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In summary, the light speed barrier can be overcome by warping space-time, but this would lead to an infinite universe. It is currently unknown if the universe is finite or infinite, but if it is finite then traveling indefinitely in any direction would bring you back to your starting point.f

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Astronomy and Astrophysics News on Phys.org

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I recommend the link in my signature.

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So does that mean that traveling indefinitely in anyone direction will bring us back to our starting position, or will we just keep going forever getting infinitely farther from our starting position and never getting any closer. And if the latter is the case, will it all look the same or will things change as we enter new sections of the universe?

I recommend the link in my signature.

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That depends, in theory (to the point you are questioning) on whether or not the universe is infinite or finite but unbounded. If it is infinite, we never get back, if it is finite then if we drew a geodesic it would eventually hit us in the back of the head, but in practice the light speed barrier combined with the expansion of the universe means it is impossible; we'd just travel forever in either case.So does that mean that traveling indefinitely in anyone direction will bring us back to our starting position, or will we just keep going forever getting infinitely farther from our starting position and never getting any closer. And if the latter is the case, will it all look the same or will things change as we enter new sections of the universe?

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This is currently unknown. The best measurements so far favour an infinite universe, but it is possible that the universe is in fact closed ('loops' around) and only very, very large.So does that mean that traveling indefinitely in anyone direction will bring us back to our starting position, or will we just keep going forever getting infinitely farther from our starting position and never getting any closer. And if the latter is the case, will it all look the same or will things change as we enter new sections of the universe?

The way the measurements are done is a bit like what you could do if you were to find out whether you're living on an infinite flat plane or on a sphere. You basically try to find out if the angles in the largest triangles you can draw have 180 degrees or not. If the sphere is very large, it might just look like the angles add up to 180 degrees, but once you get better instruments you might find out they don't after all.

Same here. So far the triangles seem like they add up to 180 degrees.

And to answer the last question: If the universe is closed, and you did somehow manage to 'circumnavigate' it, you would not get back in time as a result.

@phinds - finite but without a bound

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You sure about that? My understanding is that unbounded just means you can travel the surface without hitting a boundary in addition to meaning "without limit" in the sense of infinite. It's my impression that the phrase "finite but unbounded" is the standard terminology for such topology, such as the surface of the earth.finite but without a boundary. Boundedmeans more or less the same as finite.

For example, here's the first hit I got on it searching this forum

quoted from @PeterDonisThere is no such thing, any more than there is a "center" of an infinite plane or the surface of a sphere. The universe is either spatially infinite, orfinite but unbounded(we're pretty sure it's the former, but the numbers still leave an outside chance of the latter). In either case it has no center.

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http://en.wikipedia.org/wiki/Boundary_(topology)

http://en.wikipedia.org/wiki/Bounded_set

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You might be right, but if so it's in the breech not the observance (which doesn't make it right of course). A search of this forum will show numerous people using "finite but unbounded"

http://en.wikipedia.org/wiki/Boundary_(topology)

http://en.wikipedia.org/wiki/Bounded_set

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You know how easy such careless use can lead to misconceptions proliferating.

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I'm not of the opinion that widespread sloppiness justifies itself.

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