On Saturday, January 25, 2020 at 6:23:09 AM UTC-7, John Clark wrote: > > On Fri, Jan 24, 2020 at 5:50 PM 'Brent Meeker' Everything List < > [email protected] <javascript:>> wrote: > > >> I would say a infinite amount of information would be needed to >>> adequately >> >> >> > *Nobody asked about the amount of information. * >> > > Well you certainly didn't ask about it, you ignored information entirely > and I would say that was the fundamental reason your analysis failed. > > >> * > That's a red herring that LC threw in. * >> > > A red herring?! Lawrence is wise enough to know that if you're developing > a cosmological model while pretending information does not exist then > you're heading for trouble. > > *> The question was about the expansion and size of the universe.* >> > > No, the question was if the universe was infinite or finite. Yes if the > position space (aka plain ordinary space) is infinite then it would be safe > to say the universe is infinite, but that's just one attribute the universe > can have, there is also momentum space and informational content; if either > of those was infinite I would say that regardless of whether position space > was infinite or not it would be misleading at best and dead wrong at worse > to say the universe was finite. > > >> * > As in my analogy, in a finite universe there are a finite number of >> intervals of finite distance that can link any two points in the universe. >> Of course this refers to it being finite at a given time, and you raised >> the problem of defining what counts as "at the same time". The answer is >> that it is at the same time if it is at the same degree of >> expansion...operationally it means that two distant events are "at the same >> time" if the isotropic temperature of the CMB looks the same to them.* >> > > Even if we ignore Quantum Mechanics any finite level of precision used to > measure the current position and momentum of those two particles or of the > temperature of the CMB will soon (very soon because the universe is > accelerating) prove to be insufficiently precise to predict their future > position and momentum because phase space keeps getting larger at an > accelerating rate. The fundamental reason you can't make a good prediction > is you don't have enough information, an infinite amount is required and > you don't have that. > > John K Clark >
I don't think coordinate arguments will solve your problem. Suppose we have an observer at the origin of a one-dimensional space. If you consider a 1 meter line starting at the origin and increasing in length at an accelerating rate at its end point, then obviously, at any observer time t, the length of the line is finite and can be easily calculated. Now consider an expanding 4 dimensional space-time continuum. For any observer, and therefore for all observers, the volume of this space is obviously finite regardless of how fast it's expanding. So it's conceptually easy to distinguish finite from infinite volume when comparing an expanding hyper-sphere (finite) from an expanding plane (infinite). Your doubt seems to depend on the inability of observers to make the measurements when, due to expansion, both geometries have non-observable regions. So, does the distinction between finite and infinite volumes really depend upon what observers can measure? IMO, this is where the rubber hits the road. AG -- 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/b636a3df-f317-43f4-bb41-cb13109abce4%40googlegroups.com.
