# Size of universe - rewinding big bang versus "flat" universe

• B
• HomesliceMMA
In summary: Einstein's field equations.The universe was never a single point. The term singularity means a breakdown in the mathematical model, but in popular science sources this is often described as a point.
HomesliceMMA
I understand, given dark energy, given the current expansion of the universe, given its ~13.8 billion year old age, we calculate the universe is like 93 billion light years across currently. Something like that.

But I was listening to something the other day, and when they test the curvature of space, so see whether its round (curving inward, will contract again), flat (absolutely flat) or saddle shape (expanding outward), the measurements have come back that the universe is very, very flat. We can't tell if its perfectly flat, but our measurements show that it is so flat, the universe has to be TRILLIONS of light years in size to be consistent with how flat it is - if it was any smaller our instruments would detect its curvature.

So, what gives here? Is the latter one just saying "if our universe is OTHER THAN FLAT, then it would have to be trillions of light years in size, but if its flat that is perfectly consistent with a 93 billion light year diameter universe."? And that our universe is thus probably flat and is probably around 93 billion light years across?

Thanks!!!

Related question: would the universe being flat in any way be inconsistent with the big bang? I would guess not.

Another related question: If the universe is flat, does that mean it is NOT expanding (or contracting)? Because I think the vast consensus is that the universe is expanding, and that expansion is growing.

Thanks!

If the universe is flat or open (what you called "saddle shaped") then it's infinite in extent. If it's a closed universe (the one you called "round") then it's finite in extent but boundaryless - if you go far enough in one direction you come back to your starting place (although you may not have time because that kind of universe may collapse into a big crunch before you can circumnavigate it).

What the thing you have read says is that if the universe is curved then the "radius" of that curvature must be truly vast or we'd be able to see effects of that curvature. The 93 billion light years is referring to the size of the observable universe - the furthest things we can see if we look in one direction are about 45bn light years away so the diameter is twice that. So our current model is that the universe is spatially flat and infinite in size; we can see stuff in a patch that is now 90-something billion light years across.

All three types of universe (flat, closed and open) are expanding. The closed type of universe can eventually collapse again, but whether it does depends on the balance between dark energy, matter and radiation.

mattt, Imager and Bandersnatch
Thanks so much Ibix!

"So our current model is that the universe is spatially flat and infinite in size; we can see stuff in a patch that is now 90-something billion light years across."

Really, I had not realized that. I thought there were different theories, some say universe finite, some infinite, etc. So let me ask you this - how do conclude (for purposes of the model) that the universe is infinite? I mean, we think it started from a very tiny point before expanding, and if we rewind that expansion we get to that point from everything we think there is currently. Where does the infinity come into it? Why is there not a size based on what we can see today and extrapolating as to what else is out there given the expansion, etc.? The the infinity thing puzzles me.

Thanks again!

HomesliceMMA said:
I mean, we think it started from a very tiny point before expanding, and if we rewind that expansion we get to that point from everything we think there is currently.
The universe was never a single point. The term singularity means a breakdown in the mathematical model, but in popular science sources this is often described as a point.

HomesliceMMA said:
I mean, we think it started from a very tiny point before expanding,
I've already told you twice that this is wrong. If the universe is infinite then it always was.

The models of the universe as closed, flat, or open come from a formal mathematical piece of reasoning that could be sketched as feeding "everything looks more or less the same in every direction" through Einstein's field equations.

PeroK said:
The universe was never a single point. The term singularity means a breakdown in the mathematical model, but in popular science sources this is often described as a point.
I am aware of that. But regardless, it was very small. Thanks.

Ibix said:
I've already told you twice that this is wrong. If the universe is infinite then it always was.

The models of the universe as closed, flat, or open come from a formal mathematical piece of reasoning that could be sketched as feeding "everything looks more or less the same in every direction" through Einstein's field equations.
Oh, I get it, at least I think I do. Its infinite in the sense that "its everything that could be in the universe". But, regardless of that, its volume was a very teeny, tiny small fraction of what it is today, no?

But WAIT, I think I see what you are saying. I was thinking infinite in the sense that the universe goes on and on and on forever, and the further you go the more new stuff you haven't found yet you will find. Like, this conversation will be repeated somewhere else in the universe, not once, but an infinite number of times. That is not what you meant I see now.

So, do we think the diameter of the universe is like 93 light years? It sounds like no, that is the size of the universe visible to us. So what is the proposed total diameter of the universe (visible or beyond our ability to see it)?

Thanks you Ibix!!!

HomesliceMMA said:
I am aware of that. But regardless, it was very small. Thanks.
If the universe is infinite now, then it was infinite at the Big Bang. It was very dense, but not very small. The current observable universe was very small.

PeroK said:
If the universe is infinite now, then it was infinite at the Big Bang. It was very dense, but not very small. The current observable universe was very small.
Yes, the universe was infinite at the big bang, but was its volume not very small (compared to today's standards)?

Thanks for helping me with these baby steps!

phinds and PeroK
Waaaait a second. I think I got it. We have NO IDEA how big the universe was right before the big bang, it could of been HUGE, and the current best theory, based on a flat universe, is that it was infinite. Its just that OUR PORTION of the universe was small at the big bang.

Is that it more/less?

If that is right, the current best thinking is that this conversation is going on an infinite number of times in our universe right now?

Hornbein
HomesliceMMA said:
I understand, given dark energy, given the current expansion of the universe, given its ~13.8 billion year old age, we calculate the universe is like 93 billion light years across currently. Something like that.

But I was listening to something the other day, and when they test the curvature of space, so see whether its round (curving inward, will contract again), flat (absolutely flat) or saddle shape (expanding outward), the measurements have come back that the universe is very, very flat. We can't tell if its perfectly flat, but our measurements show that it is so flat, the universe has to be TRILLIONS of light years in size to be consistent with how flat it is - if it was any smaller our instruments would detect its curvature.

So, what gives here? Is the latter one just saying "if our universe is OTHER THAN FLAT, then it would have to be trillions of light years in size, but if its flat that is perfectly consistent with a 93 billion light year diameter universe."? And that our universe is thus probably flat and is probably around 93 billion light years across?

Thanks!!!
The 93 billion light year across portion is the observable universe. Given how smooth and regular the observable universe is, it's reasonable to expect that the universe is much larger than this, but we can't know how much larger.

The relationship between curvature and size isn't likely to be significant. It's possible for a flat universe to wrap back on itself (if it's the shape of a torus). It's possible for a universe where we measure closed curvature within our observable patch to have infinite extent (as long as the closed curvature is only a local phenomenon).

Basically there's no way to tell for sure just how big the universe is. It's probably many times the size of our observable patch that we can measure directly, but there's really no way to know.

@HomesliceMMA it is obvious that you have "learned" your cosmology from pop-sci. I had the same problem; when I came here I had to unlearn all kinds of things that I "knew". My advice is to forget everything you think you know, because most of it will be wrong. Get a good basic text on cosmology instead.

Pop-sci (book, TV, whatever) is entertainment, not education.

mattt, gmax137, PeterDonis and 1 other person
HomesliceMMA said:
Waaaait a second. I think I got it. We have NO IDEA how big the universe was right before the big bang, it could of been HUGE, and the current best theory, based on a flat universe, is that it was infinite. Its just that OUR PORTION of the universe was small at the big bang.

Is that it more/less?
Yes, that's right.
HomesliceMMA said:
If that is right, the current best thinking is that this conversation is going on an infinite number of times in our universe right now?
That's one possibility, yes.

HomesliceMMA said:
If that is right, the current best thinking is that this conversation is going on an infinite number of times in our universe right now?
Exceedingly unlikely. Can't say impossible but the HUP means that for a universe to evolve twice in exactly the same way to that level of detail, the number of coincidental changes would have to be way far beyond too staggering to believe. That is, the universe is not deterministic, it is statistical and indeterminate.

I don't know anything about cosmology, but this notion that infinite universe means "this conversation is going on an infinite number of times" just doesn't make sense to me. The set of real numbers is infinite, and yet there is only one "2" and only one ##\sqrt 3##. The numbers do not repeat, why should the conversations?

gmax137 said:
I don't know anything about cosmology, but this notion that infinite universe means "this conversation is going on an infinite number of times" just doesn't make sense to me. The set of real numbers is infinite, and yet there is only one "2" and only one ##\sqrt 3##. The numbers do not repeat, why should the conversations?
It does appear to be consistent with the known laws of physics. See the following paper: https://arxiv.org/abs/astro-ph/0302131

Abstract:
Abstract: I survey physics theories involving parallel universes, which form a natural four-level
hierarchy of multiverses allowing progressively greater diversity. Level I: A generic prediction of
inflation is an infinite ergodic universe, which contains Hubble volumes realizing all initial conditions
— including an identical copy of you about 10^10^29m away. Level II: In chaotic inflation, other
thermalized regions may have different physical constants, dimensionality and particle content. Level
III: In unitary quantum mechanics, other branches of the wavefunction add nothing qualitatively
new, which is ironic given that this level has historically been the most controversial. Level IV:
Other mathematical structures give different fundamental equations of physics. The key question is
not whether parallel universes exist (Level I is the uncontroversial cosmological concordance model),
but how many levels there are. I discuss how multiverse models can be falsified and argue that there
is a severe “measure problem” that must be solved to make testable predictions at levels II-IV.

It seems to me that all of your questions, in all of your threads can be answered by studying a bit more cosmology. May be you can just ask about resources (textsbooks, lecture notes those kind of things not videos and blogs).

phinds
Imagine two parallel perfect laser beams. If they stay parallel forever we say the Universe is flat. Calling it "straight" might have been better, but that's what we've got. If the beams converge then the Universe is spherical. If they diverge then U is hyperbolic.

As to that stuff about the conversation going on an infinite number of times I don't take that seriously. I'd say this comes up from people who don't know measure theory. To make a long story short, probability zero is not the same as impossible. I expect that in an infinite Universe your conversation has probability zero.

Basic measure theory is quite simple, it's just abstract and not widely taught. Suffice to say that all finite subsets of an infinite set have measure zero. Even an infinite subset may or may not have measure zero.

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phinds
gmax137 said:
I don't know anything about cosmology, but this notion that infinite universe means "this conversation is going on an infinite number of times" just doesn't make sense to me. The set of real numbers is infinite, and yet there is only one "2" and only one ##\sqrt 3##. The numbers do not repeat, why should the conversations?
Shouldn't the bearers of this infinity of conversations state whether they are talking about an infinite universe, or an infinity of universes, etc. For our one universe, I agree with you.

gmax137 said:
this notion that infinite universe means "this conversation is going on an infinite number of times" just doesn't make sense to me.
It's based on the claim that the number of possible conversations is smaller (in more technical language, has lesser cardinality) than the number of places in an infinite universe that a conversation could take place. If that is true, then the fact that any given conversation must happen an infinite number of times follows from the pigeonhole principle.

AFAIK claims like that are never actually proven in the literature, they are simply assumed (and in fact they are implicitly assumed, at least in the literature that I've read). I personally don't find such claims very credible.

PeroK and phinds
PeterDonis said:
It's based on the claim that the number of possible conversations is smaller (in more technical language, has lesser cardinality) than the number of places in an infinite universe that a conversation could take place.

That claim doesn't ring true to me. Here's a short list of conversations:

conversation A1: me: "one" you: "two"
conversation B1: me: "one" you: "three"
conversation C1: me: "one" you: "four"
... and so on. Then when we finish all of those ,
conversation A2: me: "two" you: "two"
conversation B2: me: "two" you: "three"
conversation C2: me: "two" you: "four"
... and so on.

If that is true, then the fact that any given conversation must happen an infinite number of times follows from the pigeonhole principle.

Not being a mathematician it is above my head a bit to extend the pigeonholes to an infinite number of places. After all, there's always room for one more guest at Hilbert's Hotel. Or better, maybe each room has two guests, talking to each other. Another pair arrives, and there is a room for them...

gmax137 said:
Not being a mathematician it is above my head a bit to extend the pigeonholes to an infinite number of places.
It's simple: there are multiple infinite cardinalities, and they are ordered with respect to size. For example, the cardinality of the set of possible conversations is countably infinite, i.e., ##\omega##. But that is the smallest possible infinite cardinality. So if the cardinality of the set of possible places for a conversation to happen is any other infinite cardinality than ##\omega##, then it will be impossible to fill all of those places with conversations if you only use each conversation once.

gmax137 said:
After all, there's always room for one more guest at Hilbert's Hotel.
But there isn't room for an uncountable infinity of guests.

gmax137
PeterDonis said:
It's simple: there are multiple infinite cardinalities, and they are ordered with respect to size. For example, the cardinality of the set of possible conversations is countably infinite, i.e., ##\omega##. But that is the smallest possible infinite cardinality. So if the cardinality of the set of possible places for a conversation to happen is any other infinite cardinality than ##\omega##, then it will be impossible to fill all of those places with conversations if you only use each conversation once.
The cardinality of all such places, in an infinite universe, is countable.

martinbn said:
The cardinality of all such places, in an infinite universe, is countable.
Why?

PeterDonis said:
Why?
Say the space is ##\mathbb R^3##, the each such conversation happens in a small part of space and we can assume that all these parts are disjoint. The in each of them pick a point with rational coordinates. This way you get a bijection of all conversation places and some points with rational coordinates. These points are countable.

martinbn said:
Say the space is ##\mathbb R^3##, the each such conversation happens in a small part of space and we can assume that all these parts are disjoint. The in each of them pick a point with rational coordinates. This way you get a bijection of all conversation places and some points with rational coordinates. These points are countable.
Do you know if anyone has published this kind of argument as a rebuttal to the common claims in the literature about significant things, like conversations or people, being repeated an infinite number of times in an infinite universe?

Because if no one has, I sure wish someone would.

PeterDonis said:
Do you know if anyone has published this kind of argument as a rebuttal to the common claims in the literature about significant things, like conversations or people, being repeated an infinite number of times in an infinite universe?

Because if no one has, I sure wish someone would.
I dont know. May be some can write and insight. Or may be there was already one about cardinalities, so it can have a second part. But in a way it is clear that you can have only counably many disjoint say spheres in space.

martinbn said:
I dont know. May be some can write and insight. Or may be there was already one about cardinalities, so it can have a second part. But in a way it is clear that you can have only counably many disjoint say spheres in space.
Well a different consideration is whether the number of possible conversations less than some maximum length (e.g. 120 years at the ludicrous extreme) is finite. I presume it is. Then the argument of repeated conversations still applies.

mattt
phinds said:
Exceedingly unlikely. Can't say impossible but the HUP means that for a universe to evolve twice in exactly the same way to that level of detail, the number of coincidental changes would have to be way far beyond too staggering to believe. That is, the universe is not deterministic, it is statistical and indeterminate.
What is HUP? Yes, absolutely, the chances of any universe come out the same twice are very, very, VERY slim, but if there IS an infinite number of universe, that would have to happen, not once, but INFINITELY. That is why the notion of infinity in this context is so silly to me. Just not believable.

gmax137 said:
I don't know anything about cosmology, but this notion that infinite universe means "this conversation is going on an infinite number of times" just doesn't make sense to me. The set of real numbers is infinite, and yet there is only one "2" and only one ##\sqrt 3##. The numbers do not repeat, why should the conversations?

See my post above. What you are claiming to be "infinite" matters - sometimes it can make sense, other times it doesn't. For example, if you say there can be an infinite number of numbers, starting with 1 and counting forward by 1 at a time, forever and ever, there CAN be an infinite number of numbers, in theory. But if you did that you would NEVER hit an infinite number of numbers. You would get to 1 million. Or 1 billion. Or 1 trillion, and so on and so on, but you would never get to infinity. So there is nothing weird about that statement or formulation.

But if you say "the size of the universe is infinite", then, assuming the physical properties in each is the same at least, this conversation is going on not just once, but an infinite number of times. So in this context in my mind at least that is just silly. You guys are rejecting it like I am, but I'm telling you that is what infinity literally means in this context.

There is only one number 2 in your example because it involves starting with a 1 or 0 and counting forward, but never going back or repeating. If you change it to say there is an infinite amount of random numbers, then there will not just be two 2s, there will be an INFINITE number of 2s.

HomesliceMMA said:
then, assuming the physical properties in each is the same at least
But that's my POINT. The universe is indeterminate and statistical, so "same physical properties" is very misleading. The HUP is the Heisenberg Uncertainty Principle and if you don't understand it, you should stop this conversation until you do. The "same physical properties" WOULD lead to the same outcomes in a deterministic universe but we don't live in one of those.

Hornbein said:
Imagine two parallel perfect laser beams. If they stay parallel forever we say the Universe is flat. Calling it "straight" might have been better, but that's what we've got. If the beams converge then the Universe is spherical. If they diverge then U is hyperbolic.

As to that stuff about the conversation going on an infinite number of times I don't take that seriously. I'd say this comes up from people who don't know measure theory. To make a long story short, probability zero is not the same as impossible. I expect that in an infinite Universe your conversation has probability zero.

Basic measure theory is quite simple, it's just abstract and not widely taught. Suffice to say that all finite subsets of an infinite set have measure zero. Even an infinite subset may or may not have measure zero.

Well, can you explain that in plain English? If the universe is infinite in size (and like I said the physical properties are the same in all parts, that sort of thing), this conversation WOULD be happening an infinite number of times. That is what infinite necessarily means in that context. That is why I submit that an infinite universe is BS.

phinds said:
But that's my POINT. The universe is indeterminate and statistical, so "same physical properties" is very misleading. The HUP is the Heisenberg Uncertainty Principle and if you don't understand it, you should stop this conversation until you do. The "same physical properties" WOULD lead to the same outcomes in a deterministic universe but we don't live in one of those.

Yes, absolutely indeterminate, but you'd still get there eventually. Yes, all the probabilities would have to have come out exactly the same, one photon or electron that goes a different way because its "roll of the dice" differed would obviously mean the conversation was not happening twice. But, if one says the universe is infinite, you'd just keep going farther along, until you find one that matches. If our physics only applies to our patch of the universe, or there is only matter in our universe, then that would not likely hold true. But if the same physical properties exist, etc., there would have to be infinite conversations like this one.

HomesliceMMA said:
... there would have to be infinite conversations like this one.
see post #19

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