Assuming big bang = true, now is universe =/= sphere?

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Assuming big bang = true, now is universe =/= sphere?

Postby mosc » Tue Nov 04, 2008 8:34 pm UTC

Assuming big bang = true, now is universe =/= sphere?

I've heard it said that the universe has no shape but I've also seen the supporting evidence for the Big Bang which would point to an explosion at a fixed location. How would the shape of the universe itself not be a spherical expanding ball with radius equal to the age of the universe in light-years? If that is true, than how come we cannot pinpoint the "center". Shouldn't we be able to gauge how far we are from the "edge" of the universe and the "center"?

I did take 2 semesters of College Physics and my gut is that I'm messing up some kind of relativistic observer frame. Bah.
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Re: Assuming big bang = true, now is universe =/= sphere?

Postby Xanthir » Tue Nov 04, 2008 8:49 pm UTC

mosc wrote:Assuming big bang = true, now is universe =/= sphere?

I've heard it said that the universe has no shape but I've also seen the supporting evidence for the Big Bang which would point to an explosion at a fixed location. How would the shape of the universe itself not be a spherical expanding ball with radius equal to the age of the universe in light-years? If that is true, than how come we cannot pinpoint the "center". Shouldn't we be able to gauge how far we are from the "edge" of the universe and the "center"?

I did take 2 semesters of College Physics and my gut is that I'm messing up some kind of relativistic observer frame. Bah.

No, you're messing up topology. ^_^

This is a fairly common topic, so I'll just use the standard analogy. The universe is a balloon. The BB was the balloon getting filled up with air. Your problem is that you view us as inhabiting the inside of the balloon. In reality, the universe-as-we-know-it is the surface of the balloon. Even though the balloon itself has a center, the surface does *not*. It can expand infinitely without every originating from any particular point.
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Re: Assuming big bang = true, now is universe =/= sphere?

Postby Liet Kynes » Tue Nov 04, 2008 9:08 pm UTC

I do believe that the universe is a hyper-donut but I don't remember exactly.

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Re: Assuming big bang = true, now is universe =/= sphere?

Postby mosc » Tue Nov 04, 2008 9:13 pm UTC

The surface of a balloon though is 2D, I'm not following that analogy. It also implies that the universe had a great deal of structure before the big bang which I have not heard before.
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Re: Assuming big bang = true, now is universe =/= sphere?

Postby Liet Kynes » Tue Nov 04, 2008 9:23 pm UTC

This is assuming that we live in a multi-verse and that 11 dimension string theory is correct. I don't remember exactly where I heard it though.

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Re: Assuming big bang = true, now is universe =/= sphere?

Postby Xanthir » Tue Nov 04, 2008 9:54 pm UTC

mosc wrote:The surface of a balloon though is 2D, I'm not following that analogy.

Yes. The structure as a whole is 3d and has a center, but the surface is 2d and does *not*. Just increase the dimensions of each by one, so that you have a 3d universe as a surface on a 4d (or higher) object.
It also implies that the universe had a great deal of structure before the big bang which I have not heard before.

It doesn't imply that at all. What are you seeing in my statement that leads you to believe this?

@Liet: There are hidden assumptions behind what I've stated, but this is still a relatively uncontroversial explanation of why there's no 'center of the universe'. It doesn't require any more than 4 dimensions existing. It *definitely* doesn't depend on a multiverse or string theory (at least, not directly). All you need is an infinitely compact 4d structure which then expanded for some reason.

Though, of course, there's always another way of talking about this whole thing - *we're* the center of the (visible) universe. This is because the visible universe is "everything in our light cone", and our light cone defines roughly a spherical shell centered on us. Of course, every point is the center of the visible universe, it's just that every point has a slightly different visible universe.
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Re: Assuming big bang = true, now is universe =/= sphere?

Postby ThinkerEmeritus » Tue Nov 04, 2008 9:59 pm UTC

Liet Kynes wrote:This is assuming that we live in a multi-verse and that 11 dimension string theory is correct. I don't remember exactly where I heard it though.


Not really. The balloon is a metaphor for how a 3D expanding volume might behave. The fourth spatial dimension doesn't exist, it just helps us visualize the expansion of space everywhere, not just out from a center.

The extra dimensions in string theory are all tiny, and even if they exist they didn't expand during the big bang and the other dimensions didn't expand into them. In membrane theory there is an extra large dimension (more than one?). I'm not up on the details of membrane theory, but I don't believe that the big bang expanded into the extra dimension. The normal 3 just got larger without expanding into anything.
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Re: Assuming big bang = true, now is universe =/= sphere?

Postby Liet Kynes » Tue Nov 04, 2008 10:11 pm UTC

Xanthir wrote:
mosc wrote:The surface of a balloon though is 2D, I'm not following that analogy.

Yes. The structure as a whole is 3d and has a center, but the surface is 2d and does *not*. Just increase the dimensions of each by one, so that you have a 3d universe as a surface on a 4d (or higher) object.
It also implies that the universe had a great deal of structure before the big bang which I have not heard before.

It doesn't imply that at all. What are you seeing in my statement that leads you to believe this?

@Liet: There are hidden assumptions behind what I've stated, but this is still a relatively uncontroversial explanation of why there's no 'center of the universe'. It doesn't require any more than 4 dimensions existing. It *definitely* doesn't depend on a multiverse or string theory (at least, not directly). All you need is an infinitely compact 4d structure which then expanded for some reason.

Though, of course, there's always another way of talking about this whole thing - *we're* the center of the (visible) universe. This is because the visible universe is "everything in our light cone", and our light cone defines roughly a spherical shell centered on us. Of course, every point is the center of the visible universe, it's just that every point has a slightly different visible universe.


Okay, I could just be remembering it incorrectly.

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Re: Assuming big bang = true, now is universe =/= sphere?

Postby yy2bggggs » Wed Nov 05, 2008 2:57 am UTC

I'm not quite sure the balloon analogy is even clarifying in any way. The shape of the universe is certainly not constrained to a sphere the size of c*age for multiple reasons:
  • It's the observable universe that is constrained by c, not the universe itself.
  • Space itself is expanding, not traveling. c doesn't limit the speed by which space expands.

Refer to this:
http://www.astro.ucla.edu/~wright/infpoint.html
(...but just because it'll help clarify; note IANAC)
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Re: Assuming big bang = true, now is universe =/= sphere?

Postby seladore » Wed Nov 05, 2008 2:30 pm UTC

Liet Kynes wrote:I do believe that the universe is a hyper-donut but I don't remember exactly.


A 'hyper-doughnut' is also called a torus. It's a way to make the universe closed, but keep the flat ([imath]\Omega = 1[/imath]) topology.

Not sure if this is still in vogue though, I'm not a theorist.

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Re: Assuming big bang = true, now is universe =/= sphere?

Postby SpitValve » Wed Nov 05, 2008 3:28 pm UTC

In GR, the universe can be flat, hyperbolic, or spherical. The shape depends on the amount of mass in the universe. If it's exactly a certain value, the universe is flat. If it's slightly on either side, it's hyperbolic or spherical. Observations show the mass agrees with the critical value, but due to the nature of uncertainties, a spherical or hyperbolic universe can never be ruled out. (i.e. even if your measurement is 1.000000±0.000001, it's still a logical jump to say the real value is exactly 1 - although it is definitely a very sensible logical jump to make).

So most people believe the universe is either flat, or so close to flat as to make little difference.

The fairly-accepted-but-not-really-canon theory for why this is is inflation: even if the universe is spherical or hyperbolic, it expanded extremely rapidly ("inflated") at very early times, and stretched out so that it's pretty much flat.

----------

On another note, even if the universe started as a point explosion in a classical universe (no GR space-stretching etc) - say, take all the galaxies, put them in one point and give them all random velocities - each galaxy would still observe all other galaxies moving away from it at a speed proportional to their distance - i.e. Hubble's law. Unless you were close to the maximum speed (i.e. the edge of the expanding sphere), you would still not be able to find the "centre" of the universe.

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Re: Assuming big bang = true, now is universe =/= sphere?

Postby mosc » Wed Nov 05, 2008 5:39 pm UTC

yy2bggggs wrote:Refer to this:
http://www.astro.ucla.edu/~wright/infpoint.html
(...but just because it'll help clarify; note IANAC)

Yeah, I'm remembering this better from relativity. It is some screwed up observer frame. Things travel faster than light, they just don't travel faster than light in your observer frame. Bleh, I can never keep my head around this stuff.
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Re: Assuming big bang = true, now is universe =/= sphere?

Postby Xanthir » Wed Nov 05, 2008 6:16 pm UTC

yy2bggggs wrote:I'm not quite sure the balloon analogy is even clarifying in any way. The shape of the universe is certainly not constrained to a sphere the size of c*age for multiple reasons:
  • It's the observable universe that is constrained by c, not the universe itself.
  • Space itself is expanding, not traveling. c doesn't limit the speed by which space expands.

I said nothing of the sort, though. I specifically mentioned the "visible universe" in a later post, which *is* roughly a sphere of radius c*age, but I called it out as specifically the visible universe.

The balloon analogy has no relation to the universe-as-a-sphere. The universe is the surface of the balloon. There are no constraints placed on the speed of balloon expansion.
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Re: Assuming big bang = true, now is universe =/= sphere?

Postby yy2bggggs » Wed Nov 05, 2008 6:27 pm UTC

Xanthir wrote:I said nothing of the sort, though.
I didn't mean to come off as addressing what you said; I was mainly addressing the OP.
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Re: Assuming big bang = true, now is universe =/= sphere?

Postby Xanthir » Wed Nov 05, 2008 6:44 pm UTC

yy2bggggs wrote:
Xanthir wrote:I said nothing of the sort, though.
I didn't mean to come off as addressing what you said; I was mainly addressing the OP.

Ah, np then. At this point I'd forgotten what the OP even said; had I remembered it would have been clear who you were referring to.
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Re: Assuming big bang = true, now is universe =/= sphere?

Postby mosc » Wed Nov 05, 2008 7:53 pm UTC

but the observable universe IS a sphere of radius c*age?
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Re: Assuming big bang = true, now is universe =/= sphere?

Postby Xanthir » Wed Nov 05, 2008 8:06 pm UTC

Xanthir wrote:
yy2bggggs wrote:
Xanthir wrote:I said nothing of the sort, though.
I didn't mean to come off as addressing what you said; I was mainly addressing the OP.

Ah, np then. At this point I'd forgotten what the OP even said; had I remembered it would have been clear who you were referring to.

Depends on exactly how you want to talk about it. Ideally, yes, for obvious reasons - the light from things farther than c*age from us hasn't had time to reach us yet.

In reality, though, the stretching of space complicates things. Light that is *just now* reaching us may have been originally emitted much closer than c*age distance from us, but stretching space effectively slowed it by lengthening the distance it has to travel while it was in flight. On the other hand, when it *does* reach us, it's possible for the thing it came from to be much further than c*age distance from us, again due to space stretching.

But if you just imagine a sphere of radius c*age, you won't be too far off.
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Re: Assuming big bang = true, now is universe =/= sphere?

Postby yy2bggggs » Wed Nov 05, 2008 8:35 pm UTC

Imagine two ants placed at the same spot on an infinitely elastic, very long strand of taffy. The ants, let's say, travel at a rate of about 1cm per second, but one of the ants is just sitting there cleaning his antennae--the other ant starts walking. So, normally, the traveling ant takes 100 seconds to traverse the meter.

Suppose, now, that you start tugging on the taffy. Every second you pull enough taffy such that the middle point reaches you. The 1/4 point from the other end gets pulled to the halfway point; the 1/8th point in the other end to the 1/4 point, etc; in other words, your space is doubling distance every second.

Now, as the ant walks for 1 second, it travels 1cm of "ordinary" distance, but that distance in itself stretches to 2cm. So after 1 second, the ants are 2cm apart. Mark this spot. Now, at the end of 2 seconds, the ant is 2cm away from your mark. However, the space between your mark and the grooming ant has stretched as well--so it was 2cm away when you made the mark, but now it's 4cm from the grooming ant. So at the end of t=2, the ants are 6cm apart.

Continue, and you get at t=3, 14cm apart. t=4, 30cm. t=5, 62cm. So by t=6, the ants are 126cm apart--the meter has already been traversed between 5 and 6 seconds. Now if you measure speed of the ant by a naive distance apart divided by the time, then the ant's "speed" is going nuts. At t=1, 2cm/sec. t=2, 6cm/sec. Now at t=6 it's near 1.2 meters per second.

But when you look closely you'll see nothing really has changed in terms of speed. The ant is only going 1cm/sec. The taffy is stretching at the same rate--every unit of taffy becomes 2 units long each second. The difference is the amount of taffy between that doubles--as the ants build a distance between them, that's the amount of space that doubles; hence, that's the amount of additional space per unit time ("speed") the ants travel apart.

(Edit: The numbers don't really work out exactly as specified--this example is for overall illustration only).

The "speed" of increasing distance between the ants is not a function of how fast the ants are going, or how fast the space is expanding, but rather, how much space there already is between them that is expanding. Space works like this taffy--it's expanding very, very, very slowly... but it does it everywhere. And grab enough of it (and there's plenty to work with), and you can get the relative "speed" to be greater than c.
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Re: Assuming big bang = true, now is universe =/= sphere?

Postby telcontar42 » Wed Nov 05, 2008 8:59 pm UTC

As I understand it, your problem you have is assuming that the big bang started from a point. At the time of the big bang, the universe was not at a point, it was infinite. The big bang happened everywhere. When we say the universe has been expanding since the big bang, we mean that space has been expanding. If you picture a 3D grid extending through space with the distance between lines of the grid being one meter (and the definition of the meter being based on the speed of light). the distance between grid lines expands. Object that are one grid line apart initially are one meter apart but at a later time, they are two meters apart because the distance between grid lines is two meters. At the time of the big bang, the distance between grid lines was just really small, so everything was close together, even though the universe was infinite.

It helped me to understand it better to see it mathematically. You might know the space-time interval in special relativity:
[math]ds^{2}=c^{2}dt^{2}-dx^{2}-dy^{2}-dz^{2}[/math]
The Friedmann-Lemaître-Robertson-Walker metric in general relativity for flat space is this:
[math]ds^{2}=c^{2}dt^{2}-a(t)(dx^{2}+dy^{2}+dz^{2})[/math]
So, you can see, there is just a time dependent scale factor on the spatial part of the space-time interval. a(t) approaches zero as you approach the time of the big bang. As time increases, a(t) increases and the universe expands.

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Re: Assuming big bang = true, now is universe =/= sphere?

Postby hideki101 » Wed Nov 05, 2008 9:42 pm UTC

mosc wrote:but the observable universe IS a sphere of radius c*age?

My guess is that the observable Universe is a sphere, due to the fact that all we can see is a sphere [/redundancy]. But outside of that, we have no idea in hell what is going on.

For analogies, I think that a rising loaf of bread with stuff inside is another analogy that helps with the visualization. Imagine that the seeds in the bread are galaxies. when the bread rises, it expands in every dimension , pushing all the galaxies farther apart. If you combine this analogy with the balloon analogy, you could imagine a 3-D omnidirectional expansion(bread) in a non-centralized space(balloon)
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Re: Assuming big bang = true, now is universe =/= sphere?

Postby Ashi » Thu Nov 06, 2008 12:37 am UTC

yy2bggggs wrote:Imagine two ants placed at the same spot on an infinitely elastic, very long strand of taffy. The ants, let's say, travel at a rate of about 1cm per second, but one of the ants is just sitting there cleaning his antennae--the other ant starts walking.


Even if you didn't intend that to be humorous, I loved it. :wink:

Thanks for all the posts; I had a loose concept of Big Bang theory before, but I think I solidly can understand the basics now. If only the same were true for String Theory :P
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Re: Assuming big bang = true, now is universe =/= sphere?

Postby doogly » Tue Nov 11, 2008 4:24 pm UTC

There's nothing special about c*age. This is multiplying when you should be integrating.

Also, spheres are not the same as balls. A ball has a sphere as its boundary, but is not itself a sphere. We seem to have flat geometry, and the observable part is has a sphere as a boundary, but it is not a sphere.

Maybe now I'm just getting down to nitpicky stuff, but I arrived late and cosmology is my bread and butter so I had to input something.
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Re: Assuming big bang = true, now is universe =/= sphere?

Postby mosc » Tue Nov 11, 2008 5:22 pm UTC

If our matter once occupied the same volume as all other matter and then we exploded in all directions, how is anything "outside" of the visible universe sphere of c*age?
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Re: Assuming big bang = true, now is universe =/= sphere?

Postby yy2bggggs » Tue Nov 11, 2008 5:43 pm UTC

mosc wrote:If our matter once occupied the same volume as all other matter and then we exploded in all directions, how is anything "outside" of the visible universe sphere of c*age?

Aside from the fact that I provided link with nice diagrams explaining this, and an analogy of how spatial expansion affects the scenario, what sort of answer are you looking for? I don't mean to sound insulting--I'm just not quite sure what your point of confusion is at this time.

Oh, and many welcomes to doogly, especially for such a thread.
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Re: Assuming big bang = true, now is universe =/= sphere?

Postby seladore » Tue Nov 11, 2008 5:46 pm UTC

mosc wrote:If our matter once occupied the same volume as all other matter and then we exploded in all directions, how is anything "outside" of the visible universe sphere of c*age?


We didn't explode in all directions... space itself is expanding, individual galaxies aren't moving through space. (not systematically with the Hubble flow, anyway)

This is why c*age isn't special - there is no limit on the relative velocity between two galaxies in the universe, as they aren't moving away from each other through space. The space between them is expanding, so there isn't a speed limit of c.

If you integrate dt, you get about 93 billion light years for the 'edge' - though again, this isn't necessarily anything special.

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Re: Assuming big bang = true, now is universe =/= sphere?

Postby Tac-Tics » Tue Nov 11, 2008 7:17 pm UTC

When you assume, "big bang = true" you realize that "1+1=2" is a big bang statement, right? And that scientists believe the word started with an event called "true"?

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Re: Assuming big bang = true, now is universe =/= sphere?

Postby seladore » Tue Nov 11, 2008 8:06 pm UTC

Tac-Tics wrote:When you assume, "big bang = true" you realize that "1+1=2" is a big bang statement, right? And that scientists believe the word started with an event called "true"?

DON'T ABUSE THE EQUAL SIGN!


Or that the variable 'big bang' is being assigned the logic operator 'true'.

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Re: Assuming big bang = true, now is universe =/= sphere?

Postby doogly » Wed Nov 12, 2008 1:05 am UTC

Thank you for the welcome!

And yeah mosc, you are thinking about the rules of special relativity, and applying them to questions about space and time. Space and time are an extra level of weird.
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