JL & John,
IMO an absolute infinity seems to be a hard thing for a mind to wrap itself around. Personally I spent close to thirty years forcing my "mind" to accept what my "brain " "knew".
An infinity must necessarily have no beginning and no end. It simply must exist. This is completely foreign to the human experience and we are not well equipped mentally to deal with infinity. Yes we can discuss one, think about one, and even claim to visualize one but I am afraid that our sophisticated discussions of one are always backed up by a little mental reservation that there must be an end to it somewhere-sometime.
But "mechanically speaking" there seems to be no need for an end to either time or space that is not predicated by our point of view. Our point of view is "mechanically" limited by the very nature of light. So is the point of view of every other intelligent being that may exist or ever existed. Everything that exists exists in the very center of a Universe that "looks" like it is "expanding". Since it "looks like" it is expanding it also looks like it has an "epicenter" ie. a Big Bang a "Creation", or a mathematical "singularity". It also must have a region of Cosmic Microwave Background Radiation (CMBR) activity. I also suspect that there must be a region of Cosmic Extra Long Wave Radiation activity except that the nature of ELF (Extra Low Frequency) ( used in Submarine communications) may preclude our observing one. Submarines and planets operate within somewhat different environments. :wink:
When I tried to persuade my mind that an infinity may possibly exist I used the trick of drawing a straight line with a pencil forever. When the pencil needed replacing I got a whole factory full of pencils and kept on mentally drawing a straight line. When the factory ran out of pencils I bought a forest and made pencils. When I ran out of trees I got a planet and made pencils out of its trees. Finally (I think) my mind accepted the fact that there would always be planets to make pencils out of to draw straight lines with. I actually spent years at it, ruminating in the back of my mind much of the time.
I have spoken on these threads to people who have much more "proven" abilities in mathematics than I ever hope to attain. Even these persons who claimed to be able to easily understand the concept of infinity or eternity presented clearly erroneous examples as indications of their understanding. It is rough to get your mind around, no doubt about it.
IMO since an infinity is so difficult for us to understand we invented Gods, religion, "Big Bangs" and alternate dimensions to deal with infinities so as we can go about the more immediate business of killing sabretoothed tigers or making a living which happen to be a little more pressing considering our needs to stay alive and eat.
Jl, Specifically I can see no mechanical reason why the Universe needs to be limited in time or space. Since there is nothing to limit it why should we assume it is limited merely because our view of the Universe is limited by "mechanical problems beyond our control", ie. the nature of light. Perhaps also by natural limits on our imaginations.
If you cannot get your mind wrapped around an infinity of space or volume, rest assured, you are not alone. It's the most difficult thing to do that I have ever pursued. I am certainly not sure that I have done it myself yet
Best, M