Re: Inflation and the total size of the universe

[John Clark]

On Thu, Apr 16, 2020 at 3:51 PM Alan Grayson  wrote:


> *>It surely does have a basis in experience. We've never seen any process
> that can occur in zero time duration! AG *
>

Therefore one should be extremely cautious about confidently asserting what
can and can not happen during zero time duration, such as finite stuff can
but infinite stuff can't.

John K Clark

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Re: Inflation and the total size of the universe

[Alan Grayson]

On Thursday, April 16, 2020 at 1:32:23 PM UTC-6, Brent wrote:
>
>
>
> On 4/16/2020 6:07 AM, Alan Grayson wrote: 
> > But what seems impossible is for our universe to begin at some 
> > instant, and being infinite in spatial extent at that instant-- which 
> > is what Clark asserts. AG 
>
> Why does that seem more impossible than beginning at a finite size from 
> nothing at some instant?  And why is what "seems" of any significance 
> where one's intuition has no basis in experience? 
>
> Brent 
>

It surely does have a basis in experience. We've never seen any process 
that can occur in zero time duration! AG 

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Re: Inflation and the total size of the universe

['Brent Meeker' via Everything List]

On 4/16/2020 6:07 AM, Alan Grayson wrote:
But what seems impossible is for our universe to begin at some 
instant, and being infinite in spatial extent at that instant-- which 
is what Clark asserts. AG 


Why does that seem more impossible than beginning at a finite size from 
nothing at some instant?  And why is what "seems" of any significance 
where one's intuition has no basis in experience?


Brent

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Re: Inflation and the total size of the universe

[Alan Grayson]

On Thursday, April 16, 2020 at 5:50:27 AM UTC-6, Lawrence Crowell wrote:
>
> On Wednesday, April 15, 2020 at 8:50:35 PM UTC-5, Alan Grayson wrote:
>>
>>
>>
>> On Sunday, April 12, 2020 at 5:46:46 PM UTC-6, Lawrence Crowell wrote:
>>>
>>> On Saturday, April 11, 2020 at 6:30:00 PM UTC-5, Alan Grayson wrote:



 On Saturday, April 11, 2020 at 3:36:28 PM UTC-6, Lawrence Crowell wrote:
>
> On Saturday, April 11, 2020 at 2:26:58 PM UTC-5, Alan Grayson wrote:
>>
>>
>>
>> On Saturday, April 11, 2020 at 9:10:19 AM UTC-6, Lawrence Crowell 
>> wrote:
>>>
>>> On Friday, April 10, 2020 at 8:45:22 PM UTC-5, Alan Grayson wrote:



 On Sunday, March 29, 2020 at 12:03:10 PM UTC-6, Lawrence Crowell 
 wrote:
>
> On Sunday, March 29, 2020 at 1:57:12 AM UTC-5, Alan Grayson wrote:
>>
>>
>>
>> On Saturday, March 28, 2020 at 5:38:33 PM UTC-6, Lawrence Crowell 
>> wrote:
>>>
>>> On Saturday, March 28, 2020 at 5:27:51 AM UTC-5, Alan Grayson 
>>> wrote:



 On Wednesday, March 25, 2020 at 4:25:43 PM UTC-6, Lawrence 
 Crowell wrote:
>
> On Wednesday, March 25, 2020 at 2:17:39 PM UTC-5, Alan Grayson 
> wrote:
>
>>
>>
>> On Wednesday, March 25, 2020 at 9:57:44 AM UTC-6, Lawrence 
>> Crowell wrote:
>>>
>>> On Wednesday, March 25, 2020 at 10:24:30 AM UTC-5, Alan 
>>> Grayson wrote:



 On Wednesday, March 25, 2020 at 2:58:45 AM UTC-6, Lawrence 
 Crowell wrote:
>
> On Wednesday, March 25, 2020 at 1:28:21 AM UTC-5, Alan 
> Grayson wrote:
>>
>>
>>
>> On Tuesday, March 24, 2020 at 6:21:50 PM UTC-6, Lawrence 
>> Crowell wrote:
>>>
>>> On Tuesday, March 24, 2020 at 6:19:41 PM UTC-5, Alan 
>>> Grayson wrote:



 On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence 
 Crowell wrote:
>
> Inflation was initiate 10^{-35}sec after the quantum 
> fluctuation appearance of the observable cosmos, and this 
> had a duration of 
> 10^{-30}sec. The cosmological constant averaged around Λ 
> = 10^{48}m^{-2}. 
> If I divide by the speed of light squared this comes to 
> 10^{32}s^{-2} and 
> we get √(Λ)T = 10^{2}. This means any spatial region 
> expanded by a factor 
> of 10^{√(Λ)T} which is large. The natural log of this 
> is 230 and this is not too far off from the more precise 
> calculation of 60 
> e-folds. The 60 e-folds is a phenomenological fit that 
> matches inflation 
> with the observed universe.
>
> How much of the universe is unavailable depends upon 
> whether k = -1, 0 or 1. The furthest out some quantum 
> might emerge and have 
> an influence is for a Planck scale quantum to now be 
> inflated to the CMB 
> scale. I know I have gone through this here before, but 
> the result is the 
> furthest we can detect anything is around 1800 billion 
> light years, which 
> would be a graviton or quantum black hole that leaves an 
> imprint or 
> signature on the CMB. It is not possible from theory to 
> know what 
> percentage this is of the entire shebang, and for k = -1 
> or 0 it is an 
> infinitesimal part.
>
> LC
>

 For k=0, a flat universe, we know the answer since, as 
 you've acknowledged, it's infinite in spatial extent.  
 Consequently, since 
 the observable universe is finite in spatial extent, the 
 unobserved 
 universe must be infinite in extent (for a flat universe). 
 Can you estimate 
 the size of the unobservable universe for a positively 
 curved universe? AG

>>>

Re: Inflation and the total size of the universe

[Alan Grayson]

On Thursday, April 16, 2020 at 6:09:06 AM UTC-6, Quentin Anciaux wrote:
>
>
>
> Le jeu. 16 avr. 2020 à 03:43, Alan Grayson  > a écrit :
>
>>
>>
>> On Wednesday, April 15, 2020 at 7:25:50 AM UTC-6, John Clark wrote:
>>>
>>>
>>>
>>> On Tue, Apr 14, 2020 at 4:27 PM Alan Grayson  
>>> wrote:
>>>
>>> *> If you solve Schroedinger's equation for the wf, you get a solution 
 for all space and time. If it's physical, or shall we say ontological, how 
 can it propagate infinitely? *
>>>
>>>
>>> If it started out infinite 
>>>
>>
>>
>> I don't think you understand the implication of your supposition. It 
>> MEANS spatially infinite space came about at some INSTANT!  
>>
>
> But going *from nothing* to *anything* is problematic, there is 
> *absolutely* no known *physical process* that creates anything out of pure 
> absolute nothing... so creating "something" or "everything" from nothing is 
> as much non physical and impossible, and so talking about physical process 
> to constrain finite or infinite is dubious at best.
>

If you read me carefully, I have stated that there must be something from 
which our universe emerged. I referred to it as the "substratum". It could 
be infinite in spatial extent with an infinite past. But what seems 
impossible is for our universe to begin at some instant, and being infinite 
in spatial extent at that instant-- which is what Clark asserts. AG 

>  
>
>> Your unstated inference is that it took a time duration of ZERO for that 
>> to happen. Do you really think any physical processes can occur in a time 
>> duration of zero? But let's suppose it happened in finite time, or possibly 
>> with an infinite past. If so, the age of the universe could be much larger 
>> than 13.8 BLY, depending on how long it took to create that infinite 
>> spatial extent. It can't be spontaneously generated in a time duration of 
>> zero. However, if it occurred, it would have existed BEFORE the creation 
>> INSTANT of OUR universe. If so, it's not really part of OUR universe, but 
>> part of the "substratum" from which the BB arose. AG 
>>
>> the universe wouldn't have to propagate at all to be infinite. And finite 
>>> or infinite it makes no difference, Schrodinger's equation breaks down 
>>> at Big Bang time zero and so does every other known equation. That 
>>> situation won't change until somebody finds a quantum theory for gravity.
>>>
>>>  John K Clark
>>>
>> -- 
>> 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 everyth...@googlegroups.com .
>> To view this discussion on the web visit 
>> https://groups.google.com/d/msgid/everything-list/5324235a-3751-4463-b7fd-4c9d5f29da5d%40googlegroups.com
>>  
>> 
>> .
>>
>
>
> -- 
> All those moments will be lost in time, like tears in rain. (Roy 
> Batty/Rutger Hauer)
>

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Re: Inflation and the total size of the universe

[Quentin Anciaux]

Le jeu. 16 avr. 2020 à 03:43, Alan Grayson  a
écrit :

>
>
> On Wednesday, April 15, 2020 at 7:25:50 AM UTC-6, John Clark wrote:
>>
>>
>>
>> On Tue, Apr 14, 2020 at 4:27 PM Alan Grayson  wrote:
>>
>> *> If you solve Schroedinger's equation for the wf, you get a solution
>>> for all space and time. If it's physical, or shall we say ontological, how
>>> can it propagate infinitely? *
>>
>>
>> If it started out infinite
>>
>
>
> I don't think you understand the implication of your supposition. It MEANS
> spatially infinite space came about at some INSTANT!
>

But going *from nothing* to *anything* is problematic, there is
*absolutely* no known *physical process* that creates anything out of pure
absolute nothing... so creating "something" or "everything" from nothing is
as much non physical and impossible, and so talking about physical process
to constrain finite or infinite is dubious at best.


> Your unstated inference is that it took a time duration of ZERO for that
> to happen. Do you really think any physical processes can occur in a time
> duration of zero? But let's suppose it happened in finite time, or possibly
> with an infinite past. If so, the age of the universe could be much larger
> than 13.8 BLY, depending on how long it took to create that infinite
> spatial extent. It can't be spontaneously generated in a time duration of
> zero. However, if it occurred, it would have existed BEFORE the creation
> INSTANT of OUR universe. If so, it's not really part of OUR universe, but
> part of the "substratum" from which the BB arose. AG
>
> the universe wouldn't have to propagate at all to be infinite. And finite
>> or infinite it makes no difference, Schrodinger's equation breaks down
>> at Big Bang time zero and so does every other known equation. That
>> situation won't change until somebody finds a quantum theory for gravity.
>>
>>  John K Clark
>>
> --
> 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/5324235a-3751-4463-b7fd-4c9d5f29da5d%40googlegroups.com
> 
> .
>


-- 
All those moments will be lost in time, like tears in rain. (Roy
Batty/Rutger Hauer)

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Re: Inflation and the total size of the universe

[Lawrence Crowell]

On Wednesday, April 15, 2020 at 8:50:35 PM UTC-5, Alan Grayson wrote:
>
>
>
> On Sunday, April 12, 2020 at 5:46:46 PM UTC-6, Lawrence Crowell wrote:
>>
>> On Saturday, April 11, 2020 at 6:30:00 PM UTC-5, Alan Grayson wrote:
>>>
>>>
>>>
>>> On Saturday, April 11, 2020 at 3:36:28 PM UTC-6, Lawrence Crowell wrote:

 On Saturday, April 11, 2020 at 2:26:58 PM UTC-5, Alan Grayson wrote:
>
>
>
> On Saturday, April 11, 2020 at 9:10:19 AM UTC-6, Lawrence Crowell 
> wrote:
>>
>> On Friday, April 10, 2020 at 8:45:22 PM UTC-5, Alan Grayson wrote:
>>>
>>>
>>>
>>> On Sunday, March 29, 2020 at 12:03:10 PM UTC-6, Lawrence Crowell 
>>> wrote:

 On Sunday, March 29, 2020 at 1:57:12 AM UTC-5, Alan Grayson wrote:
>
>
>
> On Saturday, March 28, 2020 at 5:38:33 PM UTC-6, Lawrence Crowell 
> wrote:
>>
>> On Saturday, March 28, 2020 at 5:27:51 AM UTC-5, Alan Grayson 
>> wrote:
>>>
>>>
>>>
>>> On Wednesday, March 25, 2020 at 4:25:43 PM UTC-6, Lawrence 
>>> Crowell wrote:

 On Wednesday, March 25, 2020 at 2:17:39 PM UTC-5, Alan Grayson 
 wrote:

>
>
> On Wednesday, March 25, 2020 at 9:57:44 AM UTC-6, Lawrence 
> Crowell wrote:
>>
>> On Wednesday, March 25, 2020 at 10:24:30 AM UTC-5, Alan 
>> Grayson wrote:
>>>
>>>
>>>
>>> On Wednesday, March 25, 2020 at 2:58:45 AM UTC-6, Lawrence 
>>> Crowell wrote:

 On Wednesday, March 25, 2020 at 1:28:21 AM UTC-5, Alan 
 Grayson wrote:
>
>
>
> On Tuesday, March 24, 2020 at 6:21:50 PM UTC-6, Lawrence 
> Crowell wrote:
>>
>> On Tuesday, March 24, 2020 at 6:19:41 PM UTC-5, Alan 
>> Grayson wrote:
>>>
>>>
>>>
>>> On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence 
>>> Crowell wrote:

 Inflation was initiate 10^{-35}sec after the quantum 
 fluctuation appearance of the observable cosmos, and this 
 had a duration of 
 10^{-30}sec. The cosmological constant averaged around Λ = 
 10^{48}m^{-2}. 
 If I divide by the speed of light squared this comes to 
 10^{32}s^{-2} and 
 we get √(Λ)T = 10^{2}. This means any spatial region 
 expanded by a factor 
 of 10^{√(Λ)T} which is large. The natural log of this 
 is 230 and this is not too far off from the more precise 
 calculation of 60 
 e-folds. The 60 e-folds is a phenomenological fit that 
 matches inflation 
 with the observed universe.

 How much of the universe is unavailable depends upon 
 whether k = -1, 0 or 1. The furthest out some quantum 
 might emerge and have 
 an influence is for a Planck scale quantum to now be 
 inflated to the CMB 
 scale. I know I have gone through this here before, but 
 the result is the 
 furthest we can detect anything is around 1800 billion 
 light years, which 
 would be a graviton or quantum black hole that leaves an 
 imprint or 
 signature on the CMB. It is not possible from theory to 
 know what 
 percentage this is of the entire shebang, and for k = -1 
 or 0 it is an 
 infinitesimal part.

 LC

>>>
>>> For k=0, a flat universe, we know the answer since, as 
>>> you've acknowledged, it's infinite in spatial extent.  
>>> Consequently, since 
>>> the observable universe is finite in spatial extent, the 
>>> unobserved 
>>> universe must be infinite in extent (for a flat universe). 
>>> Can you estimate 
>>> the size of the unobservable universe for a positively 
>>> curved universe? AG
>>>
>>
>> The cosmological constant is a Ricci curvature with Λ = 
>> R_{tt} for the flat k = 0 case. for k = 1 there is a spatial 
>> Ricci 
>> curvature 

Re: Inflation and the total size of the universe

[Alan Grayson]

On Sunday, April 12, 2020 at 5:46:46 PM UTC-6, Lawrence Crowell wrote:
>
> On Saturday, April 11, 2020 at 6:30:00 PM UTC-5, Alan Grayson wrote:
>>
>>
>>
>> On Saturday, April 11, 2020 at 3:36:28 PM UTC-6, Lawrence Crowell wrote:
>>>
>>> On Saturday, April 11, 2020 at 2:26:58 PM UTC-5, Alan Grayson wrote:



 On Saturday, April 11, 2020 at 9:10:19 AM UTC-6, Lawrence Crowell wrote:
>
> On Friday, April 10, 2020 at 8:45:22 PM UTC-5, Alan Grayson wrote:
>>
>>
>>
>> On Sunday, March 29, 2020 at 12:03:10 PM UTC-6, Lawrence Crowell 
>> wrote:
>>>
>>> On Sunday, March 29, 2020 at 1:57:12 AM UTC-5, Alan Grayson wrote:



 On Saturday, March 28, 2020 at 5:38:33 PM UTC-6, Lawrence Crowell 
 wrote:
>
> On Saturday, March 28, 2020 at 5:27:51 AM UTC-5, Alan Grayson 
> wrote:
>>
>>
>>
>> On Wednesday, March 25, 2020 at 4:25:43 PM UTC-6, Lawrence 
>> Crowell wrote:
>>>
>>> On Wednesday, March 25, 2020 at 2:17:39 PM UTC-5, Alan Grayson 
>>> wrote:
>>>


 On Wednesday, March 25, 2020 at 9:57:44 AM UTC-6, Lawrence 
 Crowell wrote:
>
> On Wednesday, March 25, 2020 at 10:24:30 AM UTC-5, Alan 
> Grayson wrote:
>>
>>
>>
>> On Wednesday, March 25, 2020 at 2:58:45 AM UTC-6, Lawrence 
>> Crowell wrote:
>>>
>>> On Wednesday, March 25, 2020 at 1:28:21 AM UTC-5, Alan 
>>> Grayson wrote:



 On Tuesday, March 24, 2020 at 6:21:50 PM UTC-6, Lawrence 
 Crowell wrote:
>
> On Tuesday, March 24, 2020 at 6:19:41 PM UTC-5, Alan 
> Grayson wrote:
>>
>>
>>
>> On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence 
>> Crowell wrote:
>>>
>>> Inflation was initiate 10^{-35}sec after the quantum 
>>> fluctuation appearance of the observable cosmos, and this 
>>> had a duration of 
>>> 10^{-30}sec. The cosmological constant averaged around Λ = 
>>> 10^{48}m^{-2}. 
>>> If I divide by the speed of light squared this comes to 
>>> 10^{32}s^{-2} and 
>>> we get √(Λ)T = 10^{2}. This means any spatial region 
>>> expanded by a factor 
>>> of 10^{√(Λ)T} which is large. The natural log of this 
>>> is 230 and this is not too far off from the more precise 
>>> calculation of 60 
>>> e-folds. The 60 e-folds is a phenomenological fit that 
>>> matches inflation 
>>> with the observed universe.
>>>
>>> How much of the universe is unavailable depends upon 
>>> whether k = -1, 0 or 1. The furthest out some quantum might 
>>> emerge and have 
>>> an influence is for a Planck scale quantum to now be 
>>> inflated to the CMB 
>>> scale. I know I have gone through this here before, but the 
>>> result is the 
>>> furthest we can detect anything is around 1800 billion 
>>> light years, which 
>>> would be a graviton or quantum black hole that leaves an 
>>> imprint or 
>>> signature on the CMB. It is not possible from theory to 
>>> know what 
>>> percentage this is of the entire shebang, and for k = -1 or 
>>> 0 it is an 
>>> infinitesimal part.
>>>
>>> LC
>>>
>>
>> For k=0, a flat universe, we know the answer since, as 
>> you've acknowledged, it's infinite in spatial extent.  
>> Consequently, since 
>> the observable universe is finite in spatial extent, the 
>> unobserved 
>> universe must be infinite in extent (for a flat universe). 
>> Can you estimate 
>> the size of the unobservable universe for a positively 
>> curved universe? AG
>>
>
> The cosmological constant is a Ricci curvature with Λ = 
> R_{tt} for the flat k = 0 case. for k = 1 there is a spatial 
> Ricci 
> curvature R_{rr}. This contributes to the occurrence of 
> the cosmological constant, but it is tiny. So R_{rr} 
> = δR_{tt} for δ a rather small number. The spatial sphere has 

Re: Inflation and the total size of the universe

[Alan Grayson]

On Wednesday, April 15, 2020 at 7:25:50 AM UTC-6, John Clark wrote:
>
>
>
> On Tue, Apr 14, 2020 at 4:27 PM Alan Grayson  > wrote:
>
> *> If you solve Schroedinger's equation for the wf, you get a solution for 
>> all space and time. If it's physical, or shall we say ontological, how can 
>> it propagate infinitely? *
>
>
> If it started out infinite 
>


I don't think you understand the implication of your supposition. It MEANS 
spatially infinite space came about at some INSTANT!  Your unstated 
inference is that it took a time duration of ZERO for that to happen. Do 
you really think any physical processes can occur in a time duration of 
zero? But let's suppose it happened in finite time, or possibly with an 
infinite past. If so, the age of the universe could be much larger than 
13.8 BLY, depending on how long it took to create that infinite spatial 
extent. It can't be spontaneously generated in a time duration of zero. 
However, if it occurred, it would have existed BEFORE the creation INSTANT 
of OUR universe. If so, it's not really part of OUR universe, but part of 
the "substratum" from which the BB arose. AG 

the universe wouldn't have to propagate at all to be infinite. And finite 
> or infinite it makes no difference, Schrodinger's equation breaks down at 
> Big Bang time zero and so does every other known equation. That situation 
> won't change until somebody finds a quantum theory for gravity.
>
>  John K Clark
>

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Re: Inflation and the total size of the universe

[Lawrence Crowell]

On Wednesday, April 15, 2020 at 8:25:50 AM UTC-5, John Clark wrote:
>
>
>
> On Tue, Apr 14, 2020 at 4:27 PM Alan Grayson  > wrote:
>
> *> If you solve Schroedinger's equation for the wf, you get a solution for 
>> all space and time. If it's physical, or shall we say ontological, how can 
>> it propagate infinitely? *
>
>
> If it started out infinite the universe wouldn't have to propagate at all 
> to be infinite. And finite or infinite it makes no difference, Schrodinger's 
> equation 
> breaks down at Big Bang time zero and so does every other known equation. 
> That situation won't change until somebody finds a quantum theory for 
> gravity.
>
>  John K Clark
>

This is pretty much the case. In what I wrote above about a quantum 
critical point or phase transition, quantum nonlocality will insure the 
same initial conditions are everywhere. The inflationary cosmology can be 
infinite.

LC 

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Re: Inflation and the total size of the universe

[John Clark]

On Tue, Apr 14, 2020 at 4:27 PM Alan Grayson  wrote:

*> If you solve Schroedinger's equation for the wf, you get a solution for
> all space and time. If it's physical, or shall we say ontological, how can
> it propagate infinitely? *


If it started out infinite the universe wouldn't have to propagate at all
to be infinite. And finite or infinite it makes no difference,
Schrodinger's equation
breaks down at Big Bang time zero and so does every other known equation.
That situation won't change until somebody finds a quantum theory for
gravity.

 John K Clark

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Re: Inflation and the total size of the universe

[Alan Grayson]

On Tuesday, April 14, 2020 at 8:21:37 AM UTC-6, Quentin Anciaux wrote:
>
>
>
> Le mar. 14 avr. 2020 à 16:20, Quentin Anciaux  > a écrit :
>
>>
>>
>> Le mar. 14 avr. 2020 à 16:14, Alan Grayson > > a écrit :
>>
>>>
>>>
>>> On Tuesday, April 14, 2020 at 7:54:19 AM UTC-6, Alan Grayson wrote:



 On Tuesday, April 14, 2020 at 5:28:07 AM UTC-6, John Clark wrote:
>
> On Mon, Apr 13, 2020 at 5:11 PM Alan Grayson  
> wrote:
>
> *>>> if you accept the measured age, it can't be finite or infinite in 
 spatial extent when it began*
>>>
>>>
>>> >> If something isn't finite or infinite what is the third 
>>> alternative? 
>>>
>>
>> > *It doesn't exist;*
>>
>
> OK, but then what is "it"?
>
> > *that is, your hypothesis that that when the universe began it was 
>> already infinite, or possibly finite, is false.*
>>
>
> So I ask again, if the universe isn't finite and it isn't infinite 
> what is your third alternative? And why would creating a finite amount of 
> something from nothing be easier than creating a infinite amount of 
> something from nothing? In my previous post I gave reasons for thinking 
> the 
> infinite case might actually be simpler. And if creation was not involved 
> because a finite universe always existed then why couldn't a infinite 
> universe just as easily always have existed too?
>
>   John K Clark
>

 This is getting tedious. If the universe began at some instant (having 
 zero time duration), and assuming physical processes require time, there 
 was insufficient time to create anything, finite or infinite, *at that 
 instant*. It's like a volcano erupting, and you're claiming that when 
 the eruption began, the cone was existing at that point in time. AG 

>>>
>>> You want to claim the universe began, presumably at some instant, and 
>>> also claim it was infinite in extent at that point in time. But if physical 
>>> processes require time, your claim makes no sense. AG 
>>>
>>
>> You want to claim the universe began, presumably at some instant, and 
>> also claim it was finite in extent at that point in time. But if physical 
>> processes require time, your claim makes no sense  
>>
>
> IOW nothing to finite, nothing to infinite... same fight.  
>

If you solve Schroedinger's equation for the wf, you get a solution for all 
space and time. If it's physical, or shall we say ontological, how can it 
propagate infinitely? This issue is similar to the problem of a universe 
starting with an infinity of spatial extent. If that were the case, the 
universe must have preexisted for the time required to create that alleged 
infinity. It might have had an infinite past, in which case it couldn't 
have a finite age. If the preexisting space was finite, it couldn't be 
flat, or saddle-shaped, since those spaces are infinite in spatial extent. 
AG

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>>>  
>>> 
>>> .
>>>
>>
>>
>> -- 
>> All those moments will be lost in time, like tears in rain. (Roy 
>> Batty/Rutger Hauer)
>>
>
>
> -- 
> All those moments will be lost in time, like tears in rain. (Roy 
> Batty/Rutger Hauer)
>

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Re: Inflation and the total size of the universe

[Quentin Anciaux]

Le mar. 14 avr. 2020 à 16:20, Quentin Anciaux  a écrit :

>
>
> Le mar. 14 avr. 2020 à 16:14, Alan Grayson  a
> écrit :
>
>>
>>
>> On Tuesday, April 14, 2020 at 7:54:19 AM UTC-6, Alan Grayson wrote:
>>>
>>>
>>>
>>> On Tuesday, April 14, 2020 at 5:28:07 AM UTC-6, John Clark wrote:

 On Mon, Apr 13, 2020 at 5:11 PM Alan Grayson 
 wrote:

 *>>> if you accept the measured age, it can't be finite or infinite in
>>> spatial extent when it began*
>>
>>
>> >> If something isn't finite or infinite what is the third
>> alternative?
>>
>
> > *It doesn't exist;*
>

 OK, but then what is "it"?

 > *that is, your hypothesis that that when the universe began it was
> already infinite, or possibly finite, is false.*
>

 So I ask again, if the universe isn't finite and it isn't infinite what
 is your third alternative? And why would creating a finite amount of
 something from nothing be easier than creating a infinite amount of
 something from nothing? In my previous post I gave reasons for thinking the
 infinite case might actually be simpler. And if creation was not involved
 because a finite universe always existed then why couldn't a infinite
 universe just as easily always have existed too?

   John K Clark

>>>
>>> This is getting tedious. If the universe began at some instant (having
>>> zero time duration), and assuming physical processes require time, there
>>> was insufficient time to create anything, finite or infinite, *at that
>>> instant*. It's like a volcano erupting, and you're claiming that when
>>> the eruption began, the cone was existing at that point in time. AG
>>>
>>
>> You want to claim the universe began, presumably at some instant, and
>> also claim it was infinite in extent at that point in time. But if physical
>> processes require time, your claim makes no sense. AG
>>
>
> You want to claim the universe began, presumably at some instant, and also
> claim it was finite in extent at that point in time. But if physical
> processes require time, your claim makes no sense
>

IOW nothing to finite, nothing to infinite... same fight.

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>> 
>> .
>>
>
>
> --
> All those moments will be lost in time, like tears in rain. (Roy
> Batty/Rutger Hauer)
>


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Re: Inflation and the total size of the universe

[Quentin Anciaux]

Le mar. 14 avr. 2020 à 16:14, Alan Grayson  a
écrit :

>
>
> On Tuesday, April 14, 2020 at 7:54:19 AM UTC-6, Alan Grayson wrote:
>>
>>
>>
>> On Tuesday, April 14, 2020 at 5:28:07 AM UTC-6, John Clark wrote:
>>>
>>> On Mon, Apr 13, 2020 at 5:11 PM Alan Grayson 
>>> wrote:
>>>
>>> *>>> if you accept the measured age, it can't be finite or infinite in
>> spatial extent when it began*
>
>
> >> If something isn't finite or infinite what is the third
> alternative?
>

 > *It doesn't exist;*

>>>
>>> OK, but then what is "it"?
>>>
>>> > *that is, your hypothesis that that when the universe began it was
 already infinite, or possibly finite, is false.*

>>>
>>> So I ask again, if the universe isn't finite and it isn't infinite what
>>> is your third alternative? And why would creating a finite amount of
>>> something from nothing be easier than creating a infinite amount of
>>> something from nothing? In my previous post I gave reasons for thinking the
>>> infinite case might actually be simpler. And if creation was not involved
>>> because a finite universe always existed then why couldn't a infinite
>>> universe just as easily always have existed too?
>>>
>>>   John K Clark
>>>
>>
>> This is getting tedious. If the universe began at some instant (having
>> zero time duration), and assuming physical processes require time, there
>> was insufficient time to create anything, finite or infinite, *at that
>> instant*. It's like a volcano erupting, and you're claiming that when
>> the eruption began, the cone was existing at that point in time. AG
>>
>
> You want to claim the universe began, presumably at some instant, and also
> claim it was infinite in extent at that point in time. But if physical
> processes require time, your claim makes no sense. AG
>

You want to claim the universe began, presumably at some instant, and also
claim it was finite in extent at that point in time. But if physical
processes require time, your claim makes no sense

> --
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> email to everything-list+unsubscr...@googlegroups.com.
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> https://groups.google.com/d/msgid/everything-list/12ac7c1a-9c59-4529-84e0-85acc76f81f1%40googlegroups.com
> 
> .
>


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Batty/Rutger Hauer)

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Re: Inflation and the total size of the universe

[Alan Grayson]

On Tuesday, April 14, 2020 at 7:54:19 AM UTC-6, Alan Grayson wrote:
>
>
>
> On Tuesday, April 14, 2020 at 5:28:07 AM UTC-6, John Clark wrote:
>>
>> On Mon, Apr 13, 2020 at 5:11 PM Alan Grayson  wrote:
>>
>> *>>> if you accept the measured age, it can't be finite or infinite in 
> spatial extent when it began*


 >> If something isn't finite or infinite what is the third 
 alternative? 

>>>
>>> > *It doesn't exist;*
>>>
>>
>> OK, but then what is "it"?
>>
>> > *that is, your hypothesis that that when the universe began it was 
>>> already infinite, or possibly finite, is false.*
>>>
>>
>> So I ask again, if the universe isn't finite and it isn't infinite what 
>> is your third alternative? And why would creating a finite amount of 
>> something from nothing be easier than creating a infinite amount of 
>> something from nothing? In my previous post I gave reasons for thinking the 
>> infinite case might actually be simpler. And if creation was not involved 
>> because a finite universe always existed then why couldn't a infinite 
>> universe just as easily always have existed too?
>>
>>   John K Clark
>>
>
> This is getting tedious. If the universe began at some instant (having 
> zero time duration), and assuming physical processes require time, there 
> was insufficient time to create anything, finite or infinite, *at that 
> instant*. It's like a volcano erupting, and you're claiming that when the 
> eruption began, the cone was existing at that point in time. AG 
>

You want to claim the universe began, presumably at some instant, and also 
claim it was infinite in extent at that point in time. But if physical 
processes require time, your claim makes no sense. AG 

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Re: Inflation and the total size of the universe

[Alan Grayson]

On Tuesday, April 14, 2020 at 5:28:07 AM UTC-6, John Clark wrote:
>
> On Mon, Apr 13, 2020 at 5:11 PM Alan Grayson  > wrote:
>
> *>>> if you accept the measured age, it can't be finite or infinite in 
 spatial extent when it began*
>>>
>>>
>>> >> If something isn't finite or infinite what is the third alternative? 
>>>
>>
>> > *It doesn't exist;*
>>
>
> OK, but then what is "it"?
>
> > *that is, your hypothesis that that when the universe began it was 
>> already infinite, or possibly finite, is false.*
>>
>
> So I ask again, if the universe isn't finite and it isn't infinite what is 
> your third alternative? And why would creating a finite amount of something 
> from nothing be easier than creating a infinite amount of something from 
> nothing? In my previous post I gave reasons for thinking the infinite case 
> might actually be simpler. And if creation was not involved because a 
> finite universe always existed then why couldn't a infinite universe just 
> as easily always have existed too?
>
>   John K Clark
>

This is getting tedious. If the universe began at some instant (having zero 
time duration), and assuming physical processes require time, there was 
insufficient time to create anything, finite or infinite, *at that instant*. 
It's like a volcano erupting, and you're claiming that when the eruption 
began, the cone was existing at that point in time. AG 

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Re: Inflation and the total size of the universe

[John Clark]

On Mon, Apr 13, 2020 at 5:11 PM Alan Grayson  wrote:

*>>> if you accept the measured age, it can't be finite or infinite in
>>> spatial extent when it began*
>>
>>
>> >> If something isn't finite or infinite what is the third alternative?
>>
>
> > *It doesn't exist;*
>

OK, but then what is "it"?

> *that is, your hypothesis that that when the universe began it was
> already infinite, or possibly finite, is false.*
>

So I ask again, if the universe isn't finite and it isn't infinite what is
your third alternative? And why would creating a finite amount of something
from nothing be easier than creating a infinite amount of something from
nothing? In my previous post I gave reasons for thinking the infinite case
might actually be simpler. And if creation was not involved because a
finite universe always existed then why couldn't a infinite universe just
as easily always have existed too?

  John K Clark

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Re: Inflation and the total size of the universe

[Philip Thrift]

On Monday, April 13, 2020 at 2:50:46 PM UTC-5, John Clark wrote:
>
>
>
> On Mon, Apr 13, 2020 at 2:07 PM Alan Grayson  > wrote:
>
> *> if you accept the measured age, it can't be finite or infinite in 
>> spatial extent when it began*
>
>
> If something isn't finite or infinite what is the third alternative? 
>
>  John K Clark
>
>
>>
There is a "type" of set (theory) that *locally finite* (basically 
'potentially infinite'), a set that does not have a fixed size but updates 
its size as "required" in the context of a proof (or, one would suppose, a 
physical observation).

@philipthrift


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Re: Inflation and the total size of the universe

[Alan Grayson]

On Monday, April 13, 2020 at 1:50:46 PM UTC-6, John Clark wrote:
>
>
>
> On Mon, Apr 13, 2020 at 2:07 PM Alan Grayson  > wrote:
>
> *> if you accept the measured age, it can't be finite or infinite in 
>> spatial extent when it began*
>
>
> If something isn't finite or infinite what is the third alternative? 
>
>  John K Clark
>

It doesn't exist; that is, your hypothesis that that when the universe 
began it was already infinite, or possibly finite, is false. AG 

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Re: Inflation and the total size of the universe

[John Clark]

On Mon, Apr 13, 2020 at 2:07 PM Alan Grayson  wrote:

*> if you accept the measured age, it can't be finite or infinite in
> spatial extent when it began*


If something isn't finite or infinite what is the third alternative?

 John K Clark


>

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Re: Inflation and the total size of the universe

[Alan Grayson]

On Monday, April 13, 2020 at 9:57:44 AM UTC-6, John Clark wrote:
>
> On Mon, Apr 13, 2020 at 10:09 AM Alan Grayson  > wrote:
>
> > My assumption is that it takes finite time to create anything, finite 
>> or infinite.
>
>
> If your assumption is correct then knowing that the universe is 13.8 
> billion years old is no help at all in determining if it is spatially finite 
> or infinite. 
>
> John K Clark
>

But if it's spatially finite or infinite at the creation event, its age 
can't be 13.8 BLY. It must be older, possibly infinitely older. That's my 
point. So if you accept the measured age, it can't be finite or infinite in 
spatial extent when it began. AG 

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Re: Inflation and the total size of the universe

[John Clark]

On Mon, Apr 13, 2020 at 10:09 AM Alan Grayson 
wrote:

> My assumption is that it takes finite time to create anything, finite or
> infinite.


If your assumption is correct then knowing that the universe is 13.8
billion years old is no help at all in determining if it is spatially finite
or infinite.

John K Clark

>
>

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Re: Inflation and the total size of the universe

[Alan Grayson]

On Monday, April 13, 2020 at 7:21:29 AM UTC-6, John Clark wrote:
>
> On Mon, Apr 13, 2020 at 8:52 AM Alan Grayson  > wrote:
>
> *> if it had already been spatially infinite, how long had that situation 
>> been the case?  AG*
>
>
> Another answer to your question is it would be exactly the same amount of 
> time if it had been the case that the universe had *already* been finite.
>
>  John K Clark
>

My assumption is that it takes finite time to create anything, finite or 
infinite. So if there is any part of our universe existing at creation 
time, the age of the universe would be larger than 13.8 BLY. AG

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Re: Inflation and the total size of the universe

[John Clark]

On Mon, Apr 13, 2020 at 8:52 AM Alan Grayson  wrote:

*> if it had already been spatially infinite, how long had that situation
> been the case?  AG*


Another answer to your question is it would be exactly the same amount of
time if it had been the case that the universe had *already* been finite.

 John K Clark

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Re: Inflation and the total size of the universe

[John Clark]

On Mon, Apr 13, 2020 at 8:52 AM Alan Grayson  wrote:

 >*If it had already been spatially infinite, how long had that situation
> been the case? *
>

There is uncertainty, perhaps for 5.39*10^-44 seconds or perhaps less.
Nobody knows for sure if time is quantized because we don't have a quantum
theory that incorporates General Relativity and gravity.

John K Clark

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Re: Inflation and the total size of the universe

[Lawrence Crowell]

On Monday, April 13, 2020 at 7:30:47 AM UTC-5, John Clark wrote:
>
> On Mon, Apr 13, 2020 at 4:37 AM Alan Grayson  > wrote:
>
> > *You're imagining a "start" of our universe with it being infinite in 
>> spatial extent.*
>
>
> It's a possibility.
>
>  > *So, in zero time duration, at its "creation", it expanded infinitely *
>
>
> No, I'm saying at zero time the universe may have already been spatially 
> infinite, there is nothing we know of that would rule out the possibility. 
> It is not obvious that creating an infinity of something from nothing is 
> harder than creating a finite amount of something from nothing, in fact it 
> might even be easier because if it's infinite then you don't have to worry 
> about setting bounds. For example, calculating the magnetic field that 
> surrounds a infinitely long current carrying wire is far easier than 
> calculating the magnetic field that surrounds a wire that is only of finite 
> length. And people have found an exact solution in General Relativity that 
> tells you what would happen to spacetime around a very dense infinitely 
> long rod spinning at close to the speed of light (you get a closed timelike 
> curve, aka a time machine) but when you try to do the same thing for a rod 
> of only finite length the mathematics gets so complicated nobody can figure 
> out what the hell would happen, at least so far.
>
>  John K Clark
>

It is possible an infinite space was constructed prior or during inflation. 
A part of this involves space or spacetime as constructed from quantum 
states. We might think of this projective map as a way that quantum states 
are trapped in an event horizon bubble. Suppose the universe only has one 
electron, only one up quark, only one … of every type of elementary 
particle. This particle though in a path integral sense weaves back and 
forth in time. When trapped by the event horizon any local observer 
witnesses a large number of electrons and other particles. However, this is 
a huge redundancy. There is still only one electron, but we witness a vast 
number of them as a redundancy on just one. How it is there is a 
preponderance of electrons over positrons has to do with parity and time, 
which is even more subtle. However, even with infinity there really is no 
problem, for the same initial conditions are mapped everywhere,

In order to go deeper on this would require a lot of writing here. This is 
in part how I see that space could be infinite, but with the same initial 
conditions everywhere.

LC

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Re: Inflation and the total size of the universe

[Alan Grayson]

On Monday, April 13, 2020 at 6:30:47 AM UTC-6, John Clark wrote:
>
> On Mon, Apr 13, 2020 at 4:37 AM Alan Grayson  > wrote:
>
> > *You're imagining a "start" of our universe with it being infinite in 
>> spatial extent.*
>
>
> It's a possibility.
>
>  > *So, in zero time duration, at its "creation", it expanded infinitely *
>
>
> No, I'm saying at zero time the universe may have already been spatially 
> infinite, there is nothing we know of that would rule out the possibility. 
>


Yes there is; the fact that the age of our universe is finite, as estimated 
from the creation event. If it had *already* been spatially infinite, how 
long had that situation been the case?  AG

It is not obvious that creating an infinity of something from nothing is 
> harder than creating a finite amount of something from nothing, in fact it 
> might even be easier because if it's infinite then you don't have to worry 
> about setting bounds. For example, calculating the magnetic field that 
> surrounds a infinitely long current carrying wire is far easier than 
> calculating the magnetic field that surrounds a wire that is only of finite 
> length. And people have found an exact solution in General Relativity that 
> tells you what would happen to spacetime around a very dense infinitely 
> long rod spinning at close to the speed of light (you get a closed timelike 
> curve, aka a time machine) but when you try to do the same thing for a rod 
> of only finite length the mathematics gets so complicated nobody can figure 
> out what the hell would happen, at least so far.
>
>  John K Clark
>

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Re: Inflation and the total size of the universe

[John Clark]

On Mon, Apr 13, 2020 at 4:37 AM Alan Grayson  wrote:

> *You're imagining a "start" of our universe with it being infinite in
> spatial extent.*


It's a possibility.

 > *So, in zero time duration, at its "creation", it expanded infinitely *


No, I'm saying at zero time the universe may have already been spatially
infinite, there is nothing we know of that would rule out the possibility.
It is not obvious that creating an infinity of something from nothing is
harder than creating a finite amount of something from nothing, in fact it
might even be easier because if it's infinite then you don't have to worry
about setting bounds. For example, calculating the magnetic field that
surrounds a infinitely long current carrying wire is far easier than
calculating the magnetic field that surrounds a wire that is only of finite
length. And people have found an exact solution in General Relativity that
tells you what would happen to spacetime around a very dense infinitely
long rod spinning at close to the speed of light (you get a closed timelike
curve, aka a time machine) but when you try to do the same thing for a rod
of only finite length the mathematics gets so complicated nobody can figure
out what the hell would happen, at least so far.

 John K Clark

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Re: Inflation and the total size of the universe

[Alan Grayson]

On Sunday, April 12, 2020 at 4:19:26 PM UTC-6, John Clark wrote:
>
> On Sun, Apr 12, 2020 at 5:49 PM Alan Grayson  > wrote:
>
> *>>> As the universe expands, galaxies move progressively faster away from 
 us as described by Hubble's constant, which is a geometric effect as 
 previously explained, and eventually wink out. Conversely, if we play the 
 movie backward in time, all those galaxies which previously winked out, 
 should come into view.*

>>>
>>> >> Not if the universe started out as being infinite they don't.
>>>
>>
>> *> Then our interpretation of Hubble's constant is wrong. AG *
>>
>
> Nope, the Hubble constant has nothing to do with it. And by the way, with 
> the discovery of Dark Energy we now know that the Hubble "constant" is 
> not constant.
>
> *> it's all expanding and that's why galaxies wink out. If you play the 
>> movie backward to the BB, they should all come in view, which contradicts 
>> infinite in spatial extent. AG *
>>
>
> No! If the universe started out being infinite then if you play the movie 
> backwards everything won't come back into view because everything was NEVER 
> in view. So for all we know the universe could be spatially flat or 
> positively curved or negatively curved.
>
> John K Clark
>

You're imagining a "start" of our universe with it being infinite in 
spatial extent. So, in zero time duration, at its "creation", it expanded 
infinitely (which contradicts the fact that physical processes require 
finite durations to manifest); OR that spatial infinity has a past, 
possibly infinite, contradicting the measured age of our universe. AG

>
>  
>
>>
>>>  John K Clark
>>>
>> -- 
>> 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 everyth...@googlegroups.com .
>> To view this discussion on the web visit 
>> https://groups.google.com/d/msgid/everything-list/ee0578a7-b768-48b2-ad37-ff60b148e5c1%40googlegroups.com
>>  
>> 
>> .
>>
>

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Re: Inflation and the total size of the universe

[Alan Grayson]

On Sunday, April 12, 2020 at 5:46:46 PM UTC-6, Lawrence Crowell wrote:
>
> On Saturday, April 11, 2020 at 6:30:00 PM UTC-5, Alan Grayson wrote:
>>
>>
>>
>> On Saturday, April 11, 2020 at 3:36:28 PM UTC-6, Lawrence Crowell wrote:
>>>
>>> On Saturday, April 11, 2020 at 2:26:58 PM UTC-5, Alan Grayson wrote:



 On Saturday, April 11, 2020 at 9:10:19 AM UTC-6, Lawrence Crowell wrote:
>
> On Friday, April 10, 2020 at 8:45:22 PM UTC-5, Alan Grayson wrote:
>>
>>
>>
>> On Sunday, March 29, 2020 at 12:03:10 PM UTC-6, Lawrence Crowell 
>> wrote:
>>>
>>> On Sunday, March 29, 2020 at 1:57:12 AM UTC-5, Alan Grayson wrote:



 On Saturday, March 28, 2020 at 5:38:33 PM UTC-6, Lawrence Crowell 
 wrote:
>
> On Saturday, March 28, 2020 at 5:27:51 AM UTC-5, Alan Grayson 
> wrote:
>>
>>
>>
>> On Wednesday, March 25, 2020 at 4:25:43 PM UTC-6, Lawrence 
>> Crowell wrote:
>>>
>>> On Wednesday, March 25, 2020 at 2:17:39 PM UTC-5, Alan Grayson 
>>> wrote:
>>>


 On Wednesday, March 25, 2020 at 9:57:44 AM UTC-6, Lawrence 
 Crowell wrote:
>
> On Wednesday, March 25, 2020 at 10:24:30 AM UTC-5, Alan 
> Grayson wrote:
>>
>>
>>
>> On Wednesday, March 25, 2020 at 2:58:45 AM UTC-6, Lawrence 
>> Crowell wrote:
>>>
>>> On Wednesday, March 25, 2020 at 1:28:21 AM UTC-5, Alan 
>>> Grayson wrote:



 On Tuesday, March 24, 2020 at 6:21:50 PM UTC-6, Lawrence 
 Crowell wrote:
>
> On Tuesday, March 24, 2020 at 6:19:41 PM UTC-5, Alan 
> Grayson wrote:
>>
>>
>>
>> On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence 
>> Crowell wrote:
>>>
>>> Inflation was initiate 10^{-35}sec after the quantum 
>>> fluctuation appearance of the observable cosmos, and this 
>>> had a duration of 
>>> 10^{-30}sec. The cosmological constant averaged around Λ = 
>>> 10^{48}m^{-2}. 
>>> If I divide by the speed of light squared this comes to 
>>> 10^{32}s^{-2} and 
>>> we get √(Λ)T = 10^{2}. This means any spatial region 
>>> expanded by a factor 
>>> of 10^{√(Λ)T} which is large. The natural log of this 
>>> is 230 and this is not too far off from the more precise 
>>> calculation of 60 
>>> e-folds. The 60 e-folds is a phenomenological fit that 
>>> matches inflation 
>>> with the observed universe.
>>>
>>> How much of the universe is unavailable depends upon 
>>> whether k = -1, 0 or 1. The furthest out some quantum might 
>>> emerge and have 
>>> an influence is for a Planck scale quantum to now be 
>>> inflated to the CMB 
>>> scale. I know I have gone through this here before, but the 
>>> result is the 
>>> furthest we can detect anything is around 1800 billion 
>>> light years, which 
>>> would be a graviton or quantum black hole that leaves an 
>>> imprint or 
>>> signature on the CMB. It is not possible from theory to 
>>> know what 
>>> percentage this is of the entire shebang, and for k = -1 or 
>>> 0 it is an 
>>> infinitesimal part.
>>>
>>> LC
>>>
>>
>> For k=0, a flat universe, we know the answer since, as 
>> you've acknowledged, it's infinite in spatial extent.  
>> Consequently, since 
>> the observable universe is finite in spatial extent, the 
>> unobserved 
>> universe must be infinite in extent (for a flat universe). 
>> Can you estimate 
>> the size of the unobservable universe for a positively 
>> curved universe? AG
>>
>
> The cosmological constant is a Ricci curvature with Λ = 
> R_{tt} for the flat k = 0 case. for k = 1 there is a spatial 
> Ricci 
> curvature R_{rr}. This contributes to the occurrence of 
> the cosmological constant, but it is tiny. So R_{rr} 
> = δR_{tt} for δ a rather small number. The spatial sphere has 

Re: Inflation and the total size of the universe

[Lawrence Crowell]

On Saturday, April 11, 2020 at 6:30:00 PM UTC-5, Alan Grayson wrote:
>
>
>
> On Saturday, April 11, 2020 at 3:36:28 PM UTC-6, Lawrence Crowell wrote:
>>
>> On Saturday, April 11, 2020 at 2:26:58 PM UTC-5, Alan Grayson wrote:
>>>
>>>
>>>
>>> On Saturday, April 11, 2020 at 9:10:19 AM UTC-6, Lawrence Crowell wrote:

 On Friday, April 10, 2020 at 8:45:22 PM UTC-5, Alan Grayson wrote:
>
>
>
> On Sunday, March 29, 2020 at 12:03:10 PM UTC-6, Lawrence Crowell wrote:
>>
>> On Sunday, March 29, 2020 at 1:57:12 AM UTC-5, Alan Grayson wrote:
>>>
>>>
>>>
>>> On Saturday, March 28, 2020 at 5:38:33 PM UTC-6, Lawrence Crowell 
>>> wrote:

 On Saturday, March 28, 2020 at 5:27:51 AM UTC-5, Alan Grayson wrote:
>
>
>
> On Wednesday, March 25, 2020 at 4:25:43 PM UTC-6, Lawrence Crowell 
> wrote:
>>
>> On Wednesday, March 25, 2020 at 2:17:39 PM UTC-5, Alan Grayson 
>> wrote:
>>
>>>
>>>
>>> On Wednesday, March 25, 2020 at 9:57:44 AM UTC-6, Lawrence 
>>> Crowell wrote:

 On Wednesday, March 25, 2020 at 10:24:30 AM UTC-5, Alan Grayson 
 wrote:
>
>
>
> On Wednesday, March 25, 2020 at 2:58:45 AM UTC-6, Lawrence 
> Crowell wrote:
>>
>> On Wednesday, March 25, 2020 at 1:28:21 AM UTC-5, Alan 
>> Grayson wrote:
>>>
>>>
>>>
>>> On Tuesday, March 24, 2020 at 6:21:50 PM UTC-6, Lawrence 
>>> Crowell wrote:

 On Tuesday, March 24, 2020 at 6:19:41 PM UTC-5, Alan 
 Grayson wrote:
>
>
>
> On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence 
> Crowell wrote:
>>
>> Inflation was initiate 10^{-35}sec after the quantum 
>> fluctuation appearance of the observable cosmos, and this 
>> had a duration of 
>> 10^{-30}sec. The cosmological constant averaged around Λ = 
>> 10^{48}m^{-2}. 
>> If I divide by the speed of light squared this comes to 
>> 10^{32}s^{-2} and 
>> we get √(Λ)T = 10^{2}. This means any spatial region 
>> expanded by a factor 
>> of 10^{√(Λ)T} which is large. The natural log of this is 
>> 230 and this is not too far off from the more precise 
>> calculation of 60 
>> e-folds. The 60 e-folds is a phenomenological fit that 
>> matches inflation 
>> with the observed universe.
>>
>> How much of the universe is unavailable depends upon 
>> whether k = -1, 0 or 1. The furthest out some quantum might 
>> emerge and have 
>> an influence is for a Planck scale quantum to now be 
>> inflated to the CMB 
>> scale. I know I have gone through this here before, but the 
>> result is the 
>> furthest we can detect anything is around 1800 billion light 
>> years, which 
>> would be a graviton or quantum black hole that leaves an 
>> imprint or 
>> signature on the CMB. It is not possible from theory to know 
>> what 
>> percentage this is of the entire shebang, and for k = -1 or 
>> 0 it is an 
>> infinitesimal part.
>>
>> LC
>>
>
> For k=0, a flat universe, we know the answer since, as 
> you've acknowledged, it's infinite in spatial extent.  
> Consequently, since 
> the observable universe is finite in spatial extent, the 
> unobserved 
> universe must be infinite in extent (for a flat universe). 
> Can you estimate 
> the size of the unobservable universe for a positively curved 
> universe? AG
>

 The cosmological constant is a Ricci curvature with Λ = 
 R_{tt} for the flat k = 0 case. for k = 1 there is a spatial 
 Ricci 
 curvature R_{rr}. This contributes to the occurrence of 
 the cosmological constant, but it is tiny. So R_{rr} 
 = δR_{tt} for δ a rather small number. The spatial sphere has 
 a radius R = 
 1/√(R_{rr}} ≈ 1/√(δΛ). This is then for Λ = 10^{-52}m^{-2} 
 R ≈ δ^{-1/2} 10^{26}m, or about the distance to the 
 cosmological 

Re: Inflation and the total size of the universe

['Brent Meeker' via Everything List]

On 4/12/2020 2:48 PM, Alan Grayson wrote:



On Sunday, April 12, 2020 at 2:44:56 PM UTC-6, John Clark wrote:

On Sun, Apr 12, 2020 at 4:33 PM Alan Grayson > wrote:

/> As the universe expands, galaxies move progressively faster
away from us as described by Hubble's constant, which is a
geometric effect as previously explained, and eventually wink
out. Conversely, if we play the movie backward in time, all
those galaxies which previously winked out, should come into
view./


Not if the universe started out as being infinite they don't.


*Then our interpretation of Hubble's constant is wrong. AG *

/> your hypothesis makes no geometric sense. Mustn't we assume
that if our universe is expanding,/


We don't need to assume anything, we have plenty of observational
evidence that the universe is expanding.


*If you weren't so inclined to parsing my statement, you'd see I 
wasn't questioning the expansion. AG *



/> the expansion applies to the UN-observable region?/


It applies to all of the universe, it's all expanding and
observability has nothing to do with it.


*Yes, it's all expanding and that's why galaxies wink out. If you play 
the movie backward to the BB, they should all come in view, which 
contradicts infinite in spatial extent. AG

*


Only if you play it back to zero scale factor.  Almost theories of 
cosmogony require a small but finite, Planck scale start.


Brent


**

 John K Clark

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Re: Inflation and the total size of the universe

[John Clark]

On Sun, Apr 12, 2020 at 5:49 PM Alan Grayson  wrote:

*>>> As the universe expands, galaxies move progressively faster away from
>>> us as described by Hubble's constant, which is a geometric effect as
>>> previously explained, and eventually wink out. Conversely, if we play the
>>> movie backward in time, all those galaxies which previously winked out,
>>> should come into view.*
>>>
>>
>> >> Not if the universe started out as being infinite they don't.
>>
>
> *> Then our interpretation of Hubble's constant is wrong. AG *
>

Nope, the Hubble constant has nothing to do with it. And by the way, with
the discovery of Dark Energy we now know that the Hubble "constant" is not
constant.

*> it's all expanding and that's why galaxies wink out. If you play the
> movie backward to the BB, they should all come in view, which contradicts
> infinite in spatial extent. AG *
>

No! If the universe started out being infinite then if you play the movie
backwards everything won't come back into view because everything was NEVER
in view. So for all we know the universe could be spatially flat or
positively curved or negatively curved.

John K Clark






>
>>  John K Clark
>>
> --
> 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.
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> 
> .
>

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Re: Inflation and the total size of the universe

[Alan Grayson]

On Sunday, April 12, 2020 at 2:44:56 PM UTC-6, John Clark wrote:
>
> On Sun, Apr 12, 2020 at 4:33 PM Alan Grayson  > wrote:
>
> *> As the universe expands, galaxies move progressively faster away from 
>> us as described by Hubble's constant, which is a geometric effect as 
>> previously explained, and eventually wink out. Conversely, if we play the 
>> movie backward in time, all those galaxies which previously winked out, 
>> should come into view.*
>>
>
> Not if the universe started out as being infinite they don't.
>

*Then our interpretation of Hubble's constant is wrong. AG *

>  
>
>> *> your hypothesis makes no geometric sense. Mustn't we assume that if 
>> our universe is expanding,*
>>
>
> We don't need to assume anything, we have plenty of observational 
> evidence that the universe is expanding.
>

*If you weren't so inclined to parsing my statement, you'd see I wasn't 
questioning the expansion. AG *

>
> *> the expansion applies to the UN-observable region?*
>>
>
> It applies to all of the universe, it's all expanding and observability 
> has nothing to do with it. 
>

*Yes, it's all expanding and that's why galaxies wink out. If you play the 
movie backward to the BB, they should all come in view, which contradicts 
infinite in spatial extent. AG *

>
>  John K Clark
>

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Re: Inflation and the total size of the universe

[John Clark]

On Sun, Apr 12, 2020 at 4:33 PM Alan Grayson  wrote:

*> As the universe expands, galaxies move progressively faster away from us
> as described by Hubble's constant, which is a geometric effect as
> previously explained, and eventually wink out. Conversely, if we play the
> movie backward in time, all those galaxies which previously winked out,
> should come into view.*
>

Not if the universe started out as being infinite they don't.


> *> your hypothesis makes no geometric sense. Mustn't we assume that if our
> universe is expanding,*
>

We don't need to assume anything, we have plenty of observational
evidence that the universe is expanding.

*> the expansion applies to the UN-observable region?*
>

It applies to all of the universe, it's all expanding and observability has
nothing to do with it.

 John K Clark

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Re: Inflation and the total size of the universe

[Alan Grayson]

On Sunday, April 12, 2020 at 6:12:54 AM UTC-6, John Clark wrote:
>
> On Sat, Apr 11, 2020 at 3:27 PM Alan Grayson  > wrote:
>
> *> Hyperbolic can be ruled out for the same reason flat can be ruled out. 
>> Both are infinite in spatial extent, and since the universe has a finite 
>> age and expanding at less than an infinite rate throughout its lifetime 
>> (although the rate can be changing in different epochs and possibly faster 
>> than light speed in some epochs such as inflation), it cannot be infinite 
>> in spatial extent. I've made this argument several times, which is clear 
>> and straightforward, but never got anyone to agree. I find that baffling. *
>
>
> That's because the universe could have been infinitely large from the very 
> first instant of its existence even before inflation started, I'm not 
> saying that it did I'm just saying there is no evidence that rules out that 
> possibility. And if it did start out that way then now the universe's 
> spatial curvature could be absolutely flat or even hyperbolic. And before 
> the discovery of Dark Energy people said that if the universe was 
> spherically curved then it couldn't expand forever, but with a new force 
> entering the equation that is no longer true. We now know it takes more 
> than just knowledge of the geometry of space to know the universe's 
> ultimate fate.
>
>  John K Clark
>

As the universe expands, galaxies move progressively faster away from us as 
described by Hubble's constant, which is a geometric effect as previously 
explained, and eventually wink out. Conversely, if we play the movie 
backward in time, all those galaxies which previously winked out, should 
come into view. Consequently, the hypothesis that the universe began as 
infinite seems to imply a peculiar inconsistency. This is not to say that 
the entity from which *our* universe emerged is necessarily finite -- it 
could be infinite in spatial extent and past time -- but at least for me, 
your hypothesis makes no geometric sense. Mustn't we assume that if our 
universe is expanding, the expansion applies to the UN-observable region? 
And if it does, wouldn't that region come into view if the movie is played 
backward? If it does, or must come into view, then the unobservable region 
cannot be infinite in spatial extent. AG 

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Re: Inflation and the total size of the universe

[John Clark]

On Sat, Apr 11, 2020 at 3:27 PM Alan Grayson  wrote:

*> Hyperbolic can be ruled out for the same reason flat can be ruled out.
> Both are infinite in spatial extent, and since the universe has a finite
> age and expanding at less than an infinite rate throughout its lifetime
> (although the rate can be changing in different epochs and possibly faster
> than light speed in some epochs such as inflation), it cannot be infinite
> in spatial extent. I've made this argument several times, which is clear
> and straightforward, but never got anyone to agree. I find that baffling. *


That's because the universe could have been infinitely large from the very
first instant of its existence even before inflation started, I'm not
saying that it did I'm just saying there is no evidence that rules out that
possibility. And if it did start out that way then now the universe's
spatial curvature could be absolutely flat or even hyperbolic. And before
the discovery of Dark Energy people said that if the universe was
spherically curved then it couldn't expand forever, but with a new force
entering the equation that is no longer true. We now know it takes more
than just knowledge of the geometry of space to know the universe's
ultimate fate.

 John K Clark

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Re: Inflation and the total size of the universe

[Alan Grayson]

On Saturday, April 11, 2020 at 5:30:00 PM UTC-6, Alan Grayson wrote:
>
>
>
> On Saturday, April 11, 2020 at 3:36:28 PM UTC-6, Lawrence Crowell wrote:
>>
>> On Saturday, April 11, 2020 at 2:26:58 PM UTC-5, Alan Grayson wrote:
>>>
>>>
>>>
>>> On Saturday, April 11, 2020 at 9:10:19 AM UTC-6, Lawrence Crowell wrote:

 On Friday, April 10, 2020 at 8:45:22 PM UTC-5, Alan Grayson wrote:
>
>
>
> On Sunday, March 29, 2020 at 12:03:10 PM UTC-6, Lawrence Crowell wrote:
>>
>> On Sunday, March 29, 2020 at 1:57:12 AM UTC-5, Alan Grayson wrote:
>>>
>>>
>>>
>>> On Saturday, March 28, 2020 at 5:38:33 PM UTC-6, Lawrence Crowell 
>>> wrote:

 On Saturday, March 28, 2020 at 5:27:51 AM UTC-5, Alan Grayson wrote:
>
>
>
> On Wednesday, March 25, 2020 at 4:25:43 PM UTC-6, Lawrence Crowell 
> wrote:
>>
>> On Wednesday, March 25, 2020 at 2:17:39 PM UTC-5, Alan Grayson 
>> wrote:
>>
>>>
>>>
>>> On Wednesday, March 25, 2020 at 9:57:44 AM UTC-6, Lawrence 
>>> Crowell wrote:

 On Wednesday, March 25, 2020 at 10:24:30 AM UTC-5, Alan Grayson 
 wrote:
>
>
>
> On Wednesday, March 25, 2020 at 2:58:45 AM UTC-6, Lawrence 
> Crowell wrote:
>>
>> On Wednesday, March 25, 2020 at 1:28:21 AM UTC-5, Alan 
>> Grayson wrote:
>>>
>>>
>>>
>>> On Tuesday, March 24, 2020 at 6:21:50 PM UTC-6, Lawrence 
>>> Crowell wrote:

 On Tuesday, March 24, 2020 at 6:19:41 PM UTC-5, Alan 
 Grayson wrote:
>
>
>
> On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence 
> Crowell wrote:
>>
>> Inflation was initiate 10^{-35}sec after the quantum 
>> fluctuation appearance of the observable cosmos, and this 
>> had a duration of 
>> 10^{-30}sec. The cosmological constant averaged around Λ = 
>> 10^{48}m^{-2}. 
>> If I divide by the speed of light squared this comes to 
>> 10^{32}s^{-2} and 
>> we get √(Λ)T = 10^{2}. This means any spatial region 
>> expanded by a factor 
>> of 10^{√(Λ)T} which is large. The natural log of this is 
>> 230 and this is not too far off from the more precise 
>> calculation of 60 
>> e-folds. The 60 e-folds is a phenomenological fit that 
>> matches inflation 
>> with the observed universe.
>>
>> How much of the universe is unavailable depends upon 
>> whether k = -1, 0 or 1. The furthest out some quantum might 
>> emerge and have 
>> an influence is for a Planck scale quantum to now be 
>> inflated to the CMB 
>> scale. I know I have gone through this here before, but the 
>> result is the 
>> furthest we can detect anything is around 1800 billion light 
>> years, which 
>> would be a graviton or quantum black hole that leaves an 
>> imprint or 
>> signature on the CMB. It is not possible from theory to know 
>> what 
>> percentage this is of the entire shebang, and for k = -1 or 
>> 0 it is an 
>> infinitesimal part.
>>
>> LC
>>
>
> For k=0, a flat universe, we know the answer since, as 
> you've acknowledged, it's infinite in spatial extent.  
> Consequently, since 
> the observable universe is finite in spatial extent, the 
> unobserved 
> universe must be infinite in extent (for a flat universe). 
> Can you estimate 
> the size of the unobservable universe for a positively curved 
> universe? AG
>

 The cosmological constant is a Ricci curvature with Λ = 
 R_{tt} for the flat k = 0 case. for k = 1 there is a spatial 
 Ricci 
 curvature R_{rr}. This contributes to the occurrence of 
 the cosmological constant, but it is tiny. So R_{rr} 
 = δR_{tt} for δ a rather small number. The spatial sphere has 
 a radius R = 
 1/√(R_{rr}} ≈ 1/√(δΛ). This is then for Λ = 10^{-52}m^{-2} 
 R ≈ δ^{-1/2} 10^{26}m, or about the distance to the 
 cosmological 

Re: Inflation and the total size of the universe

[Alan Grayson]

On Saturday, April 11, 2020 at 3:36:28 PM UTC-6, Lawrence Crowell wrote:
>
> On Saturday, April 11, 2020 at 2:26:58 PM UTC-5, Alan Grayson wrote:
>>
>>
>>
>> On Saturday, April 11, 2020 at 9:10:19 AM UTC-6, Lawrence Crowell wrote:
>>>
>>> On Friday, April 10, 2020 at 8:45:22 PM UTC-5, Alan Grayson wrote:



 On Sunday, March 29, 2020 at 12:03:10 PM UTC-6, Lawrence Crowell wrote:
>
> On Sunday, March 29, 2020 at 1:57:12 AM UTC-5, Alan Grayson wrote:
>>
>>
>>
>> On Saturday, March 28, 2020 at 5:38:33 PM UTC-6, Lawrence Crowell 
>> wrote:
>>>
>>> On Saturday, March 28, 2020 at 5:27:51 AM UTC-5, Alan Grayson wrote:



 On Wednesday, March 25, 2020 at 4:25:43 PM UTC-6, Lawrence Crowell 
 wrote:
>
> On Wednesday, March 25, 2020 at 2:17:39 PM UTC-5, Alan Grayson 
> wrote:
>
>>
>>
>> On Wednesday, March 25, 2020 at 9:57:44 AM UTC-6, Lawrence 
>> Crowell wrote:
>>>
>>> On Wednesday, March 25, 2020 at 10:24:30 AM UTC-5, Alan Grayson 
>>> wrote:



 On Wednesday, March 25, 2020 at 2:58:45 AM UTC-6, Lawrence 
 Crowell wrote:
>
> On Wednesday, March 25, 2020 at 1:28:21 AM UTC-5, Alan Grayson 
> wrote:
>>
>>
>>
>> On Tuesday, March 24, 2020 at 6:21:50 PM UTC-6, Lawrence 
>> Crowell wrote:
>>>
>>> On Tuesday, March 24, 2020 at 6:19:41 PM UTC-5, Alan Grayson 
>>> wrote:



 On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence 
 Crowell wrote:
>
> Inflation was initiate 10^{-35}sec after the quantum 
> fluctuation appearance of the observable cosmos, and this had 
> a duration of 
> 10^{-30}sec. The cosmological constant averaged around Λ = 
> 10^{48}m^{-2}. 
> If I divide by the speed of light squared this comes to 
> 10^{32}s^{-2} and 
> we get √(Λ)T = 10^{2}. This means any spatial region expanded 
> by a factor 
> of 10^{√(Λ)T} which is large. The natural log of this is 
> 230 and this is not too far off from the more precise 
> calculation of 60 
> e-folds. The 60 e-folds is a phenomenological fit that 
> matches inflation 
> with the observed universe.
>
> How much of the universe is unavailable depends upon 
> whether k = -1, 0 or 1. The furthest out some quantum might 
> emerge and have 
> an influence is for a Planck scale quantum to now be inflated 
> to the CMB 
> scale. I know I have gone through this here before, but the 
> result is the 
> furthest we can detect anything is around 1800 billion light 
> years, which 
> would be a graviton or quantum black hole that leaves an 
> imprint or 
> signature on the CMB. It is not possible from theory to know 
> what 
> percentage this is of the entire shebang, and for k = -1 or 0 
> it is an 
> infinitesimal part.
>
> LC
>

 For k=0, a flat universe, we know the answer since, as 
 you've acknowledged, it's infinite in spatial extent.  
 Consequently, since 
 the observable universe is finite in spatial extent, the 
 unobserved 
 universe must be infinite in extent (for a flat universe). Can 
 you estimate 
 the size of the unobservable universe for a positively curved 
 universe? AG

>>>
>>> The cosmological constant is a Ricci curvature with Λ = 
>>> R_{tt} for the flat k = 0 case. for k = 1 there is a spatial 
>>> Ricci 
>>> curvature R_{rr}. This contributes to the occurrence of the 
>>> cosmological 
>>> constant, but it is tiny. So R_{rr} = δR_{tt} for δ a rather 
>>> small number. 
>>> The spatial sphere has a radius R = 1/√(R_{rr}} ≈ 1/√(δΛ). 
>>> This is then for Λ = 10^{-52}m^{-2} R ≈ δ^{-1/2} 10^{26}m, 
>>> or about the distance to the cosmological horizon multiplied by 
>>> the 
>>> reciprocal of a small number. 
>>>
>>> The problem is that we really do not what that small number 

Re: Inflation and the total size of the universe

[Lawrence Crowell]

On Saturday, April 11, 2020 at 2:26:58 PM UTC-5, Alan Grayson wrote:
>
>
>
> On Saturday, April 11, 2020 at 9:10:19 AM UTC-6, Lawrence Crowell wrote:
>>
>> On Friday, April 10, 2020 at 8:45:22 PM UTC-5, Alan Grayson wrote:
>>>
>>>
>>>
>>> On Sunday, March 29, 2020 at 12:03:10 PM UTC-6, Lawrence Crowell wrote:

 On Sunday, March 29, 2020 at 1:57:12 AM UTC-5, Alan Grayson wrote:
>
>
>
> On Saturday, March 28, 2020 at 5:38:33 PM UTC-6, Lawrence Crowell 
> wrote:
>>
>> On Saturday, March 28, 2020 at 5:27:51 AM UTC-5, Alan Grayson wrote:
>>>
>>>
>>>
>>> On Wednesday, March 25, 2020 at 4:25:43 PM UTC-6, Lawrence Crowell 
>>> wrote:

 On Wednesday, March 25, 2020 at 2:17:39 PM UTC-5, Alan Grayson 
 wrote:

>
>
> On Wednesday, March 25, 2020 at 9:57:44 AM UTC-6, Lawrence Crowell 
> wrote:
>>
>> On Wednesday, March 25, 2020 at 10:24:30 AM UTC-5, Alan Grayson 
>> wrote:
>>>
>>>
>>>
>>> On Wednesday, March 25, 2020 at 2:58:45 AM UTC-6, Lawrence 
>>> Crowell wrote:

 On Wednesday, March 25, 2020 at 1:28:21 AM UTC-5, Alan Grayson 
 wrote:
>
>
>
> On Tuesday, March 24, 2020 at 6:21:50 PM UTC-6, Lawrence 
> Crowell wrote:
>>
>> On Tuesday, March 24, 2020 at 6:19:41 PM UTC-5, Alan Grayson 
>> wrote:
>>>
>>>
>>>
>>> On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence 
>>> Crowell wrote:

 Inflation was initiate 10^{-35}sec after the quantum 
 fluctuation appearance of the observable cosmos, and this had 
 a duration of 
 10^{-30}sec. The cosmological constant averaged around Λ = 
 10^{48}m^{-2}. 
 If I divide by the speed of light squared this comes to 
 10^{32}s^{-2} and 
 we get √(Λ)T = 10^{2}. This means any spatial region expanded 
 by a factor 
 of 10^{√(Λ)T} which is large. The natural log of this is 
 230 and this is not too far off from the more precise 
 calculation of 60 
 e-folds. The 60 e-folds is a phenomenological fit that matches 
 inflation 
 with the observed universe.

 How much of the universe is unavailable depends upon 
 whether k = -1, 0 or 1. The furthest out some quantum might 
 emerge and have 
 an influence is for a Planck scale quantum to now be inflated 
 to the CMB 
 scale. I know I have gone through this here before, but the 
 result is the 
 furthest we can detect anything is around 1800 billion light 
 years, which 
 would be a graviton or quantum black hole that leaves an 
 imprint or 
 signature on the CMB. It is not possible from theory to know 
 what 
 percentage this is of the entire shebang, and for k = -1 or 0 
 it is an 
 infinitesimal part.

 LC

>>>
>>> For k=0, a flat universe, we know the answer since, as 
>>> you've acknowledged, it's infinite in spatial extent.  
>>> Consequently, since 
>>> the observable universe is finite in spatial extent, the 
>>> unobserved 
>>> universe must be infinite in extent (for a flat universe). Can 
>>> you estimate 
>>> the size of the unobservable universe for a positively curved 
>>> universe? AG
>>>
>>
>> The cosmological constant is a Ricci curvature with Λ = 
>> R_{tt} for the flat k = 0 case. for k = 1 there is a spatial 
>> Ricci 
>> curvature R_{rr}. This contributes to the occurrence of the 
>> cosmological 
>> constant, but it is tiny. So R_{rr} = δR_{tt} for δ a rather 
>> small number. 
>> The spatial sphere has a radius R = 1/√(R_{rr}} ≈ 1/√(δΛ). 
>> This is then for Λ = 10^{-52}m^{-2} R ≈ δ^{-1/2} 10^{26}m, 
>> or about the distance to the cosmological horizon multiplied by 
>> the 
>> reciprocal of a small number. 
>>
>> The problem is that we really do not what that small number 
>> is. For various reasons I think it is δ < 5×10^{-5}This 
>> gives a radius where a Planck frequency is redshifted to a CMB 
>> scale. If it 
>> is smaller 

Re: Inflation and the total size of the universe

[Alan Grayson]

On Saturday, April 11, 2020 at 9:10:19 AM UTC-6, Lawrence Crowell wrote:
>
> On Friday, April 10, 2020 at 8:45:22 PM UTC-5, Alan Grayson wrote:
>>
>>
>>
>> On Sunday, March 29, 2020 at 12:03:10 PM UTC-6, Lawrence Crowell wrote:
>>>
>>> On Sunday, March 29, 2020 at 1:57:12 AM UTC-5, Alan Grayson wrote:



 On Saturday, March 28, 2020 at 5:38:33 PM UTC-6, Lawrence Crowell wrote:
>
> On Saturday, March 28, 2020 at 5:27:51 AM UTC-5, Alan Grayson wrote:
>>
>>
>>
>> On Wednesday, March 25, 2020 at 4:25:43 PM UTC-6, Lawrence Crowell 
>> wrote:
>>>
>>> On Wednesday, March 25, 2020 at 2:17:39 PM UTC-5, Alan Grayson wrote:
>>>


 On Wednesday, March 25, 2020 at 9:57:44 AM UTC-6, Lawrence Crowell 
 wrote:
>
> On Wednesday, March 25, 2020 at 10:24:30 AM UTC-5, Alan Grayson 
> wrote:
>>
>>
>>
>> On Wednesday, March 25, 2020 at 2:58:45 AM UTC-6, Lawrence 
>> Crowell wrote:
>>>
>>> On Wednesday, March 25, 2020 at 1:28:21 AM UTC-5, Alan Grayson 
>>> wrote:



 On Tuesday, March 24, 2020 at 6:21:50 PM UTC-6, Lawrence 
 Crowell wrote:
>
> On Tuesday, March 24, 2020 at 6:19:41 PM UTC-5, Alan Grayson 
> wrote:
>>
>>
>>
>> On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence 
>> Crowell wrote:
>>>
>>> Inflation was initiate 10^{-35}sec after the quantum 
>>> fluctuation appearance of the observable cosmos, and this had a 
>>> duration of 
>>> 10^{-30}sec. The cosmological constant averaged around Λ = 
>>> 10^{48}m^{-2}. 
>>> If I divide by the speed of light squared this comes to 
>>> 10^{32}s^{-2} and 
>>> we get √(Λ)T = 10^{2}. This means any spatial region expanded 
>>> by a factor 
>>> of 10^{√(Λ)T} which is large. The natural log of this is 
>>> 230 and this is not too far off from the more precise 
>>> calculation of 60 
>>> e-folds. The 60 e-folds is a phenomenological fit that matches 
>>> inflation 
>>> with the observed universe.
>>>
>>> How much of the universe is unavailable depends upon whether 
>>> k = -1, 0 or 1. The furthest out some quantum might emerge and 
>>> have an 
>>> influence is for a Planck scale quantum to now be inflated to 
>>> the CMB 
>>> scale. I know I have gone through this here before, but the 
>>> result is the 
>>> furthest we can detect anything is around 1800 billion light 
>>> years, which 
>>> would be a graviton or quantum black hole that leaves an 
>>> imprint or 
>>> signature on the CMB. It is not possible from theory to know 
>>> what 
>>> percentage this is of the entire shebang, and for k = -1 or 0 
>>> it is an 
>>> infinitesimal part.
>>>
>>> LC
>>>
>>
>> For k=0, a flat universe, we know the answer since, as you've 
>> acknowledged, it's infinite in spatial extent.  Consequently, 
>> since the 
>> observable universe is finite in spatial extent, the unobserved 
>> universe 
>> must be infinite in extent (for a flat universe). Can you 
>> estimate the size 
>> of the unobservable universe for a positively curved universe? AG
>>
>
> The cosmological constant is a Ricci curvature with Λ = R_{tt} 
> for the flat k = 0 case. for k = 1 there is a spatial Ricci 
> curvature 
> R_{rr}. This contributes to the occurrence of the cosmological 
> constant, but it is tiny. So R_{rr} = δR_{tt} for δ a rather 
> small number. 
> The spatial sphere has a radius R = 1/√(R_{rr}} ≈ 1/√(δΛ). 
> This is then for Λ = 10^{-52}m^{-2} R ≈ δ^{-1/2} 10^{26}m, or 
> about the distance to the cosmological horizon multiplied by the 
> reciprocal 
> of a small number. 
>
> The problem is that we really do not what that small number 
> is. For various reasons I think it is δ < 5×10^{-5}This gives 
> a radius where a Planck frequency is redshifted to a CMB scale. 
> If it is 
> smaller then there are regions of the universe completely 
> inaccessible to 
> us even as Planck modes redshifted to the cosmic horizon scale.
>
> LC
>

 FWIW, 

Re: Inflation and the total size of the universe

[Lawrence Crowell]

On Friday, April 10, 2020 at 8:45:22 PM UTC-5, Alan Grayson wrote:
>
>
>
> On Sunday, March 29, 2020 at 12:03:10 PM UTC-6, Lawrence Crowell wrote:
>>
>> On Sunday, March 29, 2020 at 1:57:12 AM UTC-5, Alan Grayson wrote:
>>>
>>>
>>>
>>> On Saturday, March 28, 2020 at 5:38:33 PM UTC-6, Lawrence Crowell wrote:

 On Saturday, March 28, 2020 at 5:27:51 AM UTC-5, Alan Grayson wrote:
>
>
>
> On Wednesday, March 25, 2020 at 4:25:43 PM UTC-6, Lawrence Crowell 
> wrote:
>>
>> On Wednesday, March 25, 2020 at 2:17:39 PM UTC-5, Alan Grayson wrote:
>>
>>>
>>>
>>> On Wednesday, March 25, 2020 at 9:57:44 AM UTC-6, Lawrence Crowell 
>>> wrote:

 On Wednesday, March 25, 2020 at 10:24:30 AM UTC-5, Alan Grayson 
 wrote:
>
>
>
> On Wednesday, March 25, 2020 at 2:58:45 AM UTC-6, Lawrence Crowell 
> wrote:
>>
>> On Wednesday, March 25, 2020 at 1:28:21 AM UTC-5, Alan Grayson 
>> wrote:
>>>
>>>
>>>
>>> On Tuesday, March 24, 2020 at 6:21:50 PM UTC-6, Lawrence Crowell 
>>> wrote:

 On Tuesday, March 24, 2020 at 6:19:41 PM UTC-5, Alan Grayson 
 wrote:
>
>
>
> On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence 
> Crowell wrote:
>>
>> Inflation was initiate 10^{-35}sec after the quantum 
>> fluctuation appearance of the observable cosmos, and this had a 
>> duration of 
>> 10^{-30}sec. The cosmological constant averaged around Λ = 
>> 10^{48}m^{-2}. 
>> If I divide by the speed of light squared this comes to 
>> 10^{32}s^{-2} and 
>> we get √(Λ)T = 10^{2}. This means any spatial region expanded by 
>> a factor 
>> of 10^{√(Λ)T} which is large. The natural log of this is 230 
>> and this is not too far off from the more precise calculation of 
>> 60 
>> e-folds. The 60 e-folds is a phenomenological fit that matches 
>> inflation 
>> with the observed universe.
>>
>> How much of the universe is unavailable depends upon whether 
>> k = -1, 0 or 1. The furthest out some quantum might emerge and 
>> have an 
>> influence is for a Planck scale quantum to now be inflated to 
>> the CMB 
>> scale. I know I have gone through this here before, but the 
>> result is the 
>> furthest we can detect anything is around 1800 billion light 
>> years, which 
>> would be a graviton or quantum black hole that leaves an imprint 
>> or 
>> signature on the CMB. It is not possible from theory to know 
>> what 
>> percentage this is of the entire shebang, and for k = -1 or 0 it 
>> is an 
>> infinitesimal part.
>>
>> LC
>>
>
> For k=0, a flat universe, we know the answer since, as you've 
> acknowledged, it's infinite in spatial extent.  Consequently, 
> since the 
> observable universe is finite in spatial extent, the unobserved 
> universe 
> must be infinite in extent (for a flat universe). Can you 
> estimate the size 
> of the unobservable universe for a positively curved universe? AG
>

 The cosmological constant is a Ricci curvature with Λ = R_{tt} 
 for the flat k = 0 case. for k = 1 there is a spatial Ricci 
 curvature 
 R_{rr}. This contributes to the occurrence of the cosmological 
 constant, but it is tiny. So R_{rr} = δR_{tt} for δ a rather small 
 number. 
 The spatial sphere has a radius R = 1/√(R_{rr}} ≈ 1/√(δΛ). 
 This is then for Λ = 10^{-52}m^{-2} R ≈ δ^{-1/2} 10^{26}m, or 
 about the distance to the cosmological horizon multiplied by the 
 reciprocal 
 of a small number. 

 The problem is that we really do not what that small number is. 
 For various reasons I think it is δ < 5×10^{-5}This gives a 
 radius where a Planck frequency is redshifted to a CMB scale. If 
 it is 
 smaller then there are regions of the universe completely 
 inaccessible to 
 us even as Planck modes redshifted to the cosmic horizon scale.

 LC

>>>
>>> FWIW, another reason I think our universe has a positive 
>>> curvature is that if it were flat, with zero curvature, and we made 
>>> many 
>>> measurements, we'd get a distribution of 

Re: Inflation and the total size of the universe

[Alan Grayson]

On Sunday, March 29, 2020 at 12:03:10 PM UTC-6, Lawrence Crowell wrote:
>
> On Sunday, March 29, 2020 at 1:57:12 AM UTC-5, Alan Grayson wrote:
>>
>>
>>
>> On Saturday, March 28, 2020 at 5:38:33 PM UTC-6, Lawrence Crowell wrote:
>>>
>>> On Saturday, March 28, 2020 at 5:27:51 AM UTC-5, Alan Grayson wrote:



 On Wednesday, March 25, 2020 at 4:25:43 PM UTC-6, Lawrence Crowell 
 wrote:
>
> On Wednesday, March 25, 2020 at 2:17:39 PM UTC-5, Alan Grayson wrote:
>
>>
>>
>> On Wednesday, March 25, 2020 at 9:57:44 AM UTC-6, Lawrence Crowell 
>> wrote:
>>>
>>> On Wednesday, March 25, 2020 at 10:24:30 AM UTC-5, Alan Grayson 
>>> wrote:



 On Wednesday, March 25, 2020 at 2:58:45 AM UTC-6, Lawrence Crowell 
 wrote:
>
> On Wednesday, March 25, 2020 at 1:28:21 AM UTC-5, Alan Grayson 
> wrote:
>>
>>
>>
>> On Tuesday, March 24, 2020 at 6:21:50 PM UTC-6, Lawrence Crowell 
>> wrote:
>>>
>>> On Tuesday, March 24, 2020 at 6:19:41 PM UTC-5, Alan Grayson 
>>> wrote:



 On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence Crowell 
 wrote:
>
> Inflation was initiate 10^{-35}sec after the quantum 
> fluctuation appearance of the observable cosmos, and this had a 
> duration of 
> 10^{-30}sec. The cosmological constant averaged around Λ = 
> 10^{48}m^{-2}. 
> If I divide by the speed of light squared this comes to 
> 10^{32}s^{-2} and 
> we get √(Λ)T = 10^{2}. This means any spatial region expanded by 
> a factor 
> of 10^{√(Λ)T} which is large. The natural log of this is 230 
> and this is not too far off from the more precise calculation of 
> 60 
> e-folds. The 60 e-folds is a phenomenological fit that matches 
> inflation 
> with the observed universe.
>
> How much of the universe is unavailable depends upon whether k 
> = -1, 0 or 1. The furthest out some quantum might emerge and have 
> an 
> influence is for a Planck scale quantum to now be inflated to the 
> CMB 
> scale. I know I have gone through this here before, but the 
> result is the 
> furthest we can detect anything is around 1800 billion light 
> years, which 
> would be a graviton or quantum black hole that leaves an imprint 
> or 
> signature on the CMB. It is not possible from theory to know what 
> percentage this is of the entire shebang, and for k = -1 or 0 it 
> is an 
> infinitesimal part.
>
> LC
>

 For k=0, a flat universe, we know the answer since, as you've 
 acknowledged, it's infinite in spatial extent.  Consequently, 
 since the 
 observable universe is finite in spatial extent, the unobserved 
 universe 
 must be infinite in extent (for a flat universe). Can you estimate 
 the size 
 of the unobservable universe for a positively curved universe? AG

>>>
>>> The cosmological constant is a Ricci curvature with Λ = R_{tt} 
>>> for the flat k = 0 case. for k = 1 there is a spatial Ricci 
>>> curvature 
>>> R_{rr}. This contributes to the occurrence of the cosmological 
>>> constant, but it is tiny. So R_{rr} = δR_{tt} for δ a rather small 
>>> number. 
>>> The spatial sphere has a radius R = 1/√(R_{rr}} ≈ 1/√(δΛ). This 
>>> is then for Λ = 10^{-52}m^{-2} R ≈ δ^{-1/2} 10^{26}m, or about 
>>> the distance to the cosmological horizon multiplied by the 
>>> reciprocal of a 
>>> small number. 
>>>
>>> The problem is that we really do not what that small number is. 
>>> For various reasons I think it is δ < 5×10^{-5}This gives a 
>>> radius where a Planck frequency is redshifted to a CMB scale. If it 
>>> is 
>>> smaller then there are regions of the universe completely 
>>> inaccessible to 
>>> us even as Planck modes redshifted to the cosmic horizon scale.
>>>
>>> LC
>>>
>>
>> FWIW, another reason I think our universe has a positive 
>> curvature is that if it were flat, with zero curvature, and we made 
>> many 
>> measurements, we'd get a distribution of measured values above and 
>> below 
>> zero due to unavoidable measurement errors. But I think we 
>> invariably get a 
>> small positive number. Is this what we actually 

Re: Inflation and the total size of the universe

[Alan Grayson]

On Sunday, March 29, 2020 at 12:03:10 PM UTC-6, Lawrence Crowell wrote:
>
> On Sunday, March 29, 2020 at 1:57:12 AM UTC-5, Alan Grayson wrote:
>>
>>
>>
>> On Saturday, March 28, 2020 at 5:38:33 PM UTC-6, Lawrence Crowell wrote:
>>>
>>> On Saturday, March 28, 2020 at 5:27:51 AM UTC-5, Alan Grayson wrote:



 On Wednesday, March 25, 2020 at 4:25:43 PM UTC-6, Lawrence Crowell 
 wrote:
>
> On Wednesday, March 25, 2020 at 2:17:39 PM UTC-5, Alan Grayson wrote:
>
>>
>>
>> On Wednesday, March 25, 2020 at 9:57:44 AM UTC-6, Lawrence Crowell 
>> wrote:
>>>
>>> On Wednesday, March 25, 2020 at 10:24:30 AM UTC-5, Alan Grayson 
>>> wrote:



 On Wednesday, March 25, 2020 at 2:58:45 AM UTC-6, Lawrence Crowell 
 wrote:
>
> On Wednesday, March 25, 2020 at 1:28:21 AM UTC-5, Alan Grayson 
> wrote:
>>
>>
>>
>> On Tuesday, March 24, 2020 at 6:21:50 PM UTC-6, Lawrence Crowell 
>> wrote:
>>>
>>> On Tuesday, March 24, 2020 at 6:19:41 PM UTC-5, Alan Grayson 
>>> wrote:



 On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence Crowell 
 wrote:
>
> Inflation was initiate 10^{-35}sec after the quantum 
> fluctuation appearance of the observable cosmos, and this had a 
> duration of 
> 10^{-30}sec. The cosmological constant averaged around Λ = 
> 10^{48}m^{-2}. 
> If I divide by the speed of light squared this comes to 
> 10^{32}s^{-2} and 
> we get √(Λ)T = 10^{2}. This means any spatial region expanded by 
> a factor 
> of 10^{√(Λ)T} which is large. The natural log of this is 230 
> and this is not too far off from the more precise calculation of 
> 60 
> e-folds. The 60 e-folds is a phenomenological fit that matches 
> inflation 
> with the observed universe.
>
> How much of the universe is unavailable depends upon whether k 
> = -1, 0 or 1. The furthest out some quantum might emerge and have 
> an 
> influence is for a Planck scale quantum to now be inflated to the 
> CMB 
> scale. I know I have gone through this here before, but the 
> result is the 
> furthest we can detect anything is around 1800 billion light 
> years, which 
> would be a graviton or quantum black hole that leaves an imprint 
> or 
> signature on the CMB. It is not possible from theory to know what 
> percentage this is of the entire shebang, and for k = -1 or 0 it 
> is an 
> infinitesimal part.
>
> LC
>

 For k=0, a flat universe, we know the answer since, as you've 
 acknowledged, it's infinite in spatial extent.  Consequently, 
 since the 
 observable universe is finite in spatial extent, the unobserved 
 universe 
 must be infinite in extent (for a flat universe). Can you estimate 
 the size 
 of the unobservable universe for a positively curved universe? AG

>>>
>>> The cosmological constant is a Ricci curvature with Λ = R_{tt} 
>>> for the flat k = 0 case. for k = 1 there is a spatial Ricci 
>>> curvature 
>>> R_{rr}. This contributes to the occurrence of the cosmological 
>>> constant, but it is tiny. So R_{rr} = δR_{tt} for δ a rather small 
>>> number. 
>>> The spatial sphere has a radius R = 1/√(R_{rr}} ≈ 1/√(δΛ). This 
>>> is then for Λ = 10^{-52}m^{-2} R ≈ δ^{-1/2} 10^{26}m, or about 
>>> the distance to the cosmological horizon multiplied by the 
>>> reciprocal of a 
>>> small number. 
>>>
>>> The problem is that we really do not what that small number is. 
>>> For various reasons I think it is δ < 5×10^{-5}This gives a 
>>> radius where a Planck frequency is redshifted to a CMB scale. If it 
>>> is 
>>> smaller then there are regions of the universe completely 
>>> inaccessible to 
>>> us even as Planck modes redshifted to the cosmic horizon scale.
>>>
>>> LC
>>>
>>
>> FWIW, another reason I think our universe has a positive 
>> curvature is that if it were flat, with zero curvature, and we made 
>> many 
>> measurements, we'd get a distribution of measured values above and 
>> below 
>> zero due to unavoidable measurement errors. But I think we 
>> invariably get a 
>> small positive number. Is this what we actually 

Re: Inflation and the total size of the universe

[Lawrence Crowell]

On Sunday, March 29, 2020 at 1:57:12 AM UTC-5, Alan Grayson wrote:
>
>
>
> On Saturday, March 28, 2020 at 5:38:33 PM UTC-6, Lawrence Crowell wrote:
>>
>> On Saturday, March 28, 2020 at 5:27:51 AM UTC-5, Alan Grayson wrote:
>>>
>>>
>>>
>>> On Wednesday, March 25, 2020 at 4:25:43 PM UTC-6, Lawrence Crowell wrote:

 On Wednesday, March 25, 2020 at 2:17:39 PM UTC-5, Alan Grayson wrote:

>
>
> On Wednesday, March 25, 2020 at 9:57:44 AM UTC-6, Lawrence Crowell 
> wrote:
>>
>> On Wednesday, March 25, 2020 at 10:24:30 AM UTC-5, Alan Grayson wrote:
>>>
>>>
>>>
>>> On Wednesday, March 25, 2020 at 2:58:45 AM UTC-6, Lawrence Crowell 
>>> wrote:

 On Wednesday, March 25, 2020 at 1:28:21 AM UTC-5, Alan Grayson 
 wrote:
>
>
>
> On Tuesday, March 24, 2020 at 6:21:50 PM UTC-6, Lawrence Crowell 
> wrote:
>>
>> On Tuesday, March 24, 2020 at 6:19:41 PM UTC-5, Alan Grayson 
>> wrote:
>>>
>>>
>>>
>>> On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence Crowell 
>>> wrote:

 Inflation was initiate 10^{-35}sec after the quantum 
 fluctuation appearance of the observable cosmos, and this had a 
 duration of 
 10^{-30}sec. The cosmological constant averaged around Λ = 
 10^{48}m^{-2}. 
 If I divide by the speed of light squared this comes to 
 10^{32}s^{-2} and 
 we get √(Λ)T = 10^{2}. This means any spatial region expanded by a 
 factor 
 of 10^{√(Λ)T} which is large. The natural log of this is 230 
 and this is not too far off from the more precise calculation of 
 60 
 e-folds. The 60 e-folds is a phenomenological fit that matches 
 inflation 
 with the observed universe.

 How much of the universe is unavailable depends upon whether k 
 = -1, 0 or 1. The furthest out some quantum might emerge and have 
 an 
 influence is for a Planck scale quantum to now be inflated to the 
 CMB 
 scale. I know I have gone through this here before, but the result 
 is the 
 furthest we can detect anything is around 1800 billion light 
 years, which 
 would be a graviton or quantum black hole that leaves an imprint 
 or 
 signature on the CMB. It is not possible from theory to know what 
 percentage this is of the entire shebang, and for k = -1 or 0 it 
 is an 
 infinitesimal part.

 LC

>>>
>>> For k=0, a flat universe, we know the answer since, as you've 
>>> acknowledged, it's infinite in spatial extent.  Consequently, since 
>>> the 
>>> observable universe is finite in spatial extent, the unobserved 
>>> universe 
>>> must be infinite in extent (for a flat universe). Can you estimate 
>>> the size 
>>> of the unobservable universe for a positively curved universe? AG
>>>
>>
>> The cosmological constant is a Ricci curvature with Λ = R_{tt} 
>> for the flat k = 0 case. for k = 1 there is a spatial Ricci 
>> curvature 
>> R_{rr}. This contributes to the occurrence of the cosmological 
>> constant, but it is tiny. So R_{rr} = δR_{tt} for δ a rather small 
>> number. 
>> The spatial sphere has a radius R = 1/√(R_{rr}} ≈ 1/√(δΛ). This 
>> is then for Λ = 10^{-52}m^{-2} R ≈ δ^{-1/2} 10^{26}m, or about 
>> the distance to the cosmological horizon multiplied by the 
>> reciprocal of a 
>> small number. 
>>
>> The problem is that we really do not what that small number is. 
>> For various reasons I think it is δ < 5×10^{-5}This gives a 
>> radius where a Planck frequency is redshifted to a CMB scale. If it 
>> is 
>> smaller then there are regions of the universe completely 
>> inaccessible to 
>> us even as Planck modes redshifted to the cosmic horizon scale.
>>
>> LC
>>
>
> FWIW, another reason I think our universe has a positive curvature 
> is that if it were flat, with zero curvature, and we made many 
> measurements, we'd get a distribution of measured values above and 
> below 
> zero due to unavoidable measurement errors. But I think we invariably 
> get a 
> small positive number. Is this what we actually get; values always 
> positive 
> but close to zero, but no negative values? TIA,AG 
>

 As yet attempt to find optical results due to spatial curvature 
 have not found 

Re: Inflation and the total size of the universe

[Alan Grayson]

On Saturday, March 28, 2020 at 5:38:33 PM UTC-6, Lawrence Crowell wrote:
>
> On Saturday, March 28, 2020 at 5:27:51 AM UTC-5, Alan Grayson wrote:
>>
>>
>>
>> On Wednesday, March 25, 2020 at 4:25:43 PM UTC-6, Lawrence Crowell wrote:
>>>
>>> On Wednesday, March 25, 2020 at 2:17:39 PM UTC-5, Alan Grayson wrote:
>>>


 On Wednesday, March 25, 2020 at 9:57:44 AM UTC-6, Lawrence Crowell 
 wrote:
>
> On Wednesday, March 25, 2020 at 10:24:30 AM UTC-5, Alan Grayson wrote:
>>
>>
>>
>> On Wednesday, March 25, 2020 at 2:58:45 AM UTC-6, Lawrence Crowell 
>> wrote:
>>>
>>> On Wednesday, March 25, 2020 at 1:28:21 AM UTC-5, Alan Grayson wrote:



 On Tuesday, March 24, 2020 at 6:21:50 PM UTC-6, Lawrence Crowell 
 wrote:
>
> On Tuesday, March 24, 2020 at 6:19:41 PM UTC-5, Alan Grayson wrote:
>>
>>
>>
>> On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence Crowell 
>> wrote:
>>>
>>> Inflation was initiate 10^{-35}sec after the quantum fluctuation 
>>> appearance of the observable cosmos, and this had a duration of 
>>> 10^{-30}sec. The cosmological constant averaged around Λ = 
>>> 10^{48}m^{-2}. 
>>> If I divide by the speed of light squared this comes to 
>>> 10^{32}s^{-2} and 
>>> we get √(Λ)T = 10^{2}. This means any spatial region expanded by a 
>>> factor 
>>> of 10^{√(Λ)T} which is large. The natural log of this is 230 
>>> and this is not too far off from the more precise calculation of 60 
>>> e-folds. The 60 e-folds is a phenomenological fit that matches 
>>> inflation 
>>> with the observed universe.
>>>
>>> How much of the universe is unavailable depends upon whether k = 
>>> -1, 0 or 1. The furthest out some quantum might emerge and have an 
>>> influence is for a Planck scale quantum to now be inflated to the 
>>> CMB 
>>> scale. I know I have gone through this here before, but the result 
>>> is the 
>>> furthest we can detect anything is around 1800 billion light years, 
>>> which 
>>> would be a graviton or quantum black hole that leaves an imprint or 
>>> signature on the CMB. It is not possible from theory to know what 
>>> percentage this is of the entire shebang, and for k = -1 or 0 it is 
>>> an 
>>> infinitesimal part.
>>>
>>> LC
>>>
>>
>> For k=0, a flat universe, we know the answer since, as you've 
>> acknowledged, it's infinite in spatial extent.  Consequently, since 
>> the 
>> observable universe is finite in spatial extent, the unobserved 
>> universe 
>> must be infinite in extent (for a flat universe). Can you estimate 
>> the size 
>> of the unobservable universe for a positively curved universe? AG
>>
>
> The cosmological constant is a Ricci curvature with Λ = R_{tt} for 
> the flat k = 0 case. for k = 1 there is a spatial Ricci curvature 
> R_{rr}. 
> This contributes to the occurrence of the cosmological constant, 
> but it is tiny. So R_{rr} = δR_{tt} for δ a rather small number. The 
> spatial sphere has a radius R = 1/√(R_{rr}} ≈ 1/√(δΛ). This is 
> then for Λ = 10^{-52}m^{-2} R ≈ δ^{-1/2} 10^{26}m, or about the 
> distance to the cosmological horizon multiplied by the reciprocal of 
> a 
> small number. 
>
> The problem is that we really do not what that small number is. 
> For various reasons I think it is δ < 5×10^{-5}This gives a 
> radius where a Planck frequency is redshifted to a CMB scale. If it 
> is 
> smaller then there are regions of the universe completely 
> inaccessible to 
> us even as Planck modes redshifted to the cosmic horizon scale.
>
> LC
>

 FWIW, another reason I think our universe has a positive curvature 
 is that if it were flat, with zero curvature, and we made many 
 measurements, we'd get a distribution of measured values above and 
 below 
 zero due to unavoidable measurement errors. But I think we invariably 
 get a 
 small positive number. Is this what we actually get; values always 
 positive 
 but close to zero, but no negative values? TIA,AG 

>>>
>>> As yet attempt to find optical results due to spatial curvature have 
>>> not found anything. The curvature of spacetime is mostly due to how 
>>> space 
>>> is embedded in spacetime.
>>>
>>> LC
>>>
>>
>> But you haven't directly addressed my hypothesis regarding the 
>> measurements. AG 
>>
>
> So far as I know 

Re: Inflation and the total size of the universe

[Lawrence Crowell]

On Saturday, March 28, 2020 at 5:27:51 AM UTC-5, Alan Grayson wrote:
>
>
>
> On Wednesday, March 25, 2020 at 4:25:43 PM UTC-6, Lawrence Crowell wrote:
>>
>> On Wednesday, March 25, 2020 at 2:17:39 PM UTC-5, Alan Grayson wrote:
>>
>>>
>>>
>>> On Wednesday, March 25, 2020 at 9:57:44 AM UTC-6, Lawrence Crowell wrote:

 On Wednesday, March 25, 2020 at 10:24:30 AM UTC-5, Alan Grayson wrote:
>
>
>
> On Wednesday, March 25, 2020 at 2:58:45 AM UTC-6, Lawrence Crowell 
> wrote:
>>
>> On Wednesday, March 25, 2020 at 1:28:21 AM UTC-5, Alan Grayson wrote:
>>>
>>>
>>>
>>> On Tuesday, March 24, 2020 at 6:21:50 PM UTC-6, Lawrence Crowell 
>>> wrote:

 On Tuesday, March 24, 2020 at 6:19:41 PM UTC-5, Alan Grayson wrote:
>
>
>
> On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence Crowell 
> wrote:
>>
>> Inflation was initiate 10^{-35}sec after the quantum fluctuation 
>> appearance of the observable cosmos, and this had a duration of 
>> 10^{-30}sec. The cosmological constant averaged around Λ = 
>> 10^{48}m^{-2}. 
>> If I divide by the speed of light squared this comes to 
>> 10^{32}s^{-2} and 
>> we get √(Λ)T = 10^{2}. This means any spatial region expanded by a 
>> factor 
>> of 10^{√(Λ)T} which is large. The natural log of this is 230 and 
>> this is not too far off from the more precise calculation of 60 
>> e-folds. 
>> The 60 e-folds is a phenomenological fit that matches inflation with 
>> the 
>> observed universe.
>>
>> How much of the universe is unavailable depends upon whether k = 
>> -1, 0 or 1. The furthest out some quantum might emerge and have an 
>> influence is for a Planck scale quantum to now be inflated to the 
>> CMB 
>> scale. I know I have gone through this here before, but the result 
>> is the 
>> furthest we can detect anything is around 1800 billion light years, 
>> which 
>> would be a graviton or quantum black hole that leaves an imprint or 
>> signature on the CMB. It is not possible from theory to know what 
>> percentage this is of the entire shebang, and for k = -1 or 0 it is 
>> an 
>> infinitesimal part.
>>
>> LC
>>
>
> For k=0, a flat universe, we know the answer since, as you've 
> acknowledged, it's infinite in spatial extent.  Consequently, since 
> the 
> observable universe is finite in spatial extent, the unobserved 
> universe 
> must be infinite in extent (for a flat universe). Can you estimate 
> the size 
> of the unobservable universe for a positively curved universe? AG
>

 The cosmological constant is a Ricci curvature with Λ = R_{tt} for 
 the flat k = 0 case. for k = 1 there is a spatial Ricci curvature 
 R_{rr}. 
 This contributes to the occurrence of the cosmological constant, 
 but it is tiny. So R_{rr} = δR_{tt} for δ a rather small number. The 
 spatial sphere has a radius R = 1/√(R_{rr}} ≈ 1/√(δΛ). This is 
 then for Λ = 10^{-52}m^{-2} R ≈ δ^{-1/2} 10^{26}m, or about the 
 distance to the cosmological horizon multiplied by the reciprocal of a 
 small number. 

 The problem is that we really do not what that small number is. For 
 various reasons I think it is δ < 5×10^{-5}This gives a radius 
 where a Planck frequency is redshifted to a CMB scale. If it is 
 smaller 
 then there are regions of the universe completely inaccessible to us 
 even 
 as Planck modes redshifted to the cosmic horizon scale.

 LC

>>>
>>> FWIW, another reason I think our universe has a positive curvature 
>>> is that if it were flat, with zero curvature, and we made many 
>>> measurements, we'd get a distribution of measured values above and 
>>> below 
>>> zero due to unavoidable measurement errors. But I think we invariably 
>>> get a 
>>> small positive number. Is this what we actually get; values always 
>>> positive 
>>> but close to zero, but no negative values? TIA,AG 
>>>
>>
>> As yet attempt to find optical results due to spatial curvature have 
>> not found anything. The curvature of spacetime is mostly due to how 
>> space 
>> is embedded in spacetime.
>>
>> LC
>>
>
> But you haven't directly addressed my hypothesis regarding the 
> measurements. AG 
>

 So far as I know there is no signal above the noise on this.

 LC

>>>
>>> Do the measurements show a spread around zero, including of course 
>>> negative values, or just positive values close to zero? This is 

Re: Inflation and the total size of the universe

[Alan Grayson]

On Wednesday, March 25, 2020 at 4:25:43 PM UTC-6, Lawrence Crowell wrote:
>
> On Wednesday, March 25, 2020 at 2:17:39 PM UTC-5, Alan Grayson wrote:
>
>>
>>
>> On Wednesday, March 25, 2020 at 9:57:44 AM UTC-6, Lawrence Crowell wrote:
>>>
>>> On Wednesday, March 25, 2020 at 10:24:30 AM UTC-5, Alan Grayson wrote:



 On Wednesday, March 25, 2020 at 2:58:45 AM UTC-6, Lawrence Crowell 
 wrote:
>
> On Wednesday, March 25, 2020 at 1:28:21 AM UTC-5, Alan Grayson wrote:
>>
>>
>>
>> On Tuesday, March 24, 2020 at 6:21:50 PM UTC-6, Lawrence Crowell 
>> wrote:
>>>
>>> On Tuesday, March 24, 2020 at 6:19:41 PM UTC-5, Alan Grayson wrote:



 On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence Crowell 
 wrote:
>
> Inflation was initiate 10^{-35}sec after the quantum fluctuation 
> appearance of the observable cosmos, and this had a duration of 
> 10^{-30}sec. The cosmological constant averaged around Λ = 
> 10^{48}m^{-2}. 
> If I divide by the speed of light squared this comes to 10^{32}s^{-2} 
> and 
> we get √(Λ)T = 10^{2}. This means any spatial region expanded by a 
> factor 
> of 10^{√(Λ)T} which is large. The natural log of this is 230 and 
> this is not too far off from the more precise calculation of 60 
> e-folds. 
> The 60 e-folds is a phenomenological fit that matches inflation with 
> the 
> observed universe.
>
> How much of the universe is unavailable depends upon whether k = 
> -1, 0 or 1. The furthest out some quantum might emerge and have an 
> influence is for a Planck scale quantum to now be inflated to the CMB 
> scale. I know I have gone through this here before, but the result is 
> the 
> furthest we can detect anything is around 1800 billion light years, 
> which 
> would be a graviton or quantum black hole that leaves an imprint or 
> signature on the CMB. It is not possible from theory to know what 
> percentage this is of the entire shebang, and for k = -1 or 0 it is 
> an 
> infinitesimal part.
>
> LC
>

 For k=0, a flat universe, we know the answer since, as you've 
 acknowledged, it's infinite in spatial extent.  Consequently, since 
 the 
 observable universe is finite in spatial extent, the unobserved 
 universe 
 must be infinite in extent (for a flat universe). Can you estimate the 
 size 
 of the unobservable universe for a positively curved universe? AG

>>>
>>> The cosmological constant is a Ricci curvature with Λ = R_{tt} for 
>>> the flat k = 0 case. for k = 1 there is a spatial Ricci curvature 
>>> R_{rr}. 
>>> This contributes to the occurrence of the cosmological constant, 
>>> but it is tiny. So R_{rr} = δR_{tt} for δ a rather small number. The 
>>> spatial sphere has a radius R = 1/√(R_{rr}} ≈ 1/√(δΛ). This is then 
>>> for Λ = 10^{-52}m^{-2} R ≈ δ^{-1/2} 10^{26}m, or about the distance 
>>> to the cosmological horizon multiplied by the reciprocal of a small 
>>> number. 
>>>
>>> The problem is that we really do not what that small number is. For 
>>> various reasons I think it is δ < 5×10^{-5}This gives a radius 
>>> where a Planck frequency is redshifted to a CMB scale. If it is smaller 
>>> then there are regions of the universe completely inaccessible to us 
>>> even 
>>> as Planck modes redshifted to the cosmic horizon scale.
>>>
>>> LC
>>>
>>
>> FWIW, another reason I think our universe has a positive curvature is 
>> that if it were flat, with zero curvature, and we made many 
>> measurements, 
>> we'd get a distribution of measured values above and below zero due to 
>> unavoidable measurement errors. But I think we invariably get a small 
>> positive number. Is this what we actually get; values always positive 
>> but 
>> close to zero, but no negative values? TIA,AG 
>>
>
> As yet attempt to find optical results due to spatial curvature have 
> not found anything. The curvature of spacetime is mostly due to how space 
> is embedded in spacetime.
>
> LC
>

 But you haven't directly addressed my hypothesis regarding the 
 measurements. AG 

>>>
>>> So far as I know there is no signal above the noise on this.
>>>
>>> LC
>>>
>>
>> Do the measurements show a spread around zero, including of course 
>> negative values, or just positive values close to zero? This is where the 
>> rubber hits the road IMO. If no negative results, there is the suggestion 
>> the curvature is NOT zero. AG 
>>
>>>
> There is a spread, but that is noise. Statistical variances of error 
> convey no information. 
>

Re: Inflation and the total size of the universe

[Lawrence Crowell]

On Wednesday, March 25, 2020 at 2:17:39 PM UTC-5, Alan Grayson wrote:

>
>
> On Wednesday, March 25, 2020 at 9:57:44 AM UTC-6, Lawrence Crowell wrote:
>>
>> On Wednesday, March 25, 2020 at 10:24:30 AM UTC-5, Alan Grayson wrote:
>>>
>>>
>>>
>>> On Wednesday, March 25, 2020 at 2:58:45 AM UTC-6, Lawrence Crowell wrote:

 On Wednesday, March 25, 2020 at 1:28:21 AM UTC-5, Alan Grayson wrote:
>
>
>
> On Tuesday, March 24, 2020 at 6:21:50 PM UTC-6, Lawrence Crowell wrote:
>>
>> On Tuesday, March 24, 2020 at 6:19:41 PM UTC-5, Alan Grayson wrote:
>>>
>>>
>>>
>>> On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence Crowell 
>>> wrote:

 Inflation was initiate 10^{-35}sec after the quantum fluctuation 
 appearance of the observable cosmos, and this had a duration of 
 10^{-30}sec. The cosmological constant averaged around Λ = 
 10^{48}m^{-2}. 
 If I divide by the speed of light squared this comes to 10^{32}s^{-2} 
 and 
 we get √(Λ)T = 10^{2}. This means any spatial region expanded by a 
 factor 
 of 10^{√(Λ)T} which is large. The natural log of this is 230 and 
 this is not too far off from the more precise calculation of 60 
 e-folds. 
 The 60 e-folds is a phenomenological fit that matches inflation with 
 the 
 observed universe.

 How much of the universe is unavailable depends upon whether k = 
 -1, 0 or 1. The furthest out some quantum might emerge and have an 
 influence is for a Planck scale quantum to now be inflated to the CMB 
 scale. I know I have gone through this here before, but the result is 
 the 
 furthest we can detect anything is around 1800 billion light years, 
 which 
 would be a graviton or quantum black hole that leaves an imprint or 
 signature on the CMB. It is not possible from theory to know what 
 percentage this is of the entire shebang, and for k = -1 or 0 it is an 
 infinitesimal part.

 LC

>>>
>>> For k=0, a flat universe, we know the answer since, as you've 
>>> acknowledged, it's infinite in spatial extent.  Consequently, since the 
>>> observable universe is finite in spatial extent, the unobserved 
>>> universe 
>>> must be infinite in extent (for a flat universe). Can you estimate the 
>>> size 
>>> of the unobservable universe for a positively curved universe? AG
>>>
>>
>> The cosmological constant is a Ricci curvature with Λ = R_{tt} for 
>> the flat k = 0 case. for k = 1 there is a spatial Ricci curvature 
>> R_{rr}. 
>> This contributes to the occurrence of the cosmological constant, but 
>> it is tiny. So R_{rr} = δR_{tt} for δ a rather small number. The spatial 
>> sphere has a radius R = 1/√(R_{rr}} ≈ 1/√(δΛ). This is then for Λ = 
>> 10^{-52}m^{-2} R ≈ δ^{-1/2} 10^{26}m, or about the distance to the 
>> cosmological horizon multiplied by the reciprocal of a small number. 
>>
>> The problem is that we really do not what that small number is. For 
>> various reasons I think it is δ < 5×10^{-5}This gives a radius where 
>> a Planck frequency is redshifted to a CMB scale. If it is smaller then 
>> there are regions of the universe completely inaccessible to us even as 
>> Planck modes redshifted to the cosmic horizon scale.
>>
>> LC
>>
>
> FWIW, another reason I think our universe has a positive curvature is 
> that if it were flat, with zero curvature, and we made many measurements, 
> we'd get a distribution of measured values above and below zero due to 
> unavoidable measurement errors. But I think we invariably get a small 
> positive number. Is this what we actually get; values always positive but 
> close to zero, but no negative values? TIA,AG 
>

 As yet attempt to find optical results due to spatial curvature have 
 not found anything. The curvature of spacetime is mostly due to how space 
 is embedded in spacetime.

 LC

>>>
>>> But you haven't directly addressed my hypothesis regarding the 
>>> measurements. AG 
>>>
>>
>> So far as I know there is no signal above the noise on this.
>>
>> LC
>>
>
> Do the measurements show a spread around zero, including of course 
> negative values, or just positive values close to zero? This is where the 
> rubber hits the road IMO. If no negative results, there is the suggestion 
> the curvature is NOT zero. AG 
>
>>
There is a spread, but that is noise. Statistical variances of error convey 
no information. So far we really do not know. In fact, if you think about 
it, no matter now accurately we measure the curvature of space, say by 
cosmic lensing etc, we can never absolutely verify k = 0. We might be able 
to get k = 1, if that is the case and the radius of curvature 

Re: Inflation and the total size of the universe

[Alan Grayson]

On Wednesday, March 25, 2020 at 9:57:44 AM UTC-6, Lawrence Crowell wrote:
>
> On Wednesday, March 25, 2020 at 10:24:30 AM UTC-5, Alan Grayson wrote:
>>
>>
>>
>> On Wednesday, March 25, 2020 at 2:58:45 AM UTC-6, Lawrence Crowell wrote:
>>>
>>> On Wednesday, March 25, 2020 at 1:28:21 AM UTC-5, Alan Grayson wrote:



 On Tuesday, March 24, 2020 at 6:21:50 PM UTC-6, Lawrence Crowell wrote:
>
> On Tuesday, March 24, 2020 at 6:19:41 PM UTC-5, Alan Grayson wrote:
>>
>>
>>
>> On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence Crowell wrote:
>>>
>>> Inflation was initiate 10^{-35}sec after the quantum fluctuation 
>>> appearance of the observable cosmos, and this had a duration of 
>>> 10^{-30}sec. The cosmological constant averaged around Λ = 
>>> 10^{48}m^{-2}. 
>>> If I divide by the speed of light squared this comes to 10^{32}s^{-2} 
>>> and 
>>> we get √(Λ)T = 10^{2}. This means any spatial region expanded by a 
>>> factor 
>>> of 10^{√(Λ)T} which is large. The natural log of this is 230 and 
>>> this is not too far off from the more precise calculation of 60 
>>> e-folds. 
>>> The 60 e-folds is a phenomenological fit that matches inflation with 
>>> the 
>>> observed universe.
>>>
>>> How much of the universe is unavailable depends upon whether k = -1, 
>>> 0 or 1. The furthest out some quantum might emerge and have an 
>>> influence is 
>>> for a Planck scale quantum to now be inflated to the CMB scale. I know 
>>> I 
>>> have gone through this here before, but the result is the furthest we 
>>> can 
>>> detect anything is around 1800 billion light years, which would be a 
>>> graviton or quantum black hole that leaves an imprint or signature on 
>>> the 
>>> CMB. It is not possible from theory to know what percentage this is of 
>>> the 
>>> entire shebang, and for k = -1 or 0 it is an infinitesimal part.
>>>
>>> LC
>>>
>>
>> For k=0, a flat universe, we know the answer since, as you've 
>> acknowledged, it's infinite in spatial extent.  Consequently, since the 
>> observable universe is finite in spatial extent, the unobserved universe 
>> must be infinite in extent (for a flat universe). Can you estimate the 
>> size 
>> of the unobservable universe for a positively curved universe? AG
>>
>
> The cosmological constant is a Ricci curvature with Λ = R_{tt} for the 
> flat k = 0 case. for k = 1 there is a spatial Ricci curvature R_{rr}. 
> This 
> contributes to the occurrence of the cosmological constant, but it is 
> tiny. So R_{rr} = δR_{tt} for δ a rather small number. The spatial sphere 
> has a radius R = 1/√(R_{rr}} ≈ 1/√(δΛ). This is then for Λ = 
> 10^{-52}m^{-2} R ≈ δ^{-1/2} 10^{26}m, or about the distance to the 
> cosmological horizon multiplied by the reciprocal of a small number. 
>
> The problem is that we really do not what that small number is. For 
> various reasons I think it is δ < 5×10^{-5}This gives a radius where 
> a Planck frequency is redshifted to a CMB scale. If it is smaller then 
> there are regions of the universe completely inaccessible to us even as 
> Planck modes redshifted to the cosmic horizon scale.
>
> LC
>

 FWIW, another reason I think our universe has a positive curvature is 
 that if it were flat, with zero curvature, and we made many measurements, 
 we'd get a distribution of measured values above and below zero due to 
 unavoidable measurement errors. But I think we invariably get a small 
 positive number. Is this what we actually get; values always positive but 
 close to zero, but no negative values? TIA,AG 

>>>
>>> As yet attempt to find optical results due to spatial curvature have not 
>>> found anything. The curvature of spacetime is mostly due to how space is 
>>> embedded in spacetime.
>>>
>>> LC
>>>
>>
>> But you haven't directly addressed my hypothesis regarding the 
>> measurements. AG 
>>
>
> So far as I know there is no signal above the noise on this.
>
> LC
>

Do the measurements show a spread around zero, including of course negative 
values, or just positive values close to zero? This is where the rubber 
hits the road IMO. If no negative results, there is the suggestion the 
curvature is NOT zero. AG 

>  
>
>>  
>>>
  
>
>>
>> On Sunday, March 22, 2020 at 11:55:19 PM UTC-5, Alan Grayson wrote:

 According to some cosmologists, Krauss?, the duration of inflation 
 is about 10^-35 seconds, which is presumably the duration necessary to 
 create isotropy and homogeneity in a universe of age 13.8 BY. If these 
 assumptions are correct, can we use them to compute the fraction of 
 the 
 universe which is now UN-observable? TIA, AG

>>>

-- 
You received this 

Re: Inflation and the total size of the universe

[Lawrence Crowell]

On Wednesday, March 25, 2020 at 10:24:30 AM UTC-5, Alan Grayson wrote:
>
>
>
> On Wednesday, March 25, 2020 at 2:58:45 AM UTC-6, Lawrence Crowell wrote:
>>
>> On Wednesday, March 25, 2020 at 1:28:21 AM UTC-5, Alan Grayson wrote:
>>>
>>>
>>>
>>> On Tuesday, March 24, 2020 at 6:21:50 PM UTC-6, Lawrence Crowell wrote:

 On Tuesday, March 24, 2020 at 6:19:41 PM UTC-5, Alan Grayson wrote:
>
>
>
> On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence Crowell wrote:
>>
>> Inflation was initiate 10^{-35}sec after the quantum fluctuation 
>> appearance of the observable cosmos, and this had a duration of 
>> 10^{-30}sec. The cosmological constant averaged around Λ = 
>> 10^{48}m^{-2}. 
>> If I divide by the speed of light squared this comes to 10^{32}s^{-2} 
>> and 
>> we get √(Λ)T = 10^{2}. This means any spatial region expanded by a 
>> factor 
>> of 10^{√(Λ)T} which is large. The natural log of this is 230 and 
>> this is not too far off from the more precise calculation of 60 e-folds. 
>> The 60 e-folds is a phenomenological fit that matches inflation with the 
>> observed universe.
>>
>> How much of the universe is unavailable depends upon whether k = -1, 
>> 0 or 1. The furthest out some quantum might emerge and have an influence 
>> is 
>> for a Planck scale quantum to now be inflated to the CMB scale. I know I 
>> have gone through this here before, but the result is the furthest we 
>> can 
>> detect anything is around 1800 billion light years, which would be a 
>> graviton or quantum black hole that leaves an imprint or signature on 
>> the 
>> CMB. It is not possible from theory to know what percentage this is of 
>> the 
>> entire shebang, and for k = -1 or 0 it is an infinitesimal part.
>>
>> LC
>>
>
> For k=0, a flat universe, we know the answer since, as you've 
> acknowledged, it's infinite in spatial extent.  Consequently, since the 
> observable universe is finite in spatial extent, the unobserved universe 
> must be infinite in extent (for a flat universe). Can you estimate the 
> size 
> of the unobservable universe for a positively curved universe? AG
>

 The cosmological constant is a Ricci curvature with Λ = R_{tt} for the 
 flat k = 0 case. for k = 1 there is a spatial Ricci curvature R_{rr}. This 
 contributes to the occurrence of the cosmological constant, but it is 
 tiny. So R_{rr} = δR_{tt} for δ a rather small number. The spatial sphere 
 has a radius R = 1/√(R_{rr}} ≈ 1/√(δΛ). This is then for Λ = 
 10^{-52}m^{-2} R ≈ δ^{-1/2} 10^{26}m, or about the distance to the 
 cosmological horizon multiplied by the reciprocal of a small number. 

 The problem is that we really do not what that small number is. For 
 various reasons I think it is δ < 5×10^{-5}This gives a radius where a 
 Planck frequency is redshifted to a CMB scale. If it is smaller then there 
 are regions of the universe completely inaccessible to us even as Planck 
 modes redshifted to the cosmic horizon scale.

 LC

>>>
>>> FWIW, another reason I think our universe has a positive curvature is 
>>> that if it were flat, with zero curvature, and we made many measurements, 
>>> we'd get a distribution of measured values above and below zero due to 
>>> unavoidable measurement errors. But I think we invariably get a small 
>>> positive number. Is this what we actually get; values always positive but 
>>> close to zero, but no negative values? TIA,AG 
>>>
>>
>> As yet attempt to find optical results due to spatial curvature have not 
>> found anything. The curvature of spacetime is mostly due to how space is 
>> embedded in spacetime.
>>
>> LC
>>
>
> But you haven't directly addressed my hypothesis regarding the 
> measurements. AG 
>

So far as I know there is no signal above the noise on this.

LC
 

>  
>>
>>>  

>
> On Sunday, March 22, 2020 at 11:55:19 PM UTC-5, Alan Grayson wrote:
>>>
>>> According to some cosmologists, Krauss?, the duration of inflation 
>>> is about 10^-35 seconds, which is presumably the duration necessary to 
>>> create isotropy and homogeneity in a universe of age 13.8 BY. If these 
>>> assumptions are correct, can we use them to compute the fraction of the 
>>> universe which is now UN-observable? TIA, AG
>>>
>>

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Re: Inflation and the total size of the universe

[Alan Grayson]

On Wednesday, March 25, 2020 at 2:58:45 AM UTC-6, Lawrence Crowell wrote:
>
> On Wednesday, March 25, 2020 at 1:28:21 AM UTC-5, Alan Grayson wrote:
>>
>>
>>
>> On Tuesday, March 24, 2020 at 6:21:50 PM UTC-6, Lawrence Crowell wrote:
>>>
>>> On Tuesday, March 24, 2020 at 6:19:41 PM UTC-5, Alan Grayson wrote:



 On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence Crowell wrote:
>
> Inflation was initiate 10^{-35}sec after the quantum fluctuation 
> appearance of the observable cosmos, and this had a duration of 
> 10^{-30}sec. The cosmological constant averaged around Λ = 10^{48}m^{-2}. 
> If I divide by the speed of light squared this comes to 10^{32}s^{-2} and 
> we get √(Λ)T = 10^{2}. This means any spatial region expanded by a factor 
> of 10^{√(Λ)T} which is large. The natural log of this is 230 and this 
> is not too far off from the more precise calculation of 60 e-folds. The 
> 60 
> e-folds is a phenomenological fit that matches inflation with the 
> observed 
> universe.
>
> How much of the universe is unavailable depends upon whether k = -1, 0 
> or 1. The furthest out some quantum might emerge and have an influence is 
> for a Planck scale quantum to now be inflated to the CMB scale. I know I 
> have gone through this here before, but the result is the furthest we can 
> detect anything is around 1800 billion light years, which would be a 
> graviton or quantum black hole that leaves an imprint or signature on the 
> CMB. It is not possible from theory to know what percentage this is of 
> the 
> entire shebang, and for k = -1 or 0 it is an infinitesimal part.
>
> LC
>

 For k=0, a flat universe, we know the answer since, as you've 
 acknowledged, it's infinite in spatial extent.  Consequently, since the 
 observable universe is finite in spatial extent, the unobserved universe 
 must be infinite in extent (for a flat universe). Can you estimate the 
 size 
 of the unobservable universe for a positively curved universe? AG

>>>
>>> The cosmological constant is a Ricci curvature with Λ = R_{tt} for the 
>>> flat k = 0 case. for k = 1 there is a spatial Ricci curvature R_{rr}. This 
>>> contributes to the occurrence of the cosmological constant, but it is 
>>> tiny. So R_{rr} = δR_{tt} for δ a rather small number. The spatial sphere 
>>> has a radius R = 1/√(R_{rr}} ≈ 1/√(δΛ). This is then for Λ = 
>>> 10^{-52}m^{-2} R ≈ δ^{-1/2} 10^{26}m, or about the distance to the 
>>> cosmological horizon multiplied by the reciprocal of a small number. 
>>>
>>> The problem is that we really do not what that small number is. For 
>>> various reasons I think it is δ < 5×10^{-5}This gives a radius where a 
>>> Planck frequency is redshifted to a CMB scale. If it is smaller then there 
>>> are regions of the universe completely inaccessible to us even as Planck 
>>> modes redshifted to the cosmic horizon scale.
>>>
>>> LC
>>>
>>
>> FWIW, another reason I think our universe has a positive curvature is 
>> that if it were flat, with zero curvature, and we made many measurements, 
>> we'd get a distribution of measured values above and below zero due to 
>> unavoidable measurement errors. But I think we invariably get a small 
>> positive number. Is this what we actually get; values always positive but 
>> close to zero, but no negative values? TIA,AG 
>>
>
> As yet attempt to find optical results due to spatial curvature have not 
> found anything. The curvature of spacetime is mostly due to how space is 
> embedded in spacetime.
>
> LC
>

But you haven't directly addressed my hypothesis regarding the 
measurements. AG 

>  
>
>>  
>>>

 On Sunday, March 22, 2020 at 11:55:19 PM UTC-5, Alan Grayson wrote:
>>
>> According to some cosmologists, Krauss?, the duration of inflation is 
>> about 10^-35 seconds, which is presumably the duration necessary to 
>> create 
>> isotropy and homogeneity in a universe of age 13.8 BY. If these 
>> assumptions 
>> are correct, can we use them to compute the fraction of the universe 
>> which 
>> is now UN-observable? TIA, AG
>>
>

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Re: Inflation and the total size of the universe

[Lawrence Crowell]

On Wednesday, March 25, 2020 at 1:28:21 AM UTC-5, Alan Grayson wrote:
>
>
>
> On Tuesday, March 24, 2020 at 6:21:50 PM UTC-6, Lawrence Crowell wrote:
>>
>> On Tuesday, March 24, 2020 at 6:19:41 PM UTC-5, Alan Grayson wrote:
>>>
>>>
>>>
>>> On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence Crowell wrote:

 Inflation was initiate 10^{-35}sec after the quantum fluctuation 
 appearance of the observable cosmos, and this had a duration of 
 10^{-30}sec. The cosmological constant averaged around Λ = 10^{48}m^{-2}. 
 If I divide by the speed of light squared this comes to 10^{32}s^{-2} and 
 we get √(Λ)T = 10^{2}. This means any spatial region expanded by a factor 
 of 10^{√(Λ)T} which is large. The natural log of this is 230 and this 
 is not too far off from the more precise calculation of 60 e-folds. The 60 
 e-folds is a phenomenological fit that matches inflation with the observed 
 universe.

 How much of the universe is unavailable depends upon whether k = -1, 0 
 or 1. The furthest out some quantum might emerge and have an influence is 
 for a Planck scale quantum to now be inflated to the CMB scale. I know I 
 have gone through this here before, but the result is the furthest we can 
 detect anything is around 1800 billion light years, which would be a 
 graviton or quantum black hole that leaves an imprint or signature on the 
 CMB. It is not possible from theory to know what percentage this is of the 
 entire shebang, and for k = -1 or 0 it is an infinitesimal part.

 LC

>>>
>>> For k=0, a flat universe, we know the answer since, as you've 
>>> acknowledged, it's infinite in spatial extent.  Consequently, since the 
>>> observable universe is finite in spatial extent, the unobserved universe 
>>> must be infinite in extent (for a flat universe). Can you estimate the size 
>>> of the unobservable universe for a positively curved universe? AG
>>>
>>
>> The cosmological constant is a Ricci curvature with Λ = R_{tt} for the 
>> flat k = 0 case. for k = 1 there is a spatial Ricci curvature R_{rr}. This 
>> contributes to the occurrence of the cosmological constant, but it is 
>> tiny. So R_{rr} = δR_{tt} for δ a rather small number. The spatial sphere 
>> has a radius R = 1/√(R_{rr}} ≈ 1/√(δΛ). This is then for Λ = 
>> 10^{-52}m^{-2} R ≈ δ^{-1/2} 10^{26}m, or about the distance to the 
>> cosmological horizon multiplied by the reciprocal of a small number. 
>>
>> The problem is that we really do not what that small number is. For 
>> various reasons I think it is δ < 5×10^{-5}This gives a radius where a 
>> Planck frequency is redshifted to a CMB scale. If it is smaller then there 
>> are regions of the universe completely inaccessible to us even as Planck 
>> modes redshifted to the cosmic horizon scale.
>>
>> LC
>>
>
> FWIW, another reason I think our universe has a positive curvature is that 
> if it were flat, with zero curvature, and we made many measurements, we'd 
> get a distribution of measured values above and below zero due to 
> unavoidable measurement errors. But I think we invariably get a small 
> positive number. Is this what we actually get; values always positive but 
> close to zero, but no negative values? TIA,AG 
>

As yet attempt to find optical results due to spatial curvature have not 
found anything. The curvature of spacetime is mostly due to how space is 
embedded in spacetime.

LC
 

>  
>>
>>>
>>> On Sunday, March 22, 2020 at 11:55:19 PM UTC-5, Alan Grayson wrote:
>
> According to some cosmologists, Krauss?, the duration of inflation is 
> about 10^-35 seconds, which is presumably the duration necessary to 
> create 
> isotropy and homogeneity in a universe of age 13.8 BY. If these 
> assumptions 
> are correct, can we use them to compute the fraction of the universe 
> which 
> is now UN-observable? TIA, AG
>


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Re: Inflation and the total size of the universe

[Alan Grayson]

On Tuesday, March 24, 2020 at 6:21:50 PM UTC-6, Lawrence Crowell wrote:
>
> On Tuesday, March 24, 2020 at 6:19:41 PM UTC-5, Alan Grayson wrote:
>>
>>
>>
>> On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence Crowell wrote:
>>>
>>> Inflation was initiate 10^{-35}sec after the quantum fluctuation 
>>> appearance of the observable cosmos, and this had a duration of 
>>> 10^{-30}sec. The cosmological constant averaged around Λ = 10^{48}m^{-2}. 
>>> If I divide by the speed of light squared this comes to 10^{32}s^{-2} and 
>>> we get √(Λ)T = 10^{2}. This means any spatial region expanded by a factor 
>>> of 10^{√(Λ)T} which is large. The natural log of this is 230 and this 
>>> is not too far off from the more precise calculation of 60 e-folds. The 60 
>>> e-folds is a phenomenological fit that matches inflation with the observed 
>>> universe.
>>>
>>> How much of the universe is unavailable depends upon whether k = -1, 0 
>>> or 1. The furthest out some quantum might emerge and have an influence is 
>>> for a Planck scale quantum to now be inflated to the CMB scale. I know I 
>>> have gone through this here before, but the result is the furthest we can 
>>> detect anything is around 1800 billion light years, which would be a 
>>> graviton or quantum black hole that leaves an imprint or signature on the 
>>> CMB. It is not possible from theory to know what percentage this is of the 
>>> entire shebang, and for k = -1 or 0 it is an infinitesimal part.
>>>
>>> LC
>>>
>>
>> For k=0, a flat universe, we know the answer since, as you've 
>> acknowledged, it's infinite in spatial extent.  Consequently, since the 
>> observable universe is finite in spatial extent, the unobserved universe 
>> must be infinite in extent (for a flat universe). Can you estimate the size 
>> of the unobservable universe for a positively curved universe? AG
>>
>
> The cosmological constant is a Ricci curvature with Λ = R_{tt} for the 
> flat k = 0 case. for k = 1 there is a spatial Ricci curvature R_{rr}. This 
> contributes to the occurrence of the cosmological constant, but it is 
> tiny. So R_{rr} = δR_{tt} for δ a rather small number. The spatial sphere 
> has a radius R = 1/√(R_{rr}} ≈ 1/√(δΛ). This is then for Λ = 
> 10^{-52}m^{-2} R ≈ δ^{-1/2} 10^{26}m, or about the distance to the 
> cosmological horizon multiplied by the reciprocal of a small number. 
>
> The problem is that we really do not what that small number is. For 
> various reasons I think it is δ < 5×10^{-5}This gives a radius where a 
> Planck frequency is redshifted to a CMB scale. If it is smaller then there 
> are regions of the universe completely inaccessible to us even as Planck 
> modes redshifted to the cosmic horizon scale.
>
> LC
>

FWIW, another reason I think our universe has a positive curvature is that 
if it were flat, with zero curvature, and we made many measurements, we'd 
get a distribution of measured values above and below zero due to 
unavoidable measurement errors. But I think we invariably get a small 
positive number. Is this what we actually get; values always positive but 
close to zero, but no negative values? TIA,AG 

>  
>
>>
>> On Sunday, March 22, 2020 at 11:55:19 PM UTC-5, Alan Grayson wrote:

 According to some cosmologists, Krauss?, the duration of inflation is 
 about 10^-35 seconds, which is presumably the duration necessary to create 
 isotropy and homogeneity in a universe of age 13.8 BY. If these 
 assumptions 
 are correct, can we use them to compute the fraction of the universe which 
 is now UN-observable? TIA, AG

>>>

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Re: Inflation and the total size of the universe

[Lawrence Crowell]

On Tuesday, March 24, 2020 at 6:19:41 PM UTC-5, Alan Grayson wrote:
>
>
>
> On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence Crowell wrote:
>>
>> Inflation was initiate 10^{-35}sec after the quantum fluctuation 
>> appearance of the observable cosmos, and this had a duration of 
>> 10^{-30}sec. The cosmological constant averaged around Λ = 10^{48}m^{-2}. 
>> If I divide by the speed of light squared this comes to 10^{32}s^{-2} and 
>> we get √(Λ)T = 10^{2}. This means any spatial region expanded by a factor 
>> of 10^{√(Λ)T} which is large. The natural log of this is 230 and this is 
>> not too far off from the more precise calculation of 60 e-folds. The 60 
>> e-folds is a phenomenological fit that matches inflation with the observed 
>> universe.
>>
>> How much of the universe is unavailable depends upon whether k = -1, 0 or 
>> 1. The furthest out some quantum might emerge and have an influence is for 
>> a Planck scale quantum to now be inflated to the CMB scale. I know I have 
>> gone through this here before, but the result is the furthest we can detect 
>> anything is around 1800 billion light years, which would be a graviton or 
>> quantum black hole that leaves an imprint or signature on the CMB. It is 
>> not possible from theory to know what percentage this is of the entire 
>> shebang, and for k = -1 or 0 it is an infinitesimal part.
>>
>> LC
>>
>
> For k=0, a flat universe, we know the answer since, as you've 
> acknowledged, it's infinite in spatial extent.  Consequently, since the 
> observable universe is finite in spatial extent, the unobserved universe 
> must be infinite in extent (for a flat universe). Can you estimate the size 
> of the unobservable universe for a positively curved universe? AG
>

The cosmological constant is a Ricci curvature with Λ = R_{tt} for the flat 
k = 0 case. for k = 1 there is a spatial Ricci curvature R_{rr}. This 
contributes to the occurrence of the cosmological constant, but it is tiny. 
So R_{rr} = δR_{tt} for δ a rather small number. The spatial sphere has a 
radius R = 1/√(R_{rr}} ≈ 1/√(δΛ). This is then for Λ = 10^{-52}m^{-2} R ≈ 
δ^{-1/2} 
10^{26}m, or about the distance to the cosmological horizon multiplied by 
the reciprocal of a small number. 

The problem is that we really do not what that small number is. For various 
reasons I think it is δ < 5×10^{-5}This gives a radius where a Planck 
frequency is redshifted to a CMB scale. If it is smaller then there are 
regions of the universe completely inaccessible to us even as Planck modes 
redshifted to the cosmic horizon scale.

LC
 

>
> On Sunday, March 22, 2020 at 11:55:19 PM UTC-5, Alan Grayson wrote:
>>>
>>> According to some cosmologists, Krauss?, the duration of inflation is 
>>> about 10^-35 seconds, which is presumably the duration necessary to create 
>>> isotropy and homogeneity in a universe of age 13.8 BY. If these assumptions 
>>> are correct, can we use them to compute the fraction of the universe which 
>>> is now UN-observable? TIA, AG
>>>
>>

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Re: Inflation and the total size of the universe

[Alan Grayson]

On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence Crowell wrote:
>
> Inflation was initiate 10^{-35}sec after the quantum fluctuation 
> appearance of the observable cosmos, and this had a duration of 
> 10^{-30}sec. The cosmological constant averaged around Λ = 10^{48}m^{-2}. 
> If I divide by the speed of light squared this comes to 10^{32}s^{-2} and 
> we get √(Λ)T = 10^{2}. This means any spatial region expanded by a factor 
> of 10^{√(Λ)T} which is large. The natural log of this is 230 and this is 
> not too far off from the more precise calculation of 60 e-folds. The 60 
> e-folds is a phenomenological fit that matches inflation with the observed 
> universe.
>
> How much of the universe is unavailable depends upon whether k = -1, 0 or 
> 1. The furthest out some quantum might emerge and have an influence is for 
> a Planck scale quantum to now be inflated to the CMB scale. I know I have 
> gone through this here before, but the result is the furthest we can detect 
> anything is around 1800 billion light years, which would be a graviton or 
> quantum black hole that leaves an imprint or signature on the CMB. It is 
> not possible from theory to know what percentage this is of the entire 
> shebang, and for k = -1 or 0 it is an infinitesimal part.
>
> LC
>

For k=0, a flat universe, we know the answer since, as you've acknowledged, 
it's infinite in spatial extent.  Consequently, since the observable 
universe is finite in spatial extent, the unobserved universe must be 
infinite in extent (for a flat universe). Can you estimate the size of the 
unobservable universe for a positively curved universe? AG

On Sunday, March 22, 2020 at 11:55:19 PM UTC-5, Alan Grayson wrote:
>>
>> According to some cosmologists, Krauss?, the duration of inflation is 
>> about 10^-35 seconds, which is presumably the duration necessary to create 
>> isotropy and homogeneity in a universe of age 13.8 BY. If these assumptions 
>> are correct, can we use them to compute the fraction of the universe which 
>> is now UN-observable? TIA, AG
>>
>

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Re: Inflation and the total size of the universe

[John Clark]

On Mon, Mar 23, 2020 at 10:54 AM Alan Grayson 
wrote:


> *> Krauss, for example, says the universe was "a billionth of a billionth
> the size of a proton" before inflation began.*


Krauss was talking about the size of the observable universe, the size of
the un-observable universe before inflation was certainly larger than that,
but how much larger is unknown, it might have been infinite. Or it might
not.

John K Clark





>
> On Monday, March 23, 2020 at 8:16:15 AM UTC-6, John Clark wrote:
>>
>> On Mon, Mar 23, 2020 at 12:55 AM Alan Grayson 
>> wrote:
>>
>> *> According to some cosmologists, Krauss?, the duration of inflation is
>>> about 10^-35 seconds, which is presumably the duration necessary to create
>>> isotropy and homogeneity in a universe of age 13.8 BY. If these assumptions
>>> are correct, can we use them to compute the fraction of the universe which
>>> is now UN-observable? TIA, AG*
>>>
>>
>> I don't see how. For all we know the UN-observable part might be
>> infinite, or it might not be.
>>
>>  John K Clark
>>
>
> Krauss, for example, says the universe was "a billionth of a billionth the
> size of a proton" before inflation began. So, assuming it was always
> expanding at a constant rate, albeit possibly changing in time, for a
> finite time of 13.8 BY, the total size could never have been infinite in
> spatial extent. AG
>
> --
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> 
> .
>

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Re: Inflation and the total size of the universe

[Lawrence Crowell]

Inflation was initiate 10^{-35}sec after the quantum fluctuation appearance 
of the observable cosmos, and this had a duration of 10^{-30}sec. The 
cosmological constant averaged around Λ = 10^{48}m^{-2}. If I divide by the 
speed of light squared this comes to 10^{32}s^{-2} and we get √(Λ)T = 
10^{2}. This means any spatial region expanded by a factor of 10^{√(Λ)T} 
which is large. The natural log of this is 230 and this is not too far off 
from the more precise calculation of 60 e-folds. The 60 e-folds is a 
phenomenological fit that matches inflation with the observed universe.

How much of the universe is unavailable depends upon whether k = -1, 0 or 
1. The furthest out some quantum might emerge and have an influence is for 
a Planck scale quantum to now be inflated to the CMB scale. I know I have 
gone through this here before, but the result is the furthest we can detect 
anything is around 1800 billion light years, which would be a graviton or 
quantum black hole that leaves an imprint or signature on the CMB. It is 
not possible from theory to know what percentage this is of the entire 
shebang, and for k = -1 or 0 it is an infinitesimal part.

LC

On Sunday, March 22, 2020 at 11:55:19 PM UTC-5, Alan Grayson wrote:
>
> According to some cosmologists, Krauss?, the duration of inflation is 
> about 10^-35 seconds, which is presumably the duration necessary to create 
> isotropy and homogeneity in a universe of age 13.8 BY. If these assumptions 
> are correct, can we use them to compute the fraction of the universe which 
> is now UN-observable? TIA, AG
>

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Re: Inflation and the total size of the universe

[Alan Grayson]

On Monday, March 23, 2020 at 8:16:15 AM UTC-6, John Clark wrote:
>
> On Mon, Mar 23, 2020 at 12:55 AM Alan Grayson  > wrote:
>
> *> According to some cosmologists, Krauss?, the duration of inflation is 
>> about 10^-35 seconds, which is presumably the duration necessary to create 
>> isotropy and homogeneity in a universe of age 13.8 BY. If these assumptions 
>> are correct, can we use them to compute the fraction of the universe which 
>> is now UN-observable? TIA, AG*
>>
>
> I don't see how. For all we know the UN-observable part might be 
> infinite, or it might not be.
>
>  John K Clark
>

Krauss, for example, says the universe was "a billionth of a billionth the 
size of a proton" before inflation began. So, assuming it was always 
expanding at a constant rate, albeit possibly changing in time, for a 
finite time of 13.8 BY, the total size could never have been infinite in 
spatial extent. AG 

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Re: Inflation and the total size of the universe

[John Clark]

On Mon, Mar 23, 2020 at 12:55 AM Alan Grayson 
wrote:

*> According to some cosmologists, Krauss?, the duration of inflation is
> about 10^-35 seconds, which is presumably the duration necessary to create
> isotropy and homogeneity in a universe of age 13.8 BY. If these assumptions
> are correct, can we use them to compute the fraction of the universe which
> is now UN-observable? TIA, AG*
>

I don't see how. For all we know the UN-observable part might be infinite,
or it might not be.

 John K Clark

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