Cosmological principles and their results

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Quarlep
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I am studying cosmolgy and when I thougt about cosmological princples and copernic principle I thougth something.We are observing things and we see the past of objects.From the cosmolgycal principles (isotropy and homogeneity) all observers must see the universe same ,so let's suppose we observe a star 12 billion years ago than let's think there's a creature in that star.What will it see ?

Copernic principle says we are not special so that creature will see what I see same thing but this idea takes us a the universe is infinite . I am confused can somebody help me ?
 
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The copernican principle does not say that the alien will see exactly what you will see. The universe is only isotropic when you get to the multi-billion light-year scale. Under that it is very anisotropic. The copernican principle says that we here on Earth are not 'special', that we are not in a preferred frame of reference. Prior to modern astronomy and cosmology, it was thought that the Earth was the center of the universe, making us 'special' in that regards. Copernicus' heliocentric model of the solar system did away with that principle, since the Earth couldn't be the center of the universe if it was revolving around the Sun.

An alien located 12 billion light years away and looking in our direction in the 'now' would see our little area of the universe as it appeared 12 billion years ago. All they would see would be highly redshifted galaxies still in the process of forming.
 
What you see is 12 billion years old. What a local resident would see is 12 billion years more recent.

"Seeing the same thing" only means that on cosmological scales the distribution of matter is very similar, it certainly doesn't mean that observations of a particular object, taken 12billion years apart, would be the same.