Center of the Universe

James R.,

MacM:

I want to see your ballon have the accelerating rate between dots progressively around the ballon. That is the observation.

That's what you get when you blow up the balloon at an increasing rate.

Your ballon analogy is hog wash.

You wouldn't be able to tell the difference.
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AND: Actually I believe you are wrong here.

Inflating the ballon at an ever increasing rate would only increase the rate of a linear expansion. What we observe is a progressive acclerating expansion. That is the rate of expansion is as one raven indicated in his concentric circles analogy. Your current example has each circle expanding at the same but increasing rate.


Knowing to believe only half of
what you hear is a sign of
intelligence. Knowing which
half to believe will make you a
genius.
 
RE math/ace

The fact is, the universe does have a center - it is the four dimensional center of this balloon. If we could go there, we would be travelling backward in time to the big bang.
Think of it this way - four dimensionally, the entire past and future of the universe is "already" there. The complex interactions we observe in matter are just the complex ways that the puzzle pieces fit together four dimensionally. The rules for the way they are laid out somehow constrain our consciousness to only be aware of things that lie on the (relative) interior of this 4-D balloon (the past). They also constrain our consciousness to perceive a "flow" of time, when in fact all past and future simply exists "now", in different layers of the balloon, from a 4-D perspective.
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Well, if the entire past and future of the universe is "already" there, (as if eg. our history was our shadow in Time) then only our perception moves in a completely quiet universe (where the Old Rome rules unchanged/unchanging next to the airport of Rome). All is ready and done: only our mind/consciousness is flying around. But the question then would be who prepared the show? Could anybody then see the arisal the Big Bang as an accident/al process?: this concept has some religious aspect - by which I am not saying it cannot be/is not true.
 
Originally posted by MacM
Now all the dots move apart at an equal but higher rate. I want to see your ballon have the accelerating rate between dots progressively around the ballon. That is the observation. Your ballon analogy is hog wash.
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Hypothetically - if you had a lung big enough - you start out by blowing a certain volume of air per second and then end by blowing a larger amount of volume per second you will have accelerated the rate of blowing, thus accelerating the rate of expansion of the balloon. The analogy works!

Originally posted by MacM
ANS:Right and that is why this analogy sucks big time. It can produce linear expansion at different rates. It cannot produce accelerating expansion over the surface of the ballon.
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Seems to me like your contradicting yourself here. If we can produce two different rates of expansion as you say, you should be able to produce not only those two rates, but all the rates in between. How do you go from there to arguing that the balloon analogy can't produce an accelerating expansion over the surface of the balloon?
 
AndersHermansson,

Inflating the ballon at an ever increasing rate would only increase the rate of a linear expansion. What we observe is a progressive acclerating expansion. That is the rate of expansion is as one raven indicated in his concentric circles analogy. Your current example has each circle expanding at the same but increasing rate./b]
Click to expand...



ANS: Read the above again slowly and think about it.

Increasing the rate of expansion of the ballon only increases the rate the dots move apart but every dot moves apart at the same rate.

Our observation is the farther away the dots are the faster they are moving away.

It is not the same as changing the expansion rate of the ballon.

Each dot on the ballon must see dots progressively farther away moving away at increasing speed. It is not the same as the ballon's linear expansion.

Knowing to believe only half of
what you hear is a sign of
intelligence. Knowing which
half to believe will make you a
genius.
 
Originally posted by MacM
AndersHermansson,
ANS: Read the above again slowly and think about it.
Increasing the rate of expansion of the ballon only increases the rate the dots move apart but every dot moves apart at the same rate.
Click to expand...

I thought about it, and I think you must be wrong!

Proof:
Let A, B, C be three points on an horizontal axis X, each with one unit of space between the two others.

Axis X here represents one dimension being expanded at a rate of .1 unit of space per unit of time. After one unit of time the length of space between each point A, B, C will have increased to 1.1 units. Therefore, the distance between A and C must be 1.1 + 1.1 = 2.2 and that increase must have occured during one unit of time and is double that of the space between A and B or B and C.

Might seem abit unnecessary but I need practice in scientific rigor! :)
 
The first time I saw this, they used the surface of the ballon as the proof. With a thick enough ballon, you can demonstrate that points on the inside of the balloon seperate slower then points on the outside. This is assuming you are measuring linear speed, as in a radially system its all at the same speed.
 
AndersHermanssos,

thought about it, and I think you must be right!
Click to expand...
:D

It would be progressive. Damn.



Knowing to believe only half of
what you hear is a sign of
intelligence. Knowing which
half to believe will make you a
genius.
 
Originally posted by MacM
one raven,




ANS: Fair presentation but it doesn't even get half way.

1 - What happens if you continue to look toward circle #2 and see #1, then Ground Zero and then back out to #1, #2 and #3?

2 - What happens if you look tangent to the circle (which is what we do when we look in any direction). Draw yourself a line from a dot on #3. The only line that has the correct function partially is a radial line.

Our observation is circles within circles from every dot on the circles.
Click to expand...
The analogy still works.

Look at the attached diagram.
(keeping in mind that I never claimed to be an artist and MSPaint is severely limited :D.)

There are 8 concentric circles.
There are 16 lines radiating out from the center showing linear motion from the center.
The pink arrowheads show the direction of motion.
There are at least 1 world on each concentric circle from which you could consider the Point Of View.

Each of the worlds are moving out from the center in this uniform expansion.
Each of the concentric rings is accelerating faster than the ring closer to the center.

Which of these worlds would not percieve all other worlds moving AWAY from them?

Yellow world's POV:
Since Grey world is accelerating slower, it appears to be moving away from it. (we already covered this).
Orange world apprears to be moving away because it is moving away from it.

Grey world's POV:
Yellow seems to be moving away from it because Yellow is accelerating at a faster rate.
Same goes for Brown world.

Green world's POV (either one):
Blue world (on the same linear plane) seems to be moving away since Boue world is accelerating faster.
Other Green world appears to be moving away also...
This is where the Inverase Square function comes in.
If all the worlds are uniformly radiating omnidirectionally and in a straight line from the center, as each world travels further from the center it also travels perpendicularly from the world next to it.
Simple way to demonstrate that, is to look at the two Blue worlds.
The Blue worlds are on the same linear plane as the Green worlds respectively.
Eventually, the Green worlds will be at the point in space as the Blue worlds are now.
If you look at the diagram, the Blue worlds are further apart than the Green worlds are, right?
Therefore Green world1 appears to be travelling AWAY from Green world2.

I ask again...
Which of these worlds would not percieve all other worlds moving AWAY from them?
 
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Originally posted by James R
<b>one raven:</b>

The solution to your difficulties lies in the fact that the universe has no centre. There is no single point in space from which everything else is expanding.
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I don't see how that is possible.
If all the galaxies appear to be moving away from one another because the universe is expanding uniformly there must be a center point from which they are all expanding.

How else would it be uniform expansion?

It would be a haphazzard expansion with Galaxy A moving away from Point Z, Galaxy B moving away from point Y and Galaxy C moving away from Point X.
Depending on where Points X, Y and Z are, some Galaxies will inevitably appear to be moving towards us.
Am I missing something glaringly obvious?
 
one_raven:

That's the whole point of the balloon analogy.

You need to imagine that the entire universe is on the <b>surface</b> of the balloon. The centre of the balloon (inside) is not part of the 2D universe represented by the surface.

Paint dots on the surface to represent galaxies, then blow the balloon up. Each dot sees all the other dots move away from it along the surface as the balloon expands. However, none of the dots can be said to be the centre of the universe. The <b>surface</b> of the balloon has no centre. Only the 3D balloon has a centre.

Applying this to our universe, we have a 3D space with no centre in the space. The hypothetical centre of expansion for our universe exists in a higher dimensional space, just as the centre of expansion for the balloon universe exists in a higher-dimensional space.
 
Why is it not considered to have a center?
What problems would that pose?
 
Originally posted by one_raven
Why is it not considered to have a center?
What problems would that pose?
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Today's astronomers agree on the universe being approximately flat (would you like some links----the summary of recent WMAP results, all the recent review articles of current model of universe etc)

So the balloon image is bad---surface of balloon is finite and curved but cosmologist's picture of U is infinite and not curved

rather like an infinite flat sheet of graph paper

where you put the center is arbitrary, as with graph paper you can put the x = 0 y = 0 origin anywhere, no problem----just realize that it is arbitrary

answer to your question: why is it not given a center, what problems would it cause? The universe IS given a center when people do largescale 3D sky surveys. Often the center is put right at our galaxy!

Why not?

Our galaxy is as good a center as we could possibly choose. But any other galaxy would also work as well (in principle)

Imagine an infinite sheet of graph paper in which all the squares are growing in size

any point can be chosen to serve arbitrarily as the "center of exapansion" but no point is any better than another----any point will do

spatial flatness is an important part of the consensus model cosmos these days

Remember that just because the experts say "spatially flat, accelerated expansion" you or anyone does not have to believe the expert opinion----you are free to believe in the balloon or in anything else---everybody is responsible for his own beliefs and is free to doubt professional consensus. However before you go off on your own personal tangent it is not a bad idea to see what
the professional cosmologist view is and a good sample is
a review article by Charles Lineweaver that came out this year and is online

http://arxiv.org/astro-ph/0305179

"Inflation and the Cosmic Microwave Background"

other sciforums people may recommend other survey articles and they will all say pretty much the same. This paper is as good as any and I recommend it because it is authoritative, up to date, written for a wide audience, and has good diagrams. Lineweaver was a leader of the COBE satellite microwave background study through the 1990s and he is world-class.

Ned Wright is a similarly prominent figure, or Michael Turner, Wendy Freedman who led the HST project determining the value of the Hubble parameter is another---they all give essentially the same picture-----"large-scale flat" in a 3D sense, not like the balloon. So any point will do as "center" if you need a point of reference. You can get their websites and survey articles and stuff with google.
 
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Originally posted by MacM
AndersHermanssos,

:D

It would be progressive. Damn.



Knowing to believe only half of
what you hear is a sign of
intelligence. Knowing which
half to believe will make you a
genius.
Click to expand...

:D
 
This is the way I think about it.

Imagine there is only one point on the ballon from which say , new surface is being created. The surface are of the ballon will be getting larger but there is a center of expansion there.

Now imagine two points on the ballon at opposite sides. There is no center of expansion anymore but the surface area is still getting larger (assuming pressure of inside of ballon is uniform at all points on the surface).

Now bring the number of these points to infinity and u get a great model of the universe where each point is moving away from each other in all directions and there is no center at all (or it would seem that u are at the center).

Of course, this actually happens in a real ballon because each aton (or molecule rather) in the ballon is moving away from each other at the same rate in a uniform expansion to accomodate the extra air being blown in.
 
Take two dots painted on a spherical balloon. Suppose the distance between them is L, measured <b>along the surface</b> of the balloon.

The distance L is related to the radius R of the balloon and the angle <font face="symbol">q</font> (in radians) subtended by the great circle path between the two points by:

L = R<font face="symbol">q</font>

Now blow up the balloon. The rate of change of the radius R is dR/dt, where t is the time. That means the rate of change of L is given by:

dL/dt = (dR/dt) <font face="symbol">q</font>,

or, in terms of L:

dL/dt = (dR/dt) L/R ........... (*)

It should be noted that <font face="symbol">q</font> is a constant as the balloon is blown up, but both L and R vary with time t.

The expression dL/dt is the velocity of one dot as seen by the other. Notice that the velocity is proportional to the distance L of one dot from the other. Thus, the formula (*) is exactly analogous to the Hubble law for the balloon, where the "Hubble constant" is (dR/dt)/R.

If dR/dt is constant (i.e. the balloon is blown up at a constant rate), then the "Hubble constant" is actually constant. If, on the other hand, dR/dt is not constant, we have a model of accelerating or decelerating expansion of our 2D balloon-surface universe.
 
ORW,

The further the dots on the balloon are, the faster they expand from each other.

Your arguments give me a headache
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Just as the further you look out into the universe the faster the stars are receeding.

Seems simple enough. If the dots are 1 inch apart at some point in time during inflation and you inflate the ballon until the dots are 2 inches apart,

You can see that the 1st dot from you will have moved 1 inch. during that same time the 2nd dot away will have moved 2 inches.

That is acceleration. The dots progressively move further in the same time frame.

Take an asprin and call in the morning.:D


Knowing to believe only half of
what you hear is a sign of
intelligence. Knowing which
half to believe will make you a
genius.
 
Originally posted by MacM

That is acceleration. The dots progressively move further in the same time frame.
Click to expand...

This is not acceleration, this is velocity.
 
1100f,


quote:
--------------------------------------------------------------------------------
Originally posted by MacM

That is acceleration. The dots progressively move further in the same time frame.


--------------------------------------------------------------------------------



This is not acceleration, this is velocity.




I think you misinterpreted my statement. If we look outward into the universe we see stars farther way receeding at higher velocity and from that we infer that there must be an acceleration involved. We don't see accleration directly.

The same holds true with the ballon example. If the movement of the dots become progressively larger then it represents acceleration although you are looking at relative velocities to make that judgement.

Knowing to believe only half of
what you hear is a sign of
intelligence. Knowing which
half to believe will make you a
genius
 
Originally posted by James R
Take two dots painted on a spherical balloon. Suppose the distance between them is L, measured <b>along the surface</b> of the balloon.

The distance L is related to the radius R of the balloon and the angle <font face="symbol">q</font> (in radians) subtended by the great circle path between the two points by:

L = R<font face="symbol">q</font>

Now blow up the balloon. The rate of change of the radius R is dR/dt, where t is the time. That means the rate of change of L is given by:

dL/dt = (dR/dt) <font face="symbol">q</font>,

or, in terms of L:

dL/dt = (dR/dt) L/R ........... (*)

It should be noted that <font face="symbol">q</font> is a constant as the balloon is blown up, but both L and R vary with time t.

The expression dL/dt is the velocity of one dot as seen by the other. Notice that the velocity is proportional to the distance L of one dot from the other. Thus, the formula (*) is exactly analogous to the Hubble law for the balloon, where the "Hubble constant" is (dR/dt)/R.

If dR/dt is constant (i.e. the balloon is blown up at a constant rate), then the "Hubble constant" is actually constant. If, on the other hand, dR/dt is not constant, we have a model of accelerating or decelerating expansion of our 2D balloon-surface universe.
Click to expand...

Just a little correction:
If dR/dt is constant (let us call this constant K), then R = Kt + R<SUB>0</SUB>. In that case the Hubble paramater will be given by:

H(t) = (dR/dt)/R = K/(Kt + R<SUB>0</SUB>), which is not constant. But then, because L = R<font face="symbol">q</font>, by using equation (*), you find that dL/dt = K<font face="symbol">q</font>. If you want the Hubble parameter to be constant, you must solve dR/dt = HR(t) whose solution is that R should grow exponentially.

But still, your treatment of the distance between any two points is correct, and the Hubble law still hold between points on the surface of an inflating balloon (and of course between two objects on a constant curvature on a 3D space).

Originally posted by MacM


I think you misinterpreted my statement. If we look outward into the universe we see stars farther way receeding at higher velocity and from that we infer that there must be an acceleration involved. We don't see accleration directly.

The same holds true with the ballon example. If the movement of the dots become progressively larger then it represents acceleration although you are looking at relative velocities to make that judgement.
Click to expand...

If you take the distance between two points at two different times, you can say something only about their velocity, you cannot say nothing about their relative acceleration.

As shown in this post, if the rate at which the radius of the sphere grows at a constant rate, the Hubble law still hold, but their is no acceleration between any two points.
 
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