On 1/25/2020 6:10 PM, Lawrence Crowell wrote:
On Saturday, January 25, 2020 at 6:49:36 PM UTC-6, Brent wrote: On 1/25/2020 4:32 PM, Lawrence Crowell wrote:On Saturday, January 25, 2020 at 6:23:54 AM UTC-6, John Clark wrote: On Fri, Jan 24, 2020 at 5:21 PM Bruce Kellett <[email protected]> wrote: >> And I've heard a bunch of bad analogies but I still haven't heard a direct answer to my question: What is the difference between a "finite" universe that is expanding and accelerating forever and an infinite universe that is expanding and accelerating forever? /> If you don't understand Brent's answer in terms of the range of values in coordinate maps, then you will never understand the difference./ Then I guess I'll never understand the difference. > A finite universe has a finite range of coordinate values. NOPE! Brent specifically said"/I'm assuming a continuum spacetime. So even a 1cm interval takes an infinite *number* of labels/". Thus even if the universe is not expanding at all and even if it's only 1cm across a infinite number of labels with a infinite rage of coordinate values printed on them would be needed. Nope. Space and spacetime are an epiphenomenology. They are mental perceptual models that result from large N-entanglements of quantum states. There are no infinite sets of points and labels, that would in fact be uncountably infinite. These things only exist in our mathematical representations or axiomatic systems. Now, what information we can get about space from the IR domain of energy at extreme distances, such as with burstars etc,, is the representation of what we call space being smooth fits the data. This does not mean that fundamentally there is an actual smooth continuum of space.I don't disagree, but you're getting further and further from saying what it means for spacetime to be finite versus infinite. Since it's our mathematical model, that should have a simple mathematical answer. BrentThere seems to be some sort of issue with the idea of continuum or space having an infinite number of points. I see this as a modern day version of asking how many angels can dance on a pin.
I have no issue with it. But it doesn't mean that a spherical spacetime is infinite. The infinity of metric distance in a Riemannian space is not the same as the infinite cardinality of point in a real interval.
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