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[Andir]

If you look out and grab a set of 1000 galaxies in space... record their positions relative to a set of other stars, they should (in twenty/thirty/etc. years) be at a point that is further away from each other.  All of them... with a VERY small margin of error.

Now, as far as the redshift thing... we should be able to take those 1000 galaxies and measure the shift, then through simple geometry determine what they are floating away from.  If everything is expanding, everything is expanding away from their origin points and it should be as easy as tracing back all the galaxies to their origins.

If the expansion is real that is.

Sorry, last edit:

I'm going to draw this in a line, but it's no different in 3D space:

                     ... <- here is the origin of the big bang...

          .           .            . <- here are the galaxies now
         .            .             . <- here are the galaxies in (say) 50 years

I think you can see from that... if we see all those galaxies going away from that point in the center, the one in the center must be either travelling toward us or away from us.  We can then assume that the origin point should be in that direction.

[malimbar04]

Correct me if I'm wrong, but doesn't the speed of massless things (speed of light in a vacuum) and relativity come into play here? There is no universal medium or absolute position, only relative positions. The galaxies are traveling away from us at near the speed of light, but from their perspective we're traveling away from them at that speed. If we each measured a third galaxy (even correcting for the time it takes light to reach us), our positional information would say it's at two different points.

[Il Palazzo]

If the expansion is real that is.

No, sir, no. That it's not a matter of the expansion being real or not. Rather it's a matter of your less-than-perfect of comprehension of geometry.

If you look out and grab a set of 1000 galaxies in space... record their positions relative to a set of other stars, they should (in twenty/thirty/etc. years) be at a point that is further away from each other.  All of them... with a VERY small margin of error.

It is not so. If it were to happen like this, then you'd quickly end up with a part of the sky devoid of all galaxies, while the opposite part would be a one big cluster of galaxies. This is something you'd see if you were moving very fast through the otherwise static(or at least much slower than yourself) universe.
Needless to say, this is not what the observations show. The angular(a.k.a. tangential) component of galactic velocities is very small when compared to the radial velocities associated with the expansion(some hundreds of kilometers per second compared to up to the speed of light at the edges of the observable universe), as well as being "random", i.e. each galaxy is only moving across their bit of surrounding space as the gravitational influences guide them, not uniformly as it's to be expected when considering the expansion of all space.
Once again, the expansion of the universe does not produce any tangential velocities. Your example with the cartesian system shows that precisely.

Now, as far as the redshift thing... we should be able to take those 1000 galaxies and measure the shift, then through simple geometry determine what they are floating away from.  If everything is expanding, everything is expanding away from their origin points and it should be as easy as tracing back all the galaxies to their origins.

Indeed, it's what I'm trying to tell you - you can do that simple analysis for each and every point of the universe, and in each case you'll end up with the same result: the universe appears to have it's center exactly where you're standing.

Regarding your 1D analogy:
you, the observer, are the comma. Dots are the other galaxies you see. t=time. For convenience's sake, I'll draw only five objects, but of course, the number of dots on each side of the observer could be infinite(but observably limited by the speed of light and the age of the universe).
t1 some arbitrary moment in the past of the universe
        . . , . .     
Distance between each is x. 

t2 some time later, the space has stretched by a factor of 2.
      .  .  ,  .  .   
Distance from "," to the nearest "." is 2x. Distance to the next "." on each side is 4x.

t3 even later, the space streched by another factor of 2.
  .    .    ,    .    .
Distances are now -8x, -4x, 4x, 8x. The farther the observed point is, the faster it receeds from you. It appears that the center of the universe is where the comma is!

Now, who says you need to be stuck on the comma? Imagine teleporting to the rightmost dot(now marked as "I"). You see this:

t1       , . I . .
t2     ,  .  I  .  .
t3 ,    .    I    .    .

You observe exactly the same effect as you did standing on the comma. Where's the center of the universe then? The answer is, of course, nowhere. There never was a single point in space that was the origin of the "explosion" of matter, because that's not what the Big Bang was.
Going back to the balloon analogy, similarly you can't point to any single place on the surface of the balloon and say that the rest of it is expanding from there.

[Andir]

No, you are mistaking the point I was getting at....

We are not in that grouping.  We are observing that grouping.  If we observe a grouping of stars that does not move as fast as the others, that's likely a point along the vector of origin...

                    . <- we are here

                  . .  . <- we observe three other stars here

If those stars separate (like they should in an expanding universe) and we are moving away from an origin point (let's say we were at one point in the position of the the middle one but the expansion moved us to where we are) the two outside stars will move at different vectors than the inside one (if it even appears to be moving at all... according to the redshift theory it will be moving away from us, but the other two will be moving even further than that because they will be moving away from that center)  So you can extrapolate from that data that the center star is along our plane of movement from our origin.  Thus, the origin of our point in space should lie along that vector in space.  Now, if the center one if moving down and the two outside ones are moving downward as well (not just outward) you can assume that the point we used to be lies somewhere above that point.  It's simple freaking geometry and there's nothing wrong with my understanding of it.  (I'd appreciate it if you'd drop the whole condescending attitude.  Please.)

Think of it like those silly flying through space screen savers... if you got rid of the lines between the two points and did that by hand you'd be able to tell what general direction you are heading in.  Your point of origin is toward the origins of all the rest of those stars.  I hate using this example because the stars in those programs don't move relative to each other like they should, but that's not the point.  We should see some vector of movement in all the stars around us.  That movement should point us to the positions we came from... even if everything is pushing away from each other, we are still being pushed away from another point, our point of origin so we should not see that we are in the center if there truly is expansion from a point of big bang origin.

[Shade-o]

This hardly seems relevant to the topic, and all this "My good sir, your calculations are flawed! My diagram shall reveal the truth, THUSLY!" is somewhat baffling.

[Phmcw]

(flame removed)

[Shades]

Andir don't forget that your not talking straight line vectors and a 3d graph here as 'absolution' motion will be effected by gravity, further more the position of stars further away is not only increasingly inaccurate, both due to warping of light and because of the sheer distance, but also increasingly old due to the time it takes for the information to reach us. So not only do you have to take into consideration the effect of systems on other systems historically you also have to do so on an estimate of the currently location using positional data that could be light years incorrect.

I'm sure with enough information it can be calculated but it's certainly not simple geometry.

[Il Palazzo]

Andir, sorry for the attitude, but your insistence on misinterpreting the whole idea of expansion lends itself very easily to being a prick. I appologise. I could pull a Shrugging Khan here and say that I'm just stating the facts, but seeing how in some years from now I'm supposed to start teaching people, I should probably thank you for pointing out my arsehole'ry.

Spoiler: for out of topicness (click to show/hide)

From what I gather, you're making a wrong assumption right from the start: you say that you're not observing the universe from any one of the dots, rather you're somewhere outside the expanding universe looking at the stars. This makes no sense, as you'd have to occupy some fifth(or fourth spatial) dimension to do that, and needless to say, you never will.
Imagine the balloon example - for as long as you're a 2D creature living on the 2D space of the balloon's surface, it doesn't make any sense to you to name a point outside your 2D universe that you could call its center. As long as you're bound to those two dimensions it just doesn't make any sense to ask questions like "where does the balloon start" or "from which point does it come from".
Always, you have to observe the universe from a point in space within the universe.

If you do that, then applying the principle of expanding space to your thought experiments will always give you the same results: everything is receeding from you, the observer, wherever you are, and the farther the object is, the faster the recession, with all vectors pointing outwards from the point of the observation.
This is exactly what we observe, and it's exactly what you'd observe when imagining that you're confined to the 2D space of the balloon.

Here, let me activate my uber-paint-powers:
You're at the green dot, and the blue dots are the stars you see in the sky.
A & B are the angles that separate the stars as you observe them. If they don't change then the stars appear to be stuck in their corresponding spots.

As you can see, if you increase all the distances between objects equally, the relative positions of the stars will remain unchanged.
All the velocity vectors in that picture are colinear with the distances, and point towards whichever of the dots you occupy when making the measurements.

The cartesian system of coordinates is very useful to testing this. Choose some arbitraty number of points on the plane(or in 1D, or in 3D) and measure all the distances between those points. Now multiply all the coordinates by some constant(like 2 or 10 for the ease of calculations), and measure all the distances again. You'll notice that for each point you chose, the distances to it's neighbours increased in such a way, that the farther the point, the further it moved away. Also, all the displacement vectors that you draw will point outwards from any one of the points that you choose.
Using the cartesian coordinate system it's also easy to show that the angles between the points remain constant as you expand the space between them(multiply the coordinates), which reflects the largely static situation of the objects in the sky.

I'm sure with enough information it can be calculated but it's certainly not simple geometry.

Eh, sure it is, in principle. Same as you try and understand physics while imagining weightless pulleys and dragless surfaces.

[Andir]

Andir don't forget that your not talking straight line vectors and a 3d graph here as 'absolution' motion will be effected by gravity,

I know there won't be straight lines, but there should be a bias in the directions.  If you take a large enough sample and most of those are going in X vector then that would conclude that the opposite of that is the origin.

[Andir]

Andir, sorry for the attitude, but your insistence on misinterpreting the whole idea of expansion lends itself very easily to being a prick. I appologise. I could pull a Shrugging Khan here and say that I'm just stating the facts, but seeing how in some years from now I'm supposed to start teaching people, I should probably thank you for pointing out my arsehole'ry.

Spoiler: for out of topicness (click to show/hide)

From what I gather, you're making a wrong assumption right from the start: you say that you're not observing the universe from any one of the dots, rather you're somewhere outside the expanding universe looking at the stars. This makes no sense, as you'd have to occupy some fifth(or fourth spatial) dimension to do that, and needless to say, you never will.
Imagine the balloon example - for as long as you're a 2D creature living on the 2D space of the balloon's surface, it doesn't make any sense to you to name a point outside your 2D universe that you could call its center. As long as you're bound to those two dimensions it just doesn't make any sense to ask questions like "where does the balloon start" or "from which point does it come from".
Always, you have to observe the universe from a point in space within the universe.

If you do that, then applying the principle of expanding space to your thought experiments will always give you the same results: everything is receeding from you, the observer, wherever you are, and the farther the object is, the faster the recession, with all vectors pointing outwards from the point of the observation.
This is exactly what we observe, and it's exactly what you'd observe when imagining that you're confined to the 2D space of the balloon.

Here, let me activate my uber-paint-powers:
You're at the green dot, and the blue dots are the stars you see in the sky.
A & B are the angles that separate the stars as you observe them. If they don't change then the stars appear to be stuck in their corresponding spots.

As you can see, if you increase all the distances between objects equally, the relative positions of the stars will remain unchanged.
All the velocity vectors in that picture are colinear with the distances, and point towards whichever of the dots you occupy when making the measurements.

The cartesian system of coordinates is very useful to testing this. Choose some arbitraty number of points on the plane(or in 1D, or in 3D) and measure all the distances between those points. Now multiply all the coordinates by some constant(like 2 or 10 for the ease of calculations), and measure all the distances again. You'll notice that for each point you chose, the distances to it's neighbours increased in such a way, that the farther the point, the further it moved away. Also, all the displacement vectors that you draw will point outwards from any one of the points that you choose.
Using the cartesian coordinate system it's also easy to show that the angles between the points remain constant as you expand the space between them(multiply the coordinates), which reflects the largely static situation of the objects in the sky.

I'm sure with enough information it can be calculated but it's certainly not simple geometry.

Eh, sure it is, in principle. Same as you try and understand physics while imagining weightless pulleys and dragless surfaces.

No, I understand that the angles will be the same... but using your own images... D4 and D5 would show you your trajectory.  The point between those lines would appear to not move while the points at the end of those lines would appear to be moving further away from it.  If you have a bunch of points at the middle point that don't appear to be moving as much as the groups of points on the corners you can estimate that that direction is either the origin or the destination or your expansion.  Make sense?

Edit: er... nevermind my last edit if you read it.

[Il Palazzo]

Andir don't forget that your not talking straight line vectors and a 3d graph here as 'absolution' motion will be effected by gravity,

I know there won't be straight lines, but there should be a bias in the directions.  If you take a large enough sample and most of those are going in X vector then that would conclude that the opposite of that is the origin.

But there is no other uniform motion on the large scale than the one associated with the redshift. All that you can find out by analysing the local movement of galaxies is where the center of gravity of any particular cluster lies. So the Andromeda Galaxy is moving towards the Milky Way, because these two objects are gravitationally attracted to each other stong enough to outset the expanding space effect by far. Would you conclude that the center of the universe is somewhere between the two galaxies then?

No, I understand that the angles will be the same... but using your own images... D4 and D5 would show you your trajectory.  The point between those lines would appear to not move while the points at the end of those lines would appear to be moving further away from it.  If you have a bunch of points at the middle point that don't appear to be moving as much as the groups of points on the corners you can estimate that that direction is either the origin or the destination or your expansion.  Make sense?

But they wouldn't move in any other way than radially. Their position on the sky wouldn't change. I could draw more points and more lines on that picture, and they would all follow the same set of rules. Their movement would be proportional to their distance from you, and it'd look like they're receeding from you, regardless of which point you're standing at.

ninja edit:

Edit: Actually, by your own drawing, the lines D1 and D3 are too long... because they are not C*d1 and C*d3 (respective)

What? Why not? Draw it within the cartesian coordinate system. They are proportional to the d1 and d3, as they should be.

[ECrownofFire]

The thing is, you CAN'T observe that effect, because there IS no point of origin. If there was one, then it would be true, but because there is none, you just can't. You are trying to observe movement away from a point that doesn't exist.

[Phmcw]

I did not insult you, just pointed that you obviously misunderstand the underlying theory.
Yo can go on and on, but basically you don't understand the concept of expansion, and fail to visualize how it would apply to space.
Beside your proposition for an "experimental proof" are made without so much as an inch of research on actual astronomy.
I said that you should take a course on the matter if you are really interested and actually think yours ideas are worth two cent, and I rest my case.

But instead you choose to be offended, well go for it.

If you'd understand the theory, you would not search for a center of the expansion, which make no sense at all.

The thing is, you CAN'T observe that effect, because there IS no point of origin. If there was one, then it would be true, but because there is none, you just can't. You are trying to observe movement away from a point that doesn't exist.

Actually, it's because the tough experiment he propose is a basic way to detect the effect of a big explosion and come from a flawed vision of what thee big bang is. If he understood that we are speaking about an expansion of space, he'd understand why it can' work ( technical impossibilities notwithstanding).

[Andir]

But there is no other uniform motion on the large scale than the one associated with the redshift. All that you can find out by analysing the local movement of galaxies is where the center of gravity of any particular cluster lies. So the Andromeda Galaxy is moving towards the Milky Way, because these two objects are gravitationally attracted to each other stong enough to outset the expanding space effect by far. Would you conclude that the center of the universe is somewhere between the two galaxies then?

The dataset is too small.  You would need to observe the same effect in a large number of stars in the same direction not altering their location in the sky comparatively.  (edit: and not having a drastically different redshift than the "corners")

But they wouldn't move in any other way than radially. Their position on the sky wouldn't change. I could draw more points and more lines on that picture, and they would all follow the same set of rules. Their movement would be proportional to their distance from you, and it'd look like they're receeding from you, regardless of which point you're standing at.

But at different speeds away from you... if they were radial, the shifts would be the same, but then the whole idea that Andromeda sees the same radial expansion would mean that stars would collide due to all the galaxies expanding away from each other.  It can't be radial expansion for every point within.  Not if it stays consistent in the sky.  If the expansion was radial, it would appear to shift in the sky depending on which star you were on.  In order for that to work, everything would have to expand away from each other at different speeds and that should be measurable.

What? Why not? Draw it within the cartesian coordinate system. They are proportional to the d1 and d3, as they should be.

Ignore that... it was me waking up.

[Andir]

The thing is, you CAN'T observe that effect, because there IS no point of origin. If there was one, then it would be true, but because there is none, you just can't. You are trying to observe movement away from a point that doesn't exist.

If there is no point of origin, then we are not expanding and the big bang is false.  The Big bang itself says we were once smaller and that means we are moving away from where we were.