Why can we see stars that are billions of light years away if the
Universe is only 6000 years old?
The universe is finite, not infinite.  It has a center and it has a boundary.  It is still expanding.  If it is still expanding, then it had a beginning.  If it had a beginning, then it has a Beginner.  If it had a beginning, then it must also have an ending. 

                                  Space, time, mass, energy, and velocity are all relative. 

As predicted by Einstein's theories of Relativity, gravity distorts time.  We see this evidenced right here on earth by a comparison of the Colorado Atomic Clock and the Greenwich Atomic Clock.  The Colorado clock runs faster than the Greenwich clock, as predicted by the General Theory of Relativity.  Time is not constant.  There are different time-frames of reference throughout the universe.  D. Russell Humphreys, Ph.D. explains in his book "Starlight and Time" the effects of Gravitational Time Dilation.  His explanation, which is fully supported by Einstein's theories of Relativity, is presented in a clear and easy to understand format.  He details how light from stars that are billions of lightyears away can traverse the distance to earth in only a few thousand Earth years.
How old is the Earth?
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