Re: flat vs asymptotically flat universe

[agrayson2000]

On Sunday, November 12, 2017 at 1:42:13 PM UTC-7, agrays...@gmail.com wrote:
>
>
>
> On Thursday, November 9, 2017 at 4:42:45 PM UTC-7, Brent wrote:
>>
>> Cosmologist think the universe is spatially flat.  That just means 
>> triangles have interior angles summing to 180deg.  It doesn't have anything 
>> to do with extent.  But the universe is not flat in spacetime; it's 
>> expanding and at an increasing rate.
>>
>> Brent
>>
>
> I don't understand how a flat universe has nothing to do with extent.
>
> I don't understand the distinction; spatially flat (and therefore 
> presumably infinite in extent?), but not flat in spacetime. 
>
> Also, when it was discovered that the expansion is accelerating, did the 
> solutions of the field equations which allowed tunneling from a vacuum and 
> presumably automatically came with a positive CC (indicating expansion), 
> also automatically come with a spatially flat (and presumably infinite in 
> extent) geometry? Hard to grasp how a universe emerging from a vacuum could 
> start out spatially flat and therefore IMO infinite in extent.  
>
> TIA.
>

I must have committed some unforgivable crime. I am just not sure what, 
exactly, it was. I wrote to Ned Wright and Lawrence Krauss, asking how a 
universe of finite age could be infinite in spatial extent. Including you, 
Brent, I am 0 for 3. I suppose the answer could be that it tunneled out of 
the Multiverse, and was infinite in spatial extent at that initial time. 
Hard to imagine such an event. 

>
>> On 11/9/2017 3:10 PM, agrays...@gmail.com wrote:
>>
>> IIUC, the difference is huge. In the former case, the universe is open, 
>> spatially infinite with infinite mass (assuming a nonzero mass distribution 
>> on large scale everywhere), whereas the latter is closed, finite in spatial 
>> extent and mass. But I notice that most cosmologists claim the universe is 
>> *flat*, as in mathematically flat. Are they just speaking loosely and 
>> really mean the universe is ASYMPTOTICALLY flat? I find it contradictory 
>> for a universe which is finite in age, to be truly mathematically FLAT. TIA.
>> -- 
>> 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-li...@googlegroups.com.
>> To post to this group, send email to everyth...@googlegroups.com.
>> Visit this group at https://groups.google.com/group/everything-list.
>> For more options, visit https://groups.google.com/d/optout.
>>
>>
>>

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Re: flat vs asymptotically flat universe

[agrayson2000]

On Thursday, November 9, 2017 at 4:42:45 PM UTC-7, Brent wrote:
>
> Cosmologist think the universe is spatially flat.  That just means 
> triangles have interior angles summing to 180deg.  It doesn't have anything 
> to do with extent.  But the universe is not flat in spacetime; it's 
> expanding and at an increasing rate.
>
> Brent
>

I don't understand how a flat universe has nothing to do with extent.

I don't understand the distinction; spatially flat (and therefore 
presumably infinite in extent?), but not flat in spacetime. 

Also, when it was discovered that the expansion is accelerating, did the 
solutions of the field equations which allowed tunneling from a vacuum and 
presumably automatically came with a positive CC (indicating expansion), 
also automatically come with a spatially flat (and presumably infinite in 
extent) geometry? Hard to grasp how a universe emerging from a vacuum could 
start out spatially flat and therefore IMO infinite in extent.  

TIA.

>
> On 11/9/2017 3:10 PM, agrays...@gmail.com  wrote:
>
> IIUC, the difference is huge. In the former case, the universe is open, 
> spatially infinite with infinite mass (assuming a nonzero mass distribution 
> on large scale everywhere), whereas the latter is closed, finite in spatial 
> extent and mass. But I notice that most cosmologists claim the universe is 
> *flat*, as in mathematically flat. Are they just speaking loosely and 
> really mean the universe is ASYMPTOTICALLY flat? I find it contradictory 
> for a universe which is finite in age, to be truly mathematically FLAT. TIA.
> -- 
> 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-li...@googlegroups.com .
> To post to this group, send email to everyth...@googlegroups.com 
> .
> Visit this group at https://groups.google.com/group/everything-list.
> For more options, visit https://groups.google.com/d/optout.
>
>
>

-- 
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To unsubscribe from this group and stop receiving emails from it, send an email 
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Re: flat vs asymptotically flat universe

[Bruno Marchal]

On 11 Nov 2017, at 21:50, agrayson2...@gmail.com wrote:




On Saturday, November 11, 2017 at 12:40:45 PM UTC-7, Bruno Marchal  
wrote:


On 11 Nov 2017, at 07:59, agrays...@gmail.com wrote:




On Friday, November 10, 2017 at 11:32:13 PM UTC-7,  
agrays...@gmail.com wrote:



On Friday, November 10, 2017 at 11:22:45 PM UTC-7, Brent wrote:


On 11/10/2017 10:01 PM, agrays...@gmail.com wrote:



On Friday, November 10, 2017 at 2:16:04 PM UTC-7, Brent wrote:


On 11/10/2017 1:01 PM, agrays...@gmail.com wrote:



On Friday, November 10, 2017 at 12:19:05 PM UTC-7, Brent wrote:


On 11/10/2017 4:06 AM, Alan Grayson wrote:



On Thu, Nov 9, 2017 at 10:32 PM, Brent Meeker  
 wrote:



On 11/9/2017 9:15 PM, Alan Grayson wrote:



On Thu, Nov 9, 2017 at 10:05 PM, Brent Meeker  
 wrote:



On 11/9/2017 8:55 PM, agrays...@gmail.com wrote:



On Thursday, November 9, 2017 at 8:00:45 PM UTC-7, Brent wrote:


On 11/9/2017 6:23 PM, Alan Grayson wrote:
The difference between spatially flat and asymptotically flat  
for a huge universe would be virtually impossible to  
distinguish by measuring the sum of angles in a triangle.  
Moreover, I don't see how spatially flat can have nothing to  
do with extent, since in applying Euclidean geometry we  
surely seem to be dealing with an infinitely extended plane.  
TIA.


Not necessarily.  You could have periodic boundary  
conditions.  But most cosmologists do assume the universe is  
infinite in spatial extent.  Of course the flatness isn't  
measured by triangulation.  It's measured by comparing the  
spatial spectrum of the CMB variations to model predictions  
with different mass densities.

https://arxiv.org/pdf/astro-ph/0004404

Brent

However flatness is measured, the criterion still seems  
Euclidean and hence infinite in extent if one believes the  
triangle measured has combined angles of 180 degrees. And I  
don't see how this is distinguishable from asymptotically flat  
for a huge but finite universe.


It's not.

That's my point. No way of distinguishing flat from  
asymptotically flat for a huge universe, so the assumption of  
infinite spatial extent by cosmologists seems unwarranted. But  
as you note below, the universe could have begun with infinite  
spatial extent. But ours didn't AFAIK. It began as  
astronomically tiny and expanded via inflation.


But you don't know that.  According to Einstein's equations the  
visible part of the universe started at zero size.  Of course no  
one takes that entirely seriously since at very small distances  
quantum mechanics must invalidate Einstein's equations.


Brent

If you're invoking QM, aren't you conceding it started out very  
small, if not exactly zero size? So it seems more plausible to  
assume it started out very small, surely not infinite. But  
according to your previous statements and those that I have read  
by cosmologists, the assumption of infinite spatial extent is  
generally accepted and IMO unwarranted.


If it's flat or has negative curvature then the equations imply  
it's infinite or perhaps periodic (no matter what the scale  
factor is).  If the curvature is positive then it's finite and  
closed and the scale factor can be taken to be the radius, so it  
indeed starts small in the absolute sense.  Atkatz and Pagels  
showed that only FRW universes that are closed (positive  
curvature) or De Sitter (flat with a positive cosmological  
constant) can "tunnel out of nothing".


http://www.quantum-gravitation.de/media/99f63994b9064eb68004fff2.pdf

So most cosmologists liked the closed universe model, until it  
was found that expansion is accelerating.  So now more of them  
look to some modification of the De Sitter space universe.


Brent

Modification of De Sitter will be flat and therefore open. I find  
the open universe model in contradiction to the finite age of the  
universe. Is this unreasonable?


Well, if you have an infinite universe, and toward the past it is  
scaled by a factor a, and a->0 does the universes size go to zero?


Why is the closed universe model less favored when it was  
discovered that expansion is accelerating?


Because the De Sitter universe that can "tunnel from the vacuum"  
automatically has a positive cosmological constant.


Brent

Unfortunately, my understanding of the scale factor and  
cosmological constant as they relate to the various geometries is  
insufficient to appreciate your comments. Maybe you could restate  
your above comments with that in mind. TIA.


Didn't you read Vic's "Comprehensible Cosmos"?  Why are you over  
here on the everythinglist asking physics questions anyway, Alan?   
You should try the stackechange or quora.


Brent

I wasn't aware of those sites.  Since "everything" includes  
physics, I thought this group would be appropriate. And I see some  
topics here include physics. I don't see the harm.



Sometimes we discuss physics, but in general it is in or through  

Re: flat vs asymptotically flat universe

[agrayson2000]

On Saturday, November 11, 2017 at 12:40:45 PM UTC-7, Bruno Marchal wrote:
>
>
> On 11 Nov 2017, at 07:59, agrays...@gmail.com  wrote:
>
>
>
> On Friday, November 10, 2017 at 11:32:13 PM UTC-7, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Friday, November 10, 2017 at 11:22:45 PM UTC-7, Brent wrote:
>>>
>>>
>>>
>>> On 11/10/2017 10:01 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Friday, November 10, 2017 at 2:16:04 PM UTC-7, Brent wrote: 



 On 11/10/2017 1:01 PM, agrays...@gmail.com wrote:



 On Friday, November 10, 2017 at 12:19:05 PM UTC-7, Brent wrote: 
>
>
>
> On 11/10/2017 4:06 AM, Alan Grayson wrote:
>
>
>
> On Thu, Nov 9, 2017 at 10:32 PM, Brent Meeker  
> wrote:
>
>>
>>
>> On 11/9/2017 9:15 PM, Alan Grayson wrote:
>>
>>
>>
>> On Thu, Nov 9, 2017 at 10:05 PM, Brent Meeker  
>> wrote:
>>
>>>
>>>
>>> On 11/9/2017 8:55 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, November 9, 2017 at 8:00:45 PM UTC-7, Brent wrote: 



 On 11/9/2017 6:23 PM, Alan Grayson wrote:

 The difference between spatially flat and asymptotically flat for a 
 huge universe would be virtually impossible to distinguish by 
 measuring the 
 sum of angles in a triangle. Moreover, I don't see how spatially flat 
 can 
 have nothing to do with extent, since in applying Euclidean geometry 
 we 
 surely seem to be dealing with an infinitely extended plane. TIA.


 Not necessarily.  You could have periodic boundary conditions.  But 
 most cosmologists do assume the universe is infinite in spatial 
 extent.  Of 
 course the flatness isn't measured by triangulation.  It's measured by 
 comparing the spatial spectrum of the CMB variations to model 
 predictions 
 with different mass densities.   
 https://arxiv.org/pdf/astro-ph/0004404

 Brent

>>>
>>> However flatness is measured, the criterion still seems Euclidean 
>>> and hence infinite in extent if one believes the triangle measured has 
>>> combined angles of 180 degrees. And I don't see how this is 
>>> distinguishable 
>>> from asymptotically flat for a huge but finite universe. 
>>>
>>>
>>> It's not.
>>>
>>
>> That's my point. No way of distinguishing flat from asymptotically 
>> flat for a huge universe, so the assumption of infinite spatial extent 
>> by 
>> cosmologists seems unwarranted. But as you note below, the universe 
>> could 
>> have begun with infinite spatial extent. But ours didn't AFAIK. It began 
>> as 
>> astronomically tiny and expanded via inflation.
>>
>>
>> But you don't know that.  According to Einstein's equations the 
>> visible part of the universe started at *zero* size.  Of course no 
>> one takes that entirely seriously since at very small distances quantum 
>> mechanics must invalidate Einstein's equations.
>>
>> Brent
>>
>
> If you're invoking QM, aren't you conceding it started out very small, 
> if not exactly zero size? So it seems more plausible to assume it started 
> out very small, surely not infinite. But according to your previous 
> statements and those that I have read by cosmologists, the assumption of 
> infinite spatial extent is generally accepted and IMO unwarranted. 
>
>
> If it's flat or has negative curvature then the equations imply it's 
> infinite or perhaps periodic (no matter what the scale factor is).  If 
> the 
> curvature is positive then it's finite and closed and the scale factor 
> can 
> be taken to be the radius, so it indeed starts small in the absolute 
> sense.  Atkatz and Pagels showed that only FRW universes that are closed 
> (positive curvature) or De Sitter (flat with a positive cosmological 
> constant) can "tunnel out of nothing".  
>
>
> http://www.quantum-gravitation.de/media/99f63994b9064eb68004fff2.pdf
>
> So most cosmologists liked the closed universe model, until it was 
> found that expansion is accelerating.  So now more of them look to some 
> modification of the De Sitter space universe.  
>
> Brent
>

 Modification of De Sitter will be flat and therefore open. I find the 
 open universe model in contradiction to the finite age of the universe. Is 
 this unreasonable? 


 Well, if you have an infinite universe, and toward the past it is 
 scaled by a factor a, and a->0 does the universes size go to zero?

 Why is the closed universe model less favored when it was discovered 
 that expansion is accelerating? 


 Because 

Re: flat vs asymptotically flat universe

[Bruno Marchal]

On 11 Nov 2017, at 07:59, agrayson2...@gmail.com wrote:




On Friday, November 10, 2017 at 11:32:13 PM UTC-7,  
agrays...@gmail.com wrote:



On Friday, November 10, 2017 at 11:22:45 PM UTC-7, Brent wrote:


On 11/10/2017 10:01 PM, agrays...@gmail.com wrote:



On Friday, November 10, 2017 at 2:16:04 PM UTC-7, Brent wrote:


On 11/10/2017 1:01 PM, agrays...@gmail.com wrote:



On Friday, November 10, 2017 at 12:19:05 PM UTC-7, Brent wrote:


On 11/10/2017 4:06 AM, Alan Grayson wrote:



On Thu, Nov 9, 2017 at 10:32 PM, Brent Meeker  
 wrote:



On 11/9/2017 9:15 PM, Alan Grayson wrote:



On Thu, Nov 9, 2017 at 10:05 PM, Brent Meeker  
 wrote:



On 11/9/2017 8:55 PM, agrays...@gmail.com wrote:



On Thursday, November 9, 2017 at 8:00:45 PM UTC-7, Brent wrote:


On 11/9/2017 6:23 PM, Alan Grayson wrote:
The difference between spatially flat and asymptotically flat  
for a huge universe would be virtually impossible to  
distinguish by measuring the sum of angles in a triangle.  
Moreover, I don't see how spatially flat can have nothing to  
do with extent, since in applying Euclidean geometry we surely  
seem to be dealing with an infinitely extended plane. TIA.


Not necessarily.  You could have periodic boundary conditions.   
But most cosmologists do assume the universe is infinite in  
spatial extent.  Of course the flatness isn't measured by  
triangulation.  It's measured by comparing the spatial spectrum  
of the CMB variations to model predictions with different mass  
densities.

https://arxiv.org/pdf/astro-ph/0004404

Brent

However flatness is measured, the criterion still seems  
Euclidean and hence infinite in extent if one believes the  
triangle measured has combined angles of 180 degrees. And I  
don't see how this is distinguishable from asymptotically flat  
for a huge but finite universe.


It's not.

That's my point. No way of distinguishing flat from  
asymptotically flat for a huge universe, so the assumption of  
infinite spatial extent by cosmologists seems unwarranted. But  
as you note below, the universe could have begun with infinite  
spatial extent. But ours didn't AFAIK. It began as  
astronomically tiny and expanded via inflation.


But you don't know that.  According to Einstein's equations the  
visible part of the universe started at zero size.  Of course no  
one takes that entirely seriously since at very small distances  
quantum mechanics must invalidate Einstein's equations.


Brent

If you're invoking QM, aren't you conceding it started out very  
small, if not exactly zero size? So it seems more plausible to  
assume it started out very small, surely not infinite. But  
according to your previous statements and those that I have read  
by cosmologists, the assumption of infinite spatial extent is  
generally accepted and IMO unwarranted.


If it's flat or has negative curvature then the equations imply  
it's infinite or perhaps periodic (no matter what the scale factor  
is).  If the curvature is positive then it's finite and closed and  
the scale factor can be taken to be the radius, so it indeed  
starts small in the absolute sense.  Atkatz and Pagels showed that  
only FRW universes that are closed (positive curvature) or De  
Sitter (flat with a positive cosmological constant) can "tunnel  
out of nothing".


http://www.quantum-gravitation.de/media/99f63994b9064eb68004fff2.pdf

So most cosmologists liked the closed universe model, until it was  
found that expansion is accelerating.  So now more of them look to  
some modification of the De Sitter space universe.


Brent

Modification of De Sitter will be flat and therefore open. I find  
the open universe model in contradiction to the finite age of the  
universe. Is this unreasonable?


Well, if you have an infinite universe, and toward the past it is  
scaled by a factor a, and a->0 does the universes size go to zero?


Why is the closed universe model less favored when it was  
discovered that expansion is accelerating?


Because the De Sitter universe that can "tunnel from the vacuum"  
automatically has a positive cosmological constant.


Brent

Unfortunately, my understanding of the scale factor and  
cosmological constant as they relate to the various geometries is  
insufficient to appreciate your comments. Maybe you could restate  
your above comments with that in mind. TIA.


Didn't you read Vic's "Comprehensible Cosmos"?  Why are you over  
here on the everythinglist asking physics questions anyway, Alan?   
You should try the stackechange or quora.


Brent

I wasn't aware of those sites.  Since "everything" includes physics,  
I thought this group would be appropriate. And I see some topics  
here include physics. I don't see the harm.



Sometimes we discuss physics, but in general it is in or through  
relations with fundamental problems, including the mind-body problem,  
notably.


You might look at the Space-Times Series (it exists on 

Re: flat vs asymptotically flat universe

[agrayson2000]

On Friday, November 10, 2017 at 11:59:15 PM UTC-7, agrays...@gmail.com 
wrote:
>
>
>
> On Friday, November 10, 2017 at 11:32:13 PM UTC-7, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Friday, November 10, 2017 at 11:22:45 PM UTC-7, Brent wrote:
>>>
>>>
>>>
>>> On 11/10/2017 10:01 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Friday, November 10, 2017 at 2:16:04 PM UTC-7, Brent wrote: 



 On 11/10/2017 1:01 PM, agrays...@gmail.com wrote:



 On Friday, November 10, 2017 at 12:19:05 PM UTC-7, Brent wrote: 
>
>
>
> On 11/10/2017 4:06 AM, Alan Grayson wrote:
>
>
>
> On Thu, Nov 9, 2017 at 10:32 PM, Brent Meeker  
> wrote:
>
>>
>>
>> On 11/9/2017 9:15 PM, Alan Grayson wrote:
>>
>>
>>
>> On Thu, Nov 9, 2017 at 10:05 PM, Brent Meeker  
>> wrote:
>>
>>>
>>>
>>> On 11/9/2017 8:55 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, November 9, 2017 at 8:00:45 PM UTC-7, Brent wrote: 



 On 11/9/2017 6:23 PM, Alan Grayson wrote:

 The difference between spatially flat and asymptotically flat for a 
 huge universe would be virtually impossible to distinguish by 
 measuring the 
 sum of angles in a triangle. Moreover, I don't see how spatially flat 
 can 
 have nothing to do with extent, since in applying Euclidean geometry 
 we 
 surely seem to be dealing with an infinitely extended plane. TIA.


 Not necessarily.  You could have periodic boundary conditions.  But 
 most cosmologists do assume the universe is infinite in spatial 
 extent.  Of 
 course the flatness isn't measured by triangulation.  It's measured by 
 comparing the spatial spectrum of the CMB variations to model 
 predictions 
 with different mass densities.   
 https://arxiv.org/pdf/astro-ph/0004404

 Brent

>>>
>>> However flatness is measured, the criterion still seems Euclidean 
>>> and hence infinite in extent if one believes the triangle measured has 
>>> combined angles of 180 degrees. And I don't see how this is 
>>> distinguishable 
>>> from asymptotically flat for a huge but finite universe. 
>>>
>>>
>>> It's not.
>>>
>>
>> That's my point. No way of distinguishing flat from asymptotically 
>> flat for a huge universe, so the assumption of infinite spatial extent 
>> by 
>> cosmologists seems unwarranted. But as you note below, the universe 
>> could 
>> have begun with infinite spatial extent. But ours didn't AFAIK. It began 
>> as 
>> astronomically tiny and expanded via inflation.
>>
>>
>> But you don't know that.  According to Einstein's equations the 
>> visible part of the universe started at *zero* size.  Of course no 
>> one takes that entirely seriously since at very small distances quantum 
>> mechanics must invalidate Einstein's equations.
>>
>> Brent
>>
>
> If you're invoking QM, aren't you conceding it started out very small, 
> if not exactly zero size? So it seems more plausible to assume it started 
> out very small, surely not infinite. But according to your previous 
> statements and those that I have read by cosmologists, the assumption of 
> infinite spatial extent is generally accepted and IMO unwarranted. 
>
>
> If it's flat or has negative curvature then the equations imply it's 
> infinite or perhaps periodic (no matter what the scale factor is).  If 
> the 
> curvature is positive then it's finite and closed and the scale factor 
> can 
> be taken to be the radius, so it indeed starts small in the absolute 
> sense.  Atkatz and Pagels showed that only FRW universes that are closed 
> (positive curvature) or De Sitter (flat with a positive cosmological 
> constant) can "tunnel out of nothing".  
>
>
> http://www.quantum-gravitation.de/media/99f63994b9064eb68004fff2.pdf
>
> So most cosmologists liked the closed universe model, until it was 
> found that expansion is accelerating.  So now more of them look to some 
> modification of the De Sitter space universe.  
>
> Brent
>

 Modification of De Sitter will be flat and therefore open. I find the 
 open universe model in contradiction to the finite age of the universe. Is 
 this unreasonable? 


 Well, if you have an infinite universe, and toward the past it is 
 scaled by a factor a, and a->0 does the universes size go to zero?

 Why is the closed universe model less favored when it was discovered 
 that expansion is accelerating? 


 Because the De Sitter universe that can "tunnel from the vacuum" 

Re: flat vs asymptotically flat universe

[agrayson2000]

On Friday, November 10, 2017 at 11:32:13 PM UTC-7, agrays...@gmail.com 
wrote:
>
>
>
> On Friday, November 10, 2017 at 11:22:45 PM UTC-7, Brent wrote:
>>
>>
>>
>> On 11/10/2017 10:01 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Friday, November 10, 2017 at 2:16:04 PM UTC-7, Brent wrote: 
>>>
>>>
>>>
>>> On 11/10/2017 1:01 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Friday, November 10, 2017 at 12:19:05 PM UTC-7, Brent wrote: 



 On 11/10/2017 4:06 AM, Alan Grayson wrote:



 On Thu, Nov 9, 2017 at 10:32 PM, Brent Meeker  
 wrote:

>
>
> On 11/9/2017 9:15 PM, Alan Grayson wrote:
>
>
>
> On Thu, Nov 9, 2017 at 10:05 PM, Brent Meeker  
> wrote:
>
>>
>>
>> On 11/9/2017 8:55 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, November 9, 2017 at 8:00:45 PM UTC-7, Brent wrote: 
>>>
>>>
>>>
>>> On 11/9/2017 6:23 PM, Alan Grayson wrote:
>>>
>>> The difference between spatially flat and asymptotically flat for a 
>>> huge universe would be virtually impossible to distinguish by measuring 
>>> the 
>>> sum of angles in a triangle. Moreover, I don't see how spatially flat 
>>> can 
>>> have nothing to do with extent, since in applying Euclidean geometry we 
>>> surely seem to be dealing with an infinitely extended plane. TIA.
>>>
>>>
>>> Not necessarily.  You could have periodic boundary conditions.  But 
>>> most cosmologists do assume the universe is infinite in spatial extent. 
>>>  Of 
>>> course the flatness isn't measured by triangulation.  It's measured by 
>>> comparing the spatial spectrum of the CMB variations to model 
>>> predictions 
>>> with different mass densities.   
>>> https://arxiv.org/pdf/astro-ph/0004404
>>>
>>> Brent
>>>
>>
>> However flatness is measured, the criterion still seems Euclidean and 
>> hence infinite in extent if one believes the triangle measured has 
>> combined 
>> angles of 180 degrees. And I don't see how this is distinguishable from 
>> asymptotically flat for a huge but finite universe. 
>>
>>
>> It's not.
>>
>
> That's my point. No way of distinguishing flat from asymptotically 
> flat for a huge universe, so the assumption of infinite spatial extent by 
> cosmologists seems unwarranted. But as you note below, the universe could 
> have begun with infinite spatial extent. But ours didn't AFAIK. It began 
> as 
> astronomically tiny and expanded via inflation.
>
>
> But you don't know that.  According to Einstein's equations the 
> visible part of the universe started at *zero* size.  Of course no 
> one takes that entirely seriously since at very small distances quantum 
> mechanics must invalidate Einstein's equations.
>
> Brent
>

 If you're invoking QM, aren't you conceding it started out very small, 
 if not exactly zero size? So it seems more plausible to assume it started 
 out very small, surely not infinite. But according to your previous 
 statements and those that I have read by cosmologists, the assumption of 
 infinite spatial extent is generally accepted and IMO unwarranted. 


 If it's flat or has negative curvature then the equations imply it's 
 infinite or perhaps periodic (no matter what the scale factor is).  If the 
 curvature is positive then it's finite and closed and the scale factor can 
 be taken to be the radius, so it indeed starts small in the absolute 
 sense.  Atkatz and Pagels showed that only FRW universes that are closed 
 (positive curvature) or De Sitter (flat with a positive cosmological 
 constant) can "tunnel out of nothing".  


 http://www.quantum-gravitation.de/media/99f63994b9064eb68004fff2.pdf

 So most cosmologists liked the closed universe model, until it was 
 found that expansion is accelerating.  So now more of them look to some 
 modification of the De Sitter space universe.  

 Brent

>>>
>>> Modification of De Sitter will be flat and therefore open. I find the 
>>> open universe model in contradiction to the finite age of the universe. Is 
>>> this unreasonable? 
>>>
>>>
>>> Well, if you have an infinite universe, and toward the past it is scaled 
>>> by a factor a, and a->0 does the universes size go to zero?
>>>
>>> Why is the closed universe model less favored when it was discovered 
>>> that expansion is accelerating? 
>>>
>>>
>>> Because the De Sitter universe that can "tunnel from the vacuum" 
>>> automatically has a positive cosmological constant.
>>>
>>> Brent
>>>
>>
>> Unfortunately, my understanding of the scale factor and cosmological 
>> constant as they relate to the various geometries is insufficient to 
>> appreciate your comments. Maybe you 

Re: flat vs asymptotically flat universe

[agrayson2000]

On Friday, November 10, 2017 at 11:22:45 PM UTC-7, Brent wrote:
>
>
>
> On 11/10/2017 10:01 PM, agrays...@gmail.com  wrote:
>
>
>
> On Friday, November 10, 2017 at 2:16:04 PM UTC-7, Brent wrote: 
>>
>>
>>
>> On 11/10/2017 1:01 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Friday, November 10, 2017 at 12:19:05 PM UTC-7, Brent wrote: 
>>>
>>>
>>>
>>> On 11/10/2017 4:06 AM, Alan Grayson wrote:
>>>
>>>
>>>
>>> On Thu, Nov 9, 2017 at 10:32 PM, Brent Meeker  
>>> wrote:
>>>


 On 11/9/2017 9:15 PM, Alan Grayson wrote:



 On Thu, Nov 9, 2017 at 10:05 PM, Brent Meeker  
 wrote:

>
>
> On 11/9/2017 8:55 PM, agrays...@gmail.com wrote:
>
>
>
> On Thursday, November 9, 2017 at 8:00:45 PM UTC-7, Brent wrote: 
>>
>>
>>
>> On 11/9/2017 6:23 PM, Alan Grayson wrote:
>>
>> The difference between spatially flat and asymptotically flat for a 
>> huge universe would be virtually impossible to distinguish by measuring 
>> the 
>> sum of angles in a triangle. Moreover, I don't see how spatially flat 
>> can 
>> have nothing to do with extent, since in applying Euclidean geometry we 
>> surely seem to be dealing with an infinitely extended plane. TIA.
>>
>>
>> Not necessarily.  You could have periodic boundary conditions.  But 
>> most cosmologists do assume the universe is infinite in spatial extent.  
>> Of 
>> course the flatness isn't measured by triangulation.  It's measured by 
>> comparing the spatial spectrum of the CMB variations to model 
>> predictions 
>> with different mass densities.   
>> https://arxiv.org/pdf/astro-ph/0004404
>>
>> Brent
>>
>
> However flatness is measured, the criterion still seems Euclidean and 
> hence infinite in extent if one believes the triangle measured has 
> combined 
> angles of 180 degrees. And I don't see how this is distinguishable from 
> asymptotically flat for a huge but finite universe. 
>
>
> It's not.
>

 That's my point. No way of distinguishing flat from asymptotically flat 
 for a huge universe, so the assumption of infinite spatial extent by 
 cosmologists seems unwarranted. But as you note below, the universe could 
 have begun with infinite spatial extent. But ours didn't AFAIK. It began 
 as 
 astronomically tiny and expanded via inflation.


 But you don't know that.  According to Einstein's equations the visible 
 part of the universe started at *zero* size.  Of course no one takes 
 that entirely seriously since at very small distances quantum mechanics 
 must invalidate Einstein's equations.

 Brent

>>>
>>> If you're invoking QM, aren't you conceding it started out very small, 
>>> if not exactly zero size? So it seems more plausible to assume it started 
>>> out very small, surely not infinite. But according to your previous 
>>> statements and those that I have read by cosmologists, the assumption of 
>>> infinite spatial extent is generally accepted and IMO unwarranted. 
>>>
>>>
>>> If it's flat or has negative curvature then the equations imply it's 
>>> infinite or perhaps periodic (no matter what the scale factor is).  If the 
>>> curvature is positive then it's finite and closed and the scale factor can 
>>> be taken to be the radius, so it indeed starts small in the absolute 
>>> sense.  Atkatz and Pagels showed that only FRW universes that are closed 
>>> (positive curvature) or De Sitter (flat with a positive cosmological 
>>> constant) can "tunnel out of nothing".  
>>>
>>>
>>> http://www.quantum-gravitation.de/media/99f63994b9064eb68004fff2.pdf
>>>
>>> So most cosmologists liked the closed universe model, until it was found 
>>> that expansion is accelerating.  So now more of them look to some 
>>> modification of the De Sitter space universe.  
>>>
>>> Brent
>>>
>>
>> Modification of De Sitter will be flat and therefore open. I find the 
>> open universe model in contradiction to the finite age of the universe. Is 
>> this unreasonable? 
>>
>>
>> Well, if you have an infinite universe, and toward the past it is scaled 
>> by a factor a, and a->0 does the universes size go to zero?
>>
>> Why is the closed universe model less favored when it was discovered that 
>> expansion is accelerating? 
>>
>>
>> Because the De Sitter universe that can "tunnel from the vacuum" 
>> automatically has a positive cosmological constant.
>>
>> Brent
>>
>
> Unfortunately, my understanding of the scale factor and cosmological 
> constant as they relate to the various geometries is insufficient to 
> appreciate your comments. Maybe you could restate your above comments with 
> that in mind. TIA. 
>
>
> Didn't you read Vic's "Comprehensible Cosmos"?  Why are you over here on 
> the everythinglist asking physics questions anyway, Alan?  You should try 
> the 

Re: flat vs asymptotically flat universe

[Brent Meeker]

On 11/10/2017 10:01 PM, agrayson2...@gmail.com wrote:



On Friday, November 10, 2017 at 2:16:04 PM UTC-7, Brent wrote:



On 11/10/2017 1:01 PM, agrays...@gmail.com  wrote:



On Friday, November 10, 2017 at 12:19:05 PM UTC-7, Brent wrote:



On 11/10/2017 4:06 AM, Alan Grayson wrote:



On Thu, Nov 9, 2017 at 10:32 PM, Brent Meeker
 wrote:



On 11/9/2017 9:15 PM, Alan Grayson wrote:



On Thu, Nov 9, 2017 at 10:05 PM, Brent Meeker
 wrote:



On 11/9/2017 8:55 PM, agrays...@gmail.com wrote:



On Thursday, November 9, 2017 at 8:00:45 PM UTC-7,
Brent wrote:



On 11/9/2017 6:23 PM, Alan Grayson wrote:

The difference between spatially flat and
asymptotically flat for a huge universe would
be virtually impossible to distinguish by
measuring the sum of angles in a triangle.
Moreover, I don't see how spatially flat can
have nothing to do with extent, since in
applying Euclidean geometry we surely seem to
be dealing with an infinitely extended plane.
TIA.


Not necessarily. You could have periodic
boundary conditions.  But most cosmologists do
assume the universe is infinite in spatial
extent. Of course the flatness isn't measured
by triangulation. It's measured by comparing
the spatial spectrum of the CMB variations to
model predictions with different mass densities.
https://arxiv.org/pdf/astro-ph/0004404


Brent


However flatness is measured, the criterion still
seems Euclidean and hence infinite in extent if
one believes the triangle measured has combined
angles of 180 degrees. And I don't see how this is
distinguishable from asymptotically flat for a
huge but finite universe.


It's not.


That's my point. No way of distinguishing flat from
asymptotically flat for a huge universe, so the
assumption of infinite spatial extent by cosmologists
seems unwarranted. But as you note below, the universe
could have begun with infinite spatial extent. But ours
didn't AFAIK. It began as astronomically tiny and
expanded via inflation.


But you don't know that. According to Einstein's
equations the visible part of the universe started at
/*zero*/ size.  Of course no one takes that entirely
seriously since at very small distances quantum
mechanics must invalidate Einstein's equations.

Brent


If you're invoking QM, aren't you conceding it started out
very small, if not exactly zero size? So it seems more
plausible to assume it started out very small, surely not
infinite. But according to your previous statements and
those that I have read by cosmologists, the assumption of
infinite spatial extent is generally accepted and IMO
unwarranted.


If it's flat or has negative curvature then the equations
imply it's infinite or perhaps periodic (no matter what the
scale factor is).  If the curvature is positive then it's
finite and closed and the scale factor can be taken to be the
radius, so it indeed starts small in the absolute sense.
Atkatz and Pagels showed that only FRW universes that are
closed (positive curvature) or De Sitter (flat with a
positive cosmological constant) can "tunnel out of nothing".


http://www.quantum-gravitation.de/media/99f63994b9064eb68004fff2.pdf



So most cosmologists liked the closed universe model, until
it was found that expansion is accelerating.  So now more of
them look to some modification of the De Sitter space universe.

Brent


Modification of De Sitter will be flat and therefore open. I find
the open universe model in contradiction to the finite age of the
universe. Is this unreasonable?


Well, if you have an infinite universe, and toward the past it is
scaled by a factor a, and a->0 does the universes size go to zero?


Why is the closed universe model less favored when it was
discovered that expansion is accelerating?


Because the De Sitter universe that can "tunnel from the vacuum"
automatically has a positive cosmological constant.

Re: flat vs asymptotically flat universe

[agrayson2000]

On Friday, November 10, 2017 at 2:16:04 PM UTC-7, Brent wrote:
>
>
>
> On 11/10/2017 1:01 PM, agrays...@gmail.com  wrote:
>
>
>
> On Friday, November 10, 2017 at 12:19:05 PM UTC-7, Brent wrote: 
>>
>>
>>
>> On 11/10/2017 4:06 AM, Alan Grayson wrote:
>>
>>
>>
>> On Thu, Nov 9, 2017 at 10:32 PM, Brent Meeker  
>> wrote:
>>
>>>
>>>
>>> On 11/9/2017 9:15 PM, Alan Grayson wrote:
>>>
>>>
>>>
>>> On Thu, Nov 9, 2017 at 10:05 PM, Brent Meeker  
>>> wrote:
>>>


 On 11/9/2017 8:55 PM, agrays...@gmail.com wrote:



 On Thursday, November 9, 2017 at 8:00:45 PM UTC-7, Brent wrote: 
>
>
>
> On 11/9/2017 6:23 PM, Alan Grayson wrote:
>
> The difference between spatially flat and asymptotically flat for a 
> huge universe would be virtually impossible to distinguish by measuring 
> the 
> sum of angles in a triangle. Moreover, I don't see how spatially flat can 
> have nothing to do with extent, since in applying Euclidean geometry we 
> surely seem to be dealing with an infinitely extended plane. TIA.
>
>
> Not necessarily.  You could have periodic boundary conditions.  But 
> most cosmologists do assume the universe is infinite in spatial extent.  
> Of 
> course the flatness isn't measured by triangulation.  It's measured by 
> comparing the spatial spectrum of the CMB variations to model predictions 
> with different mass densities.   
> https://arxiv.org/pdf/astro-ph/0004404
>
> Brent
>

 However flatness is measured, the criterion still seems Euclidean and 
 hence infinite in extent if one believes the triangle measured has 
 combined 
 angles of 180 degrees. And I don't see how this is distinguishable from 
 asymptotically flat for a huge but finite universe. 


 It's not.

>>>
>>> That's my point. No way of distinguishing flat from asymptotically flat 
>>> for a huge universe, so the assumption of infinite spatial extent by 
>>> cosmologists seems unwarranted. But as you note below, the universe could 
>>> have begun with infinite spatial extent. But ours didn't AFAIK. It began as 
>>> astronomically tiny and expanded via inflation.
>>>
>>>
>>> But you don't know that.  According to Einstein's equations the visible 
>>> part of the universe started at *zero* size.  Of course no one takes 
>>> that entirely seriously since at very small distances quantum mechanics 
>>> must invalidate Einstein's equations.
>>>
>>> Brent
>>>
>>
>> If you're invoking QM, aren't you conceding it started out very small, if 
>> not exactly zero size? So it seems more plausible to assume it started out 
>> very small, surely not infinite. But according to your previous statements 
>> and those that I have read by cosmologists, the assumption of infinite 
>> spatial extent is generally accepted and IMO unwarranted. 
>>
>>
>> If it's flat or has negative curvature then the equations imply it's 
>> infinite or perhaps periodic (no matter what the scale factor is).  If the 
>> curvature is positive then it's finite and closed and the scale factor can 
>> be taken to be the radius, so it indeed starts small in the absolute 
>> sense.  Atkatz and Pagels showed that only FRW universes that are closed 
>> (positive curvature) or De Sitter (flat with a positive cosmological 
>> constant) can "tunnel out of nothing".  
>>
>>
>> http://www.quantum-gravitation.de/media/99f63994b9064eb68004fff2.pdf
>>
>> So most cosmologists liked the closed universe model, until it was found 
>> that expansion is accelerating.  So now more of them look to some 
>> modification of the De Sitter space universe.  
>>
>> Brent
>>
>
> Modification of De Sitter will be flat and therefore open. I find the open 
> universe model in contradiction to the finite age of the universe. Is this 
> unreasonable? 
>
>
> Well, if you have an infinite universe, and toward the past it is scaled 
> by a factor a, and a->0 does the universes size go to zero?
>
> Why is the closed universe model less favored when it was discovered that 
> expansion is accelerating? 
>
>
> Because the De Sitter universe that can "tunnel from the vacuum" 
> automatically has a positive cosmological constant.
>
> Brent
>

Unfortunately, my understanding of the scale factor and cosmological 
constant as they relate to the various geometries is insufficient to 
appreciate your comments. Maybe you could restate your above comments with 
that in mind. TIA. 

>
>
>

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Re: flat vs asymptotically flat universe

[Brent Meeker]

On 11/10/2017 1:01 PM, agrayson2...@gmail.com wrote:



On Friday, November 10, 2017 at 12:19:05 PM UTC-7, Brent wrote:



On 11/10/2017 4:06 AM, Alan Grayson wrote:



On Thu, Nov 9, 2017 at 10:32 PM, Brent Meeker
 wrote:



On 11/9/2017 9:15 PM, Alan Grayson wrote:



On Thu, Nov 9, 2017 at 10:05 PM, Brent Meeker
 wrote:



On 11/9/2017 8:55 PM, agrays...@gmail.com 
wrote:



On Thursday, November 9, 2017 at 8:00:45 PM UTC-7,
Brent wrote:



On 11/9/2017 6:23 PM, Alan Grayson wrote:

The difference between spatially flat and
asymptotically flat for a huge universe would be
virtually impossible to distinguish by measuring
the sum of angles in a triangle. Moreover, I don't
see how spatially flat can have nothing to do with
extent, since in applying Euclidean geometry we
surely seem to be dealing with an infinitely
extended plane. TIA.


Not necessarily.  You could have periodic boundary
conditions. But most cosmologists do assume the
universe is infinite in spatial extent.  Of course
the flatness isn't measured by triangulation.  It's
measured by comparing the spatial spectrum of the
CMB variations to model predictions with different
mass densities.
https://arxiv.org/pdf/astro-ph/0004404


Brent


However flatness is measured, the criterion still seems
Euclidean and hence infinite in extent if one believes
the triangle measured has combined angles of 180
degrees. And I don't see how this is distinguishable
from asymptotically flat for a huge but finite universe.


It's not.


That's my point. No way of distinguishing flat from
asymptotically flat for a huge universe, so the assumption
of infinite spatial extent by cosmologists seems
unwarranted. But as you note below, the universe could have
begun with infinite spatial extent. But ours didn't AFAIK.
It began as astronomically tiny and expanded via inflation.


But you don't know that.  According to Einstein's equations
the visible part of the universe started at /*zero*/ size. Of
course no one takes that entirely seriously since at very
small distances quantum mechanics must invalidate Einstein's
equations.

Brent


If you're invoking QM, aren't you conceding it started out very
small, if not exactly zero size? So it seems more plausible to
assume it started out very small, surely not infinite. But
according to your previous statements and those that I have read
by cosmologists, the assumption of infinite spatial extent is
generally accepted and IMO unwarranted.


If it's flat or has negative curvature then the equations imply
it's infinite or perhaps periodic (no matter what the scale factor
is).  If the curvature is positive then it's finite and closed and
the scale factor can be taken to be the radius, so it indeed
starts small in the absolute sense.  Atkatz and Pagels showed that
only FRW universes that are closed (positive curvature) or De
Sitter (flat with a positive cosmological constant) can "tunnel
out of nothing".

http://www.quantum-gravitation.de/media/99f63994b9064eb68004fff2.pdf



So most cosmologists liked the closed universe model, until it was
found that expansion is accelerating.  So now more of them look to
some modification of the De Sitter space universe.

Brent


Modification of De Sitter will be flat and therefore open. I find the 
open universe model in contradiction to the finite age of the 
universe. Is this unreasonable?


Well, if you have an infinite universe, and toward the past it is scaled 
by a factor a, and a->0 does the universes size go to zero?


Why is the closed universe model less favored when it was discovered 
that expansion is accelerating?


Because the De Sitter universe that can "tunnel from the vacuum" 
automatically has a positive cosmological constant.


Brent


TIA.
--
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Re: flat vs asymptotically flat universe

[Alan Grayson]

On Fri, Nov 10, 2017 at 12:19 PM, Brent Meeker  wrote:

>
>
> On 11/10/2017 4:06 AM, Alan Grayson wrote:
>
>
>
> On Thu, Nov 9, 2017 at 10:32 PM, Brent Meeker 
> wrote:
>
>>
>>
>> On 11/9/2017 9:15 PM, Alan Grayson wrote:
>>
>>
>>
>> On Thu, Nov 9, 2017 at 10:05 PM, Brent Meeker 
>> wrote:
>>
>>>
>>>
>>> On 11/9/2017 8:55 PM, agrayson2...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, November 9, 2017 at 8:00:45 PM UTC-7, Brent wrote:



 On 11/9/2017 6:23 PM, Alan Grayson wrote:

 The difference between spatially flat and asymptotically flat for a
 huge universe would be virtually impossible to distinguish by measuring the
 sum of angles in a triangle. Moreover, I don't see how spatially flat can
 have nothing to do with extent, since in applying Euclidean geometry we
 surely seem to be dealing with an infinitely extended plane. TIA.


 Not necessarily.  You could have periodic boundary conditions.  But
 most cosmologists do assume the universe is infinite in spatial extent.  Of
 course the flatness isn't measured by triangulation.  It's measured by
 comparing the spatial spectrum of the CMB variations to model predictions
 with different mass densities.
 https://arxiv.org/pdf/astro-ph/0004404

 Brent

>>>
>>> However flatness is measured, the criterion still seems Euclidean and
>>> hence infinite in extent if one believes the triangle measured has combined
>>> angles of 180 degrees. And I don't see how this is distinguishable from
>>> asymptotically flat for a huge but finite universe.
>>>
>>>
>>> It's not.
>>>
>>
>> That's my point. No way of distinguishing flat from asymptotically flat
>> for a huge universe, so the assumption of infinite spatial extent by
>> cosmologists seems unwarranted. But as you note below, the universe could
>> have begun with infinite spatial extent. But ours didn't AFAIK. It began as
>> astronomically tiny and expanded via inflation.
>>
>>
>> But you don't know that.  According to Einstein's equations the visible
>> part of the universe started at *zero* size.  Of course no one takes
>> that entirely seriously since at very small distances quantum mechanics
>> must invalidate Einstein's equations.
>>
>> Brent
>>
>
> If you're invoking QM, aren't you conceding it started out very small, if
> not exactly zero size? So it seems more plausible to assume it started out
> very small, surely not infinite. But according to your previous statements
> and those that I have read by cosmologists, the assumption of infinite
> spatial extent is generally accepted and IMO unwarranted.
>
>
> If it's flat or has negative curvature then the equations imply it's
> infinite or perhaps periodic (no matter what the scale factor is).  If the
> curvature is positive then it's finite and closed and the scale factor can
> be taken to be the radius, so it indeed starts small in the absolute
> sense.  Atkatz and Pagels showed that only FRW universes that are closed
> (positive curvature) or De Sitter (flat with a positive cosmological
> constant) can "tunnel out of nothing".
>
> http://www.quantum-gravitation.de/media/99f63994b9064eb68004ff
> f2.pdf
>
> So most cosmologists liked the closed universe model, until it was found
> that expansion is accelerating.  So now more of them look to some
> modification of the De Sitter space universe.
>
> Brent
>

Modification of De Sitter will be flat and therefore open. I find the open
universe model in contradiction to the finite age of the universe. Is this
unreasonable? Why is the closed universe model less favored when it was
discovered that expansion is accelerating? TIA.

-- 
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Re: flat vs asymptotically flat universe

[agrayson2000]

On Friday, November 10, 2017 at 12:19:05 PM UTC-7, Brent wrote:
>
>
>
> On 11/10/2017 4:06 AM, Alan Grayson wrote:
>
>
>
> On Thu, Nov 9, 2017 at 10:32 PM, Brent Meeker  > wrote:
>
>>
>>
>> On 11/9/2017 9:15 PM, Alan Grayson wrote:
>>
>>
>>
>> On Thu, Nov 9, 2017 at 10:05 PM, Brent Meeker > > wrote:
>>
>>>
>>>
>>> On 11/9/2017 8:55 PM, agrays...@gmail.com  wrote:
>>>
>>>
>>>
>>> On Thursday, November 9, 2017 at 8:00:45 PM UTC-7, Brent wrote: 



 On 11/9/2017 6:23 PM, Alan Grayson wrote:

 The difference between spatially flat and asymptotically flat for a 
 huge universe would be virtually impossible to distinguish by measuring 
 the 
 sum of angles in a triangle. Moreover, I don't see how spatially flat can 
 have nothing to do with extent, since in applying Euclidean geometry we 
 surely seem to be dealing with an infinitely extended plane. TIA.


 Not necessarily.  You could have periodic boundary conditions.  But 
 most cosmologists do assume the universe is infinite in spatial extent.  
 Of 
 course the flatness isn't measured by triangulation.  It's measured by 
 comparing the spatial spectrum of the CMB variations to model predictions 
 with different mass densities.   
 https://arxiv.org/pdf/astro-ph/0004404

 Brent

>>>
>>> However flatness is measured, the criterion still seems Euclidean and 
>>> hence infinite in extent if one believes the triangle measured has combined 
>>> angles of 180 degrees. And I don't see how this is distinguishable from 
>>> asymptotically flat for a huge but finite universe. 
>>>
>>>
>>> It's not.
>>>
>>
>> That's my point. No way of distinguishing flat from asymptotically flat 
>> for a huge universe, so the assumption of infinite spatial extent by 
>> cosmologists seems unwarranted. But as you note below, the universe could 
>> have begun with infinite spatial extent. But ours didn't AFAIK. It began as 
>> astronomically tiny and expanded via inflation.
>>
>>
>> But you don't know that.  According to Einstein's equations the visible 
>> part of the universe started at *zero* size.  Of course no one takes 
>> that entirely seriously since at very small distances quantum mechanics 
>> must invalidate Einstein's equations.
>>
>> Brent
>>
>
> If you're invoking QM, aren't you conceding it started out very small, if 
> not exactly zero size? So it seems more plausible to assume it started out 
> very small, surely not infinite. But according to your previous statements 
> and those that I have read by cosmologists, the assumption of infinite 
> spatial extent is generally accepted and IMO unwarranted. 
>
>
> If it's flat or has negative curvature then the equations imply it's 
> infinite or perhaps periodic (no matter what the scale factor is).  If the 
> curvature is positive then it's finite and closed and the scale factor can 
> be taken to be the radius, so it indeed starts small in the absolute 
> sense.  Atkatz and Pagels showed that only FRW universes that are closed 
> (positive curvature) or De Sitter (flat with a positive cosmological 
> constant) can "tunnel out of nothing".  
>
>
> http://www.quantum-gravitation.de/media/99f63994b9064eb68004fff2.pdf
>
> So most cosmologists liked the closed universe model, until it was found 
> that expansion is accelerating.  So now more of them look to some 
> modification of the De Sitter space universe.  
>
> Brent
>

Modification of De Sitter will be flat and therefore open. I find the open 
universe model in contradiction to the finite age of the universe. Is this 
unreasonable? Why is the closed universe model less favored when it was 
discovered that expansion is accelerating? TIA.

-- 
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Re: flat vs asymptotically flat universe

[Brent Meeker]

On 11/10/2017 4:06 AM, Alan Grayson wrote:



On Thu, Nov 9, 2017 at 10:32 PM, Brent Meeker > wrote:




On 11/9/2017 9:15 PM, Alan Grayson wrote:



On Thu, Nov 9, 2017 at 10:05 PM, Brent Meeker
> wrote:



On 11/9/2017 8:55 PM, agrayson2...@gmail.com
 wrote:



On Thursday, November 9, 2017 at 8:00:45 PM UTC-7, Brent wrote:



On 11/9/2017 6:23 PM, Alan Grayson wrote:

The difference between spatially flat and
asymptotically flat for a huge universe would be
virtually impossible to distinguish by measuring the
sum of angles in a triangle. Moreover, I don't see how
spatially flat can have nothing to do with extent,
since in applying Euclidean geometry we surely seem to
be dealing with an infinitely extended plane. TIA.


Not necessarily.  You could have periodic boundary
conditions. But most cosmologists do assume the universe
is infinite in spatial extent.  Of course the flatness
isn't measured by triangulation.  It's measured by
comparing the spatial spectrum of the CMB variations to
model predictions with different mass densities.
https://arxiv.org/pdf/astro-ph/0004404


Brent


However flatness is measured, the criterion still seems
Euclidean and hence infinite in extent if one believes the
triangle measured has combined angles of 180 degrees. And I
don't see how this is distinguishable from asymptotically
flat for a huge but finite universe.


It's not.


That's my point. No way of distinguishing flat from
asymptotically flat for a huge universe, so the assumption of
infinite spatial extent by cosmologists seems unwarranted. But as
you note below, the universe could have begun with infinite
spatial extent. But ours didn't AFAIK. It began as astronomically
tiny and expanded via inflation.


But you don't know that.  According to Einstein's equations the
visible part of the universe started at /*zero*/ size.  Of course
no one takes that entirely seriously since at very small distances
quantum mechanics must invalidate Einstein's equations.

Brent


If you're invoking QM, aren't you conceding it started out very small, 
if not exactly zero size? So it seems more plausible to assume it 
started out very small, surely not infinite. But according to your 
previous statements and those that I have read by cosmologists, the 
assumption of infinite spatial extent is generally accepted and IMO 
unwarranted.


If it's flat or has negative curvature then the equations imply it's 
infinite or perhaps periodic (no matter what the scale factor is). If 
the curvature is positive then it's finite and closed and the scale 
factor can be taken to be the radius, so it indeed starts small in the 
absolute sense.  Atkatz and Pagels showed that only FRW universes that 
are closed (positive curvature) or De Sitter (flat with a positive 
cosmological constant) can "tunnel out of nothing".


http://www.quantum-gravitation.de/media/99f63994b9064eb68004fff2.pdf

So most cosmologists liked the closed universe model, until it was found 
that expansion is accelerating.  So now more of them look to some 
modification of the De Sitter space universe.


Brent

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Re: flat vs asymptotically flat universe

[Alan Grayson]

On Thu, Nov 9, 2017 at 10:32 PM, Brent Meeker  wrote:

>
>
> On 11/9/2017 9:15 PM, Alan Grayson wrote:
>
>
>
> On Thu, Nov 9, 2017 at 10:05 PM, Brent Meeker 
> wrote:
>
>>
>>
>> On 11/9/2017 8:55 PM, agrayson2...@gmail.com wrote:
>>
>>
>>
>> On Thursday, November 9, 2017 at 8:00:45 PM UTC-7, Brent wrote:
>>>
>>>
>>>
>>> On 11/9/2017 6:23 PM, Alan Grayson wrote:
>>>
>>> The difference between spatially flat and asymptotically flat for a huge
>>> universe would be virtually impossible to distinguish by measuring the sum
>>> of angles in a triangle. Moreover, I don't see how spatially flat can have
>>> nothing to do with extent, since in applying Euclidean geometry we surely
>>> seem to be dealing with an infinitely extended plane. TIA.
>>>
>>>
>>> Not necessarily.  You could have periodic boundary conditions.  But most
>>> cosmologists do assume the universe is infinite in spatial extent.  Of
>>> course the flatness isn't measured by triangulation.  It's measured by
>>> comparing the spatial spectrum of the CMB variations to model predictions
>>> with different mass densities.
>>> https://arxiv.org/pdf/astro-ph/0004404
>>>
>>> Brent
>>>
>>
>> However flatness is measured, the criterion still seems Euclidean and
>> hence infinite in extent if one believes the triangle measured has combined
>> angles of 180 degrees. And I don't see how this is distinguishable from
>> asymptotically flat for a huge but finite universe.
>>
>>
>> It's not.
>>
>
> That's my point. No way of distinguishing flat from asymptotically flat
> for a huge universe, so the assumption of infinite spatial extent by
> cosmologists seems unwarranted. But as you note below, the universe could
> have begun with infinite spatial extent. But ours didn't AFAIK. It began as
> astronomically tiny and expanded via inflation.
>
>
> But you don't know that.  According to Einstein's equations the visible
> part of the universe started at *zero* size.  Of course no one takes that
> entirely seriously since at very small distances quantum mechanics must
> invalidate Einstein's equations.
>
> Brent
>

If you're invoking QM, aren't you conceding it started out very small, if
not exactly zero size? So it seems more plausible to assume it started out
very small, surely not infinite. But according to your previous statements
and those that I have read by cosmologists, the assumption of infinite
spatial extent is generally accepted and IMO unwarranted.

>
>
>
>> Moreover, it seems contradictory that a universe which has expanded for a
>> finite duration, could be infinite in spatial extent. TIA.
>>
>>
>> It can if it starts off infinite.  Remember the expansion in Einstein's
>> equation is just a *factor*, not an absolute value.
>>
>> Brent
>>
>
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Re: flat vs asymptotically flat universe

[Brent Meeker]

On 11/9/2017 9:15 PM, Alan Grayson wrote:



On Thu, Nov 9, 2017 at 10:05 PM, Brent Meeker > wrote:




On 11/9/2017 8:55 PM, agrayson2...@gmail.com
 wrote:



On Thursday, November 9, 2017 at 8:00:45 PM UTC-7, Brent wrote:



On 11/9/2017 6:23 PM, Alan Grayson wrote:

The difference between spatially flat and asymptotically
flat for a huge universe would be virtually impossible to
distinguish by measuring the sum of angles in a triangle.
Moreover, I don't see how spatially flat can have nothing to
do with extent, since in applying Euclidean geometry we
surely seem to be dealing with an infinitely extended plane.
TIA.


Not necessarily.  You could have periodic boundary
conditions.  But most cosmologists do assume the universe is
infinite in spatial extent.  Of course the flatness isn't
measured by triangulation.  It's measured by comparing the
spatial spectrum of the CMB variations to model predictions
with different mass densities.
https://arxiv.org/pdf/astro-ph/0004404


Brent


However flatness is measured, the criterion still seems Euclidean
and hence infinite in extent if one believes the triangle
measured has combined angles of 180 degrees. And I don't see how
this is distinguishable from asymptotically flat for a huge but
finite universe.


It's not.


That's my point. No way of distinguishing flat from asymptotically 
flat for a huge universe, so the assumption of infinite spatial extent 
by cosmologists seems unwarranted. But as you note below, the universe 
could have begun with infinite spatial extent. But ours didn't AFAIK. 
It began as astronomically tiny and expanded via inflation.


But you don't know that.  According to Einstein's equations the visible 
part of the universe started at /*zero*/ size. Of course no one takes 
that entirely seriously since at very small distances quantum mechanics 
must invalidate Einstein's equations.


Brent




Moreover, it seems contradictory that a universe which has
expanded for a finite duration, could be infinite in spatial
extent. TIA.


It can if it starts off infinite.  Remember the expansion in
Einstein's equation is just a /*factor*/, not an absolute value.

Brent



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Re: flat vs asymptotically flat universe

[Alan Grayson]

On Thu, Nov 9, 2017 at 10:05 PM, Brent Meeker  wrote:

>
>
> On 11/9/2017 8:55 PM, agrayson2...@gmail.com wrote:
>
>
>
> On Thursday, November 9, 2017 at 8:00:45 PM UTC-7, Brent wrote:
>>
>>
>>
>> On 11/9/2017 6:23 PM, Alan Grayson wrote:
>>
>> The difference between spatially flat and asymptotically flat for a huge
>> universe would be virtually impossible to distinguish by measuring the sum
>> of angles in a triangle. Moreover, I don't see how spatially flat can have
>> nothing to do with extent, since in applying Euclidean geometry we surely
>> seem to be dealing with an infinitely extended plane. TIA.
>>
>>
>> Not necessarily.  You could have periodic boundary conditions.  But most
>> cosmologists do assume the universe is infinite in spatial extent.  Of
>> course the flatness isn't measured by triangulation.  It's measured by
>> comparing the spatial spectrum of the CMB variations to model predictions
>> with different mass densities.
>> https://arxiv.org/pdf/astro-ph/0004404
>>
>> Brent
>>
>
> However flatness is measured, the criterion still seems Euclidean and
> hence infinite in extent if one believes the triangle measured has combined
> angles of 180 degrees. And I don't see how this is distinguishable from
> asymptotically flat for a huge but finite universe.
>
>
> It's not.
>

That's my point. No way of distinguishing flat from asymptotically flat for
a huge universe, so the assumption of infinite spatial extent by
cosmologists seems unwarranted. But as you note below, the universe could
have begun with infinite spatial extent. But ours didn't AFAIK. It began as
astronomically tiny and expanded via inflation.

>
> Moreover, it seems contradictory that a universe which has expanded for a
> finite duration, could be infinite in spatial extent. TIA.
>
>
> It can if it starts off infinite.  Remember the expansion in Einstein's
> equation is just a *factor*, not an absolute value.
>
> Brent
>
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Re: flat vs asymptotically flat universe

[Brent Meeker]

On 11/9/2017 8:55 PM, agrayson2...@gmail.com wrote:



On Thursday, November 9, 2017 at 8:00:45 PM UTC-7, Brent wrote:



On 11/9/2017 6:23 PM, Alan Grayson wrote:

The difference between spatially flat and asymptotically flat for
a huge universe would be virtually impossible to distinguish by
measuring the sum of angles in a triangle. Moreover, I don't see
how spatially flat can have nothing to do with extent, since in
applying Euclidean geometry we surely seem to be dealing with an
infinitely extended plane. TIA.


Not necessarily.  You could have periodic boundary conditions. 
But most cosmologists do assume the universe is infinite in
spatial extent.  Of course the flatness isn't measured by
triangulation.  It's measured by comparing the spatial spectrum of
the CMB variations to model predictions with different mass
densities.
https://arxiv.org/pdf/astro-ph/0004404


Brent


However flatness is measured, the criterion still seems Euclidean and 
hence infinite in extent if one believes the triangle measured has 
combined angles of 180 degrees. And I don't see how this is 
distinguishable from asymptotically flat for a huge but finite universe.


It's not.

Moreover, it seems contradictory that a universe which has expanded 
for a finite duration, could be infinite in spatial extent. TIA.


It can if it starts off infinite.  Remember the expansion in Einstein's 
equation is just a /*factor*/, not an absolute value.


Brent

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Re: flat vs asymptotically flat universe

[agrayson2000]

On Thursday, November 9, 2017 at 8:00:45 PM UTC-7, Brent wrote:
>
>
>
> On 11/9/2017 6:23 PM, Alan Grayson wrote:
>
> The difference between spatially flat and asymptotically flat for a huge 
> universe would be virtually impossible to distinguish by measuring the sum 
> of angles in a triangle. Moreover, I don't see how spatially flat can have 
> nothing to do with extent, since in applying Euclidean geometry we surely 
> seem to be dealing with an infinitely extended plane. TIA.
>
>
> Not necessarily.  You could have periodic boundary conditions.  But most 
> cosmologists do assume the universe is infinite in spatial extent.  Of 
> course the flatness isn't measured by triangulation.  It's measured by 
> comparing the spatial spectrum of the CMB variations to model predictions 
> with different mass densities.   
> https://arxiv.org/pdf/astro-ph/0004404
>
> Brent
>

However flatness is measured, the criterion still seems Euclidean and hence 
infinite in extent if one believes the triangle measured has combined 
angles of 180 degrees. And I don't see how this is distinguishable from 
asymptotically flat for a huge but finite universe. Moreover, it seems 
contradictory that a universe which has expanded for a finite duration, 
could be infinite in spatial extent. TIA. 

>
>
> On Thu, Nov 9, 2017 at 4:42 PM, Brent Meeker  > wrote:
>
>> Cosmologist think the universe is spatially flat.  That just means 
>> triangles have interior angles summing to 180deg.  It doesn't have anything 
>> to do with extent.  But the universe is not flat in spacetime; it's 
>> expanding and at an increasing rate.
>>
>> Brent
>>
>> On 11/9/2017 3:10 PM, agrays...@gmail.com  wrote:
>>
>> IIUC, the difference is huge. In the former case, the universe is open, 
>> spatially infinite with infinite mass (assuming a nonzero mass distribution 
>> on large scale everywhere), whereas the latter is closed, finite in spatial 
>> extent and mass. But I notice that most cosmologists claim the universe is 
>> *flat*, as in mathematically flat. Are they just speaking loosely and 
>> really mean the universe is ASYMPTOTICALLY flat? I find it contradictory 
>> for a universe which is finite in age, to be truly mathematically FLAT. TIA.
>> -- 
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Re: flat vs asymptotically flat universe

[Brent Meeker]

On 11/9/2017 6:23 PM, Alan Grayson wrote:
The difference between spatially flat and asymptotically flat for a 
huge universe would be virtually impossible to distinguish by 
measuring the sum of angles in a triangle. Moreover, I don't see how 
spatially flat can have nothing to do with extent, since in applying 
Euclidean geometry we surely seem to be dealing with an infinitely 
extended plane. TIA.


Not necessarily.  You could have periodic boundary conditions.  But most 
cosmologists do assume the universe is infinite in spatial extent.  Of 
course the flatness isn't measured by triangulation. It's measured by 
comparing the spatial spectrum of the CMB variations to model 
predictions with different mass densities.

https://arxiv.org/pdf/astro-ph/0004404

Brent



On Thu, Nov 9, 2017 at 4:42 PM, Brent Meeker > wrote:


Cosmologist think the universe is spatially flat.  That just means
triangles have interior angles summing to 180deg.  It doesn't have
anything to do with extent.  But the universe is not flat in
spacetime; it's expanding and at an increasing rate.

Brent

On 11/9/2017 3:10 PM, agrayson2...@gmail.com
 wrote:

IIUC, the difference is huge. In the former case, the universe is
open, spatially infinite with infinite mass (assuming a nonzero
mass distribution on large scale everywhere), whereas the latter
is closed, finite in spatial extent and mass. But I notice that
most cosmologists claim the universe is *flat*, as in
mathematically flat. Are they just speaking loosely and really
mean the universe is ASYMPTOTICALLY flat? I find it contradictory
for a universe which is finite in age, to be truly mathematically
FLAT. TIA.
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Re: flat vs asymptotically flat universe

[Alan Grayson]

The difference between spatially flat and asymptotically flat for a huge
universe would be virtually impossible to distinguish by measuring the sum
of angles in a triangle. Moreover, I don't see how spatially flat can have
nothing to do with extent, since in applying Euclidean geometry we surely
seem to be dealing with an infinitely extended plane. TIA.

On Thu, Nov 9, 2017 at 4:42 PM, Brent Meeker  wrote:

> Cosmologist think the universe is spatially flat.  That just means
> triangles have interior angles summing to 180deg.  It doesn't have anything
> to do with extent.  But the universe is not flat in spacetime; it's
> expanding and at an increasing rate.
>
> Brent
>
> On 11/9/2017 3:10 PM, agrayson2...@gmail.com wrote:
>
> IIUC, the difference is huge. In the former case, the universe is open,
> spatially infinite with infinite mass (assuming a nonzero mass distribution
> on large scale everywhere), whereas the latter is closed, finite in spatial
> extent and mass. But I notice that most cosmologists claim the universe is
> *flat*, as in mathematically flat. Are they just speaking loosely and
> really mean the universe is ASYMPTOTICALLY flat? I find it contradictory
> for a universe which is finite in age, to be truly mathematically FLAT. TIA.
> --
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Re: flat vs asymptotically flat universe

[Brent Meeker]

Cosmologist think the universe is spatially flat.  That just means 
triangles have interior angles summing to 180deg.  It doesn't have 
anything to do with extent.  But the universe is not flat in spacetime; 
it's expanding and at an increasing rate.


Brent

On 11/9/2017 3:10 PM, agrayson2...@gmail.com wrote:
IIUC, the difference is huge. In the former case, the universe is 
open, spatially infinite with infinite mass (assuming a nonzero mass 
distribution on large scale everywhere), whereas the latter is closed, 
finite in spatial extent and mass. But I notice that most cosmologists 
claim the universe is *flat*, as in mathematically flat. Are they just 
speaking loosely and really mean the universe is ASYMPTOTICALLY flat? 
I find it contradictory for a universe which is finite in age, to be 
truly mathematically FLAT. TIA.

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