Infinite Universe....Fate?

[robross]

I may be really out of line, but my understanding is that this is what the original poster was interested in. Why do Incomplete and DrRocket have to be arguing over manifolds or whatever? Is it really important to this question? I thought the question was based on a hypothetical.

Somewhere along the thread a poster mis-interpreted the OP and mentioned the word "multiverse" and all sorts of confusion has followed

"Multiverse" is usually used in the context of a set of theories which do not address the OP.

The OP's point is simple. If our observable universe continues on to infinity, there will be infinite space, and infinite galaxies, planets, stars, etc, all obeying the normal physics as in our own local corner of the universe.

In such an infinite universe, any thing that is physically allowable by the laws of physics must occur. So there are an infinite amount of planets in which humans evolved and named their planet Earth, and infinite variations of the same as well, where they named their planet Zaphrax, but otherwise everything else is the same. This is what happens with infinities.

This is one reason why I don't think our universe is actually infinite in extent, although because it sounds "weird" is not adequate reason to dismiss it.

Rob

[Jens]

This is one reason why I don't think our universe is actually infinite in extent, although because it sounds "weird" is not adequate reason to dismiss it.

Thanks. I think this is the question that the OP had. And my own question is, why would that weirdness be any reason to reject the idea of an infinite universe? I realize that it is true, but don't see any problem with it at all. I can readily accept that there could be an infinite number of beings who look exactly like me.

[robross]

Thanks. I think this is the question that the OP had. And my own question is, why would that weirdness be any reason to reject the idea of an infinite universe? I realize that it is true, but don't see any problem with it at all. I can readily accept that there could be an infinite number of beings who look exactly like me.

Well, I for one have never encountered an infinite amount of any physical substance. We experience "abstract" ideas about infinities, such as being able to travel the circumference of a circle eternally. But as far as concrete, countable infinities, that is something I have no experience with. Now, I have to accept that there are many such things I do not have experience with, things described by Relativity and QM for one, so I have to be prepared to accept things that are counter intuitive.

However, if the Big Bang holds, and so far it seems to, that means at some time shortly after the BB, there was an *infinite* amount of matter and energy concentrated in one small volume of an expanding universe. How can an infinite amount of matter and energy be concentrated in a finite amount of space? And how would inflation have affected an infinite amount of 'stuff'? And how would a finite volume of initial space grow to be infinite?

I just have a problem conceptualizing this.


Rob

[Jens]

However, if the Big Bang holds, and so far it seems to, that means at some time shortly after the BB, there was an *infinite* amount of matter and energy concentrated in one small volume of an expanding universe. How can an infinite amount of matter and energy be concentrated in a finite amount of space?

Well I can understand that concern. If the BB happened, then I think it is rational to conclude that the universe is not infinite. But my understanding is that the OP had a concern that he/she would be somehow fated to take every possible action at some point, and hence would not have free-will. At least that's my interpretation. And I don't think that that concern is a real one. Because my assumption is that even if there are an infinite number of beings that are identical to me, they are still not me.

[Incomplete]

However, if the Big Bang holds, and so far it seems to, that means at some time shortly after the BB, there was an *infinite* amount of matter and energy concentrated in one small volume of an expanding universe.

No, it doesn't mean that. It means that an infinite amount of matter and energy was concentrated in an infinite amount of volume. If the universe has infinite volume at any time, it always did (except possibly right at the BB singularity itself, but that's singular and we can't say anything about it).

[robross]

No, it doesn't mean that. It means that an infinite amount of matter and energy was concentrated in an infinite amount of volume. If the universe has infinite volume at any time, it always did (except possibly right at the BB singularity itself, but that's singular and we can't say anything about it).

And how do you go from a singularity to infinite volume? How would we be able to back-track the expansion of the universe to a singularity if there is an infinite amount of matter and space between us and the singularity?

Rob

[Incomplete]

And how do you go from a singularity to infinite volume?

Think of it like this. Take a segment of the real line, say the interval -1 to 1. That interval is the space in a finite universe, or it's a finite piece of an infinite universe. What the expansion does is it multiplies that interval by a function of t, so that it stretches as t gets bigger. Let's just say it multiplies it by t (t^2/3 would be more realistic).

So when t=1, the "volume" of our universe is 2 (the distance from -1 to 1). When t=10, it's 20, etc. OK?

Great, so go back in time, and when t=0 it's 0. So a finite universe, or any finite piece of an infinite universe, has 0 volume at the BB. Even if you don't believe the answer at t=0 exactly, since it's singular, you can take the limit as t->0, and you get 0 volume that way too.

But now take the whole real line, from -infinity to infinity. That has infinite volume at t=1, infinite at t=10, infinite at t=.000000000000000001. At t=0 it's not defined, because that's a singularity. But it's infinite for all t>0.

How would we be able to back-track the expansion of the universe to a singularity if there is an infinite amount of matter and space between us and the singularity?

Because there's a finite amount of *time* back to it, and in addition we only see a finite amount of the space.

[robross]

But now take the whole real line, from -infinity to infinity. That has infinite volume at t=1, infinite at t=10, infinite at t=.000000000000000001. At t=0 it's not defined, because that's a singularity. But it's infinite for all t>0.

That's a pretty big discontinuity, to go from no volume, or tiny volume, to infinite volume, in finite time. Are there any hypothesized mechanisms for how this would work?

And how would a universe of infinite energy reconcile itself with energy conservation laws? You could destroy energy in one location without violating conservation, since the amount of energy is infinite, so destroying some still leaves you with infinite energy.

Rob

[Incomplete]

That's a pretty big discontinuity, to go from no volume, or tiny volume, to infinite volume, in finite time.

If there's any change at all it happens in zero time. But that's not the right way to think about it.

Are there any hypothesized mechanisms for how this would work?

No. Look, t=0 is a singularity. It's something that inherently doesn't make sense. And we have no reason to think it's there at all, because we have no reason to trust the known laws of physics there (in fact we have very good reasons not to trust them). So forget about t=0, just cut off the spacetime at t=.000000000000000000000000000000000000000000001 seconds where we still can trust physics. At that time the volume is infinite.

And how would a universe of infinite energy reconcile itself with energy conservation laws?

Energy conservation is local. Energy can't just disappear somewhere and instantly reappear somewhere far away. It flows.

[neilzero]

We are fated to some outcomes, but not to most. I don't follow the logic that our fate is determined by infinite or finite universe, nor do I think outcomes are in pairs, why not in threes or 99s? Neil

[astromark]

So we have an impasse; Some small issue regarding the way you interpret the definitions of words we use... It happens a lot round here. The usual outcome is un necessary. Tolerance and understanding it would seem is fleetingly rare. Back in post 30 I see a whole lot of mathematics... I almost ran and hid. Some people do math., some do not...
But no, I am interested in this discussion and its outcome.
The question which some see differently than I. Would I be right in this assumption?
That as the universe was once a finite mass expanding and still is into what might be infinty. Can I and is it right to call it infinite. Remembering that If there was at some time past a limit on its mass then it must be finite. Its a big question... Do we have all the facts to bring a correct conclusion ?
Does the 'Finite but unbound survive as the most logicically correct conclusion ?

[Jens]

Astromark, the problem is that although it is an interesting question -- is the universe infinite, or finite and bounded, or finite and unbounded -- it really has nothing to do with the title of this thread. If you want to talk about that, I think it would be best to start a new thread. This thread is supposed to be about the notion of "fate in an infinite universe."

[dhd40]

If the BB happened, then I think it is rational to conclude that the universe is not infinite.

This is something I don´t understand. Why can´t the (a) BB happen in an infinite universe? Are there any scientific arguments against this?

[astromark]

This is something I don´t understand. Why can´t the (a) BB happen in an infinite universe? Are there any scientific arguments against this?

Yes and its real easy... If all that is was once in one place. That being described as a singlarity. then there being a great expansion we call the Big Bang then at that moment it would seem there was a actual size to the universe it must be concluded that it was finite. It can continue to expand for infinity. Thus the Finite but unbound... I trust this helps, mark.

[Incomplete]

This is something I don´t understand. Why can´t the (a) BB happen in an infinite universe? Are there any scientific arguments against this?

No, there are no arguments against it. The standard cosmological model is a universe that's spatially infinite and had a big bang 13.7 Gys ago.

[phunk]

The big bang doesn't say that the whole universe was in one place. It says that all of our *observable* universe was in a tiny volume. It's possible that it just went from infinity to a bigger infinity at the big bang.

[astromark]

'Phunk' That might be your view. That is absolutely not the mainstream view. The BB was the beginning of the universe. Not just part of it.
If you confuse the question... the answer just gets lost.

[phunk]

No, you got my point almost completely backwards. Let me phrase differently.

I'm not saying that the big bang was a subset of the universe, I'm saying our observable universe was a subset of the big bang.

If you squeeze all of our observable universe down to a tiny volume, that doesn't mean that the whole universe was that tiny volume, just our observable part. It could have been infinite before the expansion, and it went to a bigger, lower density infinity during the big bang.

[cosmocrazy]

The big bang doesn't say that the whole universe was in one place. It says that all of our *observable* universe was in a tiny volume. It's possible that it just went from infinity to a bigger infinity at the big bang.

I don't see how infinity can become a bigger infinity? Infinity is exactly what it is - no defined end - no defined size. A singularity can be infinite since its very definition is that it occupies no space/time, it has no volume or size in anyway but yet can contain everything within it. My brain hurts now

[phunk]

By the way, that our observable universe is a subset of the whole thing, and therefore a subset of the big bang, is mainstream and very well established.

[phunk]

I don't see how infinity can become a bigger infinity? Infinity is exactly what it is - no defined end - no defined size. A singularity can be infinite since its very definition is that it occupies no space/time, it has no volume or size in anyway but yet can contain everything within it. My brain hurts now

Ask a mathematician, one infinite set can be larger than another. A simple example, integers vs real numbers. There are no defined endpoints for either set, but you can only fit a finite number of integers between any two numbers, but you can fit an infinite number of reals.

[robross]

No, there are no arguments against it. The standard cosmological model is a universe that's spatially infinite and had a big bang 13.7 Gys ago.

This is the first time I have heard that the "standard" model says the universe is spatially infinite. I've always heard it to be "finite and unbounded."

Can you define what you mean by "spatially infinite?"

Rob

[Incomplete]

This is the first time I have heard that the "standard" model says the universe is spatially infinite. I've always heard it to be "finite and unbounded."

Where have you read that? To me that's a confusing choice of words. I'll explain:

"Finite" almost certainly means "finite volume", or "compact" in math lingo. "Unbounded" in common usage means infinite, which makes that "finite and unbounded" an bad choice of phrase to use in any sort of pop physics setting. But probably "unbounded" was intended to mean "without boundary". A manifold which is compact and without boundary (the surface of a sphere is a good 2D example) is called "closed".

There are three standard options for the spatial geometry of the universe (meaning the geometry of space at fixed time): closed, which means finite volume but without boundary, and specifically a 3-sphere; flat, which means an uncurved 3-volume, the 3D analogue of a flat 2D plane; and open, a 3D hyperbolic manifold with infinite volume and negative curvature.

There is no evidence for spatial curvature, hence the preferred option is the second. Notice that only one of the three has finite volume.

Can you define what you mean by "spatially infinite?"

I mean that at any fixed time, the spatial volume of the universe is infinite.

[Ken G]

To me, one can certainly ask the philosophical question, "what if the universe is spatially infinite?" However, one cannot make this into a physics question, there is no way. It's not even a physics question if the observable universe is demonstrably closed and finite, because you can always assert other such pocket universes outside what we can observe, and the assertion is not falsified by any data. There is no point in saying "but it's invalid to assert such pocket universes if we can't observe them", because we can't observe an infinite universe under any circumstances-- the observably closed and finite case adds no further restrictions there that we didn't have from the original question.

It's also not a physics question if the observable universe is flat as far as you can see, because you still have no idea what it does beyond what you can see. Certainly, it is natural to assume what lies out there is "more of the same", a la Occam's Razor, but that particular "more of the same" takes on a very different quality when you say that something infinite could ever be more of the same of something finite-- that's so much more of the same it ain't the same at all.

The bottom line is, there is no possible way that you can make the question "is there an infinite volume of universe out there" a physics question, expressly because physics is tested by observation, and you cannot observe an infinite volume. It is really replacing what physics is with something that it isn't, to take any dataset and say "this shows there is not an infinite volume out there", or any dataset and say "this shows there is an infinite volume out there." Either way, what can be observed is being used to make claims about what we already know cannot be observed, and that's just not physics.

So if it's not a physics question, it is a pure philosophy question, and is not informed by physics in any way. The question could have been asked ten thousand years ago, and can be asked ten thousand years from now. One merely needs to clarify one's reasons for asking it. If it brings some insight into ethics or issues of fate, then let's hear the insights, but the logic cannot go the other way-- there is no logic that says "because we have an infinite universe, therefore...", the logic can only go "if we imagine an infinite universe, then we conclude...." which in turn gives us something to think about that informs what we can observe, which is a finite volume. So far, I have not seen any such deducible insight, so I am unconvinced of the value of asking the question.

[Incomplete]

The bottom line is, there is no possible way that you can make the question "is there an infinite volume of universe out there" a physics question, expressly because physics is tested by observation, and you cannot observe an infinite volume.

In quantum mechanics, a particle can be in a superposition of two eigenstates of (say) spin. But when you measure the spin of the particle you get only one result, and moreover you alter the state in such a way that you can never find any trace of the other part of the superposition.

Does that make asking about the part you didn't observe a "philosophical question"? People might have used almost identical logic and said so before the 60's, but Bell proved them wrong.

How do you know we can't use that "philosophical" ensemble of pocket universes, or just the infinite extent of our own, to make quantitative statistical predictions about what we observe, and then test them?

[Boratssister]

[QUOTE=robross;1560959]Well, I for one have never encountered an infinite amount of any physical substance. We experience "abstract" ideas about infinities, such as being able to travel the circumference of a circle eternally. But as far as concrete, countable infinities, that is something I have no experience with. Now, I have to accept that there are many such things I do not have experience with, things described by Relativity and QM for one, so I have to be prepared to accept things that are counter intuitive.

However, if the Big Bang holds, and so far it seems to, that means at some time shortly after the BB, there was an *infinite* amount of matter and energy concentrated in one small volume of an expanding universe. How can an infinite amount of matter and energy be concentrated in a finite amount of space? And how would inflation have affected an infinite amount of 'stuff'? And how would a finite volume of initial space grow to be infinite?

I just have a problem conceptualizing this.







May be our big bang was just a little spark, a bit of static on seas of static. All the matter in our universe may be simply due to a break down of that spark. How does a spark breakdown?
If a universe is infinatly big then why not infinatly small, may be all the energy comes from the infinatly small . An infinatly small universe would have all the matter and energy our universe has but on a smaller dimension. May be the big bang was Infact the observers moving into a smaller dimension, like falling into a blackhole. Who knows? Someone said there is as many stars in the universe as atoms in a human body , in effect humans are halfway to the stars, between the big and the small . The big bang ? Little spark more like.

[Boratssister]

You don't need a multiverse for fate to have a bearing. It seems to me our universe is remarkably finetuned. May be the only way to have a universe is to have it exactly like ours is now and was in the past and in the future, which would mean we are all just going through the motions... A bit depressing . However if our universe is the only way a universe can be , has been and will be ,we will be guaranteed to exist in any new universe . Smile!

[astromark]

Oh Its good to see some support.. No Phunk. I do not expect you to understand but I will try just one last time...
Finite but unbound. = Finite does mean a limited amount of mass. But unbound = means that it can and is expanding for infinity... and its that simple. Do not over complicate the simple. The easy is the most likely. You say the mainstream view is as you have said. No. Wrong ! That you are suggesting that the known universe is only part of it is expectable. What is wrong is that the BB was only a part of the universe. No, that is wrong. Can you see a difference ?
Have you also noticed that we have three threads all arguing this point. interesting...

[phunk]

What is wrong is that the BB was only a part of the universe. No, that is wrong. Can you see a difference ?

Of course I can see the difference, that was the entire point of my other post.

Let me explain a third way. I said the BB was everything, but our observable universe is only part of everything. We don't know how much is outside our observable universe now, therefore we don't know how much was outside the tiny volume that expanded into our observable universe either.

[Cougar]

If the universe is infinite in extent, then it contains an infinite set of "observable universes". This would encompass all initial conditions....

An "infinite" universe... has absolutely nothing to do with admitting multiple initial conditions.

I think the Doctor has you on this point, Incomplete. Yes, there would be an infinite set of observable universes, which is simply dependent on an observer's location. But if there's just one universe that is infinite in extent, then there need be only one set of initial conditions. You could add more, I suppose, since such regions are unobservable anyway. You could add pink unicorns, too, but neither is very Occam-friendly.

If there are an infinite number of pocket universes within an overarching multiverse, then each could have different initial conditions, and since we're talking infinite, ridiculously improbable events would eventually happen in some pocket universe.

But here's the problem with the whole scenario that the OP puts forward:

Alan Heavens... at the University of Edinburgh... observed 90,000 distant galaxies... [and] concluded that 5 billion years ago the overall star-formation rate began steadily decreasing to the rate we see today. -- Jeff Kanipe

If the hypothetical infinite universe is more or less like the observable part we can see, then it appears it would eventually become an infinitely large graveyard.