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Name: Hans
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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 universe.

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 Hadron Collider.

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
Physics Instructor
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".

Vince Calder

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 flat; and 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:

Sincere regards,

Mike Stewart

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