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When looking at the night sky, we see lots of stars. Several places tell you that the light of those stars has traveled to many light years to reach Earth and there may be others where light has not made it here yet. How can this be?

Assume we accept the Big Bang Theory that suggests the universe began in a single point (or at least very small space). When the "bubble" that is the universe reaches 1 light year in diameter, the light from one end should have been shinning the whole time, so the other side should still be able to see it. Continue on until the Universe is at present size, and the light should still be visible by the same logic.

So how can there be systems from which light has not reached us yet?

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See this question. We didn't originate from a single infinitely dense point in space time in the Big Bang. This is a common misconception. Search this forum for flrw metric for many, many related questions. See also my answer to this question for more background. –  John Rennie Mar 26 at 17:03
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In classical sense, Universe accelerated to faster than light. I think this helps. :) –  Sachin Shekhar Mar 26 at 17:09
    
Also related: Horizon problem in the standard cosmological model. This explains how different regions of the universe can be out of causal contact i.e. farther apart than light could reach in the time since the Big Bang. –  John Rennie Mar 26 at 17:24
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The situation here is much simpler: Stars did not form at the instant of the big bang, therefore their light did not have the time to reach us. E.g. consider a star formed a day ago, but two light-days away, its light will not have reached us within that day. –  pfnuesel Mar 26 at 17:27
    
Possible duplicates: physics.stackexchange.com/q/26549/2451 , physics.stackexchange.com/q/60519/2451 and links therein. –  Qmechanic Mar 26 at 17:41

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up vote 5 down vote accepted

Besides the comments, stars have formed well after the Big Bang. Depending on where they are in the universe, it will take a while for us to see them.

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Remember, the Big Bang theory is just that- a theory. I predict astrophysicists will soon discover galaxies 15,20,25, billion years old. Then what?

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That's fine, but for the sake of argument we assume the theory is correct and continue along. Such is the way of some of Science and Mathematics. –  David Starkey Mar 31 at 15:31

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