I enjoyed this video, but I wonder about Fraser’s statement that cosmologists think if you travel in one direction long enough you’ll eventually end up back where you are. That is one model, but not the only one. It depends on space being curved, and tests currently show it to be flat.

Of course, space could be curved but the curvature might be too slight to show up within the current precision of our instruments. It seems like the last I read on this indicated that this level of precision indicates that if space is curved, then the universe is at least 250 times the size of the observable universe.

None of this means that every location isn’t at the center of its observable universe. In that sense, Fraser’s statement that every location is the center of the universe still holds.

###### Related articles

- Universe May Be Curved, Not Flat (scientificamerican.com)
- Viewpoint: Is the Lopsided Universe an Open Universe? (physics.aps.org)
- The Curvature of the Universe Explained – Video (news.softpedia.com)

Isn’t every spot “the centre” of the universe simply because nothing travels faster than light, and the universe is 13.7 billion years old? It’s the edge of the observable universe because we can’t see any further… Good post though 🙂

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Thanks and excellent point. I remembered right after the post went public that the speed of light was an issue. We can’t travel faster than light, and the universe is constantly expanding, making anything beyond our cosmological horizon forever unreachable, so we’ll never be able to go in one direction long enough to arrive back at the same “spot”.

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No worries! I think that what is meant by travelling long enough to get to the same spot is analogous to walking around the earths surface. A surface is 2D, but if you walk around the 3D Earth for long enough you will get back to the same spot. In 3D space, this is not possible as we are not 4D beings. However, some have postulated that it may be possible by going ‘through’ a Kerr black hole. Check out this video: http://m.youtube.com/watch?v=JkxieS-6WuA

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Thanks. An interesting video. Of course, any dimensions past the 4th become controversial, which he notes in the opening screen.

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Hi SAP,

It’s not correct that the only way to end up back where you started is if space is curved. Space could have a toroid topology, which would mean it wraps around without being curved. You can picture this like space being “tiled” with identical cubes in all directions. This is actually consistent with space being flat. Space being curved is another thing. Both allow you to end up back where you started. I think it’s like the difference between a sphere and a torus.

If space is not infinite, then you must certainly end up back where you started. There is no other option unless we are to believe that there is a big wall somewhere preventing further travel.

But of course space may be infinite. In that case, the idea that you end up back where you began if you travel the length of the universe is not strictly wrong because the length is infinite so it’s more a case of “not even wrong”.

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Hi DM,

I’m not quite understanding how space could be a toroid but not be curved, unless by tiled you mean that it bends at discrete angles at certain boundaries. If so, I’d be interested in the reasoning behind that theory.

Good point on infinite space. If space is infinite, and you could somehow travel in one direction faster than light, eventually you might end up in a region with an identical configuration of matter as this one. That wouldn’t really be the same “spot”, but it would feel identical to it.

On the wall conjecture, one thing I’ve often wondered about bubble universes is whether there would be a physical boundary at the edge of the bubble. If space isn’t curved or looped back on itself in some way, it seems like you could reach it. (Given a magical FTL drive that is.)

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Hi SAP,

It has to do with what cosmologists mean by curved space and how topology is really only about how points are connected to other points and not actually about the shape of surfaces. A toroid space would be like the videogame Asteroids, where if you go off one side of the screen you come back in at the other side. You can visualise this from the point of view of the pilot as being like space being an infinite plane which is tiled with identical space, a bit like one of those horrible repeating animated gif backgrounds on geocities-era websites. Sample: http://www.fg-a.com/animated_backgrounds1.shtml

But unlike the Level I multiverse, this is not simply the idea that eventually you’re going to find a similar or even identical arrangement of matter if you travel for long enough. This is the idea instead that space is finite in size and wraps around, so that at a definite interval you will find yourself back where you started.

Extending this to 3D you can imagine it would look like an infinite space being tiled into identical cubic volumes, though space is actually finite and it’s just wrapping around.

This may be how you visualised a curved space, but a curved space works differently and is more difficult to visualise (for me at least). All I can offer is a link to show that a toroid space is not actually curved.

http://en.wikipedia.org/wiki/Shape_of_the_universe#Flat_universe

“In three dimensions, there are 10 finite closed flat 3-manifolds, of which 6 are orientable and 4 are non-orientable. The most familiar is the 3-Torus. See the doughnut theory of the universe.”

Bubble universes work differently. In the bubble universe, the boundary is what an observer within would perceive as the big bang. Space-time gets bent in funny ways so that travelling towards the bubble is the same as travelling back in time, and the big bang singularity is equivalent to the border. Bubble universes can therefore appear to have an infinite space enclosed in a finite volume, because of the way they keep expanding forever and because of the way time is distorted.

Tegmark covers this stuff in his book.

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Thanks for the explanation. I guess it depends on whether the topology of the universe is detectable by those of us within it. Many of the physics articles I’ve read assumed it would be, but that might just be as assumption they’re making because to assume otherwise is to give up on observation.

I need to do more reading on bubble universes. Maybe Tegmark’s book is the place to do it.

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