On 2/5/2020 4:42 AM, 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.

No.  Those are sufficient conditions, but not necessary.

Brent

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