Unhappiness with the universe

[John Clark]

On Thu, Jan 2, 2020 at 2:30 AM Alan Grayson <agrays...@gmail.com> wrote:
 

> If we're convinced it's finite in age, then it can't be infinite in spatial extent. AG

We don't know for sure our universe is infinite in size and we'll never know for sure because we'll never be able to measure precisely zero curvature with no error at all, but we do know it's pretty damn flat, if it's curved it's so slight that a light beam would have to go at least 500 times as far as our telescopes can see for it to return where it started. So if you respect the empirical evidence for the Big Bang but the idea of a beginning of a infinitely sized universe makes you unhappy then the Multiverse idea offers you an obvious solution, you get an infinitely large infinitely old Multiverse but with the observable universe having a beginning and being only finitely large. However I understand the Multiverse makes you unhappy too. I fear you may be destined to be unhappy.

By the way ... does the inverse also make you unhappy, something infinitely old but finite in spatial extent?

John K Clark

[Lawrence Crowell]

The expansion factor in the FLRW metric, or approximately the de Sitter metric, is exp(√{Λ/3}r) for Λ = 10^{-52}m^{-2}. Now for the most early universe at the Planck scale we think of the expansion fac-tor expanding the Planck scale ℓ_p = √{Għ/c^3} = 1.6×10^{-35}m to the scale of the cosmological horizon 10^{10}light years or 10^{26}m. This means (√{Λ/3}r ≈ 140 and so the radial distance is 140 times the horizon distance or about 1.9 trillion light years. The CMB is out to 46 billion light years. This is the absolute furthest we can receive any information from the distant past observable universe. This would involve gravitational wave or graviton data on the CMB that originated at the earliest moments. It is possible I think that we may observe this. 

If we can observe this information it might in time be possible to determine if there is any net curvature to the universe out to this scale. If no curvature is found we can only say the universe is flat out the to uncertainty imposed by this fundamental limit on quantum bit information available. We are fundamen-tally limited by the horizon limits of the observable universe.

LC

[Philip Thrift]

On Sunday, January 12, 2020 at 9:58:06 AM UTC-6, John Clark wrote:

There always this possibility:

There's only a finite number of particles in the universe and only the right finite amount of "space" they fit in, whatever its shape is.

@philipthrift 

[Alan Grayson]

What makes me unhappy are humans who embrace stupidity. AG 

[Alan Grayson]

On Sunday, January 12, 2020 at 8:58:06 AM UTC-7, John Clark wrote:

All the models pictorially represented, have the Universe beginning very small, and inflation is claimed to increase its size from, say, much smaller than a proton, to about the size of the Earth or Solar System in a few Planck intervals. If it begins small, or if you run the clock backward it becomes progressively smaller, how could it have started with infinite spatial extent? Don't you see something wrong with the model?  AG

[Pierz]

Grayson, it's been explained to you, but you fail to compute. I had the very same thought, when I first heard about inflation and the flat, infinite universe, but my thought after that was: obviously I have misunderstood something, because clearly the model makes mathematical sense or 100% of cosmologists - very smart people by definition - would have seen the obvious flaw. So I took the time to improve my understanding. Your thought process on the other hand seems to be: "it seems contradictory, therefore the world's cosmologists must have missed this glaring logical problem I have identified. (The fact that I can't actually do the maths myself is unlikely to be relevant)." Then you post here and go round in circles with your obtuse misunderstandings of the explanations you receive. And finally you complain about being "not taken seriously". Do *you* see anything wrong with the model? 

 

[Alan Grayson]

No. It hasn't been explained to me. I thank you, but unfortunately your pov is too typical. You assert I am mistaken, but fail to say exactly how, in what way. Since you claim to understand my error due to your extensive research, why not clue me (us) in? As I recall, you did make some effort previously, whereupon I critiqued it, but got no reply. AG 

 

[Alan Grayson]

If you recall, Brent made a serious effort to explain it via the FLRW solution to Einstein's Field Equations. I asked how that solution solves for k, a parameter related to curvature, whereupon Brent posted that the sign is all that matters, and that it's folded into the initial condition of the BB. But do we know that initial condition? I don't think so. If I am right, then we get any curvature we have a bias for, by choosing appropriate initial conditions. Maybe Brent will respond to my objection. We'll see. At least this shows that my thinking in these matters is not as amateurish as you seem to suggest. AG

 

[Alan Grayson]

On Sunday, January 12, 2020 at 8:58:06 AM UTC-7, John Clark wrote:

My hunch, and that's all it is, is that "the substratum" from which the BB emerged, is infinitely old, and the concept of spatial extent probably doesn't apply to it. There could be many BB's, possibly an infinite number, but all finite in spatial extent if they had beginnings. AG 

John K Clark

[smitra]

On 13-01-2020 07:18, Alan Grayson wrote:
> On Sunday, January 12, 2020 at 8:58:06 AM UTC-7, John Clark wrote:
>
>> On Thu, Jan 2, 2020 at 2:30 AM Alan Grayson <agrays...@gmail.com>
>> wrote:
>>

>>> _> If we're convinced it's finite in age, then it can't be
>>> infinite in spatial extent. AG _

>>
>> We don't know for sure our universe is infinite in size and we'll
>> never know for sure because we'll never be able to measure precisely
>> zero curvature with no error at all, but we do know it's pretty damn
>> flat, if it's curved it's so slight that a light beam would have to
>> go at least 500 times as far as our telescopes can see for it to
>> return where it started. So if you respect the empirical evidence
>> for the Big Bang but the idea of a beginning of a infinitely sized
>> universe makes you unhappy then the Multiverse idea offers you an
>> obvious solution, you get an infinitely large infinitely old
>> Multiverse but with the observable universe having a beginning and
>> being only finitely large. However I understand the Multiverse makes
>> you unhappy too. I fear you may be destined to be unhappy.
>>
>> By the way ... does the inverse also make you unhappy, something
>> infinitely old but finite in spatial extent?
>

> MY HUNCH, AND THAT&#39;S ALL IT IS, IS THAT "THE SUBSTRATUM" FROM
> WHICH THE BB EMERGED, IS INFINITELY OLD, AND THE CONCEPT OF SPATIAL
> EXTENT PROBABLY DOESN&#39;T APPLY TO IT. THERE COULD BE MANY BB&#39;S,
> POSSIBLY AN INFINITE NUMBER, BUT ALL FINITE IN SPATIAL EXTENT IF THEY
> HAD BEGINNINGS. AG

Or there is no such thing as a universe. There only exists a multiverse
of algorithms. One such algorithm is "program AG" who thinks he lives in
a large universe and who is pondering about whether its infinite. But
what really exists are the large number of algorithms. AG as he exists
right now, one second ago, one second into the future all all different
members of the multiverse.

Saibal

[Stathis Papaioannou]

The model says that a subset of the universe starts small and gets bigger. This is not inconsistent with the whole universe starting and remaining infinite in spatial extent.

--

Stathis Papaioannou

[Alan Grayson]

I thought I made that clear; what I am calling "the universe" is precisely the SUBSET you refer to, which starts small and gets bigger. It is THAT SUBSET which cosmologists claim has infinite spatial extent, based on measurements. What you're calling "the whole universe" includes the underlying entity on which the BB started, and on which measurements CANNOT be made. It could be infinite in spatial extent, or is possibly an entity for which the concept of spatial extent might not exist. AG

[Alan Grayson]

Could be. Maybe it's all simulation. But that's a different subject and has nothing to do with the issue I am trying to resolve. AG 

[Quentin Anciaux]

As the bigbang is a singularity at the start... what prevents it to contain an infinite content in a zero/small volume, after all it's a singularity and we know only things after the big bang started ? and after inflation (which I understand is only space metric which inflate), there is still an infinite content.  

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[Alan Grayson]

On Monday, January 13, 2020 at 2:38:57 AM UTC-7, Quentin Anciaux wrote:

Le lun. 13 janv. 2020 à 10:28, Alan Grayson <agrays...@gmail.com> a écrit :

On Monday, January 13, 2020 at 1:33:01 AM UTC-7, stathisp wrote:

On Mon, 13 Jan 2020 at 13:48, Alan Grayson <agrays...@gmail.com> wrote:

On Sunday, January 12, 2020 at 8:58:06 AM UTC-7, John Clark wrote:

On Thu, Jan 2, 2020 at 2:30 AM Alan Grayson <agrays...@gmail.com> wrote:
 

> If we're convinced it's finite in age, then it can't be infinite in spatial extent. AG

We don't know for sure our universe is infinite in size and we'll never know for sure because we'll never be able to measure precisely zero curvature with no error at all, but we do know it's pretty damn flat, if it's curved it's so slight that a light beam would have to go at least 500 times as far as our telescopes can see for it to return where it started. So if you respect the empirical evidence for the Big Bang but the idea of a beginning of a infinitely sized universe makes you unhappy then the Multiverse idea offers you an obvious solution, you get an infinitely large infinitely old Multiverse but with the observable universe having a beginning and being only finitely large. However I understand the Multiverse makes you unhappy too. I fear you may be destined to be unhappy.

By the way ... does the inverse also make you unhappy, something infinitely old but finite in spatial extent?

John K Clark

All the models pictorially represented, have the Universe beginning very small, and inflation is claimed to increase its size from, say, much smaller than a proton, to about the size of the Earth or Solar System in a few Planck intervals. If it begins small, or if you run the clock backward it becomes progressively smaller, how could it have started with infinite spatial extent? Don't you see something wrong with the model?  AG

The model says that a subset of the universe starts small and gets bigger. This is not inconsistent with the whole universe starting and remaining infinite in spatial extent.

--

Stathis Papaioannou

I thought I made that clear; what I am calling "the universe" is precisely the SUBSET you refer to, which starts small and gets bigger. It is THAT SUBSET which cosmologists claim has infinite spatial extent, based on measurements. What you're calling "the whole universe" includes the underlying entity on which the BB started, and on which measurements CANNOT be made. It could be infinite in spatial extent, or is possibly an entity for which the concept of spatial extent might not exist. AG

As the bigbang is a singularity at the start... what prevents it to contain an infinite content in a zero/small volume, after all it's a singularity and we know only things after the big bang started ? and after inflation (which I understand is only space metric which inflate), there is still an infinite content.  

The BB is only a singularity as far as GR is concerned, because GR fails at that point in time. When we have a better theory, the alleged singularity at T = 0 will go away. What you call "infinite content in zero/ small volume" makes no sense, which is why we call this condition is called a singularity! How could the content be space, if you've have zero or small volume. This idea is immediately, and obviously, self contradictory. AG 

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[Quentin Anciaux]

Le lun. 13 janv. 2020 à 10:50, Alan Grayson <agrays...@gmail.com> a écrit :

On Monday, January 13, 2020 at 2:38:57 AM UTC-7, Quentin Anciaux wrote:

Le lun. 13 janv. 2020 à 10:28, Alan Grayson <agrays...@gmail.com> a écrit :

On Monday, January 13, 2020 at 1:33:01 AM UTC-7, stathisp wrote:

On Mon, 13 Jan 2020 at 13:48, Alan Grayson <agrays...@gmail.com> wrote:

On Sunday, January 12, 2020 at 8:58:06 AM UTC-7, John Clark wrote:

On Thu, Jan 2, 2020 at 2:30 AM Alan Grayson <agrays...@gmail.com> wrote:
 

> If we're convinced it's finite in age, then it can't be infinite in spatial extent. AG

We don't know for sure our universe is infinite in size and we'll never know for sure because we'll never be able to measure precisely zero curvature with no error at all, but we do know it's pretty damn flat, if it's curved it's so slight that a light beam would have to go at least 500 times as far as our telescopes can see for it to return where it started. So if you respect the empirical evidence for the Big Bang but the idea of a beginning of a infinitely sized universe makes you unhappy then the Multiverse idea offers you an obvious solution, you get an infinitely large infinitely old Multiverse but with the observable universe having a beginning and being only finitely large. However I understand the Multiverse makes you unhappy too. I fear you may be destined to be unhappy.

By the way ... does the inverse also make you unhappy, something infinitely old but finite in spatial extent?

John K Clark

All the models pictorially represented, have the Universe beginning very small, and inflation is claimed to increase its size from, say, much smaller than a proton, to about the size of the Earth or Solar System in a few Planck intervals. If it begins small, or if you run the clock backward it becomes progressively smaller, how could it have started with infinite spatial extent? Don't you see something wrong with the model?  AG

The model says that a subset of the universe starts small and gets bigger. This is not inconsistent with the whole universe starting and remaining infinite in spatial extent.

--

Stathis Papaioannou

I thought I made that clear; what I am calling "the universe" is precisely the SUBSET you refer to, which starts small and gets bigger. It is THAT SUBSET which cosmologists claim has infinite spatial extent, based on measurements. What you're calling "the whole universe" includes the underlying entity on which the BB started, and on which measurements CANNOT be made. It could be infinite in spatial extent, or is possibly an entity for which the concept of spatial extent might not exist. AG

And so what do you see not contradictory in the existence of the universe itself ? Either it has always been, or not, and if not, that makes no sense. I see nothing contradictory to have something infinite, so it could always has  been infinite in content, seeing it as zero volume is a mistake because that presuppose  a volume in another space. What I'm saying is that there was infinite content (and still is) but all metrics (space) was of zero extends, and inflation extended the "space" not the content.

Anyway, in the end, there can't be an explanation which make sense. The fact we're here in the first place being able to ask question is magical.

Quentin

As the bigbang is a singularity at the start... what prevents it to contain an infinite content in a zero/small volume, after all it's a singularity and we know only things after the big bang started ? and after inflation (which I understand is only space metric which inflate), there is still an infinite content.  

The BB is only a singularity as far as GR is concerned, because GR fails at that point in time. When we have a better theory, the alleged singularity at T = 0 will go away. What you call "infinite content in zero/ small volume" makes no sense, which is why we call this condition is called a singularity! How could the content be space, if you've have zero or small volume. This idea is immediately, and obviously, self contradictory. AG 

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

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[Alan Grayson]

On Monday, January 13, 2020 at 2:54:48 AM UTC-7, Quentin Anciaux wrote:

Le lun. 13 janv. 2020 à 10:50, Alan Grayson <agrays...@gmail.com> a écrit :

On Monday, January 13, 2020 at 2:38:57 AM UTC-7, Quentin Anciaux wrote:

Le lun. 13 janv. 2020 à 10:28, Alan Grayson <agrays...@gmail.com> a écrit :

On Monday, January 13, 2020 at 1:33:01 AM UTC-7, stathisp wrote:

On Mon, 13 Jan 2020 at 13:48, Alan Grayson <agrays...@gmail.com> wrote:

On Sunday, January 12, 2020 at 8:58:06 AM UTC-7, John Clark wrote:

On Thu, Jan 2, 2020 at 2:30 AM Alan Grayson <agrays...@gmail.com> wrote:
 

> If we're convinced it's finite in age, then it can't be infinite in spatial extent. AG

We don't know for sure our universe is infinite in size and we'll never know for sure because we'll never be able to measure precisely zero curvature with no error at all, but we do know it's pretty damn flat, if it's curved it's so slight that a light beam would have to go at least 500 times as far as our telescopes can see for it to return where it started. So if you respect the empirical evidence for the Big Bang but the idea of a beginning of a infinitely sized universe makes you unhappy then the Multiverse idea offers you an obvious solution, you get an infinitely large infinitely old Multiverse but with the observable universe having a beginning and being only finitely large. However I understand the Multiverse makes you unhappy too. I fear you may be destined to be unhappy.

By the way ... does the inverse also make you unhappy, something infinitely old but finite in spatial extent?

John K Clark

All the models pictorially represented, have the Universe beginning very small, and inflation is claimed to increase its size from, say, much smaller than a proton, to about the size of the Earth or Solar System in a few Planck intervals. If it begins small, or if you run the clock backward it becomes progressively smaller, how could it have started with infinite spatial extent? Don't you see something wrong with the model?  AG

The model says that a subset of the universe starts small and gets bigger. This is not inconsistent with the whole universe starting and remaining infinite in spatial extent.

--

Stathis Papaioannou

I thought I made that clear; what I am calling "the universe" is precisely the SUBSET you refer to, which starts small and gets bigger. It is THAT SUBSET which cosmologists claim has infinite spatial extent, based on measurements. What you're calling "the whole universe" includes the underlying entity on which the BB started, and on which measurements CANNOT be made. It could be infinite in spatial extent, or is possibly an entity for which the concept of spatial extent might not exist. AG

And so what do you see not contradictory in the existence of the universe itself ? Either it has always been, or not, and if not, that makes no sense. I see nothing contradictory to have something infinite, so it could always has  been infinite in content, seeing it as zero volume is a mistake because that presuppose  a volume in another space. What I'm saying is that there was infinite content (and still is) but all metrics (space) was of zero extends, and inflation extended the "space" not the content.

I don't think you understand the issue I've raised; namely, if our bubble has a finite age and is expanding, it must be finite in spatial extent since the expansion rate is finite. But a flat universe, claimed by most, maybe all cosmologists, is infinite in spatial extent. How could it start infinite in spatial extent, yet be tiny in the beginning? I conclude that our universe, that is, our bubble (which doesn't include the substratum from which it arose), must be spherical and closed. AG

Anyway, in the end, there can't be an explanation which make sense. The fact we're here in the first place being able to ask question is magical.

Quentin

As the bigbang is a singularity at the start... what prevents it to contain an infinite content in a zero/small volume, after all it's a singularity and we know only things after the big bang started ? and after inflation (which I understand is only space metric which inflate), there is still an infinite content.  

The BB is only a singularity as far as GR is concerned, because GR fails at that point in time. When we have a better theory, the alleged singularity at T = 0 will go away. What you call "infinite content in zero/ small volume" makes no sense, which is why we call this condition is called a singularity! How could the content be space, if you've have zero or small volume. This idea is immediately, and obviously, self contradictory. AG 

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

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[Quentin Anciaux]

Le lun. 13 janv. 2020 à 11:10, Alan Grayson <agrays...@gmail.com> a écrit :

On Monday, January 13, 2020 at 2:54:48 AM UTC-7, Quentin Anciaux wrote:

Le lun. 13 janv. 2020 à 10:50, Alan Grayson <agrays...@gmail.com> a écrit :

On Monday, January 13, 2020 at 2:38:57 AM UTC-7, Quentin Anciaux wrote:

Le lun. 13 janv. 2020 à 10:28, Alan Grayson <agrays...@gmail.com> a écrit :

On Monday, January 13, 2020 at 1:33:01 AM UTC-7, stathisp wrote:

On Mon, 13 Jan 2020 at 13:48, Alan Grayson <agrays...@gmail.com> wrote:

On Sunday, January 12, 2020 at 8:58:06 AM UTC-7, John Clark wrote:

On Thu, Jan 2, 2020 at 2:30 AM Alan Grayson <agrays...@gmail.com> wrote:
 

> If we're convinced it's finite in age, then it can't be infinite in spatial extent. AG

We don't know for sure our universe is infinite in size and we'll never know for sure because we'll never be able to measure precisely zero curvature with no error at all, but we do know it's pretty damn flat, if it's curved it's so slight that a light beam would have to go at least 500 times as far as our telescopes can see for it to return where it started. So if you respect the empirical evidence for the Big Bang but the idea of a beginning of a infinitely sized universe makes you unhappy then the Multiverse idea offers you an obvious solution, you get an infinitely large infinitely old Multiverse but with the observable universe having a beginning and being only finitely large. However I understand the Multiverse makes you unhappy too. I fear you may be destined to be unhappy.

By the way ... does the inverse also make you unhappy, something infinitely old but finite in spatial extent?

John K Clark

All the models pictorially represented, have the Universe beginning very small, and inflation is claimed to increase its size from, say, much smaller than a proton, to about the size of the Earth or Solar System in a few Planck intervals. If it begins small, or if you run the clock backward it becomes progressively smaller, how could it have started with infinite spatial extent? Don't you see something wrong with the model?  AG

The model says that a subset of the universe starts small and gets bigger. This is not inconsistent with the whole universe starting and remaining infinite in spatial extent.

--

Stathis Papaioannou

I thought I made that clear; what I am calling "the universe" is precisely the SUBSET you refer to, which starts small and gets bigger. It is THAT SUBSET which cosmologists claim has infinite spatial extent, based on measurements. What you're calling "the whole universe" includes the underlying entity on which the BB started, and on which measurements CANNOT be made. It could be infinite in spatial extent, or is possibly an entity for which the concept of spatial extent might not exist. AG

And so what do you see not contradictory in the existence of the universe itself ? Either it has always been, or not, and if not, that makes no sense. I see nothing contradictory to have something infinite, so it could always has  been infinite in content, seeing it as zero volume is a mistake because that presuppose  a volume in another space. What I'm saying is that there was infinite content (and still is) but all metrics (space) was of zero extends, and inflation extended the "space" not the content.

I don't think you understand the issue I've raised; namely, if our bubble has a finite age and is expanding, it must be finite in spatial extent since the expansion rate is finite. But a flat universe, claimed by most, maybe all cosmologists, is infinite in spatial extent. How could it start infinite in spatial extent, yet be tiny in the beginning? I conclude that our universe, that is, our bubble (which doesn't include the substratum from which it arose), must be spherical and closed. AG

If the content was infinite, but space metric inflated from zero to something, the result is still infinite and space arise, as there was an infinity of space whose metric got bigger, there is still infinity after inflation, just more empty space in between matter. 

Anyway, in the end, there can't be an explanation which make sense. The fact we're here in the first place being able to ask question is magical.

Quentin

As the bigbang is a singularity at the start... what prevents it to contain an infinite content in a zero/small volume, after all it's a singularity and we know only things after the big bang started ? and after inflation (which I understand is only space metric which inflate), there is still an infinite content.  

The BB is only a singularity as far as GR is concerned, because GR fails at that point in time. When we have a better theory, the alleged singularity at T = 0 will go away. What you call "infinite content in zero/ small volume" makes no sense, which is why we call this condition is called a singularity! How could the content be space, if you've have zero or small volume. This idea is immediately, and obviously, self contradictory. AG 

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[Alan Grayson]

On Monday, January 13, 2020 at 3:13:57 AM UTC-7, Quentin Anciaux wrote:

Le lun. 13 janv. 2020 à 11:10, Alan Grayson <agrays...@gmail.com> a écrit :

On Monday, January 13, 2020 at 2:54:48 AM UTC-7, Quentin Anciaux wrote:

Le lun. 13 janv. 2020 à 10:50, Alan Grayson <agrays...@gmail.com> a écrit :

On Monday, January 13, 2020 at 2:38:57 AM UTC-7, Quentin Anciaux wrote:

Le lun. 13 janv. 2020 à 10:28, Alan Grayson <agrays...@gmail.com> a écrit :

On Monday, January 13, 2020 at 1:33:01 AM UTC-7, stathisp wrote:

On Mon, 13 Jan 2020 at 13:48, Alan Grayson <agrays...@gmail.com> wrote:

On Sunday, January 12, 2020 at 8:58:06 AM UTC-7, John Clark wrote:

On Thu, Jan 2, 2020 at 2:30 AM Alan Grayson <agrays...@gmail.com> wrote:
 

> If we're convinced it's finite in age, then it can't be infinite in spatial extent. AG

We don't know for sure our universe is infinite in size and we'll never know for sure because we'll never be able to measure precisely zero curvature with no error at all, but we do know it's pretty damn flat, if it's curved it's so slight that a light beam would have to go at least 500 times as far as our telescopes can see for it to return where it started. So if you respect the empirical evidence for the Big Bang but the idea of a beginning of a infinitely sized universe makes you unhappy then the Multiverse idea offers you an obvious solution, you get an infinitely large infinitely old Multiverse but with the observable universe having a beginning and being only finitely large. However I understand the Multiverse makes you unhappy too. I fear you may be destined to be unhappy.

By the way ... does the inverse also make you unhappy, something infinitely old but finite in spatial extent?

John K Clark

All the models pictorially represented, have the Universe beginning very small, and inflation is claimed to increase its size from, say, much smaller than a proton, to about the size of the Earth or Solar System in a few Planck intervals. If it begins small, or if you run the clock backward it becomes progressively smaller, how could it have started with infinite spatial extent? Don't you see something wrong with the model?  AG

The model says that a subset of the universe starts small and gets bigger. This is not inconsistent with the whole universe starting and remaining infinite in spatial extent.

--

Stathis Papaioannou

I thought I made that clear; what I am calling "the universe" is precisely the SUBSET you refer to, which starts small and gets bigger. It is THAT SUBSET which cosmologists claim has infinite spatial extent, based on measurements. What you're calling "the whole universe" includes the underlying entity on which the BB started, and on which measurements CANNOT be made. It could be infinite in spatial extent, or is possibly an entity for which the concept of spatial extent might not exist. AG

And so what do you see not contradictory in the existence of the universe itself ? Either it has always been, or not, and if not, that makes no sense. I see nothing contradictory to have something infinite, so it could always has  been infinite in content, seeing it as zero volume is a mistake because that presuppose  a volume in another space. What I'm saying is that there was infinite content (and still is) but all metrics (space) was of zero extends, and inflation extended the "space" not the content.

I don't think you understand the issue I've raised; namely, if our bubble has a finite age and is expanding, it must be finite in spatial extent since the expansion rate is finite. But a flat universe, claimed by most, maybe all cosmologists, is infinite in spatial extent. How could it start infinite in spatial extent, yet be tiny in the beginning? I conclude that our universe, that is, our bubble (which doesn't include the substratum from which it arose), must be spherical and closed. AG

If the content was infinite, but space metric inflated from zero to something, the result is still infinite and space arise, as there was an infinity of space whose metric got bigger, there is still infinity after inflation, just more empty space in between matter. 

Forget about matter. I am discussing spatial extent. If it starts small, and expands at any rate less than infinite, its spatial extent cannot be infinite. AG 

Anyway, in the end, there can't be an explanation which make sense. The fact we're here in the first place being able to ask question is magical.

Quentin

As the bigbang is a singularity at the start... what prevents it to contain an infinite content in a zero/small volume, after all it's a singularity and we know only things after the big bang started ? and after inflation (which I understand is only space metric which inflate), there is still an infinite content.  

The BB is only a singularity as far as GR is concerned, because GR fails at that point in time. When we have a better theory, the alleged singularity at T = 0 will go away. What you call "infinite content in zero/ small volume" makes no sense, which is why we call this condition is called a singularity! How could the content be space, if you've have zero or small volume. This idea is immediately, and obviously, self contradictory. AG 

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[Quentin Anciaux]

Le lun. 13 janv. 2020 à 11:21, Alan Grayson <agrays...@gmail.com> a écrit :

On Monday, January 13, 2020 at 3:13:57 AM UTC-7, Quentin Anciaux wrote:

Le lun. 13 janv. 2020 à 11:10, Alan Grayson <agrays...@gmail.com> a écrit :

On Monday, January 13, 2020 at 2:54:48 AM UTC-7, Quentin Anciaux wrote:

Le lun. 13 janv. 2020 à 10:50, Alan Grayson <agrays...@gmail.com> a écrit :

On Monday, January 13, 2020 at 2:38:57 AM UTC-7, Quentin Anciaux wrote:

Le lun. 13 janv. 2020 à 10:28, Alan Grayson <agrays...@gmail.com> a écrit :

On Monday, January 13, 2020 at 1:33:01 AM UTC-7, stathisp wrote:

On Mon, 13 Jan 2020 at 13:48, Alan Grayson <agrays...@gmail.com> wrote:

On Sunday, January 12, 2020 at 8:58:06 AM UTC-7, John Clark wrote:

On Thu, Jan 2, 2020 at 2:30 AM Alan Grayson <agrays...@gmail.com> wrote:
 

> If we're convinced it's finite in age, then it can't be infinite in spatial extent. AG

We don't know for sure our universe is infinite in size and we'll never know for sure because we'll never be able to measure precisely zero curvature with no error at all, but we do know it's pretty damn flat, if it's curved it's so slight that a light beam would have to go at least 500 times as far as our telescopes can see for it to return where it started. So if you respect the empirical evidence for the Big Bang but the idea of a beginning of a infinitely sized universe makes you unhappy then the Multiverse idea offers you an obvious solution, you get an infinitely large infinitely old Multiverse but with the observable universe having a beginning and being only finitely large. However I understand the Multiverse makes you unhappy too. I fear you may be destined to be unhappy.

By the way ... does the inverse also make you unhappy, something infinitely old but finite in spatial extent?

John K Clark

All the models pictorially represented, have the Universe beginning very small, and inflation is claimed to increase its size from, say, much smaller than a proton, to about the size of the Earth or Solar System in a few Planck intervals. If it begins small, or if you run the clock backward it becomes progressively smaller, how could it have started with infinite spatial extent? Don't you see something wrong with the model?  AG

The model says that a subset of the universe starts small and gets bigger. This is not inconsistent with the whole universe starting and remaining infinite in spatial extent.

--

Stathis Papaioannou

I thought I made that clear; what I am calling "the universe" is precisely the SUBSET you refer to, which starts small and gets bigger. It is THAT SUBSET which cosmologists claim has infinite spatial extent, based on measurements. What you're calling "the whole universe" includes the underlying entity on which the BB started, and on which measurements CANNOT be made. It could be infinite in spatial extent, or is possibly an entity for which the concept of spatial extent might not exist. AG

And so what do you see not contradictory in the existence of the universe itself ? Either it has always been, or not, and if not, that makes no sense. I see nothing contradictory to have something infinite, so it could always has  been infinite in content, seeing it as zero volume is a mistake because that presuppose  a volume in another space. What I'm saying is that there was infinite content (and still is) but all metrics (space) was of zero extends, and inflation extended the "space" not the content.

I don't think you understand the issue I've raised; namely, if our bubble has a finite age and is expanding, it must be finite in spatial extent since the expansion rate is finite. But a flat universe, claimed by most, maybe all cosmologists, is infinite in spatial extent. How could it start infinite in spatial extent, yet be tiny in the beginning? I conclude that our universe, that is, our bubble (which doesn't include the substratum from which it arose), must be spherical and closed. AG

If the content was infinite, but space metric inflated from zero to something, the result is still infinite and space arise, as there was an infinity of space whose metric got bigger, there is still infinity after inflation, just more empty space in between matter. 

Forget about matter. I am discussing spatial extent. If it starts small, and expands at any rate less than infinite, its spatial extent cannot be infinite. AG 

But space is the thing in between matter, without any matter, there is no space... at the start, there was no extend in between matter, after inflation there is, if there was an infinity of matter, then after inflation there are still infinity and spatial extend even if not infinite in between two things, is infinite globally. 

Anyway, in the end, there can't be an explanation which make sense. The fact we're here in the first place being able to ask question is magical.

Quentin

As the bigbang is a singularity at the start... what prevents it to contain an infinite content in a zero/small volume, after all it's a singularity and we know only things after the big bang started ? and after inflation (which I understand is only space metric which inflate), there is still an infinite content.  

The BB is only a singularity as far as GR is concerned, because GR fails at that point in time. When we have a better theory, the alleged singularity at T = 0 will go away. What you call "infinite content in zero/ small volume" makes no sense, which is why we call this condition is called a singularity! How could the content be space, if you've have zero or small volume. This idea is immediately, and obviously, self contradictory. AG 

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[Stathis Papaioannou]

The visible universe started small and got bigger, but no-one claims the visible universe is infinite. But maybe the universe continues forever beyond the visible universe. This is not inconsistent with the universe having a beginning and expanding.

--

Stathis Papaioannou

[John Clark]

On Mon, Jan 13, 2020 at 1:18 AM Alan Grayson <agrays...@gmail.com> wrote:

> My hunch, and that's all it is, is that "the substratum" from which the BB emerged, is infinitely old, and the concept of spatial extent probably doesn't apply to it. There could be many BB's, possibly an infinite number, but all finite in spatial extent if they had beginnings. AG

If, as this one does, all the Big Bang's have a finite number of particles and are all of finite spatial extent then there is only a finite number of ways those particles can be arranged. But if there are a infinite number of those Big Bang's then in one of them (actually in a infinite number of them) there must be an arrangement of particles that are identical to you in every way except he spells his last name "Greyson" not "Grayson". So I guess both Mr. Greyson and Mr. Grayson have changed their minds and now believe in the existence of the Multiverse.

John K Clark

[John Clark]

On Mon, Jan 13, 2020 at 4:50 AM Alan Grayson <agrays...@gmail.com> wrote:

> The BB is only a singularity as far as GR is concerned, because GR fails at that point in time.

General Relativity is not the only thing that fails at the singularity, Quantum Mechanics does too. In physics what a "singularity" means is the place where our current theories break down and start producing nonsensical results like infinite curvature and negative probabilities.

 John K Clark

[John Clark]

On Mon, Jan 13, 2020 at 5:10 AM Alan Grayson <agrays...@gmail.com> wrote:

> if our bubble has a finite age and is expanding, it must be finite in spatial extent since the expansion rate is finite.

Space would not have to expand infinitely fast just faster than light, and that is allowed under General Relativity, in fact that is exactly what Inflation hypothesizes. If that is indeed the case then no matter how fast 2 particles are moving away from each other they can keep getting further and further apart forever and never meet each other again. And that's what a universe with infinite spatial extent means.

 John K Clark

[Alan Grayson]

Due to the expansion of the universe, distant galaxies will eventually wink-out as they enter the non-observable region. This is a purely geometric effect of expansion, and will occur whether the rate is faster than the SoL or not.  Moreover, infinite spatial extent means that a beam of light will never return to its starting point, as it would for a spherical surface. For a flat surface, a beam in any direction never returns to its starting point. THIS is what infinite spatial extent MEANS., not what your wrote above. AG 

[Alan Grayson]

Specifically, how does QM fail at the singularity where GR fails? AG 

[Alan Grayson]

While GR allows expansion faster than the SoL, this is NOT a necessary condition for one particle to enter the non-observable region from another particle's pov. All that's needed is for the expansion to continue long enough. This is because the winking out is purely a geometric effect of the expansion. AG 

[John Clark]

On Mon, Jan 13, 2020 at 8:05 AM Alan Grayson <agrays...@gmail.com> wrote:

 > infinite spatial extent means that a beam of light will never return to its starting point, as it would for a spherical surface. For a flat surface, a beam in any direction never returns to its starting point. THIS is what infinite spatial extent MEANS.

I agree. And if inflation is correct and in the very early universe the distance between any 2 points expanded faster than light then they've moved beyond their observable horizon and once you've done that you can't go back, so even today a beam of light sent from one of those points can never reach the other.

 John K Clark

 

[Alan Grayson]

I think you're making the assumption that the possible arrangement of a finite set of particles of finite extent corresponds to a countable set. But if space is continuous, that assumption fails, and with it your entire thesis. There is only ONE Grayson, thankfully. AG

[John Clark]

On Mon, Jan 13, 2020 at 8:13 AM Alan Grayson <agrays...@gmail.com> wrote:

> the winking out is purely a geometric effect of the expansion.

I have no idea what you mean by that but if something is beyond your observable horizon then nothing you do can have any effect on it and nothing it does can have any effect on you.

John K Clark

[Alan Grayson]

What I am claiming is that the universe beyond what is observable is NOT infinite in spatial extent. It's finite because it starts out small and has been expanding for finite time. AG 

--

Stathis Papaioannou

[Alan Grayson]

Right, and that's how the non-observable region is created during inflation, but it would occur independent of the rate of expansion, provided the expansion continues. Like I said, it's a purely geometric effect of expansion. AG 

 

[John Clark]

On Mon, Jan 13, 2020 at 8:18 AM Alan Grayson <agrays...@gmail.com> wrote:

>> If, as this one does, all the Big Bang's have a finite number of particles and are all of finite spatial extent then there is only a finite number of ways those particles can be arranged. But if there are a infinite number of those Big Bang's then in one of them (actually in a infinite number of them) there must be an arrangement of particles that are identical to you in every way except he spells his last name "Greyson" not "Grayson". So I guess both Mr. Greyson and Mr. Grayson have changed their minds and now believe in the existence of the Multiverse.

> I think you're making the assumption that the possible arrangement of a finite set of particles of finite extent corresponds to a countable set. But if space is continuous, that assumption fails, and with it your entire thesis.

Regardless of if there are a infinite number of particles in a line an inch long or just a ridiculously astronomically large number of them there would certainly be enough to include something that had all your observable characteristics except for the way it spelled its last name.

 

> There is only ONE Grayson, thankfully. 

Um... there are two ways that could be interpreted....

John K Clark

[Alan Grayson]

Suppose you're sitting at the origin of a one-dimension space. A line 100 meters long will increase 1 meter per unit time if the rate of expansion is 1% per unit time. If the line is a 1000 meters long, the end point moves away 10 meters per unit time, and so forth. So if the line is long enough, the length will eventually increase more than 300,000 km, for any rate of expansion per unit time. 300,000 km is the distance light travels in one second. Thus, the end point will eventually increase in distance more than can be overcome by light traveling at c. This is what I mean by a purely geometric effect. Brent showed me this awhile back, and it was an A-HA moment!  Winking out of distant galaxies does NOT depend on the rate of expansion; only that it continues. AG 

[John Clark]

On Mon, Jan 13, 2020 at 8:34 AM Alan Grayson <agrays...@gmail.com> wrote:

>> if inflation is correct and in the very early universe the distance between any 2 points expanded faster than light then they've moved beyond their observable horizon and once you've done that you can't go back, so even today a beam of light sent from one of those points can never reach the other.

> Right, and that's how the non-observable region is created during inflation, but it would occur independent of the rate of expansion, provided the expansion continues. Like I said, it's a purely geometric effect of expansion. AG 

Then I'm not sure what we're arguing about. Have you endowed the word "purely" with some meaning not in common usage? 

John K Clark

 

 

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[Quentin Anciaux]

--

It is the space that is expanding, so you can have it starting infinite at the big bang, just everything was nearer and nearer. So if it started infinitely dense, everything was at one point without any space, then space emerged, and it was already infinite in spatial extend at that point.

Why are you ok with something starting infinitely dense, and not with infinite amount of matter, that our observable part doesn't contains an infinity of matter is normal, but that was an infinitely small part of the infinitely dense starting point.

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[Alan Grayson]

That's your claim, but an assertion isn't a proof. Personally, I don't believe in repeats, and I think the proof, if there is one, has to do with continuity or uncountability. AG 

[John Clark]

Alan Grayson <agrays...@gmail.com> wrote:

> Suppose you're sitting at the origin of a one-dimension space. A line 100 meters long will increase 1 meter per unit time if the rate of expansion is 1% per unit time. If the line is a 1000 meters long, the end point moves away 10 meters per unit time, and so forth. So if the line is long enough, the length will eventually increase more than 300,000 km, for any rate of expansion per unit time. 300,000 km is the distance light travels in one second. Thus, the end point will eventually increase in distance more than can be overcome by light traveling at c. This is what I mean by a purely geometric effect. Brent showed me this awhile back, and it was an A-HA moment!  Winking out of distant galaxies does NOT depend on the rate of expansion; only that it continues. AG 

OK suppose you look to your right as far as you can and measure the temperature at that point, and then look to the left and do the same thing. You will find that the two temperatures are the same to one part in a hundred thousand; and yet if inflation is wrong and the universal expansion rate was always about what it is now those 2 points could have NEVER been in casual contact with each other. So why are the two temperatures so similar?

 John K Clark 

[Bruno Marchal]

On 13 Jan 2020, at 10:54, Quentin Anciaux <allc...@gmail.com> wrote:

Le lun. 13 janv. 2020 à 10:50, Alan Grayson <agrays...@gmail.com> a écrit :

On Monday, January 13, 2020 at 2:38:57 AM UTC-7, Quentin Anciaux wrote:

Le lun. 13 janv. 2020 à 10:28, Alan Grayson <agrays...@gmail.com> a écrit :

On Monday, January 13, 2020 at 1:33:01 AM UTC-7, stathisp wrote:

On Mon, 13 Jan 2020 at 13:48, Alan Grayson <agrays...@gmail.com> wrote:

On Sunday, January 12, 2020 at 8:58:06 AM UTC-7, John Clark wrote:

On Thu, Jan 2, 2020 at 2:30 AM Alan Grayson <agrays...@gmail.com> wrote:
 

> If we're convinced it's finite in age, then it can't be infinite in spatial extent. AG

We don't know for sure our universe is infinite in size and we'll never know for sure because we'll never be able to measure precisely zero curvature with no error at all, but we do know it's pretty damn flat, if it's curved it's so slight that a light beam would have to go at least 500 times as far as our telescopes can see for it to return where it started. So if you respect the empirical evidence for the Big Bang but the idea of a beginning of a infinitely sized universe makes you unhappy then the Multiverse idea offers you an obvious solution, you get an infinitely large infinitely old Multiverse but with the observable universe having a beginning and being only finitely large. However I understand the Multiverse makes you unhappy too. I fear you may be destined to be unhappy.

By the way ... does the inverse also make you unhappy, something infinitely old but finite in spatial extent?

John K Clark

All the models pictorially represented, have the Universe beginning very small, and inflation is claimed to increase its size from, say, much smaller than a proton, to about the size of the Earth or Solar System in a few Planck intervals. If it begins small, or if you run the clock backward it becomes progressively smaller, how could it have started with infinite spatial extent? Don't you see something wrong with the model?  AG

The model says that a subset of the universe starts small and gets bigger. This is not inconsistent with the whole universe starting and remaining infinite in spatial extent.

--

Stathis Papaioannou

I thought I made that clear; what I am calling "the universe" is precisely the SUBSET you refer to, which starts small and gets bigger. It is THAT SUBSET which cosmologists claim has infinite spatial extent, based on measurements. What you're calling "the whole universe" includes the underlying entity on which the BB started, and on which measurements CANNOT be made. It could be infinite in spatial extent, or is possibly an entity for which the concept of spatial extent might not exist. AG

And so what do you see not contradictory in the existence of the universe itself ? Either it has always been, or not, and if not, that makes no sense. I see nothing contradictory to have something infinite, so it could always has  been infinite in content, seeing it as zero volume is a mistake because that presuppose  a volume in another space. What I'm saying is that there was infinite content (and still is) but all metrics (space) was of zero extends, and inflation extended the "space" not the content.

Anyway, in the end, there can't be an explanation which make sense. The fact we're here in the first place being able to ask question is magical.

Eventually the magic can be reduced to the magic of the laws of addition and multiplication of natural numbers (or integers, or rational number, or complex number, but not real numbers, note).

From 2+2=4 & Co, or from KKK = K & Co, we can prove the existence of all universal (Turing complete) entities, and that explains both consciousness and the appearance of a physical reality. That one has to be “many-worlds” like, and obey some logical formalism, and up to now, the Digital Mechanist theory is confirmed by the facts. That would not be the case if we did have evidence that the observable obey Boolean logic. That gives the only precise and testable theory of both consciousness and matter compatible with Digital Mechanism.

Now, the machine’s physics is not advanced enough to say anything about the Big Bang. By some aspect, mechanism favours string theory, but on different aspects it fits far better with loop gravity. To decide more on this there is a long sequence of mathematical problem to solve, notably to extract some operator algebra from the machine’s already derived quantum logics. The quantum logics are graded, and if they verify some conditions, the appearance of space would come from a sort of percolation mechanism on coherent set of first person sharable experiences. 

Physicalism has not been disprove, but it is disproved in any theory assuming enough of Mechanism to make sense of a theory like the theory of evolution, which foresaw the digitalness needed to make sense of the evolution of physical mechanism.

Bruno

Quentin

As the bigbang is a singularity at the start... what prevents it to contain an infinite content in a zero/small volume, after all it's a singularity and we know only things after the big bang started ? and after inflation (which I understand is only space metric which inflate), there is still an infinite content.  

The BB is only a singularity as far as GR is concerned, because GR fails at that point in time. When we have a better theory, the alleged singularity at T = 0 will go away. What you call "infinite content in zero/ small volume" makes no sense, which is why we call this condition is called a singularity! How could the content be space, if you've have zero or small volume. This idea is immediately, and obviously, self contradictory. AG 

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[John Clark]

On Mon, Jan 13, 2020 at 8:49 AM Alan Grayson <agrays...@gmail.com> wrote:

>  Personally, I don't believe in repeats, and I think the proof, if there is one, has to do with continuity or uncountability. 

General Relativity says there are an infinite number of states in spacetime that something can be in, but Quantum Mechanics says the number is only astronomically large. As far as the question of personal identity is concerned I don't see how it makes any difference which one is correct. If personal identity is so delicate that moving one electron less than the Planck Length is important then you become a radically different person every time you take a sip of coffee.

 John K Clark

[Stathis Papaioannou]

On Tue, 14 Jan 2020 at 00:25, Alan Grayson 

What I am claiming is that the universe beyond what is observable is NOT infinite in spatial extent. It's finite because it starts out small and has been expanding for finite time. AG 

The universe could have started off infinite and expanded rather than starting off finite and then expanding infinitely fast.

--

Stathis Papaioannou

[Alan Grayson]

I wasn't denying inflation as an hypothesis to explain homogeneity. All I was asserting that one doesn't need faster than light expansion to produce regions that are not observable. AG 

[Alan Grayson]

On Monday, January 13, 2020 at 7:28:27 AM UTC-7, John Clark wrote:

On Mon, Jan 13, 2020 at 8:49 AM Alan Grayson <agrays...@gmail.com> wrote:

>  Personally, I don't believe in repeats, and I think the proof, if there is one, has to do with continuity or uncountability. 

General Relativity says there are an infinite number of states in spacetime that something can be in, but Quantum Mechanics says the number is only astronomically large.

There are systems for which the eigen spectrum of possible experimental outcomes is continuous, thus infinite. AG 

[Brent Meeker]

On 1/13/2020 2:10 AM, Alan Grayson wrote:

The model says that a subset of the universe starts small and gets bigger. This is not inconsistent with the whole universe starting and remaining infinite in spatial extent.

--

Stathis Papaioannou

I thought I made that clear; what I am calling "the universe" is precisely the SUBSET you refer to, which starts small and gets bigger. It is THAT SUBSET which cosmologists claim has infinite spatial extent, based on measurements.

First, a proper subset of an infinite set can also be infinite (in fact that's one definition of "infinite").  Second, nobody measures an infinite portion of the universe.  We can only measure the curvature of the part we can see. Third, it is not clear what is THAT SUBSET to which you refer.  Cosmologists are aware that only an initially infinite subset of space can be infinite after a finite expansion.  They refer to a part of the universe that is beyond observation as being within the "particle horizon" because it consists of the evolved locations of things which are seen now as they were 14 billion years ago.  Those things are now 49 billion light years away due to the expansion...which is sometimes referred to as the present diameter of the observable universe.https://en.wikipedia.org/wiki/Particle_horizon

Brent

[Brent Meeker]

On 1/13/2020 2:21 AM, Alan Grayson wrote:

Forget about matter. I am discussing spatial extent. If it starts small, and expands at any rate less than infinite, its spatial extent cannot be infinite. AG 

But so what?  What is "it"?  and what are you worried about?  If "it" is some portion of the universe we can see, it's finite.  The inference that the universe is infinite is based on curvature measure in the part we can see.  It doesn't prove the universe is infinite...proof is for mathematicians...but it makes it the way to bet.

Brent

[Alan Grayson]

On Monday, January 13, 2020 at 11:12:36 AM UTC-7, Brent wrote:

On 1/13/2020 2:10 AM, Alan Grayson wrote:

The model says that a subset of the universe starts small and gets bigger. This is not inconsistent with the whole universe starting and remaining infinite in spatial extent.

--

Stathis Papaioannou

I thought I made that clear; what I am calling "the universe" is precisely the SUBSET you refer to, which starts small and gets bigger. It is THAT SUBSET which cosmologists claim has infinite spatial extent, based on measurements.

First, a proper subset of an infinite set can also be infinite (in fact that's one definition of "infinite"). 

True. AG

 

Second, nobody measures an infinite portion of the universe.

I never made that claim. AG

 

  We can only measure the curvature of the part we can see.

I never claimed otherwise. How could we measure what we can't (in some sense) see? Impossible! AG

 

Third, it is not clear what is THAT SUBSET to which you refer. 

I'm referring to the observable and non-observable regions. When cosmologists claim the universe is flat, they're referring to these regions and nothing else. It does NOT include the underlying entity from which our bubble emerged. Thus, a subset of a possibly larger totality. AG 

 

Cosmologists are aware that only an initially infinite subset of space can be infinite after a finite expansion.

So, at the instant of the BB, that is"initially", there's a process which creates an infinity of space having zero time duration? How is this different from a singularity? This is where I have a problem. There is no process that can create anything, let alone a spatial infinity, with no time passing. AG

[Alan Grayson]

On Monday, January 13, 2020 at 11:20:41 AM UTC-7, Brent wrote:

On 1/13/2020 2:21 AM, Alan Grayson wrote:

Forget about matter. I am discussing spatial extent. If it starts small, and expands at any rate less than infinite, its spatial extent cannot be infinite. AG 

But so what?  What is "it"?  and what are you worried about?  If "it" is some portion of the universe we can see, it's finite.  The inference that the universe is infinite is based on curvature measure in the part we can see. 

IT, the universe, has (IMO) a very small but positive curvature, which is what we measure. Since we can't precisely measure zero curvature, as JC earlier stated, there's no way to distinguish the two cases -- flat and infinite in spatial extent versus spherical and finite in spatial extent -- on measurements. But since flat and infinite at the instant of the BB implies a singularity, I reject that model. AG 

[John Clark]

On Mon, Jan 13, 2020 at 1:08 PM Alan Grayson <agrays...@gmail.com> wrote:

> There are systems for which the eigen spectrum of possible experimental outcomes is continuous, thus infinite. AG 

If infinite distances makes you squeamish I don't see how you can consistently embrace infinite outcomes. And besides this is not mathematics, in physics nothing is provably infinite, nobody has ever found an infinite number of anything.

John K Clark

[Philip Thrift]

On Monday, January 13, 2020 at 12:20:41 PM UTC-6, Brent wrote:

 The inference that the universe is infinite is based on curvature measure in the part we can see. 

 

Brent

The universe could be perfectly "flat" and finite in extent.

Our galaxy could just be well within the interior of the finite space of the universe that it seems "the same" from any direction.

@philipthrift

 

[Brent Meeker]

On 1/13/2020 10:51 AM, Alan Grayson wrote:

On Monday, January 13, 2020 at 11:12:36 AM UTC-7, Brent wrote:

On 1/13/2020 2:10 AM, Alan Grayson wrote:

The model says that a subset of the universe starts small and gets bigger. This is not inconsistent with the whole universe starting and remaining infinite in spatial extent.

--

Stathis Papaioannou

I thought I made that clear; what I am calling "the universe" is precisely the SUBSET you refer to, which starts small and gets bigger. It is THAT SUBSET which cosmologists claim has infinite spatial extent, based on measurements.

First, a proper subset of an infinite set can also be infinite (in fact that's one definition of "infinite"). 

True. AG

 

Second, nobody measures an infinite portion of the universe.

I never made that claim. AG

 

  We can only measure the curvature of the part we can see.

I never claimed otherwise. How could we measure what we can't (in some sense) see? Impossible! AG

 

Third, it is not clear what is THAT SUBSET to which you refer. 

I'm referring to the observable and non-observable regions. When cosmologists claim the universe is flat, they're referring to these regions and nothing else. It does NOT include the underlying entity from which our bubble emerged. Thus, a subset of a possibly larger totality. AG 

 

Cosmologists are aware that only an initially infinite subset of space can be infinite after a finite expansion.

So, at the instant of the BB, that is"initially", there's a process which creates an infinity of space having zero time duration?

No.  If space is infinite then it was infinite at the start.  Or it might be finite and simply so inflated that our measure of curvature can't distinguish it from flat(=infinite).  Although there are ways space can be infinite on one slice but infinite on another slice (assuming time is future infinite).

Brent

How is this different from a singularity? This is where I have a problem. There is no process that can create anything, let alone a spatial infinity, with no time passing. AG

 

  They refer to a part of the universe that is beyond observation as being within the "particle horizon" because it consists of the evolved locations of things which are seen now as they were 14 billion years ago.  Those things are now 49 billion light years away due to the expansion...which is sometimes referred to as the present diameter of the observable universe.https://en.wikipedia.org/wiki/Particle_horizon

Brent

What you're calling "the whole universe" includes the underlying entity on which the BB started, and on which measurements CANNOT be made. It could be infinite in spatial extent, or is possibly an entity for which the concept of spatial extent might not exist. AG

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[Brent Meeker]

On 1/13/2020 11:02 AM, Alan Grayson wrote:

On Monday, January 13, 2020 at 11:20:41 AM UTC-7, Brent wrote:

On 1/13/2020 2:21 AM, Alan Grayson wrote:

Forget about matter. I am discussing spatial extent. If it starts small, and expands at any rate less than infinite, its spatial extent cannot be infinite. AG 

But so what?  What is "it"?  and what are you worried about?  If "it" is some portion of the universe we can see, it's finite.  The inference that the universe is infinite is based on curvature measure in the part we can see. 

IT, the universe, has (IMO) a very small but positive curvature, which is what we measure. Since we can't precisely measure zero curvature, as JC earlier stated, there's no way to distinguish the two cases -- flat and infinite in spatial extent versus spherical and finite in spatial extent -- on measurements. But since flat and infinite at the instant of the BB implies a singularity, I reject that model. AG

Fine.  Nobody thinks there was a singularity.

Brent

[Alan Grayson]

They think it's infinite at the beginning but always represent it as very small at the beginning. That's a great way to communicate. Would you buy a used car from one of those guys? AG 

[Philip Thrift]

On Monday, January 13, 2020 at 2:59:42 PM UTC-6, Alan Grayson wrote:

They think it's infinite at the beginning but always represent it as very small at the beginning. That's a great way to communicate. Would you buy a used car from one of those guys? AG 

One way to contrive (formulate) this pure-mathematically:

@ time 0: There's a very small 3D ball with a "particle" at every rational point - (x,y,z) where x,y,x are rational numbers - in the interior of the ball.

@ time 1 unit of Planck time: The particles are spread out "infinitely" but the spacing between the points is a small positive number (like some units of Planck distance)

@ time 2 units of Planck time:  The spacing between the points increases.

and so on.

@philipthrift

 

[Stathis Papaioannou]

The  visible universe is very small at the beginning, but the visible universe, at the beginning as now, may not be all that there is.

--

Stathis Papaioannou

[Brent Meeker]

No they represent all the universe we can interact with as small then.  If you have something to question, how about quoting it explicitly; instead of your interpretation.

Brent

That's a great way to communicate. Would you buy a used car from one of those guys? AG 

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[Alan Grayson]

On Monday, January 13, 2020 at 5:12:33 PM UTC-7, Brent wrote:

On 1/13/2020 12:59 PM, Alan Grayson wrote:

On Monday, January 13, 2020 at 1:22:05 PM UTC-7, Brent wrote:

On 1/13/2020 11:02 AM, Alan Grayson wrote:

On Monday, January 13, 2020 at 11:20:41 AM UTC-7, Brent wrote:

On 1/13/2020 2:21 AM, Alan Grayson wrote:

Forget about matter. I am discussing spatial extent. If it starts small, and expands at any rate less than infinite, its spatial extent cannot be infinite. AG 

But so what?  What is "it"?  and what are you worried about?  If "it" is some portion of the universe we can see, it's finite.  The inference that the universe is infinite is based on curvature measure in the part we can see. 

IT, the universe, has (IMO) a very small but positive curvature, which is what we measure. Since we can't precisely measure zero curvature, as JC earlier stated, there's no way to distinguish the two cases -- flat and infinite in spatial extent versus spherical and finite in spatial extent -- on measurements. But since flat and infinite at the instant of the BB implies a singularity, I reject that model. AG

Fine.  Nobody thinks there was a singularity.

Brent

They think it's infinite at the beginning but always represent it as very small at the beginning.

No they represent all the universe we can interact with as small then.  If you have something to question, how about quoting it explicitly; instead of your interpretation.

Brent

How about if I quote you? You wrote earlier it could be infinite "at the start", "initially". This suggests at the instant of the BB, it became infinite. I interpret this to mean a process resulting in infinite extent. which took zero time; hence a singularity.  Your other alternative is that it inflated hugely in a finite time interval. I can see this, but then it couldn't be infinite in spatial extent. AG 

That's a great way to communicate. Would you buy a used car from one of those guys? AG 

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[Alan Grayson]

It's not a matter of, or a case of being squeamish with infinite outcomes. I just don't see how cosmologists can claim the universe is flat -- which means infinite in spatial extent -- if it starts small and expands for a finite time. OTOH, one can claim, as Brent does, that it's infinite in spatial extent from the start. But this is a singularity at the creation time, the BB. A process which results in infinite spatial extent cannot take in place in finite time, or in the case of the BB, in zero time. AG

[Brent Meeker]

On 1/13/2020 5:52 PM, Alan Grayson wrote:

On Monday, January 13, 2020 at 5:12:33 PM UTC-7, Brent wrote:

On 1/13/2020 12:59 PM, Alan Grayson wrote:

On Monday, January 13, 2020 at 1:22:05 PM UTC-7, Brent wrote:

On 1/13/2020 11:02 AM, Alan Grayson wrote:

On Monday, January 13, 2020 at 11:20:41 AM UTC-7, Brent wrote:

On 1/13/2020 2:21 AM, Alan Grayson wrote:

Forget about matter. I am discussing spatial extent. If it starts small, and expands at any rate less than infinite, its spatial extent cannot be infinite. AG 

But so what?  What is "it"?  and what are you worried about?  If "it" is some portion of the universe we can see, it's finite.  The inference that the universe is infinite is based on curvature measure in the part we can see. 

IT, the universe, has (IMO) a very small but positive curvature, which is what we measure. Since we can't precisely measure zero curvature, as JC earlier stated, there's no way to distinguish the two cases -- flat and infinite in spatial extent versus spherical and finite in spatial extent -- on measurements. But since flat and infinite at the instant of the BB implies a singularity, I reject that model. AG

Fine.  Nobody thinks there was a singularity.

Brent

They think it's infinite at the beginning but always represent it as very small at the beginning.

No they represent all the universe we can interact with as small then.  If you have something to question, how about quoting it explicitly; instead of your interpretation.

Brent

How about if I quote you? You wrote earlier it could be infinite "at the start", "initially". This suggests at the instant of the BB, it became infinite.

No. "Became" would not be "at the start".  That's why I want see what you quoting.  You ability to interpret seems inventive to say the least.

Brent

I interpret this to mean a process resulting in infinite extent. which took zero time; hence a singularity.  Your other alternative is that it inflated hugely in a finite time interval. I can see this, but then it couldn't be infinite in spatial extent. AG 

That's a great way to communicate. Would you buy a used car from one of those guys? AG 

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[Alan Grayson]

On Monday, January 13, 2020 at 7:48:01 PM UTC-7, Brent wrote:

On 1/13/2020 5:52 PM, Alan Grayson wrote:

On Monday, January 13, 2020 at 5:12:33 PM UTC-7, Brent wrote:

On 1/13/2020 12:59 PM, Alan Grayson wrote:

On Monday, January 13, 2020 at 1:22:05 PM UTC-7, Brent wrote:

On 1/13/2020 11:02 AM, Alan Grayson wrote:

On Monday, January 13, 2020 at 11:20:41 AM UTC-7, Brent wrote:

On 1/13/2020 2:21 AM, Alan Grayson wrote:

Forget about matter. I am discussing spatial extent. If it starts small, and expands at any rate less than infinite, its spatial extent cannot be infinite. AG 

But so what?  What is "it"?  and what are you worried about?  If "it" is some portion of the universe we can see, it's finite.  The inference that the universe is infinite is based on curvature measure in the part we can see. 

IT, the universe, has (IMO) a very small but positive curvature, which is what we measure. Since we can't precisely measure zero curvature, as JC earlier stated, there's no way to distinguish the two cases -- flat and infinite in spatial extent versus spherical and finite in spatial extent -- on measurements. But since flat and infinite at the instant of the BB implies a singularity, I reject that model. AG

Fine.  Nobody thinks there was a singularity.

Brent

They think it's infinite at the beginning but always represent it as very small at the beginning.

No they represent all the universe we can interact with as small then.  If you have something to question, how about quoting it explicitly; instead of your interpretation.

Brent

How about if I quote you? You wrote earlier it could be infinite "at the start", "initially". This suggests at the instant of the BB, it became infinite.

No. "Became" would not be "at the start".  That's why I want see what you quoting.  You ability to interpret seems inventive to say the least.

Brent

 

Why do I have to quote anyone? I am just using basic logic and trying to resolve an apparent inconsistency. So, if not at the start, then during inflation. How could inflation produce infinite spatial extent?  The rate of expansion might be incredibly huge, but not infinite. AG

I interpret this to mean a process resulting in infinite extent. which took zero time; hence a singularity.  Your other alternative is that it inflated hugely in a finite time interval. I can see this, but then it couldn't be infinite in spatial extent. AG 

That's a great way to communicate. Would you buy a used car from one of those guys? AG 

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[Brent Meeker]

On 1/13/2020 7:50 PM, Alan Grayson wrote:

On Monday, January 13, 2020 at 7:48:01 PM UTC-7, Brent wrote:

On 1/13/2020 5:52 PM, Alan Grayson wrote:

On Monday, January 13, 2020 at 5:12:33 PM UTC-7, Brent wrote:

On 1/13/2020 12:59 PM, Alan Grayson wrote:

On Monday, January 13, 2020 at 1:22:05 PM UTC-7, Brent wrote:

On 1/13/2020 11:02 AM, Alan Grayson wrote:

On Monday, January 13, 2020 at 11:20:41 AM UTC-7, Brent wrote:

On 1/13/2020 2:21 AM, Alan Grayson wrote:

Forget about matter. I am discussing spatial extent. If it starts small, and expands at any rate less than infinite, its spatial extent cannot be infinite. AG 

But so what?  What is "it"?  and what are you worried about?  If "it" is some portion of the universe we can see, it's finite.  The inference that the universe is infinite is based on curvature measure in the part we can see. 

IT, the universe, has (IMO) a very small but positive curvature, which is what we measure. Since we can't precisely measure zero curvature, as JC earlier stated, there's no way to distinguish the two cases -- flat and infinite in spatial extent versus spherical and finite in spatial extent -- on measurements. But since flat and infinite at the instant of the BB implies a singularity, I reject that model. AG

Fine.  Nobody thinks there was a singularity.

Brent

They think it's infinite at the beginning but always represent it as very small at the beginning.

No they represent all the universe we can interact with as small then.  If you have something to question, how about quoting it explicitly; instead of your interpretation.

Brent

How about if I quote you? You wrote earlier it could be infinite "at the start", "initially". This suggests at the instant of the BB, it became infinite.

No. "Became" would not be "at the start".  That's why I want see what you quoting.  You ability to interpret seems inventive to say the least.

Brent

 

Why do I have to quote anyone?

Because you keep asking about what other people, cosmologists, physicists, putatively believe...except we are then supposed to rely on your interpretation of what you think they believe.

I am just using basic logic and trying to resolve an apparent inconsistency. So, if not at the start, then during inflation. How could inflation produce infinite spatial extent?  The rate of expansion might be incredibly huge, but not infinite. AG

That's why I wrote that it was infinite at the start.  "At the start" means before any expansion.  I don't know how to make it any clearer or more explicit.  Yet you keep pretending there's a need for expansion to make it infinite "after the start".

Brent

[Alan Grayson]

Well, you finally made your position (almost) clear. For most people I think, "at the start" means when the BB event occurred. So, do you mean after the BB event, but before inflation started? Is this the time frame when the universe became spatially infinite? TIA, AG

[Brent Meeker]

In that model, which isn't necessarily right and I'm not here to defend only explain, the universe is never finite.  Not before.  Not after.  Not ever.

Brent

[Alan Grayson]

My objective is to determine which model IS right, or at least is closer to the truth than the flat universe model. I get the feeling that you're more interested in ridiculing this effect, than getting closer to the truth of what's out there. The model I find most persuasive is that of a hypersphere, closed and finite in spatial extent. I am baffled why cosmologists think the universe that emerged with the BB is flat. Nonetheless, I tend to believe the substrate from which the BB emerged, is infinite in spatial extent and has an infinite past. It might be flat as well, or possibly something to which the concept of space doesn't apply. But we have no possible observations of that substrate. So I've restricted my analysis to OUR universe, the thing that arose with the BB. AG 

[Alan Grayson]

I meant to write above, " ... more interested in ridiculing this EFFORT ... "  AG 

[Alan Grayson]

It isn't. There exists a non-observable region, which is likely hugely larger than the observable region. AG 

--

Stathis Papaioannou

[John Clark]

On Mon, Jan 13, 2020 at 9:03 PM Alan Grayson <agrays...@gmail.com> wrote:

>> If infinite distances makes you squeamish I don't see how you can consistently embrace infinite outcomes. And besides this is not mathematics, in physics nothing is provably infinite, nobody has ever found an infinite number of anything.

> It's not a matter of, or a case of being squeamish with infinite outcomes. I just don't see how cosmologists can claim the universe is flat -- which means infinite in spatial extent -- if it starts small and expands for a finite time.

Infinity is not a number, infinity is a process that evolves in time. If a cosmologists says the universe is infinite he means that a pulse of light will keep getting more distant from its starting point and never return. I don't know if the universe is infinite or not but I see nothing obviously absurd with the idea. And when cosmologists say the universe started at a singularity what they mean is it started at a place they don't understand, they never claimed to know everything. In physics "singularity" doesn't mean infinite density or zero volume, it means "our theories break down here and produce ridiculous results".

 John K Clark

 

[Alan Grayson]

On Tuesday, January 14, 2020 at 3:06:48 AM UTC-7, John Clark wrote:

On Mon, Jan 13, 2020 at 9:03 PM Alan Grayson <agrays...@gmail.com> wrote:

>> If infinite distances makes you squeamish I don't see how you can consistently embrace infinite outcomes. And besides this is not mathematics, in physics nothing is provably infinite, nobody has ever found an infinite number of anything.

> It's not a matter of, or a case of being squeamish with infinite outcomes. I just don't see how cosmologists can claim the universe is flat -- which means infinite in spatial extent -- if it starts small and expands for a finite time.

Infinity is not a number, infinity is a process that evolves in time. If a cosmologists says the universe is infinite he means that a pulse of light will keep getting more distant from its starting point and never return.

That's what I mean! Only it's not true if the universe is spherical. Let's forget it. These discussions are worthless. AG

[Bruce Kellett]

On Tue, Jan 14, 2020 at 9:30 PM Alan Grayson <agrays...@gmail.com> wrote:

On Tuesday, January 14, 2020 at 3:06:48 AM UTC-7, John Clark wrote:

On Mon, Jan 13, 2020 at 9:03 PM Alan Grayson <agrays...@gmail.com> wrote:

>> If infinite distances makes you squeamish I don't see how you can consistently embrace infinite outcomes. And besides this is not mathematics, in physics nothing is provably infinite, nobody has ever found an infinite number of anything.

> It's not a matter of, or a case of being squeamish with infinite outcomes. I just don't see how cosmologists can claim the universe is flat -- which means infinite in spatial extent -- if it starts small and expands for a finite time.

Infinity is not a number, infinity is a process that evolves in time. If a cosmologists says the universe is infinite he means that a pulse of light will keep getting more distant from its starting point and never return.

That's what I mean! Only it's not true if the universe is spherical.

It is true for a de Sitter universe as a solution of the Einstein equations. If the universe is spherical, it will eventually recontract, and light cannot get right round and back to its starting point before the universe recontracts to a point. If the universe is expanding via dark energy, even if spherical, light still cannot get round because of the expansion. In other words, you can never see the back of your own head no matter what the geometry of the universe!!!!!

Bruce

[Alan Grayson]

Since it's not a perfect sphere, light never exactly returns to its starting point. That's just an approximation for discussion purposes. So let it contract. The point is that if the universe starts off small and expands at any finite rate for a finite time (aka, the age of the universe), it can't be flat, which implies spatially infinite. Sure it's nearly flat, but not exactly flat, like a huge sphere. I don't know why this is so hard to see. AG

[Quentin Anciaux]

The only thing expansion tells us is that our observable part of the universe started small... nothing tells us that it was all there is... the universe could have been infinite, and our observable part is an infinitesimal portion of it... as of singularity, yes that means our theories break down, but I seen nothing bad in infinity or even infinitely dense... all in all, that's the magical part of reality... at one point, something miraculous happened. That something is reality.

In the end, I can't see more than let there be light at the bottom, it's as nonsensical as anything else for that. There is no reason, no logic for us to be here. It just is.

 

Let's forget it. These discussions are worthless. AG

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[John Clark]

On Tue, Jan 14, 2020 at 6:47 AM Alan Grayson <agrays...@gmail.com> wrote:

 

> >It is true for a de Sitter universe as a solution of the Einstein equations. If the universe is spherical, it will eventually recontract, and light cannot get right round and back to its starting point before the universe recontracts to a point. If the universe is expanding via dark energy, even if spherical, light still cannot get round because of the expansion. In other words, you can never see the back of your own head no matter what the geometry of the universe!!!!!

Bruce

> Since it's not a perfect sphere [...]

Because we're talking about curved Spacetime and not curved space and because non-Euclidean geometry must be used (due to that minus sign that sneaks into Pythagoras formula if time is one of the dimensions) it's misleading to call it a "sphere", it's even misleading to call it the surface of a 4D sphere. What we really want to know is it the geometry of the universe is open or closed.

   

> light never exactly returns to its starting point. That's just an approximation 

That's what happens in a de Sitter universe, its flat and open and you get a de Sitter universe if the universe is not dominated by matter but by the Cosmological Constant, which is probably Dark Energy. Already about 74% of the matter/energy in our universe is in the form of Dark Energy, and as time progresses that percentage can only increase and we'll get closer and closer to a pure de Sitter universe. That's because the Cosmological Constant is a property of empty space, so as the accelerating universe creates more space it also creates more Dark Energy, however the total amount of matter (both regular and dark) remains fixed.  And in a de Sitter universe the distance between any 2 non-accelerating points will, given enough time, eventually be moving apart faster than the speed of light.

 

> Let's forget it. These discussions are worthless.

It appears you are not following your own advice.

John K Clark

[Alan Grayson]

On Tuesday, January 14, 2020 at 10:27:27 AM UTC-7, John Clark wrote:

On Tue, Jan 14, 2020 at 6:47 AM Alan Grayson <agrays...@gmail.com> wrote:

 

> >It is true for a de Sitter universe as a solution of the Einstein equations. If the universe is spherical, it will eventually recontract, and light cannot get right round and back to its starting point before the universe recontracts to a point. If the universe is expanding via dark energy, even if spherical, light still cannot get round because of the expansion. In other words, you can never see the back of your own head no matter what the geometry of the universe!!!!!

Bruce

> Since it's not a perfect sphere [...]

Because we're talking about curved Spacetime and not curved space and because non-Euclidean geometry must be used (due to that minus sign that sneaks into Pythagoras formula if time is one of the dimensions) it's misleading to call it a "sphere", it's even misleading to call it the surface of a 4D sphere. What we really want to know is it the geometry of the universe is open or closed.

Hypersphere; closed; if you believe it's age is finite. AG 

   

> light never exactly returns to its starting point. That's just an approximation 

That's what happens in a de Sitter universe, its flat and open and you get a de Sitter universe if the universe is not dominated by matter but by the Cosmological Constant, which is probably Dark Energy.

Since it's not perfectly homogeneous, a beam of light can be bent, this way and that way, so it's unlikely to return exactly to its point of origin. You know, what we OBSERVE and MEASURE is an expanding universe, so an ad hoc insertion of an infinite spatial extent is suspect. AG

[Alan Grayson]

On Tuesday, January 14, 2020 at 11:56:51 AM UTC-7, Alan Grayson wrote:

On Tuesday, January 14, 2020 at 10:27:27 AM UTC-7, John Clark wrote:

On Tue, Jan 14, 2020 at 6:47 AM Alan Grayson <agrays...@gmail.com> wrote:

 

> >It is true for a de Sitter universe as a solution of the Einstein equations. If the universe is spherical, it will eventually recontract, and light cannot get right round and back to its starting point before the universe recontracts to a point. If the universe is expanding via dark energy, even if spherical, light still cannot get round because of the expansion. In other words, you can never see the back of your own head no matter what the geometry of the universe!!!!!

Bruce

> Since it's not a perfect sphere [...]

Because we're talking about curved Spacetime and not curved space and because non-Euclidean geometry must be used (due to that minus sign that sneaks into Pythagoras formula if time is one of the dimensions) it's misleading to call it a "sphere", it's even misleading to call it the surface of a 4D sphere. What we really want to know is it the geometry of the universe is open or closed.

Hypersphere; closed; if you believe it's age is finite. AG 

   

> light never exactly returns to its starting point. That's just an approximation 

That's what happens in a de Sitter universe, its flat and open and you get a de Sitter universe if the universe is not dominated by matter but by the Cosmological Constant, which is probably Dark Energy.

Since it's not perfectly homogeneous, a beam of light can be bent, this way and that way, so it's unlikely to return exactly to its point of origin. You know, what we OBSERVE and MEASURE is an expanding universe, so an ad hoc insertion of an infinite spatial extent is suspect. AG

It's like a leaf on a tree. The leaf is our universe, closed and finite in spatial extent. It's attached to what I've called "the substratum", analogous to a tree, possibly infinite in spatial extent and having an infinite past. Let's call it "the Tree of Life". Our universe is connected to it, has been since the BB, which is why it's expanding, like a leaf growing.  AG

[Bruno Marchal]

On 14 Jan 2020, at 11:06, John Clark <johnk...@gmail.com> wrote:

On Mon, Jan 13, 2020 at 9:03 PM Alan Grayson <agrays...@gmail.com> wrote:

>> If infinite distances makes you squeamish I don't see how you can consistently embrace infinite outcomes. And besides this is not mathematics, in physics nothing is provably infinite, nobody has ever found an infinite number of anything.

> It's not a matter of, or a case of being squeamish with infinite outcomes. I just don't see how cosmologists can claim the universe is flat -- which means infinite in spatial extent -- if it starts small and expands for a finite time.

Infinity is not a number, infinity is a process that evolves in time.

That is Aristotle potential infinite. Cantorial actual infinities are treated by sets in set theory, and behave like numbers (we can add them, but it is not commutative, we can multiply them, exponentiate them, etc.

It is doubtful that there are actual infinities in the observable realm, and if we are machines, that is a priori undecidable. Now, with a non mechanist theory of mind, all notions are open.

If a cosmologists says the universe is infinite he means that a pulse of light will keep getting more distant from its starting point and never return. I don't know if the universe is infinite or not but I see nothing obviously absurd with the idea.

It is easy to prove that the physical (observable) universe has to be infinite, and contains non computable elements once we bet on Mechanism in the cognitive science. And without mechanism, also, but for very different reason.

And when cosmologists say the universe started at a singularity what they mean is it started at a place they don't understand, they never claimed to know everything. In physics "singularity" doesn't mean infinite density or zero volume, it means "our theories break down here and produce ridiculous results”.

Yes, and to invoke a singularity in an explanation is not much different than invoking a god or a primary universe. That explains nothing and such terms designates our ignorance.

Bruno

 John K Clark

 

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[Alan Grayson]

On Tuesday, January 14, 2020 at 3:37:22 PM UTC-7, Alan Grayson wrote:

On Tuesday, January 14, 2020 at 11:56:51 AM UTC-7, Alan Grayson wrote:

On Tuesday, January 14, 2020 at 10:27:27 AM UTC-7, John Clark wrote:

On Tue, Jan 14, 2020 at 6:47 AM Alan Grayson <agrays...@gmail.com> wrote:

 

> >It is true for a de Sitter universe as a solution of the Einstein equations. If the universe is spherical, it will eventually recontract, and light cannot get right round and back to its starting point before the universe recontracts to a point. If the universe is expanding via dark energy, even if spherical, light still cannot get round because of the expansion. In other words, you can never see the back of your own head no matter what the geometry of the universe!!!!!

Bruce

> Since it's not a perfect sphere [...]

Because we're talking about curved Spacetime and not curved space and because non-Euclidean geometry must be used (due to that minus sign that sneaks into Pythagoras formula if time is one of the dimensions) it's misleading to call it a "sphere", it's even misleading to call it the surface of a 4D sphere. What we really want to know is it the geometry of the universe is open or closed.

Hypersphere; closed; if you believe it's age is finite. AG 

   

> light never exactly returns to its starting point. That's just an approximation 

That's what happens in a de Sitter universe, its flat and open and you get a de Sitter universe if the universe is not dominated by matter but by the Cosmological Constant, which is probably Dark Energy.

Since it's not perfectly homogeneous, a beam of light can be bent, this way and that way, so it's unlikely to return exactly to its point of origin. You know, what we OBSERVE and MEASURE is an expanding universe, so an ad hoc insertion of an infinite spatial extent is suspect. AG

It's like a leaf on a tree. The leaf is our universe, closed and finite in spatial extent. It's attached to what I've called "the substratum", analogous to a tree, possibly infinite in spatial extent and having an infinite past. Let's call it "the Tree of Life". Our universe is connected to it, has been since the BB, which is why it's expanding, like a leaf growing.  AG

A fruit tree is a better analogy, since most fruits are approximately spherical, as is our universe (hyper-spherical); observable and non-observable regions. It must be somehow connected to its source or origin, but how that connection manifests is currently above my pay grade. The problem with current models of a flat universe is that the infinity of spatial extent implied, seems like an ad hoc hypothesis, not organically connected with the rest of the theory. AG 

[Alan Grayson]

On Wednesday, January 15, 2020 at 7:35:52 AM UTC-7, Bruno Marchal wrote:

On 14 Jan 2020, at 11:06, John Clark <johnk...@gmail.com> wrote:

On Mon, Jan 13, 2020 at 9:03 PM Alan Grayson <agrays...@gmail.com> wrote:

>> If infinite distances makes you squeamish I don't see how you can consistently embrace infinite outcomes. And besides this is not mathematics, in physics nothing is provably infinite, nobody has ever found an infinite number of anything.

> It's not a matter of, or a case of being squeamish with infinite outcomes. I just don't see how cosmologists can claim the universe is flat -- which means infinite in spatial extent -- if it starts small and expands for a finite time.

Infinity is not a number, infinity is a process that evolves in time.

That is Aristotle potential infinite. Cantorial actual infinities are treated by sets in set theory, and behave like numbers (we can add them, but it is not commutative, we can multiply them, exponentiate them, etc.

It is doubtful that there are actual infinities in the observable realm, and if we are machines, that is a priori undecidable. Now, with a non mechanist theory of mind, all notions are open.

If a cosmologists says the universe is infinite he means that a pulse of light will keep getting more distant from its starting point and never return. I don't know if the universe is infinite or not but I see nothing obviously absurd with the idea.

It is easy to prove that the physical (observable) universe has to be infinite, and contains non computable elements once we bet on Mechanism in the cognitive science. And without mechanism, also, but for very different reason.

And when cosmologists say the universe started at a singularity what they mean is it started at a place they don't understand, they never claimed to know everything. In physics "singularity" doesn't mean infinite density or zero volume, it means "our theories break down here and produce ridiculous results”.

Yes, and to invoke a singularity in an explanation is not much different than invoking a god or a primary universe. That explains nothing and such terms designates our ignorance.

What's your problem? No one invokes "singularity" as an explanation of anything; other than the fact that any theory which has one, cannot be applicable at the space-time point of its occurrence.  AG

 

Bruno

 John K Clark

 

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[Alan Grayson]

On Wednesday, January 15, 2020 at 4:19:59 PM UTC-7, Alan Grayson wrote:

On Tuesday, January 14, 2020 at 3:37:22 PM UTC-7, Alan Grayson wrote:

On Tuesday, January 14, 2020 at 11:56:51 AM UTC-7, Alan Grayson wrote:

On Tuesday, January 14, 2020 at 10:27:27 AM UTC-7, John Clark wrote:

On Tue, Jan 14, 2020 at 6:47 AM Alan Grayson <agrays...@gmail.com> wrote:

 

> >It is true for a de Sitter universe as a solution of the Einstein equations. If the universe is spherical, it will eventually recontract, and light cannot get right round and back to its starting point before the universe recontracts to a point. If the universe is expanding via dark energy, even if spherical, light still cannot get round because of the expansion. In other words, you can never see the back of your own head no matter what the geometry of the universe!!!!!

Bruce

> Since it's not a perfect sphere [...]

Because we're talking about curved Spacetime and not curved space and because non-Euclidean geometry must be used (due to that minus sign that sneaks into Pythagoras formula if time is one of the dimensions) it's misleading to call it a "sphere", it's even misleading to call it the surface of a 4D sphere. What we really want to know is it the geometry of the universe is open or closed.

Hypersphere; closed; if you believe it's age is finite. AG 

   

> light never exactly returns to its starting point. That's just an approximation 

That's what happens in a de Sitter universe, its flat and open and you get a de Sitter universe if the universe is not dominated by matter but by the Cosmological Constant, which is probably Dark Energy.

Since it's not perfectly homogeneous, a beam of light can be bent, this way and that way, so it's unlikely to return exactly to its point of origin. You know, what we OBSERVE and MEASURE is an expanding universe, so an ad hoc insertion of an infinite spatial extent is suspect. AG

It's like a leaf on a tree. The leaf is our universe, closed and finite in spatial extent. It's attached to what I've called "the substratum", analogous to a tree, possibly infinite in spatial extent and having an infinite past. Let's call it "the Tree of Life". Our universe is connected to it, has been since the BB, which is why it's expanding, like a leaf growing.  AG

A fruit tree is a better analogy, since most fruits are approximately spherical, as is our universe (hyper-spherical); observable and non-observable regions. It must be somehow connected to its source or origin, but how that connection manifests is currently above my pay grade. The problem with current models of a flat universe is that the infinity of spatial extent implied, seems like an ad hoc hypothesis, not organically connected with the rest of the theory. AG 

Since there's no preferred point in space-time, the connection to the BB must be everywhere, at every point in space-time. AG 

Already about 74% of the matter/energy in our universe is in the form of Dark Energy, and as time progresses that percentage can only increase and we'll get closer and closer to a pure de Sitter universe. That's because the Cosmological Constant is a property of empty space, so as the accelerating universe creates more space it also creates more Dark Energy, however the total amount of matter (both regular and dark) remains fixed.

Why does the total amount of matter, both regular and dark, remain fixed as the universe expands? AG

[John Clark]

On Wed, Jan 15, 2020 at 6:54 PM Alan Grayson <agrays...@gmail.com> wrote:

>> Already about 74% of the matter/energy in our universe is in the form of Dark Energy, and as time progresses that percentage can only increase and we'll get closer and closer to a pure de Sitter universe. That's because the Cosmological Constant is a property of empty space, so as the accelerating universe creates more space it also creates more Dark Energy, however the total amount of matter (both regular and dark) remains fixed.

> Why does the total amount of matter, both regular and dark, remain fixed as the universe expands? AG

The simple answer is in General Relativity there is a mechanism for creating new space but not for creating new matter. The Cosmological Constant is the energy that is always inherent in space even when it has no matter in it. General Relativity says that this vacuum energy will cause space to accelerate, that is to say more space will be created, so unlike the matter in it vacuum energy will not become diluted as the universe expands but will remain constant in both space and time. According to General Relativity the curvature of Spacetime (NOT the curvature of space) is determined by the energy and momentum in it, and as Sean Carroll says "the manifestation of spacetime curvature is simply the fact that space is expanding". And if vacuum energy is constant then the spacetime curvature (NOT spatial curvature) of the universe is constant so the universe is accelerating at a fixed rate, that is to say it always takes a fixed amount of time to double in size.

General Relativity allows for the existence of vacuum energy but does not insist on it,  Einstein's theory has no way to calculate it's value, it could be anything even zero and can only be determined by observation. For many years astronomers thought the value was indeed zero and so they could forget about it, but then in the late 1990's they found that the universe was accelerating and the vacuum energy density consistent with this was 6*10^-10 joules per cubic meter.  

Curiously unlike General Relativity with Quantum Mechanics you CAN calculate the value of vacuum energy, however when you do so you find it is in error by a factor of 10^120; it's been called the worst discrepancy between theory and observation in the entire history of science. So if the goal is to find a Theory Of Everything maybe people should leave General Relativity alone and monkey around with Quantum Mechanics rather than the reverse, it might be worth a try.

By the way, we don't know for sure that vacuum energy is the cause of Dark Energy but it seems like the best guess at the moment. 

 John K Clark

[Alan Grayson]

On Thursday, January 16, 2020 at 6:06:40 AM UTC-7, John Clark wrote:

On Wed, Jan 15, 2020 at 6:54 PM Alan Grayson <agrays...@gmail.com> wrote:

>> Already about 74% of the matter/energy in our universe is in the form of Dark Energy, and as time progresses that percentage can only increase and we'll get closer and closer to a pure de Sitter universe. That's because the Cosmological Constant is a property of empty space, so as the accelerating universe creates more space it also creates more Dark Energy, however the total amount of matter (both regular and dark) remains fixed.

> Why does the total amount of matter, both regular and dark, remain fixed as the universe expands? AG

The simple answer is in General Relativity there is a mechanism for creating new space but not for creating new matter.

Then what theory do we appeal to, to explain the emergence of matter, ordinary and/or dark? AG

 

The Cosmological Constant is the energy that is always inherent in space even when it has no matter in it. General Relativity says that this vacuum energy will cause space to accelerate, that is to say more space will be created, so unlike the matter in it vacuum energy will not become diluted as the universe expands but will remain constant in both space and time. According to General Relativity the curvature of Spacetime (NOT the curvature of space) is determined by the energy and momentum in it, and as Sean Carroll says "the manifestation of spacetime curvature is simply the fact that space is expanding".

If curvature is caused by energy and momentum in space-time, Carroll's statement doesn't make sense. AG

[John Clark]

On Thu, Jan 16, 2020 at 1:25 PM Alan Grayson <agrays...@gmail.com> wrote:

>> as Sean Carroll says "the manifestation of spacetime curvature is simply the fact that space is expanding".

> If curvature is caused by energy and momentum in space-time, Carroll's statement doesn't make sense. AG

Has it ever occured to you that if a professor of physics at one of the best universities in the world makes a statement about physics that makes no sense to you it might not be because he is talking nonsense but because you don't understand something? It makes no sense to you because you assume spatial curvature and spacetime curvature mean the same thing. But you're wrong, they don't. And they don't because the time dimension behaves in a fundamentally different way than any of the 3 spatial dimensions do; more specifically if you want to use Pythagoras theorem in spaceTIME (not to be confused with space) to calculate a distance in spaceTIME then you have to stick in a minus sign that Euclid and Pythagoras knew nothing about.

John K Clark

[Alan Grayson]

I f
John K Clark

You're referring, of course, to the Lorentz metric with the minus sign. Yeah, I've heard of it -- used in pseudo Riemannian manifolds, and without it those space-time causal cones wouldn't make sense. But I read again and again that "curvature" of space-time is caused by the presence of mass/energy, so I find Carroll's comment puzzling. He seems to be saying that expansion is caused by curvature, when it's generally thought to be caused by dark energy. Also, as you know, I am not an enthusiast (to put it mildly) of the Many Worlds theory of Everett, but Carroll is. So I don't pray at the feet of physicists, even those from prestigious universities. AG

[Alan Grayson]

On Thursday, January 16, 2020 at 6:06:40 AM UTC-7, John Clark wrote:

On Wed, Jan 15, 2020 at 6:54 PM Alan Grayson <agrays...@gmail.com> wrote:

>> Already about 74% of the matter/energy in our universe is in the form of Dark Energy, and as time progresses that percentage can only increase and we'll get closer and closer to a pure de Sitter universe. That's because the Cosmological Constant is a property of empty space, so as the accelerating universe creates more space it also creates more Dark Energy, however the total amount of matter (both regular and dark) remains fixed.

> Why does the total amount of matter, both regular and dark, remain fixed as the universe expands? AG

The simple answer is in General Relativity there is a mechanism for creating new space but not for creating new matter.

What theory do we rely on to explain the emergence of matter, regular and/or dark? AG

[Brent Meeker]

On 1/16/2020 3:17 PM, Alan Grayson wrote:

On Thursday, January 16, 2020 at 2:02:22 PM UTC-7, John Clark wrote:

On Thu, Jan 16, 2020 at 1:25 PM Alan Grayson <agrays...@gmail.com> wrote:

>> as Sean Carroll says "the manifestation of spacetime curvature is simply the fact that space is expanding".

> If curvature is caused by energy and momentum in space-time, Carroll's statement doesn't make sense. AG

Has it ever occured to you that if a professor of physics at one of the best universities in the world makes a statement about physics that makes no sense to you it might not be because he is talking nonsense but because you don't understand something? It makes no sense to you because you assume spatial curvature and spacetime curvature mean the same thing. But you're wrong, they don't. And they don't because the time dimension behaves in a fundamentally different way than any of the 3 spatial dimensions do; more specifically if you want to use Pythagoras theorem in spaceTIME (not to be confused with space) to calculate a distance in spaceTIME then you have to stick in a minus sign that Euclid and Pythagoras knew nothing about.
I f
John K Clark

You're referring, of course, to the Lorentz metric with the minus sign. Yeah, I've heard of it -- used in pseudo Riemannian manifolds, and without it those space-time causal cones wouldn't make sense. But I read again and again that "curvature" of space-time is caused by the presence of mass/energy, so I find Carroll's comment puzzling. He seems to be saying that expansion is caused by curvature, when it's generally thought to be caused by dark energy.

"Dark energy" is a place-holder name for whatever is responsible for the accelerating expansion of the universe.  So it could be curvature (i.e. just an intrinsic constant of spacetime) or it could be a quantum field that would have a corresponding particle that we could look for.  And what would be puzzling about Carroll having a different opinion than what is "generally thought" when it is a completely unsettled empirical question on which experts may be expected to have different theories.  In fact there isn't any "generally thought" consensus, and science doesn't go by consensus anyway.  What puzzles me is that you spend so much time writing to these email lists when your level of understanding would be improved a lot more by reading a book, e.g. David Mahon's "Relativity Demystified" or Robert Wald's "General Relativity" or "Gravity" by Jim Hartle or even Vic's "Comprehensible Cosmos".

Brent

Also, as you know, I am not an enthusiast (to put it mildly) of the Many Worlds theory of Everett, but Carroll is. So I don't pray at the feet of physicists, even those from prestigious universities. AG

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[Alan Grayson]

On Thursday, January 16, 2020 at 4:45:41 PM UTC-7, Brent wrote:

On 1/16/2020 3:17 PM, Alan Grayson wrote:

On Thursday, January 16, 2020 at 2:02:22 PM UTC-7, John Clark wrote:

On Thu, Jan 16, 2020 at 1:25 PM Alan Grayson <agrays...@gmail.com> wrote:

>> as Sean Carroll says "the manifestation of spacetime curvature is simply the fact that space is expanding".

> If curvature is caused by energy and momentum in space-time, Carroll's statement doesn't make sense. AG

Has it ever occured to you that if a professor of physics at one of the best universities in the world makes a statement about physics that makes no sense to you it might not be because he is talking nonsense but because you don't understand something? It makes no sense to you because you assume spatial curvature and spacetime curvature mean the same thing. But you're wrong, they don't. And they don't because the time dimension behaves in a fundamentally different way than any of the 3 spatial dimensions do; more specifically if you want to use Pythagoras theorem in spaceTIME (not to be confused with space) to calculate a distance in spaceTIME then you have to stick in a minus sign that Euclid and Pythagoras knew nothing about.
I f
John K Clark

You're referring, of course, to the Lorentz metric with the minus sign. Yeah, I've heard of it -- used in pseudo Riemannian manifolds, and without it those space-time causal cones wouldn't make sense. But I read again and again that "curvature" of space-time is caused by the presence of mass/energy, so I find Carroll's comment puzzling. He seems to be saying that expansion is caused by curvature, when it's generally thought to be caused by dark energy.

"Dark energy" is a place-holder name for whatever is responsible for the accelerating expansion of the universe.  So it could be curvature (i.e. just an intrinsic constant of spacetime) or it could be a quantum field that would have a corresponding particle that we could look for.  And what would be puzzling about Carroll having a different opinion than what is "generally thought" when it is a completely unsettled empirical question on which experts may be expected to have different theories.  In fact there isn't any "generally thought" consensus, and science doesn't go by consensus anyway.  What puzzles me is that you spend so much time writing to these email lists when your level of understanding would be improved a lot more by reading a book, e.g. David Mahon's "Relativity Demystified" or Robert Wald's "General Relativity" or "Gravity" by Jim Hartle or even Vic's "Comprehensible Cosmos".

Brent

Sure, it's a placeholder; everyone knows that. And AFAIK, curvature isn't a constant of space-time. It's a tensor field value that changes, depending on location and time. In any event, most professional comments about expansion do NOT claim that curvature causes expansion. Carroll seems to be an outlier and I was asking for a window into his opinion. Isn't that obvious? I am not going by any consensus here.  AG

Also, as you know, I am not an enthusiast (to put it mildly) of the Many Worlds theory of Everett, but Carroll is. So I don't pray at the feet of physicists, even those from prestigious universities. AG

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[John Clark]

On Thu, Jan 16, 2020 at 7:45 PM Alan Grayson <agrays...@gmail.com> wrote:

> Carroll seems to be an outlier

Nobody, including Carroll, claims to know for certain what causes the universe's spacetime curvature, it might be the energy of empty space, aka the Cosmological Constant, or it might be caused by something else. Some have proposed that maybe the spacetime curvature is caused by "quintessence", a hypothetical fifth fundamental force that, unlike vacuum energy, would not be constant but would increase with time; if that's true the acceleration of the universe would be accelerating and there is only 22 billion years remaining before the entire universe is destroyed in a Big Rip. It will take further observations, not theory, before we know if the acceleration is itself accelerating, but whatever the cause of the spacetime curvature Carroll is not an outlier, few if any physicists would disagree with Carroll's statement that "the manifestation of spacetime curvature is simply the fact that space is expanding".

 > I don't pray at the feet of physicists, even those from prestigious universities

But you do pray at the feet of Flying Saucer Men from Roswell New Mexico, and I consider that to be...ah... unwise. So the next time you think you are the first to find a glaringly obvious blunder that generations of physicists with boiling water IQ's have all failed to notice you might want to have a little humility and consider the possibility that maybe just maybe the confusion does not lie with them but with you.   

 John K Clark

 

[Alan Grayson]

It's hard to adequately respond to such a display of arrogance and stupidity. I imagine you would have confidently ridiculed those who reported rocks falling from the sky. The dispute about whether UFO's are alien spacecraft is just about the interpretation of the data available, and clearly you have not made an honest, objective effort to familiarize yourself with what's available. If I may say so, it's an odd schizophrenic aspect of your character structure, given that you fully embrace the most ridiculous interpretation of QM conceivable.

I never said Carroll IS an outlier. Rather, I said he SEEMS to be an outlier. Do you see the difference? Can you read plain English? He seems to ME an outlier because whenever I read anything about Einstein's field equations, it's invariably stated that curvature is caused by the presence of energy/momentum, which is one of the postulates of GR. Maybe I am confusing curvature of space with that of space-time. I dunno. 

Further, since, IMO, Carroll embraces about the dumbest interpretation of QM possible, MW, I really don't think his IQ is as high as you believe. And I am in very good company in this evaluation; Steven Weinberg. 

As for my conjectures about the flatness and the shape of our universe, I think you (and Brent) fail to see the singularity I pointed to; namely, IF at T = 0, the universe began as small, it could never have evolved infinite spatial extent characteristic of flatness since expansion goes at a finite rate, and the universe is generally thought be 13.8 billion year old, a FINITE number. OTOH, if an infinite spatial extent was created at the instant of the BB, it would fall into the category of a singularity since no physical process can occur with a time duration of zero. I sent an email to a noted cosmologist about this (whose name slips my mind), someone Brent referenced, but never received a reply.

AG

 John K Clark

 

[Bruno Marchal]

Of course, as I guess you now, by using an imaginary time (defining t’ = it), we can come back to the Pythagorean theorem, without the minus sign, and restore Euclideanity. That leads to something called Euclidian Relativity. I do often that for pedagogical purpose. Not sure if this is really fundamental. 

Bruno

John K Clark

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[John Clark]

On Fri, Jan 17, 2020 at 8:24 AM Alan Grayson <agrays...@gmail.com> wrote:

 

> IF at T = 0, the universe began as ...[Blah Blah]... I sent an email to a noted cosmologist about this (whose name slips my mind), someone Brent referenced, but never received a reply.

Gee I wonder why.

John K Clark

 

[Alan Grayson]

I'll give you the benefit of the doubt, and assume you also have the IQ of boiling water, in centigrade. AG 

 

[John Clark]

On Fri, Jan 17, 2020 at 2:34 PM Alan Grayson <agrays...@gmail.com> wrote:

> I'll give you the benefit of the doubt, and assume you also have the IQ of boiling water, in centigrade. AG 

Kelvin. What did you think the "K" stood for?

John K Clark

[John Clark]

On Fri, Jan 17, 2020 at 9:58 AM Bruno Marchal <mar...@ulb.ac.be> wrote:

 

>> the time dimension behaves in a fundamentally different way than any of the 3 spatial dimensions do; more specifically if you want to use Pythagoras theorem in spaceTIME (not to be confused with space) to calculate a distance in spaceTIME then you have to stick in a minus sign that Euclid and Pythagoras knew nothing about.

> Of course, as I guess you now, by using an imaginary time (defining t’ = it), we can come back to the Pythagorean theorem, without the minus sign, and restore Euclideanity. That leads to something called Euclidian Relativity. I do often that for pedagogical purpose. Not sure if this is really fundamental. 

Yes, you can use that to represent a curved path in 4D (one of time 3 of space) Minkowski Space where Special Relativity lives, but as you say that doesn't really get to the fundamental issue because Minkowski Space is flat and Special Relativity says nothing about gravity, for that you need General Relativity and GR doesn't live in Minkowski Space.

In General Relativity curved Spacetime is what gravity is, and in GR if there is any curvature in the Spacetime of the universe, and we know there is because we know that gravity exists, then, unless vacuum energy also exists and is fine tuned to one very precise value, the universe can not be stable, it must be either expanding or contracting. There are thermodynamic reasons to think it can't be contracting so it must be expanding.

And that is why no physicist would say that Carroll's statement  "the manifestation of spacetime curvature is simply the fact that space is expanding" was controversial .

John K Clark

[Alan Grayson]

The question is, what does he mean? Is space expanding BECAUSE of curvature? If so it's expanding because of gravity, since you wrote that gravity and curvature are equivalent. But since gravity is attractive (as far as we know), how could it be responsible for expansion (as distinguished from contraction)? AG 

John K Clark

[John Clark]

On Fri, Jan 17, 2020 at 5:03 PM Alan Grayson <agrays...@gmail.com> wrote:

>> Yes, you can use that to represent a curved path in 4D (one of time 3 of space) Minkowski Space where Special Relativity lives, but as you say that doesn't really get to the fundamental issue because Minkowski Space is flat and Special Relativity says nothing about gravity, for that you need General Relativity and GR doesn't live in Minkowski Space.

In General Relativity curved Spacetime is what gravity is, and in GR if there is any curvature in the Spacetime of the universe, and we know there is because we know that gravity exists, then, unless vacuum energy also exists and is fine tuned to one very precise value, the universe can not be stable, it must be either expanding or contracting. There are thermodynamic reasons to think it can't be contracting so it must be expanding.

And that is why no physicist would say that Carroll's statement  "the manifestation of spacetime curvature is simply the fact that space is expanding" was controversial .

> The question is, what does he mean? Is space expanding BECAUSE of curvature? If so it's expanding because of gravity, since you wrote that gravity and curvature are equivalent. But since gravity is attractive (as far as we know), how could it be responsible for expansion (as distinguished from contraction)? AG 

If the universe consisted of a cloud of particles that were not moving with respect to each other the gravitational attraction between the particles would indeed cause the universe to contract, but the particles ARE moving with respect to each other, so what will happen? It depends on how they are moving, but General Relativity can tell you one thing, unless you invoke a very fine tuned vacuum energy (aka the Cosmological Constant) that cloud of particles will NOT remain the same size, it will either expand or contract. We learn from observation that it's expanding which is consistent with thermodynamic reasoning.

John K Clark

[Lawrence Crowell]

Sometimes a picture works best. Below is a diagram that represents how space can be flat in a curved spacetime that expands space.

LC

 

[Alan Grayson]

I still find Carroll's remark as puzzling. He seems to attribute the cause of expansion to curvature, and thus to gravity, but gravity is attractive and could not, by itself, result in expansion. AG 

[Alan Grayson]

 Can you elaborate further? Not clear what this diagram demonstrates. AG

[Brent Meeker]

And even if you fine tuned to be exactly in equilibrium, it would be an unstable equilibrium and quickly shift into collapse or expansion...as was pointed out to Einstein when he used the CC to model a static universe.

Brent

We learn from observation that it's expanding which is consistent with thermodynamic reasoning.

John K Clark

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[Alan Grayson]

I suppose one could say that certain configurations of matter, hence curvature, can result in expansion or contraction. But from my pov, it's an abuse of language. Opinions can differ. AG

[Lawrence Crowell]

This is a sort of light cone diagram. The curves are null rays tangent to light cones.

I keep referring to this, but I illustrate here how gravitation can generate a repulsive acceleration. This thread is approaching 100 comments where it then splits and becomes inconvenient. 

LC

https://physics.stackexchange.com/questions/257476/how-did-the-universe-shift-from-dark-matter-dominated-to-dark-energy-dominate/257542#257542

[Philip Thrift]

On Saturday, January 18, 2020 at 2:00:23 AM UTC-6, Lawrence Crowell wrote:

https://physics.stackexchange.com/questions/257476/how-did-the-universe-shift-from-dark-matter-dominated-to-dark-energy-dominate/257542#257542

Proof that physics = witchcraft with equations.

Maybe programming (implementing simulations in programs) would be better.

@philipthrift