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Topic: Re: Infinity (Read 1122 times) |
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towr
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Re: Infinity
« on: May 8th, 2005, 2:59pm » |
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on May 8th, 2005, 12:45pm, alien wrote:I have a few probably silly questions about infinity that could also be considered as riddles.
1) Does an infinite space exist always or can it have a beginning and end?
a) Lots of relevant scientists support the theory that universe is infinite. But they also think that universe had a beginning called Big Bang. Isn't that paradoxical? If universe had a beginning, and if the explosion called Big Bang didn't had infinite speed, how can this universe be infinite? It is still expanding at great speed, but it always has an end. Right? |
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As long as the universe expands with the speed of light (or at least the very edge of what youy'd include moves with that speed), then practically the universe is infinite. Because you can't go faster than the spee dof light, end thus never leave it no matter how far you travel. It is endless.
There is a more theoretic way to get infiniteness from finiteness. Take the range (0..1], no take {1/r | r in (0..1]} = [1..inf). A simple tranformation, and you have infiniteness.
Just a matter of flipping a finite range inside out. 
Quote:| b) If this universe is infinite, does that mean that it can never contract? Because if it doesn't have en end, where would contraction begin? |
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It could start anywhere. Of course if it starts just in any one place, then it would take an infinity to affect the farthest parts. If on the otherhand the contraction occurs at every point at the same time it may be another matter.
Just flip the whole things right-side in again 
Quote:| 2) This universe is described by all relevant scientists as a moving universe, never resting universe. So isn't it logical to conclude that, if this universe is infinite, infinity can be also described as a motion? Does infinity have an infinite speed that is so fast that is has become infinitely still? Am I talking nonsense? |
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For starters it seems you're confusing 'is'es. If a man is nice, and a man is black, that doesn't mean nice is black. So if the universe is infinite, and the universe is moving, doesn't mean infinity is moving or a motion.
More importantly though, it is parts of the universe that move with regard to each other. Whether the universe itself is moving is a strange idea. If the universe is everything anywhere, with regard to what could it change position? There would have to be something outside it, but then the universe would be everything.
Quote:| 3) This is more of a riddle. Imagine a finite length AB. And then, in an instant, it becomes infinite. Is it possible that you can still find or see A or B? |
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Not along that infinite path I'd imagine. So not if every path between the two was infinite. (but that's not necessarily the case)
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Icarus
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Re: Infinity
« Reply #1 on: May 8th, 2005, 6:33pm » |
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I pretty much agree with towr, but would like to address a few matters he didn't.
Quote:| Lots of relevant scientists support the theory that universe is infinite. |
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Really? Who? I have not heard of mainstream scientists supporting the concept of an infinite universe. It has been pretty well established that the universe was finite in spacial extent since well before the introduction of the big bang theory. Since it's introduction, most everyone agrees that it is finite in age as well. The only thing about the universe that is suspected to be infinite is its future - but even that is only in bare existance. Though the universe will continue to exist, it is expected to die - utterly cease in activity other than a certain quantum minimum that does not count. This is called the "Heat Death" of the universe. And unless a "big crunch" comes, or some other fate not in keeping with current observational evidence, it is the future.
How do we know that universe is not infinite? A fairly simple argument shows that universe infinite in both age and size is extremely unlikely: If the universe was infinite in both, then in any direction you looked, somewhere along that line in the past was a star whose light is reaching earth now. I.e., we would be inundated by light from all directions. This is manifestly not the case, so the universe is apparently limited in either space or time. By the big bang theory, it is limited in both.
So you are in fact correct in your conclusion in 1a. What you are wrong in is your belief that "relevant" scientists don't know this.
Quote:| If this universe is infinite, does that mean that it can never contract? Because if it doesn't have en end, where would contraction begin? |
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If the universe were infinite spacially, it could not contract while remaining spacially infinite. It could contract in parts, but would have to make up for it by expanding in other parts. However, it is possible for an infinite universe to contract by ceasing to be infinite, and only take a finite amount of time to do it. The rate of contraction must initially be infinite, but this does not necessarily violate the light-speed limit, which only applies to matter. It should be noted that during the "inflationary period" in the big bang theory, it is believed that space expanded faster than the speed of light.
Also: do not mistake "endless" for "infinite". The universe is generally believed to be endless spacially, but not infinite. How is this possible? Well, a circle is also endless, but not infinite. In the same way, space closes back into itself in spacial directions. Relativity prevents it from doing the same in the temporal directions, so the universe must have a definite beginning, a definite end, or it is infinite in those directions (separately: it can have definite beginning but be infinite in the future direction).
Quote:| 3) Imagine a finite length AB. And then, in an instant, it becomes infinite. Is it possible that you can still find or see A or B? |
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This question is ill-posed. The idea is not well defined, so any answer is possible. I can easily define spaces mathematically which have actual points infinitely far apart, but in our standard geometric space, this does not occur. In the real universe, the concept is non-sensical.
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Deedlit
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Re: Infinity
« Reply #2 on: May 8th, 2005, 6:57pm » |
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on May 8th, 2005, 12:45pm, alien wrote:I have a few probably silly questions about infinity.
1) Does an infinite space exist always or can it have a beginning and end?
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This is a question we don't know the answer to, and I would say it is one of the fundamental questions about the universe. Unfortunately, we can only answer this question directly if we can show that the universe is finite - for example, if we can see that the universe "wraps around" (so that light from the same objects reach us from two different directions), or if we show that the universe has positive curvature, suggesting that it curves into a 4-dimensional sphere, which is of course finite (measurements have shown the curvature to be very near zero - so it could still be very slightly positive). Otherwise, it will remain one of those fundamentally unanswerable questions, since we can never see beyond the edge of the observable universe (the point where light takes the age of the universe to reach us).
A lot of people lean towards a finite universe, since the idea of an infinite universe has some unsettling implications. Mainly, that every possible finite universe that can occur, should occur infinitely many times. For instance, there should be an infinite number of versions of Earth, in which a being basically identical to you named Beatrice is king of the world, and a being basically identical to me named Thor runs a chain of self-serve fast food restaurants.  And I'm writing a post almost exactly like this one, except that William had already restored the full functionality of this forum and I decide to write the whole thing in Greek. You get the idea - anything that can happen, does happen, infinitely often!
Einstein opined that he believed the universe was finite, though not for the reason described above.
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a) Lots of relevant scientists support the theory that universe is infinite. But they also think that universe had a beginning called Big Bang. Isn't that paradoxical? If universe had a beginning, and if the explosion called Big Bang didn't had infinite speed, how can this universe be infinite? It is still expanding at great speed, but it always has an end. Right?
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This is one of the biggest confusions about cosmology. The Big Bang wasn't really an explosion in the regular sense, and it doesn't have to expand from a point. If the universe is infinite, then it would be infinite at any time in the past (but see the different notion of "current universe" below). So how can an infinite universe be expanding? Imagine an infinite grid of points placed at integer coordinates - we can imagine "stretching" this grid so that the points keep getting farther and farther apart. This is all we mean by the expansion of the universe - the galactic clusters are pulling away from each other in a uniform fashion.
It's not uncommon to read popular articles where some scientist talks about when the universe was "the size of a pea," or something like that - the thing is, they are talking about when the observable universe was the size of a pea, not the whole shebang. How can scientists omit this important information? Because it's common to consider the "universe" to be everything we can observe - this conforms to the philisophical position that reality is only that that can be perceived. But note that this universe goes backwards in time the farther it goes away from us. So it comes to an end at the beginning of the universe. This is a reasonable notion of "current universe" to a physicist, who commonly mixes space and time, but the average person likes to keep his space and time separate. So he wants the size of the universe where every point is at the "current time", i.e. the universe is the same age at every point, and this universe could certainly be infinite.
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b) If this universe is infinite, does that mean that it can never contract? Because if it doesn't have en end, where would contraction begin?
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Just picture the same infinite grid of points, except the points start moving closer together. The universe will always remain of infinite size, but that will be small consolation as we all get crushed together into a point!
It's worth noting that even Newton made this mistake about infinity - he thought that in an infinite universe, gravity would not cause objects to move together, since the is no "center" for everything to move towards - but the correct answer is that they do, and there's no need for a "center" for everything to move closer to each other.
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2) This universe is described by all relevant scientists as a moving universe, never resting universe. So isn't it logical to conclude that, if this universe is infinite, infinity can be also described as a motion? Does infinity have an infinite speed that is so fast that is has become infinitely still? Am I talking nonsense?
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I don't know what it would mean for a universe to be moving, and I haven't heard any scientist describe it as such - so I would say yes, you are talking nonsense. 
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Deedlit
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Re: Infinity
« Reply #3 on: May 8th, 2005, 7:28pm » |
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It looks like I disagree on many points with Icarus.
on May 8th, 2005, 6:33pm, Icarus wrote:Really? Who? I have not heard of mainstream scientists supporting the concept of an infinite universe. It has been pretty well established that the universe was finite in spacial extent since well before the introduction of the big bang theory.
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This is certainly not true!
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Though the universe will continue to exist, it is expected to die - utterly cease in activity other than a certain quantum minimum that does not count. This is called the "Heat Death" of the universe.
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Pretty much - you can see some more details about the future of the universe here:
http://math.ucr.edu/home/baez/end.html
But at the end, he adds this very interesting observation:
Quote:However, Leonard Susskind has recently pointed out that in thermal equilibrium at any nonzero temperature, any system exhibits random fluctuations. The lower the temperature they smaller these are, but they are always there. These fluctuations randomly explore the space of all possible states of your system. So eventually, if you wait long enough, these random fluctuations will carry the system to whatever state you like. Well, that's a bit of an exaggeration: these fluctuations can't violate conservation laws. But conservation of energy doesn't count here, since at a nonzero temperature, a system is really in a state of all possible energies. So it's possible, for example, that a ice cube at the freezing point of water will melt or even boil due to random fluctuations. The reason we never see this happen is that such big fluctuations are incredibly rare.
Carrying this thought to a ridiculous extreme, what this means is that even if the universe consists of more or less empty space at a temperature of 10-30 kelvin, random fluctuations will occaisionally create atoms, molecules... and even solar systems and galaxies! The bigger the fluctuation, the more rarely it happens - but eternity is a long time. So eventually there will arise, sheerly by chance, a person just like you, with memories just like yours, reading a webpage just like this.
In short: maybe the universe has already ended!
However, the time it takes for really big fluctuations like this to occur is truly huge. It dwarfs all the time scales I've mentioned so far. So, it's probably not worth worrying about this issue too much: we don't know enough physics to make reliable predictions on such long time scales. |
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This is manifestly not the case, so the universe is apparently limited in either space or time. By the big bang theory, it is limited in both.
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The big bang doesn't require a finite universe.
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If the universe were infinite spacially, it could not contract while remaining spacially infinite. It could contract in parts, but would have to make up for it by expanding in other parts.
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This isn't true - hopefully my infinite grid model explains this. Of course, the usual cosmological models don't include universes that are closed in time and infinite in space, but it's not a logical impossibility.
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However, it is possible for an infinite universe to contract by ceasing to be infinite, and only take a finite amount of time to do it. The rate of contraction must initially be infinite, but this does not necessarily violate the light-speed limit, which only applies to matter.
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I don't know how this would work - assuming homogeneity of the universe, the mass of an infinite universe would be infinite. So contracting to a finite space would require infinite density everywhere. On the other hand, if the mass of the universe was finite, then an infinite universe would have to be empty outside some finite space.
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| « Last Edit: May 8th, 2005, 7:28pm by Deedlit » |
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Deedlit
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Re: Infinity
« Reply #4 on: May 8th, 2005, 7:44pm » |
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on May 8th, 2005, 2:59pm, towr wrote:
As long as the universe expands with the speed of light (or at least the very edge of what youy'd include moves with that speed), then practically the universe is infinite. |
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Icarus pointed out that the speed of light limit does not apply to the expansion of space, and that the theory of inflation suggests that the universe greatly exceeded this limit during the early stages. I will add that this isn't limited to the inflationary period - in fact, under current cosmological models, distance objects that we can see are already moving away from us faster than the speed of light!
Try this cosmological calculator:
http://www.earth.uni.edu/~morgan/ajjar/Cosmology/cosmos.html
and plug in Omega = .27, and Lambda = .73, in accordance with recent results from WMAP. For z > 1.4, you'll see that an object with that redshift is receding from us at more than the speed of light.
Another interesing observation: plug in a large value like z = 1000000, and we get the current distance of that object at 46.78 billion light years! Why isn't it 13.86 billion, the age of the universe in years? The reason is that, while the light from the object that is now reaching us has travelled 13.86 billion light years, the universe was expanding that whole time, so the total distance has increased greatly. For the same reason, the distance of the object at the time the light left it is 0.0 billion light years! (it's actually about 46,780 light years).
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towr
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Re: Infinity
« Reply #5 on: May 9th, 2005, 1:24am » |
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on May 8th, 2005, 7:44pm, Deedlit wrote:| Icarus pointed out that the speed of light limit does not apply to the expansion of space, and that the theory of inflation suggests that the universe greatly exceeded this limit during the early stages. |
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That's also still contested. But regardless. Light travelling to the outskirts of the universe travel, not surprisingly, with the speed of light. So that is some measure of expansion. What we can observe grows, and we can't observe further away, because we can't get information from there with a speed faster than light, even if there existed. Which was all I meant to say. We can't practically get beyond the horizon
Quote:| I will add that this isn't limited to the inflationary period - in fact, under current cosmological models, distance objects that we can see are already moving away from us faster than the speed of light! |
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I find that hard to believe, as the observable speed for any object is supposed to be limited to the speed of light.
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| « Last Edit: May 9th, 2005, 1:25am by towr » |
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Re: Infinity
« Reply #6 on: May 9th, 2005, 1:33am » |
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on May 8th, 2005, 6:57pm, Deedlit wrote:| A lot of people lean towards a finite universe, since the idea of an infinite universe has some unsettling implications. Mainly, that every possible finite universe that can occur, should occur infinitely many times. |
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That's abuse of statistics. The probability may be 100%, but that doesn't mean it will happen, nor that it will happen infinitely often. Least of all that it should.
And it also assumes the universe has a random structure, which is very doubtfull. Not everything has to happen in an infinite universe, it really depends on it's nature. In fact only things that can happen somewhere may happen infinitely often elsewhere. If it's fundamentally impossible for you to run a selve-serve food chain, than it won't be the case anywhere in the universe.
And then there's the whole orders of infinity problem. The universe may be infinite, but yet too small to hold all possible events, because the cradinality of the latter set is greater. In fact you may have the problem that the universe as a whole would have to both contain itself, and be in every possible state. (It's a bit of wild speculation, granted. But still.)
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towr
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Re: Infinity
« Reply #7 on: May 9th, 2005, 1:45am » |
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on May 8th, 2005, 6:33pm, Icarus wrote:| How do we know that universe is not infinite? A fairly simple argument shows that universe infinite in both age and size is extremely unlikely: If the universe was infinite in both, then in any direction you looked, somewhere along that line in the past was a star whose light is reaching earth now. I.e., we would be inundated by light from all directions. |
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I don't think this has to be the case. It depends on how stars are distributed throughout the universe.
Assume say the universe is roughly planar. Lay a grid over it, put a star at each integer grid point. Light diminishes by the inverse of square of the distance. So we get [sum]1/(n^2+m^2) which is finite.
We also can't see light below some threshold, so if the stars are far enough apart this means we can't see anything but stars which are close.
Another thing is that light is emited as a finite number of photons per star/object. So for any given star in an infinite universe the probability of one of it's photons reaching us is zero. Which in itself should make it interesting to find out what the total expected amount of light is.
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Grimbal
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Re: Infinity
« Reply #8 on: May 9th, 2005, 1:56am » |
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In a static view of the universe, infinite in extent and with an overall uniform distribution of stars, you would see a star in every direction and the sky would be lit like the surface of the sun.
Imagine concentric shells around the Earth. Each shell having the same thickness. The density of stars being the same, each shell would reduce by some (small) proportion the amount of sky not covered by a star. Therefore, the "black" in the sky would diminish exponentially with the distance of how far you can see.
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Deedlit
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Re: Infinity
« Reply #9 on: May 9th, 2005, 2:48am » |
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on May 9th, 2005, 1:24am, towr wrote:
That's also still contested. But regardless. Light travelling to the outskirts of the universe travel, not surprisingly, with the speed of light.
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I understand that it is normal to drop the "observable" adjective here, but I think this convention has caused a lot of confusion among poeple who aren't aware of the distinction.
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I find that hard to believe, as the observable speed for any object is supposed to be limited to the speed of light. |
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Before more confusion is sewn, I should probably mention the different distance metrics for distances on a cosmological scale. A good primer is:
http://astronomy.sussex.ac.uk/~sjo/ teach/dist2003/reading/dist_ref.pdf
These distances are similar for short distances (say, less than a billion light-years) but start to diverge as things get farther away. What you say is correct for the light-travel distance to an object; the faster-than-light recession is for other distance metrics, like proper or comoving.
Basically, what you are saying is correct for the size of the "look-back" universe, the light-cone that extends backwards towards the big bang, has a radius equal to the age of the universe. I just don't think this is what people are usually asking about when they ask about the size of the universe. Rather, they want the size of the cross-section of space-time corresponding to a particular time. (pick a reasonable frame of reference) This could be infinite for all we know, and the natural distance metric to use in this case is either proper distance or comoving distance. (giving a radius of 46-47 billion light years for the stuff within our field of vision)
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Deedlit
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Re: Infinity
« Reply #10 on: May 9th, 2005, 3:17am » |
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on May 9th, 2005, 1:33am, towr wrote:
That's abuse of statistics. The probability may be 100%, but that doesn't mean it will happen, nor that it will happen infinitely often. Least of all that it should.
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The "least of all" reason that something should happen, is that it happens 100% of the time?!! That doesn't sound right at all. Of course, in probability theory we have events that occur exactly 0% of the time, like flipping an infinite number of coins and getting all heads. But in a real-life situation, you shouldn't expect this to ever occur. A scientist would find such an occurrence an untenable situation, an indication that something is wrong with the model of the universe that they are using.
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And it also assumes the universe has a random structure, which is very doubtfull.
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It's a general assumption in cosmology that the universe is homogeneous and isotropic (it looks roughly the same from every point, and in every direction). I'll assume this is what you mean by "has a random structure". I don't see why this is doubtful, though; if we don't want infinitely many planet Earths, we would need the correct conditions in the Universe for the existence of Earth to only occur within a finite sphere around us; no matter how big this is, it's still basically an infinitely small point compared to an infinite universe. So there's just this single point where a planet Earth could form. This seems much more doubtful to me!
Quote:| In fact only things that can happen somewhere may happen infinitely often elsewhere. If it's fundamentally impossible for you to run a selve-serve food chain, than it won't be the case anywhere in the universe. |
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Of course! I wasn't suggesting that impossible things happen; I specifically picked things that could happen - a being with my exact genetic material and who lived a life similar to mine, could reasonably inherit a chain of restaurants.
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And then there's the whole orders of infinity problem. The universe may be infinite, but yet too small to hold all possible events, because the cradinality of the latter set is greater.
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I wasn't talking about infinitely improbable events. Any physical system with bounded volume and bounded energy can only exist in finitely many distince quantum mechanical states. For the observable universe this has been calculated at about 10^10^120. Maybe some of these can't occur - that's fine. But the rest occur with some positive probability, and over an infinite set of such disjoint physical systems (assuming a homogeous infinite universe, of course), each occurs infinitely often. (OK, the probability that they all occur infinitely often is 100%.)
For infinite regions of space however, we can probably embed infinitely many disjoint events in it, so we have a continuum number of possibilities. Cosmological models are generally manifolds over R, and these are second countable, so we shouldn't expect any repitition of the infinite region, at least not by coincidence.
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| « Last Edit: May 9th, 2005, 3:21am by Deedlit » |
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Re: Infinity
« Reply #11 on: May 9th, 2005, 6:25am » |
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See what happens when you ask about infinity around here?!
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Icarus
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Re: Infinity
« Reply #12 on: May 9th, 2005, 6:40pm » |
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on May 8th, 2005, 7:28pm, Deedlit wrote:| It looks like I disagree on many points with Icarus. |
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Don't worry - you'll eventually start getting it right!
More seriously, since much of this discussion deals with matters beyond observation, or even direct implication, it is hardly surprising that there are disagreements. One thing I am curious about is whether we are even using the same definition of "universe". Some of your comments seem to suggest otherwise to me. The first, and most basic, definition of the universe of an observer is "everything that can have some possible effect on the observer, or upon which the observer can have some possible effect". A somewhat better choice is the smallest possible set containing the observer and closed under the "has an effect on or is effected by" condition. A third definition is "The smallest complete connected spacetime continuum containing everything included in the second definition."
This is what I am refering to. De Sitter space or other super-spacetimes are not included.
on May 8th, 2005, 7:28pm, Deedlit wrote:| This is certainly not true! |
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I believe it is - except there might have been a controversy over whether age or size or both were finite. The argument I gave and Grimbal expanded on is at least as old as Mach, definitely preceding the big bang theory, and was (and is) widely held. In order for it to fail, you have to make certain assumptions about the distribution of matter that are not supported by observation.
on May 8th, 2005, 7:28pm, Deedlit wrote:| The big bang doesn't require a finite universe. |
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Unless you assume that the rate of expansion was infinite at some point, yes it does! You cannot start out with a finite quantity, have it grow at finite rates (no matter how large) for a finite amount of time, and end up with an infinite result. Under the big bang theory, the universe started as a point and is finite in age. The only way it could be infinite now is if its growth was infinite at some point. I have never heard any cosmologist suggest such. Even hyper-inflation is believed to have been at a finite growth rate.
on May 8th, 2005, 7:28pm, Deedlit wrote:| This isn't true - hopefully my infinite grid model explains this. Of course, the usual cosmological models don't include universes that are closed in time and infinite in space, but it's not a logical impossibility. |
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I did not state this as well as I originally thought. It is indeed possible for an infinite space to contract everywhere in the sense that all points move closer together, while remaining infinite. The map y = x/2 is a simple example of such a contraction on R.
However, I understood alien's remarks to refer to the concept of a "Big Crunch" - essentially the reverse of the big bang, where-in the entire universe collapses back into a point. For the same reason it is impossible in the big bang theory for the universe to be infinite now without infinite growth rates (effectively, instantaneous change in size), it is also impossible for an infinite universe to contract into a finite one in finite time without an infinite rate of contraction.
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on May 9th, 2005, 1:45am, towr wrote:
I don't think this has to be the case. It depends on how stars are distributed throughout the universe. |
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There are many scenarios under which the argument fails. But if the visible part of the universe is a good indication of how matter is distributed, the argument holds. Between the idea that matter visible to us does not reflect the overall distribution, and the idea that the universe is finite, I believe the finite universe to be far more likely.
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Re: Infinity
« Reply #13 on: May 9th, 2005, 9:02pm » |
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on May 9th, 2005, 6:40pm, Icarus wrote:
Don't worry - you'll eventually start getting it right!
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Same to you!
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More seriously, since much of this discussion deals with matters beyond observation, or even direct implication, it is hardly surprising that there are disagreements.
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Certainly, but what I was taking issue with was your contention that
Quote:| It has been pretty well established that the universe was finite in spacial extent since well before the introduction of the big bang theory. |
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This would mean that the matter was not really so much in disagreement, and that no one really talks about the universe being infinite anymore. This is contradicted, for example, by Ned Wright's cosmology FAQ:
http://www.astro.ucla.edu/~wright/cosmology_faq.html
(look under the questions
Is the Universe really infinite or just really big?, and
How can the Universe be infinite if it was all concentrated into a point at the Big Bang? )
or John Baez's physics FAQ:
http://math.ucr.edu/home/baez/physics/Relativity/GR/centre.html
particularly this line:
Quote:| The universe may be finite in size and growing like the surface of an expanding balloon but it could also be infinite. |
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or, look up most discussions of the Freidmann models - it is generally pointed out, in these models, the universe is either finite in both time and space, or infinite in both time and space.
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One thing I am curious about is whether we are even using the same definition of "universe". Some of your comments seem to suggest otherwise to me. The first, and most basic, definition of the universe of an observer is "everything that can have some possible effect on the observer, or upon which the observer can have some possible effect".
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The first half of the above definition is of course finite, whereas the second half will be infinite. If we restrict the universe to a particular time, then the region that can eventually affect us can be infinite or finite; the recent observations that the universe is accelerating suggest that it is finite.
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A somewhat better choice is the smallest possible set containing the observer and closed under the "has an effect on or is effected by" condition. A third definition is "The smallest complete connected spacetime continuum containing everything included in the second definition."
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Yes, this is generally what I was considering. Incidentally, for what cosmological models are these two different?
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I believe it is - except there might have been a controversy over whether age or size or both were finite. The argument I gave and Grimbal expanded on is at least as old as Mach, definitely preceding the big bang theory, and was (and is) widely held.
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Olbers' paradox no longer holds if the universe is finite in age. Let me point out that an argument like Olbers' paradox, does not, and cannot, say anything about what is outside our causal universe - by definition, nothing outside the causal universe can affect us, so our observations will be precisely the same whether any stuff on the outside is there or not!
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Unless you assume that the rate of expansion was infinite at some point, yes it does! You cannot start out with a finite quantity, have it grow at finite rates (no matter how large) for a finite amount of time, and end up with an infinite result.
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As I said in my reply to alien, if the universe is currently infinite, it should be infinite at every time in the past. What about t=0? Asking how big the universe was at that point probably makes as much sense as asking whether 0*infinity = 0. In any case, it seems to me no stranger to go from a point to infinite space, as from a point to a space of positive volume - both require an "infinite rate of expansion" at zero.
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Under the big bang theory, the universe started as a point and is finite in age.
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This is the misunderstanding I was talking about in my answer to alien. When people talk about the universe contracting to a point as t -> 0, they mean the causal, or observable, universe. Wright's cosmology FAQ talks about this.
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it is also impossible for an infinite universe to contract into a finite one in finite time without an infinite rate of contraction.
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Yes, I agree.
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alien
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NATIONAL GEOGRAPHIC, MAY 2005
Infinite Beginnings
Pushing the limits of theory and imagination in true Einsteinian fashion, cosmologists are daring to speculate that ours is not the only universe. The big bang that created everything we know of space and time could be just one of an infinite number of beginnings, yielding a never ending sequence of universes. The scenario, shown in this artist's concept, emerges from inflation theory, a descendant of Einstein's general theory of relativity. Relativity implies that space and time can stretch to vast dimensions from a tiny starting point; inflation describes how our own universe ballooned in its first moments and suggests that the same thing can happen anywhere, at any time. The result: an eternal expanse of space erupting with bubbles of energy, or big bangs, each the seed of a universe. Not all universes will be alike. While a cosmos like our own glows with galaxies (at lower right), others may contain more dimensions or different forms of matter. In some, even the laws of physics work differently (twisted universe at upper left).
The Invisible Web
Something out there holds swarms of galaxies together and keeps their stars from flying apart, but scientists still haven't learned what this invisible substance is. Known as dark matter, it gathers to form a colossal cosmic scaffolding. Astronomers believe that galaxies formed at the densest points in this weblike structure, and the dark matter continues to hold them in place with its gravity. Its bulky presence can be detected by tracking stars on the outskirts of galaxies, which move at speeds that would be impossible if only visible matter-a galaxy's other stars and gas-were pulling on them. Astronomers have also mapped this unseen substance with the help of an effect predicted by Einstein's general relativity: Dark matter's gravity wrinkles space-time, bending light rays as they pass. Such measurements indicate that dark matter could make up 90 percent of the universe's total mass. These days, cosmologists are searching for the identity of dark matter, trying to detect the elusive substance responsible for arranging everything we see in the sky.
Fast Forward: The Big Rip?
The death of the universe could rival its birth in explosive drama if puzzling form of energy continues to accelerate the expansion of space-time. Since the 1920s astronomers have thought the expansion was slowing down, but recent observations of distant stars reveal that the stretching of space is actually speeding up. If it picks up even more, the universe could be headed for a "big rip." An artist's conception of this scenario-one of many possible fates-shows how, some 20 billion years from now, unchecked expansion could tear matter apart, from galaxies all the way down to atoms. The driving force is a mysterious "dark energy" that counteracts gravity's pull and might ultimately defeat all the forces that bind matter. Einstein was the first to introduce the notion of repulsive gravity, but he later disavowed it. Dark energy, says cosmologist Michael S. Turner, who coined the term, "has the destiny of the universe in its hands. " Although we live in the best of times, under a sky full of stars, it will grow ever darker and emptier as space-time expands.
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rmsgrey
Uberpuzzler
    
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Re: Infinity
« Reply #15 on: May 10th, 2005, 9:53am » |
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One of the ideas that's been knocking around for a while is that our observable universe is a bubble inflated from a small region in the early universe, and that someday our observation threshhold will expand to include regions beyond our bubble, with potentially wildly different physical properties.
As far as Olbers' paradox goes, it does rely on the average temperature of the universe being rather high - if you have clusters of galaxies separated by regions of moderately dense cool matter (say, around 3K) it should be possible to create a model which closely resembles our observed universe but is infinite in extent.
As Icarus points out, this means that our observed universe is a special region - though it may be one of myriad special regions. On the other hand, the surface of the planet Earth is a (non-unique) special region - though until sufficient evidence was accumulated against it, it was assumed that most of the universe was much like our little corner.
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Deedlit
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Re: Infinity
« Reply #16 on: May 10th, 2005, 10:56pm » |
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on May 10th, 2005, 9:53am, rmsgrey wrote:One of the ideas that's been knocking around for a while is that our observable universe is a bubble inflated from a small region in the early universe, and that someday our observation threshhold will expand to include regions beyond our bubble, with potentially wildly different physical properties.
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I take it you are talking about something like this:
Quote:Cosmic bubble solves cosmological conundrum
John Gribbin
Cosmologists baffled by the apparent evidence that the Universe is younger than the stars it contains may have been guilty of reading too much into our immediate surroundings in the Universe. According to a group of Chinese researchers, the problem is that we live in a low- density bubble which is not typical of the Universe at large. When the appropriate measurements are made on large enough scales, everything slots into place.
The kind of scales cosmologists deal with are much greater than the distances between stars. They are interested in the distance between clusters of galaxies, and regard a whole galaxy of several hundred billion stars, like our Milky Way, merely as a "test particle" in the Universe at large. Their efforts to measure the scale of the Universe are rather like trying to measure the distribution of island archipelagos across the Pacific Ocean from a base on one of those islands -- with the added complication that each archipelago is moving apart from every other archipelago as the Universe expands. But stars are useful in one respect to cosmologists. The ages of the oldest stars in our Galaxy are at least 12 billion years, and obviously the Universe must be older than the stars it contains. The puzzle, highlighted by recent observations using the Hubble Space Telescope, is that the simplest interpretation of measurements of the distances to nearby clusters of galaxies and the rate at which they are moving apart suggests that the Universe started expanding from a point (the Big Bang) only 8 billion years ago.
But this interpretation depends, among other things, on the assumption that the Universe contains exactly enough matter, overall, for gravity to one day bring the expansion to a halt. This critical density is required by the detailed theory of the Big Bang, called inflation, which most cosmologists favour. If the density of the Universe is less than the critical density, it alters the dynamics of the situation and extends estimates of the age of the Universe. The key question, which has not really been considered much by cosmologists until now, is how typical the region of the Universe over which we can make these measurements is. Just as the hypothetical Pacific islander mapping the known "universe" may be unaware of the existence of the continents on either side of the ocean, so our local bubble of space may not give us enough information to predict the behaviour of the entire Universe. Xiang-Ping Wu, of the Beijing Astronomical Observatory, and several colleagues, suggest in a paper to be published in the Astrophysical Journal that this is indeed the case. They point out that although this kind of study of the Universe extends out to distances of a few hundred million light years, if the measurements made for clusters at different distances are analysed separately, instead of all being lumped together to give one average figure, they show that the density of matter in the Universe increases the further out we look. On a scale of about 30 million light years, the density os only 10 per cent of the critical value, while on a scale of 300 million light years it may be as much as 90 per cent of the critical value.
The direct implication of this is that on the scale over which recent measurements of the expansion of the Universe have been made, the expansion rate (given by the so-called Hubble constant) is bigger than the overall average expansion rate by as much as 40 per cent. That means that the age of the Universe has been underestimated by 40 per cent, which is almost exactly the correction needed to boost the age from about 8 billion years to about 12 billion years, matching the ages of the oldest stars. In cosmological terms, it may be that our Pacific islanders have just discovered America. |
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Pretty nifty idea, but the impetus for the theory - that the apparent age of the oldest stars is greater than the apparent age of the universe - has been obviated by the discovery that the rate of expansion is accelerating. This raises the age of the universe to ~14 billion years, so no problem. And of course, an accelerating universe makes it unlikely that we'll get to see much more of the universe than we do now.
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As Icarus points out, this means that our observed universe is a special region - though it may be one of myriad special regions. On the other hand, the surface of the planet Earth is a (non-unique) special region - though until sufficient evidence was accumulated against it, it was assumed that most of the universe was much like our little corner. |
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Well, we know that the universe is of finite age, so Olbers' paradox goes away. So we don't really need the universe to be a special region. Of course, it could still be - but I think this strikes most physicists as somewhat unnatural.
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rmsgrey
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Re: Infinity
« Reply #17 on: May 11th, 2005, 9:20am » |
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on May 10th, 2005, 10:56pm, Deedlit wrote:Pretty nifty idea, but the impetus for the theory - that the apparent age of the oldest stars is greater than the apparent age of the universe - has been obviated by the discovery that the rate of expansion is accelerating. This raises the age of the universe to ~14 billion years, so no problem. And of course, an accelerating universe makes it unlikely that we'll get to see much more of the universe than we do now.
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Actually, the apparent homogeneity of the visible universe also motivates some speculations that there's a threshhold beyond which the character of the universe changes radically - unless you assume that the Big Bang "just happened" to produce a near-smooth universe rather than a very lumpy one, you need some form of smoothing effect to iron out the lumps in the region which became our visible universe. Such a smoothing would have to be mediated by light-speed (or slower) interactions, so only cover a limited region - without inflation, you get the problem that the smooth region would be rather smaller than the visible universe. With inflation, you can have the entire visible universe expanded from a smoothed region, and then have lumpy regions or differently smoothed bubbles outside the visible universe.
Inflation does include a significant smoothing effect, but not enough to smooth out a genuinely lumpy big bang.
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