Why is there no "center" of the universe?

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Why is there no "center" of the universe?

Postby ossicle » Sat Aug 01, 2009 5:11 pm UTC

Hello,

The answer to this question may be beyond my comprehension, but I'll ask anyway.

While I understand (at least the words) in phrases like:

"[The metric expansion of space] is defined by the relative separation of parts of the universe and not by motion "outward" into preexisting space. (The universe is not expanding "into" anything outside of itself.)" (http://en.wikipedia.org/wiki/Metric_expansion_of_space)

and

"The Big Bang is not an explosion of matter moving outward to fill an empty universe. Instead, space itself expands with time everywhere and increases the physical distance between two comoving points." (http://en.wikipedia.org/wiki/Big_bang)

-- I don't understand why the expansion of space isn't spherical, i.e., why all galaxies aren't located within and/or on the surface of a sphere whose radius is constantly increasing, and thus why we can't extrapolate backwards to center of that sphere, i.e., the single point where the Big Bang occurred.

I realize I'm completely failing to understand something fundamental about the model; anyone care to try to explain it?

Thanks!

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Re: Why is there no "center" of the universe?

Postby Angua » Sat Aug 01, 2009 5:17 pm UTC

I'm pretty fuzzy on the details, so if someone else comes along with a better explanation, listen to them.

Take a rubber band (preferably a large one) and draw dots at equal points along the outside. The outside of your band is going to be like the universe. When you stretch the band out evenly (imagine rolling it down a cone so it slowly expands circularly) each and every point moves away from each other, there is no centre to the expansion (as you are only concerned with the outside edge of the band, the inside and hole in the middle of the band cannot be seen by anything on the outside of the rubber band).

The universe is like this but in more dimensions.
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Re: Why is there no "center" of the universe?

Postby ossicle » Sat Aug 01, 2009 5:48 pm UTC

Angua wrote:I'm pretty fuzzy on the details, so if someone else comes along with a better explanation, listen to them.

Take a rubber band (preferably a large one) and draw dots at equal points along the outside. The outside of your band is going to be like the universe. When you stretch the band out evenly (imagine rolling it down a cone so it slowly expands circularly) each and every point moves away from each other, there is no centre to the expansion (as you are only concerned with the outside edge of the band, the inside and hole in the middle of the band cannot be seen by anything on the outside of the rubber band).

The universe is like this but in more dimensions.


Thanks very much. If that's indeed a good analogy, then my challenge lies in better understanding why there is no center to the expansion. If you or anyone else can further explain your words, "there is no centre to the expansion (as you are only concerned with the outside edge of the band, the inside and hole in the middle of the band cannot be seen by anything on the outside of the rubber band)," please feel free!

I kinda-sorta know what you mean, but getting rid of that incorrect intuition -- that one can indeed draw a line from any point on the rubber band, to the center of the circle defined by the cone at a given moment -- seems to be the crux of the matter.

-Oss

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Re: Why is there no "center" of the universe?

Postby Cup of Dirt » Sat Aug 01, 2009 6:16 pm UTC

Another analogy -- picture an infinite sheet of graph paper, and imagine that the grid lines are gradually getting further apart. The paper isn't expanding into any "outside" space, because it's already infinite. But pictures drawn on the paper will expand and move away from one another. The paper is the universe, and the grid lines describe the metric1 of spacetime. The pictures are matter.

Now, push rewind. The grid lines get close together, and the pictures contract, but the universe is still infinite -- there's always more graph paper out there. Rewind until the grid spacing is very tiny, and then push play.2 The graph paper expands again, and the pictures, which were bunched close together, start to move away from one another again. This is the Big Bang. But the thing to realize is that the paper was always infinite,3 and there were always pictures everywhere -- matter did not start at a localized point and explode outward. The Big Bang happened everywhere. Matter is now moving apart because the size of space itself is expanding.

Have you heard of the Cosmic Microwave Background Radiation? It's the radiation emitted when atoms first formed, a few hundred thousand years after the Big Bang. When it was first emitted, it was very energetic, but we now observe it red-shifted to microwaves. That is because the CMBR we now see was emitted 13.7 billion years ago, and 13.7 billion lightyears away, shortly after the Big Bang. The wavefront of the radiation expanded in every direction, including towards our region of space. But the space through which the radiation was moving was expanding, so the waves got stretched out, or red-shifted, along the way, and now we see microwaves. CMBR was also presumably emitted in our region of space, but it is long gone now -- its wavefront is now a sphere 13.7 billion years across, and if there is anyone out there with a radio telescope, they observe the same red-shifted background radiation we do.

So when people talk about the size of the universe, now or during the Big Bang, what do they mean? They're talking about the observable universe, which is now 13.7 billion light-years across. But that's just because the universe is 13.7 billion years old -- there is probably more stuff out past 13.7 billion light-years, but the light it emitted when it was first created at the beginning of the universe has not reached us yet. Similarly, a nanosecond after the Big Bang, the observable universe was a light-nanosecond (about a foot) across, because light had only had time to travel that far. But of course, everyone's observable universe is different; it's just a sphere centered on your location with a radius of the age of the universe times the speed of light.

1A metric is a function that defines the distance between any two points in a space -- this is not just the standard Euclidean distance because space is curved by gravity and the expansion of the universe. You can see the connection between metric and curvature if you think about the length of a path between two points on the surface of a sphere -- the curvature makes the distance formula different from the one used in flat space.

2The analogy seems to break down if you try to shrink the graph paper spacings down to zero. What happens then? No one knows -- cosmological theory gets very sketchy at very short times after the Big Bang, and it's completely unknown what was happening at t = 0.

3The universe may not actually be infinite -- it might be closed. In that case, the it doesn't look like an infinite sheet of graph paper, but like a balloon being blown up. But, again, in a closed universe, the distribution of matter would be uniform, the Big Bang was something that happened at every point in space, and the expansion of the universe is a consequence of the size of space itself expanding, not any independent movement of matter. I used the example of an open universe because I think it gets the point across better.
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Re: Why is there no "center" of the universe?

Postby antonfire » Sat Aug 01, 2009 6:19 pm UTC

Where, on the rubber band, would you put this "center"?

There was some discussion on this topic in this thread, I believe.


Cup of Dirt wrote:2The analogy seems to break down if you try to shrink the graph paper spacings down to zero. What happens then? No one knows -- cosmological theory gets very sketchy at very short times after the Big Bang, and it's completely unknown what was happening at t = 0.
It's also not clear whether that question is even meaningful.
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Re: Why is there no "center" of the universe?

Postby skeptical scientist » Sat Aug 01, 2009 6:50 pm UTC

ossicle wrote:I don't understand ... why all galaxies aren't located within and/or on the surface of a sphere whose radius is constantly increasing...
That's not a bad analogy. It seems like you are already imagining the typical description of the expansion of space: imagine the universe as the surface of an expanding sphere in three-space. The galaxies are all moving away from each other (as distance is measured inside the sphere - as the length of the shortest path within the sphere that connects two points) and are all moving away from a central point in the ambient 3-dimensional space (as the length of the shortest path in the ambient space). The difference between the analogy and reality (besides the universe being 3-d* rather than 2-d) is that there is no ambient space for our universe (so far as we can detect). The ambient space in the analogy was just a tool to help us visualize what is going on, but as far as we can tell, nothing exists apart from the universe (the expanding sphere in our analogy), so there is no central point. There are only points on the surface of the sphere, and certainly none of those points are the center of the expansion, so there is no center.

Short version: what is the center of a sphere? Well, we know that. But imagine that nothing exists apart from the surface of the sphere. Now what's the center?

_______
*At least on large scales. Some theories predict a fine structure involving more dimensions, but this is more or less irrelevant to the question at hand (so far as I understand it).
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Re: Why is there no "center" of the universe?

Postby ossicle » Sat Aug 01, 2009 6:53 pm UTC

Thank you very, very much Cup of Dirt. You've definitely increased my understanding of the situation -- I expect as much as it could be. [EDIT: You too, ss!]

Antonfire, I take your point -- since there's nothing other than the rubber band, there can't be said to be a center for all the points on it.

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Re: Why is there no "center" of the universe?

Postby Cup of Dirt » Sat Aug 01, 2009 9:25 pm UTC

ossicle -- You're welcome, glad that made sense. Thanks for posting the "Metric Expansion of Space" Wikipedia article -- if anyone's interested, they should check it out, because they do a pretty good explanation of the rubber band picture. I thought this was particularly interesting:

The notion of "more space" is local, not global; we do not know how much space there is in total. The embedding diagram has been arbitrarily cut off a few billion years past the Earth and the quasar, but it could be extended indefinitely, even infinitely, provided we imagine it as curling into a "spiral of constant radius" rather than a circle.


So the "cone" isn't a circular cone if the universe is infinite in space; it's an infinite spiral, projected upward and outward. The universe at any given time is a spiral drawn on the surface of this strange shape. I guess to an observer, there would be no privileged points on the sprial, because you just see an infinite outward curve on one side and an infinite inward curve on the other no matter where on the spiral you were. Anyone heard of this picture before? Does it have any validity?
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Re: Why is there no "center" of the universe?

Postby Josephine » Sat Aug 01, 2009 11:16 pm UTC

Sorry, pet peeve:

Cup of Dirt wrote:They're talking about the observable universe, which is now 13.7 billion light-years across. But that's just because the universe is 13.7 billion years old


no, no, no. the universe is 14.6 billion light years in radius[1]
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Re: Why is there no "center" of the universe?

Postby RogerMurdock » Sun Aug 02, 2009 1:11 am UTC

nbonaparte1 wrote:Sorry, pet peeve:

Cup of Dirt wrote:They're talking about the observable universe, which is now 13.7 billion light-years across. But that's just because the universe is 13.7 billion years old


no, no, no. the universe is 14.6 billion light years in radius[1]


You cite wikipedia, but their answer differs from yours.

The comoving distance from Earth to the edge of the visible universe (also called particle horizon) is about 14 billion parsecs (46.5 billion light-years) in any direction.
....
The visible universe is thus a sphere with a diameter of about 28 billion parsecs (about 93 billion light-years).

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Re: Why is there no "center" of the universe?

Postby Josephine » Sun Aug 02, 2009 2:27 am UTC

Ah. I saw parsecs and thought light years. It is, however, still larger than 13.7 bilion ly.
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Re: Why is there no "center" of the universe?

Postby Cup of Dirt » Sun Aug 02, 2009 3:00 am UTC

Wow, thanks for the correction. That's pretty interesting. Sorry about spreading the misconception.
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Re: Why is there no "center" of the universe?

Postby Josephine » Sun Aug 02, 2009 3:34 am UTC

Okay, back on topic, is there a center in more dimensions? The 2d surface of a balloon has a 3d center. Is there a 4d center of the universe?
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Re: Why is there no "center" of the universe?

Postby mr-mitch » Sun Aug 02, 2009 3:41 am UTC

The truth is, there probably is a centre of the universe. We can't imagine it nor find it because we don't know how! We're too used to having only 3 dimensions.

The rubber band is a good example. It should be obvious that the centre of that expansion is the rough mean of where you're applying the force and should be around the centre of the actual rubber band/circle.
It isn't limited to dots on the outside. You could put 3D objects on the outside, and have some relay such that the 3D expansion of the objects is matched to the 2D expansion of the surface. Then you have added another dimension, the plane of the rubber band (hollow circle part) which acts as time with respect to the expansion. You can visit any point in time at any point of expansion just by changing the size/whatever of the rubber band. The centre then of course is the point with respect all other expansion occurs, which is the centre of the rubber band.

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Re: Why is there no "center" of the universe?

Postby SummerGlauFan » Sun Aug 02, 2009 5:58 am UTC

Disclaimer: I will probably do a very bad job of explaining this.

Anywho, I was watching an episode of The Universe on the History Channel, and they said that they were able to measure the angle of a laser against the perceived "edge" of space.

Based on the angle (which I believe was 90 degrees) they were able to conclude that space in fact has no limit; basically, space is not expanding, it's just that the matter in the visible universe is moving apart through momentum. So, while there would be a center to the clump of matter that makes up the visible universe, the actual universe (i.e. space) has no center.
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Re: Why is there no "center" of the universe?

Postby Turambar » Sun Aug 02, 2009 7:05 am UTC

SummerGlauFan wrote:Based on the angle (which I believe was 90 degrees) they were able to conclude that space in fact has no limit; basically, space is not expanding, it's just that the matter in the visible universe is moving apart through momentum. So, while there would be a center to the clump of matter that makes up the visible universe, the actual universe (i.e. space) has no center.


Space is expanding--the bulk motion of matter alters spacetime.

As for the size of the observable universe, well, the farthest any light beam reaching us has traveled is about 13.7 billion light years, but the emitter of that light beam is now around 46 billion light years distant from us. And receding from us at faster than the speed of light. This is the difference between the luminosity distance and the comoving distance.
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Re: Why is there no "center" of the universe?

Postby Tass » Sun Aug 02, 2009 9:09 am UTC

mr-mitch wrote:The truth is, there probably is a centre of the universe. We can't imagine it nor find it because we don't know how! We're too used to having only 3 dimensions.

The rubber band is a good example. It should be obvious that the centre of that expansion is the rough mean of where you're applying the force and should be around the centre of the actual rubber band/circle.
It isn't limited to dots on the outside. You could put 3D objects on the outside, and have some relay such that the 3D expansion of the objects is matched to the 2D expansion of the surface. Then you have added another dimension, the plane of the rubber band (hollow circle part) which acts as time with respect to the expansion. You can visit any point in time at any point of expansion just by changing the size/whatever of the rubber band. The centre then of course is the point with respect all other expansion occurs, which is the centre of the rubber band.


There may very well exist higher dimensions, but there may not as well. You can have curved space without embedding it in a higher dimension. You are used to live in an almost-euclidean three dimensional space, so you can imagine curved two dimensional surfaces because you know the third. You can then sort of imagine how the three dimensional space could be curved if there was a fourth, but the truth is it is not necessary. There are some forms of curvature which can not simply be explained by a higher dimension. The constant positive curvature 2D/3D space can be perfectly described as a sphere/hypersphere surface although there are no need for the 3rd/4th dimension to actually exist. The space with constant negative surface is usually described as being like a saddle surface (the periphery of a circle will be more than pi times longer than the diameter - there is always "more" space "around" a given area than inside it), but in reality you can never make a saddle in three dimensions where the curvature is constant, yet the constant negative 2d space can be perfectly mathematically described.

Actually all this curvature discussion has not got much to do with wether the universe has a center. In the case of a closed (positive curvature) universe it gives a nice intuitive understanding of how it at least doesn't have a center within the three dimensions we know. However, it might as well be open or even flat, in this case Cup of Dirts excellent post gives a good idea how something can be infinite (and therefore centerless) and yet expand.

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Re: Why is there no "center" of the universe?

Postby thoughtfully » Sun Aug 02, 2009 9:52 am UTC

nbonaparte1 wrote:Okay, back on topic, is there a center in more dimensions? The 2d surface of a balloon has a 3d center. Is there a 4d center of the universe?

Any 4-sphere has a center. In the case of the model we're using, the fourth dimension is time, and the center is when t=0, or teh big bang.
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Re: Why is there no "center" of the universe?

Postby Cup of Dirt » Sun Aug 02, 2009 4:05 pm UTC

Tass wrote:There may very well exist higher dimensions, but there may not as well. You can have curved space without embedding it in a higher dimension. You are used to live in an almost-euclidean three dimensional space, so you can imagine curved two dimensional surfaces because you know the third. You can then sort of imagine how the three dimensional space could be curved if there was a fourth, but the truth is it is not necessary. There are some forms of curvature which can not simply be explained by a higher dimension. The constant positive curvature 2D/3D space can be perfectly described as a sphere/hypersphere surface although there are no need for the 3rd/4th dimension to actually exist.


Wow. This. My differential geometry book kept emphasizing treating surfaces on their own without reference to a higher Euclidean space for them to be embedded in. I never really got what they were talking about until now. This is an important point to realize.

Would it be fair to picture the curvature of, say, a 2-D space, as the distortion of the grid lines that would, in Euclidean space, be straight? I guess you could find a distortion scheme that would be equivalent to any conventionally-imagined curvature. That way you could imagine the curvature of space without actually picturing a physical curving surface, which unavoidably suggests a higher-dimensional space that might not actually exist.
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Re: Why is there no "center" of the universe?

Postby Turambar » Sun Aug 02, 2009 6:34 pm UTC

thoughtfully wrote:
nbonaparte1 wrote:Okay, back on topic, is there a center in more dimensions? The 2d surface of a balloon has a 3d center. Is there a 4d center of the universe?

Any 4-sphere has a center. In the case of the model we're using, the fourth dimension is time, and the center is when t=0, or teh big bang.

Exarctly. The essence of relativity is that there are 4 dimensions an object moves through (three spatial and one temporal), and it moves through them with a total velocity of c. So if it's stationary in the three spatial dimensions, then it's moving at maximum speed through time. If it's going at light speed, then it's not moving at all through time. Minkowski space, basically.
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Re: Why is there no "center" of the universe?

Postby doogly » Sun Aug 02, 2009 8:36 pm UTC

nbonaparte1 wrote:Okay, back on topic, is there a center in more dimensions? The 2d surface of a balloon has a 3d center. Is there a 4d center of the universe?

Says your canonical but completely unnecessary embedding.
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Re: Why is there no "center" of the universe?

Postby Charlie! » Mon Aug 03, 2009 8:33 am UTC

thoughtfully wrote:
nbonaparte1 wrote:Okay, back on topic, is there a center in more dimensions? The 2d surface of a balloon has a 3d center. Is there a 4d center of the universe?

Any 4-sphere has a center. In the case of the model we're using, the fourth dimension is time, and the center is when t=0, or teh big bang.

Not so fast. Any 4-dimensional center we specify needs 4 coordinates. You can't specify the center of a sphere by saying "well, we know that x=0."

I don't think the question is really a meaningful one. If we just look at the visible universe (heh), and define the center to be the average of all the spacetime vectors pointing to all the points in the universe (a typical definition for center), an evenly-curved universe should, I think, always have the center be exactly at the observer at about t=(current time)/2. Or maybe some other fraction, depending on how you include points and sometimes curvature.

Uneven universes should get a little more difficult, and usually a little more unsolvable.
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Re: Why is there no "center" of the universe?

Postby PM 2Ring » Mon Aug 03, 2009 4:57 pm UTC

Tass wrote:There may very well exist higher dimensions, but there may not as well. You can have curved space without embedding it in a higher dimension. [...] You can then sort of imagine how the three dimensional space could be curved if there was a fourth, but the truth is it is not necessary.
Most certainly. And if a higher dimension does nothing, apart from sitting around for us to embed the universe in, it's dubious whether we can say it really physically exists when it's not even mathematically necessary.

Tass wrote:There are some forms of curvature which can not simply be explained by a higher dimension.
I don't think so. Any curved space can be embedded in a Euclidean space, but it will take more than one extra dimension, apart from the simple case of positive curvature. (But I Am Not A Topologist). Here's an interesting article from MathPages. Embedding Non-Euclidean Spaces in Euclidean Spaces

Tass wrote:The constant positive curvature 2D/3D space can be perfectly described as a sphere/hypersphere surface although there are no need for the 3rd/4th dimension to actually exist. The space with constant negative surface is usually described as being like a saddle surface (the periphery of a circle will be more than pi times longer than the diameter - there is always "more" space "around" a given area than inside it), but in reality you can never make a saddle in three dimensions where the curvature is constant, yet the constant negative 2d space can be perfectly mathematically described.
Non-Euclidean geometry can be fun. There are a few applets on the Net that let you play with tesselations in 2D space of constant negative curvature (hyperbolic space), usually using the Poincaré disk model. There are lots more regular tesselations in hyperbolic space than in flat space... :) About a year ago, I read about various ways of making models of hyperbolic tesselations. Some people were having much fun constructing them using paper. Of couurse, they don't sit flat in our space. Another mathematician has utilised her skills in handicrafts to crochet hyperbolic tesselations.

Tass wrote: In the case of a closed (positive curvature) universe it gives a nice intuitive understanding of how it at least doesn't have a center within the three dimensions we know. However, it might as well be open or even flat, in this case Cup of Dirts excellent post gives a good idea how something can be infinite (and therefore centerless) and yet expand.
Yes, well done, Cup of Dirt. This stuff was easier to explain back in the days when we thought the universe had positive curvature. :)

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Re: Why is there no "center" of the universe?

Postby Turambar » Wed Aug 05, 2009 6:58 pm UTC

Charlie! wrote:I don't think the question is really a meaningful one. If we just look at the visible universe (heh), and define the center to be the average of all the spacetime vectors pointing to all the points in the universe (a typical definition for center), an evenly-curved universe should, I think, always have the center be exactly at the observer at about t=(current time)/2. Or maybe some other fraction, depending on how you include points and sometimes curvature.


I guess the difficulty is that in three of those four dimensions, the universe expands indiscriminately in both directions. Time seems to think it deserves to be special and different for some reason. IT HAS NO DISCIPRINE!
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Re: Why is there no "center" of the universe?

Postby danpilon54 » Wed Aug 12, 2009 4:16 am UTC

Charlie! wrote:
thoughtfully wrote:
nbonaparte1 wrote:Okay, back on topic, is there a center in more dimensions? The 2d surface of a balloon has a 3d center. Is there a 4d center of the universe?

Any 4-sphere has a center. In the case of the model we're using, the fourth dimension is time, and the center is when t=0, or teh big bang.

Not so fast. Any 4-dimensional center we specify needs 4 coordinates. You can't specify the center of a sphere by saying "well, we know that x=0."


I think it might be like defining the origin in spherical coordinates. It is simply r=0. To assign the origin a theta or phi would be meaningless as it is ill-defined.
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Re: Why is there no "center" of the universe?

Postby roflcopter » Fri Aug 14, 2009 6:07 am UTC

Exarctly. The essence of relativity is that there are 4 dimensions an object moves through (three spatial and one temporal), and it moves through them with a total velocity of c. So if it's stationary in the three spatial dimensions, then it's moving at maximum speed through time. If it's going at light speed, then it's not moving at all through time. Minkowski space, basically.



Extremely off topic, but holy crap, you are my savior... This one post has made relativity clear to me, I had all the mathematics and theory down, but I can now picture and imagine what the numbers mean.

And just to ask, c is the speed of light, but in this case it seems as if it could be more aptly called the speed of time. What are your thoughts on this?

-rofl

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Re: Why is there no "center" of the universe?

Postby PM 2Ring » Fri Aug 14, 2009 11:34 am UTC

roflcopter wrote:And just to ask, c is the speed of light, but in this case it seems as if it could be more aptly called the speed of time.
It could be. But everything moves through spacetime at c, so I prefer to call c the conversion factor between space & time (ie a spatial displacement of 1 light-second is equivalent to a temporal displacement of 1 second (with a factor of i thrown in somewhere to account for the Minkowski metric)).

The fact that light moves through regular space at c caused a little bit of confusion at the end of the 19th century / start of the 20th, because people assumed that the weird phenomena were caused by something to do with electromagnetism. It was one of Einstein's brilliant insights to realize that the weird phenomena were due to geometry, not electromagnetism, and that any object with zero rest mass has no option but to travel at c.

Wiki has good articles on spacetime geometry, starting here: http://en.wikipedia.org/wiki/Four-vector

Also see this excellent article on Special Relativity by Australian sci-fi author & computer programmer, Greg Egan.

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Re: Why is there no "center" of the universe?

Postby Josephine » Fri Aug 14, 2009 12:34 pm UTC

roflcopter wrote:Extremely off topic, but holy crap, you are my savior... This one post has made relativity clear to me, I had all the mathematics and theory down, but I can now picture and imagine what the numbers mean.


I'd have to agree with that. Now I see the elegance of it all.
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Re: Why is there no "center" of the universe?

Postby Bobber » Fri Aug 14, 2009 1:40 pm UTC

Turambar wrote:Exarctly. The essence of relativity is that there are 4 dimensions an object moves through (three spatial and one temporal), and it moves through them with a total velocity of c. So if it's stationary in the three spatial dimensions, then it's moving at maximum speed through time. If it's going at light speed, then it's not moving at all through time. Minkowski space, basically.

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Re: Why is there no "center" of the universe?

Postby mikhail » Fri Aug 14, 2009 3:04 pm UTC

Turambar wrote:
thoughtfully wrote:
nbonaparte1 wrote:Okay, back on topic, is there a center in more dimensions? The 2d surface of a balloon has a 3d center. Is there a 4d center of the universe?

Any 4-sphere has a center. In the case of the model we're using, the fourth dimension is time, and the center is when t=0, or teh big bang.

Exarctly. The essence of relativity is that there are 4 dimensions an object moves through (three spatial and one temporal), and it moves through them with a total velocity of c. So if it's stationary in the three spatial dimensions, then it's moving at maximum speed through time. If it's going at light speed, then it's not moving at all through time. Minkowski space, basically.

[Bold emphasis mine] That's a very interesting perspective, new to me. Not the idea of a 4-D hypersphere of the four dimensions - I've heard Hawking use that to explain why there's no "end of the universe" and yet the universe is expanding. (I score in the 99th percentile on spatial reasoning, and I still don't quite get the implications of an infinite universe in that model - it seems there's a periodicity to space, but the period is infinite? Perhaps I've picked up something wrong.)

The new part for me is the idea that the length of the total velocity vector must be c, which I like. However, I'm confused by the implications for light, which has a speed c in the three spatial dimensions alone, and therefore seems to be required to not move in time according to your model. What does that mean, or does the model break for light?

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Re: Why is there no "center" of the universe?

Postby PM 2Ring » Fri Aug 14, 2009 3:21 pm UTC

does the model break for light?
It doesn't exactly break, but light speed is special. From http://en.wikipedia.org/wiki/Four-velocity
Wiki wrote: In other words, the norm or magnitude of the four-velocity is always exactly equal to the speed of light. Thus all objects can be thought of as moving through spacetime at the speed of light. This provides a way of understanding time-dilation: as an object like a rocket accelerates from our perspective, it moves faster through space, but slower through time in order to keep the four-velocity constant. Thus to an observer, a clock on the rocket moves slower, as do the clocks in any reference frame that is not comoving with them. Light itself provides a special case- all of its motion is through space, so it does not have any "left over" four-velocity to move through time. Therefore light, and anything else traveling at light speed, do not experience the "flow" of time.


Light speed motion is special in relativity (as should be expected :) ). The "distance" between two events in spacetime is equal to the proper time experienced by an observer travelling between those two events. But the Minkowski metric says that this distance is always zero on light-like paths. So all vectors connecting points on such paths are a kind of null vector, and null vectors can't really be compared properly with each other, or with vectors of finite length.

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Re: Why is there no "center" of the universe?

Postby Josephine » Sat Aug 15, 2009 10:36 am UTC

Turambar, I think you just enlightened 3 of us.

And by the way, if photons are stopped in time, how can they have quantum effects?
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Re: Why is there no "center" of the universe?

Postby Charlie! » Sat Aug 15, 2009 8:36 pm UTC

nbonaparte1 wrote:Turambar, I think you just enlightened 3 of us.

And by the way, if photons are stopped in time, how can they have quantum effects?

Because it's also a wave, and waves don't care as much for that "stopped in time" stuff.

So odd :P
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Re: Why is there no "center" of the universe?

Postby Sharlos » Mon Aug 17, 2009 12:38 am UTC

Ok, now I'm just getting my head around something moving through space yet being stopped in time.

Also, theoretical particles such as tachyons or whatever they are called, how do they theoretically behave temporally? They move back in time or something?

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Re: Why is there no "center" of the universe?

Postby Josephine » Mon Aug 17, 2009 2:25 am UTC

I would assume so. A total velocity of C would mean going backwards in time if you're going faster.
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Re: Why is there no "center" of the universe?

Postby nyeguy » Mon Aug 17, 2009 3:02 am UTC

I have to agree with the the people who just totally had relativity click. But I still have a question about this:
RogerMurdock wrote:The comoving distance from Earth to the edge of the visible universe (also called particle horizon) is about 14 billion parsecs (46.5 billion light-years) in any direction.
....
The visible universe is thus a sphere with a diameter of about 28 billion parsecs (about 93 billion light-years).

If the universe has only been expanding for ~14 billion years, how does it have a radius of 46.5 light years?
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Re: Why is there no "center" of the universe?

Postby Birk » Mon Aug 17, 2009 3:08 am UTC

nyeguy wrote:I have to agree with the the people who just totally had relativity click. But I still have a question about this:
RogerMurdock wrote:The comoving distance from Earth to the edge of the visible universe (also called particle horizon) is about 14 billion parsecs (46.5 billion light-years) in any direction.
....
The visible universe is thus a sphere with a diameter of about 28 billion parsecs (about 93 billion light-years).

If the universe has only been expanding for ~14 billion years, how does it have a radius of 46.5 light years?


The expansion of the universe is not subject to the local speed limit of c.

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Re: Why is there no "center" of the universe?

Postby Josephine » Mon Aug 17, 2009 4:09 am UTC

Correct. Ever heard of the Alcubierre warp drive? Same concept. Space isn't limited to C.
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Re: Why is there no "center" of the universe?

Postby Diadem » Mon Aug 17, 2009 1:36 pm UTC

Sharlos wrote:Also, theoretical particles such as tachyons or whatever they are called, how do they theoretically behave temporally? They move back in time or something?

A common misconception, but: No.

To move faster than the speed of light you'd have to move, not backwards in time, but perpendicular in time. You'd be moving in imaginary time. Imagine time not as an ordinary number (t = x) but as a complex number (t = x + i y). An object moving faster than the speed of light would now be moving on the imaginary time axis. That is fine in mathematics, where we can use complex numbers and do the math. But it doesn't make any physical sense.

Which is why we are so confident that you can not go faster than the speed of light. Going backwards in time is already problematic, and leads to all kinds of paradoxes. But imaginary time, we don't even know what that means.

Incidently, this also leads to temporal paradoxes. There's no escaping those. But it's more suble than merely 'moving backwards in time'.
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Re: Why is there no "center" of the universe?

Postby Tac-Tics » Mon Aug 17, 2009 8:10 pm UTC

I don't know jack shit about cosmology, but I used to wonder this same thing. After learning some differential geometry, it's clear why it's not absurd.

A center is a kind of a average. The midpoint between two points is the "center" between those points: it's the average position of both. If you have a circle of points, the center is the average of the position of all of them.

To take an average, you sum (or integrate) the data you want to average, then divide by the volume of the data. In Euclidean space, if you want to find the midpoint of points A and B, it's (A+B)/2. If you want to find the average value of a function over an interval [a, b], you integrate it on that interval and divide by (b-a).

But in higher level geometry, we're not working with Euclidean space. We're working on a manifold of some kind. It acts LOCALLY like Euclidean space, but from a bird's eye view, it might be something else entirely.

The crux of the problem is that you can't add points on a manifold! (Riemannian) manifolds are required to be locally diffeomorphic. That means each neighborhood of a manifold has a coordinate chart which maps each point to a unique coordinate on some subset of R^n. All the math you do on the manifold is governed by these charts.

Now, say you take a chart to work with that covers all the points you want to average together. You take their map coordinates, add them up for a result. There are cases where the coordinate is way off the chart's boundaries. You can't map it back to any point on the manifold.

This isn't a proof, but it means at the very least, if you want to average a set of points, you can't do it quite so naively.


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