Curious About Astronomy

[AlecBGreen]

http://curious.astro.cornell.edu

A great resource for anyone interested in space-related topics. It is setup in a Q&A format. Excellent stuff in here! This one is really stumping me though.

Is the Earth at the centre of the Universe?
By the discussion I was reading, being that there is 15 billion light years to either "side" of us, am I to assume that this means that earth is the center of the universe? Or was that just an example?

From our vantage point on the Earth, we infer that the observable Universe is 15 billion light-years in size in every direction that we look - in other words, we infer that we are at the center of a sphere 15 billion light-years in radius.

This does not mean, however, that we are at the centre of the Universe; it just means that we are at the centre of our observable Universe. A fundamental principle in our understanding of the Universe itself, called the Cosmological Principle, states that the Universe is homogeneous and isotropic on the largest scales. That means that on the whole, the Universe as seen from any vantage point (even one that is 15 billion light-years away from us!) will measure a spherical observable Universe with a radius of 15 billion light-years. (emphasis mine)

How does this make sense? It turns out that there are a couple of possibilities. First, the Universe could be much, much bigger than the part which we actually observe. If the Universe has the geometry of a "flat sheet" that we assume everyday on Earth, then the Cosmological Principle implies that the Universe must be infinite, since every observer at every "Universe edge" must observe the same global parameters. On the other hand, it is possible that the Universe's geometry is not flat, but curved like a sphere or a saddle. In this case, the Universe would "wrap" around at the edges: just as on the surface of the Earth, you would come back to where you started if you walked in one direction for long enough. Recent observations indicate that the first scenario is most likely true - we see a piece of the infinite, flat Universe that is 15 billion light-years in radius.

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What do they mean by a flat sheet universe? Is it a difference between Euclidian and non-Euclidian geometry?