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Effort to get us all on the same page (balloon analogy)

by marcus
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derekmcd
#19
Oct6-08, 04:05 PM
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Whenever I use the balloon analogy, I always add the caveat, prior to questions about what's inside/outside the balloon, that the inside represents the past with the center being t=0, the surface is the present and "outside" the balloon is the future.

Get them to focus on the inside/outside of the balloon as a timeline rather than focus on some physical manifestation.
marcus
#20
Oct6-08, 08:19 PM
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Quote Quote by TalonD View Post
"No, the matter that emitted the CMB light which we are now getting was, when it emitted the light, at a distance of 41 MILLION lightyears from our matter.
You should get this number for yourself by going to Ned Wright calculator and putting in z = 1090. this is the redshift of the CMB light. It says that while the light has been traveling towards us the universe has expanded by a factor of 1090 (and the wavelength of the light increased by the same factor)

Since both our matter and the matter that emitted the light are stationary, and the distance between is NOW 45 billion, it must be that the distance THEN was 45 billion divided by 1090!
If you divide 45 billion by 1090 you will get 41 million.
therefore the distance to the matter then, when it emitted the light, was 41 million lightyears."

So if the light was emitted from a distance of 41 million light years but it took 3.7 billion years to get here
just to correct the typo, I think you meant 13.7, not 3.7.

...then was the universe expanding faster than the speed of light at that time?
Yes very much so. There are always portions of space which are receding from us at faster than light. There were then (when the light was emitted) and there are now (as we receive the light.)
is that what is meant by the inflationary period of expansion?
No. The CMB light was emitted around Year 380,000. Long after the inflation episode (a speculative scenario) is supposed to have ended.

And the expansion has slowed down now because it only takes 41 million yrs for us to see the light from a galaxy that is 41 million light years away right now. or maybe a bit longer because there is still expansion?
That is right! Expansion has slowed enormously since Year 380,000 when the CMB light got loose and started on its way. However there are still portions of space (albeit considerably farther away) that are receding from us at greater than c.

The physicists here then always say that extra dimensions aren't necessary, that the universe can expand without having another dimension to expand into. Do we know for certain one way or the other or is it just two different opinions?
Cosmology is a mathematical science. There is no mathematical necessity for a surrounding space for our space to expand into. All expansion means is a pattern of increasing distances between object stationary with respect to CmB. It is a bunch of distances that are increasing according to Hubble law, not a material that is swelling up.

do we know or is there some prevailing opinion if the universe is infinite or finite? If it is finite and you traveled far enough in a straight line would you end up back where you started having gone all the way around? or is that an instance of where the baloon analogy breaks down?
We don't know. think of a really immense balloon. so big that the surface looks flat to you.

in the limit, as the size of the balloon goes to infinity, the analogy carries over.

and we don't know whether nature's reality is a truly flat, truly infinite case, or whether it is only a nearly flat, finite but very large case.

Astronomers are working on that.

The most recent data was the WMAP5 report (fifth year data from the WMAP satellite) where it said that the data was still consistent with either case, infinite or finite. But that if it were finite then they could give a lower bound estimate for the socalled radius of curvature (analogous to the radius of the balloon). the radius of curvature of our real space, said the WMAP people, is at least 104 billion LY with 95 percent confidence
http://www.physicsforums.com/showthr...51#post1636651
(see this PF thread on the WMAP5 data, post #4 has the radius of curvature)

It might be infinite, an infinite radius of curvature is equivalent to zero curvature, complete flatness. So far all we have is the at least figure, the 95% confident lower bound. Dont hold your breath. But it's getting slowly better
George Jones
#21
Oct8-08, 02:10 AM
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Quote Quote by oldman View Post
Does space expand ...

I’ll go further: General Relativity, the foundation of modern cosmology, seems to me something not easily understood in the context of everyday experience. In particular, ‘expansion’ turns out to be not a simple concept. The Hubble flow may kinematically look like ‘motion’ in our local domain (where Special Relativity is adequate). But it is a quite different phenomenon.

Isn't it?
There has recently been an interesting column and discussion about this over at Cosmic Variance,

http://cosmicvariance.com/2008/10/06/does-space-expand/.
oldman
#22
Oct9-08, 01:52 AM
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Quote Quote by George Jones View Post
There has recently been an interesting column and discussion about this over at Cosmic Variance,

http://cosmicvariance.com/2008/10/06/does-space-expand/.
Thanks very much indeed, George. I hadn't been aware of this long discussion. It seems that analogy-interpretation is now generating interest among serious cosmologists, like Carroll and Peacock, yet.
Quote Quote by Sean Carroll
There seems to be something in the air these days that is making people speak out against the idea that space is expanding......
. High time, too, I say. But I won't pursue this topic here. I'll start a new thread.
TalonD
#23
Oct14-08, 09:38 AM
P: 177
I think I grasp something that I hadn't before. When it is said that in the beginning the universe was the size of a pea or mellon or whatever fruit, what is really being referred to is the currently visible part of the universe. The part that we can see out to the CMB. But the universe extends past that radius perhaps even infinitely? So instead of envisioning a small dense sphere the size of a pea, that density actually extends in all three dimensions an infinite distance. And it's only a small pea sized portion of that we are physically located in and can see. I know this is about the ballon model, but switch over to the raisin bread model for a second. What we can see now is just a small volume of a much larger volume, and at the beginning our volume was very much smaller than it is now but still just part of a very much larger volume. Does any of that make sense, is that anywhere near a correct picture or anything like what is main stream thought?
robertm
#24
Oct14-08, 11:30 AM
P: 290
You seem to be conceptually dead on TalonD. When one hears the term 'the universe' it is generally referring to what is currently visible out to a radius determined by Hubble's law. So when stating that 'the universe' was the size of a (insert small round object), what is meant is that there has been a massive change in the density and volume of all the stuff that is currently available for observation. As for what is beyond this observational boundary, the best we have so far is the new WMAP data Marcus referred to.

The concept you describe is key to understanding the expansion scenario and is at the heart of most of the confusion created by pop-science, thank you for sharing your realization.
marcus
#25
Oct15-08, 07:06 PM
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Thanks to everyone who responded with helpful comments! Let's continue this effort to arrive at common understanding of at least of our basic mainstream point of departure. We may not always stay on the same page, we may vary all over the place, but we all can refer back to this kind of home base.

PF poster Atyy has suggested a wonderful online resource for basic cosmology, the EINSTEIN ONLINE website maintained by the Albert Einstein Institute (AEI) in Germany.
Thanks Atyy! Here is the index page:

http://www.einstein-online.info/en/s...ogy/index.html

The material here is unusually up-to-date, which makes a difference in cosmology. All appears to be 2006 or later. The main author is Markus Possel, a physics PhD with a special interest in physics outreach, writing and website design for wide audience.

In an earlier post, Atyy particularly recommended this page:
http://www.einstein-online.info/en/s...ngs/index.html
This distinguishes two different senses in which people use the term Big Bang. I think it makes a really helpful distinction! Hopefully more people will read this page.

Here is Atyy's post that gives several Einstein Online links:
http://physicsforums.com/showpost.ph...6&postcount=14
======================

EDIT to piggyback a reply to the next, by RobertM:

Robert, that is actually a very smart teaching strategy! What Derek suggests in post #19 is a way of preventing students from starting to visualize an unnecessary extra spatial dimension (which our hide-and-seek instincts make us all want to do). Making it a time dimension 'uses it up' and gets it out of the way of imagining a pure and simple 3-sphere.
thanks for pointing that out. I almost missed Derek's point.
robertm
#26
Oct15-08, 07:57 PM
P: 290
An excellent resource that I have somehow managed to avoid discovering. Thanks to Atyy and Marcus for making this site more widely known.

I would like to point out the suggestion derekmcd made in post 19 seems to be quite a simplistic means by which to convey the idea of 'three spacial dimensions and one temporal' not needing to be embedded in a forth spatial to have geometry. That seems to be quite a large hurdling point for many who do not know the mathematics.
marcus
#27
Oct17-08, 04:25 PM
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The basic purpose of a thread like this would be achievable if new arrivals at the forum would read it (or a few posts containing a condensed version) before posting and would get free of some common misconceptions about the standard cosmology model. The standard should be like a home base point of reference. If you are going to explore alternatives at least first understand the common home ground from which you consciously deviate.

A kind of voluntary beginners workout for people who want to discuss cosmology on the forum. You may have ideas of things you'd recommend.

I'd say that there are some good things online to READ, like Ned Wright's cosmo tutorial and Einstein Online. (I think Einstein Online is great, I don't agree with everything said there but the information is up to date and excellently organized. The AEI is a class act.)

And studying the balloon analogy is certainly on the short list of basic workouts for beginners. It is not supposed to teach you what space IS. It trains your visual imagination to visualize how DISTANCES between stationary objects INCREASE and how light signals MOVE. After wordlessly studying the balloon analogy enough, it should be easy to understand how the CMB light was emitted from matter 42 Mly from us and 13.7 Gy later on the day when the light arrives here the matter that emitted it is now 46 Gly from us.
The distance between two essentially stationary patches of matter has increased 1090-fold and the wavelengths of light have increased by the same ratio as the distances.

The analogy doesn't teach you what space IS, it teaches your visual imagination how distances CHANGE. Hubble Law is a pattern of increasing distances measured simultaneously between stationary objects. Understanding/visualizing that law is basic.

We don't know whether universe is spatial finite or infinite but the balloon analogy is a good teacher in either case. Infinite means think of a much bigger balloon. Or of zooming in so close that the balloon you have looks flat, as it would to a very tiny observer. All the analogy is supposed to be is an approximation to help with visualizing, so the balloon's finiteness shouldn't be a problem.

All that said, what I wanted to write about is the need to GO BEYOND reading Einstein Online and visualizing the balloon analogy. Going beyond those things and PLAYING WITH COSMO CALCULATORS. They embody the standard model, with the three important numbers plugged in: .27, .73, and 71.

I am going to start a fresh post about this. In order to have efficient communication here at the forum, and get us all on roughly the same page, every new poster should have played some with a calculator either like Ned Wright's or like Morgan's.
marcus
#28
Oct17-08, 04:50 PM
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Everybody who posts here at Cosmo forum should have played around with a Standard Model calculator like Ned Wright's or Morgan's. I have the URL for Morgan's in my sig. To get Ned Wright's just google "wright calculator" or anything resembling that. It is known world wide.
Or better, google "ned wright" and go to his main cosmo tutorial page and see all the goodies including the calculator.

The primary differences are that Wright has the three basic numbers already entered for you as the default: .27, .73, 71. With Morgan, you have to put them in, in the appropriate boxes. The Standard Model needs something like those inputs to run right. In time, as more data come in, these numbers will change slightly, become more precise, more certain. These are currently-used conventional best estimates.

Once you make sure those three numbers are in, the calculator is ready to convert redshifts into distances. Another difference between Wright and Morgan is that Wright's calculator is more precise, more decimal place accuracy, and the labels are more technical.

I would suggest starting with Morgan because it is more immediately accessible. I would suggest some exercises with Morgan like this:

Check that if some light comes in with redshift 1.4, the galaxy that emitted it is now receding at speed c.

Check that if some light comes with redshift 1.65, the galaxy was receding with speed c at the time it emitted the light.

A conventional figure for the CMB redshift is 1090. Find out how far away the matter was that emitted currently received CMB on the day it emitted the light. Find out how far away that same matter is now. Find out how rapidly the distance to it (from our matter) was increasing then and how rapidly it is increasing now----the then and now recession speeds. Remember that these are not speeds of motion, they are recession speeds (rate of change of distance between two stationary objects, as per balloon analogy.)

======================

Probably we all occasionally meet people who think that the space of standard cosmology has an EDGE or some kind of boundary surface. That is a common misconception and it is one of the things the balloon analogy is supposed to help get you unconfused about. The 2D surface of the balloon has no edge. Nor would an infinitely big balloon have an edge, if you prefer to think of space as infinite. Well someone who thinks of space as having an edge, or of the portion of space occupied by matter as having one, may get the idea that there is a welldefined speed with which the universe is expanding. Some misconceptions need to be addressed up front. There is no welldefined speed of expansion, now or in the past. At any moment in time there is a pattern of increasing distances with all different expansion speeds. No one speed that we can pinpoint.
At the moment the rough average percentage increase rate is 1/140 percent every million years.

To help get rid of the most common misconceptions, let's encourage newcomers to all read the Lineweaver SciAm article from March 2005. The URL is in my sig, and in posts by many other people as well. Many PF posters have urged reading Lineweaver's SciAm piece over the years. It is specifically about common cosmo misconceptions. Einstein Online is also good on this.
marcus
#29
Oct21-08, 08:57 PM
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It's recommended that you play around with the online cosmology calculators to get used to the standard cosmology model. I'll give an example of an exploratory thing to do, that was suggested by RandallB:
Quote Quote by RandallB View Post
Marcus
Have you ever noticed a Cosmic Calculator somewhere that would allow you to adjust the age of the universe you are make the “Z” observations from?
(I’m not talking about adjusting the current age since the BB)

By that I mean changing the observations to a time prior to the here and now 13.7 Billion-yr since the BB to sometime in the past for observations that could have been made a time long ago like 7 Billion-yr after the BB while our Galaxy was forming.
The “z” for last scattering would be much smaller and the separation distance for “Then” and “Now” would be smaller as well

Likewise if measured 10 Billion-yr from now (assuming someone is still here to observe it) all those values for Last Scattering would be much larger.
I'm going to show how to do this with Morgan's calculator, with the trivial difference that we go back to when the expansion was SIX billion years old instead of SEVEN. Six, or more precisely 5.9 billion years corresponds to redshift z = 1, which is convenient. You could adjust z down slightly from 1 and get exactly 7 billion as Randall requested.

To get Morgan, google "cosmos calculator" or use the URL in my sig. To get Wright (which has more precision) google "ned wright calculator".

Here's how to use Morgan. You look thru a telescope and see a galaxy at z=1 and you want to know how to setup Morgan so it would look like one THEY would use, and give the distances corresponding to redshifts observed by them.

Put the usual numbers (for our time in history) into Morgan, namely 0.27, 0.73, 71. Let's assume flatness so that the second is always one minus the first. Put z = 1 and find that for them the expansion is 5.93 billion years old and their Hubble is not 71 (like it is for us) but instead is 120.7.

Now what is the redshift of their CMB?

Well between then and now distances have expanded by a factor of z+1 = 2. That is what redshift one means, it means distances have doubled while the light was in transit. And for us the CMB redshift is 1090, which means distances have increased by 1091 since last scatter. That means that for THEM things have increased by 545.5, so their CMB has redshift 544.5. The adding and subtracting ones is a nuisance and we sometimes forget to do it if a rough approximation will suffice.

Now we have to set up Morgan for THEM (the people in the z=1 galaxy, for whom the universe is younger). We need those three numbers x, 1-x, 120.7.
x = (z+1)^3 * 0.27 * (71/120.7)^2 = 2^3 * 0.27 * (71/120.7)^2 = 0.7474
1-x = 0.2526
The reason for the blue formula is x is supposed to be their matter fraction. Our matter fraction is 0.27 and their volumes are 8 times smaller so multipy 0.27 by 8, but their critical density is different by the square of the ratio of the two Hubbles, theirs and ours. So it works out that way.

Now we can set up. We just put these new three numbers into Morgan:
0.7474, 0.2526, 120.7

NOW we can find the distance to the last scatter surface for THEM. Remember that for them the redshift of the CMB is roughly half what it is for us, namely 544.5. For them the temperature of the CMB is roughly twice, more like 5.4 kelvin instead of 2.7 kelvin. So now we have set up the calculator we can put in z = 544.5 and it will tell us the distance to last scatter. and all that.

The only thing is precision. You might want to take those very same three numbers
(0.7474, 0.2526, 120.7) over to WRIGHT's calculator because it tells you distances with more decimal places and less roundoff. That is particularly true for the rather small distance to the matter that radiated the CMB light. It tends to get rounded off to almost nothing in Morgan's calculator.

Anyway that is one exploratory thing you can do, playing around with those things. The main thing is just to calculate distances and times for a bunch of redshifts and get used to the typical sizes of the numbers. This what I just did may have been too elaborate as an example. But RandallB asked the question and it seemed like an intriguing exercise.
oldman
#30
Oct22-08, 04:26 AM
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Quote Quote by marcus View Post
It's recommended that you play around with the online cosmology calculators to get used to the standard cosmology model.
and
Everybody who posts here at Cosmo forum should have played around with a Standard Model calculator like Ned Wright's or Morgan's.
Marcus: May I inject a reservation here?

It seems to me that this is a bit prescriptive, if your aim is to establish in this thread an agreed base for understanding the FLRW model --- in this forum it may turn out to be rather like trying to herd cats.

Quite often the trouble people have with understanding the present consensus in cosmology is that familiar concepts, like "distance", "time interval", "speed", "expansion", "faster than light", "space" and "superluminal recesssion" are used in the unfamiliar context of general relativity. Using online calculators to understand the FLRW model is a little like relying on software that calculates with the Lorentz transformations of special relativity to help you understand whether Lorentz contraction is 'physically real' or not. These calculators are useful, but do need supplementing.

I think it would help your final distillation of this thread (which I look forward to) if you began with a clarification of such base concepts.
TalonD
#31
Oct22-08, 08:43 AM
P: 177
I was wondering about the acceleration of expansion. Expansion rate increases with distance. Is that true of any spherical shell that is expanding such as the baloon? or is that a unique feature of our observable universe? What data or evidence is it that shows that our universe is expanding at an accelerating rate?
marcus
#32
Oct22-08, 09:03 AM
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Quote Quote by oldman View Post
Using online calculators to understand the FLRW model is a little like relying on software that calculates with the Lorentz transformations of special relativity to help you understand whether Lorentz contraction is 'physically real' or not.
I disagree. Physically real is not the issue. The aim is to get familiar with the standard mainstream model (after that deviate freely but know where home base is). The calculators are an embodiment of the model. Operationally the are the model in the same way that the Friedmann eqns are. If one doesn't enjoy playing with equations then one can play with the calculators and get something of the same hands-on feel.

Physically real is a separate issue. One can have one's own opinions about that.
These calculators are useful, but do need supplementing.
I definitely agree! And one should be reminded frequently that a model is just a model. The LCDM standard mainsteam model is currently the best fit to the data, but not to be confused with physical reality.

You mention some concepts. I've been thinking of adding a discussion of the scalefactor next.

I think it would help ... if you began with a clarification of such base concepts.
We need to move in that direction. I want to make this thread highly concrete. Accessible to those (possibly few) non-mathy PF members who prefer concrete hands-on stuff to abstract concepts. So I want to move towards more abstract concepts, but move gradually.

Scalefactor seems right, for now. Friedmanns, the central equations of cosmology, are about the time-evolution of the scalefactor. The basic metric implements it, gives it operational meaning. It's an easy convenient tool---just set a(t) equal to one at the present---so a(present) = 1, and then for earlier times it tells you by what factor distances were smaller than they are today.

Would the scalefactor fly, as a concept? Or is it too abstract and mathematical? Should we try to relate it to the balloon picture we started off with? Still cogitating
Anyway thanks for your comments--astute as always.
mysearch
#33
Oct25-08, 04:03 AM
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I believe that one of the issues this thread should consider is the fairly obvious fact that many people who come to the PF cosmology forum, like myself, have not had any formal education in this topic, i.e. they are self-learning from a wide variety of sources. Unfortunately, there is quite a diversity of opinions and presentation of the basics, which can lead people off in the wrong direction, especially in the absence of any educational framework, as mentioned above. Therefore, I feel the PF cosmology forum can, and does, offer an important educational service, so my comments are intended to be supportive.

Given that there are professionals, graduates, amateurs, hobbyist and beginners all accessing this forum, I am not sure whether it is possible for us all to be on same page. As such, can I ask whether the purpose of this thread is to lend a helping hand to the beginners and, in doing so, avoid us asking so many repetitive and possibly dumb questions?

If yes, what form should this help take, i.e. pointers to existing tutorials and existing threads or supplementary PF libraries. I mention the library because there doesn’t seem to be much in the cosmology section at this time or possibly I don’t know how to find it.

Purely, as an example, the following link is simply illustrative of some of my own confusion on the issue of the expansion of space, it also contains a useful link to an article on this topic: http://www.physicsforums.com/showpos...70&postcount=5

By way of reference and context, it was taken from the following thread :
http://www.physicsforums.com/showthread.php?t=265793
oldman
#34
Oct26-08, 03:34 AM
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Quote Quote by mysearch View Post
I believe that one of the issues this thread should consider is the fairly obvious fact that many people who come to the PF cosmology forum ....have not had any formal education in this topic, i.e. they are self-learning from a wide variety of sources. Unfortunately, there is quite a diversity of opinions and presentation of the basics, which can lead people off in the wrong direction .........
I agree strongly. One trouble with modern cosmology is that it monkeys with basic concepts that lots of us believe we understand as well as, say, Joe the Plumber does.

I'm thinking of concepts like 'distance', 'speed', 'space', and 'expansion'.. Joe measures distances with rulers. But cosmologists can't make such simple measurements. Instead they imagine space-faring chains of communicating observers who measure a series of 'proper' distances with rulers or radar, which they then add up to get a total 'distance'. Cosmologists need this elaboration for an imagined model of the universe that predicts that these 'proper' total distances increase with time --- which they call 'expansion'. But cosmologists have no way of checking their predictions about increasing proper distances by direct measurement! I'd like to see such complications pointed out up-front in this kind of thread before one goes on to talk of 'expanding' 'space' and 'balloon analogies'.

Cosmologists have no option but to rely on a huge body of circumstantial evidence that has been accumulated over the years, much of which confirms predictions of the model, to validate their imagined model of the universe. This evidence is very persuasive indeed, and the LCDM model, based on the best description of gravity we have, is the best description of our mysterious universe so far invented.

But there remain puzzles (the nature of dark matter and energy and the ad-hoc resolution of inherent problems with inflation). The consensus model is perhaps a working hypothesis that one should try to understand, rather than accept as dogma. Who knows when some young upstart will come along and upset the apple cart by talking of alternative kind of 'change' that 'cosmologists can believe in'?
marcus
#35
Oct26-08, 07:36 AM
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Quote Quote by oldman View Post
...Joe measures distances with rulers. But cosmologists can't make such simple measurements. Instead they imagine space-faring chains of communicating observers who measure a series of 'proper' distances with rulers or radar, which they then add up to get a total 'distance'. Cosmologists need this elaboration for an imagined model of the universe that predicts that these 'proper' total distances increase with time --- which they call 'expansion'.
That seems like a good clear statement. I've described that and highlighted it myself several times, for instance if I remember right at the beginning of a thread called "The physical meaning of expansion." It's the only way I can picture measuring distance between stationary objects in the present.

If that idealized operational definition of distance wasn't mentioned near the outset of this thread, it was an oversight. Obviously should be. Hubble law is stated in terms of present-day distance.

The general question of how astronomers infer and check their way up the ladder of different distance methods is too broad for this thread---belongs more in General Astro---but it's very interesting. Basically how you start with Joe Plumber's steel ruler and work up step by step to parallax, clusters, cepheids, supernovae....involves inference using models. We could have a thread about it. Essentially you move up to higher versions of brightness-distance and angular-size-distance, and you relate these to the present-day distance of the geometrical model (e.g. redshift), and check for consistency. It is methodical (not speculative) and it is of a piece with how you work up the ladder of distance measures from the git-go.

I think it would be fine to point all this out at the beginning of our discussion of cosmo basics. Fortunately we still are near the beginning of the thread as I envisage it so this is not so terribly out of order. We do need a thread on the astronomy distance ladder, or a good link to one, however. Maybe Ned Wright has a satisfactory page on it?

This statement I like very much, so will highlight in blue:
==quote oldman (with emphasis)==

Cosmologists have no option but to rely on a huge body of circumstantial evidence that has been accumulated over the years, much of which confirms predictions of the model, to validate their imagined model of the universe. This evidence is very persuasive indeed, and the LCDM model, based on the best description of gravity we have, is the best description of our mysterious universe so far invented.

But there remain puzzles...

==endquote==

Perhaps one thing that needs to be mentioned here is that this best description of gravity we have teaches us that we have no right to expect distances to remain the same and triangles to add up to 180 degrees inside. Gravity is geometry and geometry is something that evolves dynamically---this may cause Joe Plumber and the rest of us some qualms when we first confront it. But "General Geometrivity" is verified by experiment right here in the solar system---we must grin and bear it.

Gallileo is supposed to have said "E pur' si muove." And we can take the lesson of dynamic geometry seriously and say likewise
"E pur' si bende---e pur' si stretche---e pur' si expande." Eh!!!
oldman
#36
Nov2-08, 03:12 AM
P: 622
The balloon analogy is a simple and effective way of visualising how the universe expands. Here it is used to explain how distances between widely separated parts of the universe can increase at rates greater than c. But like all analogies, it's not perfect.

Quote Quote by "Marcus in post #5 of Superluminal Speeds and All That Jazz"
....... picture visually how distances between stationary points can increase at a c+ rate. You simply look at a(n expanding) balloon with glued pennies and with photons wriggling across the surface at a fixed rate of one inch per minute.
There will be distances between pennies which are increasing faster than one inch per minute. But no penny ever outraces a photon in its neighborhood. Ned Wright provides the two computer animations of the balloons with wrigglers. To visualize (in an unparadoxical nice consistent way) how distances can increase at c+ rates, that's all you need.
Don't forget that modern cosmology is based on General Relativity, which can describe for us how we perceive a universe filled with gravitating objects. The description has a perspective restricted by the fact that we are not Godlike creatures able to look at happenings all over the universe all at once. But that is just the perspective adopted in the balloon analogy when you 'simply look at an (expanding) balloon'. So don't take this analogy too seriously, unless I've mistaken who You are (in which case, very humble apologies).


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