Re: Are there Infinite Versions of You?

[Lawrence Crowell]

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? 
 

 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
>>
>>>  
>


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Re: Are there Infinite Versions of You?

['Brent Meeker' via Everything List]

On 2/6/2020 3:00 PM, Alan Grayson wrote:



On Wednesday, February 5, 2020 at 2:47:58 PM UTC-7, Brent wrote:



On 2/5/2020 4:09 AM, John Clark wrote:

On Wed, Feb 5, 2020 at 6:46 AM Alan Grayson > 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.


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


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


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

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Re: Are there Infinite Versions of You?

[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*

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
>
>>  

>>>

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Re: Are there Infinite Versions of You?

[Alan Grayson]

On Wednesday, February 5, 2020 at 2:47:58 PM UTC-7, Brent wrote:
>
>
>
> On 2/5/2020 4:09 AM, John Clark wrote:
>
> On Wed, Feb 5, 2020 at 6:46 AM Alan Grayson  > 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.
>
>
> 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
>

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

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Re: Are there Infinite Versions of You?

[Lawrence Crowell]

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. 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

>  
>>>
>>

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Re: Are there Infinite Versions of You?

['Brent Meeker' via Everything List]

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?


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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Re: Are there Infinite Versions of You?

['Brent Meeker' via Everything List]

On 2/5/2020 4:09 AM, John Clark wrote:
On Wed, Feb 5, 2020 at 6:46 AM Alan Grayson > 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.


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


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Re: Are there Infinite Versions of You?

[Alan Grayson]

On Wednesday, February 5, 2020 at 5:42:05 AM UTC-7, 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.
>


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

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Re: Are there Infinite Versions of You?

[Alan Grayson]

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.

>  
>>
>

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Re: Are there Infinite Versions of You?

[Lawrence Crowell]

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 

>  
>

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Re: Are there Infinite Versions of You?

[John Clark]

On Wed, Feb 5, 2020 at 6:46 AM Alan Grayson  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

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Re: Are there Infinite Versions of You?

[Alan Grayson]

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 *

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Re: Are there Infinite Versions of You?

[Lawrence Crowell]

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

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Re: Are there Infinite Versions of You?

[Alan Grayson]

On Wednesday, February 5, 2020 at 3:12:39 AM UTC-7, John Clark wrote:
>
>
>
> On Wed, Feb 5, 2020 at 3:29 AM Alan Grayson  > 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*
>

*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*

>
>  
>
>>
>>

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Re: Are there Infinite Versions of You?

[John Clark]

On Wed, Feb 5, 2020 at 3:29 AM Alan Grayson  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*



>
>

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Re: Are there Infinite Versions of You?

[Alan Grayson]

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 *

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