact that becomes more obvious when you 'zoom in' on any part.

20. Jun 19, 2004

### Gokul43201

Staff Emeritus
Does a point mass create curvature that is spherically symmetric ?