Geometry of Universe
Conventional wisdom holds that the universe's geometry is
flat. In my understanding a flat space is infinite. So the universe
should be a homogeneous infinite (expanding) space. This is not in
contradiction to the Olber's paradox because of the finite velocity
of light. But how can this view be reconciled with the big bang
model, which to me means that the universe originally was (very)
finite. Is there any possibility for the universe to change its
geometry from say elliptic (finite) to flat (infinite)? I checked
the archive and found an entry "Flat Universe". But this question
was different from the above in that it was not focused on different
geometries at different times.
One difficulty here is trying to measure the universe from within the
What is the "border" of our universe? We could call it the boundary of
matter. We could call it the boundary of what we can observe. We could
call it the boundary of where matter can exist. We could call it the
boundary of where light from the matter can reach. Of these, the first
is the only one we can even try to measure.
What is a flat universe? The universe is at least four-dimensional (3-D
space, and then time). Some theories require it to be at least eleven
dimensions. We cannot just say flat like a table top. Some dimensions
are considered flat: if you move without turning, you can never get
back to your starting point. Some dimensions are considered circular:
if you move without turning, you will come back to your original
position. This would be like a bug walking around the trunk of a tree.
The 3-D space that we see is considered to be "flat".
If you include Einstein's General Relativity as part of the model of the
universe, then the universe is not flat near very massive objects.
Inside a black hole, space could be round. This we cannot truly know
without measurement. I understand that this is one goal of the Large
Until a scientist discovers how to measure such things, we cannot know
the structure of the universe. We can make models to use, but we cannot
test the models to see how well they work.
Dr. Ken Mellendorf
Illinois Central College
I make no pretense to being a cosmologist, much less an expert in the
geometry of the Universe. But a survey of the on-line literature leaves me
with the impression that while the "conventional wisdom holds that the
Universe's geometry is flat." (your words) leads me to the conclusion that
the issue is far from settled to everyone's satisfaction. The experimental
observations are far from complete and the theoretical models and math are
daunting. My thought is keep reading and "stay tuned".
Hold your horses Hans.
You start out with statements that aren't necessarily true.
I have not seen any "conventional wisdom" that holds that the universe is
If it is flat, why does that necessarily mean that it is infinite? This
just doesn't make sense.
Please refer to the paragraph "The mainstream explanation" in this Wikipedia
article that reconciles big bang theory and Olber's paradox:
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Update: June 2012