|Oct2-08, 03:46 PM||#1|
Effort to get us all on the same page (balloon analogy)
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 in to 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
the homepage for his other cosmo resources is
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.
|Oct2-08, 04:04 PM||#2|
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.
|Oct2-08, 04:12 PM||#3|
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.
|Oct2-08, 04:50 PM||#4|
Effort to get us all on the same page (balloon analogy)
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 doesnt 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 billon 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.
|Oct2-08, 05:08 PM||#5|
|Oct2-08, 05:26 PM||#6|
|Oct2-08, 07:51 PM||#7|
So where is every one, i thought this should be mega important.
|Oct3-08, 09:35 AM||#8|
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',
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.
|Oct3-08, 12:24 PM||#9|
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!
|Oct3-08, 12:48 PM||#10|
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 univers is increasing?
5. is the cmb analagous to the horizion that you would see if you were standing on the surface of the baloon?
|Oct3-08, 01:54 PM||#11|
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.
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?
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.
|Oct3-08, 06:23 PM||#12|
Marcus, in the following
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)
you use IS. Did you mean "was" for the first on and "will be" for the second?
|Oct3-08, 07:00 PM||#13|
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.
|Oct4-08, 11:05 PM||#14|
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!
|Oct5-08, 01:19 AM||#15|
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.
|Oct5-08, 09:20 AM||#16|
|Oct5-08, 09:48 AM||#17|
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.
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
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.
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