The observable and non-observable parts of the Universe

[PainterGuy]

TL;DR Summary

I'm really confused between observable universe and unobservable universe. Did unobservable universe also originate as a result of the big bang?

Hi,

I'm only trying to understand the basic concept.

Did the big bang give rise to both observable and non-observable universe? I have been through quite a few source and it seems like that the big bang was the cause of only observable universe and not of unobservable universe.

Below I have quoted some sources with excerpts. The first quote really summaries my confusion and it clearly says that the big bang only gave rise to observable universe. Thank you!

"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."
Source: http://www.astro.ucla.edu/~wright/infpoint.html

"Sure, the current observable universe seems to have formed from the cosmic expansion of a tiny original patch of spacetime some 13.7 billion years ago. But we can not say whether such original patch of spacetime was the only existing spacetime.

It could well be that such a tiny spacetime patch representing what the current spacetime has become was but a tiny patch from a much larger, perhaps infinite spacetime landscape, and that such a tiny spacetime patch expanded into the whole current visible universe. The rest of the much larger original spacetime landscape is simply forever beyond our reach, it has expanded faster that what its light could manage to approach to us. It will forever remain out of our sight."
Source: https://qr.ae/TSWVgv

"Physicists think of "space" not as emptiness, but similar to a piece of rubber. (But they don't call it rubber; they call it the "vacuum". "Particles", in physics, are just vibrations of the vacuum.) The vacuum can expand, just like the piece of rubber. But because it goes all the way to infinity, it doesn't need more space. A clever way to say it is that "there's lots of room at infinity". (That's clever, but it doesn't really explain anything.)"
Source: https://qr.ae/TSWVDk

"Our best theories of the early universe say that there was a time when our visible universe was incredibly small, hot and dense. That’s it. You could extrapolate back from that and say “Well, looking at this graph of the size of the universe, it crosses the zero line at this time, therefore it must have come from nothing, or a point of zero size, which we call a singularity.”, but you would be mistaken in doing so. Lots of people have made this mistake, and the name also helps to create the commonly held misconception that there was a big explosion where previously there was nothing."
Source: https://qr.ae/TSWVjJ

"13.8 billion years ago, the Big Bang occurred. The Universe was filled with matter, antimatter, radiation, and existed in an ultra-hot, ultra-dense, but expanding-and-cooling state. By today, the volume containing our observable Universe has expanded to be 46 billion light years in radius...
...
By taking the Universe we have today, we can extrapolate back to the earliest stages of the hot Big Bang, and arrive at a figure for both the age and the size of the Universe together."
Source: https://www.forbes.com/sites/starts...he-entire-unobservable-universe/#3a6d380df806

 

[weirdoguy]

I have been through quite a few source and it seems like that the big bang was the cause of only observable universe and not of unobservable universe.

Big Bang was a hot dense state of universe as a whole. Observable universe is part of the universe that we - people on Earth - can observe. Unobservable universe is the other part. Nothing more, nothing less.

The first quote really summaries my confusion and it clearly says that the big bang only gave rise to observable universe.

Um, it clearly does not say that. It says that volume of observable universe was much much smaller during the BB era than it is now.

 

[Ibix]

We model the universe as spatially infinite. The observable universe is the bit of it we can see, and is finite in extent.

In the far past, everything was closer together. But something that's infinite in size remains infinite even if everything is closer together. So the universe was never smaller despite everything being closer together (welcome to infinity - please leave your intuition at the door). The observable universe, however, was smaller because there's a finite amount of stuff in it, and it was closer together. Also, the observable universe is defined as the volume we can see, and light hadn't had time to travel so far. So the observable universe could have been the size of a grapefruit (or whatever) but it is still one part of the infinite universe.

Naive modelling gives us a problem if we go back far enough - the universe remains infinite in size but the observable universe (and every possible observable universe) goes to zero size. If that sounds contradictory, it kind of is. That's the Big Bang singularity, and singularities are the maths' way of saying "dunno".

Less naive models avoid the singularity by proposing various mechanisms. Inflation is, I believe, currently the most popular, but we may well need a better theory than general relativity before we are really confident.

I haven't read all of your sources, but I'll comment on Ned Wright's. He seems to me to be talking about the singularity in that quote, where the volume of the observable universe would indeed go to zero, if we took the singularity seriously. My understanding is that the modern view does not take it seriously. I'm not sure if Wright was writing before that view took hold, dissents from that view, or is simply assuming that the average reader won't have heard of inflation and is simply not opening any cans of worms he doesn't have to in a short article. This kind of second-guessing is a perennial problem with popularisations, even by highly competent scientists, I am afraid.

 

[PainterGuy]

Thank you, both of you!

@Ibix : Your post was really helpful. It looks like that you have essentially said the same thing - that the universe is infinite in size and age, and the observable universe is what was just a singularity at the time of big bang and our current observable universe, which is finite in size and age, came into existence from that singularity. In other words, the space-time of the observable universe originated from that singularity.

I'm sorry if I have interpreted what you said incorrectly.

I'm repeating three of the sources from my previous post because these are from experts, and the fourth is a new one. Though I could quote more sources from authors who are experts as well and say the same thing.

"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. In the figure below, two views of the Universe are shown: on the left for 1 Gyr after the Big Bang, and on the right the current Universe 13 Gyr after the Big Bang (assuming that the Hubble constant is Ho = 50 km/sec/Mpc and the Universe has the critical density.)"
Source: http://www.astro.ucla.edu/~wright/infpoint.html

"Physicists think of "space" not as emptiness, but similar to a piece of rubber. (But they don't call it rubber; they call it the "vacuum". "Particles", in physics, are just vibrations of the vacuum.) The vacuum can expand, just like the piece of rubber. But because it goes all the way to infinity, it doesn't need more space. A clever way to say it is that "there's lots of room at infinity". (That's clever, but it doesn't really explain anything.)"
Source: https://qr.ae/TSWVDk

"The hot Big Bang might mark the beginning of the observable Universe as we know it, but it doesn't mark the birth of space and time itself. Before the Big Bang, the Universe underwent a period of cosmic inflation. Instead of being filled with matter and radiation, and instead of being hot, the Universe was:

• filled with energy inherent to space itself,
• expanding at a constant, exponential rate,
• and creating new space so quickly that the smallest physical length scale, the Planck length, would be stretched to the size of the presently observable Universe every 10-32 seconds.

It's true that in our region of the Universe, inflation came to an end..."
Source: https://www.forbes.com/sites/starts...he-entire-unobservable-universe/#3a6d380df806

"It is generally thought that our universe began as a tiny patch in some pre-existing space-time forming a bubble which then underwent a burst of exponential expansion. This period of inflation stretched and smoothed our universe, leaving an even distribution of matter and energy. Outside this bubble, far beyond our cosmic horizon, things might look very different. Without inflation's ironing skills, space-time could be highly irregular: smooth in one neighbourhood and with massive structures or giant black holes in another. "It could be as bizarre as one can imagine, or something rather dull," says Kashlinsky. Either way, he suggests that something outside our bubble is tugging on our galaxy clusters, causing the dark flow."
Source: https://www.sott.net/article/173808-Dark-flow-Proof-of-another-universe

 

[PeterDonis]

I'm repeating three of the sources from my previous post because these are from experts

This is the wrong criterion to use. The right criterion is, is it a textbook or a peer-reviewed paper? If it isn't, you generally should not rely on it as a source. Ordinary websites, even if they are written by experts, are still not the same as textbooks or peer-reviewed papers: they have not been reviewed by experts other than the author and they have not gone through any kind of quality control other than the author's own.

 

[PeroK]

I'm repeating three of the sources from my previous post because these are from experts, and the fourth is a new one. Though I could quote more sources from authors who are experts as well and say the same thing.

"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. In the figure below, two views of the Universe are shown: on the left for 1 Gyr after the Big Bang, and on the right the current Universe 13 Gyr after the Big Bang (assuming that the Hubble constant is Ho = 50 km/sec/Mpc and the Universe has the critical density.)"
Source: http://www.astro.ucla.edu/~wright/infpoint.html

This may have come from UCLA, but it is not very good. First, if the entire universe was not a point, then neither was the observable universe. There is no discontinuity between the (currently) observable universe and the rest of the universe that we cannot yet observe.

The part of the universe we can observe increases continuously. This is simply that as time passes light from further away has had the time to reach us.

"Physicists think of "space" not as emptiness, but similar to a piece of rubber. (But they don't call it rubber; they call it the "vacuum". "Particles", in physics, are just vibrations of the vacuum.) The vacuum can expand, just like the piece of rubber. But because it goes all the way to infinity, it doesn't need more space. A clever way to say it is that "there's lots of room at infinity". (That's clever, but it doesn't really explain anything.)"
Source: https://qr.ae/TSWVDk

This is largely nonsense and I would ignore it. Vacuum is nothing like rubber.

"The hot Big Bang might mark the beginning of the observable Universe as we know it, but it doesn't mark the birth of space and time itself. Before the Big Bang, the Universe underwent a period of cosmic inflation. Instead of being filled with matter and radiation, and instead of being hot, the Universe was:

• filled with energy inherent to space itself,
• expanding at a constant, exponential rate,
• and creating new space so quickly that the smallest physical length scale, the Planck length, would be stretched to the size of the presently observable Universe every 10-32 seconds.

It's true that in our region of the Universe, inflation came to an end..."
Source: https://www.forbes.com/sites/starts...he-entire-unobservable-universe/#3a6d380df806

This is the typical popular science muddle and is too imprecise to be of much help.

 

[weirdoguy]

@Ibix : Your post was really helpful. It looks like that you have essentially said the same thing - that the universe is infinite in size and age, and the observable universe is what was just a singularity at the time of big bang and our current observable universe, which is finite in size and age, came into existence from that singularity. In other words, the space-time of the observable universe originated from that singularity.

Huh? Ibix said no such thing. Universe is not infinite in age (at least not in the BB model), and observable universe was not a singularity at the time of big bang - that is, when the universe was in a hot dense state and was rapidly expanding. It was very small ("The size of a grapefruit" which Ibix used) but that does not mean singularity. Don't get me wrong but part of the problem is not what people write but the conclusions you draw from that are too far-reaching and far-fetched.

 

[Bandersnatch]

This may have come from UCLA, but it is not very good. First, if the entire universe was not a point, then neither was the observable universe. There is no discontinuity between the (currently) observable universe and the rest of the universe that we cannot yet observe.

I'd like to think Ned Wright deserves more credit.
In the standard big bang cosmology any finite distance contracts to a point in the t=0 limit, including what is currently our observable universe. If the universe is infinite, then it doesn't contract to a point. Why do you think this implies a discontinuity?

 

[PeroK]

I'd like to think Ned Wright deserves more credit.
In the standard big bang cosmology any finite distance contracts to a point in the t=0 limit, including what is currently our observable universe. If the universe is infinite, then it doesn't contract to a point. Why do you think this implies a discontinuity?

1) There is no way to map a point to more than a point. Continuously or otherwise.

2) If what we can see today maps to a single point at ##t=0##, then what about the universe that becomes part of our observable universe tomorrow? Either that maps back to a point or you have a discontinuity.

In any case, as far as I am aware ##t=0## is not part of the BB model.

 

[Bandersnatch]

The singularity is not a part of the space-time manifold. But the 'point' referred to in this context is always the limit of the spatial extent of any finite distance as time approaches zero (the scale factor approaches 0).
It is not meant to suggest that the 3d space we live in somehow loses dimensions. It merely means that all finite distances approach zero as we roll back the cosmic time.
Now, you can argue that it's not a correct usage of the mathematical definition of a point, but this is a distinction that should be obviously clear for anyone who already knows the subject, while being lost on anyone who doesn't.

 

[PeterDonis]

the 'point' referred to in this context is always the limit of the spatial extent of any finite distance as time approaches zero (the scale factor approaches 0). It is not meant to suggest that the 3d space we live in somehow loses dimensions.

I'm not sure this is correct. The limit you are referring to is the limit of the scale factor as ##t \rightarrow 0##. But the scale factor going to zero does not just mean that finite distances go to zero. It means that the entire spacelike hypersurface, regardless of its curvature, has zero extent, because the spatial part of the metric vanishes. This would apply equally well to the case where spacelike hypersurfaces for ##t > 0## are infinite.

 

[PainterGuy]

Thank you!

This is the wrong criterion to use. The right criterion is, is it a textbook or a peer-reviewed paper? If it isn't, you generally should not rely on it as a source. Ordinary websites, even if they are written by experts, are still not the same as textbooks or peer-reviewed papers: they have not been reviewed by experts other than the author and they have not gone through any kind of quality control other than the author's own.

I agree with you but I'm not writing an article to get it published. I was only trying to understand a concept and using those sources to elaborate my point and confusion. But on the other hand, I'd say that quoting an answer from unknown person won't be a good idea and a somewhat lazy thing to do. For example, how would you feel if I quote some stranger from another forum and say 'see what this person is saying compared to what you have said'. The purpose was to understand a concept and given my time and abilities, I'd say that I put a sincere effort to make my confusion understood and I believe this is what matters. If I had used those sources to deny someone's viewpoint, I'd agree with your more. But considering some of the replies and their tone, I should have just asked the question and saved myself some time by not quoting anything.

In my first post there were one or two answers which were written by persons who didn't seem like experts in this field and that was the reason I said "repeating three of the sources from my previous post because these are from experts".

The first source was written by Edward L. Wright, https://en.wikipedia.org/wiki/Edward_L._Wright. He is an expert in this field which means he wouldn't say some silly things. I'm sure many of the members here on PF are also very careful with their wording in their posts. Those experts would also be equally, if not more, careful with their words. Still, I'm sure that Prof. Edward L. Wright would be wrong about many things. What Prof. Wright write was considered "not very good" by @PeroK. My knowledge and information of the big bang and cosmology is extremely limited but I'd still say that Prof. Wright was right because now I can see where he was coming from.

The answer in second source was written by Richard Muller, https://en.wikipedia.org/wiki/Richard_A._Muller. The answer by Richard Muller was found to be "largely nonsense" by @PeroK but Prof. Muller was only making an analogy and his answer was not that bad if read in the context of original question.

The third source was by Ethan Siegel, https://en.wikipedia.org/wiki/Ethan_Siegel.

The fourth source was from New Scientist.

Many of the members on PF are very learned and I'm sure if they were at the right place and given proper circumstances and opportunities, they would be no less than many well-known scientists. No flattery intended. For example, I would not compare any PF member's credentials with those of Prof. Muller or Prof. Wright and then decide who is right. What we say and how we say it should be more important. You could be a really good scientist, physicist, etc. but you could be a really bad instructor.

Huh? Ibix said no such thing. Universe is not infinite in age (at least not in the BB model)

Okay. I'm sorry but did you read the following:

I'm sorry if I have interpreted what you said incorrectly.

, and observable universe was not a singularity at the time of big bang - that is, when the universe was in a hot dense state and was rapidly expanding. It was very small ("The size of a grapefruit" which Ibix used) but that does not mean singularity.

I have read at several places that there was a singularity at the time of big bang. Isn't @Ibix saying the same thing below? Anyway, cosmology is an evolving field and it looks like there are diverse interpretations/explanation of certain phenomena.

Naive modelling gives us a problem if we go back far enough - the universe remains infinite in size but the observable universe (and every possible observable universe) goes to zero size. If that sounds contradictory, it kind of is. That's the Big Bang singularity, and singularities are the maths' way of saying "dunno".

Don't get me wrong but part of the problem is not what people write but the conclusions you draw from that are too far-reaching and far-fetched.

Please don't get me wrong but part of the problem is that you got a little bit carried away with criticizing what I was writing and in the process you forgot that I was only trying to learn something! There are better ways to help others. :)I believe that I understand it now at a basic level. The universe was infinite even at the time of big bang but it's 13.8 billions years old. The big bang gave rise to the entire universe, i.e. observable and unobservable universes. It was the beginning of time and space everywhere. When we extrapolate 13.8 billion years in the past our observable universe does become a size of grapefruit, point or whatever you like but the universe would still be infinite.

The following sources could be useful here.

Post #3 by @Ibix is really helpful.

but "densely packed together" does NOT mean everything was 0 distance from everything else. In fact, the universe may well have been (and most likely was) infinite in extent at that time

You have very likely fallen prey to the pop-science canard that everything started at a single point in space and was an "explosion". It did not and was not.

Also check this post:
https://www.physicsforums.com/threads/the-universe-vs-observable-universe.938274/

"Did the Universe expand from a point? If so, doesn't the universe have to have an edge?

No. The Big Bang was not an explosion IN space. It was a process that involved ALL of space. This misconception causes more confusion than any other in cosmology. Unfortunately, many students, teachers, and scientists(!) mistakenly picture the "Big Bang" as an explosion that took place at some location in space, hurtling matter outward.

In reality, ALL of space was filled with energy right from the beginning. There was no center to the expansion, and no magical point from which matter hurtled outward. The confusion arises in part because of the amazing conclusion that the OBSERVABLE portion of the universe was once packed into an incredibly tiny volume. But that primordial pellet of matter and energy was NOT surrounded by empty space... it was surrounded by more matter and energy (which today is beyond the region we can observe.) In fact, if the whole universe is infinitely large now, then it was always infinite, including during the Big Bang as well.

To put it another way, the current evidence indicates only that the early universe - the WHOLE universe - was extremely DENSE - but not necessarily extremely small. Thus the Big Bang took place everywhere in space, not at a particular point in space."
Source: https://www.cfa.harvard.edu/seuforum/faq.htm#m12

"Is the observable Universe not all of the Universe? (Submitted March 20, 2007)

The Question
The acceptance of Big Bang theory assumes the universe is ultimately finite and therefore measurable. But given the physical and temporal constraints that govern all our activities, the observable and measurable (empiric) universe may surely only represent a fraction of what exists across space/time.

How do we know where the universe begins and ends? And therefore - how can the concept of an infinite universe (or even multiverse constructs) be ruled out?

The Answer
You are right that the observable universe may be a fraction of the universe. The total energy and total volume of the universe may be infinite (we do not know), but the energy density (energy per unit volume) of the universe is finite, and this is a more important quantity for our understanding. Various observations, such as the observed expansion of the universe, the nature of the cosmic microwave background (CMB), etc. show that the universe started with the Big Bang (at the beginning, the whole space and time was confined to a point, and then it started expanding)."
Source: https://imagine.gsfc.nasa.gov/ask_astro/cosmology.html"But if space and everything with it is expanding now, then the universe must have been much denser in the past. That is, all the matter and energy (such as light) that we observe in the universe would have been compressed into a much smaller space in the past. Einstein's theory of gravity enables us to run the "movie" of the universe backwards—i.e., to calculate the density that the universe must have had in the past. The result: any chunk of the universe we can observe—no matter how large—must have expanded from an infinitesimally small volume of space.

By determining how fast the universe is expanding now, and then "running the movie of the universe" backwards in time, we can determine the age of the universe. The result is that space started expanding 13.77 billion years ago. This number has now been experimentally determined to within 1% accuracy.

It's a common misconception that the entire universe began from a point. If the whole universe is infinitely large today (and we don't know yet), then it would have been infinitely large in the past, including during the Big Bang. But any finite chunk of the universe—such as the part of the universe we can observe today—is predicted to have started from an extremely small volume.

Part of the confusion is that scientists sometimes use the term "universe" when they're referring to just the part we can see "the observable universe". And sometimes they use the term universe to refer to everything, including the part of the universe beyond what we can see.

It's also a common misconception that the Big Bang was an "explosion" that took place somewhere in space. But the Big Bang was an expansion of space itself. Every part of space participated in it. For example, the part of space occupied by the Earth, the Sun, and our Milky Way galaxy was once, during the Big Bang, incredibly hot and dense."
Source: The Evolution of the Universe by David L. Alles

http://imageshack.com/a/img921/9660/R9n4cM.jpg
Source: Hewitt, Conceptual Physics, 8th Ed. Ch. 8, Gravity, p. 160

I'm here only to learn, not to debate or argue. If I'm way too wrong as a beginner, please do correct me. Thank you all of you!

 

[PeterDonis]

I'm not writing an article to get it published.

I wasn't talking about you, I was talking about the sources you are trying to learn from.

I was only trying to understand a concept and using those sources to elaborate my point and confusion.

And my point is that you should not be trying to do that from the sources you are using. If you want to learn the science, you should be looking at textbooks and peer-reviewed papers.

I'd say that quoting an answer from unknown person won't be a good idea and a somewhat lazy thing to do. For example, how would you feel if I quote some stranger from another forum and say 'see what this person is saying compared to what you have said'. The purpose was to understand a concept and given my time and abilities, I'd say that I put a sincere effort to make my confusion understood and I believe this is what matters. If I had used those sources to deny someone's viewpoint, I'd agree with your more. But considering some of the replies and their tone, I should have just asked the question and saved myself some time by not quoting anything.

You are completely missing my point. I am not saying you should quote someone without saying who you are quoting from. Of course you should always give references to the sources you are quoting from. I am not saying you shouldn't have bothered with references at all. Of course if you don't know about a subject to begin with you need to consult references to learn about it. I am not saying you should ask questions without giving references to where you are getting your information; doing that just makes the thread go on longer as people ask you for references.

What I am saying is that you are consulting the wrong references. If you really want to understand the science of cosmology, you need to take the time to learn it from a textbook. If you really want to understand our best current models of the universe, you need to supplement what you learn from a textbook with peer-reviewed papers.

The universe was infinite even at the time of big bang but it's 13.8 billions years old.

More precisely, according to our best current model, the universe is spatially infinite and always has been. It has been 13.8 billion years since the big bang, but the big bang was not an initial singularity. Our best current model does not make any claim one way or the other about whether there was an initial singularity; we don't know enough about what happened before the earliest state of the universe for which we have good evidence--the hot, dense, rapidly expanding state that occurs at the end of inflation in inflation models and is the proper referent of the term "big bang"--to know whether there was an initial singularity or not.

The big bang gave rise to the entire universe, i.e. observable and unobservable universes.

More precisely, the "big bang" state I just described, the one at the end of inflation, occurred through the entire universe, not just our observable universe. However, what we are calling "the entire universe" might not be everything that exists; in "eternal inflation" models, what we call "the entire universe" is just one of many (quite possibly an infinite number) of universes that were created by inflation ending in isolated "bubbles" within an eternally inflating spacetime.

It was the beginning of time and space everywhere.

No, it wasn't. See above.

When we extrapolate 13.8 billion years in the past our observable universe does become a size of grapefruit, point or whatever you like but the universe would still be infinite.

In our best current model, yes. But see above for caveats.

 

[PeroK]

The first source was written by Edward L. Wright, https://en.wikipedia.org/wiki/Edward_L._Wright. He is an expert in this field which means he wouldn't say some silly things. I'm sure many of the members here on PF are also very careful with their wording in their posts. Those experts would also be equally, if not more, careful with their words. Still, I'm sure that Prof. Edward L. Wright would be wrong about many things. What Prof. Wright write was considered "not very good" by @PeroK. My knowledge and information of the big bang and cosmology is extremely limited but I'd still say that Prof. Wright was right because now I can see where he was coming from.

One problem is trying to piece together a coherent picture from various snippets. Let's assume we want to take what Edward Wright says at face value: the observable universe started from a point, but the entire universe didn't. Your problem is that no other source is likely to make this distinction. When you read about the BB elsewhere, the author will not be using the terminology that Wright chose for this one page.

Then, you get confused because one source is saying one thing and another source is saying something else.

All I can say is that, from an elementary mathematical perspective, the first two sentences of his page do not make sense.

The answer in second source was written by Richard Muller, https://en.wikipedia.org/wiki/Richard_A._Muller. The answer by Richard Muller was found to be "largely nonsense" by @PeroK but Prof. Muller was only making an analogy and his answer was not that bad if read in the context of original question.

Muller is (IMHO) dumbing down the science too far. You can see from the tone of that page. Again your problem is that you cannot take what he says at face value. Nor expect his dumbed down analogies to be generally accepted.

If, for example, you chose to learn some GR from a university textbook, then at no stage would the author demand that you see the vacuum as a piece of rubber.

In fact, there is a fundamental difference between any substance and vacuum.

Instead you could try this Insight:

https://www.physicsforums.com/insights/inflationary-misconceptions-basics-cosmological-horizons/

My general advice is to stop reading one-pagers about cosmology and concentrate on papers where the author has more time to develop the ideas.

 

[Ibix]

I'm on an elderly borrowed phone because mine's in the shop, and I give up on trying to make the &*$£@ thing quote posts. This is mostly in reply to @PainterGuy.

I think none of the regulars here would have a problem with the claim that in a naive cosmological model (FLRW spacetime with only ordinary matter and radiation) we end up with a scale factor of zero at time zero, which is a singularity. It would mean that there were distinct points, but the distance between any two points anywhere in all of space was zero (and yes, that does seem rather problematic). The source of all the argument is how to express this without the technical terms and, when someone has said something without the technical terms, guessing what technical terms they left out. (Edit: or if they're even talking about that model in the first place.)

I think Ned Wright was talking about this naive model. I don't think that he chose the best words, because I would have made clear that no-one ever really believed in the singularity - it's almost certainly the maths' way of saying that the model goes wrong early in the universe. And it's only arguable that "no distance between points" is sensibly expressed as "the observable universe was a point".

On the other hand, Ned Wright has forgotten more cosmology than I know. Maybe he was referring to a different model (as Peter notes, there isn't only one) - our current best model avoids a singularity, but I don't know when that article was written.

Any popularisation is going to be wrong somehow, because all our models rely on mathematical concepts that don't translate well into natural language. I include things I write in that statement. You will find that they contradict each other, because different authors leave out different bits so that their descriptions are wrong in different ways.

If you really want to know cosmology, you need to learn the maths. It's challenging, but it can be done. Otherwise, it's a lot like reading a bad translation of great literature - it's really difficult to understand what all the fuss is about.

 

[timmdeeg]

I think none of the regulars here would have a problem with the claim that in a naive cosmological model (FLRW spacetime with only ordinary matter and radiation) we end up with a scale factor of zero at time zero, which is a singularity. It would mean that there were distinct points, but the distance between any two points anywhere in all of space was zero (and yes, that does seem rather problematic). The source of all the argument is how to express this without the technical terms and, when someone has said something without the technical terms, guessing what technical terms they left out. (Edit: or if they're even talking about that model in the first place.)

The whole discussion seems to be based on FLRW spacetime. Can we say that the conclusions as explained by the experts around here (e.g. regarding the BigBang, the distance between two points, the extent of the universe ...) are coordinate independent? (The discussion wasn't about expansion of space vs. galaxies moving away.)

 

[Ibix]

Peter, at least, is talking about FLRW with more exotic stuff than regular matter and radiation, which is a model that makes the singularity go away (and explains some other observations into the bargain). If Wright were referring to this model in the originally quoted article, he'd be flat wrong. That's why I specified the content of the FLRW universe I was talking about and that I guess Wright was talking about.

Some of the statements people have made are coordinate independent, but some are not. The existence of a singularity in the model I'm talking about is coordinate independent - the singularity either exists or it doesn't. But saying it occurs at time zero involves a coordinate choice - nothing stops you relabelling time zero as time ##\pi^2## if you want to do such a silly thing. The problem in this thread is more that we don't know exactly what model the original sources are talking about. For example what's in the universe? Just matter and radiation? Dark energy? Other stuff? They lead to different claims about the early universe, so a correct statement about one model is wrong about another, even on top of the possibility of a popularisation not being particularly precise.

 

[timmdeeg]

The problem in this thread is more that we don't know exactly what model the original sources are talking about. For example what's in the universe? Just matter and radiation? Dark energy? Other stuff? They lead to different claims about the early universe, so a correct statement about one model is wrong about another, even on top of the possibility of a popularisation not being particularly precise.

I think the "worth "of said sources was clarified sufficiently. The confusion arising in such a discussion would - I think - be limited if such a discussion would be limited to e.g. the FRW-universe. (As Ned Wright probably did as you mentioned). Then the predictions of the Friedmann equations what happens depending on the mixture of stuff are unambiguous.

Good luck getting your phone back sometime next year.

 

[PeterDonis]

I think Ned Wright was talking about this naive model.

I think so too, because cosmologists in general often use the naive model as a way of obtaining the times they use when communicating with lay people. For example, they might say that inflation ended ##10^{-32}## seconds after the Big Bang. What they actually mean by that is not that either there was an initial singularity in our actual universe which the term "Big Bang" refers to, or that the end of inflation actually occurred ##10^{-32}## seconds after that initial singularity. All they actually mean is that, if you take the best estimate of the temperature and density of the universe at the end of inflation, right after reheating, the naive model universe will have that temperature and density ##10^{-32}## seconds after the initial singularity.

IMO this is an extremely poor method of communication when talking to lay people. There are actually some plausible technical reasons to refer to things this way when cosmologists talk among themselves, but to do it when talking to lay people IMO just increases confusion.

 

[PAllen]

I'm not sure this is correct. The limit you are referring to is the limit of the scale factor as ##t \rightarrow 0##. But the scale factor going to zero does not just mean that finite distances go to zero. It means that the entire spacelike hypersurface, regardless of its curvature, has zero extent, because the spatial part of the metric vanishes. This would apply equally well to the case where spacelike hypersurfaces for ##t > 0## are infinite.

A quibble:

Limit of the intersection of any finite parameter space of congruence with the cosmological foliation is a well defined limit that goes to zero in the pure FLRW cosmology for all cases where a(t) -> 0 as t goes to zero.

Meanwhile, the total volume of a foliation slice for an open universe is infinite for all t > 0. Thus, to the extent it plausible to talk about a limit (mathematically, it is dubious to talk about infinity as a value in this context), you have the limit at t->0 from above being infinite. You can state this differently as: for any finite volume value, the volume of a slice of open universe is greater than this for all values of t>0. Thus, the only meaningful limit from above as t->0 is infinity.

 

[PeterDonis]

to the extent it plausible to talk about a limit

It isn't, really, but in any case I wasn't talking about taking a limit, because you don't have to. See below.

for any finite volume value, the volume of a slice of open universe is greater than this for all values of t>0. Thus, the only meaningful limit from above as t-> is infinity.

But you can also directly calculate the volume at ##t = 0## from the scale factor; since the scale factor is zero, the volume is identically zero from the metric. The fact that the spacelike slice at ##t = 0## covers an infinite range of coordinate values doesn't matter: the sum of an infinite number of zeros is still zero.

 

[PAllen]

It isn't, really, but in any case I wasn't talking about taking a limit, because you don't have to. See below.
But you can also directly calculate the volume at ##t = 0## from the scale factor; since the scale factor is zero, the volume is identically zero from the metric. The fact that the spacelike slice at ##t = 0## covers an infinite range of coordinate values doesn't matter: the sum of an infinite number of zeros is still zero.

t=0 is not part o the manifold. The limit is computed only on what is what is in the manifold. It is quite common for functional expressions to have the feature that evaluated at a discontinuity, the functional value is is different from limiting values. So, I would say your statement is:

at t=0, which is a singular point not part of the manifuld, if I naively pretend it is valid to ignore this, I get zero volume for a slice.

My statement is that (especially its second formulation) is that the limit as t->0 is infinite, because it is infinite for all t>0. I claim this is a perfectly valid statement to make, and this limit is computed only using the actual manifold.

I agree with @Bandersnatch that it is pretty clear Ned Wright was referring to these two limiting behaviors I described in my post #20.

 

[PeroK]

My statement is that (especially its second formulation) is that the limit as t->0 is infinite, because it is infinite for all t>0. I claim this is a perfectly valid statement to make, and this limit is computed only using the actual manifold.

This begs the question of whether physics must respect the discipline of pure mathematics when computing a limit.

Is a limit what a physicist can justify as valid or what meets a mathematical definition?

 

[PAllen]

This begs the question of whether physics must respect the discipline of pure mathematics when computing a limit.

Is a limit what a physicist can justify as valid or what meets a mathematical definition?

Well, the statement that the volume is infinite for all t>0 is true for a mathematician. The only mathematical quibble is whether this leads to limit statement that would satisfy a mathematician. One could certainly say the following as a mathematically valid statement:

For an open FLRW cosmology, there always exists a sequence of subregions of standard foliation such that the volume of subregions approaches infinite as t goes to zero. Here we have a sequence of finite values, so a limit is perfectly well defined.

 

[PeterDonis]

t=0 is not part o the manifold.

If it isn't, then IMO talking about the limit at that point is just as meaningless physically as talking about the directly calculated value there.

I agree with @Bandersnatch that it is pretty clear Ned Wright was referring to these two limiting behaviors I described in my post #20.

You both may be right. I personally would lean towards saying that both calculations--the limit and the direct one I gave--are not about anything physically meaningful. But in any case I think we would need to look at actual textbooks and peer-reviewed papers to see what, if any, physical meaning is actually assigned to the idea of "the spatial size of the universe at the initial singularity", and how much, if any, difference it makes in how models are used.

 

[PeterDonis]

This begs the question of whether physics must respect the discipline of pure mathematics when computing a limit.

Of course he must. The fact that physics is not the same as mathematics does not mean physicists can do mathematics wrong when they use it.

 

[PeroK]

Well, the statement that the volume is infinite for all t>0 is true for a mathematician. The only mathematical quibble is whether this leads to limit statement that would satisfy a mathematician. One could certainly say the following as a mathematically valid statement:

For an open FLRW cosmology, there always exists a sequence of subregions of standard foliation such that the volume of subregions approaches infinite as t goes to zero. Here we have a sequence of finite values, so a limit is perfectly well defined.

In general, a shared property of a sequence of sets may not be a property of the limit. For example, the sequence of sets:

##S_n = \cup_{k =1}^{\infty} [k, k + 1/n]##

Satisfies the property that each ##S_n## has infinite measure. But, the limit set is the set of positive integers, which has measure ##0##.

In terms of ##t=0## in the BB model, the conclusion that the universe as a whole still has infinite extent, but that any currently finite volume is reduced to a point is not mathematics that bears scrutiny.

 

[PAllen]

Of course he must. The fact that physics is not the same as mathematics does not mean physicists can do mathematics wrong when they use it.

Well there are precedents for this ...

 

[PAllen]

In general, a shared property of a sequence of sets may not be a property of the limit. For example, the sequence of sets:

##S_n = \cup_{k =1}^{\infty} [k, k + 1/n]##

Satisfies the property that each ##S_n## has infinite measure. But, the limit set is the set of positive integers, which has measure ##0##.

In terms of ##t=0## in the BB model, the conclusion that the universe as a whole still has infinite extent, but that any currently finite volume is reduced to a point is not mathematics that bears scrutiny.

Stated that way, no. However, I take that as shorthand for the following, statements which are fully defensible for any open FLRW cosmology:

The volume of any currently finite region, extrapolated back in time along the congruence of comoving world lines it contains, approaches zero as t -> 0.

The volume of any slice of the standard foliation is infinite for all t>0.

And statements about t=0 are meaningless because this is not part of the cosmology.

 

[PeroK]

Stated that way, no. However, I take that as shorthand for the following, statements which are fully defensible for any open FLRW cosmology:

The volume of any currently finite region, extrapolated back in time along the congruence of comoving world lines it contains, approaches zero as t -> 0.

The volume of any slice of the standard foliation is infinite for all t>0.

Mathematically that doesn't imply what you might intuitively want it to imply.

For example, let's assume your ##t=0## scenario is valid. You claim to have a set of infinite extent. But, you are unable to find any two points whose distance is non-zero. This is a contradiction.

The mathematical answer is probably that in the limit you no longer have a valid manifold. You can't talk about distances unless you have a valid metric. And, in the limit, you no longer have a valid metric.

 

[PAllen]

Mathematically that doesn't imply what you might intuitively want it to imply.

For example, let's assume your ##t=0## scenario is valid. You claim to have a set of infinite extent. But, you are unable to find any two points whose distance is non-zero. This is a contradiction.

The mathematical answer is probably that in the limit you no longer have a valid manifold. You can't talk about distances unless you have a valid metric. And, in the limit, you no longer have a valid metric.

I’m actually not suggesting those satements to imply anything other than what they say. Just that those statements are important to understand and somewhat counterintuitive. Formulating them as Ned did, I agree is not mathematically valid, but I believe he really meant these underlying statements and improperly simplified them for a nontechnical article.

 

[PeterDonis]

You claim to have a set of infinite extent.

No, that's not what he claimed. The limiting procedure @PAllen described does not construct a set and say that it is "a spacelike slice at time ##t = 0##". It only constructs a number and says that it has the same value (infinity) at ##t = 0## as it has for all ##t > 0##. Of course this is a sloppy heuristic description, but it can be made precise without having to make any claims about an infinite set of points existing at ##t = 0##.

That said, there is also a different way of proceeding, which is to use the method used to construct Penrose diagrams to add a "boundary" corresponding to ##t = 0## to the FRW spacetime manifold. This procedure does in fact lead to a boundary with an infinite set of distinct points in it, each one corresponding to a particular 3-tuple of comoving coordinates, i.e., to a distinct "spatial point" in each spacelike slice in the region ##t > 0##. Physically, this corresponds to the fact that, in the limit ##t \rightarrow 0##, every single spatial point in the FRW universe becomes causally disconnected from every other. We can then use the induced metric (if it can be called that--see further comments below) on the boundary to compute zero spatial volume for this infinite set of points (because, as I noted earlier, the sum of an infinite set of zeroes is still zero).

You claim to have a set of infinite extent. But, you are unable to find any two points whose distance is non-zero. This is a contradiction.

No, it isn't. It simply says that this...

You can't talk about distances unless you have a valid metric. And, in the limit, you no longer have a valid metric.

...is correct in the sense that there is no valid Riemannian metric on the infinite set of points at ##t = 0## constructed by the method I described above. But you do have a valid manifold, because having a valid manifold does not require having a valid Riemannian metric. And you do have a perfectly well-defined mathematical formula that assigns the value zero to the integral ##\int \int \int a(t = 0) dx dy dz## over this manifold. And this formula is derived from a thingie that looks like a metric, just not a Riemannian one.

So at this point we have a situation which, although describable consistently using math, has no description in ordinary language that really does justice to it.

 

[PeroK]

But you do have a valid manifold, because having a valid manifold does not require having a valid Riemannian metric. And you do have a perfectly well-defined mathematical formula that assigns the value zero to the integral ##\int \int \int a(t = 0) dx dy dz## over this manifold. And this formula is derived from a thingie that looks like a metric, just not a Riemannian one.

What is the definition of this metric "thingie"?

 

[PeterDonis]

What is the definition of this metric "thingie"?

##a(t) \left( dx^2 + dy^2 + dz^2 \right)## for ##t = 0##

 

[PeroK]

##a(t) \left( dx^2 + dy^2 + dz^2 \right)## for ##t = 0##

But ##a(0) = 0##?