Are there Infinite Versions of You?

[John Clark]

This video was just uploaded today:

Are there Infinite Versions of You?

John K Clark

[Bruno Marchal]

On 3 Feb 2020, at 23:47, John Clark <johnk...@gmail.com> wrote:

This video was just uploaded today:

Are there Infinite Versions of You?

OK. Nice.

Here is my short comment there:

<<

Things go the other way around (in the original contribution of your servitor). The notion of computation is an arithmetical notion, and it is relatively easy to prove that all computations are executed in all models of elementary arithmetic. Now, no universal machine, which "lives" in arithmetic, can determine which computations support her, and the machine is undetermined on all relative computations (those going through its current state of mind). That eventually necessitates to derive the physical laws from the relative statistics on all computations (in arithmetic), and that indeed eventually has shown  that the machine's observable has to obey to some quantum logics. The quantum materiality seems to be an illusion brought by the arithmetical seen from inside by infinitely distributed universal machines or numbers.

>>

In arithmetic, we dont need a monkey, nor any randomness. A (deterministic) Universal Dovetailer is enough to get both the description *and* the execution (relative emulation) of all computations, and it provides the main clue toward the solution of the probability measure problem which is that there is an important redundancy of the computations, which is highly structured (in a non computable non trivial way) and it is structured by the self-reference ability of the number/machine.

It is up to the believer in some ontology (richer than arithmetic or Turing equivalent) to explain how that ontology select the measure in arithmetic, which is hardly possible if we assume Digital Mechanism or Computationalism.

Bruno

John K Clark

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[Alan Grayson]

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 

[John Clark]

On Wed, Feb 5, 2020 at 3:29 AM Alan Grayson <agrays...@gmail.com> wrote:

> 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 

That statement makes absolutely no sense, none whatsoever. And NO, you do not understand correctly  

John K Clark

 

[Alan Grayson]

Poincare Recurrence doesn't apply for a universe with uncountably many possible states. This was suggested in the video. I might go back and give you the time stamp. In any event, since I can tie my shoes in an uncountable number of ways if space is continuous, it defies common sense to think uncountable universes come into being by such a simple act. I know you think common sense doesn't apply anymore, but alternatively, does it makes sense to totally throw it away? AG

 

[Lawrence Crowell]

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

[Alan Grayson]

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 

[John Clark]

On Wed, Feb 5, 2020 at 6:46 AM Alan Grayson <agrays...@gmail.com> wrote:

> Poincare Recurrence doesn't apply for a universe with uncountably many possible states.

If there are a uncountably infinite number of possible states then there is certainly a countably infinite number of states too. And if there are a countably infinite number of states then there is certainly a finite number of states too; 10^10^10^10^100 or any other finite number you care to name. As far as Poincare Recurrence is concerned uncountably infinite possible states for the universe to be in is VAST overkill.

John K Clark

[Lawrence Crowell]

No

LC 

 

[Alan Grayson]

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.

 

[Alan Grayson]

 The number of possible states of the H atom is countably infinite. Thus, condition 2 fails for our universe, and so does PR. AG 

[Brent Meeker]

The Poincaré recurrence theorem states that certain systems will, after a sufficiently long but finite time, return to a state arbitrarily close to (for continuous state systems), or exactly the same as (for discrete state systems), their initial state.  So it may apply equally to systems with uncountably infinite number of states.

Brent

[Brent Meeker]

No.  Those are sufficient conditions, but not necessary.

Brent

[Lawrence Crowell]

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

 

[Alan Grayson]

ISTM that a continuous state system is the same as one with uncountably infinite number of states (which characterizes our universe since free particles have an uncountably infinite number of states), yet for the latter you say Poincare recurrence "may" apply. Please clarify. AG

[Alan Grayson]

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?

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

[Brent Meeker]

It depends on the system being closed.  Obviously there need not be a recurrence time for dynamics on an infinite line, either real or integer.

Brent

[Lawrence Crowell]

It is a spatial surface that bounds a conformal patch in de Sitter, or a point in FLRW.

LC