Cosmology in crisis as evidence suggests our universe isn't flat, it's actually curved.

[Alan Grayson]

I've argued for this several times based on logic, not data, and as far as I can recall, no one took me seriously. AG

https://thenextweb.com/syndication/2019/12/17/cosmology-in-crisis-as-evidence-suggests-our-universe-isnt-flat-its-actually-curved/

[Samiya Illias]

The Quran, as I understand it, seems to suggest layers of concentric spheres. Here’s an excerpt from an old post: 

Seven Heavens  in Layers

[Al-Qur’an Chapter 67:3-4, Translator: Sahih International] [And] who created seven heavens in layers. You do not see in the creation of the Most Merciful any inconsistency. So return [your] vision [to the sky]; do you see any breaks? Then return [your] vision twice again. [Your] vision will return to you humbled while it is fatigued. 

[Al-Qur’an Chapter 71:15, Translator: Sahih International] Do you not consider how Allah has created seven heavens in layers

  

[Al-Qur’an Chapter 55:33, Translator: Muhammad Sarwar] Jinn and mankind, if you can penetrate the diameters of the heavens and the earth, do so, but you cannot do so without power and authority. 
[Al-Qur’an Chapter 55:33, Translator: Sahih International]  O company of jinn and mankind, if you are able to pass beyond the regions of the heavens and the earth, then pass. You will not pass except by authority [from Allah ].

[Al-Qur’an Chapter 16:50, Translator: Sahih International] They fear their Lord above them, and they do what they are commanded. 

Excerpt from: 

https://signsandscience.blogspot.com/2014/10/creation.html

On 21-Dec-2019, at 6:33 AM, Alan Grayson <agrays...@gmail.com> wrote:



I've argued for this several times based on logic, not data, and as far as I can recall, no one took me seriously. AG

https://thenextweb.com/syndication/2019/12/17/cosmology-in-crisis-as-evidence-suggests-our-universe-isnt-flat-its-actually-curved/

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[Alan Grayson]

On Friday, December 20, 2019 at 6:33:39 PM UTC-7, Alan Grayson wrote:

I've argued for this several times based on logic, not data, and as far as I can recall, no one took me seriously. AG

https://thenextweb.com/syndication/2019/12/17/cosmology-in-crisis-as-evidence-suggests-our-universe-isnt-flat-its-actually-curved/

What's the nature of the "crisis"? TIA, AG 

[Lawrence Crowell]

If the observable universe is a closed sphere that might be a boost for me. The FLRW constraint is

(a'/a)^2 = (8piG/3c^2) - k/a^2,

for k = 0 being flat space, k = 1 for a sphere and k = -1 for a hyperboloid. As a, the scale factor becomes large the last term is small.

The bias for flatness comes from inflation, where a region of an inflationary spacetime with large vacuum energy tunnels into a small vacuum energy. This results in so called pocket world's. There is a boundary to the high energy region. By the Gauss-Bonnett theorem this boundary has information. A type of quantum phase change may change the topology into a sphere that "pops off" the inflationary manifold. So for me this might be welcome news if the observable cosmos is spherical.

[Alan Grayson]

I argued two or three times with Brent and others, that the curvature cannot be exactly zero, or negative -- corresponding to flat or saddle-shaped universes -- because both are infinite in spatial extent, which contradicts the models of the cosmos being extremely tiny near the BB. They also contradict the concept of the cosmos expanding for finite time, at less than infinite speed.  So it seemed clear, that the cosmos must be spherical in shape, with a positive curvature, very close to zero, but not zero -- which is what is measured. I don't see why my arguments made no impact. Now I don't understand why a spherical universe somehow poses a problem for inflation, which still seems needed to explain the large scale homogeneity. AG

[Lawrence Crowell]

Your objection to flatness is wrong. During inflation the cosmic horizon scale was a million billion times smaller than a proton. That transitioned into the large scale of today. This can still happen in a flat infinite spacetime.

Inflation involves the vacuum transition to a small value in a bounded region in the de Sitter manifold of inflation. Hence flatness. If there observable universe is an expanding 3-sphere there is more to this than current phenomenology.

LC

[Alan Grayson]

On Saturday, December 21, 2019 at 2:40:33 PM UTC-7, Lawrence Crowell wrote:

Your objection to flatness is wrong. During inflation the cosmic horizon scale was a million billion times smaller than a proton. That transitioned into the large scale of today. This can still happen in a flat infinite spacetime.

How can a cosmos starting very small, expand infinitely in its spatial extension, when it can only expand at some finite rate for a finite time, 13.8 BLY? AG

[Lawrence Crowell]

It is not about a small volume becoming infinite. It is about mass-energy density becoming lower.

LC

[Alan Grayson]

On Saturday, December 21, 2019 at 5:07:28 PM UTC-7, Lawrence Crowell wrote:

It is not about a small volume becoming infinite. It is about mass-energy density becoming lower.

LC

Regardless, the flat and saddle-shaped universes are infinite in spatial extent. How can that occur if the expansion proceeds at less than an infinite rate in finite time? AG 

[Lawrence Crowell]

Sigh! Mass-energy is extensive through out. It's density keeps lowering as particles are frame dragged.

LC

[Alan Grayson]

On Saturday, December 21, 2019 at 5:52:28 PM UTC-7, Lawrence Crowell wrote:

Sigh! Mass-energy is extensive through out. It's density keeps lowering as particles are frame dragged.

LC

I don't dispute your point (though I don't see the role of frame dragging). But can you answer a simple question? Are flat and saddle-shaped universes spatially infinite or not? TIA, AG 

[Lawrence Crowell]

They are infinite with a largely homogeneous density of mass-energy.

LC

[Bruno Marchal]

I tend to make sense of your question, in the case we agree that space itself is born with the big-bang (which I am quite not sure), it is hard to imagine it could be infinite in size at any fine moment I guess Lawrence assume some space before the Big Bang, if that make sense. I think we need to solve the problem of quantum gravitation, that is a quantum theory of space-time, to handle this question.  (I am not an expert on this to be sure).

Bruno

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[Alan Grayson]

On Sunday, December 22, 2019 at 7:11:25 AM UTC-7, Bruno Marchal wrote:

On 22 Dec 2019, at 02:35, Alan Grayson <agrays...@gmail.com> wrote:

On Saturday, December 21, 2019 at 5:52:28 PM UTC-7, Lawrence Crowell wrote:

Sigh! Mass-energy is extensive through out. It's density keeps lowering as particles are frame dragged.

LC

I don't dispute your point (though I don't see the role of frame dragging). But can you answer a simple question? Are flat and saddle-shaped universes spatially infinite or not? TIA, AG 

I tend to make sense of your question, in the case we agree that space itself is born with the big-bang (which I am quite not sure), it is hard to imagine it could be infinite in size at any fine moment I guess Lawrence assume some space before the Big Bang, if that make sense. I think we need to solve the problem of quantum gravitation, that is a quantum theory of space-time, to handle this question.  (I am not an expert on this to be sure).

Bruno

LC will probably sigh again when he reads this, but if the universe is flat or saddle-shaped and therefore infinite in spatial extent as he affirms, then it must have been infinite in spatial extent when the BB occurred if it has been expanding at LESS than infinite speed during its lifetime, 13.8 BY. I see no flaw in this logic. AG

 

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[Lawrence Crowell]

I am not it was not infinite. The big bang is due, within the inflationary phenomenology, to a region of the inflationary de Sitter space being an unstable vacuum that transitioned to a lower energy. The energy density gap produced particles and radiation. So the observable universe is a bubble in the "Swiss cheese." The dS spacetime is infinite in extent.

If the observable universe is curved as a sphere it means this bubble "popped off" the inflationary manifold. This throws new unknowns into the matter.

[Alan Grayson]

On Sunday, December 22, 2019 at 10:43:36 AM UTC-7, Lawrence Crowell wrote:

I am not it was not infinite. The big bang is due, within the inflationary phenomenology, to a region of the inflationary de Sitter space being an unstable vacuum that transitioned to a lower energy. The energy density gap produced particles and radiation. So the observable universe is a bubble in the "Swiss cheese." The dS spacetime is infinite in extent.

Whatever the shape of "the universe", what exactly are you referring to -- the bubble of observable and unobservable parts that begins to expand at BB time, or the entire underlying entity from which it expands? AG

 

If the observable universe is curved as a sphere it means this bubble "popped off" the inflationary manifold. This throws new unknowns into the matter.

What are main unknowns that you focus on? AG 

[Lawrence Crowell]

Look up inflationary cosmology or eternal inflation. Wikipedia has a page on this.

LC

[Alan Grayson]

On Sunday, December 22, 2019 at 5:11:15 PM UTC-7, Lawrence Crowell wrote: 

Look up inflationary cosmology or eternal inflation. Wikipedia has a page on this.

LC

I've seen those pages and I'm somewhat familiar with the concepts. I could be mistaken, but you appear to conflate emerging universes due to eternal inflation; that is bubbles emerging from within bubbles, as distinguished from other, sort of independently emerging bubbles, emerging from some underlying substratum or entity. That is, are you referring to other bubbles within our bubble, or to the underlying entity from which our bubble emerged? Our bubble is the only bubble we can measure, whose curvature has been proposed to be positive, that is, a closed spherical form. Or succinctly put, I don't see what eternal inflation has to do with the measurements which possibly show our bubble is spherical and closed. AG

[Philip Thrift]

These Wikipedia articles are not that informative.

I found this though:

     1.6E+60 kilograms = the total mass of the universe

https://science.howstuffworks.com/dictionary/astronomy-terms/question221.htm

So that's all the mass there is. 

How its distribution is geometrically shaped and changing over time, who knows

@philipthrift 

[Lawrence Crowell]

These bubbles are not spheres, but rather balls with a boundary. The boundary contains QFT data for fields in the inflationary spacetime. If this bubble "pops off" the inflationary spacetime that boundary information defines the topology, or topological quantum numbers, for this disconnected 3-sphere.

LC

[Alan Grayson]

On Monday, December 23, 2019 at 4:55:22 AM UTC-7, Lawrence Crowell wrote:

These bubbles are not spheres, but rather balls with a boundary. The boundary contains QFT data for fields in the inflationary spacetime. If this bubble "pops off" the inflationary spacetime that boundary information defines the topology, or topological quantum numbers, for this disconnected 3-sphere.

LC

The article suggests that if our universe (observable and unobservable) is spherical (not a perfect sphere of course), it would make the inflation model for accounting for homogeneity suspect. I don't see why that would necessarily be the case. AG 

[Lawrence Crowell]

Inflation is on the dS that is spatially flat. A bubble with broken vacuum symmetry is also flat. If the observable cosmos is not flat this upsets some apple carts.

LC

[Alan Grayson]

On Monday, December 23, 2019 at 6:15:14 PM UTC-7, Lawrence Crowell wrote:

Inflation is on the dS that is spatially flat. A bubble with broken vacuum symmetry is also flat. If the observable cosmos is not flat this upsets some apple carts.

LC

I have to look up dS, but this still doesn't make sense. Inflation, if it occurs, must start. How can it be spatially flat at inception since that implies, to me, infinite in spatial extent. at the start ? AG

[Lawrence Crowell]

Look up eternal inflation by Velinde

LC

[Lawrence Crowell]

I meant Linden.

[Lawrence Crowell]

I meant Linde.

[Alan Grayson]

dS is assumed to be flat, a solution of Einstein's field equations. This doesn't mean the universe IS flat. The data referenced in the article suggests it is curved. Moreover, I don't see how inflation, eternal or not, establishes flat. Time for more sighs? AG

[Lawrence Crowell]

Velinkin has shown that eternal inflating dS or dS-like spaces are not eternal in the past. They are so into the future. What comes "before," if that makes sense, is not known. The problem is that any extension of time here into that domain, say by translation of coordinates, is questionable.

LC

[Alan Grayson]

On Thursday, December 26, 2019 at 4:04:01 AM UTC-7, Lawrence Crowell wrote:

Velinkin has shown that eternal inflating dS or dS-like spaces are not eternal in the past. They are so into the future. What comes "before," if that makes sense, is not known. The problem is that any extension of time here into that domain, say by translation of coordinates, is questionable.

LC

I am not suggesting eternal in the past; rather, that bubbles have some starting time, t=0 for a particular bubble, and since, like our bubble, they have been expanding for finite time, none cannot be infinite in spatial extent.  They can't be flat and infinite in spatial extent. AG 

[Philip Thrift]

Examining the codebases of cosmological researchers

survey here:

   https://www.quantamagazine.org/coder-physicists-are-simulating-the-universe-to-unlock-its-secrets-20180612/

I don't think that any assumption of infinite space ("infinite in spatial extent") enters in anywhere.

(but one would have to look at the code)

If it's not in the code, it's not in the theory.

@philipthrift

 

[Alan Grayson]

A flat or saddle-shaped universe extends infinitely in spacial coordinates. Otherwise it has an edge or boundary, which IMO, does NOT characterize our universe. It can't expand at some finite speed, no matter how large, and extend infinitely in space. AG  

[Alan Grayson]

[Alan Grayson]

LC keeps bring up inflation or eternal inflation, but I don't see these speculative scenarios having anything to do with the logical result I have stated above. AG

[Philip Thrift]

Such theories ("extends infinitely in spacial coordinates") are just wrong in the first place, according to Max Tegmark. So they can be eliminated at the start (and hopefully never mentioned again).

https://www.edge.org/response-detail/25344

...

Not only do we lack evidence for the infinite, but we don't actually need the infinite to do physics: our best computer simulations, accurately describing everything from the formation of galaxies to to tomorrow's weather to the masses of elementary particles, use only finite computer resources by treating everything as finite. So if we can do without infinity to figure out what happens next, surely nature can too—in a way that's more deep and elegant than the hacks we use for our computer simulations. Our challenge as physicists is to discover this elegant way and the infinity-free equations describing it—the true laws of physics. To start this search in earnest, we need to question infinity. I'm betting that we also need to let go of it.

@philipthrift

[Lawrence Crowell]

Certain horizon conditions make it so that in an infinite universe any observer can only access a finite amount of information.

LC

[Philip Thrift]

That would be the case also if there was no infinite universe as an option in the first place. According to Tegmark, there is no theory (appropriate for physics) with an infinite universe.

@philiphrift 

[Lawrence Crowell]

Sure there are! The main phenom for the cosmos is spatially flat and infinite. Red shift and horizons mean any observer can only access a finite amount of information.

LC

[Philip Thrift]

On Friday, December 27, 2019 at 6:46:26 PM UTC-6, Lawrence Crowell wrote:

Sure there are! The main phenom for the cosmos is spatially flat and infinite. Red shift and horizons mean any observer can only access a finite amount of information.

LC

The whole point is that, according to Tegmark, there should not be be a theory of physics in which "the cosmos is spatially flat and infinite". 

So how does one put that in one's pipe and smokes it?

@philipthrift

[Philip Thrift]

I don't know if Tegmark is right or wrong. but his dictum is that there should be no theories that have infinite anythings. So one has to start with that.

@philipthrift/ 

[Alan Grayson]

On Friday, December 27, 2019 at 5:46:26 PM UTC-7, Lawrence Crowell wrote:

Sure there are! The main phenom for the cosmos is spatially flat and infinite. Red shift and horizons mean any observer can only access a finite amount of information.

LC

But my main critique seems firm; since every bubble has a start, a finite age, and an expansion rate less than an infinite rate, how could it ALSO have an infinite spatial extent? It's just impossible! AG 

[Alan Grayson]

My suggestion; learn to love it! You live in a closed, approximately spherical universe (approximate, like the Earth is approximately spherically shaped), and tell us where this leads. AG 

[Lawrence Crowell]

There should not be cosmology or physics where anything infinite is observed. Horizons in spacetime make only a finite amount of information accessible to any observer. This would hold in even a flat infinite space.

In either case, finite or infinite, one is confronted with some unpleasant realities. If the universe is strictly finite there is always an uncomfortable sense that a finite set is bounded, and as such there can potentially be something outside it. If the universe is infinite then how can we completely understand it?

LC

[Philip Thrift]

If there is a finite-universe physics (FUP) and an infinite-universe physics (IUP) and IUP adds nothing better than FUP in terms of predictions, explanations, or anything other than a religious satisfaction, then what good is IUP?

@philipthrift

[Alan Grayson]

I imagine that our universe, observable and non-observable, is finite without a boundary. But the substratum from which it emerged could be infinite. AG 

[Lawrence Crowell]

Not quite. There are subtle differences that at least in principle are observable.

LC

[Philip Thrift]

On Saturday, December 28, 2019 at 7:17:30 AM UTC-6, Lawrence Crowell wrote:

Not quite. There are subtle differences that at least in principle are observable.

LC

Example?

@philipthrift 

[Alan Grayson]

On Saturday, December 28, 2019 at 6:17:30 AM UTC-7, Lawrence Crowell wrote:

Not quite. There are subtle differences that at least in principle are observable.

LC

Who are you responding to? AG 

[Alan Grayson]

On Friday, December 20, 2019 at 6:33:39 PM UTC-7, Alan Grayson wrote:

I've argued for this several times based on logic, not data, and as far as I can recall, no one took me seriously. AG

https://thenextweb.com/syndication/2019/12/17/cosmology-in-crisis-as-evidence-suggests-our-universe-isnt-flat-its-actually-curved/

I'd really appreciate it if Brent, Bruce and JC would provide their input on this issue. AG 

[Bruno Marchal]

Digital Mechanism enforces finitism (but not ultrafinitism) at the conceptual primitive level.

What exist is very clear and clearcut. 

What exist are K, S, KK, KS, SK, …, or, if you prefer, 0, S0, SS0, SSS0, …

Of course, “everything" will appear through the facts that those entities obeys laws, like Kxy = x, or x + 0 = x.

But very few laws are needed to make those entities Turing universal.

At the meta-level, we do intuit that the realm we talk about is infinite, as there is an infinity of finite number or finite combinators, or finite digital machines, and in the Turing case, we allow the machine to explore unbounded (mental and digital) space.

Yet, it can be shown that the machine who allows themselves the belief in (diverse) infinities, get more quickly powerful tools to develop the understanding of the possible relations in between machines, and eventually they might grasp the special relation between consciousness and infinity, that we get by the invariance of the first person experience in the delays of the universal dovetailer. 

That gives quantum logic, but the hard problem is to get the tensorial algebra “multiplying the isolated people in a coherent first person *plural* experience. It is a technical problem. It consists in developing the algebra of the operators given by the quantisation ([]<>p) with the box of the material modes of self-reference. 

Eventually we need the quantified modal logics of self-reference qG and qG*. Those are highly undecidable. qG is pi_2-complete, and qG* is pi_1 complete *in* the oracle of the whole arithmetical truth. The god/ONE of the machine (arithmetical truth) is overwhelmed by the its Intellect/Noùs! 

The science of machine/numbers is so complex that there is job for all universal machines and all their Oracles//Gods. Here by machine/number I mean something representable by a finite or a recursively enumerable set or function, and by "a god" a non recursively enumerable set or function. 

It is easy to modify the Turing formalism to allow a Turing machine to ask a yes-no question to some god. Add the quadruplet having the shape q_i S_j q_k q_r, with the operational meaning that if the Turing machine is in the sate q_i, observing the symbol S_j, she will ask her question to her god , and if that god answers yes, she will be in the state q_k, and if It's answer is no she will be in the state q_r. Turing used this to to generalise incompleteness to the incompleteness of the machine helped by diverse sort of gods, even just about the arithmetical reality.

In mathematics/arithmetic, some object can look small from outside and infinitely big from inside.

Best,

Bruno

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[Alan Grayson]

I don't see any problem with having infinities in a theory provided they're not measurable. For example, consider the steady state universe which was proposed in 1948 by Hermann Bondi, Thomas Gold and Fred Hoyle. It just means a universe which is homogeneous, expanding, with mass density constant  and constant creation of space and matter, and infinite in age and spatial extent -- where this spatial infinity is much like the concept of infinity in mathematics, namely, one can travel any distance, in any direction, and no matter how far, that distance can be exceeded. But what we have as our best theory today is a universe of finite age, expanding at a finite rate, yet conceived of by most cosmologists as flat and therefore infinite in spatial extent. These properties seem inherently contradictory. Something has to give. AG

[Philip Thrift]

This could be the case:

For every formal IUT (infinite universe theory) there is a formal FUT (finite universe theory - there is no infinite entity in the theory) - that is just as good in matching up to all observations. 

What has to 'give' is this:

We can never, ever know which one corresponds to reality.

@philipthrift

[Alan Grayson]

Well, the denial that the universe is closed and spherical. AG 

[Philip Thrift]

One can have a finite universe theory with a finite space metric as a function of time where the distribution of  matter does not take a 'spherical' shape. I.e.: A theory where metric as a function of time does not have to be the same everywhere and everywhen, and new matter could appear over time.

@philipthrift

[Alan Grayson]

It's "spherical", like the Earth, with hills and valleys, mountains and canyons. I'm not referring to a perfect sphere. AG

[Alan Grayson]

In the not-too-distant past, I've had this discussion with Brent. He claimed, IIRC, that the universe could have begun infinite in spatial extent. But the usual models have it starting as very small. I would like his input in this matter. AG 

[Alan Grayson]

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

@philipthrift

[Philip Thrift]

I just meant the shape of the distribution of all particles in a topological sense, no matter how it is dented up or warped.

But if the "data" says the universe is a topological 4D sphere then the metric (distances between particles) can be uniform with a finite number of particles. So there''s that.

You are where you are in the universe, but do you get the same "data" readings wherever you reposition yourself anywhere in the universe? What's the answer to that question?

@philipthrift

[Brent Meeker]

It could have begun infinite, while the part visible to us is now was then very small.

Brent

[Lawrence Crowell]

I have not weighed in on this of late. However, an infinite space that starts at t = 0, requires some nonlocal occurrence of boundary or initial conditions. This could potentially happen in quantum gravitation.

LC

[Alan Grayson]

The :substratum" from which our universe arose could have been infinite in all dimensions, space and time, but when we speak of "our universe", I think it includes the observable and non-observable regions. Since these presumably have a finite lifetime, what I am calling "our universe" must be closed and spherical. Do find any logical flaws in this argument? TIA, AG

[Alan Grayson]

On Thursday, January 2, 2020 at 10:52:07 AM UTC-7, Brent wrote:

But if during inflation the universe was expanding faster than the SoL, wouldn't what we call "the universe" include non-observable regions, and therefore that both regions were small? AG 

[Brent Meeker]

The universe, as currently theorized, does include unobservable regions.   I don't know what "both" refers to.

Brent

[Alan Grayson]

"Both" includes observable and non-observable regions. What I meant above is that during inflation, the universe expands faster than the SoL, hugely faster, and as a result the non-observable regions are created. IOW, the whole thing seems to start very small. AG 

[Alan Grayson]

To put it succinctly, inflation can explain how the unobservable region arises "naturally" in the BB process, not as I sense you model it, as somehow preexisting. AG 

[Pierz]

There are sooo many examples of this misconception on Quora. Here's one answer from Viktor Toth, who is excellent with the late explanations: https://qr.ae/TSjfO3

On Sunday, December 22, 2019 at 7:37:25 AM UTC+11, Alan Grayson wrote:

On Saturday, December 21, 2019 at 4:42:50 AM UTC-7, Lawrence Crowell wrote:

If the observable universe is a closed sphere that might be a boost for me. The FLRW constraint is

(a'/a)^2 = (8piG/3c^2) - k/a^2,

for k = 0 being flat space, k = 1 for a sphere and k = -1 for a hyperboloid. As a, the scale factor becomes large the last term is small.

The bias for flatness comes from inflation, where a region of an inflationary spacetime with large vacuum energy tunnels into a small vacuum energy. This results in so called pocket world's. There is a boundary to the high energy region. By the Gauss-Bonnett theorem this boundary has information. A type of quantum phase change may change the topology into a sphere that "pops off" the inflationary manifold. So for me this might be welcome news if the observable cosmos is spherical.

I argued two or three times with Brent and others, that the curvature cannot be exactly zero, or negative -- corresponding to flat or saddle-shaped universes -- because both are infinite in spatial extent, which contradicts the models of the cosmos being extremely tiny near the BB. They also contradict the concept of the cosmos expanding for finite time, at less than infinite speed.  So it seemed clear, that the cosmos must be spherical in shape, with a positive curvature, very close to zero, but not zero -- which is what is measured. I don't see why my arguments made no impact. Now I don't understand why a spherical universe somehow poses a problem for inflation, which still seems needed to explain the large scale homogeneity. AG

[Alan Grayson]

On Monday, January 6, 2020 at 2:18:48 PM UTC-7, Pierz wrote:

There are sooo many examples of this misconception on Quora. Here's one answer from Viktor Toth, who is excellent with the late explanations: https://qr.ae/TSjfO3

TY. I viewed this. It explains nothing. What he calls "the infinite flat sheet" at the initiation of the BB is not "our universe". Rather, what I call "our universe" is the observable and unobservable regions, where the latter is created as a result of faster-than-light inflation. Toth's infinite flat sheet is what I have referred to as the substratum from which our universe emerged. It could be flat, or even saddle-shaped, but it is not our universe with two regions as just defined. AG 

[Alan Grayson]

On Monday, January 6, 2020 at 3:00:45 PM UTC-7, Alan Grayson wrote:

On Monday, January 6, 2020 at 2:18:48 PM UTC-7, Pierz wrote:

There are sooo many examples of this misconception on Quora. Here's one answer from Viktor Toth, who is excellent with the late explanations: https://qr.ae/TSjfO3

TY. I viewed this. It explains nothing. What he calls "the infinite flat sheet" at the initiation of the BB is not "our universe". Rather, what I call "our universe" is the observable and unobservable regions, where the latter is created as a result of faster-than-light inflation. Toth's infinite flat sheet is what I have referred to as the substratum from which our universe emerged. It could be flat, or even saddle-shaped, but it is not our universe with two regions as just defined. AG 

What I claim is that our universe, consisting of observable and unobservable regions, is spherical in shape. It has to be if the age of the universe is finite. OTOH, the flat sheet Toth refers to, could be any shape, flat or non-flat. AG 

[spudb...@aol.com]

Now to this question of cosmological shape or comment rather. If the cosmos is curved then it is probably not an endless pitcher plant, as often depicted in sci mags. In this fashion, the universe is an oblate spheroid, a hyper-sphere, rotational object, no, not the mere section we know as the Hubble Volume, but the whole enchilada. Godel beams from beyond, ever knowing that what goes round, comes round.

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[Brent Meeker]

On 1/6/2020 2:00 PM, Alan Grayson wrote:

On Monday, January 6, 2020 at 2:18:48 PM UTC-7, Pierz wrote:

There are sooo many examples of this misconception on Quora. Here's one answer from Viktor Toth, who is excellent with the late explanations: https://qr.ae/TSjfO3

TY. I viewed this. It explains nothing. What he calls "the infinite flat sheet" at the initiation of the BB is not "our universe". Rather, what I call "our universe" is the observable and unobservable regions, where the latter is created as a result of faster-than-light inflation. Toth's infinite flat sheet is what I have referred to as the substratum from which our universe emerged. It could be flat, or even saddle-shaped, but it is not our universe with two regions as just defined. AG

You can call it whatever you want, but it's what is described by the FLRW solution of Einstein's equations for the cosmos.  What part is observable is relative to us.

Brent

[Alan Grayson]

On Monday, January 6, 2020 at 3:50:55 PM UTC-7, Brent wrote:

On 1/6/2020 2:00 PM, Alan Grayson wrote:

On Monday, January 6, 2020 at 2:18:48 PM UTC-7, Pierz wrote:

There are sooo many examples of this misconception on Quora. Here's one answer from Viktor Toth, who is excellent with the late explanations: https://qr.ae/TSjfO3

TY. I viewed this. It explains nothing. What he calls "the infinite flat sheet" at the initiation of the BB is not "our universe". Rather, what I call "our universe" is the observable and unobservable regions, where the latter is created as a result of faster-than-light inflation. Toth's infinite flat sheet is what I have referred to as the substratum from which our universe emerged. It could be flat, or even saddle-shaped, but it is not our universe with two regions as just defined. AG

You can call it whatever you want, but it's what is described by the FLRW solution of Einstein's equations for the cosmos.  What part is observable is relative to us.

Brent

I looked up the FLRW solution on Wiki.  https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric#Curvature 

I see there's a parameter k which determines curvature, but the mathematics doesn't seem to give what the value is, other than three possibilities;  -1 ,0, 1. If this is true, how can the solution you suggest shed any light on what the actually curvature is? Moreover, I would think measured values would trump hypothetical possibilities, and the article which I posted starting this discussion alleges that the measured value, although falling short of 5-sigma certainty, indicates a spherical shape. TIA, AG

[Brent Meeker]

On 1/6/2020 9:15 PM, Alan Grayson wrote:

On Monday, January 6, 2020 at 3:50:55 PM UTC-7, Brent wrote:

On 1/6/2020 2:00 PM, Alan Grayson wrote:

On Monday, January 6, 2020 at 2:18:48 PM UTC-7, Pierz wrote:

There are sooo many examples of this misconception on Quora. Here's one answer from Viktor Toth, who is excellent with the late explanations: https://qr.ae/TSjfO3

TY. I viewed this. It explains nothing. What he calls "the infinite flat sheet" at the initiation of the BB is not "our universe". Rather, what I call "our universe" is the observable and unobservable regions, where the latter is created as a result of faster-than-light inflation. Toth's infinite flat sheet is what I have referred to as the substratum from which our universe emerged. It could be flat, or even saddle-shaped, but it is not our universe with two regions as just defined. AG

You can call it whatever you want, but it's what is described by the FLRW solution of Einstein's equations for the cosmos.  What part is observable is relative to us.

Brent

I looked up the FLRW solution on Wiki.  https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric#Curvature 

I see there's a parameter k which determines curvature, but the mathematics doesn't seem to give what the value is, other than three possibilities;  -1 ,0, 1.

That's because the specific value of curvature can be absorbed into the initial conditions, so only the sign of k matters.

If this is true, how can the solution you suggest shed any light on what the actually curvature is? Moreover, I would think measured values would trump hypothetical possibilities, and the article which I posted starting this discussion alleges that the measured value, although falling short of 5-sigma certainty, indicates a spherical shape. TIA, AG

The FLRW solution assumes isotropy and homogeneity which together imply spherical symmetry.  But that's probably not what you mean by "shape".

Brent

On Sunday, December 22, 2019 at 7:37:25 AM UTC+11, Alan Grayson wrote:

On Saturday, December 21, 2019 at 4:42:50 AM UTC-7, Lawrence Crowell wrote:

If the observable universe is a closed sphere that might be a boost for me. The FLRW constraint is

(a'/a)^2 = (8piG/3c^2) - k/a^2,

for k = 0 being flat space, k = 1 for a sphere and k = -1 for a hyperboloid. As a, the scale factor becomes large the last term is small.

The bias for flatness comes from inflation, where a region of an inflationary spacetime with large vacuum energy tunnels into a small vacuum energy. This results in so called pocket world's. There is a boundary to the high energy region. By the Gauss-Bonnett theorem this boundary has information. A type of quantum phase change may change the topology into a sphere that "pops off" the inflationary manifold. So for me this might be welcome news if the observable cosmos is spherical.

I argued two or three times with Brent and others, that the curvature cannot be exactly zero, or negative -- corresponding to flat or saddle-shaped universes -- because both are infinite in spatial extent, which contradicts the models of the cosmos being extremely tiny near the BB. They also contradict the concept of the cosmos expanding for finite time, at less than infinite speed.  So it seemed clear, that the cosmos must be spherical in shape, with a positive curvature, very close to zero, but not zero -- which is what is measured. I don't see why my arguments made no impact. Now I don't understand why a spherical universe somehow poses a problem for inflation, which still seems needed to explain the large scale homogeneity. AG

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[Alan Grayson]

On Monday, January 6, 2020 at 10:29:06 PM UTC-7, Brent wrote:

On 1/6/2020 9:15 PM, Alan Grayson wrote:

On Monday, January 6, 2020 at 3:50:55 PM UTC-7, Brent wrote:

On 1/6/2020 2:00 PM, Alan Grayson wrote:

On Monday, January 6, 2020 at 2:18:48 PM UTC-7, Pierz wrote:

There are sooo many examples of this misconception on Quora. Here's one answer from Viktor Toth, who is excellent with the late explanations: https://qr.ae/TSjfO3

TY. I viewed this. It explains nothing. What he calls "the infinite flat sheet" at the initiation of the BB is not "our universe". Rather, what I call "our universe" is the observable and unobservable regions, where the latter is created as a result of faster-than-light inflation. Toth's infinite flat sheet is what I have referred to as the substratum from which our universe emerged. It could be flat, or even saddle-shaped, but it is not our universe with two regions as just defined. AG

You can call it whatever you want, but it's what is described by the FLRW solution of Einstein's equations for the cosmos.  What part is observable is relative to us.

Brent

I looked up the FLRW solution on Wiki.  https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric#Curvature 

I see there's a parameter k which determines curvature, but the mathematics doesn't seem to give what the value is, other than three possibilities;  -1 ,0, 1.

That's because the specific value of curvature can be absorbed into the initial conditions, so only the sign of k matters.

CMIIAW, but I don't think we know the initial conditions of the BB. If so, K could be any sign, making the shape of the universe indeterminate. I think we must rely on measurements. AG 

If this is true, how can the solution you suggest shed any light on what the actually curvature is? Moreover, I would think measured values would trump hypothetical possibilities, and the article which I posted starting this discussion alleges that the measured value, although falling short of 5-sigma certainty, indicates a spherical shape. TIA, AG

The FLRW solution assumes isotropy and homogeneity which together imply spherical symmetry.  But that's probably not what you mean by "shape".

What I mean by "shape" is that the universe is closed and finite in spatial extent. Or equivalently, a beam of light sent in any direction returns to its original starting point (approximately, since this proposed hypersphere is not a perfect hypersphere). AG 

Brent

On Sunday, December 22, 2019 at 7:37:25 AM UTC+11, Alan Grayson wrote:

On Saturday, December 21, 2019 at 4:42:50 AM UTC-7, Lawrence Crowell wrote:

If the observable universe is a closed sphere that might be a boost for me. The FLRW constraint is

(a'/a)^2 = (8piG/3c^2) - k/a^2,

for k = 0 being flat space, k = 1 for a sphere and k = -1 for a hyperboloid. As a, the scale factor becomes large the last term is small.

The bias for flatness comes from inflation, where a region of an inflationary spacetime with large vacuum energy tunnels into a small vacuum energy. This results in so called pocket world's. There is a boundary to the high energy region. By the Gauss-Bonnett theorem this boundary has information. A type of quantum phase change may change the topology into a sphere that "pops off" the inflationary manifold. So for me this might be welcome news if the observable cosmos is spherical.

I argued two or three times with Brent and others, that the curvature cannot be exactly zero, or negative -- corresponding to flat or saddle-shaped universes -- because both are infinite in spatial extent, which contradicts the models of the cosmos being extremely tiny near the BB. They also contradict the concept of the cosmos expanding for finite time, at less than infinite speed.  So it seemed clear, that the cosmos must be spherical in shape, with a positive curvature, very close to zero, but not zero -- which is what is measured. I don't see why my arguments made no impact. Now I don't understand why a spherical universe somehow poses a problem for inflation, which still seems needed to explain the large scale homogeneity. AG

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[Lawrence Crowell]

Gödel's cosmology violates the Hawking-Penrose condition T^{00} >= 0. This corresponds to the closed timelike curves in the spacetimes. The whole cosmology has a net angular momentum that frame drags geodesics into closed timelike curves.

LC

[Alan Grayson]

On Wednesday, January 8, 2020 at 3:56:50 AM UTC-7, Lawrence Crowell wrote:

Gödel's cosmology violates the Hawking-Penrose condition T^{00} >= 0. This corresponds to the closed timelike curves in the spacetimes. The whole cosmology has a net angular momentum that frame drags geodesics into closed timelike curves.

LC

Can you explain in layman's terms what this means? TIA, AG 

[Lawrence Crowell]

Energy is positive.

LC

[Alan Grayson]

On Wednesday, January 8, 2020 at 4:34:35 AM UTC-7, Lawrence Crowell wrote:

Energy is positive.

LC

Does this mean the universe is closed and shaped like a hyper-sphere? TIA, AG

[Lawrence Crowell]

Not necessarily.

LC

[Alan Grayson]

On Wednesday, January 8, 2020 at 4:34:35 AM UTC-7, Lawrence Crowell wrote:

Energy is positive.

LC

That's quite a change from your earlier position, that the net energy of the universe is zero. In any event, Brent says above that the sign of k, related to curvature in the FLRW solution of Einstein's field equations, is incorporated in the initial conditions of the BB. But since we don't really know what the BB initial conditions are, ISTM that the curvature we wind up with, is nothing more than what we assume, or what our bias is. AG

[Lawrence Crowell]

The T^{00} >= 0, which is the vev, or defines H, but the gravitational potential is negative. The sum is zero.

LC

[Alan Grayson]

On Friday, January 10, 2020 at 9:33:00 AM UTC-7, Lawrence Crowell wrote:

The T^{00} >= 0, which is the vev, or defines H, but the gravitational potential is negative. The sum is zero.

LC

Earlier you posted the total energy is positive, now it's zero. Sorry, but I can't make sense of this. Moreover, for a test particle, the gravitational potential energy depends on where in the gravity field one chooses to calculate the potential energy. As you get closer to the source of the field, the potential energy gets arbitrarily large. So it seems that gravitational potential energy is not well defined. Hopefully, you can clarify these issues. TIA, AG 

[Lawrence Crowell]

The Hamiltonian H = ½(a’)^2 - 4πGρ/3c^2 is zero. Here a is the scale factor a' the time derivative and ρ the vacuum energy density. By positive it means that ρ is;positive and the kinetic energy ½(a’)^2 is positive. The gravitational potential energy - 4πGρ/3c^2 is negative.

LC.

[Alan Grayson]

On Friday, January 10, 2020 at 6:52:47 PM UTC-7, Lawrence Crowell wrote:

The Hamiltonian H = ½(a’)^2 - 4πGρ/3c^2 is zero. Here a is the scale factor a' the time derivative and ρ the vacuum energy density. By positive it means that ρ is;positive and the kinetic energy ½(a’)^2 is positive. The gravitational potential energy - 4πGρ/3c^2 is negative.

LC.

Is gravitational potential energy well defined in Newtonian physics? I think not, for the reasons previously given. AG 

[Lawrence Crowell]

On Saturday, January 11, 2020 at 2:17:32 AM UTC-6, Alan Grayson wrote:

On Friday, January 10, 2020 at 6:52:47 PM UTC-7, Lawrence Crowell wrote:

The Hamiltonian H = ½(a’)^2 - 4πGρ/3c^2 is zero. Here a is the scale factor a' the time derivative and ρ the vacuum energy density. By positive it means that ρ is;positive and the kinetic energy ½(a’)^2 is positive. The gravitational potential energy - 4πGρ/3c^2 is negative.

LC.

Is gravitational potential energy well defined in Newtonian physics? I think not, for the reasons previously given. AG 

It is well defined. The FLRW and de Sitter spacetimes on the Hubble frame reduce to a Newtonian description, for the most part except the term -k/a^2.   This works well enough.

LC

[Alan Grayson]

On Saturday, January 11, 2020 at 3:10:40 AM UTC-7, Lawrence Crowell wrote:

On Saturday, January 11, 2020 at 2:17:32 AM UTC-6, Alan Grayson wrote:

On Friday, January 10, 2020 at 6:52:47 PM UTC-7, Lawrence Crowell wrote:

The Hamiltonian H = ½(a’)^2 - 4πGρ/3c^2 is zero. Here a is the scale factor a' the time derivative and ρ the vacuum energy density. By positive it means that ρ is;positive and the kinetic energy ½(a’)^2 is positive. The gravitational potential energy - 4πGρ/3c^2 is negative.

LC.

Is gravitational potential energy well defined in Newtonian physics? I think not, for the reasons previously given. AG 

It is well defined. The FLRW and de Sitter spacetimes on the Hubble frame reduce to a Newtonian description, for the most part except the term -k/a^2.   This works well enough.

LC

If you Int (Fdr) from some r to infinity, you get the potential energy at r, but it blows up as you get to the center of mass. For me, this indicates the PE in Newtonian gravity is not well defined. No? AG

[Lawrence Crowell]

On Saturday, January 11, 2020 at 5:37:02 AM UTC-6, Alan Grayson wrote:

On Saturday, January 11, 2020 at 3:10:40 AM UTC-7, Lawrence Crowell wrote:

On Saturday, January 11, 2020 at 2:17:32 AM UTC-6, Alan Grayson wrote:

On Friday, January 10, 2020 at 6:52:47 PM UTC-7, Lawrence Crowell wrote:

The Hamiltonian H = ½(a’)^2 - 4πGρ/3c^2 is zero. Here a is the scale factor a' the time derivative and ρ the vacuum energy density. By positive it means that ρ is;positive and the kinetic energy ½(a’)^2 is positive. The gravitational potential energy - 4πGρ/3c^2 is negative.

LC.

Is gravitational potential energy well defined in Newtonian physics? I think not, for the reasons previously given. AG 

It is well defined. The FLRW and de Sitter spacetimes on the Hubble frame reduce to a Newtonian description, for the most part except the term -k/a^2.   This works well enough.

LC

If you Int (Fdr) from some r to infinity, you get the potential energy at r, but it blows up as you get to the center of mass. For me, this indicates the PE in Newtonian gravity is not well defined. No? AG

 

That is no more of a problem than r = 0. For finite differences it works fine.

LC

[Alan Grayson]

On Saturday, January 11, 2020 at 9:58:45 AM UTC-7, Lawrence Crowell wrote:

On Saturday, January 11, 2020 at 5:37:02 AM UTC-6, Alan Grayson wrote:

On Saturday, January 11, 2020 at 3:10:40 AM UTC-7, Lawrence Crowell wrote:

On Saturday, January 11, 2020 at 2:17:32 AM UTC-6, Alan Grayson wrote:

On Friday, January 10, 2020 at 6:52:47 PM UTC-7, Lawrence Crowell wrote:

The Hamiltonian H = ½(a’)^2 - 4πGρ/3c^2 is zero. Here a is the scale factor a' the time derivative and ρ the vacuum energy density. By positive it means that ρ is;positive and the kinetic energy ½(a’)^2 is positive. The gravitational potential energy - 4πGρ/3c^2 is negative.

LC.

Is gravitational potential energy well defined in Newtonian physics? I think not, for the reasons previously given. AG 

It is well defined. The FLRW and de Sitter spacetimes on the Hubble frame reduce to a Newtonian description, for the most part except the term -k/a^2.   This works well enough.

LC

If you Int (Fdr) from some r to infinity, you get the potential energy at r, but it blows up as you get to the center of mass. For me, this indicates the PE in Newtonian gravity is not well defined. No? AG

 

That is no more of a problem than r = 0. For finite differences it works fine.

LC

But F, the gravitational force, is undefined for point sources, when r = 0. In any event, what you're calculating is finite differences, not absolute values. What good is that if you want to add rest energy using E = mc^2, and equating it with negative gravitational potential energy, to get the total energy of universe as zero. ISTM, you're adding apples with oranges. AG 

[Brent Meeker]

On 1/11/2020 3:37 AM, Alan Grayson wrote:

If you Int (Fdr) from some r to infinity, you get the potential energy at r, but it blows up as you get to the center of mass. For me, this indicates the PE in Newtonian gravity is not well defined. No? AG

No.  Once you're inside the body the potential no longer goes as 1/R.

Brent

[Alan Grayson]

I love it. I really do. I knew you had something major to contribute. LOL. Not being sarcastic. But now I need some deep thought. Firstly, what I call "the substratum", is that from which the BB emerges. It can be any shape, possibly flat, or possibly beyond any concept of shape, but likely having an infinite past. This is not "our universe", which consists of two parts, observable and non-observable, the latter arising due to expansion faster than the SoL, during inflation, or afterward. Or even due to expansion slower than the SoL since the non-observable part winks out solely due to the geometric effects of expansion. Do you find this model somehow flawed, and if so, why? TIA, AG

Brent

[Alan Grayson]

On Saturday, January 11, 2020 at 1:58:55 PM UTC-7, Brent wrote:

Another interesting question: using, say, a neutron, and Newtonian gravity, is the negative gravitational energy exactly equal to its positive rest energy, using mc^2?  AG

Brent

[Alan Grayson]

On Friday, December 20, 2019 at 6:33:39 PM UTC-7, Alan Grayson wrote:

I've argued for this several times based on logic, not data, and as far as I can recall, no one took me seriously. AG

https://thenextweb.com/syndication/2019/12/17/cosmology-in-crisis-as-evidence-suggests-our-universe-isnt-flat-its-actually-curved/

The published scientific article on which the above is based must be purchased. I will do so in the near futures and post it for our resident experts to peruse. AG 

[Brent Meeker]

Save your money.  https://arxiv.org/pdf/1911.02087.pdf

Brent

[Alan Grayson]

TY.  No one can say you didn't put your money where your mouth is! Any opinion on this paper? AG