# Into what dimension is Spacetime Curved?

1. Jan 9, 2012

### PhanthomJay

I think I may have asked this question a few years ago, but I forget the responses.

We know that gravity is the curvature of spacetime in the presence of mass and energy.. The curvature of spacetime was proved by experiment during a solar eclipse, whereby light from a star behind the sun was nevertheless observable due to its bending (curving) caused by the sun's mass.

Question: Assuming the above statements are true, was the curvature still into the 3rd spatial dimension, or was the curvature into a higher order spatial dimension? What I mean is that for a 2D surface of a sphere, the path followed by a particle or photon along its surface is curved into the 3rd dimension. Why would not 4D spacetime curvature be into the 5th dimension? Balloon analogy, anyone?

2. Jan 9, 2012

### alexg

The curvature is in the three dimensions, making space/time non-Euclidean.

3. Jan 9, 2012

### PhanthomJay

Oh, thanks.....suppose the star was known to be behind the sun located near the tangent of its surface at its right most edge..would the curvature be to the right of the sun, above the sun, or below the sun?

4. Jan 9, 2012

The left.

5. Jan 9, 2012

### PhanthomJay

Why? If the curvature was relatively small, it would still be hidden, no?

6. Jan 10, 2012

### Nabeshin

This is a limitation of our ability to visualize things, nothing more. When we imagine a 2D surface of a sphere, we automatically embed it into a 3-dimensional universe. The path taken by an object on that surface is still completely two dimensional. Indeed, to describe it, we need to make absolutely NO reference to a third dimension at all. We say that the surface has an intrinsic property, known as curvature, meaning that it is simply something about the surface which is known without reference to outside entities (in other dimensions).

So too is it the case with our 4D universe. To describe the curvature, we do NOT need to appeal to a 5th dimension through which to curve it.

7. Jan 10, 2012

### PhanthomJay

Well, yes, but seeing is sometimes believing. When the light from that star was observed, surely it appeared on one side or the other.. supposing a star was located light years away directly behind the center of the sun when observed from Earth. If spacetime curvature was large enough, would its pinpoint of light be observed to the right, left, top, or bottom of the sun? Why would one geodesic path be favored over the other?

8. Jan 10, 2012

### Cosmo Novice

Essentially if it was behind the center you would have gravitational lensing except the Sun is probably not massive enough to affect photons in such a massive way and is far too bright. The mechanism would be the same as a black hole gravitationally lensing a distant galaxy.

9. Jan 10, 2012

### Drakkith

Staff Emeritus
If the Sun were much more massive and the star was "exactly" in the right spot, the light would appear as a ring around the sun.

10. Jan 10, 2012

### alexg

Because you gave me three choices so I went with the fourth.

11. Jan 10, 2012

### PhanthomJay

That makes perfect sense, thank you for the response!

12. Jan 10, 2012

### DaveC426913

Search Einstein Rings.

13. Jan 10, 2012

### alexg

As it is, the sun will deflect a light beam passing close by 1.75 arc seconds.

14. Jan 11, 2012

### Imax

Hi PhanthomJay:
Spacetime can have a curvature near massive objects like our sun. It's not necessary to embed 4D spacetime in higher dimensions, but sometimes it's conceptually easier to imagine what could happen to 2D space when looking at it as a 3D sphere (i.e. the balloon analogy). Trying to embed a 4D spacetime in a higher dimension would mean that you need 5D, but I have enough problems imagining what could happen in 3D ?

Einstein looked at spacetime as a fabric, and that fabric could bend around large masses like our sun. Such masses can induce curvatures in 4D spacetime, including curvatures in 3D space and curvatures in time.

Last edited: Jan 11, 2012
15. Jan 12, 2012

### twofish-quant

Curvature is a metaphor.

I draw a triangle and measure it's area. It turns out to be 1/2*base*height. Then one morning I get up and I draw a triangle, and measure it's area, and it turns out that it is more or less than 1/2*base*height.

By drawing some triangles, I figure out that they behave "as if" a triangle on a sphere would behave so I call them "curved." The weird part is that the triangles don't actually have to be on a sphere. It could be that I'm somewhere that triangles are just weird.

So "curvature" is a metaphor. It's like saying that someone has a "cold personality" or that "sales of toasters are hot."

16. Jan 12, 2012

### alt

Wow! Thanks for putting it so succinctly. And, well .. so honestly!

17. Jan 13, 2012

### Imax

18. Jan 13, 2012

### twofish-quant

There are several different ways of looking at it. The way that mathematicians look at it "curvature" is this abstract thing with a precise mathematical definition which includes "curvature" on a objects in flat space.

However, this precise definition is much more general than when layman talk about "curvature".

The way that you tell if something is "curved" is that you point in a direction, you walk in a circle and then see what direction you are pointing in. If you are pointing in the same direction then the region of space that you are walking in is "flat". If not, they you are walking in "curved" space.

Now *why* space is curved is another issue. It could be that space is "curved" because you are stuck on a surface that is embedded in a "flat" space. Or to could be that you just happen to be in a region of space in which distances and angles just behave weird.

19. Jan 13, 2012

### Imax

If you take a vector and you move that vector around a loop and you end up with that vector pointing in the same direction at the point where you started from, then you’re in a space that is orientable (i.e. Minkowski space). This may not be an experiment that can explain spacetime curvature.

One experiment that can give some insight into space-time curvature is to look at a pulsar as it moves behind our Sun. For a regular pulsar, the interval between pulses should vary with time, if time has a curvature.

20. Jan 13, 2012

### alt

That seems to bring it back then, to the original question. Into what dimension is spacetime curved ?

And now that I mention spacetime, I seem to recall a thread here some months ago, from a mentor no less, to the effect that 'Spacetime is a fantasy' (or a fairytale or someting like that). I will try to find it, though I fear I probably won't understand it.