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. 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 everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/6d58cf2c-313c-4196-baca-904a885f4864%40googlegroups.com.
