Inflation and the total size of the universe

[Alan Grayson]

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

[John Clark]

On Mon, Mar 23, 2020 at 12:55 AM Alan Grayson <agrays...@gmail.com> wrote:

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

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

 John K Clark

[Alan Grayson]

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

[Lawrence Crowell]

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

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

LC

[John Clark]

On Mon, Mar 23, 2020 at 10:54 AM Alan Grayson <agrays...@gmail.com> wrote:

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

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

John K Clark

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[Alan Grayson]

On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence Crowell wrote:

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

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

LC

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

[Lawrence Crowell]

On Tuesday, March 24, 2020 at 6:19:41 PM UTC-5, Alan Grayson wrote:

On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence Crowell wrote:

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

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

LC

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

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

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

LC

[Alan Grayson]

On Tuesday, March 24, 2020 at 6:21:50 PM UTC-6, Lawrence Crowell wrote:

On Tuesday, March 24, 2020 at 6:19:41 PM UTC-5, Alan Grayson wrote:

On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence Crowell wrote:

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

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

LC

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

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

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

LC

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

[Lawrence Crowell]

On Wednesday, March 25, 2020 at 1:28:21 AM UTC-5, Alan Grayson wrote:

On Tuesday, March 24, 2020 at 6:21:50 PM UTC-6, Lawrence Crowell wrote:

On Tuesday, March 24, 2020 at 6:19:41 PM UTC-5, Alan Grayson wrote:

On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence Crowell wrote:

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

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

LC

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

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

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

LC

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

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

LC

[Alan Grayson]

On Wednesday, March 25, 2020 at 2:58:45 AM UTC-6, Lawrence Crowell wrote:

On Wednesday, March 25, 2020 at 1:28:21 AM UTC-5, Alan Grayson wrote:

On Tuesday, March 24, 2020 at 6:21:50 PM UTC-6, Lawrence Crowell wrote:

On Tuesday, March 24, 2020 at 6:19:41 PM UTC-5, Alan Grayson wrote:

On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence Crowell wrote:

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

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

LC

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

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

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

LC

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

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

LC

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

[Lawrence Crowell]

On Wednesday, March 25, 2020 at 10:24:30 AM UTC-5, Alan Grayson wrote:

On Wednesday, March 25, 2020 at 2:58:45 AM UTC-6, Lawrence Crowell wrote:

On Wednesday, March 25, 2020 at 1:28:21 AM UTC-5, Alan Grayson wrote:

On Tuesday, March 24, 2020 at 6:21:50 PM UTC-6, Lawrence Crowell wrote:

On Tuesday, March 24, 2020 at 6:19:41 PM UTC-5, Alan Grayson wrote:

On Monday, March 23, 2020 at 9:35:48 AM UTC-6, Lawrence Crowell wrote:

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

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

LC

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

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

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

LC

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

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

LC

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

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

LC

[Alan Grayson]

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

[ronaldheld]

Maybe this paper will hel.

     Ronald

[Lawrence Crowell]

There is a spread, but that is noise. Statistical variances of error convey no information. So far we really do not know. In fact, if you think about it, no matter now accurately we measure the curvature of space, say by cosmic lensing etc, we can never absolutely verify k = 0. We might be able to get k = 1, if that is the case and the radius of curvature not too huge. If the universe is absolutely flat we can never know that with complete certainty.

LC

[Alan Grayson]

Are you sure? If the curvature is zero, there would be symmetric noise around the value of zero. OTOH, if the curvature is positive we might get asymmetric noise; that is, few values in the negative range. Also, don't you think the finite age of the universe argues against a flat universe (for reasons previously argued)? AG

[Lawrence Crowell]

Very sure. Please look up Gaussian variance. Errors in data carry no information other than the spread of error.

LC

[Alan Grayson]

In the model suggested, the randomness of the errors could indicate the location of the mean value. It's called thinking out-of-the-box. AG 

[Lawrence Crowell]

I am going to have to leave this discussion here. This is not how things are done! If you want to think so, then I can't stop you.

LC

[Alan Grayson]

All I was saying was that there could be a way to distinguish zero curvature from very small positive curvature by looking at the noise distribution. Thinking outside the box is not one of your strong points. AG  

[Alan Grayson]

And the answer is, according to a physicist at Fermi lab, assuming the universe is closed, is 250; that is, the unobservable universe is about 250 times larger than the observable universe. See,  https://www.youtube.com/watch?v=u23vZsJbrjE . Incidentally, I was just using the noise distribution as a possible way to distinguish closed and finite, from flat and infinite in spatial extent. I didn't claim it would definitive proof of one case over another. AG

[Lawrence Crowell]

Not quite. What he says is a 1deg spot in CMB anisotropy due to acoustics, as predicted by such physics, is measured to be 1deg with error bars, The error bars are such that the universe could be spherical with a hemispherical distance of 250 times the diameter to the CMB. That is about 23 trillion light years. This is the lower bound, so the observable cosmos could have spherical size much larger than this and we can't detect it. This also does not eliminate the hyperbolic spatial surface,

LC

[Alan Grayson]

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

[Lawrence Crowell]

I wrote a paper in 2013, which got some attention, on how a spacetime bubble that is spherical could transition into R^3 flat space. Inflation in this scenario is similar to a stereographic projection, so a point that is a reference point at rest will have the antipodal point head off "to infinity." This was a model for how inflation could have been a form of quantum critical point or phase transition. It is then possible the post inflationary cosmos was then infinite in extent.

LC

[Alan Grayson]

Infinite in spatial extent in finite time? Seems impossible. AG 

[Alan Grayson]

A point in space can "head off" to infinity, but still this does't imply infinite in spatial extent. In an expanding universe, all points removed from any fixed point are heading off to infinity. But this doesn't mean the universe is infinite in spatial extent. Maybe more important is the fact that a closed bubble would have to tear to satisfy your model. AG

[John Clark]

On Sat, Apr 11, 2020 at 3:27 PM Alan Grayson <agrays...@gmail.com> wrote:

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

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

 John K Clark

[Alan Grayson]

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

[John Clark]

On Sun, Apr 12, 2020 at 4:33 PM Alan Grayson <agrays...@gmail.com> wrote:

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

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

 

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

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

> the expansion applies to the UN-observable region?

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

 John K Clark

[Alan Grayson]

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

On Sun, Apr 12, 2020 at 4:33 PM Alan Grayson <agrays...@gmail.com> wrote:

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

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

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

 

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

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

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

> the expansion applies to the UN-observable region?

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

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

 John K Clark

[John Clark]

On Sun, Apr 12, 2020 at 5:49 PM Alan Grayson <agrays...@gmail.com> wrote:

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

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

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

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

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

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

John K Clark

 

 John K Clark

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[Brent Meeker]

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

Brent

[Lawrence Crowell]

It is an aspect of conformal field theory. I don't have time to go into conformal blocks and OPEs. But in effect the projective map can be dynamical and that antipodal point shot to infinity in a finite time.

LC 

[Alan Grayson]

Please post the link to your paper. The likely flaw, IMO, is that since physical processes require finite non-zero durations to manifest, one cannot expand spacial extent infinitely when one is limited to finite time, namely, the finite lifetime of our universe. It can occur within the confines of pure mathematics, such as when we imagine the wf extending to infinity, but not within the limitations of the physical world. AG 

[Alan Grayson]

On Sunday, April 12, 2020 at 4:19:26 PM UTC-6, John Clark wrote:

On Sun, Apr 12, 2020 at 5:49 PM Alan Grayson <agrays...@gmail.com> wrote:

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

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

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

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

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

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

John K Clark

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

 

 John K Clark

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[John Clark]

On Mon, Apr 13, 2020 at 4:37 AM Alan Grayson <agrays...@gmail.com> wrote:

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

It's a possibility.

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

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

 John K Clark

[Alan Grayson]

On Monday, April 13, 2020 at 6:30:47 AM UTC-6, John Clark wrote:

On Mon, Apr 13, 2020 at 4:37 AM Alan Grayson <agrays...@gmail.com> wrote:

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

It's a possibility.

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

No, I'm saying at zero time the universe may have already been spatially infinite, there is nothing we know of that would rule out the possibility.

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

[Lawrence Crowell]

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

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

LC

[John Clark]

On Mon, Apr 13, 2020 at 8:52 AM Alan Grayson <agrays...@gmail.com> wrote:

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

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

John K Clark

[John Clark]

On Mon, Apr 13, 2020 at 8:52 AM Alan Grayson <agrays...@gmail.com> wrote:

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

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

 John K Clark

[Alan Grayson]

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

[John Clark]

On Mon, Apr 13, 2020 at 10:09 AM Alan Grayson <agrays...@gmail.com> wrote:

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

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

John K Clark

[Alan Grayson]

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

[John Clark]

On Mon, Apr 13, 2020 at 2:07 PM Alan Grayson <agrays...@gmail.com> wrote:

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

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

 John K Clark

[Alan Grayson]

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

[Philip Thrift]

There is a "type" of set (theory) that locally finite (basically 'potentially infinite'), a set that does not have a fixed size but updates its size as "required" in the context of a proof (or, one would suppose, a physical observation).

@philipthrift

[John Clark]

On Mon, Apr 13, 2020 at 5:11 PM Alan Grayson <agrays...@gmail.com> wrote:

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

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

> It doesn't exist;

OK, but then what is "it"?

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

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

  John K Clark

[Alan Grayson]

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

[Alan Grayson]

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

[Quentin Anciaux]

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

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[Quentin Anciaux]

Le mar. 14 avr. 2020 à 16:20, Quentin Anciaux <allc...@gmail.com> a écrit :

Le mar. 14 avr. 2020 à 16:14, Alan Grayson <agrays...@gmail.com> a écrit :

On Tuesday, April 14, 2020 at 7:54:19 AM UTC-6, Alan Grayson wrote:

On Tuesday, April 14, 2020 at 5:28:07 AM UTC-6, John Clark wrote:

On Mon, Apr 13, 2020 at 5:11 PM Alan Grayson <agrays...@gmail.com> wrote:

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

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

> It doesn't exist;

OK, but then what is "it"?

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

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

  John K Clark

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

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

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

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

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[Alan Grayson]

On Tuesday, April 14, 2020 at 8:21:37 AM UTC-6, Quentin Anciaux wrote:

Le mar. 14 avr. 2020 à 16:20, Quentin Anciaux <allc...@gmail.com> a écrit :

Le mar. 14 avr. 2020 à 16:14, Alan Grayson <agrays...@gmail.com> a écrit :

On Tuesday, April 14, 2020 at 7:54:19 AM UTC-6, Alan Grayson wrote:

On Tuesday, April 14, 2020 at 5:28:07 AM UTC-6, John Clark wrote:

On Mon, Apr 13, 2020 at 5:11 PM Alan Grayson <agrays...@gmail.com> wrote:

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

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

> It doesn't exist;

OK, but then what is "it"?

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

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

  John K Clark

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

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

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

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

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

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[John Clark]

On Tue, Apr 14, 2020 at 4:27 PM Alan Grayson <agrays...@gmail.com> wrote:

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

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

 John K Clark

[Lawrence Crowell]

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

LC 

[Alan Grayson]

On Wednesday, April 15, 2020 at 7:25:50 AM UTC-6, John Clark wrote:

On Tue, Apr 14, 2020 at 4:27 PM Alan Grayson <agrays...@gmail.com> wrote:

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

If it started out infinite

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

[Alan Grayson]

To transition from a closed spherical finite universe to an open, flat infinite universe, don't you have to punch a hole in one of the poles, effectively creating a tear in fabric of spacetime? AG

[Lawrence Crowell]

Given a point on a sphere the antipodal point is sent to ∞. How this happens is an aspect of quantum nonlocality and the geometry of entanglements which involve projective spaces. The Fubini-Study metric is the basic example.

LC

[Quentin Anciaux]

Le jeu. 16 avr. 2020 à 03:43, Alan Grayson <agrays...@gmail.com> a écrit :

On Wednesday, April 15, 2020 at 7:25:50 AM UTC-6, John Clark wrote:

On Tue, Apr 14, 2020 at 4:27 PM Alan Grayson <agrays...@gmail.com> wrote:

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

If it started out infinite

I don't think you understand the implication of your supposition. It MEANS spatially infinite space came about at some INSTANT! 

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

 

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

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

 John K Clark

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[Alan Grayson]

On Thursday, April 16, 2020 at 6:09:06 AM UTC-6, Quentin Anciaux wrote:

Le jeu. 16 avr. 2020 à 03:43, Alan Grayson <agrays...@gmail.com> a écrit :

On Wednesday, April 15, 2020 at 7:25:50 AM UTC-6, John Clark wrote:

On Tue, Apr 14, 2020 at 4:27 PM Alan Grayson <agrays...@gmail.com> wrote:

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

If it started out infinite

I don't think you understand the implication of your supposition. It MEANS spatially infinite space came about at some INSTANT! 

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

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

 

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

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

 John K Clark

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[Alan Grayson]

If you're modeling a physical process, it can't occur in finite time. Sometimes mathematics can be misleading concerning what can happen physically. But maybe with nonlocality, it might be plausible. AG 

[Brent Meeker]

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

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

Brent

[Alan Grayson]

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

[John Clark]

On Thu, Apr 16, 2020 at 3:51 PM Alan Grayson <agrays...@gmail.com> wrote:

 

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

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

John K Clark