# Finite bounded universe

1. Feb 17, 2016

### Alltimegreat1

A number of scientists subscribe to this theory. I read up on it, but none of the explanations I found really answered my questions. How should one attempt to envision a universe that is finite and bounded?

2. Feb 17, 2016

### mathman

Use torus analogy (surface) - hard to envision in three dimensions.

3. Feb 17, 2016

### mgkii

It goes something like this

Start with one dimension - say a line. Imagine a creature that lives on that line and can only perceive in one dimension - i.e. backwards and forward, nothing else. If you bend that line, the creature would not be able to perceive the bend as it still travels the line backwards and forwards. If you then bend the line right the back on itself - for example, make a circle; then that creature can keep going forever, but will come back to where it started from each time. The creature can't perceive the changes you've made, as you made them in a higher dimension.

Next do it in two dimensions - e.g. a piece of paper. The creature "living" on the paper can only perceive 2 dimensions of forward, backward, left and right, so again can't perceive the changes you're about to make in a higher dimension. If you want to go off one edge an reappear on the other, then roll the paper into a cylinder. If you want to do the same for the other two edges, then roll that cylinder into a donut shape (a torus).

Now for the hard bit... try to imagine it for three dimensions!! You can probably see immediately "how" you need to imagine it... but you'll have a better mind than me if you can actually build a mental image!

4. Feb 17, 2016

### Chalnoth

Finite and bounded?

One possible way this might happen is if our universe is a "bubble" of a different vacuum energy from its surroundings. In this model, somewhere beyond the cosmological horizon is a boundary between our value of the vacuum energy and the vacuum energy value outside. This boundary will move, at very nearly the speed of light, in the direction of lower vacuum energy (destroying everything in its path). We won't ever be able to observe it, however, as the boundary lies beyond our cosmological horizon.

But the usual thing that people talk about, and was described earlier in this thread, is a finite but unbounded universe. The surface of a sphere is like this: the area of the surface is finite, but no matter what direction you move along the surface, you'll never run into an edge. There's also the torus (doughnut-shape). A universe of this shape acts rather like the classic video game Asteroids, where moving off of one side of the screen causes your ship to appear on the opposite side of the screen.

5. Feb 18, 2016

### Alltimegreat1

Thanks for the input. Correct me if I'm wrong, but I think you're explaining a universe that is finite and unbounded. It's the bounded part that I find hard to conceptualize. From Wikipedia: "Assuming a finite universe, the universe can either have an edge or no edge. Many finite mathematical spaces, e.g., a disc, have an edge or boundary. Spaces that have an edge are difficult to treat, both conceptually and mathematically."

I'd be interested to hear more detailed theories about what this edge could be like.

6. Feb 18, 2016

### mgkii

You're not wrong.... I need to learn to concentrate more!!

7. Feb 18, 2016

### Alltimegreat1

We all need to concentrate more in order to visualize the edge of the universe.

8. Feb 18, 2016

### Bandersnatch

Personally, I've never heard of any, at least not in mainstream cosmology. Can you provide examples?

By the way, you mean finite and with a boundary. Bounded has pretty much the same mathematical meaning as finite in extent.

9. Feb 18, 2016

### Alltimegreat1

Yes, I mean finite with a boundary.

10. Feb 18, 2016

### newjerseyrunner

I think you are confused. Bounded does not mean that there is a boundary. The surface of a sphere is bounded, but it has no boundary.

11. Feb 18, 2016

### mgkii

I don't think the OP is confused - extract from wiki below suggests the use of the term is correct (or wiki is wrong)

Bounded and Unbounded
Assuming a finite universe, the universe can either have an edge or no edge. Many finite mathematical spaces, e.g., a disc, have an edge or boundary. Spaces that have an edge are difficult to treat, both conceptually and mathematically. Namely, it is very difficult to state what would happen at the edge of such a universe. For this reason, spaces that have an edge are typically excluded from consideration.

However, there exist many finite spaces, such as the 3-sphere and 3-torus, which have no edges. Mathematically, these spaces are referred to as being compact without boundary. The term compact basically means that it is finite in extent ("bounded") and is a closed set. The term "without boundary" means that the space has no edges. Moreover, so that calculus can be applied, the universe is typically assumed to be a differentiable manifold. A mathematical object that possess all these properties, compact without boundary and differentiable, is termed a closed manifold. The 3-sphere and 3-torus are both closed manifolds.

Last edited: Feb 18, 2016
12. Feb 18, 2016

### Bandersnatch

Use of finite and bounded or infinite and unbounded is correct but redundant in this context. On the other hand, it is clear from post #5 that the OP meant 'finite and with a boundary' - i.e. with and edge.
But the OP has acknowledged the mistake in post #9, so it's now just beating a dead horse.

That aside, I'd still like to get some references from the OP for scientists building/favouring a cosmology with a boundary as a feature.

13. Feb 18, 2016

### phinds

No, the surface of a sphere is unbounded. You are, perhaps, thinking not of the surface of the sphere but of the full sphere embedded in 3D space. That IS bounded, although its surface is not.

14. Feb 18, 2016

### Flatland

Would a finite but bounded Universe actually make any sense? Who are these so called scientists that supports this theory?

15. Feb 18, 2016

### phinds

I don't think so. It would have rather severe consequences. Current physics could not explain what happens at the boundary and it would defy the Cosmological Principle.

16. Feb 18, 2016

### micromass

Staff Emeritus
Nope, the surface of a sphere is bounded. It forms a bounded metric space.

17. Feb 18, 2016

### phinds

Hm. I thought, and seem to remember seeing on this forum several times, that the surface is unbounded because you can travel forever on it and never hit a boundary.

18. Feb 19, 2016

### micromass

Staff Emeritus
In mathematics, there is a huge difference between "having a boundary" and "being bounded".

19. Feb 19, 2016

### Cruz Martinez

The sphere is bounded although it has empty boundary.

20. Feb 19, 2016

### Fervent Freyja

I was under the assumption that the terms bounded and unbounded (finite and infinite) universe occurred in particular contexts and served as more of a conceptual aid alongside that datum, and as a way to help one recognize patterns later within different concepts. Also, the terms are used in all sorts of other places like topology. I cannot imagine a person wading very far in physics while trying subscribe to just one of those. Are these scientists credible, have you checked their prior work, or reputations?

My visualization of what the universe could look like has become increasingly elusive and it is difficult to maintain a focus for very long without encountering thought issues or the most unpleasant combination of running both. These terms imply much more than just topology...

There is no consensus on the shape of the universe. There is good reason that millions of scientists aren’t drawing pictures to help the public envision it… Wonder what would happen there? Would there be a war?