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Sam5
2010-Jul-24, 07:14 PM
Ha! The History Channel just showed their version of my “sphere of visibility” drawing.

http://i32.tinypic.com/20z4lnc.jpg

http://i27.tinypic.com/14mcqw1.jpg

They showed an observer having a sphere of visibility out to his “event horizon”. The observer was at the center of his own Euclidean sphere of “visibility”.

And then they showed more spheres of visibility for other observers further out than we are, with a lady astronomer saying that we have no idea how large the universe is, and that we can see only about 13.5 billion light years out to our “event horizon”. But other people a great distance from us, can see further than we can, if the universe is much larger than having a 13.5 light-year radius, but they can only see out to their own radius of visibility, and they are in the center of their own sphere of visibility.

The History Channel did not use my term “sphere of visibility”, but they illustrated it with computer graphics showing 3-D Euclidean spheres, with observers at the center of each one. :)

They showed the universe having depth. They did not use the “surface of a balloon” analogy.

I suggest we adopt this “sphere of visibility” and “radius of visibility” point of view as the standard answer to “where are we” questions.

Tobin Dax
2010-Jul-24, 07:50 PM
I suggest we adopt this “sphere of visibility” and “radius of visibility” point of view as the standard answer to “where are we” questions.

I'm under the impression that we already have. I've seen this explanation a number of times before.

Sam5
2010-Jul-24, 08:11 PM
I'm under the impression that we already have. I've seen this explanation a number of times before.

Well that's great. I'm pleased. :)

George
2010-Jul-24, 08:27 PM
And then they showed more spheres of visibility for other observers further out than we are, with a lady astronomer saying that we have no idea how large the universe is, and that we can see only about 13.5 billion light years out to our “event horizon”. But other people a great distance from us, can see further than we can, if the universe is much larger than having a 13.5 light-year radius, but they can only see out to their own radius of visibility, and they are in the center of their own sphere of visibility. I assume those distant observers who see further in one direction see less than we do in the other direction.

astromark
2010-Jul-24, 08:50 PM
No George... You are in the middle of your sphere of visibility... so is everyone else. Its space that is expanding.

Here there and everywhere that is not gravitationally bound.

By rigorous observation it is concluded that at some time ago ( 13.7 billion years ) All of this universe was very much smaller.

That it is expanding now and we can not determine a center point...

pzkpfw
2010-Jul-24, 10:06 PM
No George...

No astromark, the answer to George (who was clarifying what Sam5 meant by "can see further than us") is "yes". (But for the same reason you gave.)

In 2D:


Distance left and right that x can see:

a<- x ->b

----

Distance left and right that y can see:

c<- y ->d

----

a<- x ->b
c<- y ->d

Point d, which y can see, is "further" than x can see.
But in reverse, point a which x can see, is "further" than y can see.

pzkpfw
2010-Jul-24, 10:12 PM
Posts above this one, moved from this thread: http://www.bautforum.com/showthread.php/105493-Center-of-Universe

Sam5
2010-Jul-24, 10:32 PM
I assume those distant observers who see further in one direction see less than we do in the other direction.

Only if the universe has a physical radius no larger than what we now see. However, that would place us in the dead center of both our “sphere of visibility” and the universe itself, and it’s not likely that we would be in the center. After all, we aren’t in the center of our solar system, and we aren’t in the center of our galaxy.

So, the assumption is, with the “sphere of visibility” hypothesis, the universe is very much larger than what we can see. So, someone 13.5 billion light years away from us can see our galaxy as a tiny dot, and in the opposite direction they can see other tiny dots of galaxies, but they can’t see the whole universe, since it is so big, and they can only see within their own “sphere of visibility”.

If the universe happens to be “infinite”, then that’s the way it would be for everyone, everywhere.

So, we are looking out from within the center of our “sphere of visibility”, and someone on the tiny dots of distant galaxies photographed by Hubble are doing the same thing. And both we and they “seem” to be looking at the “whole universe” from the “center” of it, but we are actually looking at a small “sphere” of only what we can see that is inside a much bigger universe, and perhaps inside an infinitely large universe.

I based my hypothesis on some deep-field photos taken several years ago by Hubble, that show more distant galaxies than we could ever see before. Every time Hubble takes more deeper field photos, we see more distant galaxies, rather than an “end to” the universe or an “outer edge” of the universe. So we are actually stuck not knowing how big it really is, since we can’t see outside our own “sphere of visibility”.

Sam5
2010-Jul-24, 10:41 PM
In 2D:


Distance left and right that x can see:

a<- x ->b

----

Distance left and right that y can see:

c<- y ->d

----

a<- x ->b
c<- y ->d

Point d, which y can see, is "further" than x can see.
But in reverse, point a which x can see, is "further" than y can see.


That's correct, assuming a very big universe, or an infinite universe.

pzkpfw
2010-Jul-24, 10:42 PM
They showed the universe having depth. They did not use the “surface of a balloon” analogy.

Sam5, like Tobin Dax, I don't think anyone would disagree with you that this is one way to view the Universe; and it is certainly useful, and people have used that view before.

What I don't understand, is why it has to replace (as opposed to being used with) the “surface of a balloon” analogy.

Different ways (analogies, models, whatever) of viewing a situation will be useful for different things.

The balloon, for example, demonstrates how a thing that is expanding does not need to have a centre. The equivalent of the the “event horizon” for an ant on the ballon is the circle drawn around that ant. It's as far as that ant can see - which isn't all the way around the balloon. The ant is in the centre of their own circle, which expands with them in the centre. That ant asks "where is the centre of the Universe?" (not just its' own circle of the Universe), and the answer is "there is none". (Obviously the “surface of a balloon” analogy isn't perfect, using a 2D surface embedded in our 3D space to demonstrate something, etc...).

Looking at your “sphere of visibility”, we know that an observer at the very edge of what we can see, can see that same distance further on. And so on. The Universe as a whole is bigger than any one observers own “sphere of visibility” (just like it was for that ant on the balloon). Now, If we keep following the line of observers who are at the edge of the previous observers “sphere of visibility”, what happens? Do we (like your second image) hit an "edge" where there is no more to be seen? Do we (like the balloon) wrap around again and eventually get back to the same starting point? Do we just go on forever? Whether the Universe on a whole is "finite and bounded", "finite and unbounded" or "infinite" will have an effect on what the Universe is and whether it has any centre.

Your model doesn't cover that at all. All it really shows is that any observer in the Universe is in the centre of their own viewable/observable part of the Universe. But the Universe as a whole, the entire thing, does it have a centre? Your model doesn't say.

Neither does the balloon, of course, as that model is making a kind of assumption on the structure of the Universe; so my point is that neither model is "better" or "more accurate", just that they are both models a person can use to try to conceptualise what's going on.

Sam5
2010-Jul-25, 02:53 AM
Sam5, like Tobin Dax, I don't think anyone would disagree with you that this is one way to view the Universe; and it is certainly useful, and people have used that view before.

What I don't understand, is why it has to replace (as opposed to being used with) the “surface of a balloon” analogy.

I think it would be better if you ask the lady astronomer who explained the sphere-of-visibility and gigantic-universe models today on the History Channel. I’m sorry that I didn’t notice her name. If I see the show again, I'll try to watch for her name.

Sam5
2010-Jul-25, 04:07 AM
Here’s the History Channel show, part 2 of 3 parts:

http://www.youtube.com/watch?v=_QTkMUj5z78

The key segment starts at about 7:10 into this video clip. What I call our “sphere of visibility”, they call “our light horizon, a sphere 13-1/2 billion light years in all directions.” I would call that “the radius of our sphere of visibility”.

The sphere of our visibility is illustrated and animated at 7:43 into the clip. Notice that the sphere has depth and there are galaxies inside it.

The animation of the spheres of other observers’ visibility starts at about 8 minutes into the clip. This is a high-class animated version of my simple illustrations.

The narrator uses the phrase that this goes “on an on, perhaps to infinity”, so he doesn’t limit the size of the universe and he doesn’t speculate about its actual size, which I think is good, since no one seems to know its actual size.

astromark
2010-Jul-25, 06:13 AM
Being wrong has become a art form... I get a doctorate in error... I am enjoying this discussion but must admit to being somewhat confused by it.

I claim to understand infinity... but have been told I can not. Agree to disagree...

Now I have looking further in one direction than another... ? Yep, a state of confusion is upon me.

Please avoid using mathematical scripts.. I will sit in this corner until you do... try to convince me.

However. If we are talking of distant objects having accelerated into oblivion..

That light will not reach us... Then stop there. I have that on board. Its a language issue.

WaxRubiks
2010-Jul-25, 06:27 AM
I think it would be better if you ask the lady astronomer who explained the sphere-of-visibility and gigantic-universe models today on the History Channel. I’m sorry that I didn’t notice her name. If I see the show again, I'll try to watch for her name.

I just asked her and she mumbled something about dumbing down.....

speedfreek
2010-Jul-25, 11:34 AM
The key segment starts at about 7:10 into this video clip. What I call our “sphere of visibility”, they call “our light horizon, a sphere 13-1/2 billion light years in all directions.” I would call that “the radius of our sphere of visibility”.

The sphere of our visibility is illustrated and animated at 7:43 into the clip. Notice that the sphere has depth and there are galaxies inside it.

But the sphere, with a radius of 13.7 billion light-years, shown with galaxies throughout, is not actually a very accurate picture at all. It is the comoving distance to the edge of our Hubble sphere (or light horizon), but we have seen the light from objects currently beyond that distance, emitted earlier in time.

We have seen no light that originated 13.7 billion light-years away in terms of distance. The furthest proper distance we have seen is only 5.7 billion light-years (the Hubble distance as it was 9.1 billion years ago).

If we take everything and plot where everything was when the light we see was emitted, the sphere is only 5.7 GLy in radius. This is the visible universe, with everything shown as we actually see it. The light-travel time to the edge of this sphere is 9.1 billion years. Any light that has been travelling for more than 9.1 billion years was emitted from a distance closer than 5.7 Gly.

If we take everything and plot where we think everything is today, the sphere is 46.5 Gly in radius. This is the observable universe, with nothing (except local galaxies) shown as we actually see it - it is an extrapolation. The light-travel time to the edge of this sphere is 13.7 billion years, but the edge is not our Hubble horizon, it is the particle horizon, the comoving coordinate that represents where the CMBR was released. Perhaps that is what the astonomer meant when she called it our light-horizon - these terms are often used ambiguously.

So what does the 13.7 GLy radius sphere actually represent, physically? It must represent the (extrapolated) observable universe, 46.5 Gly in radius, but with a light travel time of 13.7 Gy. Outside of our local supercluster, all the galaxies are shown as we think they are, rather than what has actually been observed. The outer third of the sphere represents the "dark ages" and the very edge is the release of the CMBR. The assumption is made that galaxies will have subsequently formed throughout this sphere.

Sam5
2010-Jul-25, 03:12 PM
Speedfreak, if you have any questions about what was said in the History Channel program, I suggest you contact the professional astronomers who were interviewed in the program, and ask them about it.

I think it would be a good idea for the moderators to invite some of those professional astronomers to this board to explain what they know about this subject, and to answer questions about what they said in the program. The whole program is available on YouTube.

speedfreek
2010-Jul-25, 03:32 PM
I have no questions - the explanation was, as Frog march put it, "dumbed down" for the viewers of the History Channel.

I just wanted to try to clarify, for you, how your "sphere of visibility" is not what is actually visible, but is what's thought to have happened to what is visible in the time the light we see has been travelling for. The radius is 13.7 billion years, light travel time, but the sphere is 46.5 billion light-years in radius when thought of in those terms.

The model is indeed a good one, and was touched upon in this famous Scientific American article by Charles Lineweaver and Tamara Davis.
http://www.mso.anu.edu.au/%7Echarley/papers/LineweaverDavisSciAm.pdf

Tobin Dax
2010-Jul-25, 03:47 PM
astromark, the discussion involve two different observers. Picture two people standing on a road on a foggy day. The road has markers every half-kilometer. Each person can only see out to a 1.5 km radius from where they stand due to the fog.

One person stands at the 1.5-km marker, and can see along the road from the 0-km marker to the 3-km marker. The second person stands at the 2.5-km marker. He can see from the 1-km marker to the 4-km marker, so he can see "farther along the road" thank the first person. However, the second person can't see the 0-km marker, so he can't see "as far back" as the first person. Each person can only see 1.5 km out in any direction, but they each see a different section of the road.

When it was said that the second observer can see farther than the first, that was a sloppy use of language and measurement. Each observer can only see a region of identical radius around their position.

George
2010-Jul-25, 04:10 PM
Speedfreak, if you have any questions about what was said in the History Channel program, I suggest you contact the professional astronomers who were interviewed in the program, and ask them about it. I don't see a big problem with astronomers presenting a 13.7 billion lightyear radius since it has taken the CMBR that we see today 13.7 billion years to reach us. But the much more accurate picture is to adjust distance to allow for the huge expansion that has taken place during the 13.7 billion years for the CMBR light we see today -- it has always been there, of course, but we can only see what is arriving to us now. This is what speedfreak is demonstrating and is not in doubt within astronomy. The actual radius, however, is not super accurate since the universe has, essentially, never expanded at a simple linear rate, but perhaps 10% accuracy is close.

speedfreek
2010-Jul-25, 04:42 PM
I don't see a big problem with astronomers presenting a 13.7 billion lightyear radius since it has taken the CMBR that we see today 13.7 billion years to reach us.
Nor do I, as long as we make it clear that it is not a distance through space, it is the look-back time. :)

But expressing the look-back time in light-years can be taken to imply a distance through space, and when that is combined with a nice picture of a sphere containing galaxies it is easy to assume that our observable universe is a sphere full of galaxies with a radius of 13.7 GLy, when the sphere that represents our observable universe (the galaxies as we think they are today) is thought to be a whole lot larger than that, and the sphere that represents our "visible" universe (the galaxies as we see them) is a whole lot smaller than that.

So, I thought we needed to clarify what our "sphere of visibility" actually means. :)

George
2010-Jul-25, 05:27 PM
But expressing the look-back time in light-years can be taken to imply a distance through space, and when that is combined with a nice picture of a sphere containing galaxies it is easy to assume that our observable universe is a sphere full of galaxies with a radius of 13.7 GLy, when the sphere that represents our observable universe (the galaxies as we think they are today) is thought to be a whole lot larger than that, and the sphere that represents our "visible" universe (the galaxies as we see them) is a whole lot smaller than that. Yes, good point, it is both larger and smaller. :) That's why it is helpful to understand why this dichotomy exists. It is not something we normally experience. We know how large objects are and how large space is within our Solar system, but things change quickly beyond this since light must no longer be perceived as something giving us instantaneous information.

The most distant light known is the CMBR. If it could talk to us it would tell us it traveled 13.7 billion lightyears. Since it is customary to size things based on what is seen, then a 13.7 billion light year radius is one way to see it (accidental pun) even though it wasn't 13.7billion light years away when it left home and headed towards us. It was originally much, much closer to us. Anyone know how close?

Of course, it is the expansion that changes everything. One way to see its size is to imagine that we now instantly freeze the entire universe and assume we have the time to go out and measure it. How big would it be if we went out as far as our CMBR's original home? I think that is your 46.5 billion lightyear radius. [I thought it was a little less than that, but I'm not up on it, admittedly.]

speedfreek
2010-Jul-25, 05:59 PM
The most distant light known is the CMBR. If it could talk to us it would tell us it traveled 13.7 billion lightyears. Since it is customary to size things based on what is seen, then a 13.7 billion light year radius is one way to see it (accidental pun) even though it wasn't 13.7billion light years away when it left home and headed towards us. It was originally much, much closer to us. Anyone know how close?
Something around 40 million light-years.

pzkpfw
2010-Jul-25, 07:28 PM
Ha! The History Channel just showed their version of my “sphere of visibility” drawing.

Note "my".


http://i32.tinypic.com/20z4lnc.jpg

http://i27.tinypic.com/14mcqw1.jpg

Sam5's pictures?


[snip] The History Channel did not use my term “sphere of visibility”, but they illustrated it with computer graphics showing 3-D Euclidean spheres, with observers at the center of each one. :)

Note: "my term".


They showed the universe having depth. They did not use the “surface of a balloon” analogy.

I suggest we adopt this “sphere of visibility” and “radius of visibility” point of view as the standard answer to “where are we” questions.

Note "I suggest we adopt".

-----

So it's the same as your preferred model, it seems you've even got pictures you drew of it and you come here to suggest we always use this model, in preference to another...

...but twice, when questioned, you say "go talk to those other people".


I think it would be better if you ask the lady astronomer ...


Speedfreak, if you have any questions about what was said in the History Channel program, I suggest you contact the professional astronomers who were interviewed in the program ...

(The last one is still a dodge, as it was you who brought up this model here in this way, with post 1 of this thread, originally placed in a thread asking where the centre of the Universe is).



This is just sad. Why do you raise this issue if you do not truely wish to discuss it? Why should we bother even replying to you?

astromark
2010-Jul-25, 08:18 PM
Thanks... Tobin Dax. I am comfortable with that.

Now I shall place your fog covered roadway onto my stretching elastic band and think about the ants some more...:eh: and then freeze it all and run out a tape measure.... Ummm... It all helps the understanding. It does.

Tobin Dax
2010-Jul-25, 10:55 PM
I have to agree with pzkpfw.


Well that's great. I'm pleased. :)

You should be pleased that you figured this out on your own (which is great), not that the astronomy community has adopted your idea. I'm afraid that you may think the latter is true, but that isn't the case. That's all I was trying to point out.

RussT
2010-Jul-25, 11:10 PM
The History Channel did not use my term “sphere of visibility”, but they illustrated it with computer graphics showing 3-D Euclidean spheres, with observers at the center of each one.

They showed the universe having depth. They did not use the “surface of a balloon” analogy.

I suggest we adopt this “sphere of visibility” and “radius of visibility” point of view as the standard answer to “where are we” questions.

No one is asking Sam5 the key question here.....so I will

Sam5, based on my bold, are you taking 4D hyperspace out of the equation and suggesting that the 3d sphere of 13.7 billion light years expressed in Euclidean Geometry of a simplified Expanding 3d sphere, is the correct view???

Sam5
2010-Jul-25, 11:23 PM
You should be pleased that you figured this out on your own (which is great), not that the astronomy community has adopted your idea. I'm afraid that you may think the latter is true, but that isn't the case. That's all I was trying to point out.

Tobin, thank you very much for your comments. Now I feel that it’s ok for me to point out that I didn’t start this thread.

I would have never started this thread and certainly not with that particular post and title, because as an OP, it sounds far too arrogant.

A moderator started this thread by taking one of my posts from another thread, removing it from that other thread, and posting it here, out of context, as an OP, which makes it look like I started this thread with a very arrogant OP. But I didn’t.

The OP post in this thread actually belongs in-context, as post #14, in another thread in the Questions and Answers forum, where several people were expressing their opinions, here:
http://www.bautforum.com/showthread.php/105493-Center-of-Universe

I put my post in that other thread specifically because someone brought up the “surface of an expanding balloon” model in that thread, in post #9, and because someone else, in post #13 in that thread, said, “This analogy has been used in the past, but can create more confusion than it alleviates.”

I wanted to point out that I saw a professional astronomer in a documentary on the History Channel yesterday who used the same type of basic “sphere of visibility” model that I have used in the past, and I’ve used it as a way to get around some of the problems of the “expanding balloon surface” model, if the universe is very large or maybe infinite.

This entire model depends on the universe being bigger than is commonly believed or infinite.

I don’t believe that the entire astronomy community has adopted “my idea”. :) I saw a lady astronomer express the same basic idea, and I was proud of that, and for the first time, the History Channel made some animated illustrations of the concept, which I can’t do myself. My drawings were quite crude.

If the universe is not a lot bigger than is commonly believed, or is not infinite, then this model doesn’t work. Perhaps I jumped the gun by suggesting that we all “adopt” this idea, but I did that (on the other thread) in response to the comment on that other thread about how the balloon model “can create more confusion than it alleviates.”

Looks like maybe this “sphere of visibility” model can also create more confusion than it alleviates. :)

speedfreek
2010-Jul-25, 11:44 PM
This entire model depends on the universe being bigger than is commonly believed or infinite.
Only if the common belief is that all we can see is all that there is. I do not think that is what is commonly believed, however. :)


I don’t believe that the entire astronomy community has adopted “my idea”. :) I saw a lady astronomer express the same basic idea, and I was proud of that, and for the first time, the History Channel made some animated illustrations of the concept, which I can’t do myself. My drawings were quite crude.
The idea that the observable universe can be represented as a sphere full of galaxies with us at the centre, and that a different place in the universe will have their own observable sphere full of galaxies, and that depending on the distance between us their sphere may, or may not, overlap with ours, is firmly established in the astronomy community.

baskerbosse
2010-Jul-26, 12:15 AM
Something around 40 million light-years.

-That would mean any features observed at 13.7 billion lightyear's distance would not appear to have the size they should, -but rather the size of something at 40 million lightyear's distance?
At some point, things would appear to be bigger and bigger the further away they are.

/Peter

George
2010-Jul-26, 01:37 AM
-That would mean any features observed at 13.7 billion lightyear's distance would not appear to have the size they should, -but rather the size of something at 40 million lightyear's distance?
At some point, things would appear to be bigger and bigger the further away they are. That is correct, oddly enough, but only to a certain distance, I think.

Jim
2010-Jul-26, 02:37 AM
I would have never started this thread and certainly not with that particular post and title, because as an OP, it sounds far too arrogant.

A moderator started this thread by taking one of my posts from another thread, removing it from that other thread, and posting it here, out of context, as an OP, which makes it look like I started this thread with a very arrogant OP. But I didn’t.

Sam5, if you have a preferred title for this thread, just Report this post and ask for the title to be changed.

baskerbosse
2010-Jul-26, 03:54 AM
That is correct, oddly enough, but only to a certain distance, I think.

I thought so, but why only a certain distance?
If the universe originated from a tiny point, that point would now span the entire sky, would it not?
(Though inflation and opacity would make sure any radiation from that point will never reach us)

/Peter

George
2010-Jul-26, 04:22 AM
I thought so, but why only a certain distance?
If the universe originated from a tiny point, that point would now span the entire sky, would it not?
(Though inflation and opacity would make sure any radiation from that point will never reach us) Because what we see at great distances are galaxies and they did not exist back in the good old days when everyone was a proton. :) So the more distant ones would not have such an enlarged appearance, but I haven't really looked into this oddity. I wouldn't be surprised if I read it in Bill Keel's (ngc3314) book, "The Sky at Einstein's Feet". Maybe he can comment if he sees this.

speedfreek
2010-Jul-26, 05:51 PM
Check out the graph at the bottom of this website: http://www.atlasoftheuniverse.com/redshift.html

It shows the relationship between angular diameter and distance. As we look out into the universe, the further away something is, the smaller it looks, but only up to a certain distance (the Hubble distance, as it was, around 5.7 GLy away, 9 billion years ago). As we look at objects with longer light travel times than 9 billion years, (z=~1.6), we are looking at objects that have always had apparent recession speeds faster than light, and these objects were closer than 5.7 GLy when their light was emitted, so they start looking larger again! A galaxy with a redshift of z=7 was only around 3.5 GLy away when it emitted the light we are now seeing.



In an expanding universe, we see the galaxies near the edge of the visible universe when they were very young nearly 14 billion years ago because it has taken the light nearly 14 billion years to reach us. However, the galaxies were not only young but they were also at that time much closer to us.

The faintest galaxies visible with the Hubble Space Telescope were only a few billion light years from us when they emitted their light. This means that very distant galaxies look much larger than you would normally expect as if they were only about 2 or 3 billion light years from us (although they are also very very faint - see Luminosity Distance).

Angular Diameter Distance is a good indication (especially in a flat universe like ours) of how near the galaxy was to us when it emitted the light that we now see.

The expansion of the universe was so fast, early on, that galaxies relatively close to us were apparently receding superluminally, and from our point of view, so was their light! Only after a few billion years did their light make its way into our Hubble sphere (9 billion years ago), passing galaxies that were 5.7 GLy away at that time. So all the light we see that is older than ~9 billion years was emitted at a closer distance to us than 5.7 GLy, but that light was "moved away" from us as it made its way towards us, by the expansion of the universe.

cjl
2010-Jul-26, 05:54 PM
-That would mean any features observed at 13.7 billion lightyear's distance would not appear to have the size they should, -but rather the size of something at 40 million lightyear's distance?
At some point, things would appear to be bigger and bigger the further away they are.

/Peter

Correct. Here's a graph showing that relation. The vertical units are in kpc per arcsecond, so the peak of that scale is where objects will appear the smallest (relative to their actual size).
http://upload.wikimedia.org/wikipedia/commons/d/d0/Angular-size-redshift-relation.png

Ken G
2010-Jul-27, 09:05 AM
Yes, what the astronomer said is completely standard, we all picture it just like being at the center of an observable sphere and anyone would always view it that way in any universe with a finite age and an isotropic speed of light. The only debatable point, as speedfreak mentioned, is how to put numbers to the distances involved. This is the place where Sam5's personal view, and the popularized statements in the program, seem naive-- there are many different ways to attribute coordinate distances to that "sphere", and indeed three totally separate ones have already been mentioned, all in the context of comoving-frame observers.

Assuming we wish to use a chain of comoving-frame observers between us and the gas emitting the CMB to talk about distances, we can still get three different distances that connect us to that gas. The differences in the results are spectacular-- taking speedfreak's word for it, they result in 40 million LY if you take the comoving frame distances reckoned by that chain of observers at the universe's age when the CMB is emitted, or 13.7 billion LY if you add up the comoving frame distances as reckoned by that chain of observers at each step that the light crosses between any two observers in the chain (i.e., adding up the current comoving-frame distances when the light makes the crossing between any two observers in the chain), or 46.5 billion LY if we use the comoving distance along the complete chain as it stands at the current age of the universe.

As a nitpick of that excellent post, I'm not sure speedfreak should have used the term "proper distances" for the numbers he gave-- by my reckoning, light always travels on null geodesics, so any path taken by light is a zero proper distance. Instead, I'd say those distances, with that interesting maximum at 5.7 LY if you vary over all possible sources we can now see, is the "comoving frame coordinate distance at the time the light was emitted." So astonishingly, if someone asks you "what is the maximum distance we can see", the answer could be zero (using the proper distance between emission and absorption events), it could be 5.7 billion LY (using the maximum distance for a chain of comoving observers added up at the time of emission, and this one would not be CMB emission), it could be 13.7 billion LY (using the maximum distance added up for a chain of comoving observers at the time the light crosses each link in the chain), or it could be 46.5 billion LY (using the maximum distance for a chain of comoving observers added up at the current age of the universe). How's that for record-breaking ambiguity, a question that has four equally correct answers that vary from 0 to 46.5 billion? Such is the consequence of mistaking a question about coordinates for something that is physically specified.

speedfreek
2010-Jul-27, 05:59 PM
I was simply using the term "proper distance" in the same context as Lineweaver and Davis used it: :)

http://arxiv.org/abs/astro-ph/0310808

See the spacetime diagrams on pages 3 and 11 of that paper.

Ken G
2010-Jul-28, 03:33 AM
I was simply using the term "proper distance" in the same context as Lineweaver and Davis used it: :)

http://arxiv.org/abs/astro-ph/0310808

See the spacetime diagrams on pages 3 and 11 of that paper.Ah, I see, it is a different meaning of proper distance. I was talking about the proper distance between the events along the light path (depicted along the curves in their graph) to the event of our seeing the light, which is a zero proper distance all along those curves. They, and you, are talking about the proper distance between the events along those curves, and the Earth at the same comoving age as those events. So their proper distance involves connecting a series of events along the light path with a series of simultaneous events in Earth's history, not a proper distance to us today. I hadn't appreciated those possible different meanings for the term. These options all have to do with the way the cosmological principle gives us a useful convention for talking about global simultaneity in cosmological contexts that simply doesn't exist in other contexts. It is interesting to speculate whether we should take that as a statement of something important about our universe and the meaning of global simultaneity in it, or if it is just a happenstance convenience of a "useful" but not "preferred" coordinate system.

Sam5
2010-Jul-28, 02:02 PM
The only debatable point, as speedfreak mentioned, is how to put numbers to the distances involved. This is the place where Sam5's personal view, and the popularized statements in the program, seem naive-- there are many different ways to attribute coordinate distances to that "sphere", and indeed three totally separate ones have already been mentioned, all in the context of comoving-frame observers.

No, the sphere of visibility model shown during the History Channel program was not “naïve”, it was quite advanced. There was no need to discuss the distances, because it doesn’t matter if they used the distances the galaxies were from our own, when their light we see was emitted, or the distances they appear to be as we see their light now, or the distances they are actually at now, where they moved out to, while their light was traveling to us.

Dr. Michelle Thaller’s sphere of visibility model, as shown in the History Channel documentary, is an excellent model to explain to amateurs and newbies to show that we still have a limited view of the overall universe. Dr. Thaller is currently working for NASA. She was with Caltech when the documentary was made.

Here’s the History Channel show, part 2 of 3 parts:

http://www.youtube.com/watch?v=_QTkMUj5z78

The whole segment leading up to the animation of the spheres of visibility starts around 7:00 minutes into the clip.

After the beginning of that segment starts, Dr. Thaller says:

”We have no reason to believe that the distance we can see is the entire size of the universe. In fact it might be much bigger than that.”

And then the animation shows spheres of visibility for observers a long way away from us.

http://en.wikipedia.org/wiki/Michelle_Thaller
“Michelle Thaller (born in Waukesha, Wisconsin) is an American astronomer and research scientist. Thaller is currently the assistant director for Science Communication at NASA's Goddard Space Flight Center [1] From 1998 to 2009 she was a staff scientist at the Infrared Processing and Analysis Center, and later Manager of the Education and Public Outreach program for the Spitzer Space Telescope, at the California Institute of Technology.[2]”

Ken G
2010-Jul-28, 02:38 PM
No, the sphere of visibility model shown during the History Channel program was not “naïve”, it was quite advanced.I did not intend "naive" as a criticism of a popularized account intended as an introduction to the topic for all levels of educated people, merely to show that the approach to distance is intended for introductory audiences. It's absolutely the standard used in popularized accounts, it just shouldn't be taken too literally, as though it was intended to resolve some kind of argument you seem to imagine is raging about the size of the universe. It's just one way to coordinatize the distance, and it's important to recognize the other possibilities as well. The use of spheres is also a perfectly standard and powerful image that works in any of the coordinate systems, even though the spheres themselves are a bit different in each. No one else on this thread understands why you confer such profound importance to this fact, it's just the way everyone understands visibility in cosmology, and always has ever since the finite age of the universe was inferred.


There was no need to discuss the distances, because it doesn’t matter if they used the distances the galaxies were from our own, when their light we see was emitted, or the distances they appear to be as we see their light now, or the distances they are actually at now, where they moved out to, while their light was traveling to us.
Right, there was no need to attribute any profound importance to the distance scale chosen, and the sphere picture is also obviously the correct one. It's a good, basic, and useful way to talk about what is going on in cosmology, and I'm not aware of anyone on this forum ever claiming anything else.


Dr. Michelle Thaller’s sphere of visibility model, as shown in the History Channel documentary, is an excellent model to explain to amateurs and newbies to show that we still have a limited view of the overall universe.Yes, that's right. It's widely known-- that program is intended to be a first introduction to the topic, and achieves its goals admirably.

After the beginning of that segment starts, Dr. Thaller says:

”We have no reason to believe that the distance we can see is the entire size of the universe. In fact it might be much bigger than that.”Again, I see no evidence why you would imagine anyone on this forum ever thought anything else.



http://en.wikipedia.org/wiki/Michelle_Thaller
“Michelle Thaller (born in Waukesha, Wisconsin) is an American astronomer and research scientist. Thaller is currently the assistant director for Science Communication at NASA's Goddard Space Flight Center [1] From 1998 to 2009 she was a staff scientist at the Infrared Processing and Analysis Center, and later Manager of the Education and Public Outreach program for the Spitzer Space Telescope, at the California Institute of Technology.[2]”
Yes, she's great. I know her quite well.

Sam5
2010-Jul-28, 03:19 PM
The use of spheres is also a perfectly standard and powerful image that works in any of the coordinate systems, even though the spheres themselves are a bit different in each. No one else on this thread understands why you confer such profound importance to this fact, it's just the way everyone understands visibility in cosmology, and always has ever since the finite age of the universe was inferred.



It’s because, year after year, I have seen plenty of beginners and newbies on this board think that what we see of the universe is all there is, or almost all there is, and that’s why they keep coming on this board and asking “where did the big bang happen”, and “where is the center of the universe”. They obviously assume that all we see is all there is to the universe, and they think the “center” and “starting point” of the BB is somewhere within our own sphere of visibility.

Usually, instead of the “sphere of visibility” model being explained to them, the “expanding surface of a balloon” model is explained to them, and they usually don’t understand that. I don’t understand why it is still used here so often, if you and all the other pros knew about the “sphere of visibility” model all along.

Here are some of the balloon model threads:

http://www.bautforum.com/showthread.php/97413-Center-of-the-Universe?

http://www.bautforum.com/showthread.php/86236-The-Balloon-metaphor?

http://www.bautforum.com/showthread.php/83175-Center-of-the-universe?

http://www.bautforum.com/showthread.php/105493-Center-of-Universe?

http://www.bautforum.com/showthread.php/102766-Where-is-the-centre-of-the-Universe?

http://www.bautforum.com/showthread.php/103728-Universe-Why-are-we-in-the-middle?

http://www.bautforum.com/showthread.php/104090-In-what-direction-is-the-center-of-the-universe

This is why I said I think we should adopt the “sphere of visibility” model, to explain the situation to beginners and newbies, and avoid the “balloon” model, since the newbies generally don’t understand it.

The balloon model might be fine for the pros, but it’s not fine for the newbies and the beginners who keep asking those same questions, especially the ones who think all there is, is what we can see and what the Hubble can photograph.

speedfreek
2010-Jul-28, 06:03 PM
Sam, it is a wonder that you didn't mention this thread from mid 2008, which we both contributed to:

http://www.bautforum.com/showthread.php/78051-the-expanding-balloon-theory?

And note one of my responses on page 3:
http://www.bautforum.com/showthread.php/78051-the-expanding-balloon-theory?p=1309283#post1309283


there might be countless other observable universes within the whole universe. When our observable universe had a radius of 10cm, any coordinate in the whole universe that was further than 20cm away would now be the centre of their very own observable universe, the same size as ours, but they don't overlap ours

We go on to discuss the very model you are now suggesting, although in that thread I think it was actually me who first mentioned it. :)


we think the universe must be larger than the part we can see, and so someone somewhere where we cannot see, well, they cannot see us either. But we are all part of the same universe, just different parts that cannot see each other. If the observable universe has a co-moving radius of 46 billion light-years, there may be galaxies 50 billion light-years away whose observable universe overlaps our own, and galaxies 100 billion light-years away whose observable universe is separate from our own (no particles have ever passed between them, due to the rate of expansion).

speedfreek
2010-Jul-28, 07:16 PM
Ah, I see, it is a different meaning of proper distance. I was talking about the proper distance between the events along the light path (depicted along the curves in their graph) to the event of our seeing the light, which is a zero proper distance all along those curves.
To me, that doesn't seem to be a particularly useful measure of distance. ;) To me that is "how much distance the light would have experienced".


They, and you, are talking about the proper distance between the events along those curves, and the Earth at the same comoving age as those events.
Or as I like to put it, how far away from "here" an object was, back when it emitted the light we now see.


So their proper distance involves connecting a series of events along the light path with a series of simultaneous events in Earth's history, not a proper distance to us today. I hadn't appreciated those possible different meanings for the term. These options all have to do with the way the cosmological principle gives us a useful convention for talking about global simultaneity in cosmological contexts that simply doesn't exist in other contexts. It is interesting to speculate whether we should take that as a statement of something important about our universe and the meaning of global simultaneity in it, or if it is just a happenstance convenience of a "useful" but not "preferred" coordinate system.
Surely, how large something looks in the sky is an important, useful and preferable indicator of how far away that thing was from here, when the light we are seeing was originally emitted?

Sam5
2010-Jul-28, 07:16 PM
Sam, it is a wonder that you didn't mention this thread from mid 2008, which we both contributed to:

http://www.bautforum.com/showthread.php/78051-the-expanding-balloon-theory?

:)

Ah, thanks! :)

I’ve been searching for one of my earlier uses of the “sphere of visibility” model and my illustration, which goes back as far as 2007.

It is here on page 2 of that thread:

“Since every time we build a bigger telescope, and look out into the universe further and further, we see more galaxies, and we see no “outer edge”. So, that alone is enough to suggest that we are SOMEWHERE inside a very large universe, and we are looking out like in the next illustration, with the circle in the next illustration being our “sphere of visibility”. Outside that sphere (in the illustration) are many more galaxies in a very large universe.”

http://i32.tinypic.com/20z4lnc.jpg

:)

You present your “grid” model in post 43, and I present my “sphere of visibility” model in post 56. It looks like we are saying the same thing, but your grid model includes the expansion and is (in my opinion) too complex for a newbie or beginner to visualize. Mine’s simpler and conforms to Dr. Thaller’s 3-D animation of the spheres of visibility model (plural, “spheres”) in the History Channel documentary. I hope they keep that on YouTube a long time, because it’s the best overall illustration and summary I’ve seen on TV or the internet so far, and it’s easier for beginners to understand. :)

speedfreek
2010-Jul-28, 08:03 PM
So you did! :) Sorry, I missed that (was scanning the thread quickly and skipped when I saw the reference to Eddington! my bad).

But as we are saying, it is a completely standard and often used way to describe the situation (I was describing it myself later in that thread too!). It is indeed good for beginners, and the only reason I really posted in this thread was when I saw your post quoting the figures the astronomer gave for the radius of the observable universe. I would not normally interject based on those figures, but when they are tied in to our "sphere of visibility", illustrated with a graphic showing a sphere filled with galaxies, misconceptions could be introduced.

We do actually see a spherical space around us, filled with galaxies, with a radius of 13.7 billion years, but the most distant looking galaxies look a lot less than 13.7 Gly away, and the longest travelling light came from a place that is now a lot further away than 13.7 Gly.

So it all depends what you mean by "sphere of visibility", and how you explain that to the uninitiated.

pzkpfw
2010-Jul-28, 09:03 PM
This is why I said I think we should adopt the “sphere of visibility” model, to explain the situation to beginners and newbies, and avoid the “balloon” model, since the newbies generally don’t understand it.

So now you're back to recommending this model over the other - yet earlier when it was discussed and questioned your replies were to "ask the people involved in the documentary". That's still sad.

Sam5: how exactly does "your" model answer the question "where is the centre of the Universe"?

Sam5
2010-Jul-28, 09:19 PM
So you did! :) Sorry, I missed that (was scanning the thread quickly and skipped when I saw the reference to Eddington! my bad).

But as we are saying, it is a completely standard and often used way to describe the situation (I was describing it myself later in that thread too!). It is indeed good for beginners, and the only reason I really posted in this thread was when I saw your post quoting the figures the astronomer gave for the radius of the observable universe. I would not normally interject based on those figures, but when they are tied in to our "sphere of visibility", illustrated with a graphic showing a sphere filled with galaxies, misconceptions could be introduced.

We do actually see a spherical space around us, filled with galaxies, with a radius of 13.7 billion years, but the most distant looking galaxies look a lot less than 13.7 Gly away, and the longest travelling light came from a place that is now a lot further away than 13.7 Gly.



Well, I’m pleased. :)

We were talking about the same thing, just using different methods of explaining it.

I think your “grid” and multiple-distance method is for more advanced astronomy buffs who already know a lot about the BB, but I intended my sphere of visibility model to be for the newbies and very early beginners. It’s basically the same as Dr. Thaller’s animated model in the History Channel documentary. She mentioned the 13.7 billion light-year distance. I think she left out the different distances of your model, because that’s probably too complex to explain to the “general public” in a short documentary segment.

Sam5
2010-Jul-28, 09:23 PM
Sam5: how exactly does "your" model answer the question "where is the centre of the Universe"?

My model doesn’t have a “center of the universe”. It has only a center of a sphere of an observer’s visibility. Like on a foggy day, with a visibility of only 3 feet in all directions. Our eyes are at the center of that sphere of visibility.

Jeff Root
2010-Jul-28, 10:11 PM
pzkpfw,

I suspect that you completely misunderstood Sam's intent.

I think he said to ask people involved in the documentary about why
they used the model they did, which obviously only they can answer.

Sam's sphere of visibility model has advantages over the balloon
model, and the balloon model has advantages over the sphere of
visibility model. Mainly, they each demonstrate different aspects
of the Universe's geometry.

Coincidentally, I just wrote a post here within the last 24 hours in
which I mentioned that I discovered an interesting quirk of the human
visual system, some thirty years ago. I stressed that yes, I *did*
discover it, but unquestionably, lots and lots of people discovered
it long before I did, and I'm sure the effect has a name. Sam was
just saying, Hey, see! I'm not the only one who thinks this is a
good idea.

-- Jeff, in Minneapolis

pzkpfw
2010-Jul-28, 10:27 PM
My model doesn’t have a “center of the universe”. ...

Right; which is exactly why I don't think either model needs to replace the other; they cover different issues.

You say your model should be used to answer the "where is the centre of the Universe" question - but it doesn't cover it at all.

The balloon shows why there doesn't "need" to be a centre in the first place; even if the Universe isn't infinite.

Neither model is "perfect"; they are both useful illustrations - of different aspects of the Universe.

Sam5
2010-Jul-28, 11:07 PM
Right; which is exactly why I don't think either model needs to replace the other; they cover different issues.

You say your model should be used to answer the "where is the centre of the Universe" question - but it doesn't cover it at all.





Of course it doesn’t “cover it all”. The balloon model doesn’t “cover it all” either.

My model and Dr. Thaller’s model should be used for newbies and beginners. They are the ones who keep coming on this board and asking the question “where is the center of the universe?”.

Many of them think that Hubble has photographed the whole universe or most of it, and they think it’s a sphere, so they think they can look out at night and see the center of it, or the direction of the center, just as they can see the center of the solar system and the direction of the center of our galaxy.

Newbies see in 3-D. The balloon model is a curved 2-D model of a 4-D concept. You can’t throw the balloon model at newbies and expect them to grasp it instantly.

Advanced astronomy buffs already know the balloon model anyway, and they usually don’t come on this board and ask that question about “where is the center of the universe?”.

Speedfreak’s multi-distance “grid” model might be more technically accurate, but it’s too complex for newbies too.

You are worried about something you don’t need to be worried about.

speedfreek
2010-Jul-28, 11:14 PM
But neither my old "grid" explanation or your sphere of visibility actually give any explanation as to how the universe might not have a centre, they simply don't say anything about it. All either of them say is that there is more out there than we can see, and others might think the same thing. Whereas the balloon model shows how you might circumnavigate the universe and end up where you started, thus showing that it has no edge nor centre. I can also do this with my 3d Euclidean grid, if we imagine it wrapped onto the surface of a 3-sphere, but this is way beyond the requirements in the OP. The sphere of visibility is a good illustration of the concept of the "observable universe", but how does it show that there may be no centre to the universe?

Sam5
2010-Jul-28, 11:21 PM
But neither my old "grid" explanation or your sphere of visibility actually give any explanation as to how the universe might not have a centre, they simply don't say anything about it.



That’s not the question. That’s not in my OP. That wasn’t in Dr. Thaller’s “sphere of visibility” segment in the History Channel documentary.

That can be the topic of a different thread. Why don’t you start one? :)

speedfreek
2010-Jul-29, 12:14 AM
My model and Dr. Thaller’s model should be used for newbies and beginners. They are the ones who keep coming on this board and asking the question “where is the center of the universe?”.

So, where is the centre of the universe? I have heard the universe is expanding and wondered where it was expanding from? Where is the origin point, the starting point?

Sam5
2010-Jul-29, 12:34 AM
So, where is the centre of the universe? I have heard the universe is expanding and wondered where it was expanding from? Where is the origin point, the starting point?

LOL, you’re asking me?? I think it’s turtles all the way down! But we can’t see them because they aren’t within our “sphere of visibility”. :)

pzkpfw
2010-Jul-29, 12:46 AM
Of course it doesn’t “cover it all”. The balloon model doesn’t “cover it all” either.

I agree with this statement. However I would point out that what I wrote was not “cover it all”. Look again. The meaning of my comment was very different to what you think.


My model and Dr. Thaller’s model should be used for newbies and beginners.

You've not yet shown why. (In the context of "instead of..." another model).


They are the ones who keep coming on this board and asking the question “where is the center of the universe?”.

But you've already admitted "your" model doesn't answer this!


Many of them think that Hubble has photographed the whole universe or most of it, and they think it’s a sphere, so they think they can look out at night and see the center of it, or the direction of the center, just as they can see the center of the solar system and the direction of the center of our galaxy.

This is a valid concern, and "your" model is a nice illustration for it. (Except your second image).


Newbies see in 3-D. The balloon model is a curved 2-D model of a 4-D concept. You can’t throw the balloon model at newbies and expect them to grasp it instantly.

I don't expect them to always grasp it "instantly".

But if "your" model doesn't answer the question, how is it "better"?


Advanced astronomy buffs already know the balloon model anyway, and they usually don’t come on this board and ask that question about “where is the center of the universe?”.

That applies whichever model is used.


Speedfreak’s multi-distance “grid” model might be more technically accurate, but it’s too complex for newbies too.

That depends on the reader; and speedfreak is welcome to present that model where it seems appropriate, just as you are welcome to present whichever model you think helps.


You are worried about something you don’t need to be worried about.

That applies perhaps to both of us?

Ken G
2010-Jul-29, 08:36 AM
To me, that doesn't seem to be a particularly useful measure of distance. ;) To me that is "how much distance the light would have experienced".
It is that, but it is also the difference between conceiving of distance as being between events, or being between objects. "Proper" distance is supposed to be an invariant, because "proper" things usually are, but if distances are between objects and not events, then "proper" distances between objects depend on how you select simultaneous events for the two objects. That means it becomes dependent on the coordinate choice. So to me, if it depends on coordinate choice, it's not "proper." But I admit that in cosmology, the cosmological principle really changes the rules-- it gives us a "natural", and possibly even "preferred", though maybe just "convenient", coordinate system (the comoving age) for defining simultaneous events along the world lines of two different objects. So it gives us a kind of hybrid meaning of "proper distance" between objects-- it's kind of proper, because all observers can agree on it, but only if all observers are willing to subjugate their own perceptions of space and time to the authority of the "comoving frame."


Or as I like to put it, how far away from "here" an object was, back when it emitted the light we now see.

Right, and there's that implicit assumption that "back when" means the same thing for "here" that it does for "over there", though normally that is just a matter of coordinates. In one way, it's kind of antithetical to the spirit of relativity to assert an absolute meaning for time, but comoving age is pretty much just that. I am not sure that the cosmological principle does not violate the whole spirit of relativity-- at the least, the two are strange bedfellows. After all our effort to rid our local spacetime of the concept of an aether, has not this type of cosmological language returned us to an aether frame?


Surely, how large something looks in the sky is an important, useful and preferable indicator of how far away that thing was from here, when the light we are seeing was originally emitted?Yet it gives a pretty weird distance, where the CMB is coming from only 40 million LY away, and quasar light is coming from billions of LY away. That's a pretty awkward coordinate, though the apparent size is indeed a nice thing to be able to understand. I think you have to give the whole story, and say something like, "when we look at the CMB, we see light from gas that was only 40 million LY away when it did the emitting, but the light traveled through 13.7 billion LY of accumulated comoving-frame distance from the point of view of the matter it passed, and came from a place that is now some 46.5 billion LY away, in the process tracing a null geodesic through spacetime that represents a zero invariant separation between the emission and absorption events." At least that way one is not marrying a particular number for the distance, and the full complexity that is really there can come out.

Ken G
2010-Jul-29, 08:55 AM
On the issue of every observer seeing spheres around themselves, it is a completely standard image that I've encountered countless times over the last 25 years or so, and I'm sure it has been around since the 1930s. Why Sam5 thinks it's "his" model, or why he thinks anyone ever thought about it any differently, is somewhat mysterious. But we can all agree it is a good way to separate the objects we can see from those we cannot, and we can all agree that it does not cover at all the issue of where the center is, that is the purvey of the balloon picture (or the rising raisin bread, which is better because it is 3D, but worse because you can't put time in the picture). On the issue of whether the whole universe is just what we can see, I also don't understand why Sam5 views that as controversial. Language like "the observable universe", to distinguish it from the whole universe, is completely standard, though I don't know when that became the standard (LeMaitre himself might have imagined we are seeing the whole enchilada, the "primeval atom", but I believe that was dispensed with pretty quickly). But yes, the spheres are a simple way to discuss that-- and the distances attached to those spheres are very tricky.

speedfreek
2010-Jul-29, 05:41 PM
LOL, you’re asking me?? I think it’s turtles all the way down! But we can’t see them because they aren’t within our “sphere of visibility”. :)

Yes, I am asking you because you keep saying your model should be used to answer that very question. :)

It seems your answer is that we cannot see the centre of the universe because it is not within our sphere of visibility. So, a newbie would presumably go away thinking that the centre of the universe is somewhere else...

Sam5
2010-Jul-29, 06:43 PM
Yes, I am asking you because you keep saying your model should be used to answer that very question. :)


It's Dr. Thaller's model, as shown on the History Channel. I’ve said that Dr. Thaller’s “sphere of visibility” model should be used to show beginners and newbies what we see from our viewing position somewhere inside a universe that is vast and that might be infinite, so they will stop asking “where is the center of the universe”, since we see no “center” of the universe and we know of no “center” of the universe and we are seeing only a small part of a universe that might be infinite in size, and with no "center".

I don’t know of any center. We don’t see any evidence of any center of the universe. I think the consensus among the pros is that the universe doesn’t have a center. The History Channel’s sphere of visibility model has no center of the universe, and my old illustration has no center. It has only a “center of our sphere of visibility”.

http://i32.tinypic.com/20z4lnc.jpg

I couldn't show an infinitely large universe in my drawing, so that's why my drawing has square edges. :)

pzkpfw
2010-Jul-29, 07:20 PM
It's Dr. Thaller's model, as shown on the History Channel.

Sigh. Then why do you keep saying it's your model too?


I’ve said that Dr. Thaller’s “sphere of visibility” model should be used to show beginners and newbies what we see from our viewing position somewhere inside a universe that is vast and that might be infinite, so they will stop asking “where is the center of the universe”, since we see no “center” of the universe and we know of no “center” of the universe and we are seeing only a small part of a universe that might be infinite in size, and with no "center".

I don’t know of any center. We don’t see any evidence of any center of the universe. I think the consensus among the pros is that the universe doesn’t have a center. The History Channel’s sphere of visibility model has no center of the universe, and my old illustration has no center. It has only a “center of our sphere of visibility”.

Are you even going to acknowledge the question of whether each model illustrates different things?


http://i32.tinypic.com/20z4lnc.jpg

I couldn't show an infinitely large universe in my drawing, so that's why my drawing has square edges. :)

But what about the second drawing in your post?

That one seems to indicate an edge to the Universe, which implies a centre.

Sam5
2010-Jul-29, 08:29 PM
But what about the second drawing in your post?

That one seems to indicate an edge to the Universe, which implies a centre.

No, this is my second drawing:

http://i27.tinypic.com/14mcqw1.jpg

It looks like you’ve altered my second drawing. Why did you alter it?

My second drawing would be what someone would see if they were out near an “edge” or a “boundary” of a finite spherical universe. But that is not us, it’s not what we see, and it’s not our universe.

pzkpfw
2010-Jul-29, 08:49 PM
No, this is my second drawing:

http://i27.tinypic.com/14mcqw1.jpg

It looks like you’ve altered my second drawing. Why did you alter it?

I thought it was pretty clear: what I annotated was to demonstrate what my question about your image was (surely you saw your own image, so you'd see the difference) and even included a little note at the bottom right. (As well as uploading/attaching the annotated version, as opposed to simply re-using your own "tinypic" link).

(For that matter, you've not acknowledged misquoting me back a page ago).


My second drawing would be what someone would see if they were out near an “edge” or a “boundary” of a finite spherical universe. But that is not us, it’s not what we see, and it’s not our universe.

What do you mean, now, "it's not our universe"?

Do you mean here 1) our "visible Universe" (refering to the smaller circle) or do you mean 2) the Universe (refering to the diagram as a whole)?

If 1) then you are still impling an edge to the universe (that someone, not us, would see), which would seem to imply a centre.
If 2) then I'd ask why you even posted that second image in your post (that became post 1 of this thread).

It seems to me you are going to confuse those people who ask "where is the centre of the Universe?", when that's what you apparently want to avoid.


What "your" (whose?) model is very good at showing, is that what we can see, our entire visible Universe that we are the centre of, is not the entire Universe; but it's not very good at all in showing an answer to the question "where is the centre of the Universe?". Your model implies that if the Universe is finite, it has an edge - and thus would have a centre. That's non-mainstream, as you noted earlier: "I think the consensus among the pros is that the universe doesn’t have a center".

Sam5
2010-Jul-29, 09:03 PM
I don’t know what you are getting at. The link to the History Channel program is easy to find, and Dr. Thaller’s animation is easy to understand. Maybe she can explain the situation to you better than I can.

http://www.youtube.com/watch?v=_QTkMUj5z78

The whole segment leading up to the animation of the spheres of visibility starts around 7:00 into the clip.

After the beginning of that segment starts, Dr. Thaller says:

”We have no reason to believe that the distance we can see is the entire size of the universe. In fact it might be much bigger than that.”

And then the animation shows spheres of visibility for observers a long way away from us.

pzkpfw
2010-Jul-29, 09:22 PM
I don’t know what you are getting at. The link to the History Channel program is easy to find, and Dr. Thaller’s animation is easy to understand. Maybe she can explain the situation to you better than I can.

http://www.youtube.com/watch?v=_QTkMUj5z78

The whole segment leading up to the animation of the spheres of visibility starts around 7:00 into the clip.

After the beginning of that segment starts, Dr. Thaller says:

”We have no reason to believe that the distance we can see is the entire size of the universe. In fact it might be much bigger than that.”

And then the animation shows spheres of visibility for observers a long way away from us.

And how does that explain "where is the centre of the Universe"?

(I have no issue with the "spheres of visibility" model, nor what it is trying to illustrate. I think it's very good, in it's own way. My only issue is in your claim that it is "better" than the "balloon model" and it should be used instead of it. You've utterly failed to explain that.)

Jeff Root
2010-Jul-29, 09:49 PM
The sphere of visibility model is better in that it is easier for most
people to understand than the balloon model. Much easier, I'd say.
It shows at least one reason why there is no known center of the
Universe, while the balloon model shows how it is possible for a
universe to have no center. But it only shows that if the model is
understood. It doesn't show that if the model is misunderstood.

-- Jeff, in Minneapolis

speedfreek
2010-Jul-29, 11:05 PM
So it gives us a kind of hybrid meaning of "proper distance" between objects-- it's kind of proper, because all observers can agree on it, but only if all observers are willing to subjugate their own perceptions of space and time to the authority of the "comoving frame."
Interesting. I doubt any observer would be unwilling to subjugate their own perceptions of space and time to the authority of the comoving frame, when the "proper distance" is the distance they see things to be, by apparent size. It is how things actually look to be!

How big it looks in the sky tells us how far away it was when the light left it (if we think we know its absolute size). What could be a more obvious choice? The visible universe has a radius of less than 6 billion light-years and the early universe looks closer to us than the later universe!

The history of our expanding universe, laid out before our very measuring instruments!


After all our effort to rid our local spacetime of the concept of an aether, has not this type of cosmological language returned us to an aether frame?
Not locally, at least. But it is the only thing we might legitimately term a global frame, based on the simplest principle - right now, the age of the universe is the same, everywhere. This of course brings up the issue that there is no absolute definition of simultaneity across the universe, but surely we can relax that rule a little if all those comoving world lines lead back to the same original event?


Yet it gives a pretty weird distance, where the CMB is coming from only 40 million LY away, and quasar light is coming from billions of LY away. That's a pretty awkward coordinate, though the apparent size is indeed a nice thing to be able to understand. I think you have to give the whole story, and say something like, "when we look at the CMB, we see light from gas that was only 40 million LY away when it did the emitting, but the light traveled through 13.7 billion LY of accumulated comoving-frame distance from the point of view of the matter it passed, and came from a place that is now some 46.5 billion LY away, in the process tracing a null geodesic through spacetime that represents a zero invariant separation between the emission and absorption events." At least that way one is not marrying a particular number for the distance, and the full complexity that is really there can come out.

Yes, I agree that you have to give the full story (although I think the "beginners" might be able to get by without the zero invariant separation part! I'm not sure what I'm supposed to do with it myself! ;)). I think it works best when you tie it all in with the range of cosmological redshifts, which really helps tell the story of why we think these things.

Jeff Root
2010-Jul-30, 03:30 AM
You do say that "you have to give the full story", but I think you
need to be careful about throwing something like:


... the early universe looks closer to us than the later universe!
The later Universe is between us and the earlier Universe.
Things being in front of other things pretty much always trumps
relative size when judging distances.

So the early Universe doesn't look much like it is closer.
Just kinda sorta.

-- Jeff, in Minneapolis
______________________________

The Universe hasn't got much Spam in it...

Van Rijn
2010-Jul-30, 07:24 AM
And how does that explain "where is the centre of the Universe"?


For a finite universe, an area on the surface of a sphere is one way to picture it. There is no center.

For an infinite universe, an area on an infinite plane is another way to picture it. There is no center.

There are more complicated ways to look at it, but those seem equally straightforward to me.

pzkpfw
2010-Jul-30, 09:10 AM
For an infinite universe...

Of course, but I'm trying to see if Sam5 really understands such a pre-condition in that model (and the follow-up questions that pre-condition might then raise).

(Also, you'll note his second image was of a Universe that isn't infinite. I was trying to draw out of him why he presented that.)



... equally ...

This is of course another thing I'm hoping Sam5 will see.

Ken G
2010-Jul-30, 11:44 AM
Interesting. I doubt any observer would be unwilling to subjugate their own perceptions of space and time to the authority of the comoving frame, when the "proper distance" is the distance they see things to be, by apparent size. It is how things actually look to be!Not necessarily-- to break strongly from the comoving frame, you need to move relativistically against the Hubble flow, and then you'll get all kinds of aberration effects. How things look to be is a slippery slope! Do we believe our eyes, or that darn comoving frame coordinate system? Relativity was supposed to liberate us from the shackles of external coordinates, and be able to make our own picture that fits our own frame. Cosmology is often going the other direction, and returning us to very aether-like thinking. Yet we need the cosmological principle to help us tell a coherent story. I think the history of our universe is quite relativity challenged!

But it is the only thing we might legitimately term a global frame, based on the simplest principle - right now, the age of the universe is the same, everywhere. This of course brings up the issue that there is no absolute definition of simultaneity across the universe, but surely we can relax that rule a little if all those comoving world lines lead back to the same original event?
Right, it's something of a conundrum.



Yes, I agree that you have to give the full story (although I think the "beginners" might be able to get by without the zero invariant separation part! I'm not sure what I'm supposed to do with it myself! .It's a causality boundary-- zero invariant separation is the line between events that can have one affect the other, and events that cannot have that relationship. That's the "real meaning of separation"-- spatial separation by itself turns out to have been something of a hoax.

I think it works best when you tie it all in with the range of cosmological redshifts, which really helps tell the story of why we think these things.Yes, which is exactly what you did when you brought in all those different distances. Bravo!

speedfreek
2010-Jul-30, 05:16 PM
The later Universe is between us and the earlier Universe.
Things being in front of other things pretty much always trumps
relative size when judging distances.

So the early Universe doesn't look much like it is closer.
Just kinda sorta.

-- Jeff, in Minneapolis.

Yes, that is true - the comment I made was supposed to be light hearted, as it was based on the cosmological usage of "proper distance". We can see a galaxy at z=7 that is obviously behind a galaxy at z=1, and yet the z=7 galaxy has an angular size that tells us it was closer to us when it emitted the light we now see (3.5 Gly, 12.9 Gyrs ago) than the z=1 galaxy was when it emitted the light we see (5.4 Gly, 7.7 Gyrs ago).

If you use luminosity, redshift (comoving distance) or light-travel time, the z=7 galaxy looks a lot more distant than the z=1 galaxy, but if you use apparent size, the z=7 galaxy looks a lot closer! We see things where they were when the light left them.

Ken G
2010-Jul-30, 05:39 PM
If you use luminosity, redshift (comoving distance) or light-travel time, the z=7 galaxy looks a lot more distant than the z=1 galaxy, but if you use apparent size, the z=7 galaxy looks a lot closer! We see things where they were when the light left them.And never was there a clearer statement of how tricky the concept of distance is in cosmology! Let anyone who thinks the Big Bang is just a bunch of stuff moving away from us through a special-relativistic kind of coordinate system (you know who you are), cut out the above statement and paste it to your refrigerator.

speedfreek
2010-Jul-30, 05:53 PM
Not necessarily-- to break strongly from the comoving frame, you need to move relativistically against the Hubble flow, and then you'll get all kinds of aberration effects. How things look to be is a slippery slope! Do we believe our eyes, or that darn comoving frame coordinate system? Relativity was supposed to liberate us from the shackles of external coordinates, and be able to make our own picture that fits our own frame. Cosmology is often going the other direction, and returning us to very aether-like thinking. Yet we need the cosmological principle to help us tell a coherent story. I think the history of our universe is quite relativity challenged!

But the observer who was moving relativistically against the Hubble flow would know they were moving relativistically against the Hubble flow (or the CMBR frame), unless they had no window to the universe around them. Those aberration effects are a dead give away - most of the universe seems to be in front of you and there are directional doppler shifts, all of which can be calculated out in order to measure the universe around you.

So I still think someone moving relativistically against the Hubble flow would be willing to subjugate their perceptions of time of space to the authority of the comoving frame. Why bother trying to measure the universe without subtracting for your own local conditions? It is what we do here on Earth, naturally, when we want to measure the age or size of the observable universe - we adjust the figures to account for our own movement relative to the CMBR, or our local gravitational conditions. Is it not the obvious thing to do, wherever you are?


It's a causality boundary-- zero invariant separation is the line between events that can have one affect the other, and events that cannot have that relationship. That's the "real meaning of separation"-- spatial separation by itself turns out to have been something of a hoax.
So that's what it means! ;) Thanks, I now have another way to describe our past light cone.

Ken G
2010-Jul-30, 08:39 PM
But the observer who was moving relativistically against the Hubble flow would know they were moving relativistically against the Hubble flow (or the CMBR frame), unless they had no window to the universe around them. Those aberration effects are a dead give away - most of the universe seems to be in front of you and there are directional doppler shifts, all of which can be calculated out in order to measure the universe around you.But what to make of them? The Michelson-Morely experiment didn't say the Earth wasn't orbiting the Sun, it said the laws of physics didn't care it was orbiting the Sun. So that meant the Earth orbits the Sun because it pleases us to say so. Similarly, what the Hubble flow is doing just provides a sensible coordinate choice, one with flashing lights and buzzers attached to it. But my own frame always has lights and buzzers-- it's what I live. My proper time should be just as good as comoving age, even if it says my universe is 13.7 years old instead of 13.7 billion.



So I still think someone moving relativistically against the Hubble flow would be willing to subjugate their perceptions of time of space to the authority of the comoving frame. Why bother trying to measure the universe without subtracting for your own local conditions?Because relativity says that I should never have to subtract for my own local conditions, that's pretty much the principle of relativity. If the laws are built so that I never have to do that, yet the cosmological principle entreats me to do that, we have a bit of a philosophical quandary. Relativity says that our motion relative to the Hubble flow doesn't mean we are really moving, it just means we have a motion relative to the Hubble flow. We can still trust our eyes and say we are stationary and the Hubble flow is flowing past us, it's an option the laws of physics bend rather over backward to allow.

It is what we do here on Earth, naturally, when we want to measure the age or size of the observable universe - we adjust the figures to account for our own movement relative to the CMBR, or our local gravitational conditions. Is it not the obvious thing to do, wherever you are?It's a natural convention, but it's pure convention. No law of physics requires it, the universe seems ambivalent on the matter. At an international conference, astronomers are expected to present in English, but there is nothing about English that is required for astronomy.

George
2010-Jul-30, 08:58 PM
Yes, that is true - the comment I made was supposed to be light hearted, as it was based on the cosmological usage of "proper distance". We can see a galaxy at z=7 that is obviously behind a galaxy at z=1, and yet the z=7 galaxy has an angular size that tells us it was closer to us when it emitted the light we now see (3.5 Gly, 12.9 Gyrs ago) than the z=1 galaxy was when it emitted the light we see (5.4 Gly, 7.7 Gyrs ago). Wow! That's quirky! All because of our earlier distance and velocity (=expansion). This needs to be added to the list of new astronomy terms needed. Something that combines angular size and velocity....angulocity? :)

speedfreek
2010-Jul-30, 08:59 PM
My proper time should be just as good as comoving age, even if it says my universe is 13.7 years old instead of 13.7 billion.
Yes, and your proper time is the right time for you. It is what you measure the universe to be. But does the rest of the universe agree? ;)



Because relativity says that I should never have to subtract for my own local conditions, that's pretty much the principle of relativity. If the laws are built so that I never have to do that, yet the cosmological principle entreats me to do that, we have a bit of a philosophical quandary. Relativity says that our motion relative to the Hubble flow doesn't mean we are really moving, it just means we have a motion relative to the Hubble flow. We can still trust our eyes and say we are stationary and the Hubble flow is flowing past us, it's an option the laws of physics bend rather over backward to allow.

Perhaps we have to relax some of those relativistic principles when dealing with the universe itself - the whole thing. Is this "flouting" the rules of relativity, or acknowledging that cosmology is trying to define the whole universe in the terms of a global reference frame?

George
2010-Jul-30, 09:07 PM
But what to make of them? The Michelson-Morely experiment didn't say the Earth wasn't orbiting the Sun, it said the laws of physics didn't care it was orbiting the Sun. So that meant the Earth orbits the Sun because it pleases us to say so. Similarly, what the Hubble flow is doing just provides a sensible coordinate choice, one with flashing lights and buzzers attached to it. But my own frame always has lights and buzzers-- it's what I live. My proper time should be just as good as comoving age, even if it says my universe is 13.7 years old instead of 13.7 billion. Yes, but does the Hubble Flow give us a max. age, making it a favored flavor, perhaps?

Ken G
2010-Jul-30, 11:03 PM
Perhaps we have to relax some of those relativistic principles when dealing with the universe itself - the whole thing. Is this "flouting" the rules of relativity, or acknowledging that cosmology is trying to define the whole universe in the terms of a global reference frame?It depends on if you mean "cosmology" as a sociological phenomenon, an effort to generate a language for talking about our universe's shared history, or if you mean "cosmology" as a physical theory that makes predictions and conforms to a minimum set of axioms and laws. All too often, those two forms get confused-- and it's because of the need for a particular coordinatization for the sociological version, but not for the physical version.

Ken G
2010-Jul-30, 11:17 PM
Yes, but does the Hubble Flow give us a max. age, making it a favored flavor, perhaps? An inertial observer has the maximum proper time between any two events, of the observers who are at both, but you can get larger times between those events by resorting to the joint coordinates of two different observers at the two events, like the comoving-frame observers. I'm sure you can find coordinate systems that take longer time than the comoving frame time, so I don't know to what extent it is a maximum, but there is certainly something special about comoving-frame times, stemming from the cosmological principle. But this happens all the time in physics-- you can have a special arrangement of the matter such that a particular coordinatization recommends itself quite clearly (like the rotating frame of the Earth used for people to talk about their daily lives, complete with sunrises and coriolis effects and the "downward force of gravity"). But we don't usually confuse that with what is really happening in some absolute kind of way.

speedfreek
2010-Jul-31, 12:33 AM
It depends on if you mean "cosmology" as a sociological phenomenon, an effort to generate a language for talking about our universe's shared history, or if you mean "cosmology" as a physical theory that makes predictions and conforms to a minimum set of axioms and laws. All too often, those two forms get confused-- and it's because of the need for a particular coordinatization for the sociological version, but not for the physical version.

I was rather hoping that the former reflected the latter! I was under the impression that the cosmological principle underpins the best model in modern physical cosmology, which has predicted the figures I have been quoting and expresses them using the various distance measures we have been discussing.

Although, I must admit you don't hear much about conformal time, where the rate of expansion at the particle horizon is normalised to c and so the age of the universe is 46 billion years! (Do they do this just so the diagrams are easier to draw?)

But I suspect I have missed your meaning here.

Ken G
2010-Jul-31, 05:21 AM
I was rather hoping that the former reflected the latter!But we know it doesn't, because we know that the laws of physics used in cosmology are expressly coordinate independent. That means the laws can be written without ever mentioning a comoving observer, it's all done with the invariant separations (that least intuitive of all the ways of talking about distance!). It's true that we have a particular observational platform to use to test the theory, and that platform may lend itself better to certain coordinates (and if we moved highly relativistically through the Hubble flow, our observations would not be conveniently expressed in comoving coordinates). It's also true that the equations of the theory may not be solvable until a particularly well-chosen coordinate is applied to them, and that's where the cosmological principle helps out so much. But it appears to be an important aspect of the theory (relativity) that all its laws can be written in coordinate-free form-- that is the "language" that reality uses to talk about itself (if we have the laws right, which is a whole other issue). Reality doesn't need assumptions and coordinates that simplify the calculation, it just satisifies the laws subject to the constraints, as expressed in any coordinates.


I was under the impression that the cosmological principle underpins the best model in modern physical cosmology, which has predicted the figures I have been quoting and expresses them using the various distance measures we have been discussing. The cosmological principle is not itself a law of physics, it is a simplification, like assuming spherical symmetry to apply Newton's laws of gravity to the Earth. Newton's laws work for arbitrarily shaped objects, but we usually apply it to spheres (even though no spheres actually exist), because they are so darn much simpler, and many objects are very close to being spheres. So there's a difference between a law, and a simplification adopted in solving the equations that stem from the law.

In mundane relativity, we have coordinate-free laws, but we might wish to apply them to situations where one particular coordinate makes the solution tractable (say, a Schwarzschild black hole solution). In cosmology, we do the same-- we use the cosmological principle, in concert with comoving coordinates, to make the solution tractable, and it seems to be a close approximation to the reality. But if we have coordinate-free laws, we say that no observer must subjugate their perspective to some other system than what they themselves observe, while at the same time, we say they might be well advised to choose a particular coordinate system to make the calculations easier. If those coordinates recommend themselves clearly enough, they will spawn a whole language that uses them, but that language will never be language of the reality itself, which is fundamentally coordinate-free-- it will just be the language of computational convenience.

Now I grant you, it's a pretty artificial distinction between what is the language of a physical theory, and what is the language of computational convenience in regard to that theory-- since the goal of science is to understand, the human element always appears somewhere in the process. But that doesn't mean cosmological language isn't a sociology experiment, it means that sociology and physics are not as widely separated as we might like to imagine.


Although, I must admit you don't hear much about conformal time, where the rate of expansion at the particle horizon is normalised to c and so the age of the universe is 46 billion years! (Do they do this just so the diagrams are easier to draw?)Right, conformal time is popular for some types of calculations that cosmologists do, and it also respects the cosmological principle-- i.e., the cosmological principle also makes tractable the calculations using conformal time. You and I don't think often in terms of conformal time, so it's easy to forget that option even exists. Ultimately, I think this whole business is just like using coordinates fixed to the stars and talking about the rotation of the Earth, or coordinates fixed to the Earth and talking about sunrises and sunsets. Two different languages for the same thing, two different studies in sociology, but just one reality, and just one physical theory for predicting it.

speedfreek
2010-Jul-31, 12:21 PM
Thank you Ken, I find it too easy to forget how the only things that really matter are the invariants, and this is, as you say, due to them being the least intuitive way to describe distances in cosmology. Everything else is a matter of coordinate choice, however intuitive or convenient it may seem.

In an attempt to try to steer the conversation back towards areas within the remit of the OP, I came across Klaus Mainzer's description of the cosmological principle:

"All points in space ought to experience the same physical development, correlated in time in such a way that all points at a certain distance from an observer appear to be at the same stage of development. In that sense, all spatial conditions in the Universe must appear to be homogeneous and isotropic to an observer at all times in the future and in the past."

speedfreek
2010-Jul-31, 12:31 PM
Yes, that is true - the comment I made was supposed to be light hearted, as it was based on the cosmological usage of "proper distance".We can see a galaxy at z=7 that is obviously behind a galaxy at z=1, and yet the z=7 galaxy has an angular size that tells us it was closer to us when it emitted the light we now see (3.5 Gly, 12.9 Gyrs ago) than the z=1 galaxy was when it emitted the light we see (5.4 Gly, 7.7 Gyrs ago).
Wow! That's quirky! All because of our earlier distance and velocity (=expansion). This needs to be added to the list of new astronomy terms needed. Something that combines angular size and velocity....angulocity? :)

It's only quirky if you forget that when the z=7 galaxy emitted the light we now see, the z=1 galaxy was a lot closer to us. And when the z=1 galaxy emitted the light we now see, the z=7 galaxy was a lot more distant.

The term usually used is the angular diameter - redshift relationship. :)

bunker9603
2010-Aug-01, 06:33 PM
I was fishing in the Gulf of Mexico with a buddy of mine and we were about 50 miles off shore and when I looked around all I saw was water in all directions. From my point of view it looked like we were in the middle of the Ocean. I am sure there were other boats fishing that day that from their POV they looked like they were in the middle of the ocean.

Whenever the question of the "center of the universe" or "visible universe" comes up I am always reminded of that day.

George
2010-Aug-01, 08:14 PM
It's only quirky if you forget that when the z=7 galaxy emitted the light we now see, the z=1 galaxy was a lot closer to us. And when the z=1 galaxy emitted the light we now see, the z=7 galaxy was a lot more distant. But I think there may still be a "wow "factor here. Are there not some instances when a more distant galaxy will appear larger than a closer galaxy of equal diameter and orientation? In the most imaginary comparison, if a 100,000 lyr. dia. galaxy just happened to have been in full form at the time of recombination, it would appear -- assuming straight trig is all that is needed -- about 2.5x larger in diameter than the Andromeda galaxy.


The term usually used is the angular diameter - redshift relationship. :) I don't see a combination that has the necessary spunk like angulosity. :)

speedfreek
2010-Aug-01, 09:22 PM
But I think there may still be a "wow "factor here. Are there not some instances when a more distant galaxy will appear larger than a closer galaxy of equal diameter and orientation?
Yes, that "wow factor" theoretically applies to all galaxies with redshifts of z>~1.6 or thereabouts.

All I meant was it might be quirky when you first hear of it, but it makes sense when you consider the relative positions of the galaxies at any particular time. The z=7 galaxy is always further away (comoving distance) than the z=1 galaxy, but we are seeing them at different times in the history of the universe. The light left the z=7 galaxy when the universe was a lot smaller than when the light left the z=1 galaxy.

This might be a good time to mention the "z" that cosmological redshift is expressed in. It represents the scale factor of the universe, in the form 1+z. So, the universe is now 2 times the size it was at z=1, and 8 times the size it was at z=7. This means the universe is now ~1090 times the size it was at recombination, when the CMBR was released.


In the most imaginary comparison, if a 100,000 lyr. dia. galaxy just happened to have been in full form at the time of recombination, it would appear -- assuming straight trig is all that is needed -- about 2.5x larger in diameter than the Andromeda galaxy.
If it was formed at recombination (z=1089) and we were seeing it today, it would look like a galaxy that was 100,000 ly in diameter, ~40 million light years away. That's a whole lot further away than Andromeda, (which is 2.5 million ly away) so it would look a lot smaller.

But it would look magnitudes larger than a galaxy 100,000 ly in diameter, with a redshift of z=1.4, which looks to be 5.7 billion light years away!

Sam5
2010-Aug-01, 10:01 PM
I was fishing in the Gulf of Mexico with a buddy of mine and we were about 50 miles off shore and when I looked around all I saw was water in all directions. From my point of view it looked like we were in the middle of the Ocean. I am sure there were other boats fishing that day that from their POV they looked like they were in the middle of the ocean.

Whenever the question of the "center of the universe" or "visible universe" comes up I am always reminded of that day.

That’s a very good example. I’ve been way out in the Gulf like that too. It’s even worse on a very overcast day, because if you can’t see the sun or the stars, it’s difficult to tell which direction is which.

Another good one is the heavy-fog example, where you’ve only got about 3 feet of visibility.

George
2010-Aug-02, 03:36 PM
All I meant was it might be quirky when you first hear of it, but it makes sense when you consider the relative positions of the galaxies at any particular time. The z=7 galaxy is always further away (comoving distance) than the z=1 galaxy, but we are seeing them at different times in the history of the universe. The light left the z=7 galaxy when the universe was a lot smaller than when the light left the z=1 galaxy. I wonder if anyone has taken a galaxy like Andromeda and resized it for how another comparable to it appears to us at each z value? I would assume galacitc light aberation becomes a significant factor, which would greatly reduce the apparent sizes of the high z galaxies.


This might be a good time to mention the "z" that cosmological redshift is expressed in. It represents the scale factor of the universe, in the form 1+z. So, the universe is now 2 times the size it was at z=1, and 8 times the size it was at z=7. This means the universe is now ~1090 times the size it was at recombination, when the CMBR was released. That's cool, and something I have probably forgotten.


If it was formed at recombination (z=1089) and we were seeing it today, it would look like a galaxy that was 100,000 ly in diameter, ~40 million light years away. That's a whole lot further away than Andromeda, (which is 2.5 million ly away) so it would look a lot smaller. Yikes, I must have gotten wrapped-up in all the excitement and missed the obvious. :(


But it would look magnitudes larger than a galaxy 100,000 ly in diameter, with a redshift of z=1.4, which looks to be 5.7 billion light years away! I suspect aberation will play a significant role here, but I don't want to get off topic with it.

davejm
2010-Aug-02, 04:22 PM
Surely this 'model' is just a logical way of understanding that there's a limit to our ability to measure the size of the universe?

But as pzkpfw mentions, it can't be used as a replacement for the 'balloon' analogy. They both have their place and are useful in discussion, and they both help us when it comes to the question of our place in the universe.

The 'sphere of visibility' idea helps us get our heads around the fact there's a limit to what we can see when we look out into space, and explains why we will never be able to (visually, at least) know exactly how big the universe is. Logically, if we see the same features/objects everywhere we look, it simply means the universe is a lot bigger than we can ever test from the light we receive. It doesn't really tell us anything else, and it certainly doesn't help us know our position. If it doesn't address position, then it doesn't help anyone when it comes to understanding why no one place is the centre of the universe.

Even if we were somewhere within a static and finite universe with fixed dimensions (with edges), we still might look out and see the same objects/features in every direction; and have the same 'sphere of visibility' effect that we experience in our expanding universe. It tells us nothing of our position, other than the fact we aren't at an observable edge.

So we need something else. We need an analogy that directly shows the inflationary concept, and the 'balloon' analogy does just that. It helps us understand that the universe has expanded from a single point.

What I'm saying is, there can never be a standard answer for these types of questions. The 'sphere of visibility' thing helps us understand why we can't measure the size of the universe; and the inflating balloon analogy helps us deal with the concept that no one object is more central than any other. They are both useful in discussion, as is usually the case when these questions get asked.

speedfreek
2010-Aug-02, 10:06 PM
I wonder if anyone has taken a galaxy like Andromeda and resized it for how another comparable to it appears to us at each z value? I would assume galacitc light aberation becomes a significant factor, which would greatly reduce the apparent sizes of the high z galaxies.
I don't know of any such comparison done with Andromeda, but I know of another done with an identical sized galaxy at z=0.15, z=0.7 and z=7, it is shown in the second diagram on the webpage below (the z=0.7 has the smallest angular diameter and therefore was at the greatest distance at emission):

http://www.astro.virginia.edu/class/whittle/astr553/Topic16/t16_three_distances_2.html

The whole page (in fact the whole site (http://www.astro.virginia.edu/class/whittle/astr553/index.html)!) is worth a look.

George
2010-Aug-03, 01:49 AM
I don't know of any such comparison done with Andromeda, but I know of another done with an identical sized galaxy at z=0.15, z=0.7 and z=7, it is shown in the second diagram on the webpage below (the z=0.7 has the smallest angular diameter and therefore was at the greatest distance at emission):

http://www.astro.virginia.edu/class/whittle/astr553/Topic16/t16_three_distances_2.html
That's a quick but comprehensive view.

In playing with the graph, I can't read the values clearly, but it seems a z=7 would corespond to an original distance at emission of about 2 billion lightyears, but I could be off a billion here. It seems at z=7 our radial velocity is around 0.97c. The aberration effect would reduce the apparent angle by about 87%, but I certainly could be off somehwere. [I used the relativisic aberration formula from here (http://www.fourmilab.ch/cship/aberration.html) .]

So, I am not sure the "wow" factor is upon us. I hope it is, however, but it seems aberration is squashing it, pardon the pun. :)

speedfreek
2010-Aug-03, 05:44 PM
z=7 (or z=6.8 as shown on the graph) equates to around 3.6 Gly emission distance. See where the blue worldine on the right (the worldine of the galaxy now 28 Gly away) intersects our light cone at re=3.6 (read downwards from there to the scale along the bottom).

The wow factor is there, as a z=6.8 galaxy (~3.6 Gly emission distance) looks a whole lot larger than a z=1 galaxy (~5.2 GLy, although the figures have been revised slightly since that webpage was written)

I'm not sure relativistic aberration would be relevant here, as there is essentially no relative motion between us and those distant galaxies. :neutral:

If you are thinking in terms of apparent recession velocity, then the z=7 galaxy has always been "receding" faster than light! So, I don't think aberration can apply here.

Check out the top graph on the page below:
http://www.astro.virginia.edu/class/whittle/astr553/Topic16/t16_light_cones.html

George
2010-Aug-03, 11:30 PM
z=7 (or z=6.8 as shown on the graph) equates to around 3.6 Gly emission distance. See where the blue worldine on the right (the worldine of the galaxy now 28 Gly away) intersects our light cone at re=3.6 (read downwards from there to the scale along the bottom). ah yes, the graph you are using is much better than the first one I was using.


The wow factor is there, as a z=6.8 galaxy (~3.6 Gly emission distance) looks a whole lot larger than a z=1 galaxy (~5.2 GLy, although the figures have been revised slightly since that webpage was written). So the actual images reveal this to be the case? That would say an awful lot here. :)]


I'm not sure relativistic aberration would be relevant here, as there is essentially no relative motion between us and those distant galaxies. :neutral: I don't see how it couldn't but admit it could be my shortsightedness. The observational results should be able to easily correct me if I'm wrong.


If you are thinking in terms of apparent recession velocity, then the z=7 galaxy has always been "receding" faster than light! So, I don't think aberration can apply here. The light that reaches us has been always traveling at c, but our recesional speed, I think, must be taken into account.

Using this redshift velocity (http://astronomy.swin.edu.au/~elenc/Calculators/redshift.php) calculator, v = 290,100 kps, or v/c = 0.9677. Indeed, this recessional velocity is why we see a redshift of z = 6.8.

At the original 3.6 Gly distance, and Andromeda-sized galaxy would have appeared to be about 8 arcseconds in diameter, but at a z = 6.8 the recessional velocity will be 290,100 kps, which gives an aberration effect reducing this 8 arcseconds to about 1 arcsecond.

[I did a search on whether or not this topic has been specifcally addressed and found this (http://www.bautforum.com/showthread.php/10130). :)]

Ken G
2010-Aug-03, 11:59 PM
Using this redshift velocity (http://astronomy.swin.edu.au/~elenc/Calculators/redshift.php) calculator, v = 290,100 kps, or v/c = 0.9677. Indeed, this recessional velocity is why we see a redshift of z = 6.8.
Not in standard cosmological coordinates. In the standard coordinates, the redshift is not "because" we are moving (we aren't), it is "because" space itself has expanded while the light was underway. So z = 6.8 just means space has expanded by the factor 1+z = 7.8 while the light was getting here, just like the way a line of ants would be stretched by the factor 7.8 if the rubber tablecloth was stretched by the factor 7.8. If there are two lines originally coming from an angle that is 180 degrees apart, they will still be coming 180 degrees apart, no matter how much you stretch the tablecloth (isotropically). So there isn't aberration, unless I'm overlooking something (which is easy to do in cosmological coordinates).

George
2010-Aug-04, 03:43 AM
Not in standard cosmological coordinates. In the standard coordinates, the redshift is not "because" we are moving (we aren't), it is "because" space itself has expanded while the light was underway. So z = 6.8 just means space has expanded by the factor 1+z = 7.8 while the light was getting here, just like the way a line of ants would be stretched by the factor 7.8 if the rubber tablecloth was stretched by the factor 7.8. If there are two lines originally coming from an angle that is 180 degrees apart, they will still be coming 180 degrees apart, no matter how much you stretch the tablecloth (isotropically). So there isn't aberration, unless I'm overlooking something (which is easy to do in cosmological coordinates). Ok, this sounds mighty familiar, and I had been wondering if this was the case, once again, of the views between a Doppler effect vs. a stretching-of-the-inocent-photon-though-muscled-electromagnetically mainstream view. :)

But, as we both say, "the proof is in the pudding". Bring in the observational astronomers and lets do the size comparisons. I'm guessing that galaxy sizes at z of about 7 can be roughly estimated. If I'm right, and I'm never always wrong (except in spells), this might finally help me get on the right, or "more righter", path. Is this hypothesis, corn aside, testable in the way I claim? I hope so.

My odds aren't very good here. If this is a legitimate test of these two views, then it's probably already been done, thus I'm looking bad here. If this size comparison isn't a legitimate test, then I'm not looking that good. Somehow there is some consolation that I'm at least calling in whole galaxies to do the test.

Ken G
2010-Aug-04, 05:20 AM
But, as we both say, "the proof is in the pudding". Bring in the observational astronomers and lets do the size comparisons. Isn't that what was in that figure linked to above by speedfreek, where we saw the size of a standard galaxy at various different z? The visual size was smallest at an intermediate z value. The difference wasn't all that huge, for a pretty healthy z range, so I don't know if that's what you mean by not being all that striking, but that's because the galaxies hadn't formed at the really early times.

George
2010-Aug-04, 03:53 PM
Isn't that what was in that figure linked to above by speedfreek, where we saw the size of a standard galaxy at various different z? The visual size was smallest at an intermediate z value. The difference wasn't all that huge, for a pretty healthy z range, so I don't know if that's what you mean by not being all that striking, but that's because the galaxies hadn't formed at the really early times. Yes, the three sizes (and color shifted, too, :) ) do show the cool apparent fact (which I'm questioning) that when you get out near z=7 the galaxies will quickly appear noticeably larger than the ones rougly ranging from z = 1 to 5 or 6. [Added: But the sizes shown on the graphs linked by speedfreek are not likely actual sizes taken from specific galaxy observations, but simply the trig calc. as I have done, namely atan(galaxy size/distance at time of emission).]

But, this assumes no aberration effects apply. If what we actually observe matches the above, then my suggestion that aberrational effects should be applied would have to be false, unless we are really messed-up in determining distances, etc.

If, however, what we observe happens to show continually diminishing sizes (see attachment comparison) then aberration should exlain it. If I'm right, and I'll be happy to bet an ice cream Sundae on this --BTW, I would bet that I'm wrong :) -- then I would guess this would say something significant regarding the view that redshift is a Doppler effect versus the view that the helpless photon just gets stretched during all its travels, which it experiences in zero amount of time. [This stuff is way over my head, but what the heck, the attached was fun to try, anyway.]

[The distances I show for the time of emission could be off a little since I was reading off the graph.]

Ken G
2010-Aug-04, 04:54 PM
But, this assumes no aberration effects apply. If what we actually observe matches the above, then my suggestion that aberrational effects should be applied would have to be false, unless we are really messed-up in determining distances, etc.Oh I see. Well, I do think it must be false, as I trust that site and also it gibes with my understanding. But I could be wrong.

George
2010-Aug-04, 05:20 PM
Oh I see. Well, I do think it must be false, as I trust that site and also it gibes with my understanding. But I could be wrong. [Added: Yes, wrong like most everyone else in cosmology, but I'm not ready to go ATM just yet, since you are likely right. :) ]

I should go to the SDSS site and see what I can dig up on data for apparent galaxy sizes for different z values. I would rather someone who is more familiar with this do it. Any SDSS veterans around????

Perhaps it's time to carve this thread aberration, pun intended :), out of here and put it where it belongs.

How do I get a MODERATOR's attention to help with this? [I don't think the PM system works, but it could just be me.]

Here (http://www.bautforum.com/showthread.php/10130) is one place we could put it. [Post #91 on, I suspect.]

speedfreek
2010-Aug-04, 07:13 PM
George, the relativity calculator you are using seems to have used the "old" special relativistic Doppler interpretation of cosmological redshifts, where no redshift gives an apparent recession velocity larger than c. That special relativistic interpretation was ruled out (with a confidence level of 23 sigma, no less!) by Lineweaver and Davis in the paper I linked in post #37 earlier in this thread and their view seems to have been adopted by the mainstream. Whittle's spacetime diagrams do not use the special relativistic interpretation either (but they do match Lineweaver and Davis!). So, I think you are using a calculator that is completely incompatible with those (mainstream) spacetime diagrams.

Using Whittles spacetime diagrams, it shows a galaxy with a redshift of between z=1 and 2 has an apparent recession velocity of c where our light cone intersects its world line. Lineweaver and Davis give a figure of z=~1.4 and so does Ned Wright!

http://www.astro.ucla.edu/~wright/cosmology_faq.html#FTL

For the concordance model based on CMB data and the acceleration of the expansion measured using supernovae, a flat Universe with Omegam = 0.27, the velocity is greater than c for z > 1.407.

Now, as to the question of whether we have observational evidence (the test is known as the "Tolman test") for the angular diameter - redshift relationship, the answer is... sort of.
http://www.astr.ua.edu/keel/galaxies/obscosmo.html
(See halfway down that page)

There is a problem, in that we have to know the absolute size of a galaxy in order to make the calculation, and our estimates of that absolute size are dependent on the model of galaxy formation and evolution that is used, as we are dealing with the early universe. Surface brightness is used as an indicator of angular diameter for very distant objects, but then we also have to deal with the amount that the light has been dimmed by the expansion of the universe since the light was emitted. But so far, the results are promising:
http://arxiv.org/abs/astro-ph/0106566

George
2010-Aug-04, 09:10 PM
George, the relativity calculator you are using seems to have used the "old" special relativistic Doppler interpretation of cosmological redshifts, where no redshift gives an apparent recession velocity larger than c. That special relativistic interpretation was ruled out (with a confidence level of 23 sigma, no less!) by Lineweaver and Davis in the paper I linked in post #37 earlier in this thread and their view seems to have been adopted by the mainstream. Whittle's spacetime diagrams do not use the special relativistic interpretation either (but they do match Lineweaver and Davis!). So, I think you are using a calculator that is completely incompatible with those (mainstream) spacetime diagrams. Ok, that is now stuff that is over the stuff that was already over my head. :) But, considering your points, I assume that the relativistic calculator should be used for local redshift velocities only since co-moving space is essentially not a factor withing the Local Group, I suppose. This, however, doesn't allow much in the way of any significant z values. The relativistic equations from Wiki (http://en.wikipedia.org/wiki/Cosmological_redshift#Combining_redshifts_with_dis tance_measurements) also don't work when v > c since imaginary numbers suddenly appear when this happens.


Using Whittles spacetime diagrams, it shows a galaxy with a redshift of between z=1 and 2 has an apparent recession velocity of c where our light cone intersects its world line. Lineweaver and Davis give a figure of z=~1.4 and so does Ned Wright!

http://www.astro.ucla.edu/~wright/cosmology_faq.html#FTL


Now, as to the question of whether we have observational evidence (the test is known as the "Tolman test") for the angular diameter - redshift relationship, the answer is... sort of.
http://www.astr.ua.edu/keel/galaxies/obscosmo.html
(See halfway down that page)

There is a problem, in that we have to know the absolute size of a galaxy in order to make the calculation, and our estimates of that absolute size are dependent on the model of galaxy formation and evolution that is used, as we are dealing with the early universe. Surface brightness is used as an indicator of angular diameter for very distant objects, but then we also have to deal with the amount that the light has been dimmed by the expansion of the universe since the light was emitted. But so far, the results are promising:
http://arxiv.org/abs/astro-ph/0106566
Yes, I was thinking of the Tully-Fisher relationship, which should be useful once the redshift is taken into account. I am curious what the mainstream view is for the high z young galaxies. Are these seen at lesser z values to be fragmenting much like we see in stellar nursery nebulae? I don't recall hearing this, admittedly. Since my aberration result is so much different, it should still be relatively easy to refute any aberration effect with some general size estimates, maybe.

Sam5
2010-Aug-04, 11:18 PM
George, the relativity calculator you are using seems to have used the "old" special relativistic Doppler interpretation of cosmological redshifts, where no redshift gives an apparent recession velocity larger than c. That special relativistic interpretation was ruled out (with a confidence level of 23 sigma, no less!) by Lineweaver and Davis in the paper I linked in post #37 earlier in this thread and their view seems to have been adopted by the mainstream.






I posted a link to their original first paper on the old BA board back in 2001. It’s still on the internet. We had quiet a discussion about it on the board 9 years ago.

http://arxiv.org/PS_cache/astro-ph/pdf/0011/0011070v2.pdf

speedfreek
2010-Aug-04, 11:32 PM
Yes, that was well before my time here, but I remember discussing these concepts with you soon after I joined. You have been following this part of the saga for a while now. :)

Sam5
2010-Aug-04, 11:41 PM
It’s interesting, and I learn a lot of stuff, such as what you’ve been talking about regarding the ages and the visual sizes of galaxies.