Math Mutation 61:  Observing The Universe

    How big is the universe?  Well, there is no way for us to really
answer that question-- we need to start by talking about the
'observable universe', all the things we can actually detect.  If
something is so far  away that light travelling since the creation of
the universe would not have had time to reach us, then we are probably
out of luck.  So, let's start with that:  how big is the universe we
can actually detect?
    You might think the answer is pretty simple at first.  According
to current theories, the universe is about 13.7 billion years old, so
just draw a sphere of radius 13.7 billion light-years around the
Earth, and that describes what we can see.  But suprisingly, that
answer is wrong.  The problem is that we are in a universe that has
been expanding in more than the three dimensions we are used to:  ever
since Einstein, we have realized that any calculations at the cosmic
scale must utilize a four-dimensional structure of spacetime.   Using
an analogy with one fewer dimension, think of our space as the surface
of a giant balloon that is being slowly blown up.  Things that were
once close enough to emit light that we can observe today may get
farther and farther away as the balloon expands-- so the light that
was launched long ago can arrive at our telescopes, even though the
actual object is now farther away than that 13.7 billion light-years! 
As a result, our observable universe contains objects that are now as
many as 46.5 billion light-years away.
    An even more bizarre property of the observable universe is that
we might actually be observing a *larger* universe than the one that
actually exists, due to light that completely travels around the
universe and reaches us a second time.  In other words, the universe
might be like the hall of mirrors at a carnival, with the same objects
being visible to us many times.  Using the balloon-surface analogy
again, look at a line directly from a distant galaxy to us on the
surface of the balloon, and also at another line that loops all the
way around the balloon and then to us.  Both might be legitimate paths
for the light to reach us, and we would see them as separate images.
A question you might ask now is:  why are we so gullible?  Shouldn't
we notice immediately if some object in the sky is exactly the same as
some other one?  The problem here is that since the light must likely
traverse many billions of light-years to go all the way around the
universe, the duplicate objects will be viewed at vastly different
eras in their history.  It's not easy to know exactly what a
particular galaxy will look like in several billion years, or what it
looked like that amound of time in the past.  Some object we have
labelled as a "distant galaxy" might actually be our own Milky Way,
viewed many billions of years ago.
    Of course, we also need to keep in mind the very likely
possibility that the universe is much larger than what we can detect.
This discussion has by necessity been limited to the observable
universe, since that's all we can realistically comment upon.  But
assuming the Earth is not in the exact center, and we really are
observing only a subset, we will likely never know how big the
universe really is. 
    And this has been your math mutation for today.



References:
<li><a
href="http://en.wikipedia.org/wiki/Observable_universe">Observable
Universe at Wikipedia</a>