What happens at the end of a static, flat and finite universe?

[bilby]

It's a thought experiment; we can have whatever we can imagine. But what happens at the boundary is determined by what you imagine happening at the boundary - so if you don't know, we can't tell you.

Nobody can tell me or you can't tell me?

Amongst the options are that the ant ceases to exist; or that he re-enters the universe in one of the ways described by beero1000; or something else happens, that arises due to one or more of the infinite number of attributes of the universe that are left undefined in your thought experiment.

I would like to know why they think that a finite and flat universe "loops" back in on itself. Do you know? I read some places that it does loop back, but I also read that a flat universe implies an infinitely large universe, neither explaining how they get to that conclusion.

Nobody can tell you - it's your thought experiment, so it's entirely up to you.

 

[beero1000]

Okay, I think I get it now. They are trying to say that you don't need a closed universe to come out the other side. I always thought only a closed universe allows that.

But I would like to know why they think we would come out the other side, or see the back of a door in a universe that is small enough.

There is no other side - the universe is all that there is. These are representations of the fundamental (Dirichlet) domain of the manifold and the boundaries are just side effects of us trying to draw a picture of them locally in our Euclidean universe. In each of these universes, you could keep traveling in a straight line forever and never hit a 'wall'.

Imagine if you were Pac-man (not the player). From your perspective, there is no 'edge' of the screen, you can move forward no matter where you are, but from the player's perspective, there is an edge and Pac-man teleports to the other side once he reaches that boundary. Analogously, we'd have Pac-man's perspective (no edges, continuous motion), but the pictures I posted would be imagining the space from a player's perspective (edges, teleportation).

Can we not just have a 2d ant on a finite 2d space the size of a dinner plate? Why not? If we can, then what happens to the ant if he tries to go through the boundary?

You could, but for a variety of reasons (including trying to describe what would happen at a boundary), we've concluded that the universe doesn't have a boundary. So not like a 2D ant on a 2D dinner plate, but more like a 2D ant on a 2D Pac-man screen.

 

[beero1000]

I would like to know why they think that a finite and flat universe "loops" back in on itself. Do you know? I read some places that it does loop back, but I also read that a flat universe implies an infinitely large universe, neither explaining how they get to that conclusion.

If both were making absolute claims, both are wrong. A flat universe might be finite or infinite, and might loop back or not. Like I said, there are 18 candidate flat universe topologies, some finite and some infinite. Anyone claiming they can prove which one is our universe can go ahead and collect their Nobel prize right now...

The evidence suggests that the universe does probably loop though. Physicists are currently looking at cosmic microwave background radiation to try and find repeated antipodal patterns that would indicate those loops. Finding those would be crazy cool.

Here's a semi-recent paper: https://arxiv.org/abs/1206.2939

 

[beero1000]

More links:

3-Manifold Simulator

The Status of Cosmic Topology after Planck Data

[FONT=&quot]In the last decade, the study of the overall shape of the universe, called Cosmic Topology, has become testable by astronomical observations, especially the data from the Cosmic Microwave Background (hereafter CMB) obtained by WMAP and Planck telescopes. Cosmic Topology involves both global topological features and more local geometrical properties such as curvature. It deals with questions such as whether space is finite or infinite, simply-connected or multi-connected, and smaller or greater than its observable counterpart. A striking feature of some relativistic, multi-connected small universe models is to create multiples images of faraway cosmic sources. While the last CMB (Planck) data fit well the simplest model of a zero-curvature, infinite space model, they remain consistent with more complex shapes such as the spherical Poincaré Dodecahedral Space, the flat hypertorus or the hyperbolic Picard horn. We review the theoretical and observational status of the field.[/FONT]

 

[ryan]

Nobody can tell me or you can't tell me?

Amongst the options are that the ant ceases to exist; or that he re-enters the universe in one of the ways described by beero1000; or something else happens, that arises due to one or more of the infinite number of attributes of the universe that are left undefined in your thought experiment.

I would like to know why they think that a finite and flat universe "loops" back in on itself. Do you know? I read some places that it does loop back, but I also read that a flat universe implies an infinitely large universe, neither explaining how they get to that conclusion.

Nobody can tell you - it's your thought experiment, so it's entirely up to you.

Theory, what would theory tell us could/might happen? What might we expect with our knowledge of math, physics, philosophy/logic, etc.

 

[ryan]

There is no other side - the universe is all that there is. These are representations of the fundamental (Dirichlet) domain of the manifold and the boundaries are just side effects of us trying to draw a picture of them locally in our Euclidean universe. In each of these universes, you could keep traveling in a straight line forever and never hit a 'wall'.

Yes, a person would always be at the center just like on Earth's surface.

Can we not just have a 2d ant on a finite 2d space the size of a dinner plate? Why not? If we can, then what happens to the ant if he tries to go through the boundary?

You could, but for a variety of reasons (including trying to describe what would happen at a boundary), we've concluded that the universe doesn't have a boundary. So not like a 2D ant on a 2D dinner plate, but more like a 2D ant on a 2D Pac-man screen.

Okay, but I am really just trying to understand what the properties of the edge of the dinner plate would be if the ant tried to go past the boundary.

 

[beero1000]

Yes, a person would always be at the center just like on Earth's surface.

Can we not just have a 2d ant on a finite 2d space the size of a dinner plate? Why not? If we can, then what happens to the ant if he tries to go through the boundary?

You could, but for a variety of reasons (including trying to describe what would happen at a boundary), we've concluded that the universe doesn't have a boundary. So not like a 2D ant on a 2D dinner plate, but more like a 2D ant on a 2D Pac-man screen.

Okay, but I am really just trying to understand what the properties of the edge of the dinner plate would be if the ant tried to go past the boundary.

We don't know. Since a manifold-with-boundary is not a manifold, it will have 2 classes of points: the interior points and the boundary points. Interior points are our everyday locally Euclidean points, but the boundary points aren't locally similar to Euclidean space, so they're like nothing we've ever seen. Since we've never measured or inferred the existence of these special boundary points, so we don't know anything about them. But realistically, there's little reason to assume that the universe actually exists as a manifold-with-boundary and lots of reasons to think it doesn't.

 

[ryan]

Yes, a person would always be at the center just like on Earth's surface.

Can we not just have a 2d ant on a finite 2d space the size of a dinner plate? Why not? If we can, then what happens to the ant if he tries to go through the boundary?

You could, but for a variety of reasons (including trying to describe what would happen at a boundary), we've concluded that the universe doesn't have a boundary. So not like a 2D ant on a 2D dinner plate, but more like a 2D ant on a 2D Pac-man screen.

Okay, but I am really just trying to understand what the properties of the edge of the dinner plate would be if the ant tried to go past the boundary.

We don't know. Since a manifold-with-boundary is not a manifold, it will have 2 classes of points: the interior points and the boundary points. Interior points are our everyday locally Euclidean points, but the boundary points aren't locally similar to Euclidean space, so they're like nothing we've ever seen. Since we've never measured or inferred the existence of these special boundary points, so we don't know anything about them. But realistically, there's little reason to assume that the universe actually exists as a manifold-with-boundary and lots of reasons to think it doesn't.

Yeah, I guess I am just digging my own rabbit hole.