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1. It is gererally accepted that the age of the universe is 12-15 billion years old.

2. It is generally accepted that the Big Bang occured 12-15 billion years ago.

Paradox: The light we are seeing from the most distant objects left the position we now see them in some 12-15 billion years AGO. Yet, 12-15 billion years ago they should have been in or near the point of the big bang.

2. There is no "point of the big bang". The big bang happened everywhere, including where you are sitting right now, and in all the places that we observe quasar emission and CMB radiation. There is no paradox. But welcome to the forum stebini!

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How can it be expanding if there is no point of origon? A singularity implies a specific moment in time and space.

4. Every "point" can be said to be the home for the big bang because indeed it is. Remember that space has expanded since then, and the "points", once reunited, separated from each other.

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OK. Pick any object that is 12 billion light years away from us. We are seeing that object where it was 12 billion years ago. If the universe is 12 billion years old, where was that object at the time the universe began and how could it have been moving for 12 billion years to get to where we percieve it as being now?

6. The big bang was the creation of spacetime. All of space was contained within the singularity. Everything is moving away from everything else, but nothing is moving away from the center, because everything was (and still is) the "center".

edited to add the last sentence

7. Imagine an infinitely large chess board with ants crawling all over it, at the speed that ants crawl. Now imagine the chess board is rubber and is constantly stretching, though the ants don't know it, they just keep crawling in a straight line. If the ants are photons, that's all you need to know to imagine where the photons came from that you are seeing from 12 billion years ago. The squares on the board were originally arbitrarily small, but now they are quite large. But there are still ants all over it, crawling in straight lines. How would you express your paradox in that model? It goes away, just as it does for the Big Bang.

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Ken - Hmm. I'll have to think about that for a while.

I really like this place!

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The idea that everywhere is the center of the universe is an idea that I understand, but am not quite ready to accept yet. And I've been thinking about it for years.

10. Where on the surface of a sphere is the "center"?

11. To use a slightly different variant of Ken G's analogy... image the universe is the surface of a ballon and we and everything else are ants on the suface of that ballon. At the big band you had an infinitely tiny ballon, which has been slowly "blowing up" ever since. Even if the ants don't move, they are still moving away from each other. And as Kaptain K said, there is no "center" of the ballon, just the surface.

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Originally Posted by Kaptain K
Where on the surface of a sphere is the "center"?
This kind of question is why I am still a spot uncomfortable with with the idea. The center would be inside, not anywhere on the surface. Yes, I know you can define a two dimesional geometry which curves around a sphere. Within this definition there would be no center. I'm just not sure it's real.

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I'm a little bit confused on one issue here:
I realize fully that the amount of matter in the universe is finite, and one definition of the universe might be "all of the matter in existence and the space it occupies," however, when I say universe, I am talking about the total extents of space, even outside of the sphere of matter within the universe.
Now, in a thread I started quite a while ago, I was told that presently, astronomers believe the shape of the universe to be "flat," basically meaning that space extends on forever in all directions; in other words, space is infinite (as opposed to "closed," which would mean the universe would curve in on itself, so that if, for example, you travelled in one direction for long enough, you would eventually wind up where you started, meaning space would be finite; or "open," which I do not know the meaning of.)
However, we do know that space is, and has at least since the big bang been expanding at a finite rate. If these astronomers are correct, and the universe is in fact infinite, and space has always expanded at a finite rate, then it has to have always been infinite, even at the time of the big bang.
Now, this clearly means that space wasn't a singularity at the time of the big bang, meaning that the singularity from which arose the big bang would have to have been made up purely of matter/energy, and actually would have had to have existed in space, rather than be made up of both matter/energy and space.
If the people posting in this thread are to be believed, however, space was in fact a part of that singularity, and did not exist before the big bang. This would mean that space started out as a singularity, and has since been expanding at a finite rate - this implies that space has to be finite, meaning that the shape of the universe has to be closed, contradicting the astronomers from the first paragraph.
Who is right here, and is there any contradiction at all?

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This kind of question is why I am still a spot uncomfortable with with the idea. The center would be inside, not anywhere on the surface. Yes, I know you can define a two dimesional geometry which curves around a sphere. Within this definition there would be no center. I'm just not sure it's real.
It's not a perfect analogy unless you assume that *only* the surface of balloon/sphere is the entire universe - i.e. it makes no sense to say the center is "inside" the sphere since there *is* no "inside" for a center to be in. (Mind bending, I know, but keep thinking about it!)

And the "surface of a balloon" analogy does illustrate another reality about our universe. If you set off in straight line in *any* direction and keep going-and-going long enough, you will eventually end up exactly where you started. You won't reach the "edge" - there isn't one - either on the balloon or in our universe.

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Originally Posted by uniqueuponhim
If the people posting in this thread are to be believed, however, space was in fact a part of that singularity, and did not exist before the big bang. This would mean that space started out as a singularity, and has since been expanding at a finite rate - this implies that space has to be finite, meaning that the shape of the universe has to be closed, contradicting the astronomers from the first paragraph.
Who is right here, and is there any contradiction at all?
OK, I could be wrong, but I believe astronomers are not talking about the physical shape of the present universe when they say it's "flat" or "closed" or "open". It's more to do with the eventual fate of the universe. A closed universe is one that will stop expanding and eventually fall back in on itself (the big crunch), an open universe is one which will expand at an exponential rate, and a flat one will just keep expanding at the present rate.

I believe that in any of these three cases, what I said in the previous post holds true - if you set off in any direction in a staight line (fast enough, of course) you will eventually end up where you started.

16. ...a flat one will just keep expanding at the present rate.
Not quite. A flat universe is one in which the rate of expansion is slowing down at such a rate that v=0 at t= infinity.

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uniqueuponhim
If you want to be just a tad more confused than you were before, consider that the rate of expansion has probably changed. Indications now are that it's getting faster than it was before. This sort of crumples up and tosses into a wastepaperbasket the comparison of flat to open universe. It could have been flat before, but has become open sometime ago.

A question I have pondered is whether the big bang banged all at once, or whether it took a discrete segment of time. My initial reaction is to say that it took measurable time, but I am not sure of it.

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Originally Posted by Kaptain K
Not quite. A flat universe is one in which the rate of expansion is slowing down at such a rate that v=0 at t= infinity.
Thanks - I knew something wasn't quite right

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Originally Posted by Benign Terrorist
uniqueuponhim
A question I have pondered is whether the big bang banged all at once, or whether it took a discrete segment of time. My initial reaction is to say that it took measurable time, but I am not sure of it.
I don't think your question makes sense. As far as we know, time itself did not exist before the big bang. Yes, I know, how can there be a "before" if time did not exist...?. Good question. Suffice to say, the space-time in this universe was created in the big bang, so unless you include the first part of the expansion that resulted from the big bang, by definition the big bang did "bang" all at once.

(And now let me go crawl into a corner and whimper until my brain stops hurting).

20. First of all, the singularity is not a part of the Big Bang theory. It is a mathematical extrapolation, useful only conceptually. It has no physical significance whatsoever, as it is well known that the laws of physics as we know them or will ever know them must break down before you reach a singularity. It is a mathematical idealization, and I would give it not another thought. The Big Bang theory actually begins when the physics you know still applies to the universe. So there's never a singularity, and no need for one. It's just an initial condition. Most models try to start at what is called the Planck time, which is very very short but not zero. If the universe is infinite now, it was infinite then also. Ergo the chess board is always infinite in size (so has no boundaries), but the squares are getting bigger. That's probably the best picture to use at present.

By the way, a flat universe does not mean the expansion speed will reach zero at infinite age. It now looks like the expansion speed will only increase, forever, yet the universe could remain flat all that time (it will never be known for sure). The point is, flatness is a geometrical property-- even really huge triangles have angles that add up to 180 degrees. It is plane geometry, Euclidean. That's a fortunate simplification-- we can all sigh in relief, and maybe the textbooks will soon dispense with those infernal "closed" and "open" geometry pictures!

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Ok, I was beginning to get confused again, so I did a bit of leg work.

The "flatness" of the universe is a property of the observabled or local universe (i.e. the part of the universe that is within the 13.7 billion light years of us, since that is the maximum distance light could have travelled since the big bang). As Ken says, the flatness is a geometric property, and the current understanding is that the observable universe is flat or nearly flat.

But... the flatness, or otherwise, of the observable universe only determines the shape of the whole (global) universe to within certain boundaries. If the local universe was tightly curved, then we would have known that the global universe was also curved and could only be up to a certain size. But because the local universe is flat (or nearly so) then the geometry of the global universe is still open to question. We just don't know whether the size the global universe is finite (bounded) or infinite.

So... even if the observable universe is geometrically flat, if the universe as a whole is finite (bounded) then the "surface of a sphere" analogy still holds - you could still end up back where you started if you travel in a straight line long enough.

http://en.wikipedia.org/wiki/Shape_of_the_universe

22. Originally Posted by uniqueuponhim
However, we do know that space is, and has at least since the big bang been expanding at a finite rate. If these astronomers are correct, and the universe is in fact infinite, and space has always expanded at a finite rate, then it has to have always been infinite, even at the time of the big bang.
Now, this clearly means that space wasn't a singularity at the time of the big bang, meaning that the singularity from which arose the big bang would have to have been made up purely of matter/energy, and actually would have had to have existed in space, rather than be made up of both matter/energy and space.
You're thinking of a singularity as an infinitely small point. But "singularity" really just means "our mathematical and physical models break down here". There's nothing wrong with assuming that the universe began as a singularity of infinite extent. Indeed, if the universe is now infinite (which is perfectly possible), then it always was infinite, pretty much exactly because of the argument you give.

As far as the geometry questions, when cosmologists talk about the universe being open, flat, or closed, they really do mean its overall geometry. A flat or open universe is of infinite extent, while a closed universe is finite. However, there's been a slight twist in recent years. Without a cosmological constant, the geometry of the universe is also related to its ultimate fate. A closed universe will eventually collapse back on itself, an open universe will continue to expand, but at a rate that approaches zero, and an open universe will continue to expand at a rate that doesn't approach zero. It looks, though, like there's a nonzero cosmological constant, and in this case, the fate is not determined only by the geometry. It's possible in principle to have a closed universe that expands forever, or an open universe that eventually stops expanding. This site has a nice graph showing the possibilities, and how they relate to various values of cosmological parameters.

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It looks like most of you completely misunderstood my problem.
I'm not talking about whether or not the universe will continue to expand indefinitely, I'm not talking about the future at all, I am simply talking about the present and the past shape of the universe, period.
Maybe I didn't use the correct terminology, but here it is in simpler terms:

The space which the universe occupies is either boundless, stretching on into infinity in all directions, or it is finite, and curves in on itself in some way or another, essentially meaning that if you go in one direction long enough, then eventually you will end up where you started (like on the surface of a sphere.)

If you're confused by this, imagine a two-dimensional universe: the chess-board situation brought up earlier. Imagine you're an ant on this chessboard. Although you do not know right now which is correct, you know that either the chessboard extends infinitely in all directions, or is curved in on itself as a sphere so that if you go on in one direction long enough, you will end up back where you started. So there are your two possibilities: it is flat and goes on forever, and all of the ants on the chessboard(matter in the universe) are located in one small portion of the vast infinity of the board OR the board curves in on itself and there is only a finite amount of it.

Now, the ants on this board are intelligent, and they think they have determined a way to determine whether the board is flat or curved, by somehow measuring the flatness of the board locally. The ants have found that locally, the board is in fact very flat, and so they determine that it is likely that the entire board is flat (either that or it has such a small curvature that it is impossible to detect.) This is what happened in our universe (as far as I can tell Astronomers have measured the curvature of the universe locally, seen that it is flat, and from that have decided that it is most likely that the universe is in fact flat and extends infinitely out forever.

So, let's look at the two possibilities (curved and flat) for the big bang:

A) The universe is curved. Space is finite right now. At the time of the big bang, all of the matter/energy in the universe existed in a single point, as did space itself. After the big bang, space expanded from that point at a finite rate, carrying the matter along with it. It continued to expand for 13 billion years at a finite rate until the present (and it continues to expand.) Perfect. This can be likened to the spherical chessboard on which the ants reside expending at a finite rate, and this makes good sense.

B) The universe is flat. Space is infinite right now. Since the time of the big bang, the universe has expanded at a finite rate. We know this because we exist: if space had at any point since the big bang expanded at an infinite rate, then every point in space which existed before that expansion would now be infinitely distant from every other point, and as a consequence, every bit of matter or energy in the universe would be infinitely distant from every other bit of matter or energy. The fact that the molecules from of which I am comprised are not smeared across the infinity of space right now means that space must have always expanded at a finite rate.

So let's rewind now back to the big bang. If space is infinite now, and it has always expanded at a finite rate, then at the instant of the big bang, space must have still been infinite. If at the instant of the big bang, space was infinite, then the entirety of it could not have existed in that one point, on the contrary, that singularity would have had to have existed in space. Note that this does not preclude the big bang from being able to have happened, it simply means that space must have existed before it if we are to take space as being infinite.

So, I ask you, who is right? The astronomers telling us that space is flat(infinite) or the people telling us that space did not exist before the big bang, and that it came into existence as a result of the big bang? Or is it that my logic somehow flawed, and the two are not mutually exclusive?

24. Originally Posted by uniqueuponhim
So let's rewind now back to the big bang. If space is infinite now, and it has always expanded at a finite rate, then at the instant of the big bang, space must have still been infinite. If at the instant of the big bang, space was infinite, then the entirety of it could not have existed in that one point, on the contrary, that singularity would have had to have existed in space. Note that this does not preclude the big bang from being able to have happened, it simply means that space must have existed before it if we are to take space as being infinite.

So, I ask you, who is right? The astronomers telling us that space is flat(infinite) or the people telling us that space did not exist before the big bang, and that it came into existence as a result of the big bang? Or is it that my logic somehow flawed, and the two are not mutually exclusive?
I'll repeat my response, which might have gotten lost in the rest of my message. You're assuming that a "singularity" is a single point. There is no such requirement. Under standard cosmology, if the universe is flat, then it's infinite and always was. At the moment of the big bang, the universe was infinite in size, and very hot and dense. As time passed, it became less hot and dense by expanding (I know, I have a hard time envisioning something that's already infinite expanding, too ). If it's possible for infinitely compressed space to spontaneously appear, why is it any harder for space that's already infinitely extended to suddenly come into existence?

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I’ve always been a more than a little confused about this and it seems the more legwork I do the more perplexing it becomes.

Let’s consider for the moment that most of what has been stated so far is true:

• There was a big-bang or singularity which had no specific point of origin and space/time began at that instant.

• The perceivable universe came into being as a result of that occurrence and has since grown from infinitely small to some state between that and infinitely large.

• It has been in a constant state of consistent or accelerated expansion with the distances between everything increasing relative to that rate of that expansion.

• The universe has or does not have a center, or has a center which may exist in a dimension that is unperceivable to us.

Now if I may also include the following commonly accepted data:

• The age of universe is between 12 and 15 billion years.

• 8 billion years after the big bang the first galaxies started to form.*

• The most distant perceivable galaxies are 12-15 billion years away.

This leads back to my original paradox:

If the most distant galaxies we perceive are 12-15 billion years away;

and, the light we are seeing from those objects originated 12-15 billion years ago;

then, how is it that we are able to see objects such as galaxies at that distance?

They did not exist 12-15 billion years ago.

* Reference: Universal Time Table

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Hey stebini - you're not alone in your confusion!

But I believe you have misread the timetable you quote. It says that after 8 billion years "Most galaxies, including the Milky Way have formed". This may be sloppy prose, but it's supposed to mean that after 8 billion years most galaxies have reached middle age - i.e. they are no longer forming.

The Hubble Deep Field photographs have pretty much proved that galaxies started forming very early on (perhaps one billion years after the big bang or even sooner). BTW the latest accepted figure for the age of the universe is 13.7 billion years.

Therefore there is no problem with seeing galaxies 12 billion light years away - they did exist at that time.

27. Originally Posted by Tacitus
Therefore there is no problem with seeing galaxies 12 billion light years away - they did exist at that time.
Moreover, there's some confusion in what we mean by how far away a galaxy is, especially as quoted in popular accounts. There are several possible things we could mean by that. We might mean how far away the galaxy was from us when the light was first emitted. We might mean how far away the galaxy is now. What's usually reported is the light travel distance, which is neither of these. It's just the amount of time the light has been travelling, multiplied by the speed of light. So the galaxy we see wasn't that far away when the light was emitted, but we've been moving away ever since.

Part of the reason that it's reported this way is that journalists don't always understand the distinction. But part of the problem is also that, to be able to convert from a light travel time to the distance to the galaxy when the light was first emitted, you have to know some parameters for the universe, like how the expansion has proceeded since then. Ned Wright talks about the difference between these distances here.

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Grey, thank you for your clarification, but I'm still not 100% sure I understant it correctly. Let me go back to the ants on a checkerboard illustration and give an example and you can tell me if I'm correct:

At the instant that the big bang occured, the checkerboard existed, and was infinite, and had relatively small squares (say 1 fm across.) all of the ants were packed into an infinitessimally small point which existed on the checkerboard. After the big bang, the checkerboard began to expand, spreading out the squares, and increasing the distance between the ants. It has since continued expanding and the squares are presently a whopping 1km across.

Also, if the universe is in fact infinite, there must be a center of mass for the matter which comprises it, and this center of mass must always move at a constant velocity, and cannot accelerate. Would it be unreasonable to call this center of mass the center of the universe? Would it not also be reasonable to say that this is the point at which the big bang occured? After all, if the big bang had occured at any other point, that point would be the center of mass.

Finally, in response to the poster's original question, say an object starts out 1Gly distant from you, and over the next 2Gy, due to the expansion of the universe, that distance doubles. Now, imagine at time t=0, it is 1Gly distant, and emits a photon which travels toward you. Over the next 1Gy, the photon will have travelled 1Gly, however, due to the expansion of space, the distance between you and the star has increased to 1.41Gly. Now, at this point in time, the photon will be more than 1Gly from the star it originated from, but it won't have reached you yet. It will be a bit less than 0.41Gly from you. The exact distance it has left to travel takes a little bit of calculus to do, which I would be happy to put up here if I knew how to do the fancy shmancy integral signs and stuff, but I don't, so I'll just tell you that the distance it would have left to travel after 1Gy would be 0.219Gly, and it would reach you after a total of 1.228Gy. If it had started at a distance of 2Gly, it would take 3.41Gy for the light to reach you, and if it had started at a distance of 2.8Gly, it would take 10.2Gy to reach you, and if it were 2.9Gly or more away to begin with, it would never reach you. Of course, the universe doesn't expand at this rate, but whatever rate it does expand at, you can see that it can take a lot longer for you to see something that starts out only a couple of billion light years away than it would if space weren't expanding. Thus, objects we are seeing now as being 12Gly away, may only have been 2Gly away when they emitted their photons.

29. Originally Posted by uniqueuponhim
At the instant that the big bang occured, the checkerboard existed, and was infinite, and had relatively small squares (say 1 fm across.) all of the ants were packed into an infinitessimally small point which existed on the checkerboard. After the big bang, the checkerboard began to expand, spreading out the squares, and increasing the distance between the ants. It has since continued expanding and the squares are presently a whopping 1km across.
Mostly correct, except one thing. Change your sentence to say that all of the ants (infinitely many of them, of course) were spread throughout the infinite checkerboard. There were enough ants that they were packed really, really tightly.

Originally Posted by uniqueuponhim
Also, if the universe is in fact infinite, there must be a center of mass for the matter which comprises it, and this center of mass must always move at a constant velocity, and cannot accelerate. Would it be unreasonable to call this center of mass the center of the universe? Would it not also be reasonable to say that this is the point at which the big bang occured? After all, if the big bang had occured at any other point, that point would be the center of mass.
With the change in ant distribution, you should see that this doesn't work out. If I were to assume that ant distribution is more or less isotropic, you can see that no matter which point I pick, the ants will be uniformly distributed around it, so I could call it the center of mass. Since all points are the same, it doesn't make sense to call any specific point the center of mass, to the exclusion of the others.

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Grey, I'm pretty sure it's been well established that there isn't an infinite amount of matter in the universe.

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