# A noobie questioning the nature of space

1. Feb 21, 2015

### ax0

I'll begin by saying that while I find it all extremely fascinating, I am a complete outsider to the world of physics and mathematics, so please forgive my ignorance if what I'm asking makes no sense at all.

I have two questions about the nature of “space.”

According to what I believe was Einsteins general theory of relativity (correct me if I'm referencing the wrong theory), gravity is caused when a massive object causes space itself to “warp.” I was always taught that space is nothing but a void, rendering it intangible. If that is the case how can it interact with anything by warping? Which brings me to a potentially ignorant but nevertheless pressing question that has been pestering me: Could space itself be the elusive dark matter that astronomers and physicists have been searching for all these years? I can only imagine that this would give it a definition other than an intangible void and would give it the ability to interact with other objects.

My second question is more or less in the same thread as my first, and probably has an equal potential for ridicule. If space can “bend,” then doesn't that imply a fourth spatial dimension? I imagine a sheet of paper held out flat. As a two-dimensional surface in a three-dimensional space, I am able to bend the sheet of paper, or “warp” it. But that wouldn't be possible without the third dimension, would it?

Edit: on a side note, this thought just cropped up: If space is warped around an object with mass does that mean it is repelled by gravity?

Thanks for any insight!

Last edited: Feb 21, 2015
2. Feb 21, 2015

### Drakkith

Staff Emeritus
A good question. General Relativity describes gravitation as a geometrical change in space. (Space-time actually, but I'll just use 'space' here to keep things simple) We commonly say that objects 'bend' space. This bending can be thought of as occurring in something called a 'metric tensor'. The metric tensor is similar in some ways to a field, such as an electromagnetic field. Both describe some property at a point in space and time. For the metric, it describes the curvature at that point. This doesn't mean that empty space isn't a void, it merely means that the definition of 'void' needs a small amount of clarification when talking about space in detail.

Not a chance. It simply doesn't work that way.

Another good question. There are two 'types' of curvature. The first, and most obvious, is something called 'extrinsic curvature'. This kind of curvature can be defined with respect to a larger dimensional space. For example, a circle can clearly be seen as being curved. However, there is another type of curvature called 'intrinsic curvature'. This is defined as curvature is defined at every point within space by something called a manifold, it is not defined with respect to a larger dimension. In other words, no, the universe does not have to be embedded within 4d space in order to have curvature. If you'd like to know more just search for 'intrinsic curvature' in google and you'll find plenty of information.

No. The geometry is changing, nothing more. Nothing is being 'repelled'. Space is not a physical object that can be repelled.

If all this is confusing, don't worry. It's confusing to everyone. These are difficult concepts to understand if you haven't had the mathematical training to understand the theory. (Which I certainly haven't had either)

3. Feb 21, 2015

### Chronos

It is simpler to think of empty space as a field - which is the approach Einstein used. Under GR, gravity is responsible for what we call empty space.

4. Feb 21, 2015

### Drakkith

Staff Emeritus
That gets into the issue of 'what's the field occupying'?

5. Feb 21, 2015

### ax0

Thank you for such a detailed and comprehensive answer! So I can only assume from this information that the trampoline analogy for gravity isn't very accurate?

So if space is a field, does that make it a byproduct of matter? Like drakkith said, it does raise the question of what this field is occupying. other fields like magnetism occupy space, so..
also, what are the properties of this field to manifest a traversable three-dimensional region in which the matter that propogates it resides? (If i understand what you're saying correctly)

6. Feb 21, 2015

### Drakkith

Staff Emeritus
Lol, not really. It's just a visualization technique, nothing more. It often confuses people more than it helps them.

7. Feb 21, 2015

### Chronos

8. Feb 27, 2015

### wabbit

On this topic I recommend Carlo Rovelli's books. He puts such questions in deep perspective, exploring them from the conceptions of presocratic to hellenistic thinkers, to General Relativity and Quantum Gravity, all in a highly readable form accessible to a wide audience. Few are available in english but you can find his "What is time? What is space?" - not the most thorough one perhaps nor the most recent but an excellent short read.

Last edited: Feb 27, 2015
9. Feb 27, 2015

### phinds

Just to add to what has already been said, a good way to understand it is that we say that space-time "bends" because geodesics (the space-time equivalent of a Euclidian straight line) are NOT straight when looked at from the point of view of Euclidean geometry, they are straight when looked at in the context of Riemann geometry. Thus the "bending" is only by comparison to Euclidean geometry not to the actual reality of Riemannian space-time. This is done because pop-sci writers don't want to try to explain Riemann geometry to a lay audience, so it's simpler to talk in the more familiar terms of Euclidean geometry even though this results in an apples to oranges comparison.

10. Feb 27, 2015

### wabbit

One way to see the bending is that geodesics (the path you follow in "free flight") here on earth aren't straight lines, they're parabolas. That is a manifestation of spacetime curvature.

11. Feb 27, 2015

### phinds

True, to a REALLY good approximation, they are Euclidian parabolas. You pretty much have to get to cosmological scales or near a black hole to see them become Riemann curves.

12. Feb 27, 2015

### wabbit

Right, the point is just that they aren't straight:)
Or jump on a trampoline. Your trajectory isn't constant uniform motion, it brings you back down: spacetime curvature as you experience it.

13. Feb 27, 2015

### liometopum

If you place a bowling ball on a trampoline, you deform the 'space'. That is curvature.
If you have a large tub of water, and you pull the plug, the water goes down the drain. That is absorption.
In 3D space, both follow the inverse square law, with the degree of curvature of space, or the velocity of space, varying with distance from the deforming or absorbing source.
Can you tell the difference?

14. Feb 27, 2015

### Drakkith

Staff Emeritus

15. Feb 27, 2015

### wabbit

liometopum, if you were responding to my post : I think what you describe is an analogy. My example wasn't, I was describing (the effect of) actual spacetime curvature. And the trampoline was completely incidental, jump up from the floor if you prefer.

16. Mar 2, 2015

### Quds Akbar

Space is an actual physical entity, and objects warp with spacetime, and space is part of spacetime, gravity is the distortion of spacetime.

17. Mar 2, 2015

### phinds

Please provide a citation for that claim.

18. Mar 2, 2015

### Quds Akbar

Fabric of the Cosmos, a book.

19. Mar 2, 2015

### wabbit

20. Mar 2, 2015

### phinds

Brian Green causes some consternation on this forum with his popularizations of concepts. I think the general view is that space is just distance. It is not a material thing. "Bending" of spacetime is a reference to the fact that spacetime geodesics are Riemann straight lines, not Euclidean, and when looked at from the point of view of Euclidean geometry, they are bent. What bends is the path, not the "fabric"

EDIT: I see that I already said all that in post #9.