1. ## Infinite Universe....Fate?

Hey all, I was listening to an AstronomyCast by Cain and Gay and they were explaining how if the universe is infinite, than every possible outcome that can happen, does happen. For instance if there were a decision where I can pick up my juice or not pick up my juice, if I do not pick up my juice here, trillions of trillions of light years away the miniscule probability of my being occurring again and choosing to not pick up the juice occurs.
My question is that since it is stated that everything that should happen will/does happen, and I would say for every moment in time there are many many decisions you can do (from picking up the juice to running down the street naked etc.), to make sure that every option does occur in the universe could it be possible that we are fated to do things, and yet do not know it yet? Like let's say the situation with the juice has already occurred somewhere else and the juice is left on the table, and every other possibility of what to do with the juice is filled by some other 'me' on other worlds, and the only choice left is to pick up the juice - am I fated to pick up the juice to keep that statement true that everything that can happen does happen (assuming we live in an infinite universe)?

2. Originally Posted by AriAstronomer
... am I fated to pick up the juice to keep that statement true that everything that can happen does happen (assuming we live in an infinite universe)?
Perhaps that is a strong point in favor of the universe being finite.

3. Originally Posted by AriAstronomer
Hey all, I was listening to an AstronomyCast by Cain and Gay and they were explaining how if the universe is infinite, than every possible outcome that can happen, does happen.
That would be true for a universe infinite in time.

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Originally Posted by Argos
That would be true for a universe infinite in time.
That doesn't seem necessary. If the universe is infinite in extent, then it contains an infinite set of "observable universes". This would encompass all initial conditions and so there are infinite observable universes with "copies" of Ari drinking his/her juice and infinite "copies" of him/her not picking up the juice.

m74

5. @ m74

6. As Argos has pointed out, this would require infinite multiple universes rather than 1 infinite in size universe. we cannot imagine infinite in any sense of things, since we are unable to imagine no beginning and no end. If the universe was infinite in size why would it contain any more than 1 of me? God forbid!

7. Originally Posted by Argos
@ m74

He is talking about a situation considerably more complex. As he formulated the statement he requires an uncountably infinite number of "pocket universes" in his "multiverse" and a solution to the measure problem, just for starts.

This lies squarely in the camp of raw speculation, and there is no theory to support it. Worse, if there were a theory it would be untestable even in principle since all of these "pocket universes" would be sufficiently far away to have no causal connection to us.

So, basically, it doesn't matter if he is right or wrong. This is the worst of all possible worlds for a physical theory. Irrelevance.

8. hey, its a good explanation for de' ja vous though!

9. Do not go down that road. Its not a good explanation of anything at all. Its a load of rubbish. Philosaphy is a madness we can not fight. Like a cancer of insanity it spreads its idiotic logic. Hit the delete button. Get out of there. There is just one universe. Its very very big. Its expanding like we can not imagine and we are not in the middle... There is not another you, not drinking the juice., Oh please.... what sort of self importance makes people think like this.
Try this...We are a mistake. It should never have happened at all. Did it ?.
Across the coffee bar in the corner is a group of phillosophers that have been arguing this for over a decade. Its the end of humanity...
I am of the ' Finite but unbound school of thought.'
Last edited by astromark; 2009-Aug-25 at 09:07 PM. Reason: added.

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But Stargate, Star Trek, etc would have less plot lines without parallel universes.
Of course, even though I'm a sci-fi buff, I've never been a fan of the parallel universe theory.
So what do I do? Write a book that incorporates time travel!

Yes, my life is a contradiction.

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Originally Posted by DrRocket
He is talking about a situation considerably more complex. As he formulated the statement he requires an uncountably infinite number of "pocket universes" in his "multiverse" and a solution to the measure problem, just for starts.
Huh?

First off, probably the best theory (in the sense that it's simplest and fits all the data) about our universe is that it's spatially flat, which means it has infinite volume. Of course at the moment we can only see a finite piece of it (because it's only been around for 13.7 billion years). But if there really is an infinite spatial volume out there, then anything with non-zero probability (and some things with zero probability) is out there too.

This lies squarely in the camp of raw speculation
Not really. it's the simplest theory we have. Anything else requires an assumption, such as that only the part of the universe we can see is homogeneous, but once you get farther out something changes.

and there is no theory to support it.
All of modern observational cosmology?

Worse, if there were a theory it would be untestable even in principle since all of these "pocket universes" would be sufficiently far away to have no causal connection to us.
Not clear. A solution to the measure problem you mentioned could provide testable predictions.

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if the universe expands into the empty far out reaches of infinite space and the universe becomes cold and dead, and then another big bang occurs, then isn't it logical to suggest that the way the universe is, is the only way it could be which therefore suggests that in the next universe I will be writing this as I am writing this now! It all depends on how fine tuned our universe is.
I some how like the above theory, better than multiverses.

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Originally Posted by Argos
@ m74

Yes and no. Yes, I'm talking about the level one multiverse which is our observable universe and the rest of the supposed infinite domain that surrounds it.

@Dr. Rocket, @astromark

I don't think it is mere speculation to say that our universe is part of what may be called the Level One multiverse. As I understand, evidence garnered from the analysis of the CMB points towards a universe with zero curvature and spatially infinite. And if it is infinite, how does this not necessitate that every initial condition be satisfied?

As well, a galaxy that has a light-travel time of 13.6 by, is actually positioned 35 billion years (way beyond the hubble volume).

14. Originally Posted by Incomplete
Huh?

First off, probably the best theory (in the sense that it's simplest and fits all the data) about our universe is that it's spatially flat, which means it has infinite volume. Of course at the moment we can only see a finite piece of it (because it's only been around for 13.7 billion years). But if there really is an infinite spatial volume out there, then anything with non-zero probability (and some things with zero probability) is out there too.

It is also irrelevant to the question that was being addressed. The question being addressed was the applicability of the multiverse model to the OP,

In no way is this an endorsement of the multiverse hypothesis, which I consider to be quite irrelevant itself to the universe as we observe it.

Originally Posted by Incomplete"
Not really. it's the simplest theory we have. Anything else requires an assumption, such as that only the part of the universe we can see is homogeneous, but once you get farther out something changes.
Yes really. The multiverse hypothesis is the rawest of raw speculation.

You are addressing some issue other than that which I raised.

Originally Posted by Incomplete
All of modern observational cosmology?
Again you have the right answer to the wrong question.

Originally Posted by Incomplete
Not clear. A solution to the measure problem you mentioned could provide testable predictions.
Not in the context of the multiverse hypothesis. The probabilities assigned to "pocket universes" are irrelevant since they are causally disconnected from our little corner of the universe.

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Originally Posted by DrRocket

It is also irrelevant to the question that was being addressed. The question being addressed was the applicability of the multiverse model to the OP,

In no way is this an endorsement of the multiverse hypothesis, which I consider to be quite irrelevant itself to the universe as we observe it.
It's not irrelevant.

m74z00219 said: "If the universe is infinite in extent, then it contains an infinite set of "observable universes". This would encompass all initial conditions and so there are infinite observable universes with "copies" of Ari drinking his/her juice and infinite "copies" of him/her not picking up the juice."

And you replied: "He is talking about a situation considerably more complex. As he formulated the statement he requires an uncountably infinite number of "pocket universes" in his "multiverse" and a solution to the measure problem, just for starts."

You were wrong, and m74z00219 was right. Very simple. There is no need for "pocket universes" or a "multiverse", just plain old vanilla flat Robertson-Walker cosmology, which has (at any given time) an infinite number of Hubble volumes. Infinite volume times any non-zero probability per unit volume equals infinity; ergo there are an infinite number of copies of Ari drinking juice.

If you disagree, you'll need to provide some evidence.

Not in the context of the multiverse hypothesis. The probabilities assigned to "pocket universes" are irrelevant since they are causally disconnected from our little corner of the universe.
Are the amplitudes of the states in some quantum superposition irrelevant because in the end we only observe one? No, they're not, because they tell us the probability of observing something. Why can't a "multiverse" measure do the same?

16. Originally Posted by m74z00219
Yes and no. Yes, I'm talking about the level one multiverse which is our observable universe and the rest of the supposed infinite domain that surrounds it.

@Dr. Rocket, @astromark

I don't think it is mere speculation to say that our universe is part of what may be called the Level One multiverse. As I understand, evidence garnered from the analysis of the CMB points towards a universe with zero curvature and spatially infinite. And if it is infinite, how does this not necessitate that every initial condition be satisfied?

As well, a galaxy that has a light-travel time of 13.6 by, is actually positioned 35 billion years (way beyond the hubble volume).
The universe is most certainly not truly flat, though it may be on a large scale. That remains to be seen. There is also a belief that if it is flat then it is just Euclidean space, but that is not necessarily true. There are flat compact manifolds. Believe it or not there is such a thing as a flat torus. I have not seen aconvincing argument for excluding such a possibility.

An "infinite" universe is what is actually called an open manifold. That has absolutely nothing to do with admitting multiple initial conditions. So far as is known the initial conditions of the Big Bang are the initial conditions and the only initial conditions. From those initial conditions you can evolve a spacetime manifold with closed space-like slices (finite universe) or with open space-like slices (infinite univerese). But there is still only one set of initial conditions.

The multiverse postulates a plelthora of bangs, and a plethora of separate "pocket universes" within one big landscape. That is an entirely different kettle of fish, and a totally untestable one.

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Originally Posted by DrRocket
The universe is most certainly not truly flat, though it may be on a large scale. That remains to be seen.
It's obviously not exactly flat (look around, there's gravity); no one here is asserting otherwise. But that it is almost flat on large scales is the simplest hypothesis consistent with current theory and data, and the one accepted by most cosmologists today.

There is also a belief that if it is flat then it is just Euclidean space, but that is not necessarily true. There are flat compact manifolds. Believe it or not there is such a thing as a flat torus.
Of course, yes. All torii are flat (or can be) in the sense relevant here.

I have not seen aconvincing argument for excluding such a possibility.
And no reason to consider it either. It adds several extra parameters in the theory without making the fit to data any better. Hence, by standard scientific logic it should be disfavored.

An "infinite" universe is what is actually called an open manifold.
No, it's called "non-compact". "Open manifold" means something else (it means without boundary, which isn't the same thing as infinite; for example, the real numbers between 0 and 1 but not including the endpoints is an open but compact set).

Edit: I checked, and evidently you're correct that part of the definition of "open manifold" (as opposed to "open set") is non-compact. Still, the term you wanted was non-compact, since that simply means infinite ("open" means no boundary and no compact component).

The multiverse postulates a plelthora of bangs, and a plethora of separate "pocket universes" within one big landscape. That is an entirely different kettle of fish, and a totally untestable one.
Again, not necessarily untestable.

18. Originally Posted by Incomplete

And no reason to consider it either. It adds several extra parameters in the theory without making the fit to data any better. Hence, by standard scientific logic it should be disfavored.
Nonsense. The basic theory proceeds by assuming that the universe is homogeneous and isotropic. That in turn implies the existence of a one-parameter foliation by space-like slices, which are true Riemannian manifolds (the induced metric being positive-definite). It also results in those space-like slices being of constant curvature. Then one appeals to a classification theorem of Riemannian geometry to determine the potential topologies, which are relatable to the curvature. But it is not so simple as negative curvature implying an open manifold, a zero curvature implying Euclidean space and positive curvature inplyiing a closed manifold. It is true that positively curved manifolds will be closed. But there are other possibilities in the remaining two cases.

Your logic is flawed. There is no data that is sufficient to answer the question of the topology of the universe. That is why it is an open question. There is no reason to make any arbitrary choices at this point, and there are no parameters to be added or subtracted. General relativity is quite sufficient as it stands.

Originally Posted by Incomplete
No, it's called "non-compact". "Open manifold" means something else (it means without boundary, which isn't the same thing as infinite; for example, the real numbers between 0 and 1 but not including the endpoints is an open but compact set).

Edit: I checked, and evidently you're correct that part of the definition of "open manifold" (as opposed to "open set") is non-compact. Still, the term you wanted was non-compact, since that simply means infinite ("open" means no boundary and no compact component).
I said "open" because I meant open. If I had meant merely not compact I would have said non-compact. There is a difference in meaning between "open" in the category of differentiable manifolds and diffeomorphisms and "open" in the category of topological spaces and homeomorphisms. I meant "open".

I also meant "closed", which means compact without boundary in the category of smooth manifolds.

"Infinite" on the other hand is an inappropriate mathematical term and means neither open nor closed. It is a term used in the popular literature as a synonym for "open", but only because the writers do not understand manifolds.

In any case the model using a manifold without boundary is important to the theory. It would be quite difficult to make physical sense of a boundary for space-time. If such a thing were to exist it would be a 3-manifold without boundary, but what those 3 dimension might mean physically is a bit of a mystery. All viable models treat space-time as a Lorentzian 4-manifold without boundary.

It is also the case that you don't need to worry about components of the manifold as we are only dealing with connected manifolds. Most treatments of manifolds restrict attention to connected manifolds since there is no reason to do otherwise. Disconnected manifolds are just disjoint unions of connected manifolds.

Do you try to teach your grandmother to suck eggs ?

Originally Posted by Incomplete
Again, not necessarily untestable.
Yep untestable. Any such pocket universes are sufficiently far removed from us, in a pocket that is continuing to expand and that has expanded such that portions of our universe are already causally disconnected from us, that there is no way that in principle those other pocket universes, even if they exist, can affect or be affected by anything in our neighborhood.

19. Originally Posted by AriAstronomer
Hey all, I was listening to an AstronomyCast by Cain and Gay and they were explaining how if the universe is infinite, than every possible outcome that can happen, does happen. For instance if there were a decision where I can pick up my juice or not pick up my juice, if I do not pick up my juice here, trillions of trillions of light years away the miniscule probability of my being occurring again and choosing to not pick up the juice occurs.
I would dispute this premise. I don't think that you can exist in two places at once. I would say that a person who is identical to you in every respect will definitely exist (actually, an infinite number of such individuals will exist...) but they will not be you. You are a unique entity in time and space. So no, I don't think you're fated to do anything.

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Originally Posted by DrRocket
The basic theory proceeds by assuming that the universe is homogeneous and isotropic. That in turn implies the existence of a one-parameter foliation by space-like slices, which are true Riemannian manifolds (the induced metric being positive-definite). It also results in those space-like slices being of constant curvature. Then one appeals to a classification theorem of Riemannian geometry to determine the potential topologies, which are relatable to the curvature.
Correct.

But it is not so simple as negative curvature implying an open manifold, a zero curvature implying Euclidean space and positive curvature inplyiing a closed manifold. It is true that positively curved manifolds will be closed. But there are other possibilities in the remaining two cases.
Also correct.

Your logic is flawed. There is no data that is sufficient to answer the question of the topology of the universe. That is why it is an open question. There is no reason to make any arbitrary choices at this point, and there are no parameters to be added or subtracted.
Wrong. Take your example of a torus. In two dimensions the shape of torii are parametrized by two real numbers (or more typically by single complex number, usually called the modulus). In three dimensions I'm not sure how many moduli there are, but it's at least three. Those moduli are extra parameters (think of a very long skinny torus versus a short fat one).

Most scientists agree that if you compare two theories that fit the data equally well, the one with fewer parameters is preferred. Do you disagree?

General relativity is quite sufficient as it stands.
Non-sequitor.

I said "open" because I meant open. If I had meant merely not compact I would have said non-compact. There is a difference in meaning between "open" in the category of differentiable manifolds and diffeomorphisms and "open" in the category of topological spaces and homeomorphisms. I meant "open".
Then you were wrong, because not all infinite universes are open.

"Infinite" on the other hand is an inappropriate mathematical term and means neither open nor closed. It is a term used in the popular literature as a synonym for "open", but only because the writers do not understand manifolds.
Nope. It's a synonym for non-compact, and it's a perfectly accurate word (one should probably say "infinite volume" to remove any ambiguity). The only way confusion could arise is if we were discussing non-metric spaces, but those have no place in general relativity.

In any case the model using a manifold without boundary is important to the theory. It would be quite difficult to make physical sense of a boundary for space-time.
Actually just about every model in GR has a boundary for spaceTIME (the big bang). Models with boundaries for space, which is what we were discussing until you suddenly brought up spacetime, are less common, but they do exist.

If such a thing were to exist it would be a 3-manifold without boundary, but what those 3 dimension might mean physically is a bit of a mystery.
What?

All viable models treat space-time as a Lorentzian 4-manifold without boundary.
Again, nearly all models for the universe have a big bang.

It is also the case that you don't need to worry about components of the manifold as we are only dealing with connected manifolds.
I see you did some reading on wikipedia .

Do you try to teach your grandmother to suck eggs ?
I confess, I've never had any idea what that expression means...

Yep untestable. Any such pocket universes are sufficiently far removed from us, in a pocket that is continuing to expand and that has expanded such that portions of our universe are already causally disconnected from us, that there is no way that in principle those other pocket universes, even if they exist, can affect or be affected by anything in our neighborhood.
How do you know they must be causally disconnected and remain so forever? And even if they do, how do you know one can't "solve the measure problem" and use it to make predictions about our universe?

You keep making these bald assertions without ever backing them up.

21. Originally Posted by Incomplete

I see you did some reading on wikipedia .
Incorrect.

And it seems that I cannot teach you much about manifold theory. So, I'm done. This is pointless.

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Originally Posted by DrRocket
Incorrect.

And it seems that I cannot teach you much about manifold theory. So, I'm done. This is pointless.
This semantic issue about the precise meaning of "open" in "open manifold" really isn't very interesting, relevant, or important.

Does this mean you're not going to address any of the substantive issues I brought up?

23. Originally Posted by antoniseb
Perhaps that is a strong point in favor of the universe being finite.
I'm not really sure, but I think that this is the core of the question that the OP wanted to ask. And my answer was that this is not a strong point in favor of the universe being finite, as I mentioned in my last note. But I'd be happy to hear other opinions about this.

24. Well, well, well. look at those two debating this as if they now somthing new... They do not. Just to put it absolutely clear... Finite but unbound.
The question that 'Jens' has answered with precision. Stated is as said true.. If the universe had a beginning then it must be finite. I do not see any argument with that. Its expanding at a ever increasing rate so the unbound is added as a clarity of definition. I do not see any argument with that.
Where am I wrong... ?
and if I'm not, what are we talking of ?
Notice the deliberate failure to mention multi universes or other such unsupported dribble.
So there is but one of me in infinaty and I'm here, drinking your juice bottle....mark.

25. In my opinion this is just humans thinking too much. I wouldn't be suprised if it's just 1 universe, 1 timeline. It's born, thrives, then dies.

26. We were discussing this at work. One of the theories regarding the "infinite Universe" is that the Universe is infinite. Our local piece of the Universe is expanding within a finite area. Imagine rain hitting a small pond. The initial drop hitting the surface would be the big bang and the ripples running out is our observable part of the Universe expanding outward. Other areas of the Universe are expanding outward as well and eventually will merge into each other. The issue is that the distances between the expanding areas is so vast that you can't see each other.
Eventually each of the areas will expand outward so much that it will be spread out so far that the 'big freeze' as has been coined will occur. Then another 'rain drop' will hit and another big bang will occur and a new area will begin spreading out, maybe where two expanding areas come in contact with each other.

27. Originally Posted by Incomplete
This semantic issue about the precise meaning of "open" in "open manifold" really isn't very interesting, relevant, or important.

Does this mean you're not going to address any of the substantive issues I brought up?
I means that you have not brought up any substantive issues, and I am not going to argue with someone who adopts the demeanor of a smart alec kid who appears to not understand the words that he is using. I've seen it before and the nice thing about my current situation is that I don't have to deal with it if I don't want to.

Go take a look at Hawking and Ellis where you will find that the model for space-time is explicitly a Lorentzian manifold without boundary.

Open or closed is an open issue. The underlying question fundamentally involves the topology of space-like slices. They too are without boundary, so the question is what topologies are consistent with GR and which topology is actually realized by the solutions to the field equations that represent the universe in which we frind ourselves. Nobody knows the answer to that.

Moduli spaces are not particularly relevant except as they help to understand how topology is related to geometry. Once you recognize that flat is not necessarily Euclidean the major lesson has been learned.

In short, I'm done arguing with you on these points. I find you eminently ignorable. If you would like to learn something about the subject go read a decent book on differential geometry or differential topology. Spivak is a good source for the former and Hirsch for the latter, but there are lot of good choices.

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Originally Posted by DrRocket
I means that you have not brought up any substantive issues, and I am not going to argue with someone who adopts the demeanor of a smart alec kid who appears to not understand the words that he is using.
Translation: I caught you in several basic mistakes, and you got irritated.

Go take a look at Hawking and Ellis where you will find that the model for space-time is explicitly a Lorentzian manifold without boundary.
Not for a cosmology with a big bang, it isn't. That's not even a manifold, and if you make it one by cutting out the singularity it has a boundary. And this whole thing is a non-sequitor, since you suddenly leaped from space geometry to spacetime.

Moduli spaces are not particularly relevant except as they help to understand how topology is related to geometry. Once you recognize that flat is not necessarily Euclidean the major lesson has been learned.
So for the third time you fail to address the issue: adding topology is an unnecessary assumption that introduces new parameters without improving the fit to data. By standard scientific logic, it is thereby disfavored.

In short, I'm done arguing with you on these points. I find you eminently ignorable.
I.e. you can't.

If you would like to learn something about the subject go read a decent book on differential geometry or differential topology. Spivak is a good source for the former and Hirsch for the latter, but there are lot of good choices.

29. Originally Posted by rommel543
One of the theories regarding the "infinite Universe" is that the Universe is infinite.
I'm sure you were trying to say something more profound.

30. Originally Posted by AriAstronomer
Hey all, I was listening to an AstronomyCast by Cain and Gay and they were explaining how if the universe is infinite, than every possible outcome that can happen, does happen.
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.