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

[marcus]

To have an enjoyable cosmo forum we needed a balance between mental freedom on the one hand and a shared knowledge base on the other.
People should be free to imagine the universe the way they want, but everybody should try to understand the standard LCDM (Lambda-cold-dark-matter) model as a starting point.

I'm going to try to avoid mathematical equations in this thread because they put many people off and also to avoid using too many abbreviations like LCDM. This thread should be at the entry-level for the Cosmo forum. You are welcome to contribute ideas and comments.

The LCDM is based on a more general mathematical model called FRW or FLRW (Friedmann, Lemaître, Robertson, Walker) which is built into Ned Wrights calculator
Everybody who comes in and posts here should have played some with that calculator or one like it because in practical terms that is what a mathematical model is. Cosmology is mathematical (not verbal) and observational---it fits a mathematical model to data.
The galaxy counts, redshift surveys, supernova brightness, microwave background data and so on are all supposed to check out and match what the model says they should be.

When you use Wright's calculator you have specified three parameters (the default values are 0.73 for dark energy fraction, 0.27 for matter fraction, 71 for Hubble).
If you don't change the default settings, you get the standard LCDM. If you change them you get some other version of FLRW.

You can think of the LCDM as the fine-tuned version of the general FLRW where the parameters are chosen to get the best possible fit to our universe--to match the observational data.

So the existence of these models is always in the background but what we need to focus on here in this thread is the INTUITION. How to picture it so that if you were playing around with one of the calculators, changing the parameters and finding how far away various things were when they emitted the light we are getting etc, you would kind of know what to expect. Intuition about how the parameters effect things, and how redshifts relate to distance and recession speed.

So what I hope for is that those of us asking questions and discussing here at Cosmo forum all have a shared basic intuition---which is a kind of home base---and probably the most convenient way to get that is to properly understand the balloon analogy.

In my experience many of the misconceptions people have when they first come to this forum stem from misunderstanding what that analogy is intended to teach us. And a lot of the confusion we occasionally experience comes from getting that analogy somehow crossed up. So in this thread what I propose we do is, at least for starters, simply discuss the balloon analogy. Get clear on it. Find out any problems people have with it, if there are some.

We can do that without having to use a lot of math formulas, I think, and a minimum of technical jargon. Don't get me wrong---I'm all in favor of jargon, we simply won't need much of it here.

For people who want to get some hands-on experience with Wright's cosmo calculator it is here
http://www.astro.ucla.edu/~wright/CosmoCalc.html
the homepage for his other cosmo resources is
http://www.astro.ucla.edu/~wright/cosmolog.htm
you can always get these links just by googling "ned wright"
In my sig I have a link to MORGAN's cosmo calculator which has some valuable features and is harder to get by googling.
You might want to try that one too, it gives recession speeds.

 

[wolram]

To my mind the balloon analogy is a nuisance, gallaxies ect are not stuck to a surface, once one has read about the BA it takes some getting rid of.

 

[marcus]

I said I would try to avoid abbreviations, but I need another one: CMB for cosmic microwave background.

The balloon analogy teaches various things, but sometimes you have to concentrate in order to learn them.

One thing it teaches is what it means to be not moving with respect to CMB.

the balloon is a spherical surface and as it gradually expands a point that always stays at the same longitude and latitude is stationary with respect to CMB.

Distances between stationary points can increase, and in fact they do. They increase at a regular percentage rate (larger distances increase more). In our 3D reality this is called Hubble Law. It is about distances between points which are at rest wrt CMB.

In our 3D reality you know you are at rest wrt CMB if you point your antenna in all directions and get roughly the same temperature or peak wavelength. There is no doppler hotspot or coldspot in the CMB sky. That means you are not moving with respect to the universe.

In cosmology being at rest is a very fundamental idea, we had it even before the 1960s when the CMB was discovered. Then it was defined as being at rest with respect to the process of expansion---you could tell you were at rest with respect to the universe if the expansion around you was approximately the same in all directions---not faster one one side of the sky and slower on the other, but balanced. It is the same idea but now we use the CMB to define it because it is much more accurate. Sun and planets are traveling about 380 km/s with respect to CMB in a direction marked by the constellation Leo in the sky. It is not very fast but astronomical observations sometimes need to be corrected for that motion so as to correspond to what an observer at CMB rest would see.

Now let's take another look at the balloon and see what else it can tell us.

 

[marcus]

Now this will respond to Wolram's comment to some extent. What we observe is that the galaxies we have data for are moving very slowly with respect to CMB. Typically only a few hundred km/s! The whole Milky is only going about 500 km/s

So as a mental convenience to make it easy on our brains, an excellent first approximation is to assume that all the galaxies ARE stationary wrt CMB and that they do in fact act like pennies stuck to the surface of the balloon.

So a galaxy penny always stays at the same longitude and latitude on the balloon. And the balloon is inflating, which means that distances grow by a certain percentage every minute.
That means longer distances increase faster, which is Hubble Law (recession speed is proportional to distance v = HD). And recession speed is not real speed in the sense that it doesn't change one's longitude and latitude. Distance between two galaxies can increase even though both are at rest with respect to the CMB, the universe, the process of expansion.

Now photons of light CAN move across the surface from one longitude and latitude to another. We can think of them as moving some fixed speed like 1 inch per minute, where the inch of balloon surface is always measured at that current time.

So if you send a flash of light off in some direction, once the photons have gotten a substantial distance from you there will be a percentage rate of increase of distance (a recession speed) as well as the light's own standard speed of one inch per minute.
After a while the flash of light will be farther away from you than you would calculate if you just think say "five inches in five minutes" and don't take account of expansion.

So that is another thing the balloon analogy can tell you. It can teach you to expect light to manage to get farther away than you expect, even though it is always traveling across the surface at one inch per minute.

The material that emitted the light which we are currently receiving as CMB is now at a distance from us of 45 billion LY. The light managed to get here in slightly less than the age of the expansion which is 13.7 billion years. The material was much closer to us when the light started its journey. It didn't break any speed laws. Yet it seems to have come all the way across the balloon surface to us from a point which is now 45 billion LY away. This might strike you as paradoxical but it isn't really. The balloon analogy shows you how light can cover enormous distances is less than the expansion age.

Perhaps this could be said more clearly if I had time to edit, and fix a lightyear scale on the balloon, in inches, and work out the arithmetic systematically. But I don't right now so maybe that can be for later, or someone else can volunteer to organize this part.

Everybody should have a look at the Lineweaver Davis SciAm article that goes into this in depth, with pictures. I have a link to it in my sig---a version at princeton.edu.

 

[cristo]

To my mind the balloon analogy is a nuisance, gallaxies ect are not stuck to a surface, once one has read about the BA it takes some getting rid of.

This is a fine example why marcus' point of trying to avoid abbreviations in this thread is a good idea: what do you mean by BA?

 

[wolram]

This is a fine example why marcus' point of trying to avoid abbreviations in this thread is a good idea: what do you mean by BA?

Balloon analogy, but you are correct keep things clear of abbreviations.

 

[wolram]

So where is every one, i thought this should be mega important.

 

[oldman]

...what we need to focus on here in this thread is the INTUITION... to properly understand the balloon analogy....a lot of the confusion we occasionally experience comes from getting that analogy somehow crossed up.

I believe that a large part of the trouble many folk have in comprehending cosmology (here and elsewhere) is this:

In an effort to help ignorant folk like myself to ‘get on the same page’--- the ‘page’ on which
professional cosmologists describe their consensus — those who are very familiar with the
Friedmann - Lemaître - Robertson - Walker model tend consistently to over-interpret this
venerable and successful mathematical description of our evolving universe.

The pennies-stuck-on-a-balloon or raisins-buried-in-dough analogy mentioned here is an example. In it, an expanding balloon or rising dough models ‘space’, and pennies or raisins represent non-expanding structures held together by electromagnetic forces. But this analogy leads to much confusion. For instance:

Does space expand and should one think of it as a 'real' substance?
Do static structures experience disruptive stresses because the balloon or dough substrate is expanding?
Are non-expanding structures that cohere gravitationally, like galaxies or galaxy clusters, correctly thought of as pennies of raisins?
Matter is mostly empty space. So, does does all space expand? If not, why not? Where lie the boundaries beween expanding and static space?
Reference frames: every observer has her own personal frame-of-rest (the cosmic microwave background that she observes). Here the idea of this background as a substrate like rising dough may be useful. But is the radiation then like an personal ether?

These are simple confusions. But there are other subtle over-interpretations that can confuse. Many posts in this forum use ‘distance’ as if this were a simple concept in a cosmological context. It is not. Nor is ‘speed’ or 'velocity',

... it gives recession speeds.

My bold.

And what about ‘space’? Not an easy concept to define (although your definition of space as “a bunch of distances” is a winner, Marcus. But then, what is distance?).

However, one shouldn't run before you can walk. So analogies and metaphors are useful and necessary aids to understanding. But it should be pointed out up-front that this is what they are. I think folk should be warned of the dangers of over-interpreting what for us human beings is a purely mathematical, and sufficient though perhaps not satisfying, description of change in our evolving universe.

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?

 

[marcus]

Oldman, thanks for commenting! Your comments are always constructive and interesting, in my experience.
We need to say up front that the visualizing the balloon analogy is a mental exercise, NOT a description of how the world is or what it is made of.
Visualizing the expanding balloon with dots painted on it (except the dots do not change size, which is why people speak of discs stuck onto the surface, to make sure they don't expand as the surface does)----visualizing the expanding balloon is a way of training your imagination.

1. to picture how distances can increase between stationary objects

2. to picture distances increasing at a percentagewise rate. Like one percent per minute.
So the longer the distance the faster (inches per minute) it increases. This is Hubble Law.

3. to understand that something can be finite (finite area if 2D or finite volume if it's 3D) without having any boundary

4. to understand that something can be curved without there being an extra dimension---part of the mental exercise is to picture the balloon surface as all there is, there is no inside the balloon and there is no outside---only the balloon surface exists.
I haven't talked about this part yet.

5. to picture light traveling between stationary points, as wrigglers traveling across the balloon surface at a fixed speed of one inch per minute----and to understand how the distance from a wriggler's starting point can increase faster than one inch per minute even tho the wriggler is always only traveling at one inch per minute.

if he is traveling north, then his latitude increases. while each galaxy dot always stays at the same longitude and latitude. so he only travels one inch per mintute but his distance from the equator increasese faster (because the balloon is expanding)

it makes obvious the statement that even though distance from us to some galaxy may be increasing many times c, yet a galaxy can never catch up with and pass a photon, and it makes acceptable the idea that the stuff that radiated the CMB is now 45 billion lightyears away. We are getting light from stuff that is 45 away even though the universe is less than 14 old. People still get spooked by that news---the mental exercise of picturing the balloon can help allay that surprise.

My point is that what we have here is a versatile and rich analog because thinking about it can train our minds in several different ways. It doesn't teach just one thing.

=====================
Oldman, you are right if you saying that one should not say that the balloon is not how the world IS. The balloon is a way of picturing a pattern of changing distances and of training one's intuitive imagination. It is not a substitute for the mathematical model! People should play around with the online calculators and get used to handling the model.

The mental exercise is a way of teaching your mind what to expect so you won't be surprised when, for example, Morgan's calculator says that a certain quasar that was recently observed was receding from Milky at 3c when it emitted the light we're getting from it and is now receding at 2c. Receding is not traveling.

So I think it is of great value to patiently focus and visualize this example of a pattern of changing distances. But of course don't take it literally---empty space is not made of rubber and does not have to be imagined embedded in a fourth spatial dimension!

 

[TalonD]

are a few questions from an entry level layperson acceptable here? if not then remove this post.
1. we are stationary but with the universe is expanding, the distance between us and distant galaxies is increasing due to expansion, so does that mean that the distance between us and the cmb is also increasing?
2. the cmb is 45b lyrs away, is that actual distance right now? the light we get from it was emittied 13.7 b yrs ago, was the cmb 13.7b light yrs away from us when that light was emitted?
3. we cannot say that space is a physical thing like the rubber of the baloon. We can only say that distance is increasing?
4. if distance is increasing does that mean that the three dimensional volume of the universe is increasing?
5. is the cmb analagous to the horizion that you would see if you were standing on the surface of the baloon?

 

[marcus]

are a few questions from an entry level layperson acceptable here? if not then remove this post.
1. we are stationary but with the universe is expanding, the distance between us and distant galaxies is increasing due to expansion, so does that mean that the distance between us and the cmb is also increasing?
2. the cmb is 45b lyrs away, is that actual distance right now? the light we get from it was emittied 13.7 b yrs ago, was the cmb 13.7b light yrs away from us when that light was emitted?
3. we cannot say that space is a physical thing like the rubber of the baloon. We can only say that distance is increasing?
4. if distance is increasing does that mean that the three dimensional volume of the universe is increasing?
5. is the cmb analagous to the horizion that you would see if you were standing on the surface of the baloon?

this is exactly the most helpful kind of feedback. something like this draft essay on what you can learn from the balloon analogy has to go thru editing and revision. questions like this are exactly what are needed to help guide revision.

3. what space is, physically, is something that physicists are working on---have a look at Frank Wilczek's new book Lightness of Being which is about the leading edge understanding of empty space. make your local librarian order the book. the link is in my sig. also read the SciAm article by Loll about the emergence of spacetime from a kind of chaos at the microscopic level---this is an unproven interesting conjecture which they simulate on the computer. we don't know yet what empty space is. but we do have a mathematical model for the increasing distances---that has to do for now.

4. yes, the instantaneous 3D volume of space can be defined and estimated in the case that it is finite, and recent satellite data gives a lower bound on the volume, and it is increasing in a perfectly normal way as the cube of the scale factor.
Of course if the 3D volume of space is not finite then it becomes more complicated to talk about it increasing. But if it is finite then we have this lower bound and it is easy to discuss. If you want a link to a reference, or simply to know the volume in cubic lightyears, please let me know.

5. what passes for the LOCATION OF THE CMB ORIGIN is a large spherical surface called the surface of last scattering where the stuff is that emitted the light we are now getting.
In the past we were getting CMB light from other stuff that is nearer, but that light has already gone by us.
In the future we will be getting CMB light from other stuff that is out beyond our current surface of last scattering---but that light is still on its way and has not reached us.

All the matter in the universe, including the matter we are made of, participated in radiating the CMB light. The CMB light that our matter emitted is now 45 billion away from us, where other people can catch some if they make antennas. Every patch of matter made CMB, it is just a question of TIMING to say where the matter is whose light you are currently receiving at this moment.

So your image of a horizon has some degree of rightness about it. Not a perfect analogy but it does tell the listener to focus not on the material stuff but on the mathematical object (the spherical surface, like the crcle of horizon on earth). there was a momentary onetime event when expansion was 380,000 years old and the glowing hot fog became transparent, and released its somewhat reddish orange light. Each photon of that light is now 45 billion lightyears from its point of origin.

1. you ask is the distance to the CMB increasing? the distances between all widely separated stationary things are increasing by Hubble Law, so the distance between us and the matter which sent us the CMB light we got yesterday is increasing as part of that general process. two approximately stationary patches of matter, their distance apart increases 1/140 percent every million years.

but something else is happening. the distance to the surface of last scattering is increasing in a more serious way. we only get the CMB light from some particular batch of matter once. it passes by. tomorrow we will get light from matter that is farther away than that batch whose light we got yesterday.

Question 2 was your best question of all.

==quote==
2. the cmb is 45b lyrs away, is that actual distance right now? the light we get from it was emittied 13.7 b yrs ago, was the cmb 13.7b light yrs away from us when that light was emitted?
==endquote==

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.

that's a pretty condensed explanation don't be discouraged if it doesn't satisfy you, keep asking, thanks for the above questions.

 

[81+]

Marcus, in the following

===quote===
In the past we were getting CMB light from other stuff that IS nearer, but that light has already gone by us.
In the future we will be getting CMB light from other stuff that IS out beyond our current surface of last scattering---but that light is still on its way and has not reached us. (I've capitalized the two words I'm interested in)
===end quote===

you use IS. Did you mean "was" for the first on and "will be" for the second?

Frank

 

[marcus]

Marcus, in the following

===quote===
In the past we were getting CMB light from other stuff that IS nearer, but that light has already gone by us.
In the future we will be getting CMB light from other stuff that IS out beyond our current surface of last scattering---but that light is still on its way and has not reached us. (I've capitalized the two words I'm interested in)
===end quote===

you use IS. Did you mean "was" for the first on and "will be" for the second?

Frank

Hi Frank, good to hear from you. I think I will stick with IS, in this case. Think of concentric shells of matter. They all emitted their light at the same moment*. the inner shell we heard from yesterday (we got their light first), then today we got the light from the next shell, and tomorrow we will get the light from the next shell (light which is still on its way to us as we speak)

all this matter is stationary with respect to the process of expansion, so the shells stay in relation to each other. the inner shell matter IS closer to us than the next shell, and the outer shell IS farther from us. this comparative relation always was and is and presumably always will be.

so you could replace IS by some different words, but you don't need to because the sentence is true "as is"

*I've simplified the time scale, better to thing of million year time intervals than to think of days. just simpler to speak of yesterday today tomorrow.

 

[marcus]

Sounds like no more questions this round. So maybe I will start trying to condense and put things in better language. Ideally this kind of thing should be very short and very clear---as brief and concise as it possibly can be and still be clear to everybody. If someone else wants to help edit, they'd be most welcome!

EDIT: reply to OLDMAN
thanks, I was introduced to the raisinbread analogy in the same 5 minutes that I was introduced to the balloon. That was many years ago. I was not aware that one analogy was significantly older or more shopworn than the other! The raisinbread, as I recall, was in the form of unbaked yeasty dough and it was rising. There were drawbacks to the the dough analog because the students had to be made to understand that it was infinite, extended endlessly and had no boundary, and nevertheless it was expanding. There was no quick obvious way of describing a point that is stationary with respect to the CMB, in the dough context, while on the balloon one just says lat and long.

I tend to think of the raisinbread analogy as the more old-fashioned, because it harks back to a time in the 1990s when most people in my experience thought curvature was negative or zero. There simply wasn't enough mass to get spatial closure, it seemed. No dark energy imagined. and dark matter had not been seen by weak lensing, merely guessed at. The professors taught us the three mathematical possibilities but they pushed raisinbread dough on us because they thought k <= 0

Then since 1998 things have swung over to where spatial curvature is now thought of as either zero or positive! My sense of history apparently differs from yours, oldman, as we see trends running in opposite directions! However ignoring trends, I would still prefer the balloon in any case because of obvious advantages: it has longitude/latitude coordinates which are stationary, it has no boundary, it has the Ned Wright animations that go with it, and the animation shows wriggly photons traveling across the face of the balloon while their wavelength lengthens and their color changes from blue to red. I challenge you to draw transparent raisin bread dough with wriggly photons journeying from raisin to raisin as the dough expands No, the balloon is diagramatically more perspicuous

However you could start a thread about the bread-dough analogy, oldman!

 

[oldman]

Sounds like no more questions this round. So maybe I will start trying to condense and put things in better language...

Wish you well! Not an easy task.

You might like to look at the very careful way the concordance model is explained by 'outsiders', namely the distinguished particle physicists Quinn and Nir, in a recent popular book The Mystery of the Missing Antimatter. They choose a raisin-cookie analogy, perhaps because the balloon analogy is a bit shopsoiled. Remember that it dates from times when cosmologists were somewhat obsessed by the fascinating possibility of a spatially curved and closed universe --- aptly thought of as a 4-D version of the 2-D curved surface of a balloon. Spatial flatness rather deflates this analogy, as it were.

They also distinguish properly the difference between redshift and Doppler effect, helpfully clarifying superluminal expansion.

 

[oldman]

...the balloon is diagramatically more perspicuous

However you could start a thread about the bread-dough analogy, oldman!

Thanks, but no thanks. Its really a matter of taste -- and I defer to yours. Perhaps it's a choice like that in some elections -- not between the good and bad, but between the bad and worse! But I'm being cynical!

 

[marcus]

About analogies that's just being realistic, not cynical . We both know well, there are no perfect ones. I was glad to get the tip about Quinn and Nir. Thx.

To move on to the main course, here is Ned Wright's page with the balloon analogy animation.

http://www.astro.ucla.edu/~wright/balloon0.html

It shows a computer animation of four-fold expansion
during which the galaxies remain stationary (only the distances between them increase) and the photons move about
and while the photons move they change color from blue, to green, to yellow, to red.
as their wavelength increases.

that is just false color because if light starts out blue and its wavelength expands by a factor of four it would be invisible infrared----but it is a pedagogical graphic that gives the idea of redshift.
(also the yellow color comes out brown because of mixing with background or my browser limitations, but you get the idea)

there is another Ned Wright balloon analogy animation here
http://www.astro.ucla.edu/~wright/Balloon2.html

It does not have dark energy, so expansion eventually slows to a crawl and actually turns around. I only watched the first half. Ah! now t=60 and it is heading for a big crunch! the photons are blueshifting from red to orange to yellow to green...etc.

 

[TalonD]

"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 then was the universe expanding faster than the speed of light at that time? is that what is meant by the inflationary period of expansion? 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?

most non physicists I have noticed seem to like to argue that if the universe is expanding then it must be expanding ito something, a higher dimension because that is normal everyday experience no doubt. Abstract counterintuitive concepts being difficult to accept if you aren't used to it. 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?

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?

 

[derekmcd]

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]

"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
https://www.physicsforums.com/showthread.php?p=1636651#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]

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]

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.

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]

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 balloon 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]

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]

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/spotlights/cosmology/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/spotlights/big_bangs/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:
https://www.physicsforums.com/showpost.php?p=1914736&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]

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 spatial 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]

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]

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]

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:

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]

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]

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]

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]

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: https://www.physicsforums.com/showpost.php?p=1925070&postcount=5

By way of reference and context, it was taken from the following thread :
https://www.physicsforums.com/showthread.php?t=265793

 

[oldman]

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]

...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!