How can a big bang expand to an infinite size?

[Airbrush]

We always hear that the big bang started from a tiny point, smaller than a proton, that experienced cosmic inflation and expanded many times the speed of light for a tiny fraction of a second.  Oh, I see, that was only the observable portion of the entire universe.  Considering that anything finite can never expand to an infinite size, does that not indicate that the region of the universe we live in is probably not indicative of our universe out to a distance of, for example, a googol light years?  Or Graham's number of light years?  It would appear that our universe probably has a finite size.  Or maybe it has reached infinity through some means we don't understand?  Was the beginning of the entire universe not a tiny point, smaller than a proton, but for the universe to be infinite in size, the beginning had to be infinite in size, which doesn't make sense.

Edited November 25, 2023 by Airbrush

[Janus]

You may "always hear that", but it isn't what model actually says.  All it says is that the Universe, in it's earliest stages, was extremely hot and dense, and says nothing about it's size.  One of the still unknowns about the universe is whether it is finite or infinite.  The references to being "smaller than a proton" likely are referring with the "observable universe",  which, for all we know, could be a tiny corner of a much vaster, or even infinite universe.

[Airbrush]

On 11/25/2023 at 8:16 AM, Janus said:

You may "always hear that", but it isn't what model actually says.  All it says is that the Universe, in it's earliest stages, was extremely hot and dense, and says nothing about it's size.  One of the still unknowns about the universe is whether it is finite or infinite.  The references to being "smaller than a proton" likely are referring with the "observable universe",  which, for all we know, could be a tiny corner of a much vaster, or even infinite universe.

Can you say anything about the probability of the "universe" being finite or infinite in size?  Does it seem more likely to you that it would be FINITE in size?  It seems to me, that what we can see does not reveal what it far beyond.  Probably the universe does not look quite the same here as it does a googol light years away, it seems to me.  It could be doing things other than only expanding.  Or do you think it is a coin flip whether it is actually infinite or finite in size?

[Airbrush]

Let me try to answer my own question.  This assumes a FLAT universe. 

The way to expand to an infinite size is the big bang was infinite in size at the first Planck Time!  How else?

[Genady]

1 hour ago, Airbrush said:

This assumes a FLAT universe.

Why?

[Airbrush]

On 12/9/2023 at 9:20 AM, Genady said:

Why?

 

Thanks for your question!  Nobody has ever wanted to discuss infinity here, regarding the universe, although I introduced it many times over the years.

Because if the universe was NOT flat, then there is no infinity for our observable big bang.  We cannot see any curvature yet, but maybe it is so large that it is still undetectable.

Infinite size is possible only with a flat universe.  Am I correct?

The difference between infinity and a very, VERY large universe, is INFINITE.  "Infinity" is a problematic word and probably should not even be considered.

The number of Planck Volumes in our observable universe is only about 10^185 (or 10 to the power of 185).  That means that if you fill the observable universe with a tiny dust that is only ONE Planck Length in size, and volume, you can pack only 10^185 into it.

".... I don’t see how the universe could be infinite and yet constantly expanding. I believe it is constantly expanding but something that is infinite in size cannot be measured and you cannot just say it is now Infinite+1 and Infinite+2. Infinity is infinity. If the universe was infinite it wouldn’t need to expand anymore. It’s as big as it ever could and will be in that case."

Logically, how can the universe be infinite in size? - Astronomy Stack Exchange

 

Edited December 11, 2023 by Airbrush

[Genady]

9 minutes ago, Airbrush said:

Because if the universe was not flat, then there is no infinity for our observable big bang.  We cannot see any curvature yet, but maybe it is so large that it is still undetectable.

Infinite size is possible only with a flat universe.  Am I correct?

The difference between infinity and a very, VERY large universe, is INFINITE.  "Infinity" is a problematic word and probably should not even be considered.

An isotropic homogeneous 3D space can have spherical, flat, or hyperbolic geometry. Spherical space is necessarily finite, but both flat and hyperbolic can be infinite.

[Airbrush]

4 hours ago, Genady said:

An isotropic homogeneous 3D space can have spherical, flat, or hyperbolic geometry. Spherical space is necessarily finite, but both flat and hyperbolic can be infinite.

Yes, so assume the case the universe was either flat or hyperbolic, that allows for the possibility the universe was infinite, but how about the PROBABILITY of it?  Infinity is a long way from home.

[Genady]

13 minutes ago, Airbrush said:

Yes, so assume the case the universe was either flat or hyperbolic, that allows for the possibility the universe was infinite, but how about the PROBABILITY of it?  Infinity is a long way from home.

Flatness requires special conditions because it requires the density parameter \(\Omega = 1\), precisely. The other two happen when \(\Omega > 1\) (spherical) or \(\Omega < 1\) (hyperbolic).

I don't know how to apply PROBABILITY in the case of one (one universe).

I don't know what a problem with infinity is.

[Airbrush]

17 hours ago, Genady said:

Flatness requires special conditions because it requires the density parameter Ω=1 , precisely. The other two happen when Ω>1 (spherical) or Ω<1 (hyperbolic).

I don't know how to apply PROBABILITY in the case of one (one universe).

I don't know what a problem with infinity is.

Fair enough.  My next question is how representative is our observable universe in telling us what an infinite (flat or hyperbolic) universe is like a googol lightyears away?  Grahams number of lightyears away?  It seems to me that INFINITY requires a lot (an infinite number) of alignments for our big bang to stretch to infinity, as we see it.

Edited December 12, 2023 by Airbrush

[Genady]

58 minutes ago, Airbrush said:

how representative is our observable universe in telling us what an infinite (flat or hyperbolic) universe is like a googol lightyears away?

Perhaps we will never know.

 

1 hour ago, Airbrush said:

It seems to me that INFINITY requires a lot (an infinite number) of alignments for our big bang to stretch to infinity, as we see it.

I don't understand this.

[Airbrush]

On 12/12/2023 at 9:47 AM, Genady said:

Perhaps we will never know.

I don't understand this.

 

We may never know.  Why do scientists believe that the unfathomable number TREE3 is not infinite?

If you are walking along a sandy beach, and you scoop up a handful of sand, how much about our universe does that little handful of sand tell you?  It tells us about the minerals in sand and some other things, such as the atomic structure of this kind of matter.  It does NOT tell us about EVERYWHERE in the universe.  Our observable universe is just a handful of sand, in a universe that extends to infinity in every direction (assuming a flat or hyperbolic universe).  Our observable universe is a tiny pinprick in the vastness of infinity.  For this reason, I think that our universe, the large-scale, sponge-like structure we see is probably finite.  It just becomes less dense in one direction, until there is no matter at all, and empty space until you reach the edge of an adjacent big bang.

Edited December 17, 2023 by Airbrush

[Genady]

20 minutes ago, Airbrush said:

For this reason

I can't see a reason that connects what comes before and what comes after this phrase. Poetry, perhaps, but not a reason.

[StringJunky]

3 hours ago, Airbrush said:

 

We may never know.  Why do scientists believe that the unfathomable number TREE3 is not infinite?

If you are walking along a sandy beach, and you scoop up a handful of sand, how much about our universe does that little handful of sand tell you?  It tells us about the minerals in sand and some other things, such as the atomic structure of this kind of matter.  It does NOT tell us about EVERYWHERE in the universe.  Our observable universe is just a handful of sand, in a universe that extends to infinity in every direction (assuming a flat or hyperbolic universe).  Our observable universe is a tiny pinprick in the vastness of infinity.  For this reason, I think that our universe, the large-scale, sponge-like structure we see is probably finite.  It just becomes less dense in one direction, until there is no matter at all, and empty space until you reach the edge of an adjacent big bang.

The universe stops fractalizing beyond a certain scale and becomes homogenous.

Quote

We have made the largest-volume measurement to date of the transition to large-scale homogeneity in the distribution of galaxies. We use the WiggleZ survey, a spectroscopic survey of over 200,000 blue galaxies in a cosmic volume of ~1 (Gpc/h)^3. A new method of defining the 'homogeneity scale' is presented, which is more robust than methods previously used in the literature, and which can be easily compared between different surveys. Due to the large cosmic depth of WiggleZ (up to z=1) we are able to make the first measurement of the transition to homogeneity over a range of cosmic epochs. The mean number of galaxies N(<r) in spheres of comoving radius r is proportional to r^3 within 1%, or equivalently the fractal dimension of the sample is within 1% of D_2=3, at radii larger than 71 \pm 8 Mpc/h at z~0.2, 70 \pm 5 Mpc/h at z~0.4, 81 \pm 5 Mpc/h at z~0.6, and 75 \pm 4 Mpc/h at z~0.8. We demonstrate the robustness of our results against selection function effects, using a LCDM N-body simulation and a suite of inhomogeneous fractal distributions. The results are in excellent agreement with both the LCDM N-body simulation and an analytical LCDM prediction. We can exclude a fractal distribution with fractal dimension below D_2=2.97 on scales from ~80 Mpc/h up to the largest scales probed by our measurement, ~300 Mpc/h, at 99.99% confidence.

https://arxiv.org/abs/1205.6812

 

 

Edited December 17, 2023 by StringJunky

[Boltzmannbrain]

On 11/25/2023 at 10:55 AM, Airbrush said:

We always hear that the big bang started from a tiny point, smaller than a proton, that experienced cosmic inflation and expanded many times the speed of light for a tiny fraction of a second.  Oh, I see, that was only the observable portion of the entire universe.  Considering that anything finite can never expand to an infinite size, does that not indicate that the region of the universe we live in is probably not indicative of our universe out to a distance of, for example, a googol light years?  Or Graham's number of light years?  It would appear that our universe probably has a finite size.  Or maybe it has reached infinity through some means we don't understand?  Was the beginning of the entire universe not a tiny point, smaller than a proton, but for the universe to be infinite in size, the beginning had to be infinite in size, which doesn't make

Why would it have had to be infinity in the beginning g?  If distance is a function of time, the equation 1/(1 - t) reaches infinity in 1 second.  I don't know if something like this rate of expansion is considered in mainstream physics, but it at least works mathematically.

[Genady]

2 hours ago, StringJunky said:

The universe stops fractalizing beyond a certain scale and becomes homogenous.

 

 

The universe was much more homogeneous just after the Big Bang, as is evidenced by the isotropy of the CMB radiation. It became less homogeneous with time, presumably because of the gravitational clumping. OTOH, expansion works against clumping, and an accelerated expansion even more so. Does anybody know what will happen in the future to the "scale of homogeneity"?

11 minutes ago, Boltzmannbrain said:

If distance is a function of time, the equation 1/(1 - t) reaches infinity in 1 second

and becomes negative after that.

[Boltzmannbrain]

33 minutes ago, Genady said:

and becomes negative after that.

I think you missed the point.  I was trying to show how you can reach infinite size in a finite amount of time, whatever the formula has to be to reach 14 billion years.

[Genady]

31 minutes ago, Boltzmannbrain said:

I think you missed the point.  I was trying to show how you can reach infinite size in a finite amount of time, whatever the formula has to be to reach 14 billion years.

I did not miss that point, but my counterpoint was that it does not work mathematically. It reaches the infinity and momentarily changes to \(- \infty \) and stays negative after that. Distance cannot do this.

P.S. You want the size to reach infinity and to stay infinite. Try another formula.

Edited December 17, 2023 by Genady

[Boltzmannbrain]

15 minutes ago, Genady said:

I did not miss that point, but my counterpoint was that it does not work mathematically. It reaches the infinity and momentarily changes to −∞ and stays negative after that. Distance cannot do this.

P.S. You want the size to reach infinity and to stay infinite. Try another formula.

Okay, now I am certain you missed the point.  I will tell you it a second time.  The universe can reach infinite size in a finite amount of time, mathematically speaking. 

P.S. Try to understand the point that the poster is trying to make instead of looking for an irrelevant issue that only sidetracks the discussion.  Don't worry, you are by far not only the one that does this on discussion forums like this one.

[Genady]

1 hour ago, Boltzmannbrain said:

The universe can reach infinite size in a finite amount of time, mathematically speaking.

Mathematically speaking, it cannot reach infinite size, but it rather increases unboundedly as \(t \rightarrow 1\) from below. At \(t=1\), the formula is undetermined: mathematically speaking, \(\frac 1 0\) is undefined.

Edited December 18, 2023 by Genady

[Boltzmannbrain]

3 hours ago, Genady said:

Mathematically speaking, it cannot reach infinite size, but it rather increases unboundedly as t→1  from below. At t=1 , the formula is undetermined: mathematically speaking, 10 is undefined.

But that's what we were taught in high school.  It turns out there are ways it is allowed.  

[Genady]

3 hours ago, Boltzmannbrain said:

But that's what we were taught in high school.  It turns out there are ways it is allowed.  

The domain of the function \(\frac 1 {1-t}\) excludes \(1\), as the domain of the function \(\frac 1 x\) excludes \(0\):

(Domain of a function - Wikipedia) 

[Boltzmannbrain]

9 hours ago, Genady said:

The domain of the function 11−t excludes 1 , as the domain of the function 1x excludes 0 :

(Domain of a function - Wikipedia) 

From Division by zero - Wikipedia

Extended real line[edit]

The extended real number line is obtained from the real number system  by adding two infinity elements:  and  read as "positive infinity" and "negative infinity" respectively, which are treated as actual numbers. By adjoining the elements  and  to  it enables a formulation of a "limit at infinity" that works like a limit at any real number. When dealing with both positive and negative extended real numbers, the expression  is usually left undefined. However, in contexts where only non-negative values are considered, it is often convenient to define .

[Airbrush]

My next question is, can something finite in mass (or size) expand to an infinite size?  And please explain for me without advanced math.  Thank you.

Can anyone explain how mathematicians know that the number TREE3 is finite?

Edited December 18, 2023 by Airbrush

[Genady]

2 minutes ago, Airbrush said:

can something finite in mass (or size) expand to an infinite size?

No, in a continuous process it cannot.

 

3 minutes ago, Airbrush said:

Can anyone explain how mathematicians know that the number TREE3 is finite?

What is "number TREE3"?