Can "Infinity" ever be more than a mathematical abstraction?

By whom?

And answer me: what does what happened afterwards have to do whether space was created infinite in size?
Expansion (inflation) provides evidence that space was NOT created infinitely large in initial size, no?

IMO, expansion (inflation) is logically only possible in a permittive condition or state.
If that permittive state is potentially infinite, is at the heart of the question and the answer lies beyond our dimensional "experience".

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Expansion (inflation) provides evidence that space was NOT created infinitely large in initial size, no?
As I've already said: no, it does not. Infinite space can expand just fine. Please provide an actual counter-argument or evidence that an infinite space cannot expand or contract.

IMO, expansion (inflation) is logically only possible in a permittive condition or state.
If that permittive state is potentially infinite, is at the heart of the question and the answer lies beyond our dimensional "experience".
(Irrelevant.)

Expansion (inflation) provides evidence that space was NOT created infinitely large in initial size, no?
How can the Universe be infinite if it was all concentrated into a point at the Big Bang?

The Universe was not concentrated into a point at the time of the Big Bang. But the observable Universe was concentrated into a point. The distinction between the whole Universe and the part of it that we can see is important.
www.astro.ucla.edu/~wright/infpoint.html

Model an expanding universe of infinite spatial extent. Run the model backwards and you find the model's values of energy density (matter and EM radiation) go screwy, that is, the values approach infinite density at every point in this infinite universe. Because of such a density, the laws of physics become undefinable. Notice the infinite spatial extent is still there.

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Not to my satisfaction.
As I've already said: no, it does not. Infinite space can expand just fine. Please provide an actual counter-argument or evidence that an infinite space cannot expand or contract.
Why are you presuming that space is infinite? What is the evidence for that?
If I assume that space is finite then the question becomes if finite space can expand infinitely. We know in the past it was contracted into a singularity.
(Irrelevant.)
Only if you presume that there was space before the BB. What is the evidence for that?
My position is that space (as we know it) did not exist until the BB, starting as a singularity and with a limited (albeit near infinite) amount of energy, which prohibits infinite expansion of the created universe.
In my model, at some point expansion of space will cease. (The law of thermodynamics?)

I am not saying that the extra-universal condition would prohibit infinite expansion, just that the current universe does not have sufficient energy for infinite expansion and at this time is not already infinite in size. We would not be able to measure it. But we know the approximate size of the universe and it is definitely not infinitely large at this time. I believe that's mainstream science?

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Not to my satisfaction.
Then may I suggest that you ask for clarifications, instead of repeating the same question over again?

Why are you presuming that space is infinite? What is the evidence for that?
Please don't put words in my mouth: I've never claimed that space is infinite. My position is that both scenario's (space being infinite, and space not being infinite) are still on the table.

If I assume that space is finite then the question becomes if finite space can expand infinitely.
Why would finite space need to expand infinitely?

We know in the past it was contracted into a singularity.
False; we only know that the visible universe was concentrated into a very small spot. Anything before that we don't know, as our current understanding of the laws of nature breaks down. This has already been explained in post #664.

Only if you presume that there was space before the BB. What is the evidence for that?
(Irrelevant.)

My position is that space (as we know it) did not exist until the BB, starting as a singularity and with a limited (albeit near infinite) amount of energy, which prohibits infinite expansion of the created universe.
In my model, at some point expansion of space will cease. (The law of thermodynamics?)
I believe that's mainstream science?
As already pointed out above, that's not the mainstream scientific position, and as such, it does nothing to answer whether space is finite or not, and thus it's irrelevant.

Then may I suggest that you ask for clarifications, instead of repeating the same question over again?
"As I've already said: no, it does not. Infinite space can expand just fine. Please provide an actual counter-argument or evidence that an infinite space cannot expand or contract."
Please don't put words in my mouth: I've never claimed that space is infinite. My position is that both scenario's (space being infinite, and space not being infinite) are still on the table.
"As I've already said: no, it does not. Infinite space can expand just fine. Please provide an actual counter-argument or evidence that an infinite space cannot expand or contract."
Why would finite space need to expand infinitely?
IMO, it does not.
False; we only know that the visible universe was concentrated into a very small spot. Anything before that we don't know, as our current understanding of the laws of nature breaks down. This has already been explained in post #664.
I think it is absurd to speak of a "visible universe" to begin with. From what POV would that be? Inside or Out?

And a very small spot is not a singularity? And if it is a singularity , then can it be infinite in size? Your posit would create a very small infinity......problematic, IMO.
(Irrelevant.)
As already pointed out above, that's not the mainstream scientific position, and as such, it does nothing to answer whether space is finite or not, and thus it's irrelevant.
If there is no answer whether space is infinite or not, why are we creating models from a presumption that space IS infinite in size?

Should we not begin with what we know to be true?
I am starting from the position that space did not exist until the BB, which created space.

In any other model assuming an infinite pre-condition rather than an infinitely permittive pre-condition, infinite space is not created at all, but merely converted from a prior infinite state. If that is the case then lets replace the word "creation" with "conversion".

But there is always that pesky (limiting) start to spacetime as a finite "singularity".......

If we have merely a "conversion" from one state into another state, then the pre-space condition must have been a singularity as well, no?

My proof lies in the fact that the stuff of spacetime, matter, did not form until after the BB.

Prior to that there was only pure potential. (Bohm) and it is irrelevant if pure potential is infinite, it has no defined size.

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And if you read it carefully, you'll notice I don't claim that the universe is infinite in size.

IMO, it does not.
Well, you brought it up as an option in post #665, but I'm glad you agree with me that that's not possible.

And a very small spot is not a singularity?
Please learn what a singularity is. A small (and thus with a non-zero radius) spot is not one.

And if it is a singularity , then can it be infinite in size.
That's nonsense: a singularity is infinitely small, not infinitely large.

Your posit would create a very small infinity......problematic, IMO.
1) It's not my posit; this is the current big bang model.
2) It's not creating an infinity; just a small, dense area.

If there is no answer whether space is infinite or not, why are we creating models from a presumption that space IS infinite in size?
I don't know who this "we" is, because it's certainly not part of mainstream science.

Should we not begin with what we know to be true?
I agree.

I am starting from the position that space did not exist until the BB, which created space.
Which is not something that we know to be true, so why are you starting with that?

In any other model assuming an infinite pre-condition rather than an infinitely permittive pre-condition, infinite space is not created at all, but merely converted from a prior infinite state.

But there is always that pesky (limiting) start to spacetime as a finite "singularity".......
So in summary, your evidence that the universe is finite is a sole argument from incredulity? "I can't understand how the universe can be infinite, therefore it's not?" Because that's all the evidence you've brought to the table so far...

And if you read it carefully, you'll notice I don't claim that the universe is infinite in size.
Lol, ok then.
Please learn what a singularity is. A small (and thus with a non-zero radius) spot is not one.
" That's nonsense: a singularity is infinitely small, not infinitely large."
Please clarify the difference. Is an infinitely small "point" the same as an infinitely large "everything"? They are both singularities, no?
Moreover, how can an infinitely small point contain an infinitely large amount of energy?
That does not seem logical to me. However we know that a small but finite size object can contain an enormous amount of energy. A neutron star is just one example. OTOH, I am not at all sure that a black hole contains a large amount of energy, I know it has a very strong gravitational field. Is that caused by energy?
Of course neither formed until well after the BB.....
1) It's not my posit; this is the current big bang model.
2) It's not creating an infinity; just a small, dense area.
I agree, a finite singularity. Keyword "finite". Else we would have space outside of space, no?
I don't know who this "we" is, because it's certainly not part of mainstream science.
Where does my POV differ from "mainstream"?
Which is not something that we know to be true, so why are you starting with that?
I am not. My starting point is after the BB, which you chided me for.
Again where does my POV differ from mainstream?
So in summary, your evidence that the universe is finite is a sole argument from incredulity? "I can't understand how the universe can be infinite, therefore it's not?" Because that's all the evidence you've brought to the table so far...
No, I have brought to the table only that which is known and infinity is not part of it. That's where the speculation begins.

In my model infinite potential is contained in the singularity of a permittive pre-condition, without size restriction, before the creation of space as we know it.
Potential = That which may become reality.[/QUOTE]

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www.astro.ucla.edu/~wright/infpoint.html

Model an expanding universe of infinite spatial extent. Run the model backwards and you find the model's values of energy density (matter and EM radiation) go screwy, that is, the values approach infinite density at every point in this infinite universe. Because of such a density, the laws of physics become undefinable. Notice the infinite spatial extent is still there.
I call it a timeless infinitely permittive condition, which is not equatable with spatial or temporal dimensions at all. Its the only way you can have a "beginning".

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Lol, ok then.
Not sure how you not reading my posts carefully is funny, but I'm glad you've done so now.

Sure! A sphere the size of an atom is not a singularity, but it is a very small area.

Is an infinitely small "point" the same as an infinitely large "everything"?
Obviously not, and I don't know why you'd ask such a silly question.

They are both singularities, no?
As I've just explained to you: no.

Moreover, how can an infinitely small point contain an infinitely large amount of energy?
Since when did it contain an infinitely large amount of energy? Where did that all of a sudden come from?

But the answer is: our current theories break down in such cases, so we don't know.

That does not seem logical to me. However we know that a small but finite size object can contain an enormous amount of energy. A neutron star is just one example. OTOH, I am not at all sure that a black hole contains a large amount of energy, I know it has a very strong gravitational field. Is that caused by energy?
Partially, yes, as predicted by the general theory of relativity. I would have thought a person making any statements about cosmology and singularities would be familiar with the basics of GR, but clearly, I was wrong in assuming that.

Of course neither formed until well after the BB.....
True.

I agree, a finite singularity.
False; that small area is not a singularity; density is high, but not infinite.

Keyword "finite". Else we would have space outside of space, no?
That makes no sense... Why would there be space outside of space in that case?

Where does my POV differ from "mainstream"?
Mainstream science doesn't say the universe is finite, or infinite. Both options are still on the table.

I am not.
Right, since you like to say "Your words", now it's my turn to do that. Here's the verbatim quote I responded to:
I am starting from the position that space did not exist until the BB, which created space.
I then responded:
Which is not something that we know to be true, so why are you starting with that?
And now you are saying you're not starting with that, even though literally one post earlier you explicitly said you are starting with that.

My starting point is after the BB, which you chided me for.
That's the starting point of mainstream science as well; if you thought I was scolding you for that, you misinterpreted what I wrote.

Again where does my POV differ from mainstream?

No, I have brought to the table only that which is known and infinity is not part of it.
Exactly: we don't know whether the universe is infinite in size or not.

That's where the speculation begins.
That's indeed where your speculation begins; I haven't been speculating in this thread. In fact, I've been pointing out speculations made by others.

In my model infinite potential is contained in the singularity of a permittive pre-condition, without size restriction, before the creation of space as we know it.
Potential = That which may become reality.
(Irrelevant, because you've just admitted this is speculation (as I have been saying all along), and that's off-topic.)

Sure! A sphere the size of an atom is not a singularity, but it is a very small area.
A "single" object is not a singularity? "One" is not a singularity? "Wholeness" is not a singularity?
Does any of that make sense?

A "single" object is not a singularity? "One" is not a singularity? "Wholeness" is not a singularity?
Does any of that make sense?
It makes sense if you learn the definition of singularity: https://en.wikipedia.org/wiki/Gravitational_singularity
How can you not know this? How can you even think you are talking any kind of sense when you obviously don't know what the words mean? How can you claim to know what mainstream science says, if you don't even understand what the words used mean?

Since it's now clear Write4U has no idea what he is talking about, is taking the thread completely off-topic, and is pushing fringe, I'll stop responding to all that nonsensical rambling. Sorry for letting Write4U pollute this thread! Carry on!

Exactly: we don't know whether the universe is infinite in size or not.
Then let's drop the assertion that the universe is an expanding infinite singularity, a theoretical Hilbert Hotel model. We don't know that it is.

It makes sense if you learn the definition of singularity: https://en.wikipedia.org/wiki/Gravitational_singularity
How can you not know this? How can you even think you are talking any kind of sense when you obviously don't know what the words mean? How can you claim to know what mainstream science says, if you don't even understand what the words used mean?
Because I look further and deeper.
Singular (definition): of a matrix; having a determinant equal to zero: having the property that the matrix of coefficients of the new variables has a determinant equal to zero.
https://www.merriam-webster.com/dictionary/singular

i.e. not infinity.

How "singularity" became to mean an infinitely small point containing an infinite amount of energy is a mystery to me.
Singularity, PHYSICS, MATHEMATICS;
a point at which a function takes an infinite value, especially in space-time when matter is infinitely dense, as at the center of a black hole.
Since such quantities become infinite within the singularity, the laws of normal spacetime cannot exist
??????? The laws of spacetime cannot exist in the universal singularity or in a black hole?

Do we exist in the universal singularity or in a black hole? Was a black hole or a universal singularity the precursor to the universe?

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Since when did it contain an infinitely large amount of energy? Where did that all of a sudden come from?
Where did "inflation" suddenly come from?

A "single" object is not a singularity? "One" is not a singularity? "Wholeness" is not a singularity?
Does any of that make sense?

Physics simply doesn't make sense, that means when we deal with infinities, physics as we know it breaks down. Gives us... unreasonable answers. This is why there is a lot of attention on ''what goes on inside a black hole right now'' because there is not much logic to be found from singularities.

Physics simply doesn't make sense, that means when we deal with infinities, physics as we know it breaks down. Gives us... unreasonable answers. This is why there is a lot of attention on ''what goes on inside a black hole right now'' because there is not much logic to be found from singularities.

Yup, agree with this. When physicists talk about infinity, they just mean "a place where our known physics seems to break down." They don't mean any kind of mathematical infinity that's actualized in the physical world.

No less a luminary than Max Tegmark makes that same point. The infinities in physics are not actual infinities or even mathematical infinities.

Infinity Is a Beautiful Concept – And It’s Ruining Physics
http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/

I can't help but point out that Dirac's delta "function" is infinite-valued on an infinitesimal interval. It provides, moreover, a highly simplifying and intuitively satisfying notation for his vastly influential treatment of quantum mechanics.
(most of that last sentence was lifted from this paper--https://arxiv.org/pdf/1608.06878.pdf)