# If space is curved, could it be detected

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1. May 1, 2015

### newjerseyrunner

I was contemplating the size and shape of the universe. Our observable universe is perfectly 3D spherical, but that's a result of a finite speed of light and a beginning of time, and I was wondering if there was a way to deduce the size of the universe. I imagined the universe as a 4D sphere then imagined myself traveling through it, what would I see. Over small distances and speed I would see the universe as 3D, but at high speeds and over massive distances, the curvature should become apparent and I had a wondering.

Say we send telescopes away from earth in opposite directions and point them at exactly the same orientation towards an object at the edge of the observable universe. In a 3D space, they would appear in exactly the same location minus a small shift to account for parallax.

In 4D space, the extremely distant objects should appear to move both in space and time, and the amount that they move would be directly relational to the distance between the viewpoints, the distance to the object, and the size of the universe.

Am I correct, or would the fact that light travels along the curvature of space made it appear as though it was 3D even if it were curved?

I had this thought because I imagined moving at high speeds through a 4D sphere and what I would see, and I would see something very similar to the Lorenz transformation and it made me wonder if the universe could be a 4D sphere.

2. May 1, 2015

### Staff: Mentor

What do you mean with "4D space"?
4D spacetime?
That does not make sense.

Our space could have some global curvature (this would not make it more than 3+1-dimensional, we have 3 space and one time dimension) - but within the current experimental precision, no curvature could get detected. Such a curvature would mean angles in a triangle do not add up to 180 degrees, for example.

3. May 1, 2015

### Staff: Mentor

I'm not sure why you've tried to imagine 4 spatial dimensions. Are you thinking that the curvature of 3d space requires that it be embedded in 4 spatial dimensions? If so, this is not true. We can define the geometry of our universe as intrinsic, which means that it is curved but not in relation to some extra dimensions.

From wiki: http://en.wikipedia.org/wiki/Curvature

There is a key distinction between
extrinsic curvature, which is defined for objects embedded in another space (usually a Euclidean space) in a way that relates to the radius of curvature of circles that touch the object, and intrinsic curvature, which is defined at each point in a Riemannian manifold.

Note that General Relativity, the theory that describes the curvature of space and time, uses Riemannian manifolds extensively.

4. May 2, 2015

### Rudolf

Over time, I have formed a sense of fundamental errors in all theories related to the space-time continuum and gravity. The point is the notion that massive objects distort space. And what about the objects themselves? Do not they take part of the same space that bend? And what happens to the objects themselves as a consequence of this curvature? It is logical to assume that any particle that has mass - slightly bends space ...?

Last edited: May 2, 2015
5. May 2, 2015

### Staff: Mentor

What happens is exactly what happens here on Earth. The objects (rocks, water, atoms, fundamental particles) experience stress because gravity (spacetime curvature) wants to make them get closer together, but the other fundamental forces resist this and prevent the objects from doing so.

6. May 2, 2015

### Rudolf

Can we conclude from your words that the action is equal to counteraction, and no curvature of space there?

7. May 2, 2015

### Staff: Mentor

I'm not sure what you're asking. No curvature of space where?

8. May 2, 2015

Staff Emeritus
How could anyone conclude that?

9. May 2, 2015

### William Henley

4d space is the 3 spacial dimensions and time

10. May 2, 2015

### William Henley

Would it be possible to detect the gravity between two points on the curvature?

11. May 2, 2015

### Rudolf

I mean, I'm not sure that the curvature of space in general is taking place. Since these very massive objects are part of the space, which "bend". After all, the atoms themselves 99 percent is empty space! Something is missing here.

12. May 2, 2015

### Staff: Mentor

Well, the only thing I can tell you is that General Relativity, the most accurate gravitational theory ever devised, describes it as such and that even if GR isn't the ultimate theory of gravitation, the effects we see that are explained by curvature are not going to go away and would require something even stranger to explain adequately.

The 'bending' is not a bending as you or I might think about it. It is a change in the local geometry of this area of the universe. A massive object (or any object with mass or energy) quite literally changes the geometry of spacetime. This happens in, around, and away from the object, which is itself affected by this change of geometry, which manifests as gravity.

I don't see a connection between this not-quite-true statement and your questions on spacetime.

13. May 2, 2015

### Rudolf

I badly speak in English, so I use Google translator. Please, I'm trying to understand. And your explanation is quite understandable. As well as explaining Hawking and Tyson. However, you personally satisfied with everything in these explanations?

14. May 2, 2015

### Rudolf

I'm sorry, but I lied to you. The phrase "expressed as gravity 'does not mean anything. According to NG, If a soccer ball - a nucleus of an atom, the electrons move beyond the boundaries of the stadium. The space between them is empty, and is part of the space time continuum. What makes this matter to produce gravity, without changing its own geometry? And maybe this is already the changed geometry?

15. May 2, 2015

### Staff: Mentor

Popular descriptions of science are not the actual science. They are oversimplified attempts to describe the actual theories.
Electrons in an atom do not "move" in the way classical particles do. And there is no empty space.
General relativity gives a description that is in agreement with all experiments. Note that the bending of spacetime from a single atom is tiny. You need many atoms to get a visible effect.
Sure, and all this is well described by general relativity.

16. May 2, 2015

### Staff: Mentor

Geometry is a property of space, not of matter. An atom can change the geometry of the space it occupies, which then affects the atom itself.

Electrons exist in large orbitals, where they have a probability of being found somewhere within the orbitals. Other than the nodes, the electrons have a chance of being found anywhere. They do not orbit at some fixed distance like planets orbiting a star.

17. May 4, 2015

### newjerseyrunner

Here is a simpler version of what I'm asking. Imagine you place a camera in a tesseract. The camera is only capable of viewing a 3D cross section of the 4D object. Now imagine that there are two objects inside the tesseract that you can view. Put them anywhere as long as there is a gap between themselves and the camera. Now move the camera. Using the known 3D distance and angles between the objects and the camera, a simple projection algorithm should be able to predict how their apparent motion should change, but as we move through it, they won't move the way we'd expect. They could even vanish and reappear from view as they go in and out of the cross section.

Imagine now the cross section of the tesseract bigger than the observable universe. The small distance we can travel compared to the edges of the universe would make any fluctuation away from normal 3D projection would be so minute we wouldn't even be able to notice them except for doing measurements light years or centuries apart.

18. May 4, 2015

### Staff: Mentor

You're asking if the universe is actually 4 spatial dimensions?

19. May 5, 2015

### ShayanJ

The tesseract is a really bad analogy and sometimes it is exactly the bad analogy in your mind that's the cause of the confusion. Think in terms of spacetime itself and don't try to investigate beyond things the theory itself has to offer. Well, you can do that if you want and there is nothing wrong with it, but beware that won't be physics anymore.

20. May 5, 2015

### newjerseyrunner

Sort of, I know that there is no mathematics for that, I'm more asking if it's possible the effects of time can appear to manifest in spacial ways. Moving in space affects at high speed affects time, the further apart the objects, the more the effect of dilation, isn't that correct? If a ship really far away travels towards us, from their perspective our planet is hundreds of years in the future, but if they turn around and go the opposite direction, their perspective of our planet in the same spacial location is now hundreds of years in the past. What I'm asking is this: what happens to the apparent age and position of everything in the peripherals? What happens from the ships perspective to the rest of the virgo supercluster? Does it just appear to change in time, or would it appear to move in space as well (similar to what a gravitation a lens does.)

NOTE: Appear is probably not the right word: assume you could view Earth as it would actually appear without having to wait for light.

I'm imagining it more like a loaf of bread (Brian Greene's analogy,) I used a tesseract because of it's regular geometry and it's well known rotation animation.

Last edited: May 5, 2015
21. May 5, 2015

### Staff: Mentor

That question is too unclear for an answer.
No, time dilation does not depend on distances.
"Perspective"... those centuries are a mathematical result, they are nothing you could observe.
But you cannot, that is one the fundamental concepts of relativity. And all other thought experiments in relativity don't make sense if you can violate this one.

22. May 5, 2015

### Staff: Mentor

I'm really not sure what you're asking here. Have you studied Special Relativity at all? I believe it would answer many of these questions.

As MFB said, this isn't physically possible, so there's no reason to even consider it.

23. May 5, 2015

### Eric Jameson

This may be slightly beside the point - but does anybody ever ask themselves the fairly basic question (well, I think it's basic) - space appears to be empty - so just what is curved? I have seen it suggested that space is not empty but a seething mass of virtual particles (or whatever) - how do you get a curve in a 3D mass? Would the curve amount to a variation in the density of the virtual particles around a mass?
I accept that the "curved space" concept explains very nicely most of the observed behaviour of mass and gravity etc. - but is it just a description of the behaviour and not really an explanation of how gravitational effects etc. actually arise?
I suppose another fundamental question is - just what is an "explanation"? Comparison to effects we can see with the naked eye?
Another thing of a similar nature that puzzles me a little - is - just what is "inertia"?
As you might have guessed I am not a physicist but mainly educated in chemistry, geology and engineering - "real-world" subjects you might say.
Did Einstein ever think to himself - "Curved space - what the hell is curved - there's nothing there"?

24. May 5, 2015

### Staff: Mentor

You don't. Mass is a scalar quantity, it is not capable of being 3-dimensional. (Scalar just means it has a magnitude. Like 3 pounds. You can go up or down in the number, but that's it) General Relativity is a theory of geometry, and it is this geometry that is changing when we say that space is curved. This 'sea of virtual particles' would exist within space-time, not be space-time.

Please start a new thread if you wish to discuss these topics.

No, he never said that because he knew exactly what was curving. He's the one who developed the theory after all.

25. May 6, 2015

### Staff: Mentor

Physics cannot answer "how" or "why" questions on a fundamental level. The description with a curved spacetime works nicely: it gives the right predictions.
An attempt to mess around with virtual particles in that context does not.