Size of Universe and Speed of Light
If the speed of light is a constant and not relative. Then
assuming the universe is expanding, how come we can see an event
that took place 13.1 billion years ago when the universe was only
650 million years old. Surely the object wasn't 13.1 billion light
years away from us at the time of the event? If we can see the event
now, then the light must have been traveling for 13.1 billion years.
How can this be?
You are right, the object would not need to have been 13.1 billion light years
away from us at the time of the event. Between then and now, the spatial fabric
of the universe has expanded. Such expansion adds more distance for the light to
travel while its en route. Think of an ant trying to walk around a balloon while
somebody is blowing it up.
Of course, between 650 million years and now, the universe did not expand by a
huge amount. So, the object must have been quite far away (sorry to be vague, I
do not know the exact numbers). That is fine, though. The universe was still VERY
large at age 650 million years. It is possible (some would say likely) that the
universe was, and is, INFINITE in spatial extent, so there would have been objects
at arbitrarily large distances.
This is a very interesting and important question. In a theory of
the creation of the universe there is an extremely rapid expansion
of the universe that takes place before the slower Big Bang
expansion. The expansion is really fast and is in fact faster than
light. There is however the problem that you address in that there
has not been sufficient time since the Big Bang for light to travel
across the universe and back again. This dilemma is resolved by
understanding the enormous rate of initial expansion of the universe.
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Update: June 2012