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By looking at this picture:

http://earthspacecircle.blogspot.com/2013/01/earths-location-in-universe.html

The earth is near the center of the universe. I've read that the universe look the same no matter where the observer is located. It is the same distance everywhere.

So I understand that for general relativity the universe need to be homogeneous and isotropic, so it will look the same no matter where I am.

But what if I'm on one of the planets near the right or left of the image, then if I draw the same picture of the universe, but from my perspective, then I would be also located in the center? If that's not the case (I'm actually near an edge), then part of my sky would be completely dark, and all the sky that way won't be isotropic?

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Earth is by definition the center of the observable universe. The observable universe is the region of space such that light from the beginning of the universe can reach the observer, i.e. Earth. – Alex Becker Jan 14 '13 at 19:30
up vote 8 down vote accepted

The universe has no edge so to speak. It is, however, finite in age, so light can only have traveled a given distance to get to us. Call this distance $R$, the "radius" of the universe. Any observer, anywhere, will see out to a distance $R$ in all directions from their location.

Now two different observers will have different origins for their respective observable universes, and so will see slightly (or vastly) different patches of the "full universe." (Be careful when talking about things outside your observable patch by the way - it is very easy to end up talking about impossible scenarios that produce nonsensical results.) This can happen even if the universe is closed (read: finite), so long as its size is bigger than something like $R$.

So no, no one is at the "edge" of the universe.

By the way, general relativity in no way requires homogeneity and isotropy. These are simply assumptions cosmologists make in order to take an utterly intractable problem (evolving the whole universe) and make it absurdly simple (see the FRW metric, which, although it may look complicated at first, is pretty much the most trivial thing you can do with general relativity). The homogeneous/isotropic assumptions, by the way, turn out to be justified on cosmological scales, though this was discovered only after the early days of GR-based cosmology, once we had very deep galaxy surveys.

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There is no evidence that the universe has no edge. This is a non-sequitur based on the FLRW assumption that the universe is isotropic and homogeneous. We do not know that it is. For all we know some guy 46 billion light years away might see one half of the night sky as a mirror-image of the other, or totally black, or something else. – John Duffield Apr 19 at 13:16
    
The universe within our Hubble volume is homogenous and isotropic. Since there is likely nothing special about our Hubble volume, it is reasonable to say that the universe seems homogenous and isotropic, and thus does not seem to have an edge. Of course, there's no way to be certain. In other words, there is evidence which implies it has no edge, and a lack of evidence suggesting the opposite. – DilithiumMatrix Apr 19 at 15:25
    
Not only is there evidence (with a dash of Occam and Copernicus) that there is no inhomogeneity, there is simply no edge whatsoever in the model. Classical GR is formulated on boundaryless manifolds. If you want to talk about "edges" to the universe, you need to figure out what that means mathematically. – Chris White Apr 19 at 17:19

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