On Friday, January 24, 2020 at 4:09:06 PM UTC-6, John Clark wrote: > > On Fri, Jan 24, 2020 at 3:06 PM 'Brent Meeker' via Everything List < > [email protected] <javascript:>> wrote: > > >> >> If you're assuming that Real Numbers exist and that even a 1 cm >>> universe would need a infinite number of labels >> >> >> * > But not an infinite range of labels.* >> > > OK now it's official, I have no idea what you're talking about. > > >> I ask my question again: >>> *What is the difference between a "finite" universe that is expanding >>> and accelerating and an infinite universe that is expanding and >>> accelerating?* >> >> >> * > Imagine the Earth is expanding like a balloon and at an accelerating >> pace. * >> > > A balloon is a terrible analogy for the Earth and a inflating balloon is > an even worse analogy for a universe that will expand and accelerate > forever. With the balloon you're standing outside of it watching the > balloon expand into something that's already there, but you can't stand > outside of the universe and the universe is not expanding into anything > that's already there. > > >> *> You can't go fast enough to circumnavigate it because there's a speed >> limit. * >> > > And to call that speed limit the speed of light would be true but tends to > trivialize it, really it's something far more fundamental and profound, > it's the very speed of causality. > > >> *> In your imagination is it finite or infinite? Are there locations on >> it which are finite distances apart? Is there a set of such locations >> connecting any two points? Is the sum of the distances between locations >> of such a set finite?* >> > > I would say a infinite amount of information would be needed to adequately > describe the evolution of the phase space (all possible values of the > position and momentum of the particles in the universe) of such a expanding > accelerating universe. It's infinite because no amount of approximation > would be good enough for prediction, due to the accelerated creation of new > space there will always be more values of position and momentum that > particles can be in tomorrow than they can be in today. By the way, all > this talk about the distance between particles in a expanding accelerating > universe is rather ambiguous if you don't specify when, and "now" has no > meaning everybody agrees with. > > 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? > > John K Clark >
The distinction between an accelerated universe that is open and one that is closed is not hard to understand theoretically. I think the real question is how can an observer know which they inhabit. A spherical universe that is accelerated has a cosmological horizon that makes galaxies accelerate away faster than any signal or particle from Earth could ever catch up with. The same of course for the flat accelerated universe. If the radius of curvature of the spherical universe is large enough it might be impossible to determine which one inhabits by astronomical or astrometric means. The difference between these two is can be seen as topological, and according to why a timelike curve can't be transformed into a null ray. I attach my figure below of the dS spacetime [image: de Sitter space hyperboloid.png] The green diagonal lines are surfaces for the final states of an open cosmology and the dotted line between the two green lines is the initial state of the two cosmologies in a spatial surface. The two green lines may be identified with the I^+ in a conformal diagram. This is referred to by some as a biverse. The red curves are time evolved spatial surfaces and the blue curves are time directions. The closed spatial universe is more intuitive as analogous to the circle at the waist and a foliation of circles would be the time evolved cosmos. There is then no way to transform one type of cosmology into the other. The difference is also topological, and the different topological numbers (Betti numbers, Chern numbers etc) are associated with different quantum numbers on the open and closed spatial surfaces. In that way the two have the same physical information. This would then mean there is some possible way to ascertain whether the universe is open or closed by some quantum field information. LC -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/69ba5069-ee51-46c2-91ca-1711540b8931%40googlegroups.com.
