On Thursday, February 6, 2020 at 5:03:07 PM UTC-6, Alan Grayson wrote: > > > > On Thursday, February 6, 2020 at 4:43:20 AM UTC-7, Lawrence Crowell wrote: >> >> On Wednesday, February 5, 2020 at 6:42:05 AM UTC-6, Alan Grayson wrote: >>> >>> >>> >>> On Wednesday, February 5, 2020 at 5:10:53 AM UTC-7, Lawrence Crowell >>> wrote: >>>> >>>> >>>> >>>> On Wednesday, February 5, 2020 at 6:05:54 AM UTC-6, Alan Grayson wrote: >>>>> >>>>> >>>>> >>>>> On Wednesday, February 5, 2020 at 4:54:03 AM UTC-7, Lawrence Crowell >>>>> wrote: >>>>>> >>>>>> On Wednesday, February 5, 2020 at 2:29:44 AM UTC-6, Alan Grayson >>>>>> wrote: >>>>>>> >>>>>>> >>>>>>> >>>>>>> On Monday, February 3, 2020 at 3:48:00 PM UTC-7, John Clark wrote: >>>>>>>> >>>>>>>> This video was just uploaded today: >>>>>>>> >>>>>>>> Are there Infinite Versions of You? >>>>>>>> <https://www.youtube.com/watch?v=qT110-Q8PJI> >>>>>>>> >>>>>>>> John K Clark >>>>>>>> >>>>>>> >>>>>>> *The answer is NO, if at least one parameter of the universe can >>>>>>> continuously vary, even along a finite interval or dimension. In this >>>>>>> case, >>>>>>> the number of possible universes is UNCOUNTABLE, and IIUC, under this >>>>>>> condition Poincare Recurrence doesn't apply. AG * >>>>>>> >>>>>> >>>>>> The Poincare recurrence of 10^{100} particles, approximately how many >>>>>> particles are out to the limit of observation, is around 10^{10^{100}} >>>>>> time >>>>>> units. Those time units would be Planck units of time, but the disparity >>>>>> of >>>>>> numbers means that we can consider this to be years with little error, >>>>>> Using the idea of space = time this would mean in spatial distance there >>>>>> is >>>>>> also a sort of recurrence. So out to that distance there exists some >>>>>> repeated form of what exists here. The quantum recurrence time is >>>>>> approximately 10^{10^{10^{100}}} time units or the exponent of this. >>>>>> So further out in space would imply not only a copy of things here, but >>>>>> also the same quantum phase. This is something within just the level 1 >>>>>> multiverse. >>>>>> >>>>>> Now this distance is utterly enormous and not just beyond the >>>>>> cosmological horizon, but beyond a distance where a Planck unit is >>>>>> redshifted to the horizon scale. This distance is around 2 trillion >>>>>> light >>>>>> years, which is a mere trifle by comparison to maybe 10^{10^{100}} >>>>>> light years or so. This length is the absolute limit of any >>>>>> observation. This then means the universe has some N genus manifold >>>>>> covering, or equivalently some polytope, covering space to reflect this >>>>>> multiplicity. For the polytope with N facets the horizon scale is a >>>>>> nearly >>>>>> infinitesimal bubble in the center. >>>>>> >>>>>> There is then of course in addition the level 2 multiverse which is >>>>>> the generation of pocket worlds within an inflationary de Sitter >>>>>> manifold. >>>>>> These may then have different renormalization group flows for gauge >>>>>> coupling values and physical vacua. Another level 3, or level 2.2, is >>>>>> the >>>>>> generation of dS inflationary manifolds from AdS/CFT physics. >>>>>> >>>>>> LC >>>>>> >>>>> >>>>> *Do you agree that if any parameter of our universe logically allows >>>>> some continuum of values, PR fails? Or if our universe is finite in >>>>> spatial >>>>> extent, PR fails? AG* >>>>> >>>> >>>> No >>>> >>>> LC >>>> >>> >>> >>> >>> https://physics.stackexchange.com/questions/94122/is-poincare-recurrence-relevant-to-our-universe >>> >>> The Poincaré recurrence theorem will hold for the universe only if the >>> following assumptions are true: >>> >>> 1. 1) All the particles in the universe are bound to a finite volume. >>> 2. 2) The universe has a finite number of possible states. >>> >>> If any of these assumptions is false, the Poincaré recurrence theorem >>> will break down. >>> >> >> >> FLRW and de Sitter spacetimes have spacelike boundaries for initial and >> final states. >> > > *What's a space-like boundary? TIA, AG* >
It is a spatial surface that bounds a conformal patch in de Sitter, or a point in FLRW. LC > > In an ideal set of circumstances the final future Cauchy data is in the >> infinite future. However, this is for a pure spacetime that is a conformal >> vacuum. The existence of matter or radiation breaks this conformal >> invariance. Conformal symmetry is a spacetime form of the Huygens' >> condition for light rays, and if conformal invariance is broken then the >> spatial surface in the future is not at "t = ∞," but a finite time. >> >> 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/08ba2669-b041-4d14-8266-715438a11af0%40googlegroups.com.
